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Monitoring and control of milling with an open architecture computer numerical controller Munasinghe, Watukarage Kamal 1994

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MONITORING AND CONTROL OF MILLING WITH ANOPEN ARCHITECTURE COMPUTER NUMERICAL CONTROLLERByWatukarage Kamal MunasingheB.Sc.(Eng), University of Peradeniya, Sri Lanka, 1983A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF MECHANICAL ENGINEERINGWe accept this thesis as conformingto the required tandardTHE UNIVERSITY OF BRITISH COLUMBIASeptember, 1994© Watukarage Kamal Munasinghe, 1994In presenting this thesis in partial fulfillment of therequirements for an advanced degree at the University of BritishColumbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission forextensive copying of this thesis for scholarly purposes may begranted by the head of my department or by his or herrepresentatives. It is understood that copying or publication ofthis thesis for financial gain shall not be allowed without mywritten permission.(Signature)____________Department of &Ae ,2c\l t/\AWI\9The University of British ColumbiaVancouver, CanadaDate -Pt L994AbstractThe importance of an Open Architecture design of a Computer Numerical Controllerfor integration of process monitoring and control for unmanned intelligent machining isdemonstrated.The Hierarchical Open Architecture Multiprocessor Computer Numerical Controller(HOAM-CNC), which is used in this thesis has been designed and built in the Manufacturing Automation Laboratory of UBC. Basic milling process monitoring and controlmodules which are adaptive force control, tool breakage detection, chatter detection andsuppression have been integrated to HOAM-CNC system for intelligent machining.Adaptive force control module keeps the peak cutting force at a specified referencelevel by manipulating the feed. The purpose of adaptive force control is to avoid shankfailure of the cutter and to increase machining accuracy. Tool breakage monitoring systemis based on the residuals of two first order adaptive time series filters. Filters remove theeffect of geometric transients from average forces. In the event of a tool breakage theresiduals simultaneously violate their own adaptive thresholds. Chatter detection andsuppression algorithm uses the frequency spectrum of sound emitting from the cuttingprocess. The presence of chatter vibrations is detected when the spectrum amplitudeexceeds a predetermined threshold level. The system automatically reduces the depth ofcut until chatter vibrations diminish.All three process monitoring and control functions run in parallel in the proposed openarchitecture system. Performance of the complete CNC system is tested by intelligentmachining of a pocket.11Table of ContentsAbstract iiTable of Contents iiiList of Tables viList of Figures viiAcknowledgement x1 Introduction 11.1 Objective of the Research 21.2 Process Monitoring and Control Modules . 21.2.1 Adaptive Force Control 21.2.2 Tool Breakage Detection 31.2.3 Chatter Detection and Suppression 31.3 Integration and Parallel Execution of Process Monitoring and Control . 31.4 Organization of the Thesis 52 Literature Survey 72.1 Unmanned Machining 72.2 Adaptive Control Systems 82.3 Tool Breakage Detection 122.4 Chatter Detection and Suppression 171112.4.1 Chatter 172.4.2 Stability Lobes 242.4.3 Stability of the Milling Process 242.4.4 Sensors for Chatter Detection 252.4.5 Suppression of Chatter 273 Process Monitoring and Control 293.1 Adaptive Control of the Peak Resultant Cutting Force 293.1.1 Modeling of the Milling Process. 303.1.2 Modeling of the position Control Loop 343.1.3 Parameter Estimation . .. 373.1.4 Adaptive Control Algorithm . 393.2 Tool Breakage Detection . 423.3 Chatter Detection and Suppression . . 464 Integration of Monitoring and Control Modules to HOAM-CNC system 504.1 Introduction 504.2 HOAM-CNC System 514.3 Hardware Layout of the HOAM-CNC 514.3.1 Real Time Master. . . 514.3.2 Sub Systems 524.4 Software Organization 544.4.1 System Master 554.4.2 CNC Master 564.4.3 Axis Control Software 574.4.4 Process Monitoring and Control Software . . 57iv4.4.5 Parallel Execution of the Process Monitoring and Control Algorithms 655 Experimental Results 675.1 Experimental Setup 675.1.1 Milling Machine and Position Control Systems 685.1.2 Peak and Average Force Detection System 685.1.3 Chatter Detection System 705.2 Chatter Threshold 735.3 Experimental Results 765.3.1 Performance of the Adaptive Control Algorithm in Non Linear Region of the Cutting Forces 765.3.2 Machining of a Pocket 785.3.3 Comparison of the HOAM-CNC with a Closed Architecture CNC 866 Conclusion and Future Work 956.1 Integration of Process Monitoring and Control to HOAM-CNC 956.2 Future Work 97Bibliography 99Appendices 104A Axis Control Loops 104B Model Approximation of the Position Loop 106vList of Tables3.1 Test specifications for the demonstration of tool breakage detection algorithm 453.2 Specifications of the end mill for demonstration of chatter detection . . . 485.1 Machine parameters 685.2 Specifications of the end mill and cutting conditions for demonstration ofsetting the chatter threshold 735.3 Specifications of the end mill and cutting conditions for adaptive controltest in the non linear region of the cutting force 765.4 Specifications of the end mill for pocket machining 785.5 Cutting conditions for adaptive control tests on the Hardinge lathe . . 875.6 Test conditions for performance comparison 88A.1 Design parameters of the X-axis feed drive 105viList of Figures2.1 Mechanism of mode coupling 182.2 Regeneration of surface waviness 192.3 Diagram for deriving limit of stability 202.4 Block diagram of vibration in regenerative cutting . . 212.5 Conditions at the limit of stability 232.6 Typical stability lobe curve 252.7 Sources of process damping 263.1 Block diagram of the adaptive force control system 293.2 Geometry of end milling 303.3 Model variables of the milling process . . 333.4 Position control loop for a single axis 353.5 Actual and model responses of the velocity loop of z axis . . . 363.6 Part geometry for the tool breakage detection algorithm . . . 463.7 The measured average force over each tooth period 473.8 Residual cutting forces of the first order filter applied on first differences 473.9 Residual cutting forces of the first order filter applied on fourth differences 483.10 Variation of maximum amplitude of the spectrum of sound 494.1 Global System Architecture 524.2 Axis controller 534.3 The Software Architecture of the HOAM-CNC system 554.4 Task switching by the job manager 58vii5.1 Experimental setup 675.2 Basic structure of the moving coil microphone 715.3 Transfer function of the tool in y direction 745.4 Frequency spectrum of sound for stable cutting 755.5 Frequency spectrum of sound for unstable cutting 755.6 Variation of peak resultant cutting force - Machining in the non linearregion of cutting forces 775.7 Variation of command feed speed - Machining in the non linear region ofcutting forces 775.8 Machining of the pocket 805.9 Variation of peak resultant cutting force - Machining of the pocket . . 805.10 Variation of the command feed - Machining of the pocket 815.11 Variation of estimated parameters - Machining of the pocket 835.12 Variation of average cutting force - Machining of the pocket 835.13 Variation of residuals in machining of the pocket - first order filter appliedon first differences 845.14 Variation of residuals in machining of the pocket - first order filter appliedon second differences 845.15 Variation of maximum amplitude of the frequency spectrum of microphonesignal - Machining of the pocket 855.16 Adaptive control implementation with a closed architecture CNC . . 875.17 Variation of cutting force - test IL, closed architecture CNC 885.18 Variation of cutting force - test TM, open architecture CNC 895.19 Variation of command feed - test IL, closed architecture CNC 905.20 Variation of command feed - test TM, open architecture CNC 91viii5. CNCVariation of cutting force -Variation of cutting force -Variation of command feedVariation of command feedVariation of command feedtest IlL, closed architecture CNCtest TIM, open architecture CNC- test IlL, closed architecture CNC- test IIM, open architecture CNCsent to the controller - test IlL919292939394B.1B.2• • . 1041041081095.21 Variation of command feed sent to the controller - test IL, closed architecA.1 Position control loopA.2 Velocity control loopStep response of the position control ioopFrequency response of the position control loopixAcknowledgementI wish to express my gratitude and thanks to my wife Ranjani, for her patience,unreserved support and encouragement during the study.I am grateful to my supervisor Dr. Y. Altintas, whose encouragement and guidancewas invaluable in the successful completion of this thesis.My sincere thanks to Research Engineer Gordon Wright for his extensive help withelectronics and many constructive suggestions. At last but not least, assistance of allcolleagues in the Manufacturing Automation laboratory is greatly appreciated.xChapter 1IntroductionThe recent trend in manufacturing research has been to develop self sustained, intelligent, unmanned machining systems in order to improve the machining safety, productquality and the machine utilization. In intelligent machining systems sensors provide process information to control and monitoring algorithms. Various vision, touch, force, noiseand temperature sensors have been developed for machine tools and further research inthe area is underway. However until recently, limited computing facilities placed heavyconstraints on examination of complex new algorithms that use the sensors, for the automation of machine tools. The recent progress of semiconductor technologies have todaymade it possible to realize the intelligent machining systems.For intelligent machining, in addition to the primary task of accurately followingthe programmed tool path, Computer Numerical Control(CNC) system of the machinetool should be able to coordinate various process monitoring and control tasks. Controlsystem is expected to take prompt action in the case of a failure detection and shouldexecute process control algorithms in parallel at short time intervals.CNC systems have been and are still mainly offered as closed manufacturer specificsolutions. They are designed to carry out only the servo control task and, therefore,integration of other machining process monitoring and control functions to them is notpossible or only possible with the help of the manufacturer with major changes to hardware and software. As a result, recent research has focused on developing an OpenArchitecture CNC system. An Open Architecture CNC, by definition, can run on a1Chapter 1. Introduction 2variety of platforms and allow integration of various applications from multiple vendorsand interoperate with other applications of the system without major modifications tohardware and software [1]. Therefore, an Open Architecture CNC has the potential toallow the integration of process monitoring and control applications to a machine tool,thus making it more self sustained, intelligent and very flexible to the end user.1.1 Objective of the ResearchObjective of the research presented in this thesis is to design, develop and integratemachining process monitoring and control modules to an open architecture CNC designedand built in the manufacturing automation laboratory of UBC. Open Architecture CNC isnamed HOAM-CNC [2] which stands for Hierarchical Open Architecture MultiprocessorComputer Numerical Controller. Machining process monitoring and control modulesinclude,• An adaptive control module for cutting forces that will perform well over a widerange of cutting conditions.• A tool breakage detection module• A chatter detection and suppression module.1.2 Process Monitoring and Control Modules1.2.1 Adaptive Force ControlAdaptive force control module keeps the peak cutting force acting on the cutting tool at adesired safe level by manipulating the vector feed. The purpose of controlling the cuttingforce is two fold. In finish machining controlled cutting force limits the static deflectionsChapter 1. Introduction 3of the cutting tool thus improving the surface accuracy. In roughing operations it avoidsthe shank breakage of the cutting tool.1.2.2 Tool Breakage DetectionTool breakage detection algorithm uses the differences of average cutting forces calculatedat each tooth period. Two kinds of differences are considered. They are differencebetween the average forces over a tooth period and the tooth period before, which iscalled the first difference and the difference between average forces over a tooth periodand a tooth period one revolution before. Both differences are filtered with two separatefirst order time series filters to remove effects of geometric transients during machining.If a breakage is detected the system promptly stops all the axis so that further damagesto the machine tool and the workpiece are avoided.1.2.3 Chatter Detection and SuppressionChatter detection and suppression algorithm analyzes the sound emitting from the cutting process to detect chatter vibrations in machining. Frequency spectrum of the soundpressure is calculated in real time, and the amplitude of the spectrum is compared with aset threshold obtained from a stable machining test. If the chatter vibrations are detectedthe algorithm reduces the depth of cut to avoid chatter, and modifies the tool path toensure the removal of the total intended depth of cut.1.3 Integration and Parallel Execution of Process Monitoring and ControlHOAM-CNC has three levels of hardware and software in its hierarchy. Highestlevel has the real Time Master(RTM), which contains the user interface and co-ordinatesvarious other subsystems of level two. Level two has the motion control subsystem,Chapter 1. Introduction 4which is called the CNC master and process monitoring and control subsystems can beintegrated to this level with no changes to hardware and a minimal amount of changes tosoftware. Level 3 has axis controllers, which control each individual axis. However in thepresent implementation process monitoring and control modules are integrated to RTMas independent software modules. They are assisted by two other subsystems in the level2. One of them is the peak and average force detection subsystem, which provides theforce data for adaptive control and tool breakage detection algorithms. The other is thechatter detection subsystem which samples the sound signal from the cutting process andcalculates its spectrum in real time.Each Process monitoring and control function is executed at specified time intervalsin parallel. Adaptive force control runs once every spindle revolution. Tool breakagedetection is executed at each tooth period. Chatter detection cycle time could be anumber of revolutions. All these periods are multiples of tooth period. At every toothperiod the force detection subsystem sets a flag to indicate the process monitroing andcontrol algorithms running in RTM that another tooth period has passed. An externalpulse, generated by a spindle encoder or a pulse generator at each tooth period interruptsthe force detection subsystem to set this flag. Tooth periods are counted by the adaptivecontrol module by reading and resetting the flag. The tooth count is available to otherprocess monitoring and control modules. This tooth count is used to determine thetime that each monitoring and control function should be run. RTM runs a shell of thethree monitoring and control routines at every tooth period, however each algorithm getsincluded in the corresponding routine once for a number of tooth periods, which is equalto the period of the monitoring and control function.The Communication facilities available in the HOAM-CNC include mail boxes andmemory pipes implemented in the dual ported memory of the CNC master. Mail boxesprovide for fast real time parameter passing between RTM and CNC master. MemoryChapter 1. Introduction 5pipes are good for passing large amounts of variable sized data that is processed insequence and has less of a time constraint. Process monitoring and control modulesuse these facilities to communicate with the CNC master via the CNC interface modulewhich is a part of the RTM.For performance evaluation HOAM-CNC is interfaced to a SLO-syn 3 axis verticalknee type milling machine fitted with 3 Baldor permanent magnet DC motors. Choiceof a milling machine is based on the improtance of the milling process. Milling is amachining process widely used in the aircraft, automotive and other manufacturing industries. Machining of stamping dies for automotive body parts and turbine blades ofaircraft engines are typical milling operations. Sometimes the amount of metal convertedto chips could be as high as 90 % of the original blank. Thus any kind of improvementin machining efficiency in milling will contribute to significant savings in machining costin many operations.1.4 Organization of the ThesisThe thesis is organized as follows. A survey of literature on unmanned machining, adaptive cutting force control, tool breakage detection and chatter detection andsuppression is presented in Chapter 2.Chapter 3 explains in detail the adaptive cutting force control algorithm and parameter estimation strategy, tool breakage detection algorithm, chatter detection andsuppression algorithms.Chapter 4 presents the details of the hardware and software organizations of theHOAM-CNC and integration of process monitoring and control modules to the ROAMCNC. Each process monitoring and control algorithm is presented in pseudo-code form.Chapter 5 presents experimental results of the implementation of process monitoringChapter 1. Introduction 6and control with the HOAM-CNC. Performance of the adaptive control algorithm in thenon linear region of