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Testing procedures and hardware for the evaluation of the dynamic performance of outboard motor boat… Mytting, Christopher Bruce 2005

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Testing Procedures and Hardware for the Evaluation of the Dynamic Performance of Outboard Motor Boat Steering Systems By Christopher Bruce Mytting B.A.Sc Mechanical Engineering, The University of British Columbia, Vancouver, 2001 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M A S T E R OF APPLIED SCIENCE In THE F A C U L T Y OF G R A D U A T E STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH C O L U M B I A June 2005 © Christopher Bruce Mytting, 2005 Abstract Abstract This thesis presents testing procedures and hardware for the performance evaluation of steering systems for outboard motor driven pleasure craft. It is intended that this work provide the basis for the evaluation of existing steering systems and the rigorous development of the next generation of systems, specifically, by-wire steering systems. The testing procedures and hardware presented allow the testing of steering systems in a hardware-in-loop configuration that applies both reference inputs and external reactions to the system. Complete steering systems may be tested to assess the steering system response to simple static loads or under dynamic conditions up to the limits associated with typical use patterns. Customized testing procedures can also be formulated to include the emulation of boating conditions, or system-specific testing procedures to examine the response of specific components. The testing hardware consists of a CNC-based system with data acquisition to control system inputs and record the system response. A full description of the testing hardware is provided. An example of the utility of the testing procedures and hardware is presented by using data collected during the standard testing procedures to determine the parameters required in the modelling of a manual hydraulic steering system. To ensure that the hardware in loop simulation inputs are reasonable, boat testing procedures with a representative steering system, boat, and outboard motor combination were performed. These allowed the specification of reasonable input frequency and magnitude of steering effort as well as the measurement of the, force levels required to execute the most extreme manoeuvres likely to be encountered in practice. The data collected, the hardware used to collect the data, a summary of the witnessed operator and disturbance inputs to the steering system, and a simplified model for the prediction of steering loads during boat operation are also included. Contents iii Contents Abstract , ii Contents iii Dedication and Acknowledgements . vi 1 INTRODUCTION 1 1.1. Thesis Objective 1 1.2. Thesis Outline 3 2 BOAT STEERING SYSTEMS OVERVIEW 5 2.1. Outboard Motor Steering Systems 5 2.1.1 Manual cable 7 2.1.2 Manual hydraulic ..8 2.1.3 Power-assisted ; 10 2.1.4 Autopilot 11 2.2. By-wire Steering System ;...12 2.2.1 Advantages of by-wire steering 12 2.2.2 Challenges to by-wire system implementation 16 2.2.3 Aerospace applications and X-by-Wire project 17 2.3. Cost-effective, Fault Tolerant Control Architecture 18 3 SYSTEM EVALUATION APPARATUS 20 3.1. Hardware-in-Loop Simulations 21 3.2. SEA Design 25 3.2.1 SEA design requirements 25 3.3. SEA Hardware 26 3.3.1 Controller 28 3.3.2 Data acquisition module 29 3.3.3 Helm input unit 30 3.3.4 Tiller resistance unit 32 3.4. Adaptability of the SEA 35 3.5. Summary 36 4 MODELLING OF THE SEASTAR STEERING SYSTEM 37 Contents iv 4.1. Dynamic Response of the SeaStar 38 4.1.1 Modified frequency response test 40 4.2. Approaches to Modelling the SeaStar Steering System 45 4.2.1 Pressure calculation in SeaStar model 46 4.3. SeaStar Helm , '. 47 4.3.1 Reservoir 49 4.3.2 Spigot and piston assemblies 50 4.3.3 Spigot and piston assemblies control diagram 53 4.3.4 Spool valve 55 4.3.5 Spool dynamics 57 4.3.6 Spool valve fluid flow.... 60 4.4. SeaStar Hoses 65 4.5. SeaStar Actuator 68 4.6. Modelling Summary 72 4.7. Test and Simulation Results 73 4.7.1 Evaluation of modified frequency response test simulations 73 4.7.2 Evaluation of constant speed and load test simulations 77 4.8. Conclusions and Recommendations 84 5 TESTING PROCEDURES FOR THE PERFORMANCE ASSESSMENT OF STEERING SYSTEMS 87 5.1. Testing Hardware 88 5.2. Boat Testing Procedures 93 5.2.1 Straight line testing 93 5.2.2 Maximum load testing 97 5.2.3 Buoy tests 99 5.2.4 Testing procedure recommendations based on collected service information 104 5.3. Usage-based Testing Procedures 105 5.3.1 Disturbance load model for usage-based testing procedures 106 5.3.2 Empirical model for steering loads 111 5.3.3 Implementation of usage-based tests on SEA 114 5.3.4 Limitation of empirical model 114 5.4. Summary 115 Contents v 6 CONCLUSIONS A N D R E C O M M E N D A T I O N S FOR F U T U R E W O R K 117 6.1. Conclusions 117 6.2. Recommendations for Future Work 119 BIBLIOGRAPHY 121 APPENDIX A : SEA Fabricated Component Drawings and Calculations 124 APPENDIX B : Seastar Measured And Simulated Response Plots 147 APPENDIX C: Simulink Diagrams of SeaStar Steering System Components and Calculations .208 APPENDIX D: Boat Testing Data 224 APPENDLX E: Plots of Net Cylinder Pressure Predicted by Usage-based Testing Load Function 254 Dedication and Acknowledgements vi Dedication For my parents, Sam and Laine Mytting, for giving me the tools to make my own way in life. Acknowledgements I would like to thank the following individuals for their assistance and support during the development of this work. First, I would like to thank my supervisor, Dr. Ian Yellowley for his interest in and support of me and this work. His advice, ranging from technical to personal and professional, have proven invaluable to me during the course of this work. I would also like to express my gratitude to Kevin Oldknow and Ramin Ardekani for their assistance in the development of the testing apparatus hardware. I would like to acknowledge the sponsor of this work at Teleflex, Eric Fethcko, whose support of this work I am very grateful for. I would also bike to thank the following individuals at Teleflex for their technical support - Dana Trousil, Brian Dudra, and Graeme Dempster. Finally, I would like to thank Lisa for her support during the time I have spent on this work and her assistance in the publication of this thesis. Chapter 1. Introduction 1 Chapter 1 Introduction 1.1. Thesis Objective This thesis is concerned with the development of a methodology and associated testing procedures to quantitatively assess the performance of steering systems for outboard motor driven pleasure craft. The research presented here was undertaken in response to an increasing need for better characterisation of such systems, especially steer-by-wire variants. The hardware and software needed to perform the testing procedures is presented with an example application that demonstrates the overall utility of the system developed. Testing procedures based on service information and the emulation of real boating conditions are proposed to assess the performance of steering systems. Teleflex Canada, a British Columbia-based company that manufactures steering systems for outboard motor boats, sponsored this research in conjunction with the Process and Product Development Laboratory at the University of British Columbia. The emergence of by-wire technology in the automotive and aerospace industries provides an opportunity to bring the advantages of such systems to the users of recreational boats. By-wire systems provide many features to users but are complicated in comparison to manual systems. The system complexity introduces more potential failure modes to the system and requires comprehensive testing procedures to ensure system performance and safety for all expected operating conditions. The hardware and testing procedures detailed in this thesis allow for the testing of steering systems in a Hardware-In-Loop Simulation (HILS) Chapter 1. Introduction 2 configuration. The HTLS arrangement, called the System Evaluation Apparatus (SEA), allows complete steering systems (manual, powered, or by-wire) to be tested by simulating the operator input and disturbance loads applied to the system. The measured system response allows system identification analysis and the assessment of other performance criteria. The SeaStar Steering System, a manual hydraulic steering system manufactured by Teleflex Canada, is used as an example to validate the design and demonstrate the utility of the SEA. In order to develop testing procedures representative of service conditions, testing procedures to be performed with the SEA based on collected boating data are proposed. Reasonable limits based on the collected boating information to the system inputs for simple static testing procedures are detailed. Usage-based testing procedures that emulate the disturbance load response of a representative boat, motor, and steering system combination are proposed as a means of effectively testing the performance of steering systems that are known to exhibit non-linear behaviour. The disturbance load model is based on the steering system response and boat speed and acceleration. The work presented in this thesis, together with related work carried out within the Product and Process Development Laboratory by Mathieu Bouvier, are intended to provide the basis for developing a complete steer-by-wire system. Bouvier's thesis, "Definition of a Cost-effective, Fault-Tolerant Control Architecture: Application to the Design of a Steer-By-Wire System,"1 presents the framework of a by-wire steering system for boats. The development of a complete by-wire system requires a means of testing the performance of the system in controlled, dynamic conditions. The testing hardware presented in this 'BOUVIER, M: Definition of a Cost-effective, Fault-Tolerant Control Architecture: Application to the design of a Steer-by-Wire System. MASc Thesis, University of British Columbia, 2002. Chapter 1. Introduction 3 thesis may also be integrated with components of by-wire systems to perform hardware-specific testing procedures. 1.2. Thesis Outline This thesis is divided into six chapters. Typical boat steering systems for outboard motors are introduced in Chapter 2; the discussion includes consideration of existing manual hydraulic and mechanical steering systems, power steering systems, and autopilot systems. A discussion of the advantages and challenges of by-wire steering follows. Examples of features that improve the driving experience in the automotive industry and have application to marine pleasure craft are discussed. The challenges of by-wire steering such as increased complexity and failure modes, and the removal of mechanical backup are outlined. The chapter ends with an overview of Bouvier's control framework and the role that the testing hardware presented in this thesis can take in the development of a complete by-wire steering system. Chapter 3 introduces the System Evaluation Apparatus. HILS systems are introduced with examples including electronic control units (ECUs), antilock braking systems, and an existing test bench for outboard steering systems. The concept of operation, design specifications and models of the SEA are also included in the second chapter. Chapter 4 discusses the utility of the SEA and the testing procedures used to develop a system model of the SeaStar Steering System. Initial testing data that resulted in an investigation of the dynamics of the SeaStar are discussed. An original presentation of the frequency response of non-linear systems called the modified frequency response plot is described. The chapter includes full details of the operation of the SeaStar Steering System and approximations of system parameters used to develop a simulation model. A comparison of the measured response of the system to the simulation data demonstrates the accuracy of the model and the utility of the SEA in the analysis of steering systems. Chapter 1. Introduction 4 Chapter 5 proposes testing procedures based on data collected from boat testing. The hardware and boat testing procedures are described, followed by results and general observations related to factors such as operator limitations and the magnitude of disturbance loads encountered during boat testing. An outline of the causes of the disturbance loads and a discussion of the limitation of the boat testing data follows. A summary of findings and recommendations for expanding the research to facilitate the development of by-wire systems conclude this thesis discussion. Chapter 2. Boat steering systems overview 5 Chapter 2 Boat Steering Systems Overview 2 .1 . Outboard Motor Boat Steering Systems Boats that use outboard motors range from pleasure boats used for fishing and waterskiing (Figure 2.1) to larger ocean-going vessels with multiple engines (Figure 2.2). The power ratings of outboard motors that require steering systems range from less than 70 hp to over 200 hp. Some applications of outboard motors such as bass boats can have speeds that exceed 90 mph. Figure 2.1 Bass boat with outboard motor. Source: Ranger Boats. Chapter 2. Boat steering systems overview 6 Figure 2 .2 Boat with multiple engines. Source: Superboat Powerboats. Steering with an outboard motor is accomplished by controlling the angle between the entire motor assembly and the boat (Figure 2.3). Typically, a linear actuator (mechanical or hydraulic) is mounted to the outboard motor mount brackets and connected to the tiller of the outboard motor through a linkage. The actuator transmits force to the tiller of the outboard, causing the angle between the motor and boat centreline to change. The turning of the motor not only allows the fluid loads on the leg of the outboard to turn the boat as with a traditional rudder, but also adjusts the thrust vector of the propeller to an angle to the boat centreline. Chapter 2. Boat steering systems overview 7 Figure 2.3 Adjustment of angle between boat and motor. Source: HyDrive Engineering Pty Ltd. There are many different designs and configurations of steering systems for outboard motors currently available, but the types of steering systems fall into four main categories: manual cable, manual hydraulic, power assist, and autopilot. 2.1.1 Manual cable Cable steering systems (Figure 2.4) are manually operated systems, with the cable attaching at one end to the steering wheel of the system, and at the other to a link arm that connects the tiller arm2 to a rod that slides in and out of the tilt tube of the motor. As the operator turns the wheel, the cable is drawn into the helm body or forced from it, causing the sliding element to move through the tilt tube and force movement of the tiller through the connecting linkage. The tiller arm of the outboard motor will hereafter be referred to as simply the tiller. Chapter 2. Boat steering systems overview 8 2.1.2 Manual hydraulic Figure 2.5 shows a typical hydraulic steering system, the SeaStar steering system, and in Figure 2.6, an operational schematic. The helm of the SeaStar steering system is a rotary piston pump that converts rotational input to fluid flow. The direction of fluid flow depends on the direction of rotation to the pump input shaft. As the wheel is turned fluid is pumped, causing the hydraulic actuator to move and motor to rotate. A valve at the helm manages fluid flow from both port and starboard hoses. The valve ensures that the motor position is not affected by disturbance inputs and that the wheel position does not need to be regulated by the operator except when turning the boat. Modelling of the SeaStar steering system is the topic of Chapter 4. Chapter 2. Boat steering systems overview 9 Figure 2.5 Manual hydraulic steering system. Source: Teleflex Morse. DIRECTION OF OIL FLOW STEERING CYLINDER HELM STATION r -TILLER ARM CYLINDER ROD " MOVEMENT RUOOIR Figure 2.6 Schematic of hydraulic steering system. Source: Teleflex Morse. Chapter 2. Boat steering systems overview 10 2.1.3 Power-assisted Power-assisted steering systems operate in conjunction with manual hydraulic steering (Figure 2.7). The power-assist unit is placed in-line between the helm pump and actuator of a manual system. Pressure or flow from the manual helm pump is measured and the power-assist boosts the pressure of the fluid flowing to the actuator. The power-assist unit is designed to allow the steering system to remain functional in the event of power loss. The manual functionality is ensured by a pump bypass check valve that allows fluid to travel from the helm to the actuator should the helm line pressure exceed that provided by the pump. CYUNDER Figure 2.7 Teleflex SeaStar Power Assist. Source: Teleflex Canada. Chapter 2. Boat steering systems overview 11 2.1.4 Autopilot Autopilot systems allow a boat in open water to be piloted electronically. The operator of the boat enters a heading or desired course into the autopilot. The autopilot system senses boat heading or position with an electronic compass or GPS 3 system and modifies tiller angle to correct for course deviations. Autopilot systems are implemented in various configurations. Autopilots can be part of the hydraulic circuit, as in Figure 2.8, or may control the helm input position with an actuator with feedback from an actuator position sensor. Autopilots for cable steering systems of the latter form do not require a linear position sensor at the actuator because the wheel and rudder actuator are mechanically linked. Figure 2.8 Hydraulic system with autopilot. Source: Teleflex Canada Inc. Global Positioning System. Chapter 2. Boat steering systems overview 12 2.2. By-wire Steering System By-wire steering is defined as a steering system in which the hydraulic or mechanical connection between the helm and rudder is replaced by an electronic control arrangement (Bouvier, 2000). Operator input is sensed and the steering system drives the tiller actuator based on the system control algorithms. The main advantage of by-wire steering is the ability to adapt to suit various dynamic conditions to maximize operator comfort and safety. The main challenges of implementing by-wire systems are to ensure that the probability of complete system failure is low and that any subsystem failures that occur are handled in a graceful manner that allows the system to continue to function, though perhaps with reduced capabilities. 2.2.1 Advantages of by-wire steering By-wire steering systems can offer, many attractive features not possible with conventional manual hydraulic or mechanical systems. By-wire systems can be tuned to suit different boat configurations, individual preference, boat manoeuvres, or water conditions. This contrasts with manual systems that have inherent design compromises in an effort to ensure adequate functionality for all conditions. Manual systems are designed to provide the best practical overall performance and do not perform all functions optimally. A by-wire system can be designed to perform all tasks that it senses in a near optimal manner by reconfiguring according to control algorithms to provide the preferred or most safe system response. A discussion of variable wheel resistance and variable steering gain illustrates two basic advantages that by-wire steering systems can provide marine operators. With a by-wire system the user interface can be customized to user Chapter 2. Boat steering systems overview ' 13 preference and to boating conditions. An example from the automotive industry relating to steering wheel effort preference is found in the work of Bertollini and Hogan.4 It was determined that users prefer steering effort to increase with vehicle speed. A wheel torque of 2 N*m was preferred at less than 10 km/hr and varied near linearly to a preferred wheel effort of 4 N*m at 113 kmh. A by-wire system can easily provide controlled resistance torque that corresponds to the values determined by Bertollini and Hogan, or could be tuned to an individual's preference. Another automotive example is described by Shimizu, Kawai, Yuzuriha,5 who found that varying steering gain inversely to vehicle speed improved the safety and performance of steering systems for a variety of manoeuvres. For low speed operations, high steering angle gain allows the wheels to be turned more quickly by the driver, improving response time for obstacle avoidance and the time and effort to park. In marine systems this is directly comparable to travelling in a marina or docking. The higher the gain of the steering system at low speeds, the faster the operator can comfortably adjust the tiller angle, ;and the faster the response of the boat. Conversely, high-speed manoeuvres such as highway lane changing with an automobile require less steering gain than driving at low and average speeds. At high speeds, small variations in wheel angle can result in large lateral accelerations of the vehicle. 4 BERTOLLINI, G. & HOGAN, R: Applying Driving Simulation to Quantify Steering Effort as a Function of Vehicle Speed. SAE Technical Paper Series, 1999-01-0394. 5 SHIMIZU, Y.; KAWAI, T.; YUZURIHA, J: Improvement in Driver-Vehicle System Performance by Varying Steering Gain with Vehicle Speed and Steering Angle: VGS (Variable Gear-Ratio Steering System). SAE Technical Paper Series, 1999-01-0395. Chapter 2. Boat steering systems overview 14 With low steering gain at high speeds, the wheel angle precision required to control the vehicle is reduced. Driver fatigue is reduced from the reduction in mental load to control the wheel position and the danger of oversteer is reduced. As a consequence, the low-steering gain at high vehicle speeds improves driver comfort and overall road safety. Again, this directly compares to the operation of small boats where a sudden, substantial change of tiller angle could result in instability of the boat. To implement the automotive variable gain relationship, Shimizu developed an electromechanical variable gear ratio steering system. Figure 2.9 is an illustration of the arrangement and the principle of operation. To vary the steering ratio, the distance X is varied with road speed by a DC servo and worm gear set according to a speed steering gain relationship. Figure 2.9 Variable steering gain mechanism and operating principle. Source: SAE Technical Paper Series, 1999-01-0395. Chapter 2. Boat steering systems overview 15 A proposed by-wire system that drives the pinion gear the steering system directly could provide three advantages over the variable steering gain arrangement. First, the by-wire system would eliminate the need for a steering shaft to connect the steering mechanism to the steering wheel, increasing driver safety, and installation flexibility of the steering system. The second improvement is the reduction of the number of mechanical components required (steering shaft, worm-gear set, and sliding mechanism), reducing the weight and mechanical complexity of the assembly. The third advantage is that a by-wire system could implement steering gain relationships not possible with the mechanical arrangements. Other improvements in the implementation of a by-wire, variable gain system for boats, particularly small craft, may be obtained through the inclusion of a system model of the boat in the control algorithms. An example application is compensation for boat sliding (motion perpendicular to boat axis). In automotive steer-by-wire research Tajima and Yuhara found that the ideal ratio between the vehicle trajectory and steering wheel angle was 1:1.6 The basis of the relationship was the finding that drivers tend to look ahead 1 second of travel for all vehicle speeds. By changing the steering wheel to tire angle gain based on vehicle speed and geometry, driver performance in cornering manoeuvres was improved. A similar approach could be developed for small boats where instead of using vehicle geometry to calculate the required tiller angle, a system model that accounted for sliding would provide the required reference tiller position to allow the boat to follow the reference trajectory.7 An extension of a model such as that 6 TAJIMA, J.; YUHARA, N; SANO.S; TAKIMOTO, S: Effects of Steering System Characteristics on Control Performance from the Viewpoint of Steer-by-Wire System Design: SAE Technical Paper Series, 1999-01-0821. 