UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Monitoring and control of machining operations Sekhon, Gurbachan S. 2013

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2013_fall_sekhon_gurbachan.pdf [ 16.85MB ]
Metadata
JSON: 24-1.0074258.json
JSON-LD: 24-1.0074258-ld.json
RDF/XML (Pretty): 24-1.0074258-rdf.xml
RDF/JSON: 24-1.0074258-rdf.json
Turtle: 24-1.0074258-turtle.txt
N-Triples: 24-1.0074258-rdf-ntriples.txt
Original Record: 24-1.0074258-source.json
Full Text
24-1.0074258-fulltext.txt
Citation
24-1.0074258.ris

Full Text

MONITORING AND CONTROLOF MACHINING OPERATIONSbyGurbachan S SekhonB.A.Sc., The University of British Columbia, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Mechanical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2013? Gurbachan S Sekhon 2013AbstractThe present Computer Numerical Controlled (CNC) machine tools can provide internalstates of the machine (such as speed, feed, current, power, torque, and axis tracking errors)to external computers, which in turn can manipulate spindle speeds and feeds through Eth-ernet communication tools. This thesis presents on-line detection and avoidance of chattervibrations, on-line prediction of cutting torque and its adaptive control during milling op-erations.Chatter is detected by monitoring the frequency spectrum of sound signals during ma-chining operations. The forced vibrations that occur at spindle and tooth passing frequen-cies are removed through a comb filter. The chatter frequency and its magnitude are pre-dicted. The spindle speed is automatically changed to enter the process into the neareststability pocket if it lies within the first five stability lobes. If the process cannot be stabi-lized due to missing lobes at low speeds, the spindle speed is harmonically varied withoutviolating the power limit of the spindle drive. The algorithm is implemented on a five axisMori Seiki NMV5000 Machining Center with a FANUC 30i controller. The communi-cation with an external PC is handled through Ethernet and FOCAS command library ofFanuc.The cutting torque is also predicted by monitoring the current of a three phase inductionmotor in real time. The cutting torque is estimated through Extended Kalman Filter fromthe steady state model of the motor after removing the friction component. The estimatedtorque is used to keep the cutting torque on the machine at desired and safe levels bymanipulating the feed rate with adaptive pole placement controller.The thesis shows that it is possible to add process monitoring and control functions toiiAbstractthe machine without having to add costly and impractical sensors on the machine, leadingto safer and more productive machining operations.iiiPrefaceA version of Chapter 4 of this thesis has been published in the proceedings of the MachineTool Technologies Research Foundation (MTTRF) 2013 annual meeting. My contributionto this work was as the main author; I was responsible for the mathematical modellingand concept formulation, conducting the experiments and analyzing the data, creating theprograms used to implement the algorithms presented in the paper, and writing the paper.Keivan Ahmadi assisted in the mathematical modelling, early stages of the concept formu-lation, and editing of the published conference paper. Yusuf Altintas was the supervisor ofthis project and was involved in the concept formulation and editing the conference paper.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Detection and Suppression of Chatter . . . . . . . . . . . . . . . . . . . . 52.2 Online Estimation of Cutting Torque using Motor Current . . . . . . . . . 142.3 Adaptive Control of Machining Process . . . . . . . . . . . . . . . . . . . 163 Detection and Suppression of Chatter Vibrations . . . . . . . . . . . . . . . 183.1 Online Detection of Chatter Vibrations . . . . . . . . . . . . . . . . . . . 183.2 Suppression of Chatter Vibrations . . . . . . . . . . . . . . . . . . . . . . 223.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41vTable of Contents4 Torque Estimation Using Current Sensor . . . . . . . . . . . . . . . . . . . . 444.1 Induction Motor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2 Extended Kalman Filter Design . . . . . . . . . . . . . . . . . . . . . . . 504.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Adaptive Control of Milling Process . . . . . . . . . . . . . . . . . . . . . . . 635.1 Design of Adaptive Control Law . . . . . . . . . . . . . . . . . . . . . . . 635.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 76Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78viList of Tables3.1 Results of estimated and measured power consumed by applying SSV ofvarious amplitudes and frequencies onto 1875 revmin and 3000revmin base spin-dle speeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41viiList of Figures1.1 Example of surface marks left due to the chatter phenomenon . . . . . . . . 11.2 Example of stability lobes for the slotting of Aluminium 7075 . . . . . . . 21.3 Example of high speed milling of AL-7075 Aluminium. The simulatedpower in this case is ~20% higher than measured on the machine. . . . . . . 32.1 Diagram of the cutting process in up milling . . . . . . . . . . . . . . . . . 62.2 Chip thickness in A- ideal case, B- stable case, and C- chatter vibrations . . 72.3 Example lobes for a 12mm diameter cutter in 75% immersion down millingof Aluminium 7075. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Typical Polar Diagram of a Unidirectional (Cardioid) Microphone . . . . . 132.5 Block diagram of Adaptive Control in Milling . . . . . . . . . . . . . . . . 163.1 Example of a comb filter designed to remove a spindle frequency of 55Hzand its harmonics, with Gb = 0.7 and fb = 3Hz . . . . . . . . . . . . . . . 213.2 Block diagram of the spindle control loop . . . . . . . . . . . . . . . . . . 253.3 Overview of real time communication framework . . . . . . . . . . . . . . 273.4 Experimental Setup for Chatter Detection . . . . . . . . . . . . . . . . . . 283.5 Example of chatter detection. 50% immersion downmilling with 4mmdepth of cut and 0.1mm/tooth feedrate. Harmonics of the tooth passingfrequency are shown in green lines, while the chatter frequency is shownin red. Left: n = 12000 revmin , Right: n = 12939revmin . . . . . . . . . . . . . . 29viiiList of Figures3.6 Resulting surface finish for 50% immersion downmilling with 4mm depthof cut, and 0.1mm/tooth feedrate. . . . . . . . . . . . . . . . . . . . . . . 303.7 Results of SSS method in 75% immersion downmilling of AL-7075 alu-minium with 2 flute 12mm diameter cutter and 0.1mm/tooth feedrate. Redcrosses denote cutting conditions resulting in chatter, while green crossesdenote stable conditions. The arrows indicate the transition to stable cuttingconditions as per the SSS method . . . . . . . . . . . . . . . . . . . . . . 313.8 Application of SSS in slotting with 3.5mm depth of cut AISI-1045 steelSegment A: 3117 revmin , Segment B: 3024revmin . Harmonics of the spindlefrequency are shown in green lines, while the chatter frequency is shownin red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.9 Results of slotting AISI-1045 steel with 3.5mm depth of cut. a) stabilitylobes of the experimental setup, (b-e) FFT of cutting sound at 1385, 1435,3285, and 3600 revmin , respectively. . . . . . . . . . . . . . . . . . . . . . . . 333.10 Results of slotting AISI-1045 steel with 3.5mm depth and 1385 revmin basespindle speed without SSV (segment A) and with SSV at 4% amplitudeand 4Hz frequency (segment B) a) cutting sound, b) FFT of segment A, c)FFT of segment B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.11 Results of slotting AISI-1045 steel with 3.5mm depth and 1200 revmin basespindle speed without SSV (segment A) and with SSV at 5% amplitudeand 4Hz frequency (segment B), a) cutting sound, b) FFT of segment A, c)FFT of segment B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.12 Surface finish resulting from unstable milling at 1200 revmin (right), and sta-ble milling at 1200 revmin with SSV of 5% amplitude and 4Hz (left). Feeddirection is right to left . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35ixList of Figures3.13 FFT of experiments in slotting of AISI 1045 steel with 3.5mm depth of cutand 1200 revmin with various SSV parameters, A) Constant spindle speed, B)SSV with 1% amplitude and 3.5Hz frequency , C) SSV using 5% amplitudeand 3.5Hz frequency, D) SSV using 8% amplitude and 3.5Hz frequency . . 373.14 Cutting sound of slotting AISI 1045 steel with 3.5mm depth of cut, 1200revmin base spindle speed, and SSV with 1% amplitude and 3.5Hz frequency . 383.15 Cutting sound (A) and FFT (B) of slotting AISI1045 steel with 3.5mmdepth of cut, 1200 revmin base spindle speed, and SSV with 4% ampltiude and3.5Hz frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.16 Cutting sound and FFT of experiments in slotting of AISI 1045 steel with3.5mm depth of cut and 1200 revmin with various SSV parameters, A) SSVwith 5% amplitude and 1Hz frequency , B) SSV using 5% amplitude and2Hz frequency, C) SSV using 5% amplitude and 2.5Hz frequency, D) SSVusing 5% amplitude and 3.5Hz frequency . . . . . . . . . . . . . . . . . . 403.17 Spindle speed and power measured through FOCAS after 200% spindlespeed override was commanded from a base spindle speed of 8000 revmin . . . 413.18 Example FRFs of two different inserted endmills, a) FRF of a 20mm 4 fluteinserted endmill, b) FRF of a 25mm 2 flute inserted endmill . . . . . . . . . 434.1 Equivalent circuit for a three phase induction motor in machine coordinates 454.2 Equivalent circuit during stead state operation . . . . . . . . . . . . . . . . 484.3 Example of the measured states of the Extended Kalman Filter in the millingof AL-7075 Aluminium with a 2 flute endmill, 18000 revmin spindle speed,half immersion downmilling with 4mm depth of cut, and feedrates of 0.14 mmtoothand 0.16 mmtooth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.4 Setup of Hall Effect Transducer . . . . . . . . . . . . . . . . . . . . . . . 554.5 Flowchart of the algorithm used to estimate the cutting torque, Tcut , at eachtimestep. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57xList of Figures4.6 Results of half immersion downmilling of AL-7075 aluminium with a 2tooth cutter, various spindle speeds and feedrates, and 4mm depth of cut.The surface was cleaned between each cut, causing a small amount oftorque to be read. Blue: Average of the torque measured from the dy-namometer, Red: Torque estimated using the EKF . . . . . . . . . . . . . . 584.7 Results of slotting AISI-1045 steel at 3000 revmin with 2mm depth of cut, 4tooth cutter, and A) 0.04 mm/tooth feedrate, and B) 0.07mm/tooth feedrate.Blue: Average of the torque measured from the dynamometer, Red: Torqueestimated using the EKF . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.8 Results of half immersion downmilling of AL-7075 aluminium using a 2tooth cutter at feeds of 0.14 and 0.16 mm/tooth with 18000 revmin . The surfacewas cleaned between each cut, causing a small amount of torque to be read.When the EKF is used to estimate the torque when the spindle speed usedis within the calibration range, even if the speed was not included in thecalibration the errors remain the same. . . . . . . . . . . . . . . . . . . . . 594.9 Results of half immersion downmilling of AL-7075 aluminium using a 2tooth cutter at feeds of 0.14 and 0.16 mm/tooth with 20000 revmin . The surfacewas cleaned between each cut, causing a small amount of torque to be read.When the EKF is used to estimate the torque when the spindle speed usedis outside of the calibration range higher errors can be observed. . . . . . . 604.10 Frequency resolution obtained at different sampling frequencies and sam-pling periods using the Quinn-Fernandez method . . . . . . . . . . . . . . 625.1 Block diagram for adaptive pole placement controller . . . . . . . . . . . . 635.2 Summary of the adaptive control algorithm used. . . . . . . . . . . . . . . 695.3 Dimensions of the step part used to evaluate the adaptive control algorithm.Dimensions are in millimeters. . . . . . . . . . . . . . . . . . . . . . . . . 70xiList of Figures5.4 Dimensions of the ramp part used to evaluate the adaptive control algo-rithm. Dimensions are in millimeters. . . . . . . . . . . . . . . . . . . . . 705.5 Cutting of the step part of Figure 5.3 using the adaptive control algorithmdeveloped and the EKF of Section 4 as the torque measurement. A torquereference of Tre f = 2Nm was used, and is marked with a blank line. . . . . 725.6 Cutting of the ramp part of Figure 5.4 using the adaptive control algorithmdeveloped and the EKF of Section 4 as the torque measurement. A torquereference of Tre f = 1.9Nm was used, and is marked with a black line. . . . 725.7 Cutting of the step part of Figure 5.3 using the adaptive control algorithmdeveloped and using FOCAS to measure the torque. A torque reference ofTre f = 2.1Nm was used, and is marked with a black line. . . . . . . . . . . 735.8 Cutting of the ramp part of Figure 5.4 using the adaptive control algorithmdeveloped and using FOCAS to measure the torque. A torque reference ofTre f = 2.1Nm was used, and is marked with a black line. . . . . . . . . . . 