cutting mechanics is shown. Last section of the chapter comparesand discusses the limitations of a closed architecture CNC with regard to integration ofprocess monitoring and control.The thesis is concluded in chapter 6 with a summary of conclusions and future work.Chapter 2Literature Survey2.1 Unmanned MachiningUnmanned machining has attracted much attention of machine tool researchersin the last two decades. The absence of an operator in an unmanned machine toolleaves the supervision, monitoring and control tasks to computer controllers. Some ofthe important monitoring and control tasks are adaptive control of the chip load formaximum metal removal rate and for avoidance of tool breakage at the shank, in processtool wear and breakage detection, chatter detection and suppression, geometric adaptivecontrol for precision machining [3]. These tasks need the machine tool to be equippedwith reliable and effective sensors that will collect various signals from the machiningoperation [4]. Measurements of these signals will be used by monitoring and controlalgorithms to calculate necessary control outputs. These algorithms must be executed inparallel and may demand fast manipulation of machining parameters like feeds, speedsand even changing the position control algorithms. Complex events like part programmodification may also be necessary. Therefore the CNC system should be fully open tomonitoring and control functions. Also the same sensor signal may be used by more thanone algorithm. Therefore the information should be able to freely flow within the CNCsystem [5].Monitoring and control algorithms have been individually studied and implemented.However integration of them into one frame has not been possible due to limitations7Chapter 2. Literature Survey 8of CNC systems. In this thesis three monitoring and control algorithms are designedand integrated into the HOAM-CNC system to show the capability of an open CNCarchitecture as a potential candidate to be used in an unmanned machining system.2.2 Adaptive Control SystemsIn most of the CNC machine tools which are in use today, operating parameterssuch as feeds and spindle speeds are selected by the part programmer or the operator ofthe machine tool. Therefore the selection of these parameters depend on their experienceand knowledge about tools, tool and workpiece materials, and machining process physics.Generally they select very conservative parameters that will accommodate most adversecutting conditions for safe and quality machining. This considerably reduces the metalremoval rate. Adaptive control systems have been developed to address this problem.Adaptive control systems manipulate the operating parameters of the machine tool insuch a way that real time measured states of the machining process like force, torque,vibration are kept at desired reference levels.Adaptive control for machine tools can be classified into two categories. They are,1. Adaptive control systems with optimization (ACO) and,2. Adaptive control systems with constraints (ACe).Adaptive control systems with optimization vary the operating parameters in realtime by optimizing a given performance index, which is generally an economic functionof parameters like metal removal rate, tool wear rate etc., subject to process and systemconstraints. Although there has been a considerable research effort in ACO systems, theyhave achieved little progress due to difficulties in formulating a realistic performance indexand the lack of suitable sensors to measure the required variables like tool wear.Chapter 2. Literature Survey 9ACC systems maximize machining parameters like feed rate and cutting speed subjectto process and machine tool constraints like allowable cutting force, spindle motor torque,power etc. Practically almost all of the adaptive control systems that has been successfulare ACC type and usually manipulate only one operating parameter which in most casesis the feed rate [6].Research in the area of adaptive control of machine tools started in 1960’s. Theobjective of adaptive control was for on line adjustment of cutting conditions to optimizesome economic cost function in order to reduce the requirement of machinability data.Early AC systems were implemented in hardware and a variety of approaches and designsused. Though they demonstrated considerable increases in the production efficiency, hadlittle success if any in the industry due to reliability problems associated with sensorsand lack of understanding about the cutting process itself. Attempts in early 1970’s todevelop an ACO system with a mathematically defined economic performance index formachine tools had a limited success. When the difficulties in formulating the performanceindex and measuring all the required variables like tool wear are concerned these ACOsystems were probably too ambitious [7].The objective of ACC type adaptive control systems has been to increase the metalremoval rate during roughing operations. In majority of these ACC type systems machining feed rate is maximized while maintaining a constant reference load on the cuttingtool despite changes in the cut profile. It is reported that, with these adaptive controllers20-80 % reductions in cycle time has been achieved [7].Most of the early ACC type systems involved the use of conventional fixed gain controllers. Examples are fixed gain PD controller with a separate integral block developedby Tiusty [8], and a PT controllers developed by Stute and Goetz [9]. These controllers had major performance problems like instability and large transient overshootsChapter 2. Literature Survey 10when the machining conditions deviated from those for which the controllers were designed. For each cutting condition best controller gains were necessary to be found bytrial and error with simulations or cutting experiments. To avoid these difficulties Koren and Masory [10] attempted to make the controller gain variable so that the overallopen loop gain of the system is constant. This ACC system for cutting force had allbasic elements of a parameter adaptive control system and was implemented on a lathe.However no formal adaptive control strategy was used and the structure of the controllerwas intuitive. Selection of constants governing the estimation of the cutting process gainand the open loop adaptation gain was done on an experimental basis. The issue ofapplicability of the controller over a wide range of cutting conditions was not addressed.Daneshmand and Pak [11], Fussel and Sirinivasan [12] ,Tomizuka, Oh and Dornfeld [13] and Lauderbaugh and Ulsoy [14] applied various forms of the explicit modelreference adaptive control strategy of Landau and Lozano [15] for turning and milling.This control strategy is applicable only to minimum phase processes since it cancels nonminimum phase zeros of the process with controller poles. They assumed that the plant,which was the machining operation combined with dynamics of the feed drive servo areminimum phase. However this assumption is not realistic since the discretization of evena stable continuous time system can have non minimum phase zeros if there is a pole excess larger than 2 when sufficiently fast sampling is used [16]. This leads to unacceptableoscillations in the force response due to unbounded control feed rate commands. Furthera trial and error procedure had to be used to determine best reference model.Elbestawi, Mohamed and Liu [17] applied adaptive dead beat, discrete PID and poleplacement(derived from the MRAC scheme of Landau [15]) controllers in peripheralmilling to control the peak resultant cutting force over each spindle revolution. Deadbeat controller was considered to obtain a faster adaptation to changes in the cuttingconditions. These controllers did not perform well in non linear regions of the cuttingChapter 2. Literature Survey 11force in relation to the feed rate. To avoid this problem a non linear controller wasused with a non linear model of the cutting process. However non of these controllersaddressed the issue of possible non minimum phase zeros in the plant being controlled.To overcome the problem of non minimum phase zeros Kolarits and DeVries [18]applied a modified version of the explicit MRAC scheme of Landau and Lozano [15],where the controller does not cancel the zeros of the process. However this still neededthe selection of a regulator polynomial on a trial and error basis. Control input has aconsiderably high variance and they claimed that it is due to biasness of the estimatedcutting process parameters caused by noise, unmodeled dynamics of the peak holdingdevice and lack of excitation after changes in depth of cut. An effort to avoid this problemby changing the regulator polynomial resulted in sluggish transients. Kim and Huang [19]designed a pole placement controller considering the non minimum phasedness of cutting.This controller performed well over a wide range of cutting conditions. However locationsof closed loop poles had to be carefully selected to have better performance. Also theyfound that when the closed loop characteristic polynomial was selected to get fastertransient response, that caused oscillations in the controller output. Barthel and Shin [20]used an approach based on quasi direct adaptive control of Lozano and Landau [21]. Thisalso needed very careful selection of the regulator polynomial for relatively fast yet welldamped disturbance rejection. Weighting factor for control input needed a number ofcomputer simulations. Pien and Tomizuka [22] used a similar approach for cutting forcein 2-D milling.Jung and Oh [23] showed with a fixed parameter PT controller that surface accuracyin machining can be improved by regulating the average cutting force in the directionnormal to the cutting direction. Spence and Altintas [24] developed an adaptive poleplacement controller which used information from the parts CAD representation to knowChapter 2. Literature Survey 12part geometry changes before they actually occur. They smoothed the geometric information and supplied to the adaptive controller and then used a milling force model tocalculate the CAD assistance forces which were added to the actual on line measurementto safely reduce the feed rate before the actual geometry change occurs. The objectiveof this method was to avoid transient overshoots during sudden geometry changes andwas successful in achieving the objective.This thesis investigates the application of an adaptive optimal control strategy basedon Generalized Predictive Control method[GPC] of Clarke et al. [25] [26] in controllingpeak resultant milling forces. The control methodology predicts the plant output overseveral steps ahead and attempts to eliminate the predicted error between the referenceand the predicted outputs. Therefore the method does not need predetermination ofany characteristic polynomials like in MRAC or pole placement adaptive control. Theparticular model structure used inherently introduces an integrator in to the controllerand this eliminates the necessity to either add an integrator in an ad-hoc way to thecontroller or to use a zero phase error tracking part in series with the closed loop system toeliminate steady state tracking errors [20]. The method is very well suited to machiningsince it can control non minimum phase plants with unknown dead time. Like poleplacement self tuners, performance is not affected by over estimation of the plant orderand therefore is portable from machine to machine quite easily. This is very importantwhen the algorithm is integrated to an open architecture CNC since they are designedto run on a multitude of machine tools.2.3 Tool Breakage DetectionOne of the most important monitoring requirements in an unmanned manufacturingsystem is to detect tool breakages in-process and take prompt action to avoid furtherChapter 2. Literature Survey 13damages to the work piece and the machine tool itself caused by the broken tool. Inthe studies done so far researchers have basically used three approaches in an attempt todevelop a robust tool breakage detection algorithm. They are time series model approach,comparing average cutting forces over tooth periods and very recently the neural networksapproach.An excemption is Moriwaki’s attempt to use acoustic emission to detect a tool breakage [27]. However Altintas [28] showed that the use of acoustic emission is not practicalbecause entry and exit of the tool to and out of the workpiece can also produce similaracoustic emission bursts which may have even higher amplitudes which will make theseparation of an actual tool breakage from entry and exit transients difficult.Matsushima et al. [29] used a very high order autoregressive model(AR[28]) on thespindle motor current of a milling machine to detect tool breakages. A sudden jump inthe amplitude of the residuals of the model was attributed to a tool breakage. A similarapproach was used by Lan and Naerhiem [30] (AR[15]) using the feed forces in milling.It was noticed by Altintas [28] that the high order AR models are due to unsynchronizedcollection of current and force data with the spindle. One disadvantage of these highorder AR models is that they require larger time periods for calculations. Therefore theyare not applicable in future high speed machine tools unless ultra fast microprocessorsare used. The other disadvantage is that they forget the breakage event very fast.Using fundamental milling characteristics Altintas [28] showed that low order timeseries models can be used for tool breakage detection in milling. He showed that the timeseries has to be only long enough to cover one tooth period in order to have a reasonablyaccurate prediction. The low order AR models were possible with the synchronization ofdata collection and spindle speeds using a spindle shaft mounted encoder as a samplingclock. He first used the periodic nature of milling forces to remove deterministic dc andac components and used a time series to model the remaining part which is a functionChapter 2. Literature Survey 14of the cutter run-out and the measurement noise. A sudden increase of the measuredcutting force over the predicted value was attributed to a tool breakage. To increasethe computational speed he averaged forces over each tooth period, which automaticallyremoved the periodic pulsation. The remaining deterministic trend was removed bycomparing average force over one tooth period with the average at previous tooth period.A first order time series model was sufficient to model these first differences to detect atool breakage by considering the difference between measured and predicted differences.The method was enhanced later by using normalized first differences instead of firstdifferences to remove the effect of axial depth of cut, the feed rate and the cutter constantson first differences. To efficiently separate the entry and exit transients from a toolbreakage event second differences were used [31]. To set a threshold for normalized firstdifferences which will include the effect of run-out Altintas and Yellowley [32] used amilling force model to simulate an immersion related variable and used this variable insetting up the threshold. This eliminated the need of a trial cut to set the tool breakagedetection threshold of normalized first differences. Later on, Altintas [33] showed thatto avoid practical difficulties in measuring cutting forces in an industrial environment,feed drive current can be used instead with a first order time series model to detect toolbreakage.Tarng [34] proposed an algorithm based on the frequency content of the instantaneouscutting force in milling. He showed that all the frequency contents corresponding to a toolbreakage lies between dc and tooth passing frequency and therefore cutting force signalwas low pass filtered to extract those frequencies. This tool breakage zone containedfrequency contents of run-out also. A measure of the standard deviation of this filteredcutting force signal, above what is expected from a good tool was used to detect a toolbreakage. This algorithm is computationally expensive since the calculation of standarddeviation need a considerably larger window of force samples. Also every machiningChapter 2. Literature Survey 15operation will need a trial cut to set a threshold of the standard deviation.Revolution-oriented Processing Approach(RORPA) algorithm developed by Principeand Yoon [35] in contrast uses displacement of the tool in two perpendicular directions todetect a tool breakage. Displacement over each tooth period was averaged to smoothenit and residuals between it and an average over a number of revolutions before was calculated. The duration that the algorithm remember the tool breakage depends on thisnumber of revolutions. They used a median filter to extract slowly time varying component related to transients from displacement residuals and then subtracted that fromthe original displacement residuals to obtain the tool breakage, run-out and noise relatedcomponent. This breakage related component was normalized with the slow time varyingcomponent mentioned above and another variable related to mean displacement signalover a revolution to remove the dependence on the cutting conditions. The normalizedbreakage related component was thresholded to detect a tool breakage. However theyfound that the algorithm produces false detections if the milling speeds are higher, dueto increased noise levels. They were developing a hierarchical subsystem for their originalfour TMS32OC2O processors based tool breakage detection system to avoid this problem.The way the subsystem corrects the problem is not clear.Tarng and Lee [36] used only first differences of average cutting force over each toothperiod as proposed by Altintas [28] to detect a tool breakage. Thresold was calculated offline based on the first differences calculated using a mechanistic milling force model withan