7 The reference trajectory could only be followed to the manoeuvrability limits of the boat. Chapter 2. Boat steering systems overview 16 proposed by Browning for autopilots with smaller vessels could be extended to take these factors into account. By including a system model of the boat, the tiller position could be regulated to implement to the desired 1:1 relationship between wheel position and vessel trajectory. By-wire systems can provide many attractive features to boat operators. The preferred resistance torque at the steering wheel and optimal steering gain relationship are just two examples of features that a by-wire system can provide. Manual mechanical systems, though able to provide adequate performance for most operating conditions, can not practically adjust dynamically to suit operating conditions. 2.2.2 Challenges to by-wire system implementation A major consideration of by-wire systems in safety critical applications is the reliance on electronics and software to control the system actuator without mechanical backup. By removing the mechanical link between the operator and the actuator, the operator's ability to directly control the actuator position is eliminated. The ability of the operator to interpret problems in the system and take corrective actions is also severely limited. Further, by-wire systems have more and different types of possible failure modes than a simple mechanical system due to integration of mechanical components, electronics, and software. To ensure operator safety and system performance, the loss of the operator as primary controller and the increase of failure modes must be accounted for in the design of a by-wire system. The probability of failure must be very low, as near to zero as is practical. In order to limit the probability of complete system failures and accommodate component failures within the system, redundant BROWNING, DR A: A mathematical model to simulate small boat behaviour. SIMULATION 56:5,257-264(1991). Chapter 2. Boat steering systems overview 17 components are used in most by-wire systems. The redundancy provides multiple sources of the same information to the system controllers. In the event of component failure, the system controllers must decide which component has failed and which strategy to adopt to compensate for the loss of the component. 2.2.3 Aerospace applications and X-by-Wire project The implementation and management of redundancy in by-wire systems varies. In an aerospace application, the Boeing 777 uses triple-triple redundancy (Yeh, Y .C . 9 ) . The system uses three complete redundant systems, within which are triple redundant components. Each of the three complete systems is fault tolerant. The response of the three systems is redundant; if disagreement of measurements between the three systems is found, a voting mechanism is implemented to disable the system that disagrees with the majority. The X-by-Wire 1 0 project in the Europe adopted "exact redundancy" with "fail silence" (system outputs correct value or none at all). In order to implement fail silence, each of the redundant sub-systems must have two independent sources of information to determine if the sub-system is operating correctly. If both sources of information within a component provide similar data, then the component is considered to be operating properly. If the information disagrees, then the sub-system considers itself to be faulty and outputs no signal. 9 YEH, Y . C : Design Considerations in Boeing 777 Fly-By-Wire Computers. In Proceedings of the Third IEEE International High-Assurance Systems Engineering Symposium, 64-72 (1998). 1 0 X-By-Wire team: X-by-Wire, Safety Related Fault Tolerant Systems in Vehicles, Final Report. Published on the internet, 1998. http://www.vmars.tuwien.ac.at/projects/xbywire/docs/final.doc [accessed on September 12, 2002]. Chapter 2. Boat steering systems overview 18 2.3. Cost-effective, Fault Tolerant Control Architecture An alternate approach was developed at U B C by Bouvier to implement a relatively cost effective, fault tolerant control architecture. Bouvier's work and the work presented in this thesis were intended to support next generation research into implementing a complete, by-wire steering system for boats with outboard motors. Bouvier presented a new approach to the problem because he considered that the technological approach of the aerospace designs was "not directly transferable to large scale, cost sensitive markets." The X-by-Wife approach from the automotive industry could be improved on because fail-silence requires double redundancy within redundant systems, effectively making an X-by-Wire system quadruple redundant. The approach taken by Bouvier was to implement a fault-tolerant system based on Triple-Modular-Redundancy of components. The system performs error treatment and error detection at the actuator, sensor, and E C U levels. The system uses diversely redundant sensors to ensure that a common failure mode of a specific sensor or software fault does not affect more than one measurement of a specific property. In the event that the sensor malfunctions, software tools decide which sensor is faulty by a voting scheme. If the sensed value of two sensors indicate the same level and the third does not, the reading from the third sensor is disregarded. Diversely redundant sensors allow for cost savings because the system typically uses the most accurate sensor to base control signals on and uses the lower-quality sensors to assure that the main sensor is functioning properly. If a component fails in the system, the system must reconfigure to operate with the remaining components. If the system cannot provide the same response without the component, the system must change in a manner that ensures operator safety (or graceful degradation). Reduced capability may result from the failure Chapter 2. Boat steering systems overview 19 of the highest quality component in a redundant set, leaving less accurate measurements to base the control action on. Graceful degradation is implemented by dynamically reconfiguring the system after a component failure is detected. Dynamic reconfiguration allows the system to reconfigure during run-time rather than requiring the system to stop and restart after a component failure is detected. Bouvier's design was implemented and tested with a laboratory demonstrator that emulated the components of a by-wire steering system. The system included a power system, DC motors, digital and analogue sensors, two ECUs and a Pentium-based laptop computer. The communications hardware and power supply were the only non-redundant components. The system was verified to tolerate permanent and transient sensor faults and tolerate permanent failure of one of the ECUs or the laptop application. The component faults emulated with the laboratory demonstrator were simple tests to ensure basic functionality. The next phase of the research is to implement the architecture in a complete, working system. The testing procedures and hardware detailed in this thesis will allow the physical inputs and outputs to be controlled in testing the performance of the by-wire system and benchmarking existing manual systems to compare the by-wire system to. In the future, the by-wire system and test bench are intended to be integrated to a higher level. The test platform will test not only the performance of the system in simulated physical conditions but emulate system components. By integrating the test apparatus and the by-wire system, more sophisticated testing procedures can be applied to the by-wire system to test failure modes, and ultimately, to ensure boating safety. Chapter 3. System Evaluation Apparatus 20 Chapter 3 System Evaluation Apparatus The System Evaluation Apparatus (Figure 3.1) described in this chapter is designed to be a central tool in the development of steering systems for outboard motor boats. It allows steering systems to be tested in a Hardware-In-Loop configuration that simulates conditions expected in service. The SEA is designed to perform testing procedures that are controlled and repeatable, allowing the effects of design modifications or the comparison of the dynamic response of different steering systems to be analysed. Figure 3.1 System Evaluation Apparatus with SeaStar steering system. Photo by author. Chapter 3. System Evaluation Apparatus 21 This chapter first introduces Hardware-In-Loop simulations. Examples of other HILS applications are presented, demonstrating the utility of including varying levels of hardware in the loop during the development of systems. A specific example of a HILS test bench used for outboard steering systems is included with an explanation of the shortfalls of that design. The design specifications and information about the specific components follows. The helm input and disturbance load unit designs are then discussed, including block diagrams of the sub-systems. The chapter ends with a discussion of the adaptability of the SEA and potential of the SEA to be used as a tool in the development of advanced steering systems. 3.1. Hardware-In-Loop Simulations A HILS system is defined as incorporating "actual hardware into simulated surroundings to test functionality under a variety of conditions," (2001, Cho, Hwang, et al. 1 1). The SEA hardware incorporates the steering system of an outboard motor boat while the simulated inputs, helm position and actuator disturbance load, are applied to the steering system. In Figure 3.2, the input servomotor replaces the operator and the outboard motor is replaced by the disturbance load unit. 1 1 CHO, J.M.; HWANG, D.H.; LEE, K.C.; JEON, J.W.; PARK, D.Y.; KIM, Y.J.; IOH, J.S.. Design and Implementation of HILS System for ABS ECU of Commercial Vehicles. IEEE Proceedings 0-7803-7090-2/01. 2001. Chapter 3. System Evaluation Apparatus 22 Figure 3.2 SEA as hardware-in-Ioop simulator. Hardware-In-Loop simulators are used for a wide variety of applications. By incorporating specific components or subsystems into a simulated environment, hardware can be tested to measure its performance, ensure functionality, or identify specific parameters in a comprehensive set of simulated conditions. The components of the tested system included in a HILS depend on the parameters being investigated. If a single component is tested for functionality, all of the input to the component may be simulated. Such an example is testing Electronic Control Units (ECUs) with simulated surroundings Chapter 3. System Evaluation Apparatus 23 (Ferreira, Oliveira, Costa ). The performance of the E C U can be assessed by simulating all of the expected inputs and monitoring the response. When a single component of a system is tested it is important that the simulated inputs fully represent the inputs expected in service. Unexpected and unwanted component interactions may occur if components are tested with inaccurate simulated inputs. A typical instance of this problem in the testing of Antilock Brake System (ABS) algorithms has been reported by Cho, Hwang, Lee, Jeon,1 3 who eliminate the problem of inaccurate models by including the components or component interactions that are difficult to model. Cho et al. included the full braking system of a commercial vehicle in the loop to test the ABS algorithm. The inclusion of the braking system hardware ensured that the non-linearities of the pneumatics and solenoids that are difficult to model were accounted for, allowing the algorithm to be tested with the actual hardware rather than an approximation. The data provided by the HILS predicted the performance of the ABS system in service before having to test the system on an actual vehicle, reducing the time and expense of developing the system. Examples of HILS systems applied to boat steering systems can be found at Teleflex Canada Inc. The test bench that the SEA most closely resembles is the Boat Simulator test bench (Figures 3.3 and 3.4). Tests with the Boat Simulator are performed by setting a static load and turning the helm wheel manually. Complete steering systems or components integrated with typical hardware can be tested. Helm position and torque sensors, pressure transducers, and a linear 1 2 FERREIRA, J.A.; OLIVEIRA, J.E.; COSTA, V.A.; Modeling of Hydraulic Systems for Hardware-In-The-Loop Simulation: A Methodology Proposal. Proceedings of International Mechanical Engineering Congress and Exposition, Nashville, USA, Vol 6 p.33. 1999. 1 3 LEE, S.J. ; KIM, Y.S.; CHO, J.H.; LEE, W.S.; KIM, J.H.: ABS Hardware-In-The-Loop Simulation on a Driving Simulator. Presentation from Department of Automotive Engineering Kookmin University. Seoul, Korea. Published on the Internet 1998. http://vc.kookmin.ac.kr/publication/1998/Presentation/abshils.pdf [accessed on January 14, 2004]. Chapter 3. System Evaluation Apparatus 24 position sensor provide quantifiable measures for the assessment of the performance of a system. Heuristic measures related to operator "feel" are interpreted and recorded by the test operator. Figure 3.3 Teleflex boat simulator. Photo by author. Boat Simulator Test System P - Pressure Transducer TP - Torque and Position Sensors L - Linear Position Sensor AP -Accumulator and Pump Figure 3.4 Schematic of boat simulator. Chapter 3. System Evaluation Apparatus 25 The major drawbacks of the boat simulator as an accurate system are that the resistance module has proven to be unable to control loads in tests with substantial actuator speed or dynamics and that the helm input is manual. The boat simulator does not provide a controlled load because the pump and accumulator system does not have the bandwidth to control the pressure of the fluid during testing procedures that involve high-speed actuator movements. While manual helm input allows for subjective measures to be determined, the lack of helm input control limits the repeatability of tests. 3.2. SEA Design The SEA was designed to address the need for a test bench to perform automated dynamic testing procedures. Using a CNC-based system with data acquisition to control helm input and disturbance load while recording the response of a system was determined to be the most straightforward approach to determining the dynamic performance of steering systems. 3.2.1 S E A design requirements With the design approach determined, the design engineers at Teleflex were consulted to establish specifications for the SEA. The SEA is first required to provide mounting for all outboard steering systems on the market. The helm mount needed to accommodate all Teleflex and Ufflex helms. The resistance module needed to meet American Boating and Yachting Council specifications for steering system actuator mounts, and the resistance module needed to mimic Mercury and Yamaha outboard motor mounts. The second set of requirements is that the SEA be able to reproduce or exceed all quasi-static conditions that a manual steering system is expected to encounter and have adequate data acquisition capability to record the response of Chapter 3. System Evaluation Apparatus 26 r a system. The test bench requirements were set at a high level to avoid encountering situations where the test bench was under-powered, failed during testing, or had insufficient data acquisition capability. The design specifications for inputs and data acquisition determined for the SEA are listed in Table 3.1. Peak helm torque +/-40ftlbf i % 2n rad/s helm speed Continuous helm torque +1-25 ftlbf <i £ 67c rad/s helm speed Peak disturbance load +/-1650 Ibf @ 2.0 in /s actuator speed Continuous disturbance load +/-1000 Ibf @ 6.0 in/s actuator speed Bandwidth of helm input 10 Hz Bandwidth of tiller load 10 Hz Analogue data acquisition 8 analog channels at 1 kHz Position data acquisition Helm and tiller position at 1 kHz Table 3.1 SEA design specifications. 3.3. SEA Hardware The operating principle and component interconnections of the SEA are illustrated in Figure 3.5. Helm input is controlled with a servomotor that uses encoder and tachometer feedback. As the helm is rotated, fluid is pumped into the system actuator which back-drives the resistance ballscrew over the torque of the DC motor. The torque of the resistance motor is controlled by a current control loop in the resistance servo amplifier. (The amplifier has internal feedback that does not require external sensors.) To calculate the position of the helm and tiller, optical encoders are used. The current reference signals from the amplifiers for the helm and resistance motor are used to calculate the helm torque and disturbance force. Optional sensors such the strain gauges or pressure transducers shown in the schematic can be included in the loop to provide additional information. For reference, Table 3.2 is a complete list of the purchased Chapter 3. System Evaluation Apparatus 27 components used in the design and Appendix A contains drawings of the fabricated components. Steering System SEA 1 Cylinder I DC Servo Amp#2 Input Servo Strain Gauges Resistance Motor, Controller and DAQ 4 » HP i Monocarrier (mounted ballscrew) DC Servo Amp#l DC Power Supply E - Optical Encoder T - Tachometer Figure 3.5 SEA schematic. Chapter 3. System Evaluation Apparatus 28 Item Model Manufacturer Specifications Copely Controls Isolation Transformer (1) TR1115-15 150V @ 15A Copely Controls Unregulated Power Supply (1) PSX 140-10-1 140VDC @ 10A Copely Controls DC Brush Servo Amplifier (2) 423 +/-170V, 30A peak, 15A cont Magmotor DC Servo Motor (Helm) S28-300 30A peak, 3.1 A cont k = 67.6 ozf-in/A Magmotor DC Servo Motor (Resistance) C40-500 20A peak, 4.3A cont k= 152.2 ozf-in/A Gysin Planetary Gearbox GPL-105 24:1 Ratio 8500 ozfin output NSK Monocarrier (mounted ballscrew) MCM-10040H10-000A 10mm lead 10.9 kN Dynamic Load Rating NSK Linear Guide LAH30AN 25.7 kN Dynamic Load Rating NSK Linear Rail L1H300220 See above NTN Ball Bearing (2) UCF208-108D1 5000 Ibf Static NTN Needle Bearing NA 4902.2 RS 2000 Ibf Static Table 3.2 SEA hardware. 3.3.1 Controller The control unit is the U B C Open Architecture C N C Controller (Figure 3.6) developed in the Manufacturing Engineering Laboratory in the Department of Mechanical Engineering at the University of British Columbia. The unit has an STD bus that connects the master computer and slave cards (servo control and data acquisition cards). The master computer processor is an 80 M H z Intel 486SX processor with access to 4 Mb of R A M . The axis control card for the Chapter 3. System Evaluation Apparatus 29 helm servo loop is a Universal Systems model UE9001A that has an Intel 80C196KC processor unit. A servomotor interface card (UE9701) is attached to the axis card. It sends the reference signal to the amplifier, powers the optical encoder, and decodes the encoder pulses. Figure 3.5 UBC open architecture controller. Photo by author. 3.3.2 Data acquisition module The STD-based card used for data acquisition and reference load control is the Sensoray Model 7421 Data Acquisition Card (Figure 3.7). The Sensoray unit reads the encoder values of the resistance servo motor and controls the reference current signal of the resistance motor of the SEA. Additional sensor signals from pressure transducers or strain gauges can be recorded with the data acquisition card. The substantial flexibility (Table 3.3 specification table) of the card allows for expansion of the utility of the SEA without the need for additional hardware to be purchased and integrated in the system. A limitation of the Sensoray 7421 is that there is no on-board memory; this forces the master CPU to fetch all data and increases the computational load. Chapter 3. System Evaluation Apparatus 30 Figure 3.6 Sensoray model 7421. Source: Sensoray Company Inc. Signal Type Precision Sampling Rate Channels Quadrature Decoder 16 bit 350 kHz 3 D/A output 12 bit 50 kHz 4 A/D input 12 bit 50 kHz 8 Digital I/O 1 bit 50 kHz 24 Table 3.3 Sensoray 7421, digital and analogue I/O. 3.3.3 Helm input unit The helm input unit (Figure 3.8) is intended to provide mounting for all system helm units and control the position input to the helms during testing procedures. The helm mounting plate has bolt hole patterns that allow the installation of all Teleflex steering systems helms and the helm bracket can adjust to suit helms of different mounting face dimensions. The helm servo unit with a 24:1 gearbox provides the required steady state torque of 25 ft-lbf and easily matches the load and speed specifications. The servo control loop of the helm input (Figure 3.9) was tuned to have a time constant of 0.01 seconds with no load. Because the Chapter 3. System Evaluation Apparatus 31 reflected inertia and stiffness of test systems vary dramatically, the bandwidth of the helm input for all cases cannot be determined. Given that the power available far exceeds that of a human operator, the bandwidth of the helm input should be sufficient for testing manual systems. (leartox 0 0 System Multiple Hole Patterns Adjustment Slots Figure 3.8 CAD model representation of helm mount unit Helm Servo Loop (county Reference Helm Input Speed Error (rjdfceo) Digital Filter Zero-Order k W A Hold Figure 3.7 Helm servo loop. Chapter 3. System Evaluation Apparatus 32 3.3.4 Tiller resistance unit The tiller disturbance unit (Figure 3.10) is designed to allow the simulation of outboard motors in a Hardware-In-Loop configuration. The actuator mounting hardware conforms to A B Y C standard P17.5.2 and allows system actuators to be mounted in configurations that emulate Mercury and Yamaha outboard motors. The actuator disturbance input is provided by a back-driveable ballscrew acting over a lever arm opposite to the actuator. The disturbance load applied to a steering system during testing is a function of the lever arm geometry, motor torque and screw pitch, friction, damping, and the reflected inertia of the resistance motor and ballscrew unit. Figure 3.9 SEA resistance module. Photo by author. Chapter 3. System Evaluation Apparatus 33 A back-driveable ballscrew acting over a moment arm was chosen as the most practical and cost-effective means of applying the disturbance loads specified by the Teleflex engineers for the SEA. A ballscrew is used in the design instead of a simple lead screw because the rolling elements between the nut and screw in a ballscrew dramatically reduce friction, allowing the ballscrew to be easily back-driven. There is still friction however, and low lead ballscrews can be