74xiiNomenclaturea Axial depth of cutacomb Constant of the comb filterabcs Labels for the three phase variables (abc) in AC systems, where each areseparated by 120?. The s denotes the stator side, which is the stationarypart of the electric motorabcr Labels for the three phase variables (abc) in AC systems, where each areseparated by 120?. The r denotes the rotor side, which is the rotatingpart of the electric motorbcomb Constant of the comb filterB Coefficient of viscous frictionc Counter for harmonics of the spindle or tooth passing frequencyf Feed per tooth, or feedratefb Bandwidth of the comb filterfc Chatter frequencyfd Dominant frequency within the Fast Fourier Tranform spectrum of thesignalfe Electrical frequencyfk Series of process equations for the Extended Kalman Filterfmax Largest frequency expected within the Fast Fourier Transform spectrumfn Natural frequencyfr Frequency resolution of the Fast Fourier TransformxiiiNomenclaturefre Equivalent spindle frequency of a two pole machinefs Spindle frequencyfssv Frequency of Spindle Speed Variationft Tooth passing frequencyF Jacobian of the process equations vectorFa Axial cutting forceF?ar Representation of any of voltage, current, or flux linkage on the a-axisof an induction motor on the rotor sideF?as Representation of any of voltage, current, or flux linkage on the a-axisof an induction motor on the stator sideF?dr Representation of any of voltage, current, or flux linkage on the d-axisof an induction motor on the rotor sideF?ds Representation of any of voltage, current, or flux linkage on the d-axisof an induction motor on the stator sideF?qr Representation of any of voltage, current, or flux linkage on the q-axisof an induction motor on the rotor sideF?qs Representation of any of voltage, current, or flux linkage on the q-axisof an induction motor on the stator sideFs Sampling frequencyFt Tangential cutting forceG(z) Transfer function of the comb filterGb Gain of the comb filter at the bandwidth fbh Chip thicknesshk Series of measurement equations for the Extended Kalman FilterH Jacobian of the measurement equations vectoriabcs Stator currents in abc coordinatesi?abcr Rotor currents in abc coordinatesxivNomenclaturei?dr Rotor current in the d axisids Stator current in the d axisi?qr Rotor current in the q axisiqs Stator current in the q axisI Identity matrixI?as Amplitude of the a-phase stator currentI?ar Amplitude of the a-phase rotor currentIm Motor currentJ Spindle?s moment of inertiaj Variable to represent the complex or imaginary axisk Number of complete waves generated during cuttingknew Number of complete waves generated during cutting at the new spindlespeedkold Number of complete waves generated during cutting at the previousspindle speedKac Axial cutting force coefficientKae Axial edge cutting coefficientKk Extended Kalman Filter gainKrc Radial cutting force coefficientKre Radial edge cutting coefficientKt Torque constantKtc Tangential cutting force coefficientKte Tangential edge cutting coefficientK1 Constant for the steady state induction motor torque modelK2 Constant for the steady state induction motor torque modelLlr Rotor side leakage inductanceLls Stator side leakage inductancexvNomenclatureLM Magnetizing inductance of the motorL?r Rotor side inductanceLs Stator side inductanceL?sr Mutual inductance between the stator and rotor siden Spindle speednnew Calculated spindle speed to eliminate chatterN Number of teeth on the cutterN f f t Number of samples used to compute the Fast Fourier Transformo The order of the comb filter. It is equal to one plus the number ofnotchesP Number of poles on the motorPk Actual covariance of the Extended Kalman FilterP?k|k?1 Predicted covariance of the Extended Kalman FilterPm Power consumed by the spindle motorPmax Maximum power consumed when applying Spindle Speed Variationqd0s Labels for the three phase system in transformed coordinates, whereeach are separated by 90?. The s denotes the stator side, which is thestationary part of the motor.qd0r Labels for the three phase system in transformed coordinates, whereeach are separated by 90?. The r denotes the rotor side, which is therotating part of the motor.Q Quality factor of the comb filterQk?1 Covariance of the process noisers Stator side resistancer?r Rotor side resistanceR Covariance of the measurement noisexviNomenclatureRe Real operator, which considers only the real component and disregardsthe complex or imaginary components Motor slip, or the percent difference between the electrical frequencyand the rotor frequency of an equivalent two pole machine of aninduction motort Timet1 Time at the start of acceleration when estimating the inertiat2 Time at the end of acceleration when estimating the inertiaTcoulomb Static friction coefficientTcut Cutting torqueTelecloss Electrical losses in the motor. Only copper losses are consideredTf ric Frictional torqueTm Motor torquevabcs Voltage of the three phases on the stator side of the motorv?abcr Voltage of the three phases on the rotor side of the motorvk Zero-mean guassian noise applied to measurementwk Zero-mean guassian noise applied to processWf Energy stored in the coupling field of the motorx Position of the cutting tool in the X , or feed, direction during cuttingxk Vector of states for the Extended Kalman Filterx0 Position of the cutting tool in the feed direction one tooth period beforey Position of the cutting tool in the Y , or normal, direction during cuttingyk Vector of measurements for the Extended Kalman Filtery0 Position of the cutting tool in the normal direction one tooth periodbeforezk Measurement vector? Amplitude ratio during Spindle Speed VariationxviiNomenclature? Constant used to simplify the calculation of the comb filter parametersbased on the desired gain, Gb, and bandwidth, fb?x Deflection in the x direction?y Deflection in the y direction? Fractional wave generated during cutting?e Electrical frequency in[radsec]?r Rotor frequency in[radsec]? Spindle speed in[radsec]?? Mean spindle speed?? Amplitude of the alternating component of spindle speed during SpindleSpeed variation?1 Speed at the start of acceleration when estimating the inertia?2 Speed at the end of acceleration when estimating the inertia? Instantaneous cutter angle?start Cutter angle at start of cut?end Cutter angle at end of cut? Time constant of the spindle control loop? Variable introduced to simplify calculation of the maximum powerconsumed during Spindle Speed Variation?re Angular displacement of the rotor of an equivalent two pole motor?rm Actual angular displacement of the rotorCAD Computer Aided DesignCAM Computer Aided ManufacturingCNC Stands for Computer Numerically Controlled. Often used alone whenreferring to numerically controlled machines that have onboardcomputersDAQ Data AcquisitionxviiiNomenclatureEKF Extended Kalman Filterf loor Rounding down operatorFOCAS C++ library used to communicate with machine tools using certaincontrollers made by FANUCFRF Frequency Response FunctionMEX Stands for Matlab Executable, these are programs compiled in C, C++,or Fortran that can be run in the Matlab environmentNC Numerical ControlRLS Recursive least squaresSSS Spindle Speed Selection method for chatter suppressionSSV Spindle Speed Variation method for chatter suppressionxixAcknowledgementsI would like to start by thanking my supervisor Dr. Yusuf Altintas for his guidance andsupport throughout my master?s studies. While I struggled to be a researcher, I thank Dr.Altintas for his patience and guidance during this time.I would also like to thank Dr. Keivan Ahmadi for his help during my research. I amvery grateful for the time he spent helping me and wish him all the best in the future.It was a pleasure to be a part of the Manufacturing Automation Laboratory at UBC. Iwas able to meet many great and friendly people there, who I was able to share many greattimes with.Ofcourse, none of this would have been possible without the support of my family. Iwould like to thank my mother, Kuldeep Kaur Sekhon, and father, Avtar Singh Sekhon, fortheir constant support and love throughout my studies, both BASc and MASc. I would alsolike to thank my siblings: Ranjeet Sekhon and Dr. Mehtab Sekhon.Finally, I would like to thank NSERC for the financial support, the CANRIMT network,Sandvik-Coromant for the gracious donation of tooling, and MTTRF for the Mori SeikiNMV5000 machine that was the focus of this work.xxChapter 1IntroductionMilling is a widely used machining operation that is used in the manufacturing of mostproducts. Applications include the machining of dies and molds, large parts for aerospaceindustry, and small biomedical parts. Much of the difficulty in maximizing the productivityof milling operations lies in the prediction of the process ahead of physical trials. Due tothe wide variety of tools and materials that are used it can be difficult to obtain an accurateresult when simulating the process. Furthermore, detailed simulations require specializedequipment, time, and expertise which may not always be available. This leads to usingmore conservative values in cutting which limits productivity.One phenomenon that limits the productivity of milling operations is the occurrence ofunstable vibrations known as ?machining chatter?. Chatter results in deteriorated surfacefinish, as shown in Figure 1.1, decreased tool life, and in some cases can cause damage tothe machine itself.Figure 1.1: Example of surface marks left due to the chatter phenomenonOne method used to avoid chatter vibrations is to measure the frequency response func-tion (FRF) of the tool-workpiece combination, which gives information about the dynamicstiffness of the tool, and use this along with information about the cutting process to gen-erate stability lobes [1, 2], as shown in Figure 1.2. Stability lobes allow the Numerical1Chapter 1. IntroductionControl (NC) programmers to determine which combination of spindle speed and depth ofcut will result in unstable machining and plan accordingly.0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 1041.522.533.544.55Spindle Speed (RPM)Depth of Cut (mm)Figure 1.2: Example of stability lobes for the slotting of Aluminium 7075There are several limitations to this approach, however. Measuring a machine tool?sFRF can be a time consuming task which requires specialized equipment and must berepeated for each tool being used. Furthermore, the FRF of a machine tool?s structurechanges as a function of its position [3], and as such the stability lobes will also vary as afunction of the position of the machine tool. In addition, during the machining of thin wallparts the tool-workpiece FRF can change considerably as material is removed. Due to this,the real time detection and suppression of chatter has become a widely researched topicwithin manufacturing going back to Weck?s work in the early 1980?s [4].Limitations also exist in the monitoring of process parameters required to apply ad-vanced control schemes. Monitoring of the machining process can be done using a vari-ety of sensors, such as dynamometers, accelerometers, or even microphones. While dy-namometers are commonly used to measure forces in experimental environments, due totheir cost and the effect they have on the stiffness of the tool-workpiece combination theyare not typically used in practice. As such, the use of alternative sensors, such as currentsensors, has been investigated to estimate the forces or torques involved in the machiningprocess without affecting the process itself [5].2Chapter 1. IntroductionAnother limitation in the milling process is in the selection of the cutting speed. Thiscan be done by simulating the forces and torques in the machining of a certain part and thenselecting the feed based on the machine?s limitations. However, due to inaccuracies withinthe models and the parameters used within these models (for example, material properties),the actual forces and torques can be different from those simulated. An example is shownin Figure 1.3 in the high speed milling of AL-7075 Aluminium. In addition to this, the NCprogram itself used to manufacture the part may not be optimally designed in such a waythat it keeps the forces and torques involved in the process at a maximum.Figure 1.3: Example of high speed milling of AL-7075 Aluminium. The simulated powerin this case is ~20% higher than measured on the machine.These limitations present an opportunity for improvements by monitoring the machin-ing process and applying appropriate controls in order to maintain a desired cutting torque.By keeping the torque at a constant level, the safety of the tool and the workpiece is en-sured, productivity can be optimized, and in addition to this the surface deflections left onthe workpiece can be regulated [6], which can simplify the finishing process.To this end, this thesis presents methods for the monitoring and control of machiningprocesses in real time through the use of external sensors. To limit the effects of chattervibrations, a microphone is used to detect the occurrence of chatter, and then control signals3Chapter 1. Introductionare sent to the machine tool to suppress the vibrations. In addition to this, a method forestimating the torque using the current of the spindle motor is presented. Finally an adaptivecontrol algorithm is presented which adjusts the feedrate of the machine tool to regulate thecutting torque. This can be used to improve the productivity of a poorly optimized toolpathand ensure that the cutting forces do not reach such high levels as to cause damage to thetool or part.The rest of this thesis is organized as follows: the literature review is presented inChapter 2. In Chapter 3, the algorithm for detecting and suppressing chatter vibrationsis developed, and the experimental results of the proposed method are discussed. Chap-ter 4 presents the modelling of an induction motor, as well as the design of the ExtendedKalman Filter (EKF), and concludes with a discussion of the results obtained from experi-mental verification. Chapter 5 presents the adaptive control algorithm used, as well as theexperimental verification in the milling of two simple 3-axis parts. Finally, conclusions andfuture work are discussed in Chapter 6.4Chapter 2Literature Review2.1 Detection and Suppression of Chatter2.1.1 Background of Milling ProcessBefore discussing the literature related to chatter detection and suppression, a brief sum-mary of the dynamics of chatter is presented below. The force and chatter models areobtained from [1, 2].Milling is a cutting operation where the cutter is made up of multiple teeth which areeach used to remove some amount of material (denoted as the feed per tooth or feedrate,f(mmtooth)) during each revolution of the spindle. Cutting forces produced in milling can bedescribed as a function of the instantaneous chip thickness, h, as:Ft (?) = a(Ktch(?)+Kte) (2.1)Fr (?) = a(Krch(?)+Kre) (2.2)Fa (?) = a(Kach(?)+Kae) (2.3)where Ft , Fr, and Fa are the tangential, radial, and axial cutting forces, respectively (seeFigure 2.1), Ktc, Krc, and Kac are the corresponding cutting force coefficients, Kte, Kre, andKae are the corresponding edge cutting coefficients, a is the depth of cut (mm), and ? is the52.1. Detection and Suppression of Chattercutter angle which varies from ?start to ?end based on the radial immersion of the cutter andthe process (up-milling, down-milling, etc.).Figure 2.1: Diagram of the cutting process in up millingIdeally, the instantaneous chip thickness is a function of the cutter angle and feedrateas:h(?) = f sin(?) (2.4)However, as each tooth impacts the workpiece it excites the modes of the tool-workpiececombination causing some deflections, as shown in Figure 2.2.The actual chip thickness is then some function of the ideal chip thickness and thedeflections in the X and Y directions, ie:h(?) = f sin(?)+?xsin(?)+?ysin(?) (2.5)where ?x = x? x0 and ?y = y? y0 are the differences of the deflections in the X andY directions, respectively, at the current and previous tooth periods. As such, we cannot62.1. Detection and Suppression of ChatterFigure 2.2: Chip thickness in A- ideal case, B- stable case, and C- chatter vibrationsachieve the ideal case shown in Figure 2.2A, as there will always be some level of vibrationspresent. In stable machining, though, the vibrations of the previous and current tooth passare in phase and occur at the tooth passing frequency and its harmonics, and thereforewe obtain a (roughly) constant chip thickness. In unstable machining, the vibrations ofthe previous and current tooth pass are out of phase causing the chip thickness to growuncontrollably. The vibrations in unstable machining occur at the following frequencies[2, 7]:fc = fn? c ft ;c = {0,1,2, ...