allowable amount of run-out on the tool, added to an estimated maximum level ofnoise. The axial and radial depth of cuts necessary for the calculation of first differencesfrom the force model was estimated by geometrical modeling. This algorithm is simpleand should work well if the set threshold can represent the actual machining with agood tool closely enough. However every machining operation need the calculation ofthe corresponding threshold off lineChapter 2. Literature Survey 16Vierck and Tiusty [37] used four main features of the milling forces named AV (averagecutting force over each tooth period), PD (first differences of cutting forces), AC (accomponent of the raw cutting force signal), DC (dc component of the raw cutting forcesignal) to detect a tool breakage. They first calculated first difference sum (PDS) whichis the sum of all negative and all positive FD’s over a spindle revolution and it wasdivided by DC to remove the effect of cutting conditions on FDS. A threshold value wasdetermined based on the DC/AC and then applied to FDS/DC to detect a tool breakage.However the calculated empirical thresholds (thresholds are functions of DC/AC) werevalid only for the particular number of teeth on the cutter they used. Also the thresholdvalue gave false alarms at exit transients when the radial immersion was high. Thereforestill this algorithm is not at a stage applicable to real milling.Recently Tansel and Maclaughlin [38] proposed an algorithm based on a time seriesmodel of the cutting force. A sampling rate of 40-90 samples per tooth period was usedto predict the cutting force at any sampling period using a 20-24 order time series model,based on the parameters of the time series estimated at the end of previous tooth period.They used the sum of squares of prediction error (SSPE) of the cutting force over a toothperiod to detect a tool breakage. If the SSPE has a periodic fluctuation with a highermagnitude, that was attributed to a tool breakage. However they could not come up witha scheme to interpret the SSPE and therefore the algorithm is not applicable yet. On theother hand even if one develops a way to interpret SSPE, with 40-90 samples per toothperiod even at low spindle speeds a sampling period would not be enough to calculatemodel parameters at the end of each tooth period. Also since the model order is lessthan at least the number of samples in one tooth period, the accuracy of this model isquestionable.Most recent approach in tool breakage detection is to apply neural networks [39] [40].However the neural networks have to be trained for all the available kinds of tools andChapter 2. Literature Survey 17their failure modes. Obtaining data for all possible modes of tool failure is not an easytask and hence this is not a practical approach to the problem.In this thesis a quite simple yet fast algorithm for tool breakage detection is implemented with HOAM-CNC. Algorithm is based on the approach used by Altintas [28],but, uses an improved adaptive threshold. Chapter 3 explains details of the algorithm.2.4 Chatter Detection and Suppression2.4.1 ChatterChatter is a from of unwanted self excited vibration in metal cutting. It affectssurface finish, dimensional accuracy, tool life and the machine life. Basic characteristic ofthe self excited vibrations is that the forces acting on the vibrating system are dependenton the motion of the system itself. This characteristic distinguishes the chatter fromforce vibrations. Mode coupling and Regeneration of waviness are the two main sourcesof self excitation in metal cutting [41].Mode coupling can only be associated with situations where the relative vibrationbetween the tool and the workpiece can exist simultaneously in at least two directions.Figure 2.1 shows the mechanism of mode coupling using a single point turning operation.If the tool vibrates simultaneously in the directions X1 and X2 with the same frequency and a phase shift between the two, that results in an elliptical motion as shown.Assume that the tool moves on the elliptical path in the direction shown by the arrow.The cutting force F has the direction shown. Then, for the part of the periodic motionof the tool from A to B force F acts against this motion and takes energy away. FromB to A force drives the tool and imparts energy to its motion. Because motion B to Ais located deeper in the cut , the force is larger than for the motion from A to B andtherefore energy delivered by the force F to the periodic motion in B to A motion isChapter 2. Literature Survey 18Figure 2.1: Mechanism of mode coupling (Koenigsberger and Tlusty, 1970)larger than the energy taken away in the A to B motion. Thus periodically there is asurplus of energy sustaining vibrations against the damping losses.Regeneration of waviness, shown in figure 2.2 is caused by an oscillating tool removinga chip from an undulated surface left by the tool in the previous pass.If there is relative vibration between tool and workpiece, that surface will have wave-ness. The tool in the next pass encounters this surface and removes a chip with periodically variable thickness. The cutting force which is proportional to the chip thickness willtherefore be periodically variable. This produces vibrations and depending on conditionsderived further on, these vibrations may be at least as large as in the previous pass. Thenew surface again is wavy and in this way waviness is continuously regenerated.x1\ x/2m/Chapter 2. Literature SurveyLimit of Stability for Regenerative Chatter19Chatter mainly develops through regeneration of waviness in machining operations.Machining is called stable if any initial vibration diminishes in subsequent passes orunstable if any initial vibration increases and remains constant at the limit of stability.In the figure 2.3 the machine tool is shown as a frame M. It carries the tool on oneend and the workpiece on the other end which implies a relative cutting motion in thedirection ‘v’ between the two. Chip thickness (h) is assumed to be modulated by thepresent vibration (y) as well as by the vibration left by the previous cut (yo)(the innerand outer modulations respectively).where hm - mean uncut chip thickness.h = hm+yoy= hm+h (2.1)h is the variable dynamic component of the chip thickness and,Figure 2.2: Regeneration of surface wavinessh = Y0YChapter 2. Literature Survey 20MFigure 2.3: Diagram for deriving limit of stability (Koenigsberger and Tiusty, 1970)Since the modulations are harmonic , the vibrations can be represented by,Yo = Yosirz,(wt)y = Ysin(wt + 27rN + e) (2.2)where N and e are full and fractional number of waves between two passes.The cutting force F has the direction inclined by /3 from Y and its magnitude is assumedproportional to chip width a(normal to the plane of the paper) and to chip thickness h:F = K3ah (2.3)= Kgahm + K8ah= Ksahm + K3a(yo—y) (2.4)= Fm+Fu (2.5)Chapter 2. Literature Survey 21where the dynamic force component is,F,, = K3a(yo—y) (2.6)The total force, like the chip thickness, is the sum of a mean component (Fm) and avariable component(F,,). The cutting force coefficient K8 is considered real and ‘a’ beingreal anyway this means that the force is in phase with the chip thickness variation (yo—y).The process of self excitation is a closed loop system and is presented in the blockdiagram shown in figure 2.4.Realtive vibration between tool and the workpiece is produced through the corresponding transfer function G(w) by the variable component of the force(F,j.y = F,,G(w) (2.7)At the limit of stability any vibration would remain constant without decaying or increasing. The absolute values of amplitudes of vibrations in subsequent passes are equal.This leads to,Figure 2.4: Block diagram of vibration in regenerative cuttingYo = (2.8)Chapter 2. Literature Survey 22Substitution of the result of equation 2.8 in equations 2.6 gives,F = K5ay(e3— 1) (2.9)Then equation 2.7 is simplified to get,K3aG(w)(1 — e) = —1The value of the chip width a at the limit of stability is,ajtm = _1/K30(1 — ei6) (2.10)Since K3 is real and a is real, the equation 2.10 is satisfied if,G(1 — e) = G — (2.11)is real.Since e_jw is a unit vector,IC! = fCe_ivhI (2.12)Therefore condition in equation 2.11 will be satisfied(see figure 2.5) if,G(1 — e) = 2Re(C) (2.13)and Re(G) < 0. Hence at the limit of stability [41],aiim = —1/2K3Re(G) (2.14)If the phase shift e is left to take any value the equation 2.14 does not determine aunique value of aiim and chatter may occur at many frequencies at many values of aiim.Chapter 2. Literature Survey 23GeG(1 eJE )Figure 2.5: Conditions at the limit of stabilityThere will be a minimum of those aiim values, which represent the border line stabilitywhich is called the critical limit of stability and can be given by,(aj:m)mtn = (—1/2K3Re(G))mjn(aj:m)mtn = 1/2K3Re(G)ztm (2.15)Where Re(G)ztm is the absolutely maximum negative value of Re(G). Above analysisshowed that the critical depth of cut is very much dependent on the structural dynamicsof the machine tool. Though the analysis was done for a simpler model, this dependencystill holds true for milling.ImReChapter 2. Literature Survey 242.4.2 Stability LobesFor milling, N and the phase shift e (see equation 2.2) can be related to the chatterfrequency and spindle speed by the geometrical relationship,f C= N+— (2.16)mm 27rwhere, f chatter frequencyn = spindle speedm = number of teethm = 1 for turning.With a knowledge of the structural parameters of the machine tool, considering equation 2.16, variation of limiting depth of cut against a variable related to cutting speed canbe obtained [42]. Tiusty calls the graphical representation of it stability lobes. Figure 2.6shows a typical stability lobe curve with the spindle speed on the abscissa.The horizontal line that connects all the lowest points on the stability lobe curvesmarks the critical limit of stability. From the stability lobes it can be seen that thereare spindle speeds at which stable cutting can be sustained at depth of cuts well abovethe critical stability limit. At these cutting speeds the phase shift (e) is such that theregeneration of waves is minimized.2.4.3 Stability of the Milling ProcessStability of the actual milling process is not as sharply defined as shown in theanalysis of section 2.4.1. Many factors unaccounted for in that analysis makes the prediction of stability limit in milling much more difficult. Milling is an intermittent cuttingprocess and therefore the transition between stable and unstable milling is blurred by thetransient natural vibrations excited at every tooth period even below the limit of stability. Also the magnitude and direction of the cutting force, instantaneous chip thickness,Chapter 2. Literature Survey 250‘I0-c0CL)Spindle Speeds for Higher StabilitySpindle Speed(n)Figure 2.6: Typical stability lobe curvedirection normal to the cut, all change with time which were considered time invariantin the calculation of the limit of stability.Another phenomenon that increases the limit of stability at 1or cutting speeds isprocess damping. Physically process damping is due to the interference of the tool flankwith the slope of its motion in the cut. This is shown in figure 2.7. In position t the tool ismoving upwards and there is enough clearance between it and the surface it has just cut.In position 2 it moves into the material and the clearance is diminished. The increasedthrust cutting force acts against the velocity of the motion and generates damping [43].2.4.4 Sensors for Chatter DetectionIn the past researchers have used a variety of sensors to detect chatter. They areforce sensors, displacement related sensors and microphones.Rahman [44] used a tool post dynamometer, a proximity sensor and a microphoneto detect onset of chatter in turning. He set the speed of detection as the criteria toI ICritical Stablity LimitChapter 2. Literature Survey 26select the best sensor and concluded that the proximity sensor is the most suitable forchatter detection. However placement of a displacement probe on an active point forall expected chatter modes is a difficult task. To name a few of the difficulties, the toolspindle system may vibrate in different directions at different times depending on thechanges of structural dynamics that result from different attachments and tools on thespindle. If a chatter frequency is not located near a mode present in the cutter sensortransfer function, sensitivity to the vibration is reduced. Sensor may be placed at a nodalpoint of the chattering mode of vibration.Generally dynamometers have low bandwidths and it is further degraded when aworkpiece is mounted on them thus distorting the cutting force signal from unstablemachining or high speed machining. Additionally the sensitivity of the dynamometermay be insufficient to detect the relatively low cutting forces thus resulting in low signalto noise ratio which will make the differentiation of chatter and normal cutting difficult.Use of a microphone to capture the sound emanating from the vibrating structureto detect the chatter vibrations do not have most of the difficulties associated withdisplacement related sensors and dynamometers. It detects vibrations emanating fromany point on the machine due to any mode of vibration. Microphones have been usedfor real time detection of chatter by some researchers [45j [46] and proven to be a betterFigure 2.7: Sources of process dampingChapter 2. Literature Survey 27sensor for chatter detection than others mentioned [47].However there are problems associated with the microphones caused by reverberantand near field effects. It has been suggested to place the microphone far enough away fromthe source so that the source can be assumed as a point source. Also a microphone picksup background noise, and may corrupt the sound emanating from the cutting process.Arrangements to avoid these problems have been suggested by Delio et al [47]. In thisthesis a single microphone placed close to the cutting process is used to detect chatter.2.4.5 Suppression of ChatterChatter has been a severe problem in machining and therefore, still there is on goingresearch to find ways to avoid or suppress chatter. Research can be divided into threeareas.• Design of machine tools• Design of cutters with different geometries• Manipulation of cutting variablesAs shown in the derivation of the stability limit, by decreasing the real part of the negative transfer function of the machine tool structure, the stability limit can be increased.Physically this means increasing the dynamic stiffness of the machine tool across therequired frequency range.In milling specially, to increase the stability limit various cutter designs have beenattempted. Cutters with variable tooth pitch are known to increase the stability bydisturbing the phase between inner and outer modulations. The concept of non uniformpitch have been extended to end mills with different helix on adjacent teeth. It is reportedthat these cutters gave better stability limits with improvements in speed ranges [45].Chapter 2. Literature Survey 28However the pitch spacing of teeth in the case of variable pitch cutters or the variationof helixes depend upon the cutting conditions and workpiece geometry. Therefore it isnecessary to prepare many cutters with different tooth pitch variations and helixes, whichis very expensive to take full advantage of this method.Most of the attempts to improve stability by manipulating cutting variables have beenwith the spindle speed. Continuous variation of the spindle speed to improve stabilityhas been analyzed [48] and implemented in orthogonal cutting [49]. The same strategywas simulated for milling by Lin et al. [50]. They found that a sinusoidal variation ofthe spindle speed is the best in terms of trackability because a sinusoidal speed variationdoes not need the motor to have higher angular acceleration and angular jerk capabilities. Further higher speed variation frequencies and amplitudes of speed variations werenecessary for lower natural frequencies. However most of the existing machine spindleshave very low band widths, thus placing a limitation on the applicability of this method.Altintas and Chan [45] oscillated the spindle speed only when chatter is present to stabilize cutting. They also concluded that for good performance spindle speed oscillationrequires a high torque spindle drive with a higher bandwidth. Another approach was toiteratively adjust the spindle speed so as to achieve stable milling. Speed was adjustedsuch that the tooth passing frequency is equal to the dominant frequency in the chatterdetection sensor output spectrum if such a region exists [46] This method needs veryhigh spindle speeds to make the stabilization effective and is therefore, applicable to onlyhigh speed milling.In this thesis, as Weck [51], suggested the depth of cut is reduced until the cuttingprocess becomes stable. This is applicable to low bandwidth, low torque spindles that arein use today. Reduction of depth of cut is the surest way to avoid chatter. Disadvantage ofthis method is additional cuts are required and the milling capacity is reduced. Howeverstill this provides an increase in milling capacity over conventional milling operations.Chapter 3Process Monitoring and Control3.1 Adaptive Control of the Peak Resultant Cutting ForceThe block diagram of the adaptive control system is shown in figure 3.1. The plantto be controlled consist of two parts. They are time varying cutting process and the timeinvariant feed drive servo system. In adaptive control, generally, the parameters of onlytime varying parts are estimated on line. However in this application a problem arises ifonly the parameters of the cutting process are estimated in real time, because then theparameters of the discrete transfer function of the feed drive servo has to be calculatedevery time the sampling period is changed.Figure 3.1: Block