non-back-driveable because of the high friction angle. The ballscrew chosen (20 mm diameter, 10 mm pitch) permits back-driving but requires a larger motor than lower lead ballscrews to provide the same thrust. The large motor results in greater inertia being reflected to the system actuator. For the SEA, the reflected equivalent mass (1750 kg) is very large compared to outboard motors (approximately 600 kg for a 225 hp outboard).14 To reduce the reflected inertia of the resistance unit to a level representative of outboard motors, a software algorithm that modifies the reference load based on ballscrew acceleration can be easily implemented. To control the disturbance load, the servo amplifier is configured to operate in current control mode with the torque applied to the ballscrew considered to be equal to the product of the motor torque constant and motor current. The controller provides a reference signal to the amplifier that corresponds to the desired disturbance load. The bandwidth of the disturbance load (10 Hz) is low enough that the motor and amplifier dynamics are not considered. A motor with a gearbox or epicyclic mounted directly to the pivot of the tiller was considered for the application of disturbance loads instead of the 1 4 Appendix A includes the calculation of the reflected inertia of the resistance unit to the steering system actuator. Calculation of the reflected inertia to the steering system actuator from a representative outboard motor based on known static values and measured values from a dynamic test are also included for comparison. Chapter 3. System Evaluation Apparatus 34 ballscrew approach but was rejected for two reasons, the first being the large cost of the hardware to apply the large torque to the tiller shaft. The large thrust (1500 Ibf) of the system actuator applied over the moment arm of the tiller (8 in) would require a motor with substantial gear reduction to provide the 1000 ft*lbf torque at the output shaft. The second reason is that a gearbox of large enough ratio or epicyclic would not be back-driveable. In order to regulate the disturbance load, a force control loop would need to be implemented. A force control strategy would rely on tiller compliance and a high bandwidth, high accuracy position control loop to sense and control the disturbance load. Compared to the relative simplicity of back-driving a ballscrew operating in torque control mode and compensating for low-frequency accelerations, applying the disturbance torque directly to the tiller shaft was determined to be impractical because of the cost and complexity added to the system. The resistance unit (Figure 3.11) was modelled for use in the simulations discussed in Chapter 4 and is included here to complete the discussion of the SEA resistance unit design. The resistance unit model includes the effect of tiller geometry and models the ballscrew as a power screw with the nut and screw treated as separate components in a dynamic system. During initial testing procedures, it was observed that the simulated back-driven and measured back-driven responses of the ballscrew assembly were similar while the disturbance step inputs (torque applied to the screw) differed. The cause of the discrepancy was that the friction angle of the ballscrew provided a larger disturbance load when the ballscrew was back-driven than when applying a disturbance step input. Chapter 3. System Evaluation Apparatus 35 CI>— Applied load •9- -9-sin(lambda)2 5 s 2 < Nut and Co. meq cos(lambda)1 A cos(lambda)2 Disturbance F=»T 1:23 u friction coeff - K D Nut Position sinflambdl Sign2 Screw mean radius cos(lambda) sin(lambda) 0.003854s / t< \ rad=>ln Screw mean radiusl Ballscrew Jeq Figure 3.10 Simulink diagram of SEA resistance unit. The values of inertia of the components in the Simulink diagram in Figure 3.11 are taken from vendor information and Pro-Engineer C A D models of the system. The friction coefficient used for the simulations detailed in Chapter 4 is 0.02, though the value should be determined in future work. An estimate of the damping of the ballnut slide is included in the model but the damping between the ballscrew and nut is considered part of the coulomb friction coefficient. For systems with less damping, a model of the resistance unit that included appropriate measures of damping would be required. 3.4. Adaptabil ity of the S E A The potential utility of the SEA, beyond providing helm and disturbance input, is substantial. The programmability and system I/O allow the SEA to potentially Chapter 3. System Evaluation Apparatus 36 interact with many types of electromechanical systems. For example, in advanced systems similar to the one proposed by Bouvier, the SEA can be programmed to emulate any components that provide a signal to the steering system in addition to the physical input. This would allow not only physical testing procedures to be performed but also an assessment of the safety and performance of the steering system with the state of specific components simulated rather than directly included in the test. In addition to the programmable flexibility of the SEA, the physical design of the SEA can be modified to suit many other applications that could benefit from controlled dynamic testing procedures. Though not a specific design criteria of the SEA, this flexibility increases the potential utility that the SEA can provide. 3.5. Summary The SEA can be a very useful tool in the development of steering systems. The control of the physical inputs to the system to perform dynamic testing procedures and recording the system response can provide very useful information to designers. It allows any steering system intended for use with an outboard motor to be tested, meeting or exceeding the expected service inputs to the helm or system actuator. Because the SEA controls all inputs to the steering system and records the system response, comprehensive dynamic testing procedures can be performed to determine safety and performance under different conditions. The adaptability of the SEA further increases its potential utility in the design of steering systems- particularly advanced steering systems. The utility of the SEA in the development or modelling of manual steering systems is demonstrated in the next chapter - the modelling of the SeaStar steering system. Chapter 4. Modelling of the SeaStar steering system 37 Chapter 4 Modelling of the SeaStar Steering System After the design and assembly of the SEA, a test case was required for the development of testing procedures. The SeaStar steering system (Figure 4.1) was selected because it is representative of most steering systems currently in service. Step and frequency testing procedures performed with the SeaStar and the SEA produced unexpected results. The measured responses of the SeaStar showed substantial low-frequency resonance and non-linearities. After steps were taken to ensure that the irregularities were not caused by malfunction of the SEA or calibration issues, an investigation into the dynamics of the SeaStar was initiated. Figure 4.1 SeaStar steering system. (Source: Teleflex Canada Inc. Chapter 4. Modelling of the SeaStar steering system 38 This chapter has three main sections. The first details the response of the SeaStar to step and frequency inputs that generated the interest in developing a model of the system. To account for system non-linearities, a method of describing the overall response of the system to frequency and amplitude, called the modified frequency response, is introduced. The second section describes the Simulink model of the SeaStar that was developed to verify the unusual system response. The function of each component of the SeaStar is detailed and a block diagram or equation that describes each component is included. (See Appendix C for Simulink diagrams of the model.) The final section includes the simulation results and a discussion of the accuracy of the system model to steady state inputs. 4.1. Dynamic Response of the SeaStar The initial measured responses to step and frequency helm inputs generated interest in developing a model of the SeaStar.15 The tests were performed with no disturbance load applied to the actuator apart from the friction and inertial loads of the ballscrew and resistance servo motor. Both the step and frequency responses (Figures 4.2 and 4.3) demonstrate the low-frequency dynamics of the SeaStar when tested with the SEA. The step response has large overshoot and low-frequency oscillations, while the frequency response tests indicate a resonance at 1.6 Hz. 1 5 Appendix B contains plots of the measured and simulated response of the SeaStar to all static and dynamic testing procedures performed with the SEA. Chapter 4. Modelling of the SeaStar steering system 39 Figure 4.2 Helm velocity (45 degrees per second) step input response. 600 400 200 Helm lnput(°) Vs Tiller Output (0.001") -200 -400 -600 -800 Time (sec) Figure 4.3 Response of system to 64 degree helm amplitude of 1.6 Hz. Chapter 4. Modelling of the SeaStar steering system 40 4.1.1 Modified frequency response test Traditional frequency tests rely on the linearity of the system to extrapolate the response of the system to inputs of the same frequency. With the SeaStar system, in addition to the low-frequency dynamics, there appeared to be substantial non-linearities due to helm backlash and leakage. To explore the effects of amplitude on the linearity of the system, frequency response tests were performed with .geometrically increased input amplitudes. The resulting measured response of the system demonstrated that the system gain depended heavily on the amplitude of motion applied to the helm. Rather than generating multiple Bode plots to describe the frequency response of the system, the modified frequency response, a chart displaying the overall system response, was plotted. The modified frequency response is an original way to present the frequency response of systems with non-linearities in the operating range of the system. The approach is to plot system gain (Z-axis), with frequency (Y-axis), and amplitude (X-axis), forming a surface that describes the linearity of the system. The surface of the SeaStar modified frequency response (Figure 4.4) demonstrates the effect of deadband on low amplitude motions of all frequencies, causing the gain to drop dramatically at the smallest helm amplitude measured, 16 degrees. Also shown in the plot is the curious resonance at the 64 degree amplitude and 1.6 Hz helm input. As a comparison, Figure 4.5 is the SeaStar response linearised about the 64 degree helm amplitude of the SeaStar. The contrast between the surfaces in Figures 4.4 and 4.5 emphasizes the non-linear nature of the SeaStar and the ability of the modified frequency response to provide an overall representation of a system's dynamic response. Chapter 4. Modelling of the SeaStar steering system 41 Figure 4.4 Modified frequency response surface. Figure 4.5 SeaStar response linearised about 64 degree helm amplitude for all frequencies.. Chapter 4. Modelling of the SeaStar steering system 42 Three-dimensional plots are used in other applications to demonstrate visually the variation of system properties over two independent variables. One such example is the plotting of acoustic data for multi-axle systems with the Vold-Kalman Tracking Filter by Void, Herlufsen et a l . 1 6 The filter tracks the contribution of noise from different shafts. The filter parameters are adjusted based on the fundamental frequency of the system to isolate the signal that corresponds to each of the shafts. The data is then presented with the fundamental frequency (rpm) on the X-axis, the order frequency on the Y-axis, and signal strength on the Z-axis (Figure 4.6). In this plot, the contribution of each rotating element to the total signal for different fundamental frequencies can be examined. The components that contribute most to the overall system noise, or interact causing beating, can be modified to reduce the peak noise measurement. Figure 4.6 Order tracking plot. Source: Void Solutions. VOLD, H; HERLUFSEN, H; MAINS, M; CORWIN-RENNER, D: Multi-Axle Order Tracking wit the Vold-Kalman Tracking Filter. Void Solutions, Cincinnati Ohio. 2000. Chapter 4. Modelling of the SeaStar steering system 43 Another example of three-dimensional presentation is the technique used in the tracking of motor shaft twist resonances by Void Solutions.17 Figure 4.7 is a plot of shaft twist (Z-axis) against fundamental rpm (Y-axis) and disturbance input frequency (X-axis). During testing, the disturbance load is applied at multiples of shaft speed, and the shaft twist is measured at different shaft speeds in the expected operating range of the shaft. The shaft twist is then plotted against the shaft speed and frequency of disturbance loads. The red lines on the chart indicate the relation between shaft speed and disturbance frequency. Figure 4.7 highlights the resonance that occurs if the disturbance load is applied five times per revolution of the shaft at approximately 1700 rpm. The designer of a system that uses this motor can reference this chart easily to ensure that direct or reflected loading at this multiple of shaft speed is avoided in the design of the system. 1 7 Void Solutions: Multi-Axle Order Tracking wit the Void-Kalman Tracking Filter. White Paper Published by Void Solutions, Cincinatti Ohio. 2002. Chapter 4. Modelling of the SeaStar steering system 44 H.rfcr Figure 4.7 Twist angle, disturbance frequency, and shaft speed of small electric motor. Source: Void Solutions. The modified frequency response surface, the shaft noise and shaft twist charts each allow one to describe a wide variety of operating conditions, while presenting the data in a form that is easily referenced and understood. Verifying the causes of the surface shape by modelling the SeaStar is the topic of the following sections in this chapter. Chapter 4. Modelling of the SeaStar steering system 45 4.2. Approaches to Modelling the SeaStar Steering System An examination of the SeaStar and SEA components indicated that the low frequency resonance was caused by the interaction of the large reflected inertia of the resistance unit (which is dominated by the inertia of the DC motor) and the compliance of the SeaStar hoses. Calculations were performed based on static hose stiffness values provided by Teleflex engineering staff and the reflected inertia of the resistance unit (Appendix C). The calculated natural frequency (1.5 Hz) is very near the measured value. As an added verification, the frequency response of the SeaStar with the resistance motor removed was measured. (Appendix B contains plots of "no motor" responses.) In the range tested, no noticeable low-frequency resonances could be detected. It was further proposed that some of the system non-linearities could be described if the SeaStar spool valve were included in the model. An initial model was developed including all of the components of the SeaStar steering system, which reproduced the modified frequency response surface fairly well. However, when the model was applied to constant speed and disturbance load testing procedures (intended to correlate to existing manual test data), it did not reflect the unusual actuator drift that depended on the direction of the applied load and actuator movement. In order to demonstrate that the drift was related to the operation of the SeaStar spool valve, a simple relation of spool position and fluid pressure to leakage was developed and added to the model. A series of frequency and constant speed and load test data sets was then performed to provide an assessment of the overall performance of the complete simulation model. The SeaStar steering system is very complex and comprises many components that exhibit non-linear behaviour. The model linearises many of Chapter 4. Modelling of the SeaStar steering system 46 these behaviours to achieve a workable solution with reasonable accuracy. Typical examples of simplified parameters include the non-linear behaviour of the SeaStar hoses, the racking of the system actuator, damping coefficients, and the dynamics of fluid flow between components in the system. In addition, the geometry of these units (in common with most similar hydraulic systems) means that manufacturing tolerances can significantly affect behaviour. Conceptually, the SeaStar steering system is modelled as a series of fluid-filled control volumes. The flow of fluid between control volumes is governed by check-valves and switches and the difference in pressure between connected control volumes. The pressure of the fluid in the control volumes is a function of control volume size, compressibility of the fluid, and mass of fluid inside the control volume. The approximations made within the model will be clearly stated and explained in the following sections which discuss the component models. The final model, despite its simplicity, provides much useful information and insight into the dynamic response of the SeaStar steering system, and validates the system response measured with the SEA. 4.2.1 Pressure Calculation in SeaStar Model The calculation of the fluid pressure (P) in the model is a function of the bulk modulus (K) of the steering fluid (250,000 psi/psi), the control volume size (V), and the amount of fluid contained in the control volume. The processes are assumed to be quasistatic and isothermal. The isothermal compressibility (P) of a fluid is defined as: (4.1) Chapter 4. Modelling of the SeaStar steering system 47 For quasistatic, finite changes in control volume size, Equation 4.1 can be restated as: l K. := — P (4.2) or . : = - V | ^ > V / (4.3) For the SeaStar model, V 2 is the zero pressure volume of the fluid (Vfluid(t)), and V i the control volume size (Vcontrolvol(t)). The fluid volume is the sum of the zero pressure initial fluid volume contained in the control volume and the integral of the net flow (qfluid(t)) into the control volume (Equation 4.4). V fluidCt):=V f l u i d (CD + (4.4) This allows Equation 4.3 to be restated as Equation 4.5. 1 . v i (4.5) 4.3. SeaStar Helm The function of the SeaStar helm (Figure 4.8) is to convert operator input to fluid flow that regulates the position of the SeaStar actuator. The helm is a manually-driven rotary piston pump with valves that regulate the flow of fluid between control volumes. The transfer of fluid between the port and starboard side of the SeaStar system is controlled by the direction and angular displacement of the Chapter 4. Modelling of the SeaStar steering system 48 helm input shaft (steering wheel). This differs from typical applications of rotary piston pumps, such as hydrostatic drives. Hydrostatic drives are rotary piston pumps driven by a motor at steady speeds greater than 100 rpm and rely on swash plate angle to regulate the rate and direction of fluid flow. Figure 4.8 SeaStar helm. Source: Teleflex Canada Inc. Figure 4.9 shows the components of the helm: pistons and piston springs, piston block, valve body, reservoir, swash plate, helm shaft, spigot assembly, and spool valve assembly. Bearings, seals, and the vent plug are excluded from the illustration for simplicity. The function and modelling of the helm components will be described in the following subsections. Chapter 4. Modelling of the SeaStar steering system 49 Figure 4.9 Exploded view of simplified helm assembly. 4.3.1 Reservoir The reservoir encloses all of the components assembled between the reservoir cover and the mating face of the spool valve body. This arrangement allows for the helm components to be immersed in fluid, reducing air intrusion, and provides for a compact installation of the pump unit with no external reservoir. The reservoir is vented to atmosphere and holds only small pressures of less than 30 psi. The reservoir design includes an air pocket near the vent to accommodate the thermal expansion of the SeaStar fluid and to ensure that air, rather than oil, is vented to the outside of the helm. The reservoir is modelled as a flow source and sink. Because the reservoir is vented to atmosphere, the pressure is considered constant and zero. Chapter 4. Modelling of the SeaStar steering system 50 4.3.2 Spigot and piston assemblies The first function of the spigot is to control the flow from the reservoir into the SeaStar system through make-up check valves and the reservoir access slot (Figure 4.10). The make-up check valves allow fluid to flow into the system if the pressure on either the port or starboard side of the system falls below the reservoir pressure. In normal operation, this is to ensure that air does not enter the system if the port or starboard pressures drop below atmospheric level. The make-up check valves also permit the purging of air from the system during set-up with an external pump that pressurizes the reservoir. Figure 4.10 Spigot assembly. Chapter 4. Modelling of the SeaStar steering system 51 The make-up check valves are modelled as allowing fluid flow from the reservoir to the system as a linear factor of the spigot chamber and threshold pressure difference (Equation 4.6). The threshold pressure is used because the make-up check valve balls are preloaded with springs to ensure that the check ball remains seated. The effect of the spring loaded ball is modelled as having a threshold pressure of 2 psi and permitting fluid to flow in one direction only. iReservoifToSpigot^ , = [k' (P SpigotThreshold - P Spigot^)] tf (P SpigotThreshold " P Spigot^) 0 otherwise (4.6) The second function of the spigot is to act as a switch that determines if a piston is acting on the port or starboard side of the system. Each piston chamber has a hole that lines up with one of the slotted ports on the spigot body (Figure 4.10). The two slots on the spigot provide a flow path between the port or starboard side of the SeaStar system and the seven piston chambers. As the helm is rotated clockwise (Figure 4.11), the pistons on the port side of the helm are forced into the cylinder block by contact with the swash plate, pushing the fluid out of the chambers and into the spigot assembly through the slot on the port side of the spigot. As the pistons rise on the starboard side, fluid returns from the starboard hose through the spool valve to the piston chambers aligned with the starboard slot of the spigot. Chapter 4. Modelling of the SeaStar steering system 52 Figure 4.11 Piston movement from helm input. The piston chamber control volumes are modelled as a function of the piston stroke positions and base volume of the piston chamber. The piston position, multiplied by the cross-sectional area of the piston, plus the base volume of the piston chamber, determines the size of the piston control volume (Equation 4.7). The base volume used in the simulation is larger than the actual base volume of the chamber to improve simulation speed. V chamber1 '^9 :" V base + Y piston^>9 A piston (4-7) The helm piston positions (Equation 4.8) are considered in the model as being equal to the swash plate contact point. The dynamics of the spring-loaded pistons are not considered in the model because the natural frequency of the pistons is higher than the expected operating or testing bandwidth and the inclusion of the piston dynamics substantially slowed the simulation. Chapter 4. Modelling of the SeaStar steering system 53 Ypiston^.1) := R PistonCkcle ' s i nM " ^ + cosje(t) + i • where: 9 = helm shaft angle i = 0:6 y=14.5-180/n RpistonCrcle = 1.0625 in 4.3.3 Spigot and piston assemblies control diagram The block diagram in Figure 4.12 is used in the simulation model to represent the spigot and each of the seven pistons. Piston geometry, the piston chamber pressure, and the flow between the piston chamber and the spigot ports are modelled in this block diagram. The difference between the chamber pressure and the active spigot port pressure multiplied by a "flow factor" of unity determines the flow into and out of the piston control volume. The flow factor of unity is used to describe the passage as having no restriction to flow and ensuring that the flow factor does not create instability in the simulation. Switch 1 determines which spigot port the piston chamber port is in line with and consequently which pressure - port valve pressure (PPValve) or starboard valve pressure (PS Valve) -is subtracted from the chamber pressure to determine the flow rate. Chapter 4. Modelling of the SeaStar steering system 54 CO Figure 4.12 Simulink diagram of piston and spigot. Chapter 4. Modelling of the SeaStar steering system 55 4.3.4 Spool valve The spool valve has four main components: the spool, hose check valves, pressure relief check valves, and valve body (Figure 4.13). The purpose of the spool valve assembly is three-fold: to eliminate drift of the SeaStar actuator, to reduce . feedback to the operator due to tiller disturbance loads, and to regulate the return of fluid to the reservoir when unbalanced cylinders are installed with the system. When the wheel of the helm is static, the hose check valve springs and hose pressures force the check valves to remain closed, stopping any flow into the valve body from the hoses. This isolates the operator from feedback due to disturbance loads because the pressure in the line is not reflected to the piston chambers. Drift is eliminated by blocking the flow of fluid from the hoses and actuator, acting as a stop to hold the tiller in place when the wheel is in a static position. Should the system pressures exceed 1000 psi, the relief check valves allow fluid to be vented to the reservoir to reduce the system pressure. Chapter 4. Modelling of the SeaStar steering system 56 Figure 4.13 Spool valve layout Figure 4.14 illustrates the operation of the spool valve. As the wheel is turned clockwise, fluid is pumped into the port chamber from the spigot assembly and past the port check-valve to the port hose. The spool is moved toward the starboard check-valve, lifting the check-ball out of its seat and allowing fluid to enter the chamber from the starboard hose. To allow for the operation of an unbalanced cylinder (larger area on one side of actuator piston than the other), the spool opens a flow path to the reservoir that allows excess fluid to return when pumping to the small piston area side of the cylinder.1 8 When pumping to the large piston area side of an unbalanced actuator, less fluid returns than is pumped. Fluid is drawn from the reservoir through the make-up check valves in the spigot to compensate for the unequal fluid flow. Chapter 4. Modelling of the SeaStar steering system 57 Figure 4.14 Functional representation of spool valve. 