} (2.6)where fc is the chatter frequency, fn is close to the natural frequency of the dominant72.1. Detection and Suppression of Chattermode of the tool-workpiece combination, and ft is the tooth passing frequency. Two maincharacteristics of chatter can then be identified given the preceeding discussion:? The occurrence of chatter brings on a significant increase in the amount of cuttingforce and, consequently, tool vibration and sound, due to the increase in chip thick-ness.? Signals measured during stable milling (ie forces, vibrations, or sound) will have fre-quency content predominantly around the tooth passing frequency and its harmonics,while signals measured during an unstable milling process will contain additionalcontent at the frequencies in equation 2.6.These are the two main characteristics used to distinguish between stable and unstablemachining processes in the literature examples presented in the following section.2.1.2 Online Detection of Chatter VibrationsMany methods exist for online detection of chatter, some going back to the early 1980s [8].Methods were initially developed for the turning of long slender rods where chatter wasa severe limitation; however, over the years online chatter detection has also been madefor milling and other operations. Most methods do not require a significant amount ofinformation regarding the cutting process, and those that do only require readily availablecharacteristics such as spindle speed or the number of teeth of the cutter.Many methods for detecting chatter involve monitoring some signal, such as force,noise, or acceleration, and applying a maximum threshold to the measured value. If themeasured signal is above the threshold then the system is considered to be undergoingchatter vibrations. S.Y Tsai [9] monitored the acceleration of the tailstock during turningoperations and compared it to a predetermined reference level, which was found from stablecutting experiments, in order to detect the occurrence of chatter. Kubica and Ismail [10]82.1. Detection and Suppression of Chatterdeveloped a chatter indicator, called the R-Value, which is based on the ratio of dynamicforces, FYdynamic, to the static forces, FYstatic, in the tangential direction as:R =??ni=1 FY2dynamic?ni=1 FY2static(2.7)where n in this case is the number of samples. Dynamic and static components ofthe force are found through filtering techniques and the R-value is compared to a refer-ence threshold to determine whether chatter has occurred. The amplitude of acousticalnoise from microphone measurements has also been used as a chatter indicator in someworks. Riviere [11] compared the microphone measurements directly to a threshold todetermine whether chatter ocurred while N.C Tsai [12] used the Acoustic Chatter SignalIndex (ACSI), LI , given byLI = e0.5|v| (2.8)where v is the voltage output of the microphone. Methods based on only the ampli-tude of the measured signal do not require any information about the cutting process itself;however, the threshold must always be determined in advance based on stable cutting ex-periments. Determining the required threshold can be time consuming since it is dependanton the cutting conditions and as such needs to be calibrated individually for different cut-ters, work piece materials, and even different sensor positions (for example, in the case ofusing a microphone to detect chatter).Similar to the amplitude based techniques is the once-per-revolution signal variancedeveloped by Schmitz [13]. This technique is based on the tendency for cuts to be syn-chronous with spindle or tooth passing frequency. Due to this property, when samplingonce every tooth passing or spindle period during stable cutting there would be little tono variance, while during chatter there would be a significantly higher variance. Sincethe variance during chatter is significantly higher than stable cutting, it is more likely that92.1. Detection and Suppression of Chattera single threshold can be suitable for multiple cutting conditions, although the thresholdmust still be found in advance from stable cutting experiments. This technique requiresprior knowledge of the spindle speed during cutting since at least the spindle period mustbe known to apply the algorithm.The most commonly used method for chatter detection is to take the Fast Fourier Trans-form (FFT) of a sensor signal (for example acceleration, force, or microphone noise) andcompare the magnitudes at different frequencies [9, 11, 13, 14, 15]. Since stable cuts aresynchronous with the tooth passing frequency[2], chatter can be detected by searching thespectrum for frequencies that are not harmonics of the tooth passing or spindle frequencies,and comparing their amplitude to the spindle or tooth passing frequency?s amplitude. Thismethod requires the spindle speed, number of teeth, and knowledge of the characteristicsof air cutting in advance in order to detect chatter and can be used for any combination ofcutting conditions.2.1.3 Chatter AvoidanceFor online chatter avoidance the method used to control chatter depends greatly on themethod used to detect chatter in the first place. Weck [4] proposed a method, referred tohere as Spindle Speed Selection (SSS), where the chatter frequency is detected online andthen the tooth passing frequency is adjusted to be a sub harmonic of the chatter frequency.This work has since been implemented in a number of works, for example previously bySmith and Tlusty [16, 17] and recently by Bediaga[15], and it has also been implementedin commercial software such as Harmonizer?, Metal-MaxTM, and most recently the Man-ufacturing Automation Laboratory?s ChatterPro. While this method works well for highspeed machining operations, at lower speeds the lobes become very narrow, as illustratedin Figure 2.3, and it becomes difficult to use SSS. For example, in Figure 2.3 the lobe at6000 RPM and 1.5mm depth of cut is only 190RPM wide, or about 3Hz, compared tothe lobe at 16000 RPM and 1.5mm depth of cut which is 2200 RPM wide, or about 37Hz.102.1. Detection and Suppression of ChatterSince the lobes are more narrow at low speeds small errors in the detected chatter frequency,setting of the tooth passing frequency, or small changes in the FRF of the tool-workpiececombination can cause the system to go unstable again.Figure 2.3: Example lobes for a 12mm diameter cutter in 75% immersion down milling ofAluminium 7075.If other methods are used to detect chatter, such as the amplitude-based methods dis-cussed above or the once-per-revolution signal variance, then the chatter frequency willremain unknown, and as such SSS cannot be used. Tsai [12] proposed a chatter controlmethod where the spindle speed was ramped up or down at a rate depending on the am-plitude of microphone measurements until the amplitude of the microphone measurementwent below a minimum threshold. This forces the spindle speed towards one of the stabilitylobes.Methods involving the continuous variation of spindle speed have also been well re-searched to reduce chatter and improve the limiting depth of cut, typically at low spindlespeeds [18, 19, 20, 21]. While the method was initially developed for turning operations ithas been shown by several researchers to be applicable to milling aswell[20, 22]. Spindlespeed variation (SSV) works by varying the phase shift ? between the current and pre-vious tooth passes, which adds damping to the system and reduces the chatter amplitude112.1. Detection and Suppression of Chatter[18, 19, 22]. In [22], it was shown analytically and experimentally that SSV can be usedto suppress chatter SSV provided that the frequency and amplitude of the spindle speedvariations are above some minimum depending on the chatter frequency.Al-Regib[23] presented a method for finding the minimum amplitude and frequencyof sinusoidal speed variation that will suppress chatter. He considered the energy-basedstability of SSV, and used this to find an analytical method for finding the optimal SSVamplitude based on the chatter frequency and operational spindle speed. He also formulatedthe minimum SSV frequency required based on removing the vibrations within a toothpassing period.Many works have been aimed at predicting the stability of SSV operations as well; forexample, Brecher [24] recently presented a method where the dynamics of the spindle aswell as the FRF of the tool workpiece combination were considered to generate stabilitylobes for varying SSV parameters. Further, Seguy and Insperger [25] showed that it ispossible to apply SSV in high speed milling operations in order to eliminate some types ofchatter. The main downside of the SSV method is that it requires spindle drives assembleyswith high bandwidth and which can output high torques in order to supply the range ofamplitudes and frequencies necessary to suppress chatter at various cutting conditions.2.1.4 Sensors for Chatter DetectionThis section addresses the sensor selection for chatter detection. In general, chatter canbe characterized by very high deflections at the tool-workpiece contact zone and high chipthicknesses which results in high cutting forces. Therefore, chatter vibrations can be sensedusing measurements of the displacement of the tool tip, the acceleration of the tool tip, thecutting force and also the cutting torque, since each of these properties would be affectedby the vibrations. Further, as shown by Riviere in [11] , and Tlusty and Smith in [26], audiosignals can also be used to detect vibrations with equivalent performance to accelerometer,displacement, or dynamometers.122.1. Detection and Suppression of ChatterUse of any of the sensors comes with its own advantages and disadvantages. Dy-namometers are too costly to be used in a practical shop, and accelerometer and displace-ment sensors can be difficult to set up. On the other hand, microphones can be easy to set upto detect chatter, and require very little prior knowledge. In addition, consider the typicalpolar plot of a unidirectional microphone shown in Figure 2.4. These types of microphonesare useful at isolating sounds coming from the direction the microphone is pointing in. Assuch, noise is inherently cancelled so long as the microphone is always kept facing thecutting tool. However, microphones are still susceptible to noise sources coming from thesame direction as the desired sound.Figure 2.4: Typical Polar Diagram of a Unidirectional (Cardioid) MicrophoneIn this thesis, a unidirectional cardioid type microphone was used; however, the samealgorithms can be used with other sensors, such as accelerometers or dynamometers, with132.2. Online Estimation of Cutting Torque using Motor Currentlittle modification.2.2 Online Estimation of Cutting Torque using MotorCurrentTypically dynamometers are used to provide measurements of the cutting forces and torquesin real time. However, dynamometers have a high cost associated with them, and as a resulttheir use in industry may not be economical[27]. Furthermore, rotary dynamometers usedto measure cutting torque can significantly decrease the stiffness of the tool-workpiececombination which limits the allowable depth of cut and thus the material removal rate(MRR). As such, focus has shifted towards the indirect measurement of cutting forces andtorques which can then be utilized in, for example, adaptive control systems [28], or themonitoring of tool wear or fracture [29, 30].Feed current, in particular, has been used in many works to estimate the feed forces inmilling [31, 32, 33]. These methods are based on the tendency for feed drives to have alinear current-torque relationship, ie:Tm = KtIm (2.9)where Tm is the torque acting on the feed motor, Kt is the torque constant of the motor,and Im is the current of the motor. Once the feed drive?s torque is known it can be convertedto the feed force based on, for example, the pitch of the ball screw. This model is only validfor DC motors [34] or field-controlled induction motors [35]. As discussed by Matsubara[27], however, there are many challenges in estimating the forces from the feed motors.First, the overall torque balance can be considered as:Tm = Tinertia+Tf ric+Tcut +Telecloss (2.10)142.2. Online Estimation of Cutting Torque using Motor Currentwhere Tinertia is the component due to the moving mass, Tf ric is the component dueto friction, Telecloss are the losses in the electrical system, and Tcut is the component dueto cutting that we are interested in. In a complex 5-axis part, the direction of cut maybe constantly changing, and as such the inertial and frictional components must be prop-erly accounted for. The frictional component, in particular, can be especially difficult toaccount for when using ball screw drives and rolling guideways, as shown by Matsubara[27]. Kamigochi et al [36] developed their own linear drive and used the current of themotors to estimate the forces and torques, and were able to achieve accurate results. Sincethey developed the motors themselves, a detailed model of the motor could be used, sinceall the parameters were known. In addition, the friction in the system was minimized byusing hydrostatic guideways and linear motors.The advantage of using the spindle current is that the friction is much easier to accountfor since the spindle operates at a constant speed, and the friction in the spindle motor istypically lower than the servo drives [27]. Several researchers applied the simple model ofequation 2.9 to estimate the spindle torque [37, 38, 39, 40]. As mentioned by Oh [39] andshown in Section 4.2, the torque constant Kt for induction motors is not actually constantand is a function of both the spindle speed and the amount of load on the motor; however,it can be assumed to be constant within a small range of spindle speeds and loads. Whilethis simplifies the process, for spindle speeds and loads far from the ones used to identifythe torque constant, the model must be recalibrated should the cutting parameters change.The exception is when the motor is being driven using field-oriented control; for example,Kwon [41] was able to apply the simplified model since their spindle motor was drivenusing a variant of field-oriented control.The main contribution of this part of the thesis is the application of an induction motormodel which can be applied to a wider range of speeds and loads with a single calibration.The model used is taken from Krause [35], and is applied within an Extended Kalman Filter(EKF).152.3. Adaptive Control of Machining Process2.3 Adaptive Control of Machining ProcessThe main goals of controlling cutting forces or torques online are to both improve the pro-ductivity of the process, and to ensure that the conditions used do not exceed the limitationsof the spindle or tool. Various methods have been developed in the past; Oh [39] presenteda method for estimating the torque in drilling process using the spindle current, and thenapplying control commands using a proportional-integral-derivative (PID) controller. Thegains of the controller were obtained from experiments offline in this case. This type ofcontrol law is not practical since the controller would need recalibration anytime the cut-ting parameters change. This is the main motivation for using adaptive control algorithmsinstead, which first consist of a parameter estimation stage from which the controller gainsare calculated.Adaptive control laws, such as those used in [6, 42], have been developed in order tocontrol the machining process, and have a block diagram as shown in Figure 2.5.Figure 2.5: Block diagram of Adaptive Control in MillingThe cutting process, Gc (z), is a function of the cutting coefficients of the workpiece,and the process parameters (immersion, depth of cut, etc), which can be constantly chang-ing for a complex geometry. The goal of the adaptive controller is to, at each time interval,estimate the combination of Gc (z) and Gs (z), and then use this information to create theappropriate control law X(z)Y (z) . Previously, dynamometers were used to provide the feedbackfor the adaptive control algorithms [6, 42, 43]; however, as discussed in Section 2.2, dy-namometers have a significant cost associated with them and may affect the stiffness of162.3. Adaptive Control of Machining Processthe tool-workpiece combination. The feasibility of using spindle current as a monitoringsignal within adaptive control algorithms has been addressed in previous works such as[34, 27, 44].This thesis uses the algorithm developed by Altintas in [2, 45] and applies it for use ona commercial machine tool by implementing the algorithm on an external computer andcommunicating with the machine over Ethernet connection. Two methods of measuringthe torque are examined; one, using the spindle current to estimate the torque, and the otherby obtaining the torque estimate from the machine over Ethernet communications.17Chapter 3Detection and Suppression of ChatterVibrationsThis section details the algorithm used for detection and suppression of chatter in milling.The method here attempts to combine the spindle speed selection (SSS) method for sup-pressing chatter at high speeds with the spindle speed variation (SSV) method for suppress-ing chatter at low speeds. Detection in both cases is done using the Fast Fourier Transform(FFT) method.13.1 Online Detection of Chatter Vibrations3.1.1 Detection of Chatter using FFTAs mentioned in Section 2.1.1, in stable milling operations the sound measured containscontent at the tooth passing frequency and its harmonics, assuming there is no runout in thecutter. It is also possible to see harmonics of the spindle frequency present in the FFT ofthe signal due to effects such as runout in the cutter. As these are still stable vibrations, thefrequencies present can be described as:fd = c fs; c = {1,2, ...