diagram of the adaptive force control systemThe sampling period of adaptive control is equal to the tooth period or spindle period.PredictedoutputProcessparametersFrReferenceCutting forceFeed Drive_____CuttingFServo Process Mimum cuttingforce29Chapter 3. Process Monitoring and Control 30Therefore, every time the spindle speed is changed, it is necessary to evaluate the discretetransfer function of the feed drive servo. In milling, spindle speed is necessary to bechanged quite often, for example, when machining different materials or when the spindlespeed is oscillated for chatter avoidance. In the latter case the calculations would haveto be done very frequently in real time, which would be numerically costly. In order toavoid this problem two parts are combined and the parameters of the combined plantare estimated in real time.3.1.1 Modeling of the Milling ProcessMilling is a cutting process where a workpiece clamped on a table is fed againsta rotating multitooth cutter to remove excessive material from the workpiece. Teeth ofthe milling cutter intermittently enters and exit the workpiece and while engaged, eachtooth removes a chip with a varying thickness(see figure 3.2).Y.4xFigure 3.2: Geometry of end millingChapter 3. Process Monitoring and Control 31As a result, each tooth is subjected to a time varying force which is given by tangentialand radial force components [28].F = K3ah (3.1)Fr = KrFt (3.2)where, F - tangential cutting force componentFr - radial cutting force componenta - axial depth of cuth - uncut chip thicknessK3, Kr - specific cutting pressure, and force ratio which are workpiece material and- tool geometry related constant.For an individual tooth i tangential and radial force components can be resolved into Xand Y directions, which can be given as,F(q) —Fcosq — FrSiTLq5i (3.3)F(ç) = Frcosq — Fsinq2 (3.4)whenever 4st 4 < i.e when the tooth is in cut. If the feed rate is ft, the uncutchip thickness at any time is h = ftsinçb2.Therefore the magnitude of the instantaneous resultant cutting force acting on thetool can be given by,F(ç) = [(F())2+ (F(4))2]°5 (3.5)where z is the total number of teeth on the cutter.The instantaneous resultant cutting force is periodically varying with a frequencyequal to the tooth passing frequency of the cutter. As could be seen in the derivations, itChapter 3. Process Monitoring and Control 32is dependent on the feed rate, axial depth of cut and the radial width of cut. Axial andthe radial depth of cuts are workpiece geometry dependent and may change continuouslyalong the cut. Therefore, the magnitude of the instantaneous resultant cutting force alsowill vary accordingly in addition to its periodic variation. To avoid shank breakage ofthe cutter the criteria to be regulated is the peak value of the resultant cutting force.In finishing operations the peak value of the force normal to the finish surface must beregulated in order to constrain errors caused by static deformations of the tool withinthe dimensional tolerances of the part. The time varying transfer function between peakforce over a tooth period and the feed rate has been structurally modeled in [24] usingthe Tlusty’s static deformation model [41] in discrete form [13] and is included below forcompleteness.Using equation 3.5 at tooth period j the peak value of the instantaneous resultant cuttingforce can be approximated by,F(j) = Kahm(j) (3.6)where K is a specific cutting pressure related constant, hm(j) is the apparent maximumchip thickness and is dependent on the width of cut. In machining the cutter deflects inthe direction of the resultant cutting force. Assume the component of deflection of thecutter in the direction opposite to the feed is S(j)(see figure 3.3)The apparent maximum chip thickness over a tooth period can be defined as,hm(j) = b[ft(j1)_S(j)+8(j1)] (3.7)where, b is a parameter dependent on the width of cut. The relationship between thepeak force and the deflection is,F(j) = k3S(j) (3.8)Chapter 3. Process Monitoring and Control 33(j-1) (i)———— —7 77)_____ __f (j-1)F) tFigure 3.3: Model variables of the milling processwhere, k8 is designated as the oriented end mill stiffness in the direction opposite to thefeed motion. Equations 3.6, 3.7 and 3.8 are combined to give,F(j) . F(j) F(j-1)T71 L — ft(i — 1) — + 7 (3.9)n8aoDefining = Kab/k3tand then by rearranging equation 3.9,( + 1)F(j) - F(j -1) = kstft(j -1) (3.10)using the backward shift operator z1 and defining,—p k8p (3.11)1+p l+pthe discrete transfer function between the peak resultant cutting force over a tooth periodand the feed rate can be obtained form equation 3.10 as,G(z1)= = 1 (3.12)Chapter 3. Process Monitoring and Control 34p and q varies with the changes of the part geometry. Since a peak force is formed onceat each tooth period, the sampling period of the adaptive control algorithm should beequal to a tooth period. However in practice all teeth of the milling cutter are not equal.Different run-out on each cutting edge will cause the peak force over each tooth periodto differ. Therefore if the adaptive control algorithm is run at every tooth period, feedrate may try to follow oscillations of the peak force due to run-outs of cutting edges. Inorder to avoid this problem spindle period is used as the sampling period of the adaptivecontrol algorithm.3.1.2 Modeling of the position Control LoopThe milling machine used in the experiments has three linear feeding axes. Each axishas a recirculating ball screw drive with its own travel limits (For x, y and z directions60 cm, 40 cm and 12 cm respectively). All three axes are driven by Baldor PWMpermanent magnet dc servo motors, which are directly connected to the lead screw shafts.Adaptive control algorithm sends a new command feed rate to the CNC system at everyspindle period. This causes the position error on each axis to change accordingly resultingin a change of the analog reference voltage of the velocity control loop(see figure 3.4).The loop closure time of the position control loop is 0.2 ms. This is much smaller thanthe adaptive controller update time which is a spindle period. Therefore the digital leadlag filter can be approximated by its continuous equivalent using Tustin’s approximation.Then the feed drive servo can be modeled in the Laplace domain neglecting the zero orderhold.The lead-lag filter in the laplace domain can be presented by,D(s) = If(sf,;) (3.13)Chapter 3. Process Monitoring and Control 35Zero Order Gain ofLead-lag Filter Hold D/A Velocity LoopVelocity control loop is modeled using its step response. A first order system reasonably fits the experimental response. Figure 3.5 shows the actual and the model responsesof the velocity control loop of the z axis for a step of 1 V.A number of such experiments were done within the linear and non linear regions ofthe current amplifier of the velocity control loop and found that the first order systemcan model the response with a reasonable accuracy. However in the non linear region ofthe current amplifier the time constant increases with increasing step size due to limitedacceleration. The transfer function of the velocity control loop can be written as,KG,(s) = (3.14)TS + 1where, K is the gain and r is the time constant of the velocity control ioop. Thereforethe open loop transfer function of the position loop can be given by,C ( — D(S)KdGv(S)Ke— K’(s + a’) 3 150Sj— s — s(s + b’)(s + c’)where,K’ KIKdKKe1C = —TX (counts)Figure 3.4: Position control loop for a single axisChapter 3. Process Monitoring and Control 36Figure 3.5: Actual and model responses of the velocity ioop of z axisTherefore the closed loop transfer function of the position control loop can be given by,Gf(s) — G0(s) —1+G0(s) —K’(s + a’)s(s + b’)(s + c’) + K’(s + a’)K’(s + a’)=3 + (b’ + c’)s2 + (b’c’ + K’)s + K’a’ (3.16)Characteristic equation of the position loop is,+ (b’ + c’)s2 + (b’c’ + K’)s + K’a’ = 0 (3.17)Response of the position control ioop is dominated by the two complex conjugate polesof the characteristic polynomial given by equation 3.17. Therefore the position ioop isapproximated by an underdamped second order system(see Appendix B).Gf(s) =s2+2ws+w.0 0.02 0.04 0.06 0.08 0.1 0.12Time (sec)(3.18)Chapter 3. Process Monitoring and Control 37where, w - undamped natural frequency- damping ratioZero order hold equivalent of Cf(s) can be given by the model structure,Gf(z’) = z(b + bz’) (3.19)1 + az 1Therefore, by combining equations 3.12 and 3.19, the plant to be controlled can be givenby,G(z’) Gf(z’)G(z’) (3.20)— z2(qb’0+ qb’1z’) 3 21— (1 + az’)(1 + pz)= z2(b”o + b”iz’) (3.22)1 + a”1z+ a”2z’The model of the cutting process (G(z)) is developed considering that the input andthe output of the cutting process are discrete at tooth periods or spindle periods. Therefore in the model given by equation 3.22 there are two delays. But in reality the input tothe cutting process which is the feed rate, is not discrete. Therefore actual delay from thecommand feed to the peak force is less than one sampling period. The transfer functionof the combined plant is modified accordingly.G— F(j) — z’(bo + b1z’ +b2z) (3 23Z—f(i) — (1 +a1z +a2z)31.3 Parameter EstimationThe key property of an adaptive controller is to track variations in process dynamics.In order to do so parameters of the process should be identified with a good accuracy.Exponential Forgetting Recursive Least Squares(EFRLS) algorithm has been used widelyfor estimation of parameters of time varying processes. With the EFRLS method oldChapter 3. Process Monitoring and Control 38data are discounted at a rate determined by the forgetting factor. The basic recursiveequations of the method are,=ê(t — 1) + k(t)(F(t) —— 1)) (3.24)k(t) P(t — 1)qS(t)(A + g5T(t)P(t — 1)qS(t))’ (3.25)P(t)=(I — k(t)bT(t))P(t — 1)/) (3.26)where, 9(t) - estimated parameter vectork(t) - estimation gainP(t)- co-variance matrix- forgetting factor( E 0.95, 0.99)qS(t) - regression vector or observation vectorFor this method to work well, process should be excited by the input properly at all times.However, in the case of force adaptive control, if the part geometry does not change forsome time, this condition is not satisfied because the process does not change. This willcause the estimator to forget the proper values of the parameters, and the uncertaintyin estimation will grow. This is called estimator windup. One way to avoid this problemis to reset the covariance matrix of the EFRLS algorithm at regular intervals. Howeverthis causes unnecessary transient fluctuations in the peak resultant cutting force if thecovariance resetting coincides with a change in the cutting process. Therefore, in order toavoid above problems a version of the constant trace algorithm is used for the estimationof process parameters. The recursive equations of the algorithm are given below.= (t—1) + a(t)k(t)(F(t) — q!,T(t)O(t—1)) (3.27)k(t) = P(t — i)(t)(i + q5T(t)P(t— 1)q5(t)) (3.28)P(t) = P(t—1) — a(t)k(t)qT(t P(t—1) (3.29)Chapter 3. Process Monitoring and Control 39P(t)P(t)= Cltr(p(t)) + c21 (3.30)a(t)= 41 if jF(t)— T(t)(t— 1) > 25 (3.31)0 otherwisewhere,P(t) - auxiliary covariance - trace of the auxiliary covariance matrixand other variables are same as for EFRLS algorithm.c1 > 0, C2 0 and S is an estimate of the magnitude of the tolerable fluctuation ofthe output of the process or noise. a , ci, c2 are selected as, a=0.5, c1 =5•o/4Tq andcl/c2 iO.With this algorithm if the process is not properly excited a(t) becomes zero. Thiskeeps the parameters unchanged and the covariance matrix is constrained so that whennew information comes again, the estimation is restored without any problem.3.1.4 Adaptive Control AlgorithmAs mentioned before since the peak resultant cutting force over one spindle revolutionis regulated in this implementation, the sampling period of the adaptive control algorithmchanges when the spindle speed is changed. At higher spindle speeds this makes itnecessary to increase the number of delays in the plant model. Also it is desired to havefast response at transients when there is a change of the cutting process. Another factorto be considered is the possibility of having non minimum phase zeros in the discretetransfer function of the process as a result of sampling.An adaptive PID controller would not work in all cutting conditions, because the controller is basically tuned to cancel zeros of the plant and if the plant has non minimumChapter 3. Process Monitoring and Control 40zeros they become poles of the controller thus making the control input unstable. Poleplacement self tuners perform badly if the plant has dead time changes. GeneralizedPredictive Control method [25] has been shown to work well with all the conditions mentioned above by simulations and is therefore considered here for force control in milling.It is devised for an Auto Regressive Integrated Moving Average Exogenous (ARIMAX)model. Assumption of this model naturally adopts an integrator to the controller thuseliminating steady state offsets. This avoids the necessity to add an integrator in anad-hoc way like with many other controllers. Therefore the plant model is rearranged tobe in the form,A(z’)F(t) = B(z1)f t — 1) + (3.32)where,A(z’) = 1 +a1z +a2zB(z’) = b0 + b1z + b2z= (1—z’)(t) is assumed to be an uncorrelated random sequence. Then a k step ahead predictorfor F(t) based on equation 3.32 can be obtained using the identity,1 = Ek(z’)At + z_vFk(z_l) (3.33)deg(Ek(z’)) = k — 1deg(Fk(z1)) = deg(AL) — 1where, Ek and Fk are polynomials uniquely defined given A(z) and the predictioninterval k. Once they are calculated for one value of k simple iterations can be usedto calculate them for all other k. Then k step ahead predictor for F(t) is obtained asfollows.Chapter 3. Process Monitoring and Control 41Multiplying equation 3.32 by EkZzk gives,EkALF(t + k) = EkBIXf(t + k — 1) + Ek((t + k) (3.34)and substituting for EkAZ from equation 3.33 gives,F(t + k) EkBLf(t + k — 1) + FkF(t) + Ek(t + k) (3.35)All the noise components are in the future and therefore provided that the output dataup to time t and f(t + k — 1) are available, the optimal predictor can be given by,+ k) = EkBzf(t + Ic — 1) + FkF(t) (3.36)Let, Gk(z’) = EkB+ Ic) = Gk(z1)1Xf(t + Ic — 1) + FkF(t) (3.37)Let F(t+k) be that component of F(t + k) composed of signals which are known up-totime t. Then from equation 3.37, for k = 1, 2....,F(t + 1) = [Gi(z1)— giojzf(t) +F1(t) (3.38)F(t + 2) = [G2(z’) — z’g21 —g2o]f(t) +F2(t) (3.39)where, Gk(z’) = gko + gklz +In this optimal control strategy a quadratic cost function containing future predictederrors of the output and incremental control inputs over the control horizon consideredis minimized [25] [26].N2 N1(f, t) = E > [E(t + k) — Fr(t + k)]2 + ?. [if(t + k — 1)12 (3.40)k=N1 k=1Chapter 3. Process Monitoring and Control 42The minimum output horizon N1 is selected as 1, because the plant dead time changeswith the spindle period. The maximum output horizon N2 is selected as 4 so that it ishigher than the order of the B(z’) polynomial and covers rise time of the plant. Thecontrol horizon N is selected as 1. Then the control law that minimizes the above costfunction can be given as,1f(t) = [OrG + ;\I]’ GT(F1 — F) (3.41)where,giG F(t+1) F(t+1)g21 Fr(t+2) F(t+2)Fr= F= (3.42)g32 F(t + 3) F(t + 3)g43 Fr(t+4) F(t+4)Fr - reference force vector over the prediction horizon.3.2 Tool Breakage DetectionAs mentioned in section 3.1.1 it is known that instantaneous cutting forces are periodic with the tooth passing frequency. For tool breakage detection average cutting forcesover each tooth period are monitored [28]. This not only reduces the calculation effortrequired over the algorithms that use the instantaneous cutting force at each samplingperiod, but also acts like a low pass filter on the instantaneous cutting forces and removesthe periodic pulsation. Average forces are calculated by,F(j) = [Fg(i)]/n (3.43)Fay(j) = [F(i)]/n (3.44)Chapter 3. Process Monitoring and Control 43where, n - number of samples of the instantaneous cutting force per tooth- periodF(i) - Measured i th sample of the instantaneous cutting force in x- direction at j th tooth periodF’(i) - Measured i th sample of the instantaneous cutting force in y- direction at j th tooth periodFax(j) - average cutting force in x direction at j th tooth periodFay(j) - average cutting force in y direction at j th tooth periodAlgorithm then calculates the average resultant cutting force Fa() over each tooth period,which can be given as,Fa(j) = + Fay(j)2 (3.45)With an ideal tool and a perfect workpiece, F0(j) should remain constant during steadystate machining if the axial depth of cut and the radial width of cut are constant. Thismeans that the first order differences of the average resultant cutting force should be zeroduring steady state machining [52].LFa(j) = Fa(j) — Fcj(j — 1) = (1 —q1)Fa(j) = 0 (3.46)LFa(j) can be non zero only if there is a chipped tooth on the cutter because thetooth following the damaged tooth has to remove the extra material left by the damagedtooth. This will increase the load on the tooth following the damaged tooth and hencethe average force over that tooth period resulting in non zero first differences. Thereforea tool breakage should able to be identified within a tooth period by monitoring the firstdifferences.However in reality these first differences are non zero due to two reasons. First is dueto rapid changes in the workpiece geometry(axial depth of cut and radial width of cut)Chapter 3. Process Monitoring and Control 44between successive tooth periods. These changes could occur when the tool enters andleaves the cut, machining over holes and slots etc. Although these lead to sudden changesin the peak resultant cutting force, variation of the average forces are rather slow andthe effect of them on the first differences can be removed by filtering the first differenceswith a first order adaptive time series filter. Residual forces