4.3.5 Spool dynamics The forces acting on the spool include the net pressure force, viscous damping, and the forces resulting from engagement with the check-valve ball (including the net pressure force acting on the ball) and the spool stops. To move the ball off its seat, the spool must provide the force required to overcome the spring preload, and the difference in hose and valve chamber pressures acting on the area of the ball seat (Figure 4.15 and Equation 4.9). The interaction between the spring-loaded check-ball and the spool are modelled as only a spring force, rather than as a dynamic interaction. The spool stops are modelled as very stiff springs with the force proportional to the interference between the spool and stops. The mass of the spool and an estimated damping coefficient are also included in the modelling of the spool motion. The Simulink diagram of the spool valve motion and Chapter 4. Modelling of the SeaStar steering system 58 pressure generation inside the valve chambers is shown in Figure 4.16. The detailed Simulink diagram for the spring contact force, stops, and fluid forces acting on the spool check valves can be found in Appendix C. Volume atPp Volume atPs X spoC Figure 4.15 Forces acting on spool. F SpoolNet - P p • A S p o o l - [P s A S p o o l + i P S H - P s l • A S e a t + F S p r i n g + F S t o p ] where: PP = port valve pressure Aspooi = area of spool Ps = starboard valve pressure P S H = starboard hose pressure Fspring = force of check valve spring Fstop = force applied by spool stop Chapter 4. Modelling of the SeaStar steering system 59 Figure 4.16 Simulink diagram of spool valve. Chapter 4. Modelling of the SeaStar steering system 6 0 4.3.6 Spool valve fluid flow The pressure relief valves and spool valve are modelled in a similar fashion to the make-up check valves. For the relief valves, the threshold pressure is 1000 psi and the flow is from the hoses to the reservoir (Equation 4.10). Without consideration of the spool, the operation of the spool check-valve is similar to the relief valves, with flow allowed in one direction and proportional to the pressure difference between the hose and valve chamber minus the threshold pressure. The operation of the spool check-valve differs from the make-up check or relief valve in that the spool can unseat the ball and allow fluid to flow in the opposite direction (Figure 4.14). The flow factor past the check valve when the spool unseats the ball is modelled the same as for flow in the opposite direction with zero threshold requirement. ^ Reservoir^) :~ [ k Relief- (P HoseC1) _ P Relief)] tf P Hose > P Relief 0 otherwise (4 .10) ( 1 jValve Press C D Hose Press Flow Factor X •0.03 Port Spool/Ball Contact Point < 7s —i f & J r * U ( D I I r*fcs__l F | 0 W Figure 4.17 Simulink diagram of flow past check valve. Chapter 4. Modelling of the SeaStar steering system 61 Figure 4.18 illustrates the relation between spool position and the flow between the spool valve and the reservoir. The large steps occurring in the relation at +/- 0.090 in represent the opening of the path between the valve body and the reservoir when the spool is moved far enough to the port or starboard side. The flow factor between 0" and +/- 0.090 in (leakage) is modelled as being linearly related to the amount of overlap between the spool and valve body. (This approach is similar to that of Karpenko and Sepehri in their works examining control of a servohydraulic actuator with leakage across the piston seal, except that in this case the width of the sealing surface varies with position, and leakage is a linear factor of pressure.19 2 0 ) 1 9 KARPENKO, M; SEPEHRI, N: Fault-tolerant Control of a Servohydraulic Positioning System with Crossport Leakage. IEEE Transactions of Control Systems Technology, Vol 13, No. 1, January 2005. 2 0 KARPENKO, M; SEPEHRI, N: Robust Position Control of an Electrohydraulic Actuator with a Faulty Actuator Piston Seal. IEEE Transactions of Control Systems Technology, Vol 13, No. 1, January 2005. Chapter 4. Modelling of the SeaStar steering system 62 Port and Starboard Flow Rates vs Spool Position Flow Rate (in3/sec) 0.5*P 0.02*P -0.1 -0.09 Spool Position (in) 0.09 0.1 Starboard Port Corner Value Figure 4.1 Flow to reservoir past spool. The leakage relation was developed after it was noticed that the actuator would drift only when steering in the direction of the applied disturbance load (Figure 4.19). The simulated spool position (Figure 4.20 and Figure 4.21) shows that the spool oscillates with a mean value of approximately 0.030 in when steering with the load, is forced into contact with the spool stop at position -0.100 in, and remains there when steering into the load. It is clear that when steering with the load the spool has much less sealing surface than when steering into the load, which permits more leakage from the high pressure chamber to the reservoir. Other system components, such as the relief valves or actuator piston seal, would allow leakage that was independent of steering direction, allowing drift throughout the testing procedures.21 A larger spool stroke with greater overlap would decrease system leakage but increase helm backlash by requiring additional fluid to move the spool into a position to open the return side spool check-valve. Chapter 4. Modelling of the SeaStar steering system 400 Ibf Static Load - 90°/sec Helm Speed - No Leakage 0 1 2 3 4 5 6 7 8 9 10 Time(sec) Figure 4.19 Drift of actuator when turning in direction of applied load. Chapter 4. Modelling of the SeaStar steering system 64 „ 300 Simulated Pressures and Spool Position Q. 200 to 100 in ™ £ o o ° - -100 0.05 c~ 0 .2 - 0 0 5 en -0.15 10 Steering With Load i i i i i i Steering Into Load / _ J Steering With Lo< i id i i i i i i i i 10 Time (sec) Figure 4.20 Spool position for 90 degree per second, 400 Ibf constant speed constant load. Small Overlap Large Overlap Figure 4.21 Spool position at 0.03 in (left) and at -0.1 in (right). Chapter 4. Modelling of the SeaStar steering system 65 The leakage relation corner value was determined by iterating the corner rate value until the slope of the simulated tiller response approximately matched the measured response for the 400 lbf disturbance load, 90 degree per second test. One can see in Figure 4.22 how the leakage relation improves the simulation steady-state tracking of the measured response. 400 lbf Static Load - 90 °/sec Helm Speed -21 1 1 1 1 I I I I I I 0 1 2 3 4 5 6 7 8 9 10 Time (sec) Figure 4.22 Simulated response with leakage relation vs measured response. 4.4. SeaStar Hoses The SeaStar hoses are 7/16-in inner diameter flexible lines rated for use to 1000 psi. The hose flexibility is required for installation in many different configurations and to permit the hoses to move with the cylinder barrel during Chapter 4. Modelling of the SeaStar steering system 66 operation. The hoses used in testing procedures were 16 feet long but can be as long as 50 feet. The hoses are modelled as second order systems that correspond to Equation 4.11. In reality, the measured static stiffness is known to change with volume and the damping is also likely to be variable. The mass of the hoses is included in the linearised model though the effect of its mass is small relative to the stiffness and damping of the hose. ^hose ' = 2 ms + bs + k (4 11) To develop a simulation model that describes the response of the SeaStar System, the hose characteristics were linearised (Figure 4.23) to match the system response to a 300 Ibf step disturbance load. The static stiffness value used was derived from the manufacturer's specification for stiffness at 300 psi . 2 2 The damping coefficient was determined by adjusting the damping coefficient until the rise time and overshoot of the simulated response matched the measured response (Figure 4.24). The deviation between the measured and simulated response between 0.7 and 1.4 seconds is likely due to a viscous damping factor being used in the actuator racking equation (detailed in the next section) rather than viscous and coulomb damping factors. 22 L DUDRA, B - Chief Engineer, Marine Hydraulic Division of Teleflex Canada: Discussion^ Regarding Stiffness and Damping of SeaStar Hoses. Teleflex Canada, Richmond, BC. October 30, 2003. Chapter 4. Modelling of the SeaStar steering system 67 Net Flow -C-Initial Fluid Volme 16ft long. 0.38 ID + Cylinder Volume dV Cylinder Pos Piston Area -c-Initial Hose Volme 16ft long, 0.38 ID1 + Init Cylinder Volume Bulk Modulus 1 0.01s2+63s+1024 Hose Dynamics Pressure Figure 4.23 Simulink diagram of hose pressure. Disturbance Response: 300 lbf Step Input Figure 4.24 Simulated and measured response to 300 lbf disturbance step input Chapter 4. Modelling of the SeaStar steering system 68 4.5. SeaStar Actuator The SeaStar actuator is a hydraulic cylinder fixed at both ends of its shaft by brackets connected to the tilt tube of the outboard (Figure 4.25). The cylinder barrel is connected to the tiller with the pivot plate, moving the barrel and turning the tiller as fluid is pumped from one side of the system to the other. The mounting arrangement functions as a four-bar linkage to compensate for changes in the tiller position as the motor is turned (Figure 4.26). Figure 4.25 SeaStar cylinder mounted on SEA. Photo by author. Chapter 4. Modelling of the SeaStar steering system 69 Joints ^ ™ Links Figure 4.26 Four-bar linkage cylinder mount Photo by author. The actuator has two main non-linearities that are accounted for in the model: backlash between the pivot plate and barrel, and racking. Teleflex specifies less than 0.01 in of backlash, but the backlash was measured on the cylinder used in experiments as 0.03 in. The backlash is not noticeable to the operator of the boat but does directly offset the output position of the tiller when measured experimentally. Racking (Figure 4.27 and Figure 4.28) is largely a result of actuator geometry. The spatial limitations and mounting configuration require that the cylinder be mounted with its centreline approximately one inch below the plane of the tiller. The distance between the cylinder shaft and tiller introduce a moment to the cylinder assembly, causing the unit to rack. During some Teleflex tests, rack angles can reach 15 degrees for loads of 1500 Ibf.23 Inefficiency is TROUSIL, D - Lead Customer Service Engineer, Marine Hydraulic Division of Teleflex Canada: Discussion Regarding Bass Boat Applications. Teleflex Canada, Richmond, BC. October 29, 2003. Chapter 4. Modelling of the SeaStar steering system 70 introduced to the system by racking because the angle at which the cylinder applies force to the tiller is changed. The other issue that racking introduces is a non-linear relation between cylinder and tiller position. Like backlash, the racking is not very noticeable to the operator, but does directly affect the calculation of cylinder position from experimental measurements (Equation 4.12). Racking is a difficult relation to determine analytically because of the indeterminate structure of the actuator. An estimated 1:100 ratio of racking degree to lbf tiller load with a large viscous damping factor is used in the model (Equation 4.13). Figure 4.27 Racking of cylinder with 800 lbf. Photo by author. Chapter 4. Modelling of the SeaStar steering system 71 Tiller Plane Cylinder Centreline Figure 4.28 Geometric effects of pivot plate backlash and cylinder racking. , s X measured^ ~ X b c ' " ° ( T ^ ) X cylinder^ :~ / . . . i . X backlash (4.12) ^ disturbance1^3) Track^ := Js + bs + k 4^ where: J = 1 b = 600 k = 5284 Chapter 4. Modelling of the SeaStar steering system 72 Backlash is modelled as the interaction of stiff springs where the force transferred is proportional to the interference between components. Figure 4.29 is the block diagram used to model the force applied between the actuator barrel and pivot plate. The interference input in the diagram is the difference between the contact point of the cylinder, including racking, and the tilt plate which is connected directly to the tiller. If the magnitude of the interference is less than 0.015, no force is transferred between elements. If the interference is greater than 0.015, the elements are in contact with one another and the resultant force is proportional to the interference minus the backlash. - K D Contact Force Interference Figure 4.29 Simulink diagram of actuator backlash. 4.6. Modelling Summary The SeaStar model takes into account all of the system elements present in the SeaStar steering system. Though the modelling of the dynamics of the components is much simplified, the simulation results that follow demonstrate the Chapter 4. Modelling of the SeaStar steering system 73 model's ability to accurately predict the general behaviour of the SeaStar. The physical model developed, though simple, provides a solid basis for estimating the effect of changing system parameters on the system response. Should more detailed analysis of the system be required, the model also provides the framework for expansion to include many of the dynamic effects that have been simplified or ignored in this model. 4.7. Test and Simulation Results To demonstrate the accuracy of the SeaStar model, and ultimately to prove that the unusual measured responses of the SeaStar were not the result of malfunction of the SEA, this section compares the measured and simulated responses of the SeaStar. The simulated modified frequency response surface is compared to the surface derived from measured results to show the model's ability to predict the system response to a varied range of amplitude and frequency inputs. The effect of the spool leakage relation applied to all of the available data for constant speed and load testing procedures is summarized and the effectiveness and limitations of the relation are discussed. Representative individual simulation and measured test results are directly compared to assess the model's general ability to predict the dynamic response of the system. 4.7.1 Evaluation of modified frequency response test simulations The modified frequency response testing of the simulation model is a good way to assess the accuracy of the overall response of the system model. The unusual shape of the surface is a result of the many non-linearities of the system. By comparing the measured and simulated responses, the assumptions made in modelling of the system can be evaluated. The amplitude gain for different Chapter 4. Modelling of the SeaStar steering system 74 conditions also indicates the overall accuracy in the estimation of system inertia (dominated by the resistance servomotor) and hose dynamics. Figures 4.30 and 4.31 show the simulated and measured modified frequency response surfaces of the SeaStar Steering System. The simulated frequency response surface correlates well with the measured response surface. Both have a similar shape with a gain peak at 64 degree helm amplitude at 1.6 Hz (Figure 4.30), a near zero gain at small amplitudes, and a flat area for large amplitude motions. The response surfaces differ in that the simulated peak is higher than the measured response. This is likely the result of the simulation not providing the same level of flow restriction or errors in the estimate for the damping of the cylinder or friction in the ballscrew.24 Figure 4.30 Modified gain plot for measured SeaStar response. Appendix B contains charts comparing all of the simulated amplitude and frequency responses to measured values. Chapter 4. Modelling of the SeaStar steering system 75 Frequency (Hz) Helm Amplitude (°) Figure 4.31 Modified gain plot for simulated SeaStar response. 64° Amplitude, 1.6 Hz, No Load -1.2' 1 1 1 1 1 I 0 0.5 1 1.5 2 2.5 j Time (sec) Figure 4.32 Measured and simulated response for 64 degree helm input at 1.6 Hz. Chapter 4. Modelling of the SeaStar steering system 76 Another measure of model accuracy may be obtained by comparing the measured and simulated hose pressures (Figure 4.33). The measured and simulated hose pressures match relatively well in magnitude but there are differences in phase for the same helm input. Non-linear hose damping and stiffness that increases with pressure would allow pressure to build up more slowly than the linearised model. The match between the measured and simulated pressures and positions validate the model of the SeaStar actuator and SEA resistance unit. The near-equal net pressure and response indicates that the modelling of the SeaStar actuator and SEA resistance unit are reasonable approximations of the real systems. Figure 4.33 Comparison of measured and simulated hose pressures. Chapter 4. Modelling of the SeaStar steering system 11 4.7.2 Evaluation of constant speed and load test simulations The constant speed and load tests were initially intended to be used to validate the SEA design by comparing existing Teleflex test data from similar manual tests to results measured with the SEA. The manual test responses were difficult to compare to the SEA measured responses for a number of reasons. Manual test data available at the time had substantial helm input speed fluctuations while the SEA input rate was constant. As well, the interaction of the inertia of the SEA and the low stiffness of the hoses caused substantial low-frequency dynamics not present when tested with the manually-driven tests apparatus. The system response of the SeaStar to the constant speed and load tests was most useful in the determination and evaluation of the leakage relation detailed in Section 4.3.6. In service (Section 5.2.1) the static load is applied in one direction only; positive and negative loads are applied in the testing procedures to ensure the symmetry of the system. Evaluation of the accuracy of the simulated system response to constant speed and load tests focuses on the steady state periods,of 2.5 seconds in the tests. The errors brought about during the velocity reversal and load application were not considered in developing the spool leakage function or the evaluation of the simulation response. Actuator racking non-linearities are likely the cause of the inability of the model to track the system response during the helm velocity reversals. Table 4.1 summarizes the accuracy of the model in predicting actuator drift during the constant speed and load testing procedures.25 Drift is calculated as the difference between the average actuator speed and the reference trajectory speed during the 2.5-second steady state periods when steering with and into the Detailed tables of drift values can be found in Appendix B. Chapter 4. Modelling of the SeaStar steering system 78 applied disturbance load. The drift error listed in the tables (Equation 4.12) describes the percentage error of the simulated drift rates compared to the measured drift rates. Drift := m e a n(Speed R e f e f e n c e ) - mean(Speed M e a s u f e d ) D r i f t Measured " D r i f t Simulation D r i f t Measured (4.12) (4.13) Chapter 4. Modelling of the SeaStar steering system 79 Helm Speed (deg/sec) 45 90 180 Load Condition Drift (in/sec), Leakage Error (%), No Leakage Error (%) Drift (in/sec), Leakage Error (%), No Leakage Error (%) Drift (in/sec), Leakage Error (%), No Leakage Error (%) • 400 Into Load - 0.02, 108,2 0.11, 124, 103 With Load - 0.00, 2657, 8164 0.12, 75, 268 200 Into Load 0.01, 70, 62 - 0.35, 164, 105 With Load 0.03, 458, 427 - 0.75, 68, 17 100 Into Load 0.02, 21, 29 0.018, 35, 58 -0.07, 46, 32 With Load -0.05,106,408 0.052, 15, 177 0.20, 87.5, 113 -100 Into Load 0.01, 99, 104 0.00, 1123, 1158 0.09, 92, 94 With. Load -0.01, 58, 231 0.01,2807, 14.5 -0.13, 278, 120 -200 Into Load .01, 125, 128 0.01, 105, 29.6 0.09, 40, 92.8 With Load -0.04, 348, 343 0.02,201,176 -0.14, 390, 117 -400 Into Load -0.04, 20.3,18.3 0.04, 27.6, 53.4 0.08, 140, 138 With Load -0.01, 1626, 1899 0.02, 2029,1851 -0.09, 528, 372 Table 4.1 Actuator drift rate accuracy of simulators, with/without spool leakage. It is clear from the table that the spool leakage relation significantly improved most of the tests with a positive load. It is also clear, from examining the negative land test results, that the helm tested was not symmetrical. In most cases, the simulations