} (3.1)where fd is the dominant frequency in the FFT of the signal, and fs is the spindle1A version of this chapter has been published in the Proceedings of the Machine Tool Technologies Re-search Foundation?s Annual Meeting 2013 [46].183.1. Online Detection of Chatter Vibrationsfrequency. In unstable machining the dominant frequency is instead related to the chatterfrequency, which occurs close to one of the natural frequencies of the machine:fd = fc = fn? c ft ; c = {0,1,2, ...} (3.2)where fc is the chatter frequency and fn is one of the natural frequencies of the machine.This is the same as equation 2.6. The difference between stable and unstable machiningtherefore provides a practical means for automated chatter detection.In order to apply the FFT method, two main parameters must be selected: the samplingfrequency Fs and the number of samples used at each interval, N f f t . Based on the Nyquistsampling theorem, the sampling frequency must be at least twice the highest frequency,fmax, expected in the FFT:Fs ? 2 fmax (3.3)For conventional machine tools, we do not expect modes above ? 6000Hz; therefore,in this thesis the sampling frequency was selected as Fs = 12800Hz. The selection of N f f tdetermines the frequency resolution, fr, as:fr =FsN f f t(3.4)In addition to this, the FFT operation has the fastest computational speed if N f f t isselected as a power of 2. Therefore, in order to ensure the detected chatter frequencywas within 1Hz of the actual chatter frequency, and to ensure good computational speed,N f f t = 8092 samples was selected.In this thesis, the following algorithm is used to monitor the occurrence of chatter inmilling:? Perform FFT on the cutting sound signal in real time.193.1. Online Detection of Chatter Vibrations? Apply a comb filter on the FFT to remove the spindle frequency and its harmonics? If the magnitude of the highest peak in the filtered FFT is higher than a certain pre-defined percentage of the magnitude of the tooth passing frequency in the unfilteredsignal then the cut is unstable; otherwise, it is stable.For the second step, a comb filter is used to remove the spindle frequency and its harmonicsfrom the frequency spectrum. Designing the filter is explained in Section 3.1.2.3.1.2 Comb FilteringNotched comb filters are used to remove harmonics of a specific frequency (in this case,the spindle frequency) from a measured signal [47], and are most commonly used in music.Removal of the tooth passing frequency and its harmonics from the sound spectrum isessential in order to avoid false detection of forced vibrations [2]. A comb filter can beexpressed in the discrete time domain (z) as:G(z) =bcomb (1? z?o)1?acombz?o(3.5)where acomb and bcomb are constants and o is the order of the filter, or one plus thenumber of notches. Knowing the sampling frequency Fs, and the spindle frequency fs, thefilter order can be found as:o = f loor(Fs2fs+0.5)(3.6)where f loor is the rounding down operation, and is used to ensure that o is an integer.The constants acomb and bcomb determine the bandwidth and the ?sharpness? of thecomb filter:acomb =21+? ?1;bcomb = 1?11+? ;? =Gb?1?G2btan(o fb4)(3.7)203.1. Online Detection of Chatter Vibrationswhere Gb is the desired gain at a banwidth of fb, as shown in Figure 3.1.Figure 3.1: Example of a comb filter designed to remove a spindle frequency of 55Hz andits harmonics, with Gb = 0.7 and fb = 3HzCare must be taken in the selection of Gband fb. Due to the limitations in the resolutionof the FFT discussed previously, there will naturally be some error in the spindle frequencyin the FFT. Also, since we are using the f loor operation to determine the notches in equa-tion 3.6, the notches will not always occur exactly at the spindle frequency. Therefore, ifthe bandwidth is too narrow, we may not be able to filter out the spindle frequency and itsharmonics. Furthermore, if the bandwidth is too large, then we could possibly filter outchatter occurring near a harmonic of the spindle frequency. In this thesis, Gb = 0.7 is se-lected (this corresponds to ?3dB, which is a commonly used marker in controls), and thebandwidth is determined based on the spindle frequency as:fb =???????fsQ fr <fsQfr fr >fsQ(3.8)where Q is a quality factor determined by the operator. In this thesis, Q = 20 wasselected, ie for high speeds the bandwidth of the comb filter is set as 5% of the spindle213.2. Suppression of Chatter Vibrationsfrequency, and for low speeds the bandwidth is defaulted to the resolution of the FFT.3.2 Suppression of Chatter Vibrations3.2.1 Spindle Speed Selection (SSV)In the previous section, the chatter frequency fc is detected using the FFT method. Duringmachining each tooth generates k complete waves and ?2pi fractional waves [2], ie:fcft= k+?2pi (3.9)If the fractional wave is zero, then the previous and current tooth pass are in phase, andthe system is expected to undergo stable vibrations (ie, case B of Figure 2.2) provided thatthe limiting depth of cut is not exceeded. If the chatter frequency is known the spindlefrequency can then be changed to minimize the phase difference between subsequent toothpasses [4, 17]:nnew =60 fcknewN; knew = {1,2, ...} (3.10)where nnew is the new spindle speed[rpm], N is the number of teeth of the cutter, andknew is the number of complete waves in one tooth passing interval of the new spindlespeed. If we select knew > k, then the new spindle speed will be lower than the initialspindle speed, and if we select knew ? k, the new spindle speed will be higher than theinitial spindle speed. It is more desirable to select knew ? k, since from the stability lobetheory [1, 2], we know that, typically, at higher speeds we have a higher maximum depthof cut. Furthermore, increasing the speed will yield higher productivity from the operation.Care must be taken, however, to ensure that the resulting surface speed is not too high asthe tool will wear more quickly due to the additional heat generated.When executing the algorithm first knew ? k is attempted , and if the spindle speed is223.2. Suppression of Chatter Vibrationshigher than some operator defined maximum knew > k is selected. Regardless of the selec-tion of knew the feedrate is adjusted proportional to the spindle speed to maintain the initialprogrammed chip thickness. The spindle speed and feedrate are adjusted by manipulatedthe override values, the process of which is discussed in Section 3.3.As discussed in Section 2.1.3, SSS is effective generally at high speed cutting wherek < 5. Should SSS fail to eliminate chatter, SSV is used instead, and is discussed in Section3.2.2.3.2.2 Spindle Speed Variation (SSV)While various variation patterns have been used in literature, including random speed vari-ation [48], and triangular variation [25], it has been shown that sinusoidal variation ofspindle speed is the most effective [25] and therefore, the resulting spindle speed, ?, whenSSV is applied is given by:?= ??+ ??sin(2pi fssvt) (3.11)where ??[radsec]is the mean spindle speed, and ?? and fssv are the amplitude and fre-quency, respectively, of the sinusoidally varying spindle speed. Given a detected chatterfrequency, the optimal amplitude ?? was determined by Al-Regib [23] to be the amountthat eliminates the phase difference between subsequent cuts, ie:? = ????=60 fcnknewN?1 (3.12)where knew = k. For practical purposes, the amplitude ratio ? should be limited to avoidadverse effects to the spindle drive. In this thesis, the maximum amplitude ratio permittedwas 10%.Selection of fssv has been shown by several researchers [19, 23, 49, 50] to be less impor-tant than the selection of ??. Therefore, at the amplitude ??, we apply the highest possible233.2. Suppression of Chatter Vibrationsfssv in order to avoid chatter. The SSV frequency is limited by the spindle drive bandwidth,as it cannot go beyond this amount, and the spindle power. In practical machining, most ofthe spindle power will be used to overcome the machining loads, and thus the applicationof SSV should not consume more than a pre-specified percentage of the spindle?s availablepower. The power, Pm, required for applying SSV can be described by:Pm = J?d?dt(3.13)where J is the spindle?s moment of inertia and is identified automatically as explained inSection 3.2.3. The maximum power required for applying SSV can be found by substitutingequation 3.11 into equation 3.13:Pmax = 2pi fssv??2?Jcos(?) [1+?sin(?)] (3.14)When the power is at maximum then the derivative of the power with respect to time is zeroand thus we find ? as:dPdt= 0? ? = sin?1(?1+?1+8?24?)(3.15)Rearranging equation 3.14 for fssv yields:fssv =Pmax2pi???Jcos(?) [1+?sin(?)](3.16)Here, Pmax is the maximum power allocated to the usage of SSV, and is pre-defined bythe operator. In this thesis, the Pmax was selected as 10% of the spindle?s maximum power.In summary, the following steps are followed to program SSV:? Compute the amplitude of SSV using equation 3.12? If the amplitude obtained from equation 3.12 is larger than the threshold, set theamplitude to the threshold243.2. Suppression of Chatter Vibrations? Calculate fssv using equation 3.16? If the frequency obtained from equation 3.16 is larger than the spindle?s bandwidth,set fssv equal to the spindle?s bandwidth.In order to calculate the power the spindle?s moment of inertia must be identified in ad-vance. The process for doing so is explained in Section 3.2.3.3.2.3 Identification of Spindle Moment of Inertia and TransferFunctionA simplified block diagram of the spindle control loop is shown in Figure 3.2. The band-width of the electronics of the machine is significantly higher than the mechanical part (ie,the spindle drive), which acts as a low pass filter for the system, and as such the transferfunction can be approximated by a first order system:Figure 3.2: Block diagram of the spindle control loop?out?re f=1?s+1 (3.17)where ? is the spindle drive?s time constant with an approximate bandwidth of(1?)Hz.The time constant is identified by applying a step command to the motor and measuringthe time it takes for the spindle speed to reach ? 63% of the commanded value. The step253.2. Suppression of Chatter Vibrationscommand is generated using the communication framework described in Section 3.3, andthe instantaneous spindle speed is recorded the same way.The total motor torque is comprised of the part used to overcome friction and the partthat provides the acceleration onto the spindle shaft:Tm = Jd?dt+Tf ric (3.18)where Tmis the motor torque, and Tf ric is the frictional torque. Under high accelerationsthe friction torque is assumed to be negligible compared to the inertial loads and can beneglected. The spindle power is obtained by multiplying both sides by the spindle speed:Pm = Tm?= Jd?dt?? Pmdt = J?d? (3.19)By integrating both sides of Equation 3.19 over the time span [t1, t2] when the spindlespeed increases from ?1 to ?2, the inertia can be found asJ =2? t2t1Pmdt?22??21(3.20)The method for identifying the spindle?s moment of inertia, J, can be summarized as:? Set the spindle speed to below half of the maximum speed, keeping in mind to avoidany gearing or winding changes? Apply a 200% spindle speed override through the real time communication systemand simultaneously record spindle speed and power as a function of time? Numerically integrate the recorded power and substitute in Equation 3.20 to obtainJ.The inertia of the motor is identified in advance before cutting occurs using this algorithm,and is then used within the SSV algorithm to calculate the parameters.263.3. Experimental Setup3.3 Experimental SetupA Mori Seiki NMV 5000 vertical machining center was used for the experiments. Thealgorithm was implemented on a laptop running 32-bit Matlab which was able to acquiremicrophone signals through an NI-USB 9234 Data Acquisition (DAQ) box.Real-time communication with the machine tool was done using Fanuc?s FOCAS li-brary for Fanuc controllers. Similar libraries are available for most controllers, includingSiemens, Mitsubishi, etc. An overview of the real time communication framework can beseen in Figure 3.3.Figure 3.3: Overview of real time communication frameworkAs shown in Figure 3.3, the computer is connected to the CNC using Ethernet connec-tion. In our setup, this was done directly using a crossover cable; however, it can also bedone in a networked environment, in which case one computer could communicate withmultiple CNC machines silmultaneously. A direct Ethernet connection over crossover ca-ble provides the least communication delay of the options, though, since it is a 1 to 1 con-nection. The setup used in this thesis provided a communication delay of 7ms, includingprocessing delays, which is the time between sending the command and when the machinereceives the command (ie, the program must wait 7ms each time it sends a command to themachine). The total time it takes for the machine to respond to a command was measuredto be 100ms.FOCAS libraries provide a variety of functions mainly aimed towards monitoring ma-273.3. Experimental Setupchine status; for example, reading machine status, sending NC programs to the machine,or reading feedrate and spindle speed. With some modifications to the ladder, the FOCASlibraries can also be used to read and write to the feedrate and spindle speed override. Thisallows us to change the feed and spindle speed with a resolution of 1% of the set value, inthe range of 0-254% of the set value.As the FOCAS libraries were developed for C programs, the functionality was imple-mented using Matlab Executable (MEX) files, which adds a minor but insignificant amountof processing time.The overall experimental setup can be seen in Figure 3.4.Figure 3.4: Experimental Setup for Chatter Detection283.4. Experimental Results3.4 Experimental ResultsResults for the chatter detection and suppression algorithm are shown below. The resultsare divided into two main parts: results of SSS method, and results of the SSV method.3.4.1 Results of SSSResults of the SSS method are presented below. Cutting tests were conducted in high speedmilling of AL-7075 Aluminium and in low speed milling of AISI-1045 steel.Detection and Suppression in High Speed MillingCutting tests were conducted on AL-7075 aluminium with a 12mm diameter 2 flute end-mill.Figure 3.5: Example of chatter detection. 