of the filter can be given by,= ZF(j) — — 1) = (1 — (3.47)where q5 is estimated from measurements LFa(j) using exponentially weighted leastsquares estimation method at each tooth period.The second is the influence of run-outs which can cause large variations in residualforces Ei(j) when the local chip thickness and the immersion are small. Unless the run-outs of cutting edges and the local immersions are exactly known it is difficult to define athreshold to detect a cutter breakage from the residuals of the first order filter when thelocal chip thickness and the immersion are small. To overcome this difficulty, repeatingaverage force patterns over each spindle revolution can be used. If the average forceone revolution before is subtracted from the current average force value, the influence ofrun-outs can be eliminated. This represents the comparison of the cutting performancesof the same tooth in successive spindle revolutions.ZmFci(j) = Fa(j)_Fa(j —m)= (1 —qm)Fa(j) (3.48)where m is the number of teeth on the cutter. However these differences have the effectof geometric transients embedded in them. To remove them as much as possible now asecond first order time series filter is applied. Then the residuals of this second filter canbe given by,2(j) = (1 —q,2_l)JmF(j) (3.49)If a tool breakage event occurs, the filter given in equation 3.47 will persistently producehigh residuals thereafter, and the second filter given in equation 3.49 will produce aChapter 3. Process Monitoring and Control 45large residual spike but will eventually adapt to the chipped cutter after one revolution.To set thresholds for residual forces from both filters to detect a tool breakage, theproposed algorithm monitors the residual forces during the first five revolutions. Twicethe maximum amplitude of residual forces from each filter in those five revolutions areused as their respective thresholds. Whenever both residuals simultaneously violate theirthresholds, it is attributed to a tool breakage event.To demonstrate the effectiveness of the algorithm two end milling tests were carriedout with a good tool and with a tool having one chipped edge. Both tools had samespecifications. Part geometry for both tests were same. Geometry of the workpiece isshown in figure 3.6. Specifications of the end mill and cutting conditions used are givenin Table 3J.Cutter Cutting ConditionsDiameter 25.4 mm Workpiece Al 7075-T6Number of flutes 4 Feed rate 0.1 mm/toothHelix angle 300 Spindle speed 566 rpmMaterial HSS Depth of cut 7.62 mmTable 3.1: Test specifications for the demonstration of tool breakage detection algorithmTwo data sets were carefully assembled to illustrate a tool breakage event. Figures 3.7to 3.9 shows the measured average forces and residual cutting forces. Slow variations ofthe average force in figure 3.7 is due to geometric changes in the part. High frequencylow amplitude oscillations are due to run-outs of cutting edges. High frequency largeamplitude oscillations after tooth period 1138 is due to chipped edge.It can be seen from figure 3.8 that the first order time series filter applied on the firstdifferences removes all geometric transients. First order time series filter applied on 4thdifferences removes the oscillations produced by run-outs of the cutter(see figure 3.9). AtChapter 3. Process Monitoring and Control 46/8Figure 3.6: part geometry for the tool breakage detection algorithmthe tooth breakage event both filters violate their thresholds. However residuals of thefirst filter consistently violate the threshold while the second filter eventually adapts itselfto the damaged cutter. Tooth breakage event can be accurately detected by consideringthe residuals of both filters simultaneously for violation of their thresholds.3.3 Chatter Detection and SuppressionFor chatter detection, sound emitting from the machining process is used. For themachine tool used in the experiments, background noise is not excessive. Sound resultingfrom chatter vibrations of the cutting process is much stronger than the backgroundnoise. Therefore a single microphone located at a distance of about 6 inches is used tomeasure the sound pressure level. Fast Fourier Transform of the captured sound signalis calculated in real time at each chatter detection cycle.Figure 3.10 shows the variation of the maximum amplitude of 50 consecutive 256point frequency spectrums in stable and unstable machining with the cutting conditionsshown in table 3.2.L 126 50All dimensions in millimetersChapter 3. Process Monitoring and Control 47900800700600500S 400asLJ 3002001000-1000-200-245-400-600Figure 3.7: The measured average force over each tooth period2000400 800 1200 1600 2000Tooth Period (j)40024520000 400 800 1200 1600Tooth Period (j)Figure 3.8: Residual cutting forces of the first order filter applied on first differencesCutter Cutting ConditionsDiameter 15.875 mm Workpiece Al 7075-T6Number of flutes 2 Feed rate 0.0508 mm/toothHelix angle 300 Spindle speed 1500 rpmMaterial HSS Depth of cut, With chatter 8.89 mmOverhang 76.2 mm Depth of cut, Without chatter 2.54 mmTable 3.2: Specifications of the end mill for demonstration of chatter detectionIt can be seen from the figure 3.10 that the maximum amplitude of the spectrum ismuch larger for machining with chatter vibrations than without chatter vibrations. However it is oscillatory, because the reduction of the number of points in the time recordto 256 to avoid time constraints in this particular test reduce the frequency resolution.A threshold can be set for the maximum amplitude of the spectrum of the sound signal to detect the presence of chatter vibrations, based on the maximum amplitude ofChapter 3. Process Monitoring and Control 48300214200100- 0—100-200-214-3000 2000Figure 3.9: Residual cutting forces of the first order filter applied on fourth differences400 800 1200 1600Tooth Period (j)Ea)C,)1)-0ci)VD.1ESSxChapter 3. Process Monitoring and Control 495045403530252015105 10 15 20 25 30Chatter Detection Cycle35 40 45 50Figure 3.10: Variation of maximum amplitude of the spectrum of soundthe spectrum in chatter free machining. If the maximum amplitude of the spectrum ishigher than the preset threshold, immediate action is taken to hold the feed followed byautomatic reduction of depth of cut by a specified amount and then the NC program ismodified to ensure the removal of total programmed material. Machining is restarted andspectrum of the sound signal is checked again for chatter at the next sampling period ofthe chatter detection algorithm. If the chatter is found, again the depth of cut is reducedand the NC program is modified to remove the original programmed depth of cut [51].Chatter control system reduces the depth of cut until the chatter is fully avoided.Chapter 4Integration of Monitoring and Control Modules to HOAM-CNC system4.1 IntroductionThe value of an Open Architecture system over a closed architecture CNC lies on,1. The ability to integrate new functions to it.2. The ability to Port the CNC to another machine tool.3. Free availability of machine and system parameters within the CNC systemfor use by new functions added to it.In order to achieve above goals the hardware and software should be built from widelyavailable commercial standard components and should be very modular and scalable.Modularity makes the ability to develop, diagnose and repair and porting systems easy.Scalability allows the addition of new features and functions when needed. However ifthe user has to spend considerable efforts in re-designing and understanding low leveldesign details of the CNC system, its wide use in new applications would not be feasible.Therefore not only an open architecture system should meet the requirements of integration of new applications, interoperability and portability, but also should adapt to othermachines and processes in a short development time period.50Chapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 514.2 HOAM-CNC SystemThe HOAM-CNC system is the open architecture machine tool controller designedand build in the manufacturing automation laboratory of UBC [5] [2]. This CNC system has been built using off the shelf available components with very modular hardwareand software. Additional hardware and software modules can be added without majormodifications thus enabling the integration of new functions to the CNC system easily.Control System and Machine parameters are readily available for new applications toaccess and manipulate if necessary. This fulfills the requirements of interoperability orin other words free availability of the system and machine parameters within the openarchitecture CNC system. Very modular design of software of the HOAM-CNC systemenables the portability of the system to other platforms with a minimum effort.4.3 Hardware Layout of the HOAM-CNCThe global system architecture of HOAM-CNC is shown in figure Real Time MasterAs shown in figure 4.1 Real Time Master is the in-charge of the main bus whichis an intel 80486 processor based 33MHz computer in the present system. Main bus isthe standard ISA bus of the 486 PC. There are several processor boards or sub systemson the main bus. Each subsystem is dedicated to a specific task such as real timedata acquisition, adaptive force control, chatter detection and suppression. Additionalsubsystems can be integrated to the system as long as, they can be handled by the RealTime Master within the bandwidth of the main bus. It has been estimated that 6-10such subsystems can be handled by the real Time Master within its practical 2 Mbytes/sChapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 52CAD/CAM SystemReal-Time Master AT 486Processing UnitMain Bus (ISA Bus)___I I___ _______Adaptive Chatter Tool Force Data CNC Master ControllerControl Detection Condition Processing • ‘ - Real Time Job ManagerSystem System Monitoring System - High Level Control andSystem Interpolation Operation(TMS32OC3O DSP Chip)CNCBusAxis 1 Axis 2 - - Axis n80C1 96KC MicrocontrollerFigure 4.1: Global System Architecturetransfer rate [5].4.3.2 Sub SystemsCNC MasterCNC master controller is the core subsystem on the main bus and it is a Spectrum C30 board employing Texas Instruments TM5320C30 processor. This board has64 Kwords of SRAM of which 16 Kwords are dual ported, a user development sectionand a memory mapped secondary bus which is called the DSP link. The CNC masterhas a duty to provide a precision NC tool path trajectory and velocity values to eachaxis controller.CNC master communicates with intel 80C196KC embedded controller based axiscontrollers using the dual ported memory of each axis, which is mapped to the DSP-linksecondary bus [2]. DSP link is called the CNC bus in the HOAM-CNC implementation.Chapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 53DebuggingCommunicationsLocal Serial PWM and D/A MotorMemory Port outputs CommandIntel 80C196KC High Speed16 bit Microcontroller Inputs/External SynchronizationDSP Interrupts Quad Decoderlinkua__________________ _______________PortSRAMAnalog to Digital High Speed SynchronizationConverters Outputs Amplifier SignalsAnalog Position Signals!Force and CurrentFigure 4.2: Axis controllerA theoretical data transfer rate of 5 Mwords/s is possible. This may be much below thislimit in practice. Each axis controller has 1 K by 16 bit dual ported SRAM, RS232 serialport , 4 A/D converters, 3 PWM outputs, 4 high speed digital inputs and outputs , aquadrature decoder input and a number of interrupt lines for synchronization. Figure 4.2shows the layout of axis controllers.Process Monitoring and Control Sub SystemsIn the present system there are two other subsystems on the main bus dedicated toprocess monitoring and control.One of them is an Intel 8096 processor based real time force data acquisition board.This board has an A/D converter which samples the cutting forces measured by a forceChapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 54dynamometer in two orthogonal directions x and y at a frequency of 10KHz. The processor calculates the average forces and retains the peak values of the instantaneous cuttingforces in both x and y directions and instantaneous resultant cutting force, over a perioddetermined by an external interrupt. The pulse for this interrupt is generated by a spindle mounted encoder or a signal generator. The force values are available to any othersub system or the Real Time System Master. The other sub system is Texas Instrument’sTMS320C25 processor based Dalanco Spry model 25 board with one A/D channel forchatter detection. The board samples the voltage signal produced by the microphonelocated close to the cutting process at a frequency specified by the user, and stores inthe data memory of the RAM (maximum possible sampling frequency is 110 khz). Theprocessor then calculates the Fast Fourier spectrum of the data stored in the memory.This Fourier spectrum of the sound pressure signal is available to any other sub systemor the Real Time Master.4.4 Software OrganizationFigure 4.3 shows software organization of the HOAM-CNC system. HOAM-CNCsystem has to perform two main functions, accurate tool path control, and machiningprocess monitoring and control tasks. Associated with these functions there are fourdistinct software components. Except axis control software all software components arewritten in turbo C. Axis control software has been written in 80196 assembly to keep thespeed, because the speed of intel 80C196KC processor is an order of magnitude less thanthat of TM5320C30 DSP [2].Chapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 55- AxisO*-Axis1As2System MasterUser CNC InterfaceInterface ModuleNetworking AdaptiveInterface Control ModuleChatter Tool MonitorModule ModuleCNC MasterIRPCPipeI./RPC DStdio Pipe FetchData Pipe_________r JobMail Boxes Manaer)4Position LinearMonitor InterpolationSpline CircularInterpolation InterpolationFeedrate User DefinedControl JobApplicationsOther HOAMSubsystemsFigure 4.3: The Software Architecture of the HOAM-CNC system4.4.1 System MasterThe System Master software is running in the Real Time Master PC. It consistsof the user interface and the CNC interface module and coordinates various subsystems.System master communicates with the CNC master through shared memory pipes andmail boxes. In the current system memory pipes and mail boxes are both implementedin the C30’s dual-ported memory. Any task on the system master may access thesecommunication facilities and send or receive data with the CNC master.Memory pipes are used only for less time critical communications. For time criticalcommunications mailboxes are used, because they provide very fast real time parameterpassing. This feature can be used by other sub systems for “on-the-fly” feed changes,machine status changing and monitoring the machining operation and status. For theseapplications memory pipes are not suitable, because a full pipe may produce undesirabledelays in the response.When the system master program is executed it initializes each subsystem accordingChapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 56to data found in an initialization file. This initialization file tells the program about,what data to be sent to each subsystem. In the case of CNC, a profile of each axis isloaded followed by the code and initial conditions that each axis requires. This axis codeare interchangeable and therefore allows a greater flexibility to the end user.After the CNC subsystem is initialized, the initialization task creates the user interfacefor RTM to CNC master communications. User interface has two levels: a high level partprogram mode and a low level debugging mode. Part program mode enables loading andediting a part program and making of the part. Debugging mode allows the user toset parameters of the CNC, test new algorithms and monitor events within particularsubsystems.4.4.2 CNC MasterCNC master software runs on the TMS32OC3O based DSP subsystem. It provide facilities to communicate with the axis and distribute work to the axis controllers, performhigh level interpolation, synchronize interpolation and digital control algorithms runningon each axis controller and allow user applications to run. CNC master has a number ofbasic function blocks that the user has implemented for each of the applications and theyare registered with the RPC mechanism on the CNC master side allowing the systemmaster to call any of these functions. These function blocks are related to either toolpath control or process control and monitoring tasks and are called remote procedures.When system master requests CNC master to run a certain job application, it essentiallyis asking the CNC master to run the corresponding remote procedure. The job manager, which is a minimal real time operating system within the TMS32003O based DSPsub system, identifies the job application by its RPC tag and insert it in a job queueaccording to its priority. Job manager executes all the jobs possible within a 1 ms timeslice and remaining and any new jobs are rescheduled for the next time slice. Figure 4.4Chapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 57shows the task switching by the job manager in the case of a Remote Procedure Calling.To ensure that all the jobs eventually get executed, if a job gets rescheduled because ofits low priority, priority is increased every time it is rescheduled [2].4.4.3 Axis Control SoftwareAxis control software provides the interface between the HOAM-CNC system andthe real world machine. All the routines in axis software are interrupt driven. When C30interrupts each axis for synchronization of interpolation, axis software simply iterates theselected interpolation scheme and carry out target error correction. At the T2CAPTUREinterrupt which is a pulse sent to all axis controllers by one of the High Speed Outputinterrupts of an axis control processor, all the axis close the position control loop andcalculates the input to PWM based D/A converters subjected to 8 bit upper and lowerlimits. When a linear move is finished, each axis sets the axis status to ready andacknowledge to the CNC master so that it can send the parameters of the next linearmove if there is any. However digital control of all the axis is always active once the CNCmaster is initialized and the position is controlled at the current absolute value of eachaxis.4.4.4 Process Monitoring and Control SoftwareProcess monitoring control software consists of an adaptive control module, tool breakagemonitoring module and a chatter detection and suppression module.Chapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 58Adaptive Control ModuleAdaptive control software module is presently running in RTM. It receives themaximum force per spindle revolution from the dedicated Intel 8096 processor basedforce data collection system on the main bus. It then uses the adaptive control algorithmexplained in section 3.1 to calculate the necessary feed rate which will maintain the actualpeak cutting force at the specified reference level. This computation is done once perevery revolution. CNC interface module writes the new feed rate to a mail box and setthe feed change flag in the Dual port RAM of the CNC master and RTM interruptsthe CNC master to indicate that a feed change has to be executed. At the interruptjob manager of the CNC master identifies the feed change job by the specific flag andcalculate the new period of the interpolation pulse it sends to axis controllers. Feedchange is executed by changing the clock period to the calculated new period.Though this module is presently running in the RTM, it is portable completely totswchexitt‘C‘CwaitJob RequestEventFigure 4.4: Task switching by the job managerChapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 59a subsystem on the main bus which will run the algorithm in the subsystem itself andrequest system master only to execute the feed change.A pseudo-code of the algorithm is given below.Initialization of Adaptive Control• Initialize the co-variance matrix and auxiliary co-variance matrix.P[O] = iOi, P[o] = iOi• Initialize the parameter vector.