with no leakage were reasonably close to the measured drift Chapter 4. Modelling of the SeaStar steering system 80 rate, indicating that the spool only leaked on the positively loaded side. In most tests, as expected, the leakage when turning into the load was very small, indicating that the theory that the spool leaked very little when turning into the load was valid. In addition to demonstrating the validity of the leakage relation, the constant speed and load tests demonstrated the low-frequency dynamics seen in the modified frequency response tests. The fundamental frequency in the response was predicted well, and the overall response of the system was generally predicted with good accuracy in simulation. Figure 4.34 shows one of the most accurate simulations of the position response of the system with and without the leakage with a positive load. The simulated response matches the mean error from the reference position and the frequency and amplitude of the oscillations. The leakage relation adjusts the simulated response to match the measured response much more closely. Chapter 4. Modelling of the SeaStar steering system 81 400lbf Static Load - 180Vc/sec Helm Speed Time (sec) Figure 4.34 Responses to 180 degree per second helm input and 400 lbf disturbance load. As a comparison, Figure 4.35 shows the simulated and measured responses to a negative applied disturbance load. The fundamental frequency of the response matches well but the leakage relation results in excessive drift. The simulation that did not use the spool leakage relation tracked the measured response very well. Chapter 4. Modelling of the SeaStar steering system 82 -200 Ibf Disturbance Load 180 °/sec Helm Speed 51 1 1 1 1 1 1 i i -21 1 1 1 1 i i i i i I 0 1 2 3 4 5 6 7 8 9 10 Time (sec) Figure 4.35 Transition tracking into applied load. The simulations of the SeaStar with and without the leakage relation do not just fall into the categories of the leakage relation working or not, two simulations produced large errors for both types of simulations (Figure 4.36). The simulations performed poorly, indicating that one or more of the simplifications in the SeaStar model does not account for all types of conditions. An investigation to determine the causes of the errors should be undertaken in future work. Chapter 4. Modelling of the SeaStar steering system 83 -400 lbf Disturbance Load 90 °/sec Helm Speed Reference Position Measured Tiller Response Simulated No Leak Response _•) 51 I i I i i i i i i I 0 1 2 3 4 5 6 7 8 9 10 Time (sec) Figure 4.36 Simulation models producing large errors. The overall performance of the SeaStar model in predicting the response to constant speed and load testing procedures is good, given the many simplifications and linearization of components in the model. The frequency content of the simulated responses matches the measured responses well. The simulation results indicate that the helm spool valve tested was not symmetrical, and that the leakage relation proposed was not adequate. If a generalised response were required, a statistically significant number of systems would need to be tested to determine parameters that best described the system response. Chapter 4. Modelling of the SeaStar steering system 84 4.8. Conclusions and Recommendations During the initial, debugging phase of the SEA design, the dynamics of the SeaStar steering system, when tested with the SEA, generated interest because of low frequency resonance and response non-linearities. Response data to a wide range of excitation frequencies and amplitudes was collected. The data was analysed and a summary of the system response presented in an original form called the modified frequency response plot, which describes gain variation with frequency and amplitude. The SeaStar response plot indicated a peak resonance at 1.6 Hz and 64 degrees and emphasized the effects of non-linearities on small amplitude motions for all frequencies. The results were verified by inspecting the test bench for sensor errors and performing the same procedures with additional SeaStar systems. An investigation into the SEA and SeaStar design led to the proposal of two theories. The first is that the resonance is the effect of the interaction of the high reflected inertia of the resistance module and the compliance of the SeaStar hoses. The second theory postulated is that the non-linearities, specifically, the backlash that limits the gain for low-amplitude motions, is caused by the operation of the spool and the racking of the actuator. To validate the theories, a Simulink model of the SeaStar that included all of the functional components of the system was developed. To model the components, data collected with the SEA, information from Teleflex designers, and simple modelling based on first principles was used to determine the values of component parameters in the model. A basic model was developed that provided simulated responses generally matched the overall amplitude and frequency response of the SeaStar. To further explore the capabilities of the model, constant speed and load tests were performed to correlate to existing manual test data. When the tests were Chapter 4. Modelling of the SeaStar steering system 85 simulated, drift that depended on the relative direction of the applied load to the actuator motion was not reflected in the simulated results. A spool leakage relation that linked the amount of spool and valve overlap and pressure to leakage past the spool was added to the model. Simulations of all of the frequency and constant speed and load tests were then performed to determine the model's overall accuracy. The simulated frequency responses matched the measured responses well. The small gain of the system at small amplitudes and the resonance at 1.6 Hz was reflected in the simulated responses. The overall shape of the surface in the simulated frequency response plot was similar to that of the measured responses, indicating that the model developed is a reasonable approximation of the system. The constant speed and load simulated responses exhibited low frequency oscillations that matched the measured response well. The leakage relation was inadequate to fully describe the drift of the actuator because the drift characteristics in the measured responses were not symmetrical. The direction in which the relation was calibrated generally showed improvement in tests in that direction, while tests with the load applied in the opposite direction showed very little drift. Generally, the model reproduced the measured responses for the frequency and constant speed and load tests well. The extendibility and accuracy of the model will allow the SeaStar model to be used as an ongoing design tool by the sponsor of this research, Teleflex Canada. With the SeaStarmodel, designers can reasonably predict the effect of changing major system parameters on the performance of the SeaStar in simulations. This increases the number of design options that can be explored and decreases the time and expenses of building and testing prototypes. Teleflex manufactures many thousands of SeaStar (and similar) systems annually; any tool that assists designers in reducing costs or improving performance can have substantial financial impact on the company. Chapter 4. Modelling of the SeaStar steering system 86 Small variations in manufacturing, as shown by the asymmetrical drifting of the actuator, demonstrate the limitations of the model. To be used as a general reference model to which the response of other SeaStar systems can be compared, the model will need to be verified by comparing its response to a statistically significant number of systems. Only then can the model be said to represent the "as manufactured" SeaStar systems. The high inertia of the SEA resistance unit made the measured responses difficult to compare to conditions that may be expected in service. The low frequency resonance during frequency response tests and oscillations during constant speed and load tests of the SeaStar when tested with the SEA did not reflect typical responses measured in service. For future work it is recommended that the resistance module inertia be reduced at minimum to that of outboard motors. The process of developing the model based on the responses measured with the SEA highlight the utility of the SEA and its ability to be used as a design tool. The ability to easily perform controlled testing procedures allows the overall response of the system to be examined without concern for the repeatability of the test, or variation of input as with manual testing procedures. The ability to approximate factors of leakage within the valve from the measured actuator output is a level of examination that one would not be able to perform without a controlled testing procedure. Chapter 5. Testing procedures for the performance assessment of steering systems 87 Chapter 5 Testing Procedures for the Performance Assessment of Steering Systems In Chapter 3, the concept of Hardware-In-Loop Simulations was introduced and defined as a system that incorporates "actual hardware into simulated surroundings to test functionality under a variety of conditions." The SEA provides a platform to perform such testing procedures; the input of the operator to the helm and disturbance load applied to the actuator can be controlled while measuring the system response with sensors, as demonstrated in the development of the SeaStar model in Chapter 4. The focus of this chapter is ensuring that the "simulated surroundings" of testing procedures performed with the SEA are representative of the service conditions for which the steering system designs are intended. An experimental program was carried out with a common steering system, outboard motor, and boat combination to establish typical service conditions. Analysis of the measured data provides a basis for establishing testing criteria for steering systems intended for use in similar conditions. Justification for setting bounds on the range of system inputs for simple single input frequency or static two input testing procedures (as performed with the SeaStar in Chapter 4) are derived from the measured conditions. The data also provides the basis for the effective simulations of real situations on the SEA. The simulation of real situations or usage-based testing procedures is proposed as the best means of implementing dynamic testing procedures that are appropriate to non-linear systems such as the SeaStar. It was shown that the Chapter 5. Testing procedures for the performance assessment of steering systems 88 overall system response to a single input frequency response varied with amplitude. In reality, steering systems are one input, one output non-linear systems with disturbance loads whose response will vary depending on the amplitudes, frequencies and phase difference of the helm and disturbance inputs. Rather than attempting to map all input combinations, a usage-based testing procedure that approximates the actuator disturbance load based on simplified tiller and boat dynamics is proposed in this chapter as a practical alternative. This will allow the performance of steering systems to be assessed in a quantifiable and repeatable way in a simulated environment representative of actual service conditions. 5.1. Testing Hardware In order to record quantitative measures of service conditions, a representative boat (bass boat), motor, and steering system (SeaStar) were fitted with sensors (Table 5.1) to record system inputs during typical manoeuvres. The hardware was provided by Teleflex Canada from the variety of components used in product development programs. The applications and limitations of the testing hardware are discussed to provide a basis for the understanding and interpretation of the collected test data. Chapter 5. Testing procedures for the performance assessment of steering systems 89 Function Item Manufacturer Range, Specification, Rating Qty Platform for testing Bass Boat Ranger Boats 21 ft 1 Steering for Boat SeaStar Steering System Teleflex Canada 0-1000 psi 1 Thrust for boat Outboard Motor Mercury "250 hp 1 Record Sensor Information DAQ Module SoMat eDAQ 16 A/D, 32 I/O, 10kHz 1 Helm Position Rotary Position Bl Technologies 0 - 2pi rad 1 Helm Torque Torque Wheel Customized Futek +/- 40 ft-lbf 1 Actuator Position SmartStick Teleflex Inc. AR4102 0 - 8 in 1 Actuator Load Pressure Sensotech FP2000 0 - 2000 psi 2 Boat Acceleration Piezo-based Accelerometer CrossBow 0-10 g 1 Boat Speed Boat Speed (Visual) Hummingbird - 1 Table 5.1 Boat testing hardware. The bass boat is among the most common applications of large outboard motors that use manual hydraulic steering systems such as the SeaStar. The 21-foot Ranger bass boat with a 225 hp Mercury motor, owned by Teleflex Canada (similar to the boat shown Figure 5.1), is estimated to represent seventy percent of boats that use SeaStar steering systems. The SeaStar is used in a variety of applications with system dynamics different than in bass boat applications that may require examination in future work. For the purpose of TROUSIL, D - Lead Customer Service Engineer, Marine Hydraulic Division of Teleflex Canada: Discussion Regarding Bass Boat Applications. Teleflex Canada, Richmond, BC. October 29, 2003. Chapter 5. Testing procedures for the performance assessment of steering systems 90 Figure 5.1 Ranger similar to test boat. Source: Ranger Boats. investigating a typical case, the availability, commonality, and demanding application of the Ranger bass boat is the reason it was chosen for testing. The SoMat data acquisition module was used to record the sensor outputs during testing procedures. It is a real-time microprocessor-based unit with hard-drive storage that can be controlled either with triggers or directly from a PC through an Ethernet connection. It is a hardened unit intended for heavy industrial and automotive data acquisition applications. The unit was configured to collect data from all of the sensors at 500 Hz and was triggered during testing with a laptop PC. To record operator inputs to the system, a rotary position sensor and a customized "torque wheel" were used. The position sensor is a rotary pot mounted on the face of the helm cover over the input shaft (Figure 5.2). The torque wheel is a Futek torque sensor fitted by Teleflex engineers into a customized steering wheel (also shown in Figure 5.2) to allow the torque applied to the helm shaft to be recorded. By measuring the position and torque applied to the helm, the operator input power can be calculated and the system analysed with position or torque as an input. Chapter 5. Testing procedures for the performance assessment of steering systems 91 Figure 5.2 Helm sensors. Photo by author. At the actuator (Figure 5.3), position was measured using a Teleflex SmartStick model AR4102. It is a non-contact linear position sensor with accuracy of +/-0.01 in and bandwidth of 100 Hz. It is manufactured by Teleflex Canada for use with the SeaStar steering system to provide autopilots with actuator position information. The sensor output of 0.5 V to 4.5 V can be recorded with the SoMat data acquisition system. In the test data, the actuator position is recorded between 0 and 8 inches, 4 inches indicating that the actuator and tiller are at the centre position. Chapter 5. Testing procedures for the performance assessment of steering systems 92 Figure 5.3 Actuator sensors. Photo by author. The port and starboard hose pressures were measured with two, 2000 psi strain gauge-based pressure transducers (Figure 5.3) to provide an indirect measure of the applied force to the tiller of the outboard motor. The use of pressure transducers is practical but not ideal in this application. Alternate approaches to measuring the tiller disturbance load were considered such as applying strain-gages the tiller or the pivot plate of the SeaStar actuator. However, the time and resources required to install and calibrate the strain gauges were not available prior to performing the boat testing procedures. Pressure transducers provide the means to approximate the disturbance load applied to the tiller. In reality, the fluid pressure force applied to the actuator is affected by the friction and binding of the actuator and the effect of actuator racking and tiller angle on system geometry, as described in Chapter 4. The analysis of the data takes system geometry effects into consideration but does not include the effect of racking due to the dependence of the racking behaviour on installation. Chapter 5. Testing procedures for the performance assessment of steering systems 93 5.2. Boat Testing Procedures Testing procedures needed to be selected with care to ensure that the manoeuvres performed were representative of typical service conditions. Three types of testing procedures were proposed to explore areas of interest.27 The first type of test was straight line testing procedures. Straight line tests were intended to provide information that would allow the examination of the behaviour of the mean applied disturbance load known as propeller torque. The second testing procedure proposed was the maximum load testing to provide peak loading information. This test relied on the operator of the boat to use his experience to navigate the boat in such a way as to generate the maximum system load at high speed. The third testing procedures proposed were buoy-testing procedures. Buoy-testing procedures were intended to provide information regarding the limits of the operator input and test boat manoeuvrability, and to examine the disturbance load characteristics for different dynamic conditions. The buoy-testing procedures are also used as the basis for the disturbance load characterisation in usage-based testing procedures. The following subsections describe the testing procedures in detail and include a discussion of the analysis of the measured data.28 5.2.1 Straight line testing Much of the time boating is spent travelling in a straight line across water towards a destination. For shallow hulled vessels such as bass boats, a load known as propeller torque is applied as a mean disturbance load to the system actuator. Propeller torque increases with speed and is the dominant disturbance load in bass Appendix D contains plots of data recorded for all boat testing procedures referred to in this chapter. 2 8 All tests were performed on smooth water with a qualified, experienced operator, and in a safe manner in compliance with local by-laws. Chapter 5. Testing procedures for the performance assessment of steering systems 94 boat applications. The primary purpose of the straight line testing was to observe the effect of propeller torque and to provide steady-state cases to compare to the loads measured in turning manoeuvres. Straight line test runs were performed at speeds of 5, 10, 20, 30, 40, 50, 60, 70, 80, and 90 mph. The mean applied load due to propeller torque is illustrated by the comparison the starboard and port hose pressures in Figure 5.4 and Figure 5.5. Pressure in the port hose is generated only when turning with the applied load to correct the boat heading.29 Below speeds of 30 mph, the net hose pressure increases with speed but not in a linear fashion (Figure 5.6). At speeds between 30 mph and 90 mph (speeds at which the test boat planed) the net pressure resulting from propeller torque varied linearly to a maximum net pressure of 160 psi. The port hose pressure is generated when turning with the applied load in order to open the spool valve and allow fluid from the starboard hose to return to the helm. Chapter 5. Testing procedures for the performance assessment of steering systems 95 Straight Line Test - 50mph Helm Position (rad) 1 0 1 5 2 0 2 5 3 0 3 5 4 0 - 2 3 0 0 2 0 0 1 0 0 0 3 0 0 2 0 0 1 0 0 0 1 0 0 Tiller Position (inch) 1 0 1 5 2 0 2 5 3 0 3 5 4 0 I I I I I Port Presure (psi) .. . / * v Boat Speed (mph) 1 5 2 0 2 5 Time (sec) 3 0 3 5 4 0 Figure 5.4 Measured properties, straight line test, 50 mph. Chapter 5. Testing procedures for the performance assessment of steering systems 96 Figure 5.5 Measured properties, straight line test, 80 mph. Chapter 5. Testing procedures for the performance assessment of steering systems 97 200 180 160 140 Net 120 Pressure (psi) 100 80 60 40 20 0 10 90 100 Boat Speed(mph) Figure 5.6 Net pressure varying with boat speed. 5.2.2 Maximum load testing Maximum load testing was not a formalized testing procedure but an attempt to determine the conditions under which maximum actuator disturbance loads might occur. The testing procedure relied on the experience of the operator to perform manoeuvres that would generate the highest loads possible with the test boat. The maximum pressure measured was greater than 500 psi on hard turns at approximately 75 mph (Figure 5.7). The maximum speed of the turn is less than Chapter 5. Testing procedures for the performance assessment of steering systems 98 the straight line maximum speed because the boat slows during turning. Pressures higher than 1000 psi have been measured by engineers at Teleflex in other testing conditions and in other boat, steering system, and motor configurations. Hard Turns - 75mph Tiller Position (inch) 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 Port Presure (psi) 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 8 0 1 0 0 Time (sec) 1 8 0 Figure 5.7 Measured properties, maximum load test data. Chapter 5. Testing procedures for the performance assessment of steering systems 99 5.2.3 Buoy tests Buoy tests involve piloting the boat through a set of buoys at different boat speeds and buoy spacing (25, 33, 50, 100, 200 m). Initially, the buoy spacing was set at 200 m and navigated at 10 mph increments from 30 mph until the maximum boat speed was reached. The remaining buoy spacing test sets were incremented at 10 mph until the operator could no longer navigate the course. An examination of the measured data (Figure 5.8 and Figure 5.9) provides insight into the dynamics of the actuator disturbance load. From the data, it is clear that for all manoeuvres the actuator loading is asymmetrical and dominated by the mean load witnessed in the straight line tests. During buoy testing the pressure in the starboard hose ranged between 0 and 300 psi while the port hose pressure did not exceed 100 psi. Again, like straight line testing, it is clear that the port hose pressure is generated only to open the spool check valve and allow fluid to return to the helm from the starboard hose. Chapter 5. Testing procedures for the performance assessment of steering systems 100 10 5 0 i 10 5 0 i 300 200 100 0 300 200 100 0 100 50 0 Buoy Test - 100m spacing, 40 mph Helm Position (rad) 10 20 30 40 50 60 I I I I Tiller Position (inch) I I I I 10 20 30 40 50 60 I I I I Port Presure (psi) t *a lA^.r^-n i 1 . _ _r 10 20 30 40 50 60 Starboard Pressure (psi) 10 20 30 40 50 60 Boat Speed (mph) 10 20 30 Time (sec) 40 50 Figure 5.8 Buoy testing, 100 m spacing, 40 mph. Chapter 5. Testing procedures for the performance assessment of steering systems 101 1 0 0 1 0 0 3 0 0 2 0 0 1 0 0 Buoy Test - 33m Spacing, 50mph Helm Position (rad) Li 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 Tiller Position (inch) M 1 0 1 5 2 0 2 5 3 0 35 4 0 4 5 5 0 I I I I I I I I 1 • -— Port Presure (psi) H^MJ^^^ 1 0 0 5 0 Starboard Pressure (psi) W W I I I I I I I I • — Boat Speed (mph) I I I II I I I I I Figure 5.9 1 0 1 5 2 0 2 5 3 0 Time (sec) Buoy testing, 33 m spacing, 50 mph. 3 5 4 0 4 5 5 0 During buoy testing, the operator input of magnitude large enough to affect the course of the boat did not exceed 1 Hz; the highest fundamental frequency of buoy test navigated successfully was 0.667 Hz (Table 5.2). At witnessed boat speeds, it is unlikely that the operator would perform higher frequency manoeuvres for fear of compromising boat safety and the power limitations of the operator. The effect of high frequency, small amplitude inputs was not considered during the boat testing and may require further exploration in future work, particularly the examination of emergency manoeuvres. It may be Chapter 5. Testing procedures for the performance assessment of steering systems 102 that for boats with large time constants, i.e. large vessels, the small motions may be lost in the low bandwidth response of the boat, and for small boats, the high-frequency motions could present a safety hazard. 