50% immersion downmilling with 4mm depthof cut and 0.1mm/tooth feedrate. Harmonics of the tooth passing frequency are shownin green lines, while the chatter frequency is shown in red. Left: n = 12000 revmin , Right:n = 12939 revminFigure 3.5 demonstrates the methodology for chatter detection, and Figure 3.6 showsthe resulting surface finish. Part (a) shows the cutting sound data recorded at 12000 RPM293.4. Experimental ResultsFigure 3.6: Resulting surface finish for 50% immersion downmilling with 4mm depth ofcut, and 0.1mm/tooth feedrate.(Segment A) and 12939 RPM (Segment B). The unfiltered FFT of the cutting sound datais shown in (b), and illustrates the importance of filtering the harmonics: in (b1) the toothpassing frequency is 400Hz and its harmonics are denoted by the green lines. It can beseen here that the second and third harmonics of the tooth passing frequency (800Hz and1200Hz) have large magnitudes in the FFT and may be incorrectly identified as chatterwere they not filtered out. Part (c) shows the corresponding comb filters for both cases, andpart (d) shows the filtered FFTs for both the stable and unstable segments. As shown inpart (d1), the comb filter is able to remove the harmonics almost entirely, without affectingthe magnitude of the chatter frequency. In this example, the chatter frequency in SegmentA was detected as ~2650Hz, and the stable speed of 12960 RPM (corresponding to 108%spindle speed override) was set through FOCAS.In the example of Figure 3.5, knew = kold was selected to suppress chatter. Figure 3.7shows the results of the SSS method at various different cutting conditions in the millingof AL-7075 aluminium, and with different selections of knew.In Figure 3.7A, knew is selected as the highest lobe that does not exceed the machine?smaximum speed. In this case, productivity is improved; however, the surface speed is alsoincreased substantially. Surface speed in this case was increased 46% which will also causean increase in the amount of heat generated during cutting, and thus increasing the rate atwhich the tool wears. In cases B and C of Figure 3.7, knew = koldis selected instead; ie, thespindle speed is increased to the nearest lobe, in order to minimize the amount of additionalheat generated. In case D, knew = kold +1 is selected; ie, the spindle speed is decreased to303.4. Experimental ResultsFigure 3.7: Results of SSS method in 75% immersion downmilling of AL-7075 aluminiumwith 2 flute 12mm diameter cutter and 0.1mm/tooth feedrate. Red crosses denote cuttingconditions resulting in chatter, while green crosses denote stable conditions. The arrowsindicate the transition to stable cutting conditions as per the SSS methodthe nearest lobe, since it is not possible to increase the speed from this point, and thereforethe surface speed is decreased. Each of these selections of knew results in a stable process,and therefore the main considerations to take when selecting kneware the maximum spindlespeed of the machine tool and the maximum allowable surface speed of the tool for wearconsiderations.Note that in case D decreasing the spindle speed results in a stable process which isnot always the case. As the speed is decreased, the maximum allowable depth of cut willalso decrease, as can be seen by the narrow stability lobes here. It is therefore possible thatsuccessively selecting lower spindle speeds may result in cutting conditions that above thestability lobes. Furthermore, should the initial cutting condition lie far above the stabilitylobes, it will not be possible to select a stable cutting speed. As such, the number ofsuccessive speed changes was limited to 3 in the implementation of this algorithm, ie if themethod fails to suppress chatter 3 times, then the algorithm has failed. At this point SSV isapplied if possible; otherwise, cutting is stopped and the depth of cut must be changed.313.4. Experimental ResultsSuppression in Low Speed MillingCutting tests were conducted on AISI-1045 steel with a 25mm diameter 2 flute endmill.Figure 3.8 shows the application of the suppression and detection algorithm at lowspeed. The process is the same as was shown in Figure 3.5, and again the chatter frequencycan be identified by looking for the maximum amplitude in the filtered FFT shown in (d1).When the same process is applied in the stable process, the filtered FFT in (d2) can be seento contain no large peaks outside of the tooth passing frequency and its harmonics.Figure 3.8: Application of SSS in slotting with 3.5mm depth of cut AISI-1045 steel Seg-ment A: 3117 revmin , Segment B: 3024revmin . Harmonics of the spindle frequency are shown ingreen lines, while the chatter frequency is shown in red.Figure 3.9 shows the stability lobes of the experimental setup, along with the resultsof 4 cutting tests conducted at low spindle speeds (1385 and 1435 revmin ) and high spindlespeeds (3285 and 3600 revmin ). As shown in the results of Figure 3.9, the cutting condition of3285 revmin and 3.5mm depth of cut is well in the instable region, while 3000revmin correspondsto the next higher lobe. In Case 2 of Figure 3.9, chatter is detected at 726 Hz, and thenew spindle speed of 3600 revmin (corresponding to 10% override) is sent to the CNC throughFOCAS, and as shown in part (e), the chatter frequency is eliminated from the spectrum.When the chatter detection algorithm was applied at 1385 revmin and 3.5mm depth of323.4. Experimental ResultsFigure 3.9: Results of slotting AISI-1045 steel with 3.5mm depth of cut. a) stability lobesof the experimental setup, (b-e) FFT of cutting sound at 1385, 1435, 3285, and 3600 revmin ,respectively.cut, as indicated by Figure 3.9(b), a chatter frequency of 713Hz was detected, which cor-responds to the same mode as detected previously. After adjusting the spindle speed to1435 revmin (corresponding to lobe number 17), chatter occurs once more at approximatelythe same frequency (713Hz), as indicated in Figure3.9(c). Therefore, SSS is not effectivein suppressing chatter at such low speeds. Since the lobes are more narrow at these con-ditions, and the maximum depth of cut is also much lower, this is not a surprising result.Further, using FOCAS we only have 1% resolution on changing the spindle speed, whichcompounds the difficulty of catching into narrow lobes at such low speeds.3.4.2 Results of SSVResults of the SSV method are presented below. First, the results of the method in lowspeed milling of AISI-1045 steel will be presented. This is followed by a discussion of theinfluence of amplitude and frequency selection on the effectiveness of the method. Finally,experiments showing the accuracy of the estimated spindle inertia are shown to validate the333.4. Experimental Resultsidentification technique.Suppression of Chatter in Low Speed MillingIn Figure 3.9, the SSS algorithm failed to suppress chatter at 1385 revmin . Using Equa-tion 3.12, the optimum amplitude for SSV to suppress the chatter frequency of 773Hzis ? = 0.04; ie, an amplitude of 4% of the nominal spindle speed should be applied. Ac-cording to Equation 3.16, the maximum allowable frequency using a threshold of 10% ofthe maximum spindle power (15.5kW) is larger than the spindle?s bandwidth, and so themaximum spindle frequency fssv = 4Hz should be applied. The result of applying SSVwith 4% amplitude and 4Hz frequency is shown in Figure 3.10.Figure 3.10: Results of slotting AISI-1045 steel with 3.5mm depth and 1385 revmin basespindle speed without SSV (segment A) and with SSV at 4% amplitude and 4Hz frequency(segment B) a) cutting sound, b) FFT of segment A, c) FFT of segment BIn Figure 3.10, Segment A is measured when a constant spindle speed of 1385 revmin isapplied, while Segment B is measured when SSV is applied with 4% amplitude and 4Hzfrequency onto the nominal spindle speed of 1385 revmin . Figure 3.10b) shows the FFT of thecutting sound during Segment A, which shows the chatter frequency occuring at 773Hz.Figure 3.10c) shows the FFT of the cutting sound during Segment B. Here it can be seen343.4. Experimental Resultsthat the amplitude of chatter at 773Hz in (b) has been reduced significantly, which indicatesthat the chatter has been successfully suppressed.Figure 3.11: Results of slotting AISI-1045 steel with 3.5mm depth and 1200 revmin basespindle speed without SSV (segment A) and with SSV at 5% amplitude and 4Hz frequency(segment B), a) cutting sound, b) FFT of segment A, c) FFT of segment BFigure 3.12: Surface finish resulting from unstable milling at 1200 revmin (right), and stablemilling at 1200 revmin with SSV of 5% amplitude and 4Hz (left). Feed direction is right to leftIn Figure 3.11, chatter occurred when slotting with 3.5mm depth and 1200 revmin , witha chatter frequency of 713Hz. Using the same process as was described for the case inFigure 3.10, the SSV parameters were calculated as 5% amplitude and 3.5Hz frequency.From Figure 3.11c, it can be seen that chatter was successfully suppressed once more bythe application of SSV. Figure 3.12 shows the resulting surface finish at 1200 revmin withoutthe application of SSV (right) and after the spindle speed variation was applied (left). It canbe seen that though the chatter marks have been entirely removed, marks are still presenton the surface. The feed per tooth, f , is related to the spindle speed, n, as353.4. Experimental Resultsf =FnN(3.21)where F[mmmin]is the programmed feedrate and N is the number of teeth of the cutter.Since the spindle speed is being continuously varied, so is the feed per tooth, and thus thechip thickness and forces. This, in turn, causes fluctuations in the static deflections left onthe part, which is what can be seen when SSV is applied in Figure 3.12.Influence of Amplitude SelectionIn this section, the result of selecting amplitude too far above or below the value calculatedby equation 3.12 will be discussed. Using the same base conditions as in the example ofFigure 3.11, ie slotting of AISI 1045 steel with 3.5mm depth of cut, 1200 revmin spindle speed,and SSV parameters of 5% amplitude and 3.5Hz frequency, experiments were conductedat higher and lower amplitudes to see the effect on chatter suppression. Figure 3.13 showsthe FFTs of experiments conducted with various amplitudes at 3.5Hz frequency.Figure 3.13A shows the results when constant spindle speed is used, while C shows theresults when the parameters calculated using equations 3.12 and 3.16 are used. In 3.13Band D lower and higher amplitudes of 1% and 8%, respectively, were used. It can be seenthat when the amplitude is less than the minimum calculated by equation 3.12, as is thecase in Figure 3.13B, the magnitude of the chatter frequency is reduced but is still stronglypresent within the FFT. The case of Figure 3.13B in the time domain is shown in Figure3.14.As discussed by Seguy[25], this result can be classified as ?globally stable, but practi-cally unstable machining?; ie, while the vibrations are not increasing, this operating con-dition may still be unusable due to the high initial amplitude of the vibrations. This typeof situation seems to generally appear when the amplitude is below the minimum, but tovarying degrees. For example, the result of slotting steel with 3.5mm depth of cut, 1200revmin base spindle speed and SSV of 4% ampltiude and 3.5Hz frequency is shown in Figure363.4. Experimental ResultsFigure 3.13: FFT of experiments in slotting of AISI 1045 steel with 3.5mm depth of cutand 1200 revmin with various SSV parameters, A) Constant spindle speed, B) SSV with 1%amplitude and 3.5Hz frequency , C) SSV using 5% amplitude and 3.5Hz frequency, D)SSV using 8% amplitude and 3.5Hz frequency3.15.In Figure 3.15 the initial vibrations are again larger than the case when we use the373.4. Experimental Results0 0.5 1 1.5 2 2.5 3 3.5?0.03?0.02?0.0100.010.020.03Time (s)Voltage (V)Cutting Sound, n = 1200 + (0.01*1200)sin(2pi*3.5Hz*t) [rev/min]Figure 3.14: Cutting sound of slotting AISI 1045 steel with 3.5mm depth of cut, 1200 revminbase spindle speed, and SSV with 1% amplitude and 3.5Hz frequency0 2 4 6 8 10 12 14 16 18 20?0.02?0.0100.010.02Time (s)Voltage (V)A) Cutting Sound, n = 1200 + (0.04*1200)sin(2pi*3.5Hz*t)0 100 200 300 400 500 600 700 800 900 100000.511.52x 10?3Frequency (Hz)MagnitudeB) FFT of Cutting SoundFigure 3.15: Cutting sound (A) and FFT (B) of slotting AISI1045 steel with 3.5mm depthof cut, 1200 revmin base spindle speed, and SSV with 4% ampltiude and 3.5Hz frequencyamplitude calculated by equation 3.12; however, after some time the magnitude of thechatter frequency is almost entirely removed from the FFT.On the other hand, in the case of Figure 3.13D, overestimating the amplitude in doesnot seem to have any adverse effects on the stability of the system. If the amplitude is toofar overestimated, though, it is likely that the system would become unstable; however,383.4. Experimental Resultsthere is some small margin of error as indicated by the results of Figure3.13D, and thushaving only 1% resolution on setting the spindle speed is not a limitation for applying thismethod.Influence of Frequency SelectionIn this section, the influence of frequency selection will be discussed. Using the same baseconditions as in the previous section, ie slotting of AISI 1045 steel with 3.5mm depth ofcut, 1200 revmin spindle speed, and SSV parameters of 5% amplitude and 3.5Hz frequency,experiments were conducted at varying frequencies to see the effect on chatter suppression.Figure 3.16 shows the FFTs of experiments conducted with varying frequencies and 5%amplitude. It has been shown by many researchers that, although frequency is not a criticalparameter for SSV, it must be greater than at least some minimum value [19, 23]. Accordingto Al-Regib [23], the minimum frequency for SSV can be found as:fssv,min =N??120pi sin?1(120pi fc?N??(pi+2pik)?1?)