ê[O] = [0.01 0.01 0.01 0.01 0.01]• Initialize the observation vector.[O] = [0.0 0.0 Vmao/4 0.0 0.0]where, Vmax is the maximum allowable feed speed.• Reset the force flag.(This flag is set if the force drops below 80 N and resets afterthree revolutions from the time it increases above 80 N again. Thus if this flagis set and force is above 80 N it indicates that the cutter is entering a geometricchange after a low force region. In such a case the feed rate is reduced to a thirdof the maximum allowable feed rate to avoid excessive force overshoots).fflag = 0• Reset the spindle revolution counter.i=0• Reset the temporary counter.m=0Chapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 60Adaptive Control Algorithm• Update the force (F,) and command feed (fe) variables.F[i—2]=F[i—-1], F[i—l]=F[i]f[i—3] =f[i—2], f[i—2]=f[i—1], f[i—1j =f[i—0]• Check the peak flag register on the data acquisition subsystem. If set, read inregisters with peak forces and reset the peak flag.F[i] = peakforce(this could be the peak in X-direction, Y-direction or resultantpeak)• Form the observation vector.[i] = [—F[i—1] — F[i — 2] f[i — 1] f[i — 2] f[i — 3]]• Estimate parameters of the plant using the constant trace estimation algorithm.Ô[i] = [ai a2 b0 b1 b2]• Use the GPC algorithm to calculate the command feed rate.If F,[i] 80 N then f[i] = Vmaz and fflag = 1If F[i] > 80 N and,1. f.flag= 1, then f[i] = Vmax/3 and m=m+1if m= 3, then fflag= 0 andm = 02. fflag = 0,If f[i] > Vmaz, f[i] = VmaxElse if f[i] < 0, f[i] = 0Else f[i] = Calculated command feed• Write the f[i] to a mail box in the Dual port RAM of the CNC master.• Set the feed change flag on the CNC master.Chapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 61• Interrupt CNC master to execute the feed change.• Increment spindle revolution counter.jzj+’Tool Breakage Detection ModuleThis module is also presently running in the RTM. The module receives the averageforce over each tooth period from the dedicated force data collection system on the mainbus. Module keeps average force data over a period of one revolution in to the past fromthe current tooth period. As explained in section 3.2 first differences and differencesof average forces m tooth periods apart(m is the number of teeth on the cutter), arecalculated from the average force data. Both differences are filtered with first order timeseries filters to remove the effects of geometrical transients from them. A tool breakageis detected depending on the magnitude of residuals from both filters. If a tool breakageis detected RTM set the emergency stop flag in the CNC master and interrupts the CNCmaster to indicate the cutting operation has to be immediately stopped. CNC masterimmediately removes all interpolation jobs from the job queue and stops all axis drives.Though this module is presently running in the RTM it can also be ported to adedicated processor on the main bus quite easily so that dedicated tool breakage detectionsystem will be independent of the RTM and will seek the assistance of the RTM only ifa tool breakage is detected, to stop all feed drives.A pseudo code of the algorithm is given below.Initialization of Tool Breakage Detection• Initialize covariance matrices.P1[O] = iOi, F2[O] = iOIChapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 62• Initialize parameters of two filters.= 0.01, 2[O] = 0.01• Initialize average forces.Fa{01 = 0.0, Fa[1] = 0.0 Fa[m1 = 0.0• Initialize differences of average forces.ZFa[0] = 0, ZmFa[0] = 0• Initialize residual forces.ej[0] = 0,62[0] = 0,• Initialize tooth period counter.j=0Tool Breakage Detection Algorithm• Update variables.F0[j — 21 = Fcz[j — 1], Fa[j — 11 = Fa[j]LFa[j—1] = LFa[j], LmF[j — 1] =ZmF[j]• Estimate parameters of two time series filters. q5 [j] and 2 []• Calculate the residuals of first order and m’th order differences of average forcesfrom two first order time series filters.ei[j] = LXF[j} qiiFa[j—11= mF[j] ——1]• If e[j] >thresholdl and e2[j] >threshold21. Set the emergency stop flag on the CNC master.Chapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 632. Interrupt CNC master to execute the emergency stop.• Increment the tooth period counter.jj+1Chatter Detection ModuleChatter is detected by monitoring the maximum amplitude of the spectrum ofmachining sound with a dedicated Texas Instruments TMS320C25 processor based DSPboard as explained in section 3.3. Collection of the electrical signal produced by themicrophone, storage and calculation of the Fast Fourier Transform of the collected datais done in the dedicated chatter detection board. Other parts of the module are presentlyrunning in the RTM.If chatter is detected chatter module will request CNC master to stop all feed drivesfollowed by a reduction in the depth of cut by a small step. Since the depth of cut isreduced to get rid of chatter the NC program is then modified so that the intended fulldepth of cut is removed. This procedure is repeated every time the chatter detectionalgorithm is run, until the chatter is fully gotten rid of. Then machining continues onthe modified tool path.A pseudo code of the algorithm is given below.Initialization of the Chatter Detection and Suppression• Input sampling frequency and chatter threshold.• Set the period of the timer on the chatter detection subsystem to the samplingperiod.• Reset the chatter cycle counter.k=OChapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 64Chatter Detection and Suppression Algorithm• Down load the data acquisition code to the chatter detection subsystem.• Set the board in operation and acquire a 256 point long time record of the microphone signal.• Halt the chatter detection subsystem and transfer the time record of the microphonesignal to the RTM.• Window the time record and down load to the data memory of the chatter detectionsubsystem.• Down load the code for 256 point FFT calculation.• Set the board in operation.• When the FFT calculation is finished transfer real and imaginary parts of thespectrum to RTM• Calculate the amplitude at each frequency point and find the maximum amplitude.• If maximum amplitude> threshold,1. Command an emergency stop of all the axis.2. CNC master: Put the NC block being executed in the standard out memory pipe and wait for the RTM to acknowledge the collection of it at theRTM end of the pipe.3. CNC master: Put the absolute position at the start of the execution ofthat block in the standard out pipe.4. RTM: Collect the absolute position at the start of the current NC blockfrom the standard out pipe.Chapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 655. Execute a move in the z direction to reduce the depth of cut.6. Modify the NC program using information obtained in 2 and 4 above sothat the total depth of cut will be divided into a number of passes withthe reduced depth of cut.7. Execute the new part program.• Increment the chatter cycle counter.k=k+14.4.5 Parallel Execution of the Process Monitoring and Control AlgorithmsThree process control and monitoring algorithms are running in parallel with motioncontrol. With the input of the command “adapt” from the user interface, system masterruns initialization routines of three algorithms. On completion of initialization, eachof the initialization routines set a flag to indicate the system master that the controlroutines are ready to run.The period of each monitoring and control function is set by the user as a numberof tooth periods. In the present system at each tooth period force detection subsystemsets a flag which is read by all process monitoring and control modules and the systemmaster. A pulse from a spindle encoder or a signal generator is used to interrupt theforce detection sub system to set this flag. Adaptive control module counts tooth periodsby reading and resetting the flag. This count is also available to all process monitoringand control modules and the system master.Once the initialization is finished, system master executes a shell of three monitoringand control routines at each tooth period. However only when the tooth count is correctfor the next cycle, each algorithm gets included in the shell of monitoring and controlroutines.Chapter 4. Integration of Monitoring and Control Modules to HOAM-CNC system 66When process monitoring and control routines are executed, if a tool breakage isdetected as explained in section 4.4.4 all the axis are immediately stopped. This isfollowed by termination of all process monitoring and control functions.Chapter 55.1 Experimental SetupExperimental ResultsHOAM-CNC with process control modules was interfaced to a milling machine forperformance evaluation. Experimental setup is shown in figure 5.1.Figure 5.1: Experimental setupTo chatter detection system/signalsignal from themicrophoneForce Data ProcesdngSystemAdaptive Control and Tool ConditionMonitoring SystemAxis Controller No. 0Axis Controiler No. nCNC Master ControllerChatter Detection SystemIndustrial ATComputer67Chapter 5. Experimental Results 685.1.1 Milling Machine and Position Control SystemsThe Slo-syn vertical knee type milling machine has a 5.5 kw ac motor connected tothe spindle gear box. Spindle can run at 16 fixed speeds of 39 - 1500 rpm. Three linearfeeding axes x, y and z have recirculating ball screws with 60 cm, 40 cm and 12 cm travellimits. Axes are driven by Baldor PWM permanent magnet DC servo motors which aredirectly connected to lead screw shafts with a pitch of 5.08 mm. Specifications of themotors are given in table A.1 of Appendix A. Each motor is equipped with integralvelocity (tachogenerator) and 4000 counts per revolution position (optical encoder) feedback units. Machine parameters of each axis are shown in table 5.1.Pitch of the lead screw p 5.08 mmBasic unit of displacement 1 count 0.00127 mmTable 5.1: Machine parametersA complete block diagram of the position control system for a single axis is shown infigures A.1 and A.2. The control system has two control loops: velocity control loopwhich consist of analog amplifier, dc motor and the tachogenerator for velocity feed backand the position control loop which combines the velocity control loop with the digitallead-lag filter, D/A converter and the optical position encoder units. The digital controlloop is updated every 200 ts time intervals. Parameters of the position control loop forx axis are given in table A. Peak and Average Force Detection SystemAs explained in chapter 3, adaptive control needs the peak cutting forces over eachspindle revolution and the tool breakage detection algorithm needs the average forcevalues over each tooth period. These need first the measurement of instantaneous cuttingChapter 5. Experimental Results 69forces and then retaining the peak and calculating the average forces as necessary overrequired time periods. Therefore the peak and average force detection can be divided into two parts: Measurement of cutting forces and detection of peaks and averages.Measurement of Cutting ForcesThe workpiece in all experiments were mounted on a quartz three component Kistler9257A dynamometer for measuring three orthogonal components of the cutting force.The dynamometer has great rigidity and therefore has a very high natural frequencywhich is claimed to be above 4000 hz. However this natural frequency decreases whenthere is an additional mass i.e work piece on the dynamometer. The milling table has tobe cleaned very well before mounting the dynamometer so that the setting up of internalstresses and hence additional loads on individual measuring elements are avoided.The force transducers of the dynamometer produces charges that are proportional tothe forces that the dynamometer is subjected to, in each direction. These charges areconverted to output voltages proportional to the forces sustained, by charge amplifiers. Inthe experiments to be explained in this thesis, Kistler dual mode 5004 charge amplifierswere used. This type of charge amplifiers have 12 calibrated ranges. Measured amplitudeis linear up to 0.05 % of the full scale output. -3 db bandwidth is 180 khz and the noiseat output is 10 hz to 330 hz. The calibrated range has to be selected depending on theexpected range of forces to be measured.Cables connecting the dynamometer to charge amplifiers are special coaxial cableswith high insulation resistance and low capacitance which generates only a negligibleamount of charge when moved. End connectors too are robust, highly insulating andtemperature resistant.Chapter 5. Experimental Results 70Peak and Average DetectionPeak and average force detection system is a process monitoring and control subsystem on the main bus. It is an intel 8096 processor based in house designed and builtcard which has a 12 bit analog to digital converter. It samples the output voltages ofcharge amplifiers at a frequency of 10 khz. Charge amplifier outputs are low pass filteredat approximately four times the tooth passing frequency to remove high frequency noisebefore being sampled. Sampled charge amplifier signals are used to calculate the averageand peak values of the forces in x, y directions, and the resultant peak force over a periodspecified by the user. The period can be specified as a number of pulses generated bya spindle mounted encorder or a function generator which interrupts the processor. Afunction generator is used to produce the interrupt signal in this implementation.5.1.3 Chatter Detection SystemChatter detection system consist of a microphone and a TI TMS320C25 processorbased Dalanco Spry model 25 Digital Signal Processing board. The microphone capturesthe sound pressure emitting from chatter vibrations during machining. The DSP boardis used to sample analog sound signal and compute its Fast Fourier Transform in realtime.The advantage of using a microphone to detect chatter using the sound pressureemitting from the cutting process is that it is not in the way of actual cutting. Microphoneis basically a collector of sound, taking acoustical energy and converting it to electricalenergy. Microphone used in these experiments is a moving coil, or in other words adynamic microphone with a bandwidth of approximately 50 hz to 13 khz. Structure ofa moving coil microphone is shown in figure 5.2. This consists of a coil which has a fewturns of wire. The coil is attached to and suspended by a plastic diaphragm which isChapter 5. Experimental Results 71supported along its outer circumference. The diaphragm is free to slide back and forthalong a strong magnet. Thus when a sound wave pushes against the diaphragm, thatproduces a voltage across the ends of the coil. This voltage is indicative of the chattervibrations and is the signal sampled by the DSP board for chatter detection subsystem.DiaphramChatter Detection SubsystemChatter detection subsystem is a Texas Instruments TMS320C25 DSP based DalancoSpry model 25 board. The board has only 544 16-bit words of on chip RAM of which288 words are data memory and the remaining 256 words are program memory. Thisseverely restricts the size of a program that can run on the board and the amount ofdata that can be stored on the board at a time. Therefore the board cannot be usedas a completely independent sub system. The functions of the subsystem was limitedto sampling the voltage signal produced by the microphone and calculation of the FastFourier Transform of the windowed microphone signal. The 12 bit analog to digitalconvertor of the board can sample an analog signal at a frequency up to 110 khz.Figure 5.2: Basic structure of the moving coil microphoneChapter 5. Experimental Results 72In this implementation board samples the sound signal at a frequency higher than 2.5times the possible chatter frequency. Possible chatter frequency is estimated by measuringthe transfer function of