200m 100m 50m 33m 25m 30mph 0.067 0.134 0.268 0.406 0.536 40mph 0.089 0.179 0.358 0.542 50mph 0.112 0.224 0.447 0.677 60mph 0.134 0.268 70mph 0.156 0.313 80mph 0.179 90mph 0.2 Table 5.2 Buoy test fundamental frequencies (Hz) Table 5.3 and Table 5.4 summarize the torque and power input to the system by the operator during the buoy testing procedures. The peak torque applied in each direction to the wheel during navigation was at high speeds and 200 m buoy spacing at 191 in-lbf and -58 in-lbf. The occurrence of the peak input torques at the largest buoy spacing is related to the dominance of the propeller torque in the boat steering dynamics; both were measured at speeds greater than could be navigated at shorter buoy spacing. The power required to perform the buoy test runs were correlated to the fundamental frequency of motion. The largest average and peak power input to the helm calculated from testing procedure data was 41 W and 590 W at the highest and second highest fundamental frequencies. Chapter 5. Testing procedures for the performance assessment of steering systems 103 200m 100m 50m 33m 25m 30mph 125, -29 86,-18 74,-17 80,-28 133, -45 40mph 102, -24 147,-115 172,-35 128,-46 50mph 103, -46 83, -14 100,-38 123,-52 60mph 120, -20 118, -21 70mph 121,-58 148, -21 80mph 109, -25 90mph 191,-54 Table 5.3 Buoy tests, maximum operator input torque (in-lbf) 200m 100m 50m 33m 25m 30mph 5.7, 400 4.5, 93 2.9,99 6.0,188 40, 588 40mph 7.3, 355 8.2, 168 22,452 35,590 50mph 4.6, 221 4.0, 75 3.5,378 41,571 60mph 4.0,350 i 10,206 70mph 4.0, 108 11.5, 329 80mph 4.8. 120 90mph 12, 156 Table 5.4 Buoy test average and maximum operator power (W) The power calculations from the buoy testing procedures performed provide insight into the power transmitted by a steering system in this specific application. The calculated peak operator power provides a limit on the expected power transmitted between the operator and the tiller of the boat at a given moment. The average power values are not indicative of typical conditions but of an average maximum power transmitted during a series of manoeuvres. The power calculations do not directly provide designers with useful design criteria Chapter 5. Testing procedures for the performance assessment of steering systems 104 for manual systems because power is the product of two variables for which the relationship is unknown. It may be that at different wheel speed or wheel torque inputs the peak and maximum average operator input could significantly vary. The power data is most useful in the design of testing procedures and the analysis of performance test data, and the specification of design requirements of powered steering systems. Any testing procedure that requires more than the maximum peak or average calculated power input to the helm from buoy testing procedures can be viewed as being outside the expected operating conditions and less emphasis may be placed on the system performance at that condition. In the design of powered steering systems, 41 W and 590 W can be viewed as minimum average and peak power requirements of the system actuator if it is to reliably perform the same manoeuvres as performed in this series of boat testing. As a consequence of powering the system actuator, the power requirements may increase because the operator input power is no longer a limiting factor. Testing will be required of the powered systems to see what the power requirements would be in this application with a powered system, but the manual power data provides a baseline design requirement from which to start. 5.2.4 Testing procedure recommendations based on collected service information From the data collected during boat testing procedures it is reasonable to propose limitations on steering system inputs during testing procedures performed with the SEA. These recommendations apply to system inputs of all types of steering systems and those specific to manual systems. Testing procedures for systems intended for similar applications should meet the following criteria: Chapter 5. Testing procedures for the performance assessment of steering systems 105 For manual steering systems: • Input fundamental frequencies be less than 1 Hz • Disturbance load applied in one direction and not exceed 500lbf For manual and powered steering systems: • Average helm input power be less than 100 W • Peak helm input power be less than 1000 W • Peak helm input torque be less than +/-250 in*lbf. 5.3. Usage-Based Testing Procedures Testing procedures such as the modified frequency response and constant speed and load testing procedures described in Chapter 4 provide good measures of system performance and the data required to develop system models. The testing procedure limitations proposed in the previous section provide a basis for the planning of one input or simple two input testing procedures. In combination with background regarding normal steering system performance in the field, experienced designers can interpret the data in the optimization of manual steering system designs. Usage-based testing procedures are proposed here as a practical means to assess the performance of non-linear manual systems in conditions that limit the required interpretation of test data and to provide a means of more easily optimizing the designs of advanced steering systems. Usage-based testing allows systems to be tested in simulations on the SEA that represent the environment for which the designs are intended. The cost of actual boat testing in the development of a steering system can be reduced while making the design specifications and optimization goals more intuitive. Simulation of field conditions also allows for repeatable testing procedures when examining the response of different designs to specific conditions or manoeuvres. Chapter 5. Testing procedures for the performance assessment of steering systems 106 In the development of advanced steering systems, the utility of usage-based testing procedures is most applicable to testing the performance and stability of control strategies or algorithms. Advanced steering systems can be optimized for performance or power consumption goals. By testing the complete system in an environment that simulates the service conditions, system optimizations can be tested and tuned to obtain a level of optimization not possible with simple static input testing procedures. It would be possible to test steering systems in a method similar to the modified frequency response test in Chapter 4 that is extended to suit a one input system with applied disturbance loads. The number of variables that would be required to fully describe the performance of the system to a two input modified frequency response would sharply increase. In addition to testing the varied frequencies and amplitude input to the system helm, the disturbance load frequencies and amplitudes would be varied independently with different phases to the system input. The results from these testing procedures would need to be analysed and interpreted for the intended application. With a usage-based testing procedure, the dynamic response of a system is representative of the application, requiring fewer testing procedures and making the interpretation of the results more directly applicable and intuitive. 5.3.1 Disturbance load model for usage-based testing procedures The most significant challenge in the implementation of usage-based testing procedures is the determination of a suitable model of actuator disturbance loads. The disturbance loads are not a function of a single independent variable, i.e. time, but the non-linear dynamic interactions of the boat, steering system, and outboard motor subsystems. This section examines the simplified dynamics of a boat with an outboard motor with the aim of deriving a simple empirical model Chapter 5. Testing procedures for the performance assessment of steering systems 107 that adequately describes the disturbance load applied to a steering system based on the recorded factors during boat testing. The primary function of the steering system actuator is to control the relative angle between the centreline of the boat and the centreline of the outboard motor. The disturbance loads applied to the actuator are the function of two types of loads: inertial and fluid. Inertial loads are applied to the steering system in the simple case of rotational acceleration of the outboard motor (Figure 5.10). The inertial loading of the system is complicated by the addition of significant yaw accelerations of the boat (Figure 5.11) where the actuator is required to transmit a component of the force required to accelerate the outboard motor laterally. (The loading is due to the offset of the motor pivot point from the centre of gravity). Further complicating the inertial loads of the system are the effect of roll and pitch on the component of gravitational forces applied to the outboard motor and transmitted to the actuator. Chapter 5. Testing procedures for the performance assessment of steering systems 108 Pivot Axis of Motor Offset Motor Centre of Gravity Figure 5.10 CAD model demonstrating offset centre of gravity. Chapter 5. Testing procedures for the performance assessment of steering systems 109 The second type of load applied to the system is due to fluid interaction. Figure 5.12 illustrates the forces acting on the outboard motor and boat. The forces include lift and drag on the boat hull and leg of outboard, and thrust from the propeller. The vector directions of the forces and moments generated depend on the dynamics of the boat and motor and water conditions. The substantial yaw rates of the test boat significantly affect the angle between the various surfaces and the water flow vector (Figure 5.13) by introducing a horizontal component to the boat velocity at the rear of the boat. The interaction of the yawing of the boat and the angle of the tiller make the prediction of steering loads due to fluid interaction based on the static angle between the rudder and the centerline of the boat (as one would for simple airfoils) inappropriate. Figure 5.11 Illustration of inertial loads applied to steering system. Figure 5.13 Yaw rate effect on angle between water vector and tiller position. Chapter 5. Testing procedures for the performance assessment of steering systems 111 5.3.2 Empirical model of steering loads Upon an initial examination of the test data and faced with the real-world complexity of the system, it was decided to attempt to fit an empirical model to the boat data rather than try to build a comprehensive analytical model. An analytical model of this system is beyond the scope of this work and would be a suitable topic for a larger scale investigation than is presented in this thesis. Calculated actuator disturbance forces from the boat data were fit to linear coefficients of boat speed, boat acceleration, tiller position, tiller velocity, and tiller acceleration (Equation 5.1). The actuator disturbance force was calculated from the net cylinder pressure, piston area, and tiller position (to compensate for the actuator geometric effects discussed in Chapter 4). The coefficients of the five factors were calculated for each run using a least squares fit algorithm (Table 5.5). The Root-Mean-Squared-Error (RMSE) of the disturbance loads calculated from the linear coefficients are generally reasonable given the complicated system dynamics. - Pressure Net(t) := k j • v Boat(t) + k 2 • a Boat(t) + k 3 • e TiUei(t) + k 4 • to Ti]let(t) + k 5 • a. Tmei(t) (5.1) Chapter 5. Testing procedures for the performance assessment of steering systems 112 Speed (mph) Buoy Spacing K1 K2 K3 K4 K5 RMSE 30 200 7.2 -47.3 -122 -1214 -107 32 100 2.3 -16 -147 -510 -59 17 50 2.4 . 30 47 -530 -65 21 33 1.9 27.6 73 -296 -51 24 40 200 4 72 410 -310 -3.4 73 100 2.5 -17 -160 -426 -62 22 50 3.0 -32 -144 -180 -52 19 33 4.1 9.74 -60 -160 -33 40 50 200 0.7 22 73 -22 0.2 33 100 1.6 0.64 64 -567 -48 16 50 2.2 1.4 -124 -212 -42 30 33 2.2 9.7 -60 -160 -33 26 60 200 1.7 16.8 -42 -237 -49 37 100 2.5 91 11.8 -481 -74 30 70 200 2.2 3.8 -66 -300 -102 39 100 2.6 55.2 -128 -360 -72 45 80 200 1.6 -17 35 -281 -25 33 90 200 1.9 -37 -450 -702 -122 51 Table 5.5 Linear coefficients and RMSE of calculated vs measured net cylinder pressures. To create a generalized model of the disturbance load, the mean of the coefficients was calculated (Table 5.6). Figure 5.14 demonstrates the effect of the averaged coefficients on the accuracy of the calculated pressure. For the specific test run in Figure 5.14, both average and test specific coefficients create load with similar phase. The magnitude of the error with the average coefficients is much Chapter 5. Testing procedures for the performance assessment of steering systems 113 larger than with the test-specific coefficients. Table 5.7 compares the R M S E for each test run using average and test specific coefficients.30 k1 k2 k3 k4 k5 Mean 2.9 -1.4 -44 -385 -56 Standard Deviation 2.0 40 168 270 32 Table 5.6 Mean and standard deviation of factors applied measured parameters. Buoy Test - 33m Spacing, 50mph 4001 i —r— 1 1 50 Figure 5.14 Net measured pressure and net calculated pressures. Appendix E contains plots comparing calculated and measured test specific and average coefficients. Chapter 5. Testing procedures for the performance assessment of steering systems 114 200m 100m 50m 33m 25m 30mph 32, 75 17,30 21,26 24, 31 133, -45 40mph 73, 121 22, 30 19, 53 40, 77 50mph 33, 150 16, 73 30, 52 26, 61 60mph 37, 46 30, 59 70mph a 39, 45 45, 59 80mph 33, 108 3 90mph 51, 106 Table 5.7 Test-specific and average coefficients net pressure RMSE (psi). 5.3.3 Implementation of usage-based tests on S E A Two versions of the usage-based testing procedures can be implemented on the SEA. The first is to emulate each buoy test run or similarly collected test run individually. Each test will use the least square fit coefficients for the specific test run, assuming that boat speed and acceleration are not affected by the response of the steering system. The second version of the usage based testing procedure is to set the boat speed, acceleration, and helm input arbitrarily with the disturbance load calculated from the average coefficients. The helm input can be a reproduction of a manually driven helm input at the test bench or programmed arbitrarily. The disturbance load will be calculated from the average coefficients and system response variables. 5.3.4 Limitation of empirical model It is important to note a limitation of the data collected during the tests described in this section. The boat tests were performed with a low-bandwidth steering system. In order to extend the usage based tests to suffer systems, more boat Chapter 5. Testing procedures for the performance assessment of steering systems 115 testing will be required with a higher bandwidth system. In addition, although the boat and motor combination is representative of a typical installation of hydraulic steering systems, it is important to note that the data recorded with this combination applies only to boats of similar configuration. It is known that the disturbance load dynamics vary with boat type. In order to understand the full range of service conditions, even though the test boat is a representative case, more tests with different boat and motor configurations will need to be performed. The effect of high frequency, small amplitude inputs was not considered during the boat testing and may require further exploration in future work, particularly the examination of emergency manoeuvres. 5.4. Summary This chapter presented a test case for the implementation of usage-based tests that correspond to conditions measured with a representative boat and motor combination. The testing procedures demonstrated the service characteristics of the operator input limitations and the disturbance load. The operator and disturbance load characteristics provide a good basis to estimate the importance of the range of static and frequency testing procedures. By focusing on the witnessed ranges of system inputs, steering systems can be more easily tuned to optimize performance in service conditions. In addition to examining the general system inputs, the measured disturbance load was fit with coefficients to allow the implementation of usage-based testing procedures. The disturbance load can now be estimated as a function of boat speed and acceleration and the response of the system actuator. The function for disturbance load allows steering systems to be tested on the System Evaluation Apparatus in conditions that correlate to service conditions in addition to standard static and dynamic testing procedures. Chapter 5. Testing procedures for the performance assessment of steering systems 116 The advantages of testing systems in repeatable service-like conditions are that the testing conditions are matched to service conditions, limiting the range of dynamic testing procedures required to capture the important aspects of a system's performance. Additionally, the usage-based testing procedures based on the data collected allow steering systems to be tested in conditions that are most important to the end-user of the product - as the customer would assess the performance of the steering system in service. Chapter 6. Conclusions and recommendations for future work 117 Chapter 6 Conclusions and Recommendations for Future Work 6.1. Conclusions In order to facilitate the development of advanced steering systems for use with outboard motor driven pleasure craft, testing procedures and hardware to assess the performance and safety of such systems are required. Because many steering system components exhibit non-linear behaviour, the incorporation of components in a Hardware-In-Loop configuration allows systems to be tested with all component interactions included. Realistic inputs to the system that correlate to service conditions during testing procedures permit the system to be optimized for use in service or compensate for system non-linearities. The tools and basis of testing procedures presented in this thesis provide the means to realize the requirements for developing advanced steering systems. The System Evaluation Apparatus can perform automated, repeatable, dynamic testing procedures in a Hardware-In-Loop Simulation configuration. The SEA allows the response of steering systems to designer specified physical inputs to be evaluated or component parameter values to be determined. The development of the model of the SeaStar steering system in Chapter 4 is an example of this aspect of the utility of the SEA. The response of variations of a single design or competing systems to the same dynamic inputs can be compared for the determination of the effect of specific system parameters or benchmarking purposes. To further assist in the development of advanced steering systems, the Chapter 6. Conclusions and recommendations for future work 118 SEA can be programmed to interact with steering systems through digital I/O to emulate system components or system states. To provide a basis for developing testing procedures to test steering systems in conditions that correlate to service conditions, boat testing was performed with helm and disturbance inputs recorded. The boat and motor configuration represents a majority of outboard motor applications and provides the basis for reasonable limitations to be placed on system inputs during testing procedures. Data collected from boat testing indicated that testing procedures with the SEA should focus on testing conditions where: • the fundamental frequency of motion is less than 1 Hz • average and peak helm input power is less than 100 W and 1000 W respectively • disturbance load is applied in one direction and does not exceed 500 Ibf • peak helm input torque magnitude is less than 250 in*lbf To provide testing procedures that emulate service conditions, usage-based testing procedures are proposed. The disturbance load relationship used in usage-based testing procedures is based on a function that relates boat speed and acceleration, tiller position, tiller speed, and tiller acceleration to disturbance load. The coefficients of the parameters in the disturbance load function are based on the disturbance data collected during boat testing. By performing usage-based testing procedures, the inputs to the steering system are realistic representations of service conditions. Performance measures based on the testing procedures are more intuitive and control algorithms can be more easily optimised for power consumption or performance goals with usage-based testing procedures performed with the SEA. Further, by having testing procedures that emulate service conditions, the time and money required to perform boat testing procedures can be reduced. Chapter 6. Conclusions and recommendations for future work 119 Other contributions of this work include the modified frequency response testing procedure and the information derived from the analysis of the SeaStar steering system in Chapter 4. The modified frequency response testing procedure is a novel method of presenting the response of non-linear systems to amplitude and frequency changes. By plotting the gain against frequency and amplitude, a surface of linearity is formed that allows the overall response of a system to be more easily visualised than if multiple Bode plots that corresponded to different amplitudes were presented. ^ The SeaStar model provides an understanding of the function and complexities of various system components. It reproduces in simulation the measured response of the SeaStar steering system when tested with the SEA. The development of the model demonstrates the utility of the SEA as a tool to investigate system parameters. Additional benefits of the SeaStar model can be realised if the basic model is applied to an analysis of similar systems or variations of the SeaStar Steering System. By using the simulation model to assess the effect of changing major system parameters prior to building and testing prototypes, substantial time and cost savings can be realised. 6 . 