(3.22)In the case considered here, fssv,min = 2.5Hz is found, the results of which are shown inFigure 3.16C.The general trend seen in Figure 3.16 is that as the frequency of SSV increases, themagnitude of the chatter frequency in the FFT decreases, and therefore we have a morestable process. This result is expected, since the frequency of SSV directly influences howquickly the energy of chatter vibrations is dissipated. Thus in the method proposed here,the largest possible frequency for SSV is always used, in order to ensure that the vibrationenergy is dissipated as quickly as possible. If the minimum frequency found by equation3.22 is larger than our spindle?s bandwidth, however, the method may be able to completelyeliminate the chatter vibrations.393.4. Experimental Results0 5 10 15?0.0400.04Voltage (V) A1) n=1200(1+0.05sin(2pi*1Hz*t)) [rev/min]0 200 400 600 800 1000012x 10?3Magnitude A2) FFT of A10 2 4 6 8?0.0400.04Voltage (V) B1) n=1200(1+0.05sin(2pi*2Hz*t)) [rev/min]0 2 4 6?0.0400.04Voltage (V) C1) n=1200(1+0.05sin(2pi*2.5Hz*t)) [rev/min]0 2 4 6 8?0.0400.04Time (s)Voltage (V) D1)n=1200(1+0.05sin(2pi*3.5Hz*t)) [rev/min]0 200 400 600 800 1000012x 10?3Magnitude B2) FFT of B10 200 400 600 800 1000012x 10?3Magnitude C2) FFT of C10 200 400 600 800 1000012x 10?3Frequency (Hz)Magnitude D2) FFT of D1Figure 3.16: Cutting sound and FFT of experiments in slotting of AISI 1045 steel with3.5mm depth of cut and 1200 revmin with various SSV parameters, A) SSV with 5% amplitudeand 1Hz frequency , B) SSV using 5% amplitude and 2Hz frequency, C) SSV using 5%amplitude and 2.5Hz frequency, D) SSV using 5% amplitude and 3.5Hz frequencyEstimation of Power Consumed in Applying SSVIn Section 3.2.3, a method for automatically identifying the power consumed by applyingSSV was developed. This section discusses the accuracy of this method.First, the spindle speed was set to 8000 revmin , and 200% override was commanded whilethe speed and power were measured. Both the measurements and the commands wereexecuted through FOCAS. The resulting data from this process is shown in Figure 3.17.The power was numerically integrated and substituted into equation 3.20, to give aninertia of J = 0.0316 kgm2. This result was verified by applying various SSV amplitudesand frequencies onto various nominal speeds, measuring the power consumed and thencomparing it to the power estimated by equation 3.14. The results of the verification arelisted in Table 3.1, where the power is measured as a percentage of the maximum power.From Table 3.1 it can be seen that the inertia estimated using our methodology pro-vides a sufficient estimate of the power consumed by applying SSV. Part of the errors arebecause we are neglecting the power loss due to friction and electrical losses during the403.5. Summary0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6500100015002000Time(s)Spindle Speed (rad/sec)Inertia Identification Data0123x 104Power(Watts)Spindle SpeedPowerFigure 3.17: Spindle speed and power measured through FOCAS after 200% spindle speedoverride was commanded from a base spindle speed of 8000 revmin .Base Speed SSV Amplitude SSV Frequency Estimated Power Measured Power1875 revmin 5% 3.5 Hz 10% 12%1875 revmin 12% 2.0 Hz 12% 14%3000 revmin 1% 3.0 Hz 4% 5%3000 revmin 3% 2.0 Hz 10% 12%3000 revmin 8% 1.0 Hz 11% 13%Table 3.1: Results of estimated and measured power consumed by applying SSV of variousamplitudes and frequencies onto 1875 revmin and 3000revmin base spindle speeds.measurement of J and during the estimation of the power consumed by SSV. However, forthis application this level of accuracy is acceptable.3.5 SummaryIn this section an algorithm for the real time suppression and detection of chatter is pre-sented. The algorithm detects chatter by taking the FFT of the cutting sound and searchesthrough the spectrum to identify the potential chatter frequency, which occurs at non-harmonics of the spindle frequency. A comb filter is designed based on the measuredspindle speed and is applied to the FFT of the cutting sound to filter out the harmonics of413.5. Summarythe spindle frequency, to prevent incorrectly identifying forced vibrations as chatter. Oncechatter is detected, suppression is done using the SSS method; if this method fails, thenSSV is used at low spindle speeds. The algorithm is implemented on an external laptopcomputer which is connected to the machine over Ethernet connection. The algorithm wasverified in both high speed and low speed milling, using both the SSS and SSV methods tosuppress chatter.One limitation of this method is that surface marks due to chatter will always appearon the surface since chatter is only detected after it occurs, and the feed is stopped beforechatter is fully developed. For this reason, this method is most appropriate for roughingoperations. Another limitation of this method is that the suppression of chatter is not guar-anteed using SSS. In the tooling used here, the tool-workpiece FRF typically had only onedominant mode; for example, the tool shown in Figure 3.18A has one dominant mode at780Hz. The tool shown in Figure 3.18B, on the other hand, has flexible modes at 1200Hz,1500Hz, and 1700Hz. Using the tool of Figure 3.18B, if chatter is detected at, for example,1200Hz and SSS is applied, the new spindle speed may cause one of the other modes tochatter. For this reason, the maximum number of trials to suppress chatter must be input bythe operator in advance. If the method cannot suppress chatter within this number of trialsthen SSV is used if the spindle drive is capable, or the algorithm suggests that the axialdepth of cut be lowered. In addition to this, if the machining is done well above the lobesof the machine, then it will be impossible for the SSS method to suppress chatter, and againthe method will be stopped based on the selection of the maximum number of trials.In the following chapter the algorithm for torque estimation using a current sensor ispresented.423.5. Summary102 10300.51x 10?6Magnitude (?m/N) A) Tool?workpiece FRF of a 20mm 4 flute inserted endmill102 10300.51x 10?6Magnitude (?m/N)Frequency (Hz)B) Tool?workpiece FRF of a 25mm 2 flute inserted endmillFigure 3.18: Example FRFs of two different inserted endmills, a) FRF of a 20mm 4 fluteinserted endmill, b) FRF of a 25mm 2 flute inserted endmill43Chapter 4Torque Estimation Using CurrentSensorThis section describes the process used to estimate the cutting torque by measuring thespindle current. First, the induction motor model is presented based on Krause [35]. Then,the design of an Extended Kalman Filter (EKF) using the induction motor model is given.Finally, the experimental implementation and results are shown thereafter.4.1 Induction Motor Model4.1.1 Equivalent Circuit in Machine Reference FrameThe equivalent circuit for a three phase wye-connected symmetrical induction machine isshown below in Figure 4.1 in terms of the machine coordinates. Here, i denotes the current,r is the resistance, N is the number of turns of the coil, a, b, and c denote each of the threephases of the input power, and s and r denote the stator (stationary part of the motor) androtor (rotating side of the motor), respectively.The voltage equations can be written in matrix form based on the equivalent circuit ofFigure 4.1 as:???vabcsv?abcr???=???rs+ ddt Lsddt L?srddt (L?sr)T r?r + ddt L?r??????iabcsiabcr??? (4.1)where v is the voltage and L is the inductance.444.1. Induction Motor ModelFigure 4.1: Equivalent circuit for a three phase induction motor in machine coordinatesTo derive the torque equation the energy stored in the coupling field is found first. Foran electromagnetic system with n phases, it can be shown that the total field energy, Wf ,is[35]:Wf =12n?j=1n?k=1L jki jik (4.2)For a three phase induction motor, this yields:Wf =12(iabcs)T (Ls?LlsI) iabcs+12(iabcr)T (L?r?L?lrI)i?abcr +(iabcs)T (L?sr)i?abcr (4.3)where I is the identity matrix, and Lls and Llr are the leakage inductances of the statorand rotor side, respectively. The torque is then the derivative of the field energy with respectto the angular displacement of the rotor:Tm =?Wf??rm(4.4)where ?rm is the true angular displacement of the rotor. Typically, induction motors are454.1. Induction Motor Modelreferred to an equivalent two pole machine based on the electrical angular displacement as:?re =(P2)?rm (4.5)where P is the number of poles of the machine. Therefore,Tm =(P2)?Wf??re(4.6)Since Ls and L?r are not functions of ?r, the torque can be written as:Tm =P2(iabcs)T ???re[L?sr]i?abcr (4.7)When analyzing three phase electrical systems, the variables of current and voltageare typically transformed into an equivalent reference frame where the abc variables aretransformed into qd0 variables. This eliminates the time-varying inductances of the motorand greatly simplifies the analysis. Using the transformation to qd0 reference frame shownby Krause [35], equation 4.7 can be rewritten in terms of qd0:Tm =(32)(P2)LM(iqsi?dr? idsi?qr)(4.8)4.1.2 Steady State AnalysisFrom equation 4.8, we can see that the torque for an induction motor is proportional tothe square of current. In practice, it is difficult to measure the actual rotor currents i?drand i?qr; however, it is quite simple to measure the stator currents. In addition to this,while it is possible to go from the stator variables to the rotor variables using equation 4.1,this requires measurements of the rotor and stator resistances and inductances. The motorparameters can be identified using DC test (to find the stator resistance, rs), no-load test (tofind the stator inductance, LS +LM ), and a blocked rotor test (to find the rotor resistance,464.1. Induction Motor Modelr?r, and the leakage inductances Ls and Lr) [35]. If these variables are known, or can bemeasured, then it may be preferrable to use the full model of the induction motor. In ourcase it is not possible to conduct all of the tests required, and as such the steady state modelpresented below is used. By analyzing the steady state characteristics of the inductionmotor, it is possible to obtain a relationship between the stator current amplitude, electricalfrequency, spindle speed, and the torque, which would be much easier to implement inpractice than equation 4.8. First, the steady state quantities can be shown to be related by[35]:?2F?as = F?qs? jF?ds (4.9)?2F? ?ar = F??qr? jF??dr (4.10)Since induction motors are symmetric devices, F? can be any of the voltage, current, orflux linkage. Substituting this result into equation 4.8 yields the following expression fortorque:Te =3P2LMRe[? jI?asI?ar](4.11)Equation 4.11 gives the electrical torque developed based on the amplitude of the cur-rents in the machine variables; however, it still contains a rotor current term. To relatethe rotor current to the stator current, consider the equivalent circuit during steady stateoperation shown in Figure 4.2:Most induction motors are of the squirrel-cage rotor type, and as such V?ar is zero. There-fore, from Kirchoff?s law:I??ar =?j?eLMr?rs + j?eL?rrI?as (4.12)474.1. Induction Motor ModelFigure 4.2: Equivalent circuit during stead state operationwhere s is the slip given by:s =?e??re?e(4.13)where ?e is the electrical frequency in[radsec], and ?re is the rotor frequency of an equiv-alent two pole machine in[radsec](ie, ?re = P2?s, where ?sis the spindle frequency). Sub-stituting equation 4.12 into equation 4.11 yields the following expression for the electricaltorque based on the current amplitude:Tm =3P2(r?rs)L2M?eI?2as(r?rs)2+?2eL?rr(4.14)replacing slip in equation 4.14 with equation 4.13 yields:Tm =3P2L2Mr?rI?2as (?e??re)r?2r +(?e??re)2 L?2rr(4.15)Finally, lumping together all the constants gives the following torque relationship:Tm =K1I?2as ( fe? fre)K2 +( fe? fre)2 (4.16)where fe and fre are the electrical and rotor frequency, respectively, in [Hz], and:484.1. Induction Motor ModelK1 = 3PpiL2Mr?rL?2rr, K2 =r?2r4pi2L?2rr(4.17)In this case, since the motor parameters are unknown, the constants are found experi-mentally by conducting cutting tests at various spindle speeds and loads.4.1.3 Modelling of Motor LossesTwo main losses exist in this system: electrical and mechanical losses. Mechanical lossesare modelled using the Coulomb and Viscous friction model:Tf ric = Bpi fre+Tcoulomb (4.18)where Tf ric [Nm] is the friction torque, B[Nmrad/s]is the coefficient of viscous frictionand Tcoulomb [Nm] is the static friction coefficient.The electrical losses in the system can be considered using the following equation forcopper losses[35, 51]:Telecloss = TCu =3I?2asrs4piP fre(4.19)Therefore, the torque during cutting is:Tcut = Tm?Tf ric?Telecloss =K1I?2as ( fe? fre)K2 +( fe? fre)2 ?3I?2asrs4piP fre?Bpi fre?Tcoulomb (4.20)This model ignores other sources of electrical losses, including stray losses and ironlosses [51]. While these losses are always present, it will be seen from the results that themodel used here serves as a good approximation.494.2. Extended Kalman Filter Design4.2 Extended Kalman Filter Design4.2.1 Extended Kalman Filter ModelFrom the previous section, we can see that the system being considered has non-lineardynamics. Therefore, an Extended Kalman Filter (EKF) was designed to approximate thetorque from the current. The state equations for an EKF are given as:xk+1 = fk (xk)+wk (4.21)yk = hk (xk)+vk (4.22)where x is the vector of states, y is the vector of measurements, f is a series of processequations, h is a series of measurement equations, w and v are zero-mean Gaussian noiseswith covariance Qk and Rk, respectively, and k is the discrete time step counter. In our case,x and y can be described as:x =?????????I?asfefreTcut?????????,y =??????I?asfefre??????(4.23)The process and measurement equations are:f(xk) =??????????I?as,kfe,kfre,kK1 I?2as,k( fe,k? fre,k)K2+( fe,k? fre,k)2 ?3I?2asrs4piP fre?Bpi fre?Tcoulomb??????????(4.24)504.2. Extended Kalman Filter Designh(xk) =??????I?as,kfe,kfre,k??????(4.25)In the standard Kalman Filter, a linear process is considered and used to make an es-timate of the state at the next time step. The EKF does this for a non-linear process byattempting to linearize the model around the current estimate. For a single state system,one could take the derivative of the function and then linearize to find the next point, or inother words take the first order Taylor series estimate. In our case, the process is facilitatedby taking the Jacobian of the process and measurement models as:? f?xk= Fk =?????????1 0 0 00 1 0 00 0 1 0?Te,k? I?as,k?Te,k? fe,k?Te,k? fre,k 0?????????(4.26)?Te,k? I?s,k=2I?as,kK1(fe,k? fre,k)K2 +(fe,k? fre,k)2 ?6I?as,krs4piP fre(4.27)?Te,k? fe,k=K1I?2as,kK2 +( fe? fre)2 ?2K1I?2as,k( fe,k? fre,k)2(K2 +(fe,k? fre,k)2)2 (4.28)?Te,k? fr,k=?K1I?2asK2 +( fe? fre)2 +2K1 ( fe? fre)2 I?2as(K2 +( fe? fre)2)2 +3PI?2asrs4pi f 2re? Bpi?h?xk= Hk =??????1 0 0 00 1 0 00 0 1 0??????(4.29)514.2. Extended Kalman Filter DesignThe following steps are then executed at each time step:1. Compute I?as,k and fe,k from the spindle current. Read the spindle speed n from thecontroller and compute fre,k =P2n602. Predict the state at the current time step based on the previous time step as:x?k|k?1 = f(xk?1) (4.30)3. Predict the covariance at the current time step based on the previous time step:P?k|k?1 = Fk?1Pk?1FTk?1 +Qk?1 (4.31)4. Calculate the measurement residual:yk = zk?h(x?k|k?1)(4.32)5. Calculate the Kalman gainKk =P?k|k?1HTkHkP?k|k?1HTk +Rk(4.33)6. Estimate the state at the current time step:xk = x?k|k?1 +Kkyk (4.34)7. Estimate the covariance at the current time stepPk = (I?KkHk) P?k|k?1 (4.35)An example of the measured states from cutting AL-7075 Aluminium using a 2 flute cutter524.3. Experimental Setupwith spindle speed of 18000 revmin , half immersion downmilling with 4mm depth of cut, andfeedrates of 0.14 and 0.16 mmtooth is shown in Figure 4.3. As mentioned in Section 2.2, if alinear torque model is applied to an inductin motor, ie:Tm = Kt I?as (4.36)then the results will only be correct for a small range of loading conditions. In Fig-ure 4.3, the two loading conditions are roughly 1.7Nm, and as such the difference in thestates at the two loading conditions is therefore very small. However, it can be seen thatbetween the no load and loaded conditions both the electrical frequency and current am-plitude change significantly. As such, for a small range of loading conditions at a singlespeed, the linear torque model of Equation 4.36 could be used to obtain a rough estimate ofthe loaded torque. The main benefit of the model used in this work, which will be shown inSection 4.4, is that the model can be applied to a wide range of spindle speeds and loadingconditions without having to be recalibrated for each cutting condition.4.3 Experimental SetupThe experimental setup in this case is similar to what was discussed in Chapter 3. Currentmeasurements were taken using a CR5211S-150 hall effect current transducer from CRMagnetics. The hall effect transducer has a current limit of 150A, and outputs a ?10V DCanalog signal. The transducer was installed into the power cabinet of the machine, just afterthe output from the spindle?s amplifier, as shown in Figure 4.4.Data acquisition was done using a NI-USB 9234 DAQ, similar