the tool spindle system at the tip of the tool. Sampled time recordof the voltage signal is stored in the data memory of the board. The chatter detectionsoftware module running in the RTM receives the sampled sound data and windows thedata to avoid leakage of signal energy when the frequency spectrum is calculated. Thewindowed voltage signal is down loaded to the chatter detection subsystem and the boardcalculates its Fast Fourier Transform. Real and complex parts of the FFT are received bythe coordinating part of the chatter software module running in the RTM PC and findsthe maximum amplitude of the spectrum with the corresponding frequency. Chatteris detected by comparing the measured maximum amplitude with the predeterminedthreshold value of the amplitude for stable cutting.The total execution time of the chatter detection depends on the sampling frequencyand the number of samples in the time record of the sound signal. If the samplingfrequency is low and the number of samples is high that increases the time taken by thechatter detection module to complete one cycle. This lengthens the periods of adaptiveforce control and tool breakage detection since those two modules completely run in theRTM. To avoid this problem it was necessary to reduce the length of the time recordand increase the sampling frequency. These changes should be done carefully so thatthe frequency resolution is still sufficient for the detection of chatter vibrations. Thesampling frequency is related to the frequency resolution by,(5.1)where LS.f = frequency resolution of frequency spectrumf3 = sampling frequencyChapter 5. Experimental Results 73Cutter Cutting ConditionsDiameter 19.05 mm Workpiece Al 7075-T6 alloyNumber of flutes 4 Type of cut half immersion up millingHelix angle 00 Spindle speed 885 rpmMaterial HSS Feed rate 0.01 mm/toothOverhang 74.0 mm Depth of cut 2.54 mm for stable cutting6.35 mm for unstable cuttingTable 5.2: Specifications of the end mill and cutting conditions for demonstration ofsetting the chatter thresholdN = the number of samples, usually a power of 25.2 Chatter ThresholdSetting a threshold for the maximum magnitude of the frequency spectrum of thevoltage signal produced by the microphone is one of the important factors in chatterdetection. Figures 5.4 and 5.5 show the frequency spectrum for half immersion up millingcuts at 885 rpm using an end mill with specifications and cutting conditions given intable 5.2 for stable and unstable cutting.Figure 5.4 shows the spectrum of sound signal for a stable cut with a depth of cutof 2.54 mm. No large amplitude vibrations appear in the spectrum. However two smallvibration peaks can be seen around 550 hz and 2250 hz. These small peaks are transientvibrations which occur every time a tooth enters the cut due to tooth impacting on thethe work piece. These vibrations occur around the two frequencies mentioned, becausethe tool has two natural modes around 550 hz and 2000 hz as can be seen in figure 5.3.Figure 5.3 shows the transfer function of the tool in the y direction. The mode around2000 hz is the most flexible mode that produce large amplitude vibrations which is thetool mode. Therefore chatter vibrations with this cutter can be expected at a frequencyzECU)Eci)0C,)0U)D02Chapter 5. Experimental Results 74x1O’9876U)050LLU)V2<100Figure 5.3: Transfer function of the tool in y directionlittle higher than this frequency. Also it is evident that the spectrum does not have toothfrequency or its harmonics, which indicates the absence of forced vibrations.Figure 5.5 shows the frequency spectrum of sound for an unstable cut with a depth ofcut of 6.35 mm. The low frequency spectrum is typically identical to that of figure 5.4.However chatter produces a large peak in the spectrum at about 2250 hz as expected.Amplitude of this large peak is much larger than that in the frequency spectrum of thestable cut. Therefore chatter can be detected by setting a threshold for the maximumamplitude of the spectrum of sound signal produced by the microphone. This thresholdis predetermined from chatter free, i.e stable cutting tests.Frequency (hz)>24-C)a)Cl)a)4-0a)-D4-0E24-0a)0C’)ci)-4-0U)4-EFigure 5.4: Frequency spectrum of sound for stable cutting3000Chapter 5. Experimental Results 7530 -25 -20 -15 -10 -500 500 1000 1500 2000 2500 3000Frequency (Hz)Frequency (Hz)Figure 5.5: Frequency spectrum of sound for unstable cuttingChapter 5. Experimental Results 76Cutter Cutting ConditionsDiameter 25.4 mm Workpiece Al 7075-T6 alloyNumber of flutes 4 Depth of cut 9.0 mmHelix angle 30° Spindle speed 885 rpmMaterial HSS Reference cutting force 300 NWidth of cut 19.00 mmTable 5.3: Specifications of the end mill and cutting conditions for adaptive control testin the non linear region of the cutting force5.3 Experimental Results5.3.1 Performance of the Adaptive Control Algorithm in Non Linear Regionof the Cutting ForcesMilling forces are not linearly proportional to the chip thickness at low feed rates.First to investigate the performance of the adaptive control algorithm in this non linearregion a test was conducted by machining an Aluminum 7075-T6 alloy workpiece withonly adaptive cutting force control. The cut was straight in the x direction of the tableand had no changes in the geometry. Test conditions and the specifications of the usedend mill are given in table 5.3.Figure 5.6 and 5.7 show the variation of the peak resultant cutting force over eachspindle revolution and the variation of the command feed speed.From figure 5.6 it can be seen that the peak resultant cutting force is very wellmaintained at the reference level by the adaptive control module. Variation of the feedspeed(see figure 5.7) is also smooth though it remains at very low values throughout thecut. Therefore it can be concluded that though a linear cutting force model is assumedfor the full range of operating conditions still the proposed adaptive control algorithmfor milling is capable of controlling the peak resultant cutting force well in the non linearChapter 5. Experimental Results600001Figure 5.7: Variation of command feed speed- Machining incutting forces600600the non linear region of77z500400300200U)- 100U)0100 200 300 400 500Spindle RevolutionFigure 5.6: Variation of peak resultantof cutting forces3cutting force - Machining in the non linear regionC) 2.5U)222U)1.5c5E20C) 0.50300Spindle RevolutionChapter 5. Experimental Results 78Diameter 15.875 mmNumber of flutes 2Helix angle 300material HSSOverhang 76.2 mmspindle speed 1500 rpmTable 5.4: Specifications of the end mill for pocket machiningregion of cutting mechanics where the milling fores are not linearly proportional to thechip load.5.3.2 Machining of a PocketA pocket was machined under the supervision of HOAM-CNC with adaptive forcecontrol, tool breakage monitoring and chatter detection and suppression. The dimensionsof the pocket with the tool path is shown in figure 5.8. Depth of the pocket is 6.35 mm.Specifications of the end mill are given in table 5.4.Workpiece material was aluminum 7075-T6 alloy. End mill had a stiffness of 3162N/mm in the x direction where, the flutes lie and 2238 N/mm in the y direction which isthe no flute direction. During milling, teeth locations change as the cutter rotates, andtherefore, stiffnesses in x and y directions change. However, they will lie between theabove two values.Intelligent Pocketing StrategyAs shown in figure 5.8 walls of the pocket were machined first and then the island wasremoved. Rapid feed was set at 7.62 mm/sec. A conservative feed of 1.9 mm/sec wasprogrammed for initial penetration in to the part. Along the walls of the pocket peakforce normal to each wall was controlled. In removing the island peak resultant cuttingChapter 5. Experimental Results 79force was controlled. Reference level of the peak cutting force was set at 270 N for wallsto limit the surface error due to static deflection to 0.1 mm. a higher 600 N referencewas used for the island to avoid shank breakage of the end mill.A special strategy was used to avoid force overshoots when cutter penetrates theworkpiece during the cut after moving in the air. The strategy sets a flag if for somereason the peak resultant cutting force drops below 80 N. When the force increases above80 N and if the flag is set the feed speed is reduced to a third of the maximum allowedvalue thus avoiding the tool crashing in to the work piece after moving in the air at rapidfeed. Flag is reset after 3 adaptive control cycles.Step size of the reduction of depth for chatter avoidance was programmed at 1.0 mm.The threshold for the magnitude of the spectrum of sound for chatter detection wasdetermined experimentally and set at 16. Measurements of the machined pocket showsthat the dimensional errors are 0.095 mm and 0.065 mm across the walls of the pocketwhich are within the set tolerance of 0.1 mm.Adaptive Cutting Force ControlAdaptive control module manipulated the feed once every spindle revolution tomaintain the resultant cutting force at the specified reference levels. Figures 5.9 and 5.10shows the variation of the controlled peak resultant cutting force and feed during thefirst pass of the pocketing operation.In figure 5.9 three small overshoots are due to reduction of the depth of cut for chatteravoidance. At four corners of the pocket about a 25 % overshoot in the peak resultantcutting force is seen due to end mill entering the new direction of cut at higher feed ratesdue to reduction of the peak cutting forces. As shown in figure 5.8 point 5 to 6 on thetool path no material is removed and therefore the table moves at the maximum feed(see figure 5.10). When the tool starts to enter the island at point 6 to remove the island,Chapter 5. Experimental Results 80_-., !1IL. —- áA .1LI LiiL IIi I I1000 1500Spindle RevolutionF43.81mm1_cIi)oD33Figure 5.8: Machining of the pocket800., 700zw600050040030O200010000 500 2000 2500Figure 5.9: Variation of peak resultant cutting force - Machining of the pocketChapter 5. Experimental Results 818G)LI.CuE2E01C.)00Figure 5.10: Variation of the command feed - Machining of the pocketovershoot avoidance strategy avoids the force overshoot by reducing the feed. Howeverthis was not effective at corners of the pocket, because the peak resultant cutting forcedid not drop below 80 N.As seen in figure 5.10, each time the depth of cut is reduced to avoid chatter, the feedspeed increases to maintain the peak cutting force at the reference level.Figure 5.11 shows the estimated parameters for the first pass of the pocketing operation. From the variation of parameters it can be seen that once the parameters haveconverged to their steady values, algorithm automatically turns off the estimation untilthere is a new change in the cutting process. If there is a change in the cutting process,for example a reduction in the depth of cut, the estimation algorithm senses it from themeasured cutting force, which will deviate from the reference level more than a prespecifled amount. This helps to reduce unnecessary fluctuations in the cutting force caused bysmall variations of parameters as would be experienced with other estimation algorithms.500 1000 1500 2000 2500Spindle RevolutionChapter 5. Experimental Results 82Tool Breakage DetectionFigures 5.12, 5.13 and 5.14 shows the variations of average cutting force, residuals ofthe first order time series filter applied on first differences of the average cutting force andthe residuals of the first order time series filter applied on the second order differences.Second differences are considered because, the end mill has only two flutes.Figure 5.13 and 5.14 show that the residuals of both the filters are well within theirown thresholds set by the algorithm during the first five revolutions. Therefore the toolbreakage detection system did not produce any false alarms.Chatter Detection and SuppressionFigure 5.15 shows the variation of the maximum amplitude of the frequency spectrum of the voltage signal produced by the microphone.Chatter control system detects the presence of chatter three times in the begining ofthe machining operation. Every time the chatter is detected chatter suppression systemstops the machining operation and reduces the depth of cut by 1.0 mm and modifies thetool path program to remove the total depth of cut and continue the machining operation.As can be seen in figure 5.15 the maximum amplitude of the frequency spectrum after 3reductions of the depth of cut is well below the threshold.To show the effectiveness of the chatter detection and suppression it was necessary touse the maximum possible spindle speed of the milling machine which is 1500 rpm. Atlower speeds it was found that the effect of process damping is dominant and hence thechatter would not develop even at very high depth of cuts for the end mill used.One adaptive control execution takes approximately 2.5 ms. Tool breakage detectionruns once per every tooth period and takes approximately 2 ms. At a spindle speed of1500 rpm, one tooth period is 20 ms, which is sufficient for the execution of adaptiveChapter 5. Experimental Results 83/ bO0. 1000 1500 2000 2500Spindle Revolution250200:500Figure 5.11: Variation of estimated parameters - Machining of the pocket-. 3503000II) 0 500 1 000 1500 2000 2500 3000 3500 4000 4500 5000Tooth PeriodFigure 5.12: Variation of average cutting force - Machining of the pocketzU.1-LI00zci)C.)Cci)ci)C00ci)U)00VU,0Chapter 5. Experimental Results 84-3000 500 1000 1500 2000 2500 3000 3500 4000 4500 5000Tooth PeriodFigure 5.13: Variation of residuals in machining of the pocket - first order filter appliedon first differences300200_195.71000-100-195.7-200-3000Figure 5.14: Variation of residuals in machining of the pocket - first order filter appliedon second differences500 1000 1500 2000 2500 3000 3500 4000 4500 5000Tooth PeriodChapter 5. Experimental Results 854JJj4ms1100 200 300 400 500 600 700 800 900 1000Tooth PeriodFigure 5.15: Variation of maximum amplitude of the frequency spectrum of microphonesignal - Machining of the pocketcutting force control and tool breakage detection. Chatter detection and suppression algorithm runs once every six revolutions and takes approximately 21 ms. It was necessaryto reduce the length of the FFT to 256 points and to increase the sampling frequencyto 30 khz in order to reduce the time taken by one cycle of chatter detection to avoidlengthening the adaptive control and tool breakage detection cycle times. This reducesthe frequency resolution considerably, but was found adequate for the chatter detection.These difficulties are because, presently the adaptive control algorithm, tool breakagedetection algorithm and part of the chatter detection and suppression algorithm are running in the RTM PC. If one algorithm takes longer for one cycle of execution it prolongsthe time between two cycles of other algorithms. This difficulty can quite easily be overcome if all the process monitoring and control software modules are ported to dedicatedsubsystems on the main bus in which case process monitoring and control modules willuse RTM only to communicate with CNC master when they need to manipulate the25EEo<Cl)EE‘C0 0Chapter 5. Experimental Results 86operating parameters of the machine tool.5.3.3 Comparison of the HOAM-CNC with a Closed Architecture CNCTo compare the performance of the HOAM-CNC in process monitoring and controlwith a closed architecture CNC, adaptive cutting force control was implemented on aHardinge Superslant high precision lathe with a Fanuc GN6TC closed architecture CNC.Same adaptive control algorithm was used. No details on hardware or software is availableor provided by the manufacturer of Fanuc GN6TC CNC, and therefore the manipulationof the feed rate is possible only using the feed rate override switch. Experimental set-upfor adaptive control implementation on Hardinge Superslant lathe machine is shown infigure 5.16.Five bit feed rate override switch has a 10 % resolution with a maximum attainablefeed rate of 200 % of the programmed feed rate. This constraints the manipulation of thefeed rate so that if the programmed feed rate is not properly selected feed rate saturationcould occur. On the other hand the feed rate calculated by the adaptive control algorithmto control the cutting force at the desired reference level could be implemented only witha -5 % - +5 % error. This causes considerable fluctuations in the cutting force as will beseen in the experimental results.To manipulate the feed rate a 5 bit interface to the binary feed override switch isused. Percentage values of the programmed feed rate in the form of a five bit numberis transferred to the feed override switch via the parallel port of a 386 PC. For forcemeasurement, the same setup of the HOAM-CNC is used. The peak and average forcemeasurement subsystem of the HOAM-CNC is also employed.Chapter 5. Experimental Results 87Figure 5.16: Adaptive control implementation with a closed architecture CNCTwo turning tests were conducted using Aluminum 6061-T6 rods. A Sandwik Coromant left hand shank holder with 25.4 mmx25.4 mm cross section and 152.4 mm lengthwith a triangular insert having a +6° rake and 110 edge clearance angle were used inthe experiments. Manufacturer of the insert does not disclose the coating and substratematerials of the insert. Cutting conditions of the two tests are given in table 5.5.Spindle speed 800rpmProgrammed feed rate 0.1 mm/revDepth of cut test IL - 3 mm, test JIb - 2.5 mm to 4 mm step changeTable 5.5: Cutting conditions for adaptive control tests on the Hardinge latheKistler type 9257A3 componentpiezoelectric chargeamplifierConnection for five bitinterface to feedoverride switch80386 Computer with 8096based force data collection boardFor comparison two similar tests one with a constant depth of cut and another with aChapter 5. Experimental Results—Szci)C)0U0)CCI—4-,CU)0)CCuI—Cutter cutting conditionsDiameter 25.4 mm Workpiece Al 7075-T6 alloyNumber of flutes 4 Depth of cut test TM- 10.8 mmtest TIM- step,7.62 to 10.5 mmHelix angle 300 Spindle speed 885 rpmMaterial 1155 Reference cutting force 700 NWidth of cut 19.00 mmTable 5.6: Test conditions for performance comparisonFigures 5.17 and 5.18 show the variation of the cutting force in the tests IL and TM.It is clearly seen that the variance of the controlled cutting force is much higher with theclosed architecture CNC. This is basically caused by the resolution of the feed override88100090080070060050040030020010000Figure 5.17: Variation of cutting force - test IL, closed architecture CNCstep change in the depth of cut were conducted with HOAM-CNC on the research millingmachine. Test conditions of these tests are given in table 5.6.50 100 150 200 250 300 350 400 450Adaptive Control CyclezC)h...0LL4-C4-(1)ci)U)0Chapter 5. Experimental Results 8912001000800600400200300 400 500Spindle RevolutionFigure 5.18: Variation of cutting force - test TM, open architecture CNCswitch. Low resolution of the feed override switch forces the command feed rate to berounded off to the closest multiple of the 10 % value of the programmed feed rate. Twolarger oscillations of the cutting force around 150 and 350 tooth periods in test TL aredue to chip build up on the workpiece. Also it is seen that in test IL transient oscillationsof the cutting force are much longer than those with the HOAM-CNC. This is due tothe longer delay between the time feed override switch is over written and the actualtime axis motor starts to respond, which is about 120 ms. With the HOAM-CNC thisis approximately 2.5 ms, because, the communication time between the adaptive controlmodule and the CNC master is much less which is approximately 500 ts and the CNCmaster can execute a feed change within 1 ms. It takes approximately another 1 ms forthe axis motors to start responding.Chapter 5. Experimental Results 90>U)I..