2 . Recommendations for Future Work The System Evaluation Apparatus is intended for long-term use as a research and development tool. The control and data acquisition hardware used, though providing much flexibility for performing testing procedures, should be replaced with more modern hardware that is expected to be supported longer than the STD architecture. Another prominent issue with the SEA is the large reflected inertia of the resistance motor. A lower inertia motor with comparable performance should replace the existing motor, or an inertia compensation routine developed. Another option that could be pursued is the implementation of a force control loop to avoid the problems of the large reflected inertia. Chapter 6. Conclusions and recommendations for future work 120 If the system model of the SeaStar is to be used for development of variations of the SeaStar or similar products, a statistically significant number of systems should be tested to determine the generalised effects of system leakage and actuator non-linearities. A more in-depth study of the fluid dynamic effects on system leakage for different manufacturing tolerances would be valuable in the development of manual hydraulic steering systems. To provide more comprehensive usage-based testing procedures, more boat and motor, steering system, operator, and operating condition combinations should be tested to examine the full range of system inputs in service. The system tested is representative of a significant portion of outboard motor applications but other applications, specifically, less shallow hulled vessels than bass boats, are known to have significantly different loading characteristics. This may be of less utility for developing and evaluating manual hydraulic systems, but is important if the usage-based testing procedures are to be used to optimize control strategies for advanced steering systems. An additional important note is that the usage-based testing procedures should take into account the stiffness of the steering system. Like the suspension of an automobile, the stiffness of the steering system actuator will affect the dynamics of the disturbance response. Boat testing procedures with steering systems of varying stiffness should be performed to assess the effect of system stiffness on the disturbance load characteristics expected in service. Bibliography 121 Bibliography BERTOLLINI, G. & H O G A N , R: Applying Driving Simulation to Quantify Steering Effort as a Function of Vehicle Speed. SAE Technical Paper Series, 1999-01-0394. BOUVIER, M : Definition of a Cost-Effective, Fault-Tolerant Control Architecture: Application to the design of a Steer-by-Wire System. MASc Thesis, University of British Columbia, 2002. BROWNING, DR A: A mathematical model to simulate small boat behaviour. SIMULATION 56:5, 257-264 (1991). CHO, J .M.; H W A N G , D.H.; L E E , K.C. ; JEON, J.W.; P A R K , D.Y.; K I M , Y.J . ; JOH, J.S.. Design and Implementation of HILS System for ABS E C U of Commercial Vehicles. IEEE Proceedings 0-7803-7090-2/01. 2001. D U D R A , B - Chief Engineer, Marine Hydraulic Division of Teleflex Canada: Discussion Regarding Stiffness and Damping of SeaStar Hoses. Teleflex Canada, Richmond, BC. October 30, 2003. FERREIRA, J.A.; OLTVEIRA, J.E.; COSTA, V . A . ; Modeling of Hydraulic Systems for Hardware-In-The-Loop Simulation: A Methodology Proposal. Proceedings of International Mechanical Engineering Congress and Exposition, Nashville, USA, Vol 6 p.33. 1999. K A R P E N K O , M ; SEPEHRI, N : Fault-tolerant Control of a Servohydraulic Positioning System with Crossport Leakage. IEEE Transactions of Control Systems Technology, Vol 13, No. 1, January 2005. Bibliography 122 K A R P E N K O , M ; SEPEHRI, N : Robust Position Control of an Electrohydraulic Actuator with a Faulty Actuator Piston Seal. IEEE Transactions of Control Systems Technology, Vol 13, No. 1, January 2005. L E E , S.J.; KJJVI, Y.S.; CHO, J.H.; L E E , W.S.; KTM, J.H.: ABS Hardware-In-The-Loop Simulation on a Driving Simulator. Presentation from Department of Automotive Engineering Kookmin University. Seoul, Korea. Published on the internet 1998. http://vc.kookmin.ac.kr/publication/1998/Presentation/abshils.pdf [accessed on January 14, 2004]. SHBvlIZU, Y . ; K A W A I , T.; Y U Z U R I H A , J: Improvement in Driver-Vehicle System Performance by Varying Steering Gain with Vehicle Speed and Steering Angle: VGS (Variable Gear-Ratio Steering System). SAE Technical Paper Series, 1999-01-0395. TAJDVIA, J.; Y U H A R A , N ; SANO,S; TAKTMOTO, S: Effects of Steering System Characteristics on Control Performance from the Viewpoint of Steer-by-Wire System Design: SAE Technical Paper Series, 1999-01-0821. TROUSIL, D - Lead Customer Service Engineer, Marine Hydraulic Division of Teleflex Canada: Discussion Regarding Bass Boat Applications. Teleflex Canada, Richmond, B C . October 29, 2003. V O L D , H ; HERLUFSEN, H ; MAINS, M ; CORWIN-RENNER, D: Multi-Axle Order Tracking wit the Vold-Kalman Tracking Filter. Void Solutions, Cincinatti Ohio. 2000. Void Solutions: Multi-Axle Order Tracking wit the Vold-Kalman Tracking Filter. White Paper Published by Void Solutions, Cincinatti Ohio. 2002. Bibliography 123 X-By-Wire team: X-by-Wire, Safety Related Fault Tolerant Systems in Vehicles, Final Report. Published on the internet, 1998. http://www.vmars.tuwien.ac.at/projects/xbywire/docs/final.doc [accessed on September 12, 2002]. Y E H , Y . C : Design Considerations in Boeing 777 Fly-By-Wire Computers. In Proceedings of the Third IEEE International High-Assurance Systems Engineering Symposium, 64-72 (1998). 124 Appendix A SEA Fabricated Component Drawings and Calculations 5 . 0 0 4 . 0 0 50 50 5 . 0 0 6 . 0 0 I . 6 3 1 .31 I . 0 0 2 . 0 0 I . 3 1 . 9 1 3 . 0 0 0 . 3 1 x7 3 . 0 0 0 . 3 7 5 NOTES: M A T E R I A L : ALUMINUM 25 6 . 0 0 + !_nfr 2 . 3 8 . 2 5 H E L M M O U N T DRAWN B Y : CBM S C A L E 1 : 4 S Y S T E M E V A L U A T I O N A P P A R A T U S DRAWN ON 2 4 J U L 0 2 1 1 RI . 6 7 0 0 . 3 1 2 5 - 4 HOLES 0 2 . 8 0 50 4 . 0 0 <h 2 . 5 0 2 . 5 0 -i 3 . 0 0 _ J _ 0 . 3 7 5 DRAWN B Y : C B M DRAWN O N : 2 4 J U L 0 2 NOTES: M A T E R I A L : ALUMINUM 2 5 6 . 0 0 \ ~ - 5 . 0 0 ' - * | 2 5 HELM MOUNT M O D I F I C A T I O N S S C A L E I : 2 S Y S T E M E V A L U A T I O N A P P A R A T U S A V. S O T U B I N G ( 2 2 i n L O N G - 5 P I E C E S ) ALL mm INSIDE 1 / 2 " U N F NUT W E L D E D I N P L A C E ( 4 ) N O T F S : 1/ M A T E R I A L : S T E E L . 2 / ' B R E A K A L L S H A R P E D G E S . 0 1 . 3 / P A R T I S T O B E C L E A N W I T H NO R A G S , L O O S E B U R R S , C O N T A M I N A N T S OR C O R R O S I O N . CBM 06 06 01 S E A M O U N T A S S E M B L Y ± . 0 3 0 ' ± . o i o -± . 0 0 5 " t / s r ±3* S Y S T E M E V A L U A T I O N A P P A R A T U S B A S E . F R A M E 7 1 : 4 7 . 0 0 6 . 5 0 .38 x4-1 5 . 0 -H 1 2 . 0 -.38-r— 5 . 0 — + - 5 . 0 0 -H • 4 . 0 0 . 2 5 -1 . 5 0 -2 0 . 0 1 7 . 0 DRAWN B Y : C B M DRAWN O N : 3 0 J U L 0 2 HELM MOUNT PLATE |SCALE I : 4 | SYSTEM EVALU>TIO» >PP»»ATUS| bo Oo 6mm - I T H R E A D YAMAHA FROMT MQUMT BOSS 121 0 1 . 5 0 -I— 1 . 4 0 0 I L 1 . 2 6 CBM 0$ 06 01 Y A M A H A & MERC M O U N T I N G C O M P O N E N T S ± . 0 3 0 * ± . 0 1 0 * ± . 0 0 5 " 1/64" ± 3 " S Y S T E M E V A L U A T I O N A P P A R A T U S M O U N T - T U B E 1 : 2 1 6 3 . 0 -—- 2 . 0 0 — 0 • • 2 . 0 0 * -. 7 7 7 ( t J 1 2 . 3 7 5 I'-\ ) k - - -(• - 0 . 3 7 5 MERCURY PL»TE 111 YAMAHA PLATE IH N O T F S 1/ M A T E R I A L : S T E E L . 21 B R E A K A L L S H A R P E D G E S . 0 1 . 3 / P A R T I S TO B E C L E A N W I T H N O R A G S , L O O S E B U R R S , C O N T A M I N A N T S OR C O R R O S I O N . 1 0 . 0 0 MOUMT TUBE 121 CBM 06 06 01 Y A M A H A I MERC M O U N T I N G C O M P O N E N T S ± . 0 3 0 " ± . 0 1 0 " ± . 0 0 5 " 1/64" ± 3 " S Y S T E M E V A L U A T I O N A P P A R A T U S ME F C U R T . M O U N T I N G . P L J E 1 : 2 r~ 3 . 0 2 . 5 1 . 0 5 1 . 5 0 -3 . 0 0 -0 2 . 0 3 . 1 5 0 . 7 9 -H N O T F S : 1/ M A T E R I A L : S T E E L . . 2 / B R E A K A L L S H A R P E D G E S . 0 1 . 3 / P A R T I S T O B E C L E A N W I T H NO R A G S , L O O S E B U R R S , C O N T A M I N A N T S OR C O R R O S I O N . I . 181 r . 5 9 1 _ J _ r r I 4 * i CBM . 08 OS 01 S E A T I L L E R ±.O30" ± . O I 0 " ± . 0 0 5 " l / H ' ±3" T I T L E L I N E TWO T I L L E R 9 3 / 1 : 4 0 . 3 7 5 UNC > 4 -0 . 5 0 x 4 -h » 4 . 0 3 H - 7 . 2 5 -- 8 . 0 0 -1 0 . 0 0 -N O T F S : - 0 2 . 0 0 - 0 . 6 3 i 4 6 . 0 0 4 . 5 0 . 3 8 -2 . 0 0 -. 5 0 -1/ M A T E R I A L : M I L D S T E E L . 2 / B R E A K A L L S H A R P E D G E S . 0 1 . 3 / P A R T I S T O B E C L E A N W I T H NO R A G S , L O O S E B U R R S , C O N T A M I N A N T S OR C O R R O S I O N . • 0 0 1 2 . 0 0 CBM 07 06 01 T I L L E R M O U N T F R A M E ± . 0 3 0 " ± . 0 1 0 " ± . 0 0 5 -± 3 * S Y S T E M E V A L U A T I O N A P P A R A T U S P L A T E 6y 1 : 4 N O T F S 1/ M A T E R I A L : S T E E L 21 B R E A K A L L S H A R P E D G E S . 0 1 . 3 / P A R T I S T O B E . C L E A N W I T H NO R A G S , L O O S E B U R R S , C O N T A M I N A N T S OR C O R R O S I O N . UNITS: mm 0 R 8 CBM 03 05 01 P I V O T T O P ± . 0 3 0 -± . o i o -± . 0 0 5 " l / S I * ±3" S Y S T E M E V A L U A T I O N A P P A R A T U S P I V O T . T O P 1 : 1 N O T F S 0 2 9 . 4 0 2 8 0 2 2 23 1/ M A T E R I A L : S T E E L 2 / B R E A K A L L S H A R P E D G E S . 0 1 . 3 / P A R T I S T O B E C L E A N W I T H NO R A G S , B U R R S , C O N T A M I N A N T S OR C O R R O S I O N . S E C T I O N X-X CSH 03 05 01 P I V O T B O T T O M ± . 0 3 0 " ± . 0 1 0 ' ± . 0 0 5 " 1/64" ± 3 " S Y S T E M E V A L U A T I O N A P P A R A T U S P I V O T . B O T T O M 1 : 1 * * * Disturbance Load Position Error (count) Speed Error (rad/sec) Reference Input (z-1) ) * z(z-0.5) Hold Motor Position k encoder T 02.90 N O T E S : M A T E R I A L : ALUMINUM ANY Q U E S T I O N S OR COMMENTS P L E A S E CONTACT C H R I S MYTTING @ UBC 6 0 4 8 2 2 4 8 5 0 OR GRAEME DEMPSTER O L D C O M P O N E N T I N C L U D E D FOR R E F E R E N C E DRAWN B Y : C B M DRAWN O N : 2 4 J U L 0 2 MONOCARRIER MOUNT 2 S C A L E I : 3 S Y S T E M E V A L U A T I O N A P P A R A T U S A 0 2 . 5 0 0 . 2 5 R I . 0 0 NOTES: M A T E R I A L : ALUMINUM ANY Q U E S T I O N S OR COMMENTS P L E A S E CONTACT C H R I S MYTTING 0 UBC 6 0 4 8 2 2 4 8 5 0 25 r - . 2 5 0 I . 5 0 0 . 2 5 SET SCREW HELM REDUCER C O U P L I N G DRAWN B Y : CBM S C A L E 1:1 S Y S T E M E V A L U A T I O N A P P A R A T U S A DRAWN O N : 3 0 J U L 0 2 1 1 N O T F S : 1/ M A T E R I A L : S m a t e r i a l . 2 / B R E A K A L L S H A R P E D G E S . 0 1 . 3 / P A R T I S T O B E C L E A N W I T H NO R A G S . B U R R S , C O N T A M I N A N T S OR C O R R O S I O N . MERCURY MDUMT — 2 . 4 1 t > < < i '.j YAMAHA MOUNT CBM 06 06 01 Y A M A H A & M E R C M O U N T A S S Y ± . 0 3 0 " ± . 0 1 0 " ± .005* i / s r ±3" S Y S T E M E V A L U A T I O N A P P A R A T U S M E R C U R Y . M O U N T 1 : 2 Inertia Calculations and Notes: Chris Mytting November 4,2003 This document contains the calculations for estimating the inertia reflected to the system actuator from the SEA resistance unit and a representative outboard motor. Physical Quantities: ozf —Ibf 16 Jtillerunit 1 1 6 9 l b ™ Jtillerunit 0-342 kg m2 unit conversion From Pro-Engineer model ... in SI units blocksliderpivot 1.5kg From Manufacturer .30in ozf sec J r o t o r 1.562 10 'slug rV Jrotor 2 1 1 8 1 0 ^ g ™ 2 Jballscrew 0 6 1 2 10 kg m From Manufacturer (C40-400) http://magmotor.com/LO_Motors_C40.pdf ... in SI units From Manufacturer ballscrew 8.667 10 3 in ozf sec' ... in imperial units Ratio of Rotor and Ballscrew inertia: rotor ballscrew 34.615 Physically reasonable ratio given the size of the motor •'comb "'rotor •'ballscrew Ballscrew and Motor Rotor Inertia Jcomb 2 - 1 8 1 0 3 k « m 2 141 Equations of Motion: The remaining components are connected by equations of motion as below: x [(t) 1 — t 4in Position of cylinder as function of time starting at hard-over (8 inch complete stroke). dt Speed of cylinder *cyl*') Tiller angle as a function of time 8 inch tiller arm „ller» g i n tiller*') ^ tiller*') Tiller angular speed as a function of time xblockunitM H.5inatan tjUer(t) Ballnut inear position as a function of time (cylinder position) 11.5 inch from tiller pivot to ballscrew CL vblockunit*') f*bloctanitW Ballnut linear speed as a function of time dt ballscrew*') "blockunitW ~ — ~ Linear to angular position relationship between ballnut and 10mm ballscrew ballscrew*'} 7 ballscrew*') Ballscrew and rotor speed as a function of time dt 1 2 2 Tcomp**) mblocksliderpivot vblockunit*') t^illerunit tiller*1) kinetic energy of tiller and block (small) 1 2 ^ballscrew*') •'ballscrew •'rotor ballscrew*1) kinetic energy of ballscrew and1 rotor. 2 ^ballscrew*') meabs*1' Equivalent mass calculation of reflected mass of q v c j(t)2 ballscrew to cylinder connection Tballscrew* 4 s«) ° - 5 7 4 J Energy vs Time This is the kinetic energy of (he balscrew and the remaining hardware (red). The rotor and balscrew dominate the energy i Time (sec) Reflected Inertia vs Time This seems like a very large value, is the inertia of the servo motor reasonable? Time (sec) Rotor Inertia Check: A method to check magnitude is to consider a mild steel cylinder 4.5" long, 3.25" diameter. L 4.5in D 3.25in steel O™—, in "rotor steel J °2 L ""rotor 4.775 kg This seems physically relevant, motor weight is quoted as 171b , ± „_ * rough 2 ^"otor ^ 'roush 4 0 ^ 8 1 0 3 k S m 2 Same magnitude.... the value from the manufacturer is reasonable Outboard Motor Inertia Calculations: See notebook for sketches and rough calculations: Centre of gavity radius estimate for outboard motor As quaoted by Dana Trousil, the load of the cylinder is 300psi when at full tilt (72degrees) and tiller hard over (30deg). 50psi when tiller at 5degrees. Motor mass is 6001b. tjjl 30deg cylpress 300psi Mmotor 6001b 72dee W 1 ft ''motor ' ^ tnm "motor l n Apiston >.049in2 ^ m cylpress A _ i a o n L , i l | e r cos CG C^G M, motor S s m trim s m till 7.542 in Now need to find equivalent mass of ouboard motor: '8 12 IB — M m o t o r W m o t o r 2 L m o t o r 2 Assuming a constant mass distribution Ig 5.051 slug ft' Ln x K I Actuator Position and filler angle as a xact(t) i t — 4m function ofrjme 8in v„„(t) —x„„(t) , , d , , Speed of actuator and tiller as function of a c t dt a c t tfflW - tiliW time. dt Kinetic Energy due to rotation and translation of mass: 2 TrotW "k tillW2 TtranSW { Mmotor RCG tillM ' W « > TrotW TtransW M e ( t ) e " v a c t(t) 2 Meq(4sec) 414.168kg The inertia value is of similar value to estimates of inertia based on measurements with test boat and motor. Determination of Outboard Inertia From Measured Data Below is a chart indicating the measured response of the SeaStar Steering System to sinusoidal inputs at the helm. The system used for the tests is a 21 ft Ranger bass boat with a 225 hp Mercury outboard with a SeaStar Steering System as detailed in Chapter The net measured pressure is compared to the calculated pressure assuming that the reflected mass to the system actuator is 40 slug (584kg) and the system damping coefficient is 10 lbfsec/inch, and the coulomb friction of the cylinder is 5 lbf. The outboard inertia was iterated until the measured and calculated net cylinder pressure matched reasonably. Actuator mass = 40 slug (584kg); Damping = 10 lbf°sec/lnch; Coulomb friction = 5 lbf - Net Measured Pressure - Net Calculated Pressure | -—- Error | Time (sec) Appendix B SeaStar Measured and Simulated Response Plots 12 Ballscrew Position vs Time - Helm Input 32° Amplitude at 3.2 Hz o 0 . 6 — Measured Simulated with Leakage — Simulated without Leakage Reference Time (sec) 1 0 0 0 £ 5 0 0 £ 0 r o m - 5 0 0 Hose Pressures vs Time with Leakage Relation - Helm Input 32° Amplitude at 3.2 Hz Measured Simulated 5> 1 0 0 0 a. £ I 5 0 0 £ a. 1 0 CO - 5 0 0 Measured Simulated 1 0 0 0 S 5 0 0 2. 3 _ - 5 0 0 • z - 1 0 0 0 Measured Simulated Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 32° Amplitude at 3.2 Hz 10001 1 1 1 1 i — -500 1000 Measured Simulated -500 I 1000 500 0 -500 1000 Measured Simulated Measured Simulated Time (sec) Ballscrew Position vs Time - Helm Input 32° Amplitude at 1.6 Hz -0.5 Time (sec) Hose Pressures vs Time with Leakage Relation - Helm Input 32° Amplitude at 1.6 Hz •55 1000 Q. _> I 500 CO £ "S 0 | -500 1000 & 500 | -500 -1000 Measured Simulated Measured Simulated Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 32° Amplitude at 1.6 Hz 1000r a. a> « 500 CO £ CL T3 TO CO 1500 S1000 -500 i i — Measured {—1 Measured Simulated Time (sec) Ballscrew Position vs Time - Helm Input 32° Amplitude at 0.8 Hz Measured Simulated with Leakage — Simulated without Leakage Reference Time (sec) 6 0 0 Hose Pressures vs Time with Leakage Relation - Helm Input 32° Amplitude at 0.8 Hz Measured Simulated Q. £0 Hi £ CL ra 55 6 0 0 4 0 0 2 0 0 0 •200 I 5 0 0 Measured Simulated - 1 0 0 0 - 5 0 0 -Measured Simulated Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 32° Amplitude at 0.8 Hz 6 0 0 R ^ 4 0 0 § 2 0 0 I o o £ - 2 0 0 6 0 0 - 5 0 0 1 iW 1 1 . Measured • - Simulated -r1 W 1 Measured Simulated 1 0 0 0 1 1 1 1 1 — i I s — Measured Simulated Time (sec) Ballscrew Position vs Time - Helm Input 32° Amplitude at 0.4 Hz — Measured Simulated with Leakage — Simulated without Leakage — Reference Time (sec) Hose Pressures vs Time with Leakage Relation - Helm Input 32° Amplitude at 0.4 Hz 400 r 55 400 _> 2 200 ID i CL "B 0 (0 I $ - 2 0 0 Measured Simulated 0 200 p 0 I • r i -200 z -400 Measured Simulated 2 3 4 Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 32° Amplitude at 0.4 Hz 400 r 0) Q . £ 200 £ o •e o O. -200 I 1" 400 CL £ 5) 200 £ C L I 0 I 1-200 1 1 i i — Measured — Simulated y i i 1 r I Measured Simulated o 400 55 C L 200 3 0 z -200 Measured Simulated 3 Time (sec) 400 s Q . £ 200 • CO • ct 0 •e C -200 5> 400 Q . V | 200 ? 0 Hose Pressures vs Time with Leakage Relation - Helm Input 32° Amplitude at 0.2 Hz Measured Simulated CD o J3 ;-200 400 Measured Simulated Measured Simulated Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 32° Amplitude at 0.2 Hz 400 r — I 1 1 1 Ti p -F n — —•—~*^«—J-^-*-w— • • CL 0 •c o CL -200 55 400 a. & 3 200 CO £ 0. S 0 a 1 55 -200 Measured Simulated Measured Simulated 0 600 | 8 200 I § o z -200 i i i i Measured Simulated -i i i i i 3 Time (sec) Ballscrew Position vs Time - Helm Input 64° Amplitude at 3.2 Hz 1-51 1 1 1 i i Time (sec) 156 1500 S i 000 Hose Pressures vs Time with Leakage Relation - Helm Input 64° Amplitude at 3.2 Hz 500 0 -500 Measured Simulated '1500 1000 500 -500 2000 Measured Simulated -1000 Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 64° Amplitude at 3.2 Hz 1500r O-e o 0-500 -500 i I Measured Simulated -I I I 5> 1500 a. 1101: to 2 CL S o CO _ _ _ 55 -500 Measured Simulated 2000 Q . £ 1000 Q. -1000 Measured Simulated Time (sec) 7 5 7 Ballscrew Position vs Time - Helm Input 64° Amplitude at 1.6 Hz Measured Simulated with Leakage — Simulated without Leakage Reference i I 1 1 i i j I 0 1 2 3 4 5 6 Time (sec) Hose Pressures vs Time with Leakage Relation - Helm Input 64° Amplitude at 1.6 Hz 1500i , , 1 1 i 1 Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 64° Amplitude at 1.6 Hz Time (sec) Ballscrew Position vs Time - Helm Input 64° Amplitude at 0.8 Hz 11 1 1 i i i I 0 1 2 3 4 5 6 Time (sec) 759 1 0 0 0 Hose Pressures vs Time with Leakage Relation - Helm Input 64° Amplitude at 0.8 Hz - 5 0 0 55 6 0 0 C L 0) § 4 0 0 I 2 0 0 "S 1 o •e 55-200 1 V-£ 5 0 0 -Measured Simulated 1 1 ! — Measured . j Simulated -1 1 1 1 ! Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 64° Amplitude at 0.8 Hz 1 0 0 0 1 1 1 1 1 i — - 5 0 0 I F £ 5 0 0 - *— Measured Simulated Measured Simulated Time (sec) 1 2 Ballscrew Position vs Time - Helm Input 64° Amplitude at 0.4 Hz ir-0.8 ~ 0.6 c o c o 0.4 o CL | 0.2 to • -0.2 -0.4 h -0.6 Measured Simulated with Leakage — Simulated without Leakage — Reference o Time (sec) 600 Hose Pressures vs Time with Leakage Relation - Helm Input 64° Amplitude at 0.4 Hz Measured Simulated 5> 600 • § 400 200 § 0 a I CO -200 500 Measured Simulated CO jiT 0 a -500 -1000 Measured Simulated Time (sec) 161 Hose Pressures vs Time without Leakage Relation - Helm Input 64° Amplitude at 0.4 Hz 600 in 600 C L 1 400 in i 200 •200 -200' 1 1 ' — 1 1 l Measured Simulated S Measured Simulated 10001 1 1 1 1 —r. 5 -500 Measured Simulated Time (sec) Ballscrew Position vs Time - Helm Input 64° Amplitude at 0.2 Hz — Measured Simulated with Leakage Simulated without Leakage Reference -0.4 Time (sec) 762 500 Hose Pressures vs Time with Leakage Relation - Helm Input 64° Amplitude at 0.2 Hz -500 5> 6 0 0 Q. ID § 4 0 0 I 200 1 o 55 -200 4 0 0 to S 200 I 0 £ £ - 2 0 0 z -400 Measured Simulated Measured Simulated Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 64° Amplitude at 0.2 Hz 5001 1 n 1 1 i -£ (A Vi £ CL o CL -500 I 600 a. • 1 4 0 0 • I 200 | 0 CO 55 -200 Measured Simulated Measured Simulated 6 0 0 Time (sec) 1.5 Ballscrew Position vs Time - Helm Input 128° Amplitude at 1.6 Hz Measured Simulated with Leakage Simulated without Leakage Reference Time (sec) £ m in £ rx r o Q-1500 = 1000 500 0 -500 Hose Pressures vs Time with Leakage Relation - Helm Input 128° Amplitude at 1.6 Hz 55 1500 Q . | 1 0 0 0 in I 5 0 0 1 0 co "500, Measured Simulated Measured Simulated 2000 CO a . £ 1000 V, 1 CL 0 Measured Simulated -1000 Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 128° Amplitude at 1.6 Hz 1 5 0 0 1 0 0 0 5 0 0 0 - 5 0 0 Measured Simulated 1 5 0 0 1 0 0 0 5 0 0 0 - 5 0 0 Measured Simulated 2 0 0 0 1 0 0 0 0 1 0 0 0 Measured Simulated Time (sec) Ballscrew Position vs Time - Helm Input 128° Amplitude at 0.8 Hz - 0 . 5 Measured Simulated with Leakage — Simulated without Leakage Reference T Time (sec) 765 1 0 0 0 Hose Pressures vs Time with Leakage Relation - Helm Input 128° Amplitude at 0.8 Hz - 5 0 0 6 0 0 Measured Simulated 1 0 0 0 - 1 0 0 0 Measured Simulated Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 128° Amplitude at 0.8 Hz 1 0 0 0 1 1 — 1 1 , , - 5 0 0 Measured Simulated 55 6 0 0 a. Measured Simulated Measured Simulated Time (sec) 766 0.5 Ballscrew Position vs Time - Helm Input 128° Amplitude at 0.4 Hz — Measured Simulated with Leakage — Simulated without Leakage — Reference -0.5 h o C L ro CO -1.5 -2.5 Time (sec) Hose Pressures vs Time with Leakage Relation - Helm Input 128° Amplitude at 0.4 Hz ^ 1 0 0 0 1 1 1 1 1 — E M — o CL -500 600 Measured Simulated Measured Simulated 5 - 2 0 0 500 jD 0 0) ct -500 (-2 -1000 Measured Simulated Time (sec) 767 Hose Pressures vs Time without Leakage Relation - Helm Input 128° Amplitude at 0.4 Hz 1 0 0 0 , 1 1 1 1 i — - 5 0 0 Measured Simulated 6 0 0 4 0 0 2 0 0 S - 2 0 0 Measured Simulated 1 0 0 0 CL "ID 5 0 0 0 z - 5 0 0 Measured Simulated Time (sec) 2 . 5 Ballscrew Position vs Time - Helm Input 128° Amplitude at 0.2 Hz - 0 . 