to the chatter detectionand suppression setup, and was implemented in Matlab. Communications with the machinewere done using the FOCAS libraries, in the same process as in Chapter 3. In this case, theestimate of electrical frequency must be fairly accurate in order to get a good result. For theFFT method, this requires a large amount of samples, which will introduce some delays into534.3. Experimental Setup80 85 90 95 100 105 110050 A) Current AmplitudeI as(A)80 85 90 95 100 105 110600607615B) Electrical Frequencyf e(Hz)80 85 90 95 100 105 110599600601C) Rotor Equivalent Frequencyf re(Hz)80 85 90 95 100 105 11005 D) Cutting TorqueT cut(Nm)Time(s)Figure 4.3: Example of the measured states of the Extended Kalman Filter in the millingof AL-7075 Aluminium with a 2 flute endmill, 18000 revmin spindle speed, half immersiondownmilling with 4mm depth of cut, and feedrates of 0.14 mmtooth and 0.16mmtooth .the system. Instead, here electrical frequency was found by applying the Quinn-Fernandez[52] algorithm onto the current signal, which is summarized below. While the FFT methodhas resolution of O(T?1), where T is the number of samples, the Quinn-Fernandez methodhas a resolution of O(T?32).1. Initialize the method with frequency estimate as f?e = fre. The FFT method can alsobe used to find the initial frequency estimate; however, since typically the maximumslip for an induction motor is only 5%, the rotor frequency can be used.2. Filter the data asy(n) = I (n)??iI (n?1)+ I (n?2) (4.37)where ?i = 2cos(2pi f?eFs)is our target for estimation, i = 0,1, ...,N is the iterationnumber, and n is the sample number.544.3. Experimental SetupFigure 4.4: Setup of Hall Effect Transducer3. Find the regression coefficient, ?i:?i = ?i??i =? I (n)y(n?1)?y2 (n?1)(4.38)4. Based on the autoregressive moving average (ARMA) model used by Quinn[52],the system has the built-in constraint ? = ? . Therefore,? is a representation of theestimated error in our estimate, and as such the process is repeated by updating ?as?i+1 = ?i+2?i (4.39)5. Repeat steps 1-4 until ?is low enough (less than 10?3). The final estimate of theelectrical frequency is obtained asfe =Fs2pi cos?1(?i+12)(4.40)554.4. Experimental ResultsAs shown by Quinn [52], if the initial estimate is within O(T?1)of the final result thenit is guaranteed that the method will converge within 2 iterations. Using FFT to generatethe initial estimate ensures that this is always the case. Since typical motors have a slipbetween 1?5%, using an initial estimate of f?e = fre can also be used in most cases.At the same time, the spindle power was measured using a Model PPC-3 PortablePower Cell power measuring equipment from Load Controls LLC in order to measure theelectrical torque. Finally, a Kistler Type 9125 rotating dynamometer was used to measuringthe cutting torque.4.4 Experimental ResultsResults of the proposed torque estimation method are presented in this section. The algo-rithm used is summarized in Figure 4.5, and is executed at each spindle period. A samplingfrequency of 4096Hz and a window of 100ms was used at each timestep in order to calcu-late the current amplitude and the electrical frequency.4.4.1 Results of Torque Estimation Using Proposed EKFThe model was calibrated using cutting tests conducted on AL-7075 aluminium for highspeeds (8000 revmin -20000revmin ) and on AISI-1045 steel for low speeds (1000revmin - 3000revmin ). The electrical torque from the motor was measured by taking the power from thePPC-3 power measuring equipment and dividing it by the spindle speed in[radsec]. The EKFwas calibrated using the electrical torque and the developed friction model, and was thencompared with the average of the torque measured from the dynamometer over the sameperiod as the EKF?s estimate. Cutting tests were conducted at speeds from 8000 revmin to20000 revmin in increments of 2000revmin using half immersion downmilling process with 4mmdepth of cut, 2 tooth cutter of 20mm diameter, and feedrates from 0.08-0.16 mm/toothin 0.02mm/tooth increments in order to calibrate the filter for high speeds. For low speed564.4. Experimental ResultsFigure 4.5: Flowchart of the algorithm used to estimate the cutting torque, Tcut , at eachtimestep.calibration, tests were conducted at 1000 revmin , 2000revmin , and 3000revmin using slotting processwith 2mm depth of cut, 4 tooth cutter of 20mm diameter, and feedrates varying from 0.03-0.06 mm/tooth in 0.01mm/tooth increments. The constants were identified as K1 = 0.0171and K2 = 4.3554 in high speed and K1 = 0.0908 and K2 = 2.2524 in low speed (Equation4.17).Results for half immersion down milling of AL-7075 with 4mm depth of cut usingspindle speeds of 14000 revmin , 18000revmin , and 20000revmin are shown in Figure 4.6.In Figure 4.6A), a spindle speed of 14000 revmin was used, and two cuts were made withfeedrate of 0.08 mmtooth and 0.10mmtooth . Initially, the deflections left from previous operationsare cleaned, as can be seen by the small amount of torque picked up by both the EKF and thedynamometer. From Figure 4.6, we can see that the EKF is capable of estimating the cuttingtorque very well, with an average error of 3% and a slight delay. In Figure 4.6A), 2 holeswere placed along the path of the cut in order to observe the performance due to changes in574.4. Experimental Results10 20 30 40 50 60 70012Torque (Nm)  A) S = 14000 rev/min, Feed = 0.08, 0.10 mm/tooth75 80 85 90 95 100 105 110012Torque (Nm)  B) S = 18000 rev/min, Feed = 0.16, 0.18 mm/tooth75 80 85 90 95 100 105012Time (s)Torque (Nm)  C) S = 20000 rev/min, Feed = 0.16, 0.18 mm/toothEKFDynamometer AverageHoles in workpieceHoles in workpieceFigure 4.6: Results of half immersion downmilling of AL-7075 aluminium with a 2 toothcutter, various spindle speeds and feedrates, and 4mm depth of cut. The surface was cleanedbetween each cut, causing a small amount of torque to be read. Blue: Average of the torquemeasured from the dynamometer, Red: Torque estimated using the EKFloading condition. As can be seen, the EKF is capable of tracking the changes in torque aswell, with a slight delay. The EKF estimate also contains some overshoot (in the examplesshown in Figure 4.6, an overshoot of 0.1Nm was seen), especially when the torque changeis large for example in Figure 4.6B and C. Since we are using the steady state model, theerrors are higher when the system deviates far from the steady state operation, ie. when theloading condition is changed suddenly by a large amount relative to the maximum capacityof the motor. For example, at 20000 revmin the maximum torque of the motor is 10Nm, andwe see overshoot when the torque suddenly increases to ~20% of the maximum (2Nm).Figure 4.7 shows the results of slotting AISI-1045 steel at 3000 revmin and A) 0.04mm/toothfeedrate and B) 0.07mm/tooth feedrate.The results are similar to the case with high speed machining: there is an average of3% error and a slight delay.In the above cases, the same speed that was calibrated was used in cutting. In orderto see the result when a cutting condition outside the calibration range was used, first the584.4. Experimental Results10 11 12 13 14 15 16 17 1801234 A) Feedrate = 0.04mm/toothTime(s)Torque (Nm)6 7 8 9 10 11 12 1301234 B) Feedrate = 0.07mm/toothTime(s)Torque (Nm)  Dynamometer AverageEKFFigure 4.7: Results of slotting AISI-1045 steel at 3000 revmin with 2mm depth of cut, 4 toothcutter, and A) 0.04 mm/tooth feedrate, and B) 0.07mm/tooth feedrate. Blue: Average ofthe torque measured from the dynamometer, Red: Torque estimated using the EKFmodel was calibrated by ignoring the data set at 18000 revmin , and then algorithm was run.The results from this case can be seen in Figure 4.8.75 80 85 90 95 100 105 11000.20.40.60.811.21.41.61.82 Spindle speed = 18000 RPM, Feed=0.14, 0.16 mm/toothTime (s)Torque (Nm)  Kalman FilterDynamometer with weighted averageFigure 4.8: Results of half immersion downmilling of AL-7075 aluminium using a 2 toothcutter at feeds of 0.14 and 0.16 mm/tooth with 18000 revmin . The surface was cleaned betweeneach cut, causing a small amount of torque to be read. When the EKF is used to estimatethe torque when the spindle speed used is within the calibration range, even if the speedwas not included in the calibration the errors remain the same.594.4. Experimental ResultsThe constants estimated in this case were K1 = 0.0169 and K2 = 4.1789, which arequite similar to the constants estimated when all of the data was considered. As such theresults are almost the same as before: there is a similar amount of error (3%) since theconstants have not changed significantly.Another test was conducted where the model was calibrated by ignoring the data set at20000 revmin and then running the algorithm. The results of this test can be seen in Figure 4.9.70 75 80 85 90 95 100 10500.20.40.60.811.21.41.61.82 Spindle speed = 20000 RPM, feed = 0.14mm/tooth, 0.16mm/toothTime(s)Torque (Nm)  Kalman FilterDynamometer with weighted averageFigure 4.9: Results of half immersion downmilling of AL-7075 aluminium using a 2 toothcutter at feeds of 0.14 and 0.16 mm/tooth with 20000 revmin . The surface was cleaned betweeneach cut, causing a small amount of torque to be read. When the EKF is used to estimatethe torque when the spindle speed used is outside of the calibration range higher errors canbe observed.In this case, the constants estimated were K1 = 0.0164 and K2 = 3.7672. While K1is still quite similar to the previous case K2 has changed significantly, and in this case wehave an error of 7%. Since the slip frequency is outside of the calibrated range K2 has beenpoorly estimated which causes the error that can be seen. Errors in the friction estimationalso contribute to the overall error although to a lesser extent. Therefore, the EKF will notperform well if the cutting conditions are outside of the range that it has been calibratedfor; however, staying within the calibrated range yields accurate results.604.5. Summary4.5 SummaryIn this section the algorithm for torque estimation using a current sensor is presented. Theinduction motor model is taken from Krause [35] and is implemented within an EKF whichaccepts two main inputs: the current signal from the motor, and the spindle speed. Fromthe current signal the amplitude, I?as, and the electrical frequency, fe, are extracted. Theelectrical frequency is estimated using the Quinn-Fernandez method[52]. The motor con-stants, K1 and K2, are calibrated by conducting milling experiments and using curve fittingmethods. It was shown experimentally that the method is robust to changes in loading andspindle speed provided that they stay within the calibrated range of conditions.One limitation of this method is the need for electrical frequency estimation. Figure4.10 shows the frequency resolution of the Quinn-Fernandez method using various sam-pling frequencies and periods. A sampling period of Ts = 0.1s and a sampling frequencyof 4096Hz provides a frequency resolution of 0.5Hz, which is sufficient to estimate theelectrical frequency above 1000 revmin . Care must be taken in order to ensure that the selectedsampling period and frequency combination provides sufficient resolution for the givencutting conditions. Spindle speeds below 300 revmin require a frequency resolution less than0.1Hz, which will result in a significant delay being added to the system. The selection ofTs = 0.1s will allow for spindle speeds above 1000 revmin to be used, and as such in this thesisthe cutting conditions were selected accordingly.In the following chapter, an adaptive control algorithm for use on commercial machinetools is presented, which uses the EKF presented here as a feedback for torque measure-ment.614.5. Summary0 2000 4000 6000 8000 10000 12000 1400000.20.40.60.81 Frequency Resolution of the Quinn?Fernandez MethodSampling Frequency (Hz)Frequency Resolution (Hz) Ts=0.1sTs=0.2sTs=0.5sFigure 4.10: Frequency resolution obtained at different sampling frequencies and samplingperiods using the Quinn-Fernandez method62Chapter 5Adaptive Control of Milling ProcessThis section briefly discusses the design of an adaptive control law to regulate the cuttingtorque in the milling process. The process described by Altintas [2, 6] is used here and isadapted to be used on a commercial CNC machine.5.1 Design of Adaptive Control LawA generalized block diagram for an adaptive pole placement control algorithm can be seenin Figure 5.1 [2]. The objective of the adaptive controller is to ensure that the actual torque,Tout , follows the desired reference torque, Tre f , by manipulated the commanded feedrate,fc, adaptively.Figure 5.1: Block diagram for adaptive pole placement controllerIn Figure 5.1, the polynomials Q(z), R(z), and S(z) are the polynomials of the poleplacement controller used to calculate the desired feed command fc, and are determined inreal time based on the output of a recursive least squares (RLS) algorithm used to estimatethe parameters of the system. Since the machine tool has a much longer delay than the635.1. Design of Adaptive Control Lawcutting process, the machine tool and cutting process can be combined into a second ordersystem in discrete time domain asGp(z?1)=Tout(z?1)fc (z?1)=z?2b1+az?1(5.1)whereb1 = Kp(1? e? T?p)(5.2)a1 = e? T?p (5.3)and ?p is the time constant of the machine, and Kpis the process gain which is a functionof the tool diameter D, tangential cutting coefficient Ktc, cutting speed n, number of teethN, depth of cut a, and average engagement angle, ie:Kp =DaKtc2Nn?(cos(?st)? cos(?ex)?ex??st)(5.4)where ?st is the angle of the starting of cut, ?exis the angle of the exit of cut, and T inthis case is the control interval. Communications with the machine are done over ethernetusing FOCAS library in the same manner as described in Section 3.3. As was noted inSection 3.3, the CNC machine takes approximately 100ms to respond to commands fromFOCAS. As such, T = 0.1s was selected.Since the system parameters are a function of the tool geometry and cutting operation,they must be identified in real time. To this end, a recursive least squares (RLS) algorithmwas implemented to estimate the parameters in real time [53]. Denoting the estimatedparameters as b?1, and a?1, the following algorithm is executed at each control interval:1. Compute the gain of the RLS filter645.1. Design of Adaptive Control LawKRLS (k) =PRLS (k?1) ?? (k)? + ??T (k)PRLS (k?1) ?? (k)(5.5)?? (k) =????Tout (k?1)fc (k?1)??? (5.6)2. Update the measurement?? (k) =???a?1b?1???= ?? (k?1)+KRLS(Tout (k)? ??T (k) ?? (k?1))(5.7)3. Update the covariancePRLS (k) =PRLS (k?1)?(I?KRLS??T (k)) (5.8)Here, ? is called the ?forgetting factor? and is selected between 0.8 and 0.95 to reducethe influence of previous measurements on the result. The process is quite similar to the Ex-tended Kalman Filter developed previously, except that the RLS filter skips the predictionphase.Once the parameters are estimated the pole placement controller can be designed. Thegoal of the pole placement controller is to force the system to exhibit some desirable dy-namics. In this case, second order dynamics are selected, ie:Tout (k)Tre f (k)=Bm (z)Am (z)=1+m1 +m2z2 +m1z+m2(5.9)where m1 = ?2e???nT cos(?n?1?? 