—.. 020.18Cl)0.160.14ci)L0.122 0.0828 0.06- 0.040.02Figure 5.19: Variation of command feed - test IL, closed architecture CNCFigures 5.19 and 5.20 show the variation of command feeds as calculated by the adaptive control algorithm for test IL and test IM respectively. With the HOAM-CNC, thecalculated command feed is directly used in control, whereas with the closed architectureCNC the command feed calculated by the adaptive control algorithm is rounded off tothe closest multiple of the 10 % value of the programmed feed rate. Therefore actualcommand feed rate is different from what is calculated by the adaptive control algorithmand is shown in figure 5.21. This causes consistent fluctuations in the feed rate.Figures 5.22 and 5.23 show that at the step change of the depth of cut, cutting forceof test IlL increases by about 75 % of the reference force, whereas, with the HOAM-CNCincrease is approximately 10 %. As can be seen in figure 5.25, with the HOAM-CNC thedecrease of the feed speed to maintain the cutting force constant at the reference level isquite smooth, whereas, in the other case as shown in figure 5.24, reduction of feed rateis followed by oscillations in the feed thus causing the cutting force to oscillate.200 250 300Adaptive Control CycleChapter 5. Experimental ResultsFigure 5.20: Variation of command feed - test TM, open architecture CNC0.22 0.12ci)0.1CU 0.082E 0.0600.04Cl)0.02C)ci)xUi91Figure 5.21:CNCVariation of command feed sent to the controller- test IL, closed architecture10ci)2ci)ci)UCCU220C.)Spindle Revolution150 200 250 300Adaptive Control CycleChapter 5. Experimental Results800Z 700C)6000UC) 500CC400I—ce 300C200Ccts100Figure 5.22: Variation of cutting force - test IlL, closed architecture CNC1000900z8000o 700LI..600CUD 500Cl)CD400CU 300ci)0200100a92Adaptive Control Cycle- 100 200 300 400 500 600 700 800 900 1000Spindle RevolutionC)Figure 5.23: Variation of cutting force - test IIM, open architecture CNCChapter 5. Experimental Results 93>0.2EE0.18 -a) 0.16Cu0.140.12UD 0.1C0.08E0 0.06C)0.04a)4-CU 0.02C)- 50 100 150 200 250 300 350 400 4500 Adaptive Control CycleFigure 5.24: Variation of command feed - test IlL, closed architecture CNC5__4.5 .C)CL)-D 3Li. 2.5C 2Cu1.500.50o ioo 200 300 400 500 600 700 800 900 1000Spindle RevolutionFigure 5.25: Variation of command feed - test TIM, open architecture CNCChapter 5. Experimental Results 94>0.20.18aj 0.164-0.140.12LI0.1E 0.082o 0.06C.)D 0.04a)4-0.02ci)0W 0Figure 5.26: Variation of command feed sent to the controller - test IlL, closed architecture CNC150 200 250Adaptive Control CycleChapter 6Conclusion and Future Work6.1 Integration of Process Monitoring and Control to HOAM-CNCHOAM-CNC is an open architecture Computer Numerical Controller designed andbuilt in the Industrial Automation Laboratory of UBC. Real Time Master(RTM) is thecentral sub system of the HOAM-CNC, who organizes the operation of the CNC andcoordinates various other sub systems on its main bus. Subsystems can be divided intotwo parts, namely motion control and process monitoring and control. CNC master isthe major sub system and it coordinates axis controllers using a secondary bus which iscalled the DSP link. Process monitoring and control sub systems communicate with CNCmaster using the CNC interface module in the RTIVL Operating parameters of the CNCand design parameters of axis control loops are freely available for use and manipulationby process monitoring and control modules.In this thesis process monitoring and control modules are developed and integrated tothe HOAM-CNC. Integrated process monitoring and control functions include adaptiveforce control, tool breakage detection and chatter detection and avoidance.Adaptive control of the peak milling force at each spindle revolution avoids the shankbreakage of the cutting tool and improves machining accuracy by controlling static de—formations of the tool. The algorithm is based on the Generalized Predictive Controlmethod developed by Clarke [25] [26] and works well over a wide range of operating conditions despite the linear model assumed for the cutting process.95Chapter 6. Conclusion and Future Work 96The constant trace algorithm used for estimation of parameters of the combinedmilling process and the feed drive servo eliminates the need for resetting co-variancealgorithm to avoid estimation wind up due to lack of excitation as is necessary withthe exponentially forgetting recursive least squares algorithm. This considerably reducestransient overshoots and improves the stability of the cutting force, thus making wellsuited for milling, because excessive transient overshoots may also cause breakage of thetool.Proposed tool breakage detection algorithm eliminates the need for a trial cut todetermine a threshold for the detection of a tool breakage. The algorithm is quite simpleand efficient because, the time series filters are of very low order and no previous tests arenecessary to determine the threshold of force residuals. However, important assumptionsmade in developing the algorithm is that the tool would not break during the first fiverevolutions of the cut and cutting will not be started with a tool with a broken edge.The set threshold includes the effect of excessive run out. Therefore a tool breakage canbe detected even in the presence of large run-outs.The dynamometer that was employed to measure the forces is not suitable for anindustrial environment, because, it limits the size of the work piece and the location of iton the milling bed. All the experiments of this research were done under dry conditions.Use of coolant may cause problems due to moisture leaking in to the dynamometer andcables.Chatter is detected by considering the maximum amplitude of the frequency spectrumof sound emitting from the cutting process. Microphone is a good sensor to capture thesound energy produced by chatter vibrations when there is no background noise thatcorrupts it. It is seen that a common threshold can be set for the maximum amplitude ofthe spectrum of sound for detection of chatter vibrations based on chatter free machining.Chapter 6. Conclusion and Future Work 97All three process monitoring and control algorithms run in parallel with motion control. In the present system adaptive cutting force control module and tool breakagedetection module are pure software modules running in the RTM PC. Force data neededby both the algorithms are provided by the Intel 8096 processor based force detectionsub system. The co-ordination part of the chatter detection and suppression module isalso running in the RTM. Sampling of the sound signal and real time calculation of theFFT are done on the dedicated TMS320C25 processor based sub system.Force detection subsystem helps the RTM in parallel execution of the process monitoring and control modules. The force detection subsystem sets a flag at each toothperiod which is read and reset by the adaptive control module. This flag is accessible toall process monitoring and control modules. Adaptive control module counts the toothperiods by reading and resetting the flag. This count is also freely available to all processmonitoring and control modules. RTM runs the monitoring and control functions atspecified time periods which is determined by each module depending on the tooth period count. In the present implementation calculation time of each algorithm effects theother on efficient operation of process monitoring and control because, the RTM sharestime in executing all three algorithms.6.2 Future WorkFollowing future work is necessary to improve the present HOAM-CNC system withprocess monitoring and control, to an industry implementable stage.• Alternative sensors for measurement of cutting forces which can be located awayfrom the workpiece and tool environment, yet capable of giving accurate measurements should be investigated, specially for milling.Chapter 6. Conclusion and Future Work 98• Adaptively thresholding the spectrum of sound for chatter detection should beinvestigated.• Limited memory and inability to do floating point arithmetic with axis controllersmakes it impossible to examine complex algorithms for better position control. Newaxis controllers should be designed to cope with this situation.• Each process monitoring and control software module should be ported to its ownindependent hardware module on the main bus. It will free the RTM to functiononly as an interface for the user, and the process monitoring and control subsystemsfor communication with the CNC master. This will make the system comply moreclosely with the open architecture philosophy.• Presently the System Master is not capable of obtaining NC block informationfrom the CNC master. System Master software should be improved such that itcan obtain the NC block information from the CNC master fast and is available toall the monitoring and control sub systems.Bibliography[1] G. Pritshow, C. Daniel, G. Junghans, and W. Sperling. Open System Controllers-A Challenge for the Future of the Machine Tool Industry. Annals of the CIRP,42(1):449—452, 1993.[2] N. A. Newell. 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A Study of an Adaptive ControlSystem for Milling with Force Constraint. In 6th NAMR C Proceedings, pages 364—371. Society of Manufacturing Engineering, 1978.[9] C. Stute and F. R. Goetz. Adaptive Control System for Variable Gain in ACCSystems. In Proceedings of the 16th International Machine Tool Design and ResearchConference, pages 117—121, Manchester, UK, 1975.[10] Y. Koren and 0. Masory. Adaptive Control with Process Estimation. Annals of theCIRP, 30(1):373—376, 1981.[11] L. K. Daneshmand and H. A. Pak. Model Reference Adaptive Control of Feed Forcein Turning. Trnas. ASME, Journal of Dynamic Systems Measurement and Control,108:215—222, September 1986.99Bibliography 100[12] B.K. Fussel and K. Sirinivasan. Model Reference Adaptive Control of Force inEnd Milling Operations. In Proceedings of the American Control Conference, pages1189—1194, 1982.[13] M. Tomizuka, J.H. Oh, and D.A. Dornfield. Model Reference Adaptive Control ofthe Milling Process. In D.E. Hardt and W.J. 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Update on High Speed Milling Dynamics. Trans. ASME,Journal of Engineering Industry, 112:142—149, 1990.[43] P. K. Chan. Chatter Avoidance in Milling. Master’s thesis, University of BritishColumbia, August 1990.[44] M. Rahman. In Process Detection of Chatter Threshold. Trans. ASME, Journal ofEngineering for Industry, 110:44—50, February 1988.[45] Y. Altintas and P. Chan. In-Process Detection and Supression of Chatter in Milling.International Journal of Machine Tool Design and Research, 32:329—347, 1992.[46] S. Smith and T. Delio. Sensor-Based Control for Chatter-Free Milling by SpindleSpeed Selection. In Proce. ASME 1989 WAM, volume 18, pages 107—114, 1989.[47] T. Delio, J. Tiusty, and S. Smith. Use of Audio Signals for Chatter Detection andControl. Trans. ASME, Journal of Engineering for Industry, 114:146—157, May1992.[48] T. Inamura and T. Sata. Stability Analysis of Cutting Under Varying Spindle Speed.Annals of the CIRP, 23(1):119—120, 1974.Bibliography 103[49] T. Takemura, T. Kitamura, and T. Hoshi. Active Suppression of Chatter by Programmed Variation of Spindle Speed. Annals of the CIRP, 23(1):121—122, 1974.[50] S. C. Lin, R. E. DeVor, and S. G. Kapoor. The Effects of Variable Speed Cuttingon Vibration Control in Face Milling. Trans. ASME, Journal of Engineering forIndustry, 112:1—11, February 1990.[51] M. Weck, E. Verhagg, and M. Gather. Adaptive Control of Face Milling Operationswith Strategies for Avoiding Chatter-Vibrations and for Automatic Cut Distribution.Annals of the CIRP, 24(1):405—409, 1975.[52] Y. Altintas and W.K. Munasinghe. A Hierachical Open Architecture CNC Systemfor Machine Tools. Annals of the CIRF, 43(1):349—354, 1994.[53] C. C. H. Ma and Y. Altintas. Direct Adaptive Cutting Force Control of MillingProcesses. Automatica, 26(5) :899—902, 1990.Appendix AAxis Control LoopsThis appendix has a complete block diagram of axis control ioops of the SAJO Sbsyn three axis knee type vertical milling machine. Figure A.1 shows the position controlloop and figure A.2 shows a detailed diagram of the velocity control ioop. Table A.1specifies the parameters of the control loop for X-axis.Zero Order Gain ofLead-lag Filter Hold D/A Velocity LoopieT5—-rdViXr (counts) x (counts)Figure A.2: Velocity control loop104Appendix A. Axis Control Loops 105Component Parameter Units Transfer FunctionB 0.002256 Nm/rad.sec’ 1JeS+BDC Je 0.003767 Nm.sec’1Motor L0 0.002h L s+R,.Assembly Ra 0.4 1K 0.3 Nm/ampKb 0.3 vol/rad.secTacho Gain H9 0.08872 vol/rad.sec’Current K0 0.3264 vol/ampFeed_BackSignal S9 0.335 vol/volAmplifierTacho T9 0.3183 vol/volAmplifier T1 0.003979 sec Tg(2’tis+l)T2s+1Tg(s) T2 0.00014 SecK.Current K: 2113.5 vol/volAmplifier Tk: 0.1788K1(s) 9.20 vol limitVoltage K 203 vol/vol Kv(a+wk)Amplifier 313 rad.sec’Kr(s) V 78 vol limitEncoder Ke 636.62 cmts/rad.secD/A Kd 0.0781 vol/countZOH T 200 jsecDigital K 2.5Filter a 0.95 Kp(z—a)z—bD(z) b 0.6875Table A.1: Design parameters of the X-axis feed driveAppendix BModel Approximation of the Position LoopIn this appendix it is shown that the position loop of any axis of the milling machineused in this thesis can be approximated by a second order model. Position control loopof the z axis is used to demonstrate the model approximation.Discrete transfer function of the digital lead-lag filter,D(z) = (B.1)where,K = 1.95a = 0.951b = 0.844Experimentally determined transfer function of the velocity control loop,G(s)= 1 (B.2)where,K = 10.954r = 0.0054As explained in section 3.1.2 the sampling period of the adaptive control algorithm ismuch larger than the loop closure time of the position loop. Therefore the digital filter106Appendix B. Model Approximation of the Position Loop 107can be replaced by its continuous equivalent using the Tustin’s approximation. Tustin’sapproximation is,1+sh/2Z— 1 — sh/2h is the ioop closure time of the position control ioop, which is 200 s. The transferfunction of the lead-lag filter in the laplace domain is obtained by substituting for z inequation B.1 and can be given as,Ds— Kf(s + a’)B 3— (s+b’)where,K1 = 2.068a’ = 250.8b’ 847.458Therefore open loop transfer function of the position loop is,G0(s) = D(S)KdGv(S)Ke (B.4)— 104319.93(s + 250.8)— s(s + 185.185)(s + 847.458)Closed loop transfer function of the position control loop can be given by,— 104319.93(s + 250.8)— s(s + 185.185)(s + 847.458) + l04319.93(s + 250.8)— 104319.93(s + 250.8) B 5— s3 + 1032.643s2 + 261256.436s + 26163437.42The roots of the characteristic equation of the above transfer function are,Appendix B. Model Approximation of the Position Loop 108s = -720.403s = -156.12--}-j109.29s = -156.12-j109.29The real root is very stable and the response of the position control ioop is dominated bytwo complex conjugate poles. Therefore the position loop can be approximated by theunderdamped second order system given below.60317.7784Gf(s)= s2 + 400s + 60317.7784(B.6)The step response and the frequency response of two models are given in figures B.1and B.2. It can be seen that the two models are very closely matched.1.21/0.8/‘ Third order model0.6 / Second order model0.4 / -0.2’00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Time (sec)Figure B.1: Step response of the position control loopZero order hold equivalent of the model given by equation B.6 for a sampling periodof 40 ms, which is equal to the spindle period at 1500 rpm, is,Gj(z’) z’(bi +b2z1) (B.7)1 +a1z’ +a2zAppendix B. Model Approximation of the Position Loop 109-5\\Third order model-10Second order model(15-20-250.5 1 1.5 2 2.5 3Log frequencyFigure B.2: Frequency response of the position control ioopwhere,= 1= -5.3887e-4a1 = -5.6063e-4a2 = 1.1254e-8Since a2 is much smaller than other parameters it is neglected and the position controlloop is approximated by [53],Gf(z’)=z1(bi+b24 (B.8)


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