5 — Measured Simulated with Leakage — Simulated without Leakage Reference Time (sec) 168 Hose Pressures vs Time with Leakage Relation - Helm Input 128° Amplitude at 0.2 Hz 4 0 0 1 1 1 Measured Simulated Measured Simulated 4001 1 1 1 1 —t - 4 0 0 Measured Simulated Time (sec) 4 0 0 £ 2 0 0 £ CL •c o Q-Hose Pressures vs Time without Leakage Relation - Helm Input 128° Amplitude at 0.2 Hz - 2 0 0 Measured Simulated 4 0 0 o 2 0 0 Z5-200 CO Measured Simulated 6 0 0 Measured Simulated Time (sec) Ballscrew Position vs Time - Helm Input 256° Amplitude at 0.4 Hz — Measured Simulated with Leakage — Simulated without Leakage Reference Time (sec) Hose Pressures vs Time with Leakage Relation - Helm Input 256° Amplitude at 0.4 Hz _J0001 1 1 1 1 — I 2. -500 55 600 CL §j 400 0) CO | 200 Measured Simulated co-200 1000 55 S 500 • i o • | -500 -1000 Measured Simulated Measured Simulated Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 256° Amplitude at 0.4 Hz 10001 1 1 1 1 i — -500 Measured Simulated 600 -200 Measured Simulated Measured Simulated Time (sec) Ballscrew Position vs Time - Helm Input 256° Amplitude at 0.2 Hz 4h 2h CO CQ — Measured Simulated with Leakage — Simulated without Leakage Reference -1 Time (sec) 171 600 Hose Pressures vs Time with Leakage Relation - Helm Input 256° Amplitude at 0.2 Hz Measured Simulated 55 600 § 400 200 £ -200 Measured Simulated 400 S 200 i -200 • z -400 3 1 2 3 4 5 e ... , Measured — Simulated -Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 256° Amplitude at 0.2 Hz 600 r Measured Simulated 'en 600 i 1 1 1 1 — r a. i -200 600 Measured Simulated Time (sec) Ballscrew Position vs Time - Helm Input 512° Amplitude at 0.2 Hz -2 ro CD Measured Simulated with Leakage — Simulated without Leakage Reference -10 Time (sec) 2000 Hose Pressures vs Time with Leakage Relation - Helm Input 512° Amplitude at 0.2 Hz Time (sec) Hose Pressures vs Time without Leakage Relation - Helm Input 512° Amplitude at 0.2 Hz 2000 5> 1500 Q. 1 1000 to I 500 3 0 1 •500 Measured Simulated 2000 3 1000 9 0 I f, -1000 z -2000 Measured Simulated Time (sec) Ballscrew Position vs Time - 45° Helm Speed, 100 lbf Disturbance Load Time (sec) 174 Hose Pressures vs Time with Leakage Relation - 45° Helm Speed, 100 Ibf Disturbance Load 4001 r— 1 1 1 1 1 1 r _20fJ' 1 1 1 1 1 1 1 1 L 0 1 2 3 4 5 6 7 8 9 Time (sec) Hose Pressures vs Time without Leakage Relation - 45° Helm Speed, 100 Ibf Disturbance Load 400 r r— 1 — I 1 1 1 1 1 I I Time (sec) 775 1.5r Ballscrew Position vs Time - 90° Helm Speed, 100 lbf Disturbance Load 0.5 c 0 o co o c ; -0.5 Measured Simulated with Leakage — Simulated without Leakage — Reference -1.5 5 6 Time (sec) 10 Hose Pressures vs Time with Leakage Relation - 90° Helm Speed, 100 lbf Disturbance Load 4001 « 1000 s a 500 CO £ 1 CO _ _ _ 55 -500 200 "l 1 1 1 1 1 1 r Measured Simulated 8 9 10 Time (sec) 776 Hose Pressures vs Time without Leakage Relation - 90° Helm Speed, 100 Ibf Disturbance Load 400 8 9 10 55 1000 CL a 2 500 £ £ •2 0 CO -500 ~i r Measured Simulated 400 8 9 10 Measured Simulated Ballscrew Position vs Time -180° Helm Speed, 100 Ibf Disturbance Load CD CO -3 — Measured Simulated with Leakage — Simulated without Leakage Reference 10 Time (sec) 777 Hose Pressures vs Time with Leakage Relation -180° Helm Speed, 100 lbf Disturbance Load '» 10001 1 1 1 1 1 1 r Time (sec) Hose Pressures vs Time without Leakage Relation -180° Helm Speed, 100 lbf Disturbance Load 5001 1 1 1 1 1 1 1 r Time (sec) 178 0.5 Ballscrew Position vs Time - 45° Helm Speed, 200 Ibf Disturbance Load Measured Simulated with Leakage — Simulated without Leakage Reference 1 0 Time (sec) Hose Pressures vs Time with Leakage Relation - 45° Helm Speed, 200 Ibf Disturbance Load 6 0 0 at 1 0 0 0 Measured Simulated Time (sec) 779 Hose Pressures vs Time without Leakage Relation - 45° Helm Speed, 200 lbf Disturbance Load 600 Measured Simulated "1000 Measured Simulated 4 5 6 Time (sec) Ballscrew Position vs Time -180° Helm Speed, 200 lbf Disturbance Load Measured — Simulated with Leakage — Simulated without Leakage Reference 10 Time (sec) 180 Hose Pressures vs Time with Leakage Relation -180° Helm Speed, 200 Ibf Disturbance Load 500 Measured Simulated 0) C L •c o C L to -500 1000 8 9 10 2! S> 500 C O <u E "S 0 CO 0) O --500 500 Measured Simulated 8 9 10 g 0 -500 -1000 ~\ 1 r Measured 4 5 6 Time (sec) 9 10 1.5 Ballscrew Position vs Time - 90° Helm Speed, 400 Ibf Disturbance Load -2 Measured — Simulated with Leakage — Simulated without Leakage 4 5 6 Time (sec) 10 181 Hose Pressures vs Time with Leakage Relation - 90° Helm Speed, 400 lbf Disturbance Load 600 400 £ CL •c o a. 200 -200 5 1500 a. | 1000 1 500^ •o § 0 - O co -500 500 to B 0 £ § -500 £ * -1000 I z -1500 4 5 6 Time (sec) Measured Simulated 10 Measured Simulated 10 Measured Simulated 10 Hose Pressures vs Time without Leakage Relation - 90° Helm Speed, 400 lbf Disturbance Load 6001 1 — S 400 I 200 -200 » 1500 1 1 1 1 1 1 T L1.L1 — Measured — Simulated -1000 _l I I 1_ 4 5 6 Time (sec) 10 Measured Simulated 9 10 Ballscrew Position vs Time -180° Helm Speed, 400 Ibf Disturbance Load -2.5 Measured Simulated with Leakage Simulated without Leakage Reference 4 5 Time (sec) 10 Hose Pressures vs Time with Leakage Relation -180° Helm Speed, 400 Ibf Disturbance Load 600 r Time (sec) 183 Hose Pressures vs Time without Leakage Relation -180° Helm Speed, 400 Ibf Disturbance Load S 1500 | 1000 CO CO 0) 500 0 5} -500 Measured Simulated 10 Measured Simulated Time (sec) Ballscrew Position vs Time - 45° Helm Speed , -100 Ibf Disturbance Load Measured Simulated with Leakage Simulated without Leakage Reference 4 5 Time (sec) 184 Hose Pressures vs Time with Leakage Relation - 45° Helm Speed, -100 lbf Disturbance Load 600 600 -500 n i i r Time (sec) Measured Simulated 10 Hose Pressures vs Time without Leakage Relation - 45° Helm Speed, -100 lbf Disturbance Load 600 55 -200 1000 m 500 i o a! z -500 H r ~i r ~i 1 1 1 r 4 5 Time (sec) 10 185 Ballscrew Position vs Time - 90° Helm Speed , -100 Ibf Disturbance Load — Measured Simulated with Leakage — Simulated without Leakage Reference Time (sec) Hose Pressures vs Time with Leakage Relation - 90° Helm Speed, -100 Ibf Disturbance Load 1000 Measured Simulated 1000 Time (sec) Measured Simulated 186 Hose Pressures vs Time without Leakage Relation - 90° Helm Speed, -100 lbf Disturbance Load 10001 1 1 1 1 1 1 1 1 i I '« 10001 1 1 1 1 1 1 r 1000 Time (sec) Ballscrew Position vs Time -180° Helm Speed, -100 lbf Disturbance Load — Measured Simulated with Leakage — Simulated without Leakage Reference 10 Time (sec) 187 Hose Pressures vs Time with Leakage Relation -180° Helm Speed, -100 Ibf Disturbance Load 1000 '55 o. £ 500 et 0 o CL -500 — Measured Simulated 10 Measured Simulated Time (sec) Hose Pressures vs Time without Leakage Relation -180° Helm Speed, -100 Ibf Disturbance Load 1000 4 5 6 Time (sec) <n o 0.5 to a -0.5 Ballscrew Position vs Time - 45° Helm Speed , -200 lbf Disturbance Load 1.5 — Measured Simulated with Leakage — Simulated without Leakage Reference 4 5 6 Time (sec) 10 Hose Pressures vs Time with Leakage Relation - 45° Helm Speed, -200 lbf Disturbance Load 1000 £ 500 ft 0 -500 600 r -500 Measured Simulated 10 ~i r l r Measured Simulated 10 Measured - Simulated r r y j ' y r 4 5 Time (sec) 10 189 Hose Pressures vs Time without Leakage Relation - 45° Helm Speed, -200 Ibf Disturbance Load 1000 £ 500 to 2> o_ c o CL -500 Measured Simulated 10 -200 Measured Simulated J I I I I I I L_ 10 1000 <D 500 • to £ ct 0 z -500 -1 i i i r _ l I L . Measured Simulated | —— s | 5 6 Time (sec) 10 Ballscrew Position vs Time - 90° Helm Speed, -200 Ibf Disturbance Load Time (sec) 790 Hose Pressures vs Time with Leakage Relation - 90° Helm Speed, -200 Ibf Disturbance Load 1000 £ 500 £ £ o CL -500 1? 600 C L 4 5 6 Time (sec) — Measured Simulated 10 Hose Pressures vs Time without Leakage Relation - 90° Helm Speed, -200 Ibf Disturbance Load 1000 1000 '55 Q . af 500 i ri: o z -500 Measured JkL 4 I . L . U L * _ L _ U » _ - . _ 10 ~ i 1 1 r 4 5 6 Time (sec) 10 191 Ballscrew Position vs Time -180° Helm Speed, -200 lbf Disturbance Load Time (sec) Hose Pressures vs Time with Leakage Relation -180° Helm Speed, -200 lbf Disturbance Load 10001 1 1 1 1 1 1 1 1 i I o £ -500 1 1 1 1 1 1 1 1 1 1 1 0 1 2 3 4 5 6 7 8 9 10 '55 6001 1 1 1 1 1 1 r Time (sec) 792 Hose Pressures vs Time without Leakage Relation -180° Helm Speed, -200 lbf Disturbance Load 1000 • a. 8» 500 3 CO CO £ ft 0 •e o C -500 i IT 600 § 400 8 10 | 200 | ° 1-200 1000 CD 500 E o "5 z -500 Measured Simulated 8 9 10 Measured Simulated j i i i i i i_ 8 9 10 1 1 1 1 1 1 1 1 i I Measured 4 5 6 Time (sec) 10 1.5 Ballscrew Position vs Time - 45° Helm Speed, -400 lbf Disturbance Load nz i n -1.5 Measured Simulated with Leakage — Simulated without Leakage Reference 10 Time (sec) 194 Ballscrew Position vs Time - 90° Helm Speed, -400 lbf Disturbance Load -1.5 Measured Simulated with Leakage — Simulated without Leakage Reference 4 5 6 Time (sec) 10 Hose Pressures vs Time with Leakage Relation - 90° Helm Speed, -400 lbf Disturbance Load 1000 600 Measured Simulated Time (sec) 195 Hose Pressures vs Time without Leakage Relation - 90° Helm Speed, -400 Ibf Disturbance Load 0 1 2 3 4 5 6 7 8 9 15001 1 1 1 1 1 1 1 r Time (sec) Ballscrew Position vs Time -180° Helm Speed, -400 Ibf Disturbance Load Measured Time (sec) 796 Hose Pressures vs Time with Leakage Relation -180° Helm Speed, -400 lbf Disturbance Load 1000 r 4 5 6 Time (sec) 10 Hose Pressures vs Time without Leakage Relation -180° Helm Speed, -400 lbf Disturbance Load 1000r Time (sec) Helm Ampl i tude v s F r e q u e n c y v s G a i n - N o Motor Frequency (Hz) Amplitude (°) Bal lscrew Position vs Time - Helm Input 16° Amplitude at 3.2 Hz Time (sec) 198 Bal lscrew Position vs Time - Helm Input 16° Amplitude at 1.6 Hz 4 5 6 Time (sec) 0.35 Bal lscrew Position vs Time - Helm Input 16° Amplitude at 0.8 Hz 4 5 6 Time (sec) Bal lscrew Position vs Time - Helm Input 16° Amplitude at 0.4 Hz n 1 1 1 1 r 0.15 h 0.05 h -0.05 -0.1 -0.15 Measured (No Motor) Reference 4 5 6 Time (sec) 10 0.15 Bal lscrew Position vs Time - Helm Input 16° Amplitude at 0.2 Hz 0.05 h -0.05 -0.15 r--0.2 4 5 6 Time (sec) Bal lscrew Position vs Time - Helm Input 32° Amplitude at 3.2 Hz ~i 1 1 1 1 r Measured (No Motor) Reference Time (sec) Bal lscrew Position vs Time - Helm Input 32° Amplitude at 1.6 Hz -0.1 h Measured (No Motor) Reference r [I j i_ 4 5 6 Time (sec) 8 9 10 201 Bal lscrew Position vs Time - Helm Input 32° Amplitude at 0.8 Hz - | 1 1 r Measured (No Motor) Reference 4 5 6 Time (sec) Bal lscrew Position vs Time - Helm Input 32° Amplitude at 0.4 Hz ~ i 1 1 r Measured (No Motor) Reference 4 5 6 Time (sec) 10 202 Bal lscrew Position vs Time - Helm Input 64° Amplitude at 3.2 Hz -0.8 h -0.9 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (sec) 203 Bal lscrew Position vs Time - Helm Input 64° Amplitude at 1.6 Hz i 1 1 1 1 r Measured (No Motor) Reference Time (sec) Bal lscrew Position vs Time - Helm Input 64° Amplitude at 0.8 Hz g 0 OL -0.4 -0.6 -0.8 Measured (No Motor) Reference 4 5 6 Time (sec) 10 204 Bal lscrew Position vs Time - Helm Input 64° Amplitude at 0.4 Hz Measured (No Motor) Reference 4 5 6 Time (sec) 10 205 Bal lscrew Position vs Time - Helm Input 128° Amplitude at 0.4 Hz 0.81 r 21 1 i i i i i i i i I 0 1 2 3 4 5 6 7 8 9 10 Time (sec) Bal lscrew Position vs Time - Helm Input 128° Amplitude at 0.2 Hz 0.8 | 1 1 1 1 1 r -1 I 1 1 1 1 1 1 l i I I 0 1 2 3 4 5 6 7 8 9 10 Time (sec) 206 Bal lscrew Position vs Time - Helm Input 256° Amplitude at 0.4 Hz .2 51 1 1 i i i i i i i I 0 1 2 3 4 5 6 7 8 9 10 Time (sec) Bal lscrew Position vs Time - Helm Input 256° Amplitude at 0.2 Hz -2 1 1 1 1 1 — 1 i i i i I 0 1 2 3 4 5 6 7 8 9 10 Time (sec) Bal lscrew Position vs Time - Helm Input 512° Amplitude at 0.2 Hz Measured (No Motor) Reference J 1 1 1 1 i i i i I 0 1 2 3 4 5 6 7 8 9 10 Time (sec) 208 Appendix C Simulink Diagrams of SeaStar Steering System Components and Calculations 209 X TJ < LU CO •E o CJ o CO Li_ X o C4 C4 TJ Pre Pre CD •E I o CO o CO cl g "•si > 0 i JD Si < 0 > > TJ i_ CO O Si CD © CO 1_ 0 £) E c CO SI O 0 _> CO > "E (0 o O ~ •9 -CO w -t—' r~ co o t: to E a; 2 o Q. LL 0 2 I 0 O CD TJ 3 3 CO CO CO CO 0 CD 0- CL CD CD CO o I TJ i— CO o CD CO o I TJ &_ CO o Si CO CO CO CO t: t: o o CL CL a « .!=! cu o « S CO LL CL | O = o I— O O ll ll ll TJ r-•g.S _j .ti go. 2 3 0 _E 0 CO rr m > 5 4« CO § 8 cp w cr w CL 0 0 0 6 & ~ > > si (o 3) o w co E o o « > > cc I I c •>< M - < CL CL CL CL O >.Q 0 LU CL O-O CL c r O O LL DC CO X <Figure C l Simulink Diagram: SeaStar Steering System and SEA PPValve Pistonl CD—• Helm Pos PPValve qPort Shaft Pos --> PSValve qStar Piston2 PSValve PPValve qPort Shaft Pos -->' PSValve qStar * 0 Piston3 PPValve qPort Shaft Pos --> PSValve qStar Piston4 _5>l PPValve qPort Shaft Pos ~> PSValve qStar Piston5 PPValve qPort Shaft Pos -> PSValve qStar Piston6 PPValve qPort Shaft Pos -> PSValve qStar ^ qPValvt Piston7 PPValve qPort Shaft Pos r W PSValve qStar Abbreviations: PPValve, PSValve = Pressure Port/Starboard Valve Chambers Shaft Pos Position of Helm Shaft qPort, qStar = Flow to Port/Starboard valve chambers PPValve PSValve C D -C D -Shaft Pos Piston Number -+CD PPort PStar qPort qStar Piston Pos Papplied qPort -+CD qStar Spigot Piston Stroke Position 1 2*pi/7 -c- sin Piston Spacing E > — Piston Areal Plate Angle (14.5 deg) Piston Circle Radius R*sin(gamma) Base Cyl Vol CylinderVolume Flow Factor Bulk Modulus Product.3 Flow From Piston Control Volume 272 PPort positive = port negative = starboard Piston Pos sin Port or Starboard? Sign 0 H PStar qPort Figure C4 Simulink Diagram: Spigot PPHose cry-qPPistons qSPistons PSHose Port relief Pressure Flow Port Press Port Flow Port Make-upcheck Star Press Star Flow Star Make-upcheck Pressure Flow Star Relief Port Hose Press Port Valve Press Star Valve Press Star Hose Press Spool X f Spool Dynamics Valve Press Hose Press Flow X To port hose Valve Press X R o w PortSpool2tank Valve Press StarSpool2tank Hose Press R o w Valve Press To Star hose Net Port Flow Port Valve Pressure Spool X Star VavlePressure Net Starboard R o w Valve Volumes qPHose -KD PPValve -+CD PSValve > > * c n n C U n e i qSHose C 1 ^Pressure 1000 Relief Pressure 1 Gainl Relational Operator Switch Flow Alternate Flow Rate Figure C6 Simulink Diagram: Relief Valve - K I D Port Flow Alternate Flow if P =< 2psi Figure C7 Simulink Diagram: Make-up check 215 Port Valve Press C D — Star Valve Press Port Hose Press C D — Star Hose Press Port V Press Port H Press X F Star H Press Star V Press Spool Area — • © Ball Contact Force x Outl M Springs + 0 0.001s 2 +s Spool Dynamics x outl M Stops •CD Spool X Figure C8 Simulink Diagram: Spool Dynamics Sign Figure C9 Simulink Diagram: Contact Force between Spool and Check-ball 216 Preload x4 Figure CIO Simulink Diagram: Spring Force Applied to Spool kx1 Figure C l l Simulink Diagram: Spool Stop Force 217 ( 1 )Valve Press Hose Press .9 Flow Factor X -0.03 Flow Port Spool/Ball Contact Point Figure C12 Simulink Diagram: 'To port hose' - Flow from Valve Body to Hose Valve Press X 1-0.09 Spool Open Positon -Port Side lul -0.02 |u| CornerRate Flow Rate Figure C13 Simulink Diagram: 'PortSpool2tank' - Spool Controlled Flow to Tank 218 c r > Net Port Flow Integrator Initial Port Chamber Vol CD—•* Spool X Spool Areal 3> Initial Star Chamber Vol Net Starboard Flow 1_ * o s Integrator! Bulk Mod Port Valve Pressure -KID Bulk Modi Star Valve Pressure Figure C14 Simulink Model: 'Valve Volumes' - Pressure Generation in Spool Valve 219 Hose Block Diagrams: CJD—^Q—^ qPHose CylX Net Flow Pressure Cylinder Pos Port Hose Press Outl inl Star Relief3 GD— qSHose Cylinder Pos Pressure Net Flow Star Hose Press Outl In1 StarRelieO PHPress -K.D SHPress Figure C15 Simulink Model: Hoses Net Flow ' ' -C-Initial Fluid Volme 16ft long, 0.38 ID + Cylinder Volume dV C O -Cylinder Pos Piston Area Initial Hose Volme 16ft long, 0.38 ID1 + Init Cylinder Volume Bulk Modulus 1 0.01s2+63s+1024 Hose Dynamics Pressure! Figure C16 Simulink Model: Hose Pressure 220 Cylinder Block Diagrams: PHPres|_ SHPress Contact Contact Force Interference Backlash Force Cylinder Position Stops F stops Contact Force Port Pressure Starboard Pressure Shaft Position Cylinder Contact Force Contact point change Racking CylX -KX) FC Figure C17 Simulink Diagram: Cylinder cz>-^>-^5>-*C>*€>C)—+ Port Pressure Piston Area Starboard Pressure d > Fstops 1 0.1 s+2 Cylinder <3 Coulomb Contact Force Shaft Position Figure C18 Simulink Diagram: Cylinder Dynamics Interference Figure C19 Simulink Diagram: Backlash c r > Contact Force 1 s 2 +600S+5232 Racking sin xm Contact point change cos Figure C20 Simulink Diagram: Racking V 222 SEA Resistance Unit: FC G > Ref Contact Point Force F Ballscrew Tiller Angle Tiller Geometryl Applied load Nut Position Disturbance Ballscrew Unit Tiller Contact Point Screw Pos Tiller Angle Tiller Geometry Direction Correction Contact SEAX Figure C21 Simulink Diagram: Sea Resistance Unit Applied load • 9 -y/^sin( lambda)2 F friction 1 .5s 2 +s Nut and Co. meq cos(lambda)1 ^ / j ^ cos(lambda)2 CUD—4?> Disturbance F=>T 1:23 u friction coeff Stiffness sin(lambdp)1 3«-Sign2 Nut Position cos(lambda) sin(lambda) 1 0.003854s A rad=»in Screw mean radiusl Ballscrew Jeq Screw mean radius Figure C22 Simulink Diagram: Ballscrew Unit 223 Contact Point Force Tiller Arm Tiller Angle cos •K-F Ballscrew Torque->Force Figure C23 Simulink Diagram: Tiller Geometry 1 Tiller Arm CD—••£>-*• Screw Pos atan sin -+CD Tiller Contact Point tanpheta Tiller Angle Figure C24 Simulink Diagram: Tiller Geometry 224 Appendix D Boat Testing Data 225 Straight Line Test @ 5 mph 100 15 Time (sec) Straight Line Test @ 5 mph 15 Time (sec) 226 Straight Line Test @ 10 mph 30 Time (sec) 60 40 20 0 -20 Straight Line Test @ 10 mph - Helm Torque (in'lbf) | : 1 1 1 1 1 1 10 20 30 40 50 60 30 Time (sec) Straight Line Test @ 20 mph 4 2 0 I 200 100 0 -100 l 40 20 0 -20 I I i i i , 1 1 | — Boat Speed (mph) | 1 1 i 10 20 30 40 50 60 70 Time (sec) 100 50 0 -50 ( 40 20 0 -20 i 150 100 50 0 Straight Line Test @ 20 mph I ' J \ i i i i i Helm Torque (in'lbf) | i i / v — j "V * i i i 10 20 30 40 50 60 70 Port Pressure (psi) 10 20 30 40 50 60 70 30 40 Time (sec) 228 Straight Line Test @ 30 mph 30 Time (sec) Straight Line Test @ 30 mph 30 Time (sec) 229 Straight Line Test @ 40 mph 100 60 40 20 0 -20 Straight Line Test @ 40 mph 1 1 I i n ^ i i ' 1 i 1 1 1 Port Pressure (psi) | L h i i i i i i i i i 10 10 15 20 25 30 35 40 45 50 15 20 25 30 Time (sec) 35 40 45 50 Straight Line Test @ 50 mph 20 Time (sec) 100 40 20 0 -20 200 Straight Line Test @ 50 mph Port Pressure (psi) 10 15 20 25 30 35 40 20 Time (sec) 231 Straight Line Test @ 60 mph 30 40 Time (sec) 100 Straight Line Test @ 60 mph 20 0 -20 10 20 30 40 50 60 70 200 100 30 40 Time (sec) Straight Line Test @ 70 mph 20 25 Time (sec) 100 Straight Line Test @ 70 mph 10 15 20 25 30 35 40 45 50 200 20 25 30 Time (sec) 35 40 45 50 233 Straight Line Test @ 80 mph 40 Time (sec) 100 150 r 100 50 0 -50 L 300 Straight Line Test @ 80 mph | — Port Pressure (psi) 10 20 30 40 50 60 70 80 40 Time (sec) 234 Straight Line Test @ 90 mph 100 100 100 40 50 60 Time (sec) 100 Straight Line Test @ 90 mph 40 50 Time (sec) 235 100 m Buoy Test @ 33 mph 300 200 100 10 20 25 30 Time (sec) 100 100 m Buoy Test @ 33 mph -20 0 300 r 200 100 Port Pressure (psi) _ l L_ 10 15 20 25 30 35 40 45 50 Starboard Pressure (psi) 10 15 20 25 30 Time (sec) 35 40 45 50 100 m Buoy Test @ 40 mph 30 Time (sec) -50 I 300 200 100 m Buoy Test @ 40 mph I 1 1 1 1 i | — Starboard Pressure (psi) | 1 i i i i 10 20 30 Time (sec) 40 50 60 237 o i 400 200 0 -200 i 80 60 40 20 100 m Buoy Test @ 40 mph I I Net Actuator Pressure (psi) | I I i i i 10 —I— 20 — i — 30 i — 40 50 60 Boat Speed (mph) 10 20 30 Time (sec) 40 50 60 150 100 m Buoy Test @ 40 mph 30 Time (sec) 100 m Buoy Test @ 50 mph i i r — i 1 1 1 \ / Helm Position(rad) | i i i i i i i 20 Time (sec) 100 m Buoy Test @ 50 mph Helm Torque (in*lbf) | 10 15 20 25 30 35 40 10 15 20 25 30 35 40 15 20 25 Time (sec) 30 35 40 239 100 m Buoy Test @ 60 mph 40 50 Time (sec) 150 100 m Buoy Test @ 60 mph 40 50 Time (sec) 240 400 100 m Buoy Test @ 70 mph I I 1 1 I I I 1 I k , | , (1 | Net Actuator Pressure (psi) | — » [ v V W ^ v ] T V ' i i i i i i > i i 100 40 50 60 Time (sec) 100 150 100 m Buoy Test @ 70 mph 10 20 30 40 50 60 70 80 90 100 100 h 50 0 -50 T i i r | — Port Pressure (psi) j i i _ 400 10 20 30 40 50 60 70 80 90 100 i r-200 -0 --200 "i r Starboard Pressure (psi) 10 20 30 40 50 60 Time (sec) 70 80 90 100 241 50 m Buoy Test @ 30 mph 60 Time (sec) 50 m Buoy Test @ 30 mph 60 Time (sec) 100 120 242 50 m Buoy Test @ 40 mph 400 200 -200 100 60 Time (sec) 200 50 m Buoy Test @ 40 mph 60 Time (sec) 100 120 243 400 200 -200 50 m Buoy Test @ 50 mph 90 100 10 20 30 40 50 60 70 80 90 100 i i I i i r Net Actuator Pressure (psi) 100 40 50 60 Time (sec) 100 150 100 50 0 -50 l 150 100 50 0 -50 l 300 200 100 0 -100 T r 50 m Buoy Test @ 50 mph - i 1 1 r Helm Torque (in*lbf) I I I 1 I I I I L_ 10 20 - i r 30 40 50 60 70 80 90 100 ~i r ItWIAJl Port Pressure (psi) 10 20 30 40 50 60 70 80 90 100 ~[ 1 1 1 r - Starboard Pressure (psi) 10 20 30 40 50 60 Time (sec) 70 80 90 100 244 33 m Buoy Test @ 30 mph 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 400 -200 100 50 H 1 r | — Net Actuator Pressure (psi) _ l I I I I I I I L_ 20 40 60 80 100 120 140 160 180 200 ~i r i r Boat Speed (mph) J I I I I I I L_ 20 40 60 80 100 120 140 160 180 200 Time (sec) 150 100 50 33 m Buoy Test @ 30 mph 0 20 40 60 80 100 120 140 160 180 200 "i 1 1 1 1 1 r -50 Port Pressure (psi) - i 1 i i i i_ 0 20 40 60 80 100 120 140 160 180 200 400 -200 20 40 80 100 120 140 160 Time (sec) 180 200 245 33 m Buoy Test @ 40 mph Time (sec) 33 m Buoy Test @ 40 mph 100 150 Time (sec) 246 33 m Buoy Test @ 50 mph o i 400 200 0 -200 I 100 50 0 -50 100 100 100 I I I I I I I I I s— " - \ | — Boat Speed (mph) | i i i i i i i i i 0 10 20 30 40 50 60 Time (sec) 70 80 90 100 200 100 -100 200 100 -100 400 33 m Buoy Test @ 50 mph 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 40 50 Time (sec) 200 m Buoy Test @ 30 mph 400 200 -200 40 50 Time (sec) 200 m Buoy Test @ 30 mph 10 20 30 40 50 60 70 80 90 100 40 50 Time (sec) 248 200 m Buoy Test @ 40 mph 500 -500 40 50 Time (sec) 200 200 m Buoy Test @ 40 mph 40 50 Time (sec) 249 200 m Buoy Test @ 50 mph 50 Time (sec) 150 r 100 50 0 -50 L r 100 ~i r 200 m Buoy Test @ 50 mph "i 1 r; Helm Torque (in'lbf) i i ! i i i i_ 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 300 40 50 Time (sec) 100 250 400 200 m Buoy Test @ 60 mph 10 20 30 40 50 60 70 80 -200 100 10 20 30 40 50 60 70 80 90 40 50 Time (sec) 150 200 m Buoy Test @ 60 mph 40 50 Time (sec) 251 200 m Buoy Test @ 70 mph 400 200 -200 30 40 Time (sec) 200 200 m Buoy Test @ 70 mph -100 30 40 Time (sec) 252 200 m Buoy Test @ 80 mph 4 0 0 2 0 0 - 2 0 0 1 0 0 4 0 Time (sec) 1 5 0 200 m Buoy Test @ 80 mph 4 0 Time (sec) 20 10 0 -10 l 6 4 2 0 l 500 -500 100 50 200 m Buoy Test @ 90 mph I 1 1 I I I 1 1 Helm Position(rad) | -1 1 1 1 1 1 1 i i i i r r L _ 1 1 1 1 1 Doai opeeo (mpnj j 10 20 30 40 50 Time (sec) 60 70 80 90 200 100 h 200 m Buoy Test @ 90 mph 40 50 Time (sec) Appendix E Plots of Net Cylinder Pressure Predicted By Usage-based Testing Load Function 250 Test Boat Data -100 m Buoy Spacing, 50 mph Boat Speed Measured Best Fit Coefficients Mean Value Coefficients 350 r Test Boat Data -100 m Buoy Spacing, 60 mph Boat Speed 300 250 200 r to a. £ 1501 to to £ ^ 1001 <5 T3 C O 2 50 0 -50 -100 • -150 Measured Best Fit Coefficients — Mean Value Coefficients 10 20 30 Time (sec) 40 50 60 257 Test Boat Data -100 m Buoy Spacing, 70 mph Boat Speed 4001 1 1 1 i 31 1 1 1 1 1 30 35 40 45 50 55 Time (sec) 258 250 r Test Boat Data - 30 m Buoy Spacing, 30 mph Boat Speed Measured Best Fit Coefficients Mean Value Coefficients 100 110 Time (sec) 150 500 r 400 h Test Boat Data - 30 m Buoy Spacing, 50 mph Boat Speed Measured Best Fit Coefficients Mean Value Coefficients 35 Time (sec) 50 260 350 300 250 S 2 0 0 £ S 150 2100 50 Test Boat Data - 200 m Buoy Spacing, 50 mph Boat Speed -50 — Measured Best Fit Coefficients Mean Value Coefficients 15 20 Time (sec) 35 300 200 «=> 150 • Q. £ <0 CO £ CL 100 50 o -50 k -100 -150 Test Boat Data - 200 m Buoy Spacing, 80 mph Boat Speed 10 15 20 Time (sec) Measured Best Fit Coefficients Mean Value Coefficients 25 30 35 267 

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