2T)andm2 = e?2??nT . Here, ? and ?n are thedamping ratio and natural frequency, respectively, of the desired dynamics, while T is thecontrol interval. Following the guidelines in [2] values of ? = 0.8 and ?n = 8Hz wereselected. Based on the block diagram in 5.1, the control polynomial is given as655.1. Design of Adaptive Control LawR(z) fc (k) = Q(z)Tre f (k)?S (z)Tout (k) (5.10)Substituting in Equation 5.1 and rearranging yields:Tout (k)Tre f (k)=B(z)A(z)R(z)Q(z)+S (z)B(z)=Bm (z)Am (z)(5.11)At each control interval Bm and Am are known a-priori while B and A are known fromRLS estimation. Therefore, we can solve for the control polynomials Q, R, and S. This isdone by first checking the causality conditions, ie we must ensure that we design the controlpolynomials so that the output of the controller does not depend on the future outputs andinputs of the system. Rearranging equation 5.10 yieldsfc (k) =Q(z)R(z)Tre f (k)?S (z)R(z)Tout (k) (5.12)If the polynomials Q or S were of higher degree than R the commanded feedrate woulddepend on future measurements. Therefore the first set of causality conditions are:deg(R)? deg(Q) (5.13)deg(R)? deg(S) (5.14)The degree of R can be determined by looking at the denominator of equation 5.11, alsoknown as the Diophantine equation:R(z)A(z)+S (z)B(z) = Am (z) = z2 +m1z+m2 (5.15)Since we know deg(A) = 1, deg(B) = 0, and deg(S)? deg(R), R(z) must have degreeof 1 to match the right side of equation 5.15. The degree of S is selected as 0 for this system665.1. Design of Adaptive Control Lawsince the control interval is large. If the control interval were smaller, then deg(S)= 1 couldbe selected [53].The degree of Q is determined by looking at the numerator of equation 5.11, ie:B(z)Q(z) = Bm (z) (5.16)Since we know that deg(B) = deg(Bm) = 0, it follows that deg(Q) = 0. Therefore, thecontrol polynomials can be described as follows:R(z) = z+ r1 (5.17)S (z) = s0 (5.18)Q(z) = q0 (5.19)The corresponding Diophantine equation is then(z+ r1)(z+a1)+b1s0 = z2 +(r1 +a1)z+ r1a1 +b1s0 = z2 +m1z+m2 (5.20)From the Diophantine equation, we can see that the control polynomials can be foundas:r1 = m1?a1 (5.21)s0 =m2? r1a1b1(5.22)Also, from equation 5.16 we know that:675.1. Design of Adaptive Control Lawb1q0 = 1+m1 +m2 (5.23)Therefore:q0 =1+m1 +m2b1(5.24)Substituting this into the control polynomial of equation 5.10 yields:z fc (k)+ r1 fc (k) = q0Tre f (k)? s0Tout (k) (5.25)Scaling the equation by z?1 since we cannot operate on future inputs gives us the finalcontrol polynomial:fc (k) = q0Tre f (k?1)? s0Tout (k?1)? r1 fc (k?2) (5.26)which is executed at each time step k using the parameters estimated by the RLS algo-rithm. Since communications are done using FOCAS, the feedrate override command iscomputed as:FOV =fcfbase(5.27)where fbase is the programmed feedrate. Some precautions must be taken to ensure thatFOV stays within an acceptable region. If FOV is allowed to increase too high, it may causeexcessive heat generation in the tool, and accelerate the wear. In addition to this, the RLSalgorithm takes several iterations to converge to the correct parameters. During this time,the feedrate value calculated may be very small. As such, the following check is appliedanytime the control command FOV is calculated:FOV < FOV,min? FOV = FOV,min (5.28)685.1. Design of Adaptive Control LawFOV > FOV,max? FOV = FOV,max (5.29)where FOV,min and FOV,max are user-specified minimum and maximum feedrate values,respectively. Even with this check, the adaptive control algorithm will set the feedrate tothe maximum during air cutting, which may cause problems once the tool begins the cut.Therefore, when the measured torque Tout is below some user specified minimum torque,Tmin, the adaptive control algorithm is turned off and FOV = 100% is used.The overall adaptive control algorithm is summarized in Figure 5.2.Figure 5.2: Summary of the adaptive control algorithm used.695.2. Experimental Results5.2 Experimental ResultsResults of the adaptive control algorithm developed in this section are discussed here. Cut-ting tests were conducted at 3000 revmin on AISI-1045 steel using two parts: a part consistingof two steps as shown in Figure 5.3, and a part consisting of a ramp as shown in Fig-ure 5.4. Depth of cut for both parts was 3mm and the base programmed feedrate was480mmmin (corresponding to 0.04mmtooth ). The experimental setup for this section is the same aswas discussed in Section 4.3.Figure 5.3: Dimensions of the step part used to evaluate the adaptive control algorithm.Dimensions are in millimeters.Figure 5.4: Dimensions of the ramp part used to evaluate the adaptive control algorithm.Dimensions are in millimeters.The method was evaluated using torque measurements from two sources: the EKFdeveloped in Section 4.2, and using FOCAS directly to measure the torque. Using FOCAS,the spindle power being consumed can be measured, which can then be converted into the705.2. Experimental Resultstorque. The resolution of torque measurement from FOCAS is 1% of the maximum spindlepower, ie:TF,res =Pmax??1100[Nm] (5.30)where TF,res is the resolution of torque measurement available from FOCAS, Pmax is themaximum spindle power (22KW for our machine), and ?[radsec]is the spindle speed. Assuch at 3000 revmin the resulting torque resolution is ? 0.7Nm.5.2.1 Results of Adaptive ControlFirst, the results using the proposed EKF as the torque measurement to apply adaptivecontrol will be shown, followed by the results using FOCAS to measure the torque.Using EKF to Measure TorqueFigure 5.5 shows the results of cutting the step part in Figure 5.3 while using the EKF ofSection 4.2 to measure the torque.During air cutting the controller is disabled and the feedrate override command of 100%is sent to the machine. Although leaving the controller on could allow for some produc-tivity gains during air cutting, it can be dangerous if a higher feedrate is set and the toolencounters a heavy cutting condition. Once the cutting begins the adaptive control algo-rithm is activated and the process parameters are estimated through RLS. The controllerexperiences some overshoot while the RLS algorithm attempts to estimate the correct pa-rameters. Once the RLS algorithm has settled, we can see that the torque tends to thereference value. When the tool encounters the step to a higher radial immersion the con-troller detects a large change in torque and resets the covariance of the RLS algorithm. Ifthe covariance is not reset, the parameters estimated will take a significantly longer timeto converge to the correct values. The process is repeated when the step to a lower radial715.2. Experimental Results6 8 10 12 14 16 18 20 22 24 26?10123Time(s)Torque(Nm)02505007501000Feedrate(mm/min)Tref TcutFeedrateFigure 5.5: Cutting of the step part of Figure 5.3 using the adaptive control algorithmdeveloped and the EKF of Section 4 as the torque measurement. A torque reference ofTre f = 2Nm was used, and is marked with a blank line.immersion is detected as well.Figure 5.6 shows the results of cutting the ramp part in Figure 5.4.8 10 12 14 16 18 20 22?10123Time(s)Torque(Nm)02505007501000Feedrate(mm/min)TrefFeedrateTcutFigure 5.6: Cutting of the ramp part of Figure 5.4 using the adaptive control algorithmdeveloped and the EKF of Section 4 as the torque measurement. A torque reference ofTre f = 1.9Nm was used, and is marked with a black line.In the case of steady changes in torque, the controller is able to act accordingly and725.2. Experimental Resultsregulate the cutting torque near the desired level.Using FOCAS to Measure TorqueFigure shows the results of cutting the step part in Figure 5.3 using FOCAS to measure thetorque. Note that the output from FOCAS is the electrical power consumed by the spindle,which is then converted into the electrical torque, ie:Te =Pepi fre(5.31)where Pe is the electrical power measured by FOCAS, and Te is the resulting electricaltorque. Since the friction torque present is less than the resolution of FOCAS it is notremoved from the measurement.10 15 20 25 3001234Torque(Nm)02505007501000Time(s)Feedrate(mm/min)FOCAS MeasurementTorque Dynamometer (Average)Figure 5.7: Cutting of the step part of Figure 5.3 using the adaptive control algorithmdeveloped and using FOCAS to measure the torque. A torque reference of Tre f = 2.1Nmwas used, and is marked with a black line.The same controller was used as in the previous case, with the only difference beingthat the torque measurement was provided from FOCAS instead. The behaviour of the con-troller is quite similar to the case where the EKF is used. It can be seen that at the third step,at around 25seconds into the measurement, the controller begins to increase the feedrate735.2. Experimental Resultsbut sees no change in the torque. This causes the RLS algorithm to incorrectly estimatethe parameters, which causes the system to react much slower to the change in condition.This is the main limitation of using FOCAS as the source of torque measurement; sinceFOCAS has poor resolution, small changes in feedrate may cause no change in the torque,which affects the estimation of the parameters by the RLS algorithm. However, the mainadvantage of the FOCAS is that no additional sensors are required.Figure 5.8 shows the results of cutting the ramp part in Figure 5.4.10 15 20 25 30 3501234Time(s)Torque(Nm)02505007501000Feedrate(mm/min)FOCAS MeasurementTorque DynamometerFigure 5.8: Cutting of the ramp part of Figure 5.4 using the adaptive control algorithmdeveloped and using FOCAS to measure the torque. A torque reference of Tre f = 2.1Nmwas used, and is marked with a black line.The results here are quite similar to using the EKF as the torque measurement. In thiscase FOCAS is capable of keeping the torque within half its resolution from the desiredtorque; ie, we remain within 0.35Nm of the desired target.From these results, it can be seen that while FOCAS can also be used within the adaptivecontrol algorithm presented in order to regulate the cutting torque. This can be quite usefulsince it would require no additional sensor to be placed within the machine. However, onhigh power spindles or at lower speeds, the resolution of torque measurement would beeven worse. For example, at 1000 revmin the resolution would be ? 2Nm for the NMV5000745.3. Summaryused in these experiments. As such, care must be taken when using FOCAS within theadaptive control algorithm. However, we see that when we use a more reliable source oftorque measurement (for example, the EKF of Section 4.2), we can accurately control thecutting torque to the desired level.5.3 SummaryIn this section a method for adaptive control of commercial machine tools was presented.The method is based on previous work by Altintas [2, 6], and is modified to be implementedon an external laptop connected to a machine tool by Ethernet connection. The method usestorque measurement from either the EKF of Section 4 or directly from the machine usingFOCAS.The main limitation of this method is the delay present within the system. These largedelays in the system cause the sampling time to be large, and as such the RLS algorithmtakes some time to converge to the correct parameter estimate. Due to the delays, thissystem would not be applicable in cases where the torque is quickly and constantly varying.75Chapter 6Conclusions and Future WorkIn this thesis, methods for the monitoring and control of machining processes were inves-tigated. The overall contributions are as follows:? A method for the automatic detection and suppression of chatter in real time waspresented. The method uses the fast fourier transform of the sound spectrum in or-der to identify the occurrence of chatter, along with the chatter frequency. Usingthe detected chatter frequency, the system tries to use the Spindle Speed Selectionmethod to suppress chatter: with the measured spindle speed, and the previously in-putted number of teeth of the cutter, the method determines the stable spindle speedand sends the corresponding control signal to the machine. If chatter cannot be sup-pressed using this method, the system determines whether it is safe to apply SpindleSpeed Variation, and then applies the method. This algorithm is based on previouswork done by Smith[17] and Al-Regib[23]. This method was verified in the highspeed milling of AL-7075 aluminium and low speed milling of AISI-1045 steel.? A method to estimate the average cutting torque based on single phase current of aninduction motor and the spindle speed was developed, using the steady state modelof an induction motor within an Extended Kalman Filter. The method was verified inthe high speed milling of AL-7075 aluminium and low speed milling of AISI-1045steel.? A method for adaptive control was developed, based on previous work done by Alt-intas [6, 2]. The method is adapted to be implemented over ethernet communications76Chapter 6. Conclusions and Future Workonto commercial machine tools using either an external torque sensor or FOCAS.This method was verified in low speed milling of AISI-1045 steel.One main area for improvement in these methods is to implement them directly on themachine tool itself, rather than running through FOCAS communications. This wouldsignificantly decrease the delay present in the communications, which would improve theperformance of the control methods. More research needs to be done for Spindle SpeedVariation as well, in order to better understand the effect the technique has on stability.Since SSV is capable of increasing the maximum depth of cut allowable, it may be possi-ble to improve the productivity of roughing operations by applying SSV even if no chatteris detected. In order to do so, stability lobes need to be calculated while taking into consid-eration the applied SSV parameters, which is one potential area for future work.The Extended Kalman Filter used to estimate the torque showed accurate results with ashort delay. The method could be improved if it were possible to obtain measurements ofthe motor parameters using three identification experiments: a DC test, a blocked rotor test,and a no load test. In our setup it was not possible to run the first two tests, and as such wecould not extract the parameters. If we had the parameters of the machine not only wouldwe obtain more accurate estimates of the K1and K2 parameters without having to conductexperiments, it would also be possible to use more complex models of the induction motor[35].As was shown in Section 5, commercial machine tools already have the instrumentationnecessary to implement adaptive control. If the adaptive control algorithm presented inthis thesis was implemented directly onto the machine tool, there would be significantperformance benefits as there would be no resolution limitation on the set feedrate, therewould be less delay, and the measured torque would likely also have greater resolution.77Bibliography[1] Y. Altintas and E. Budak, ?Analytical Prediction of Stability Lobes in Milling,? CIRPAnnals - Manufacturing Technology, vol. 44, pp. 357?362, Jan. 1995.[2] Y. Altintas, Manufacturing automation: metal cutting mechanics, machine tool vibra-tions, and CNC design. Cambridge university press, 2012.[3] M. Law, ?Position-Dependent Multibody Dynamic Modeling of Machine Tools Basedon Improved Reduced Order Models,? vol. 135, no. April, pp. 1?11, 2013.[4] M. Weck, Handbook of Machine Tools Volume 3 - Automation and Control. WileyHayden, 1980.[5] M. Mannan, S. Broms, and B. Lindstr?m, ?Monitoring and adaptive control of cut-ting process by means of motor power and current measurements,? CIRP Annals-Manufacturing . . . , vol. 38, no. 1, pp. 347?350, 1989.[6] Y. Altintas, ?Direct adaptive control of end milling process,? International Journal ofMachine Tools and . . . , vol. 34, no. 4, pp. 461?472, 1994.[7] T. Insperger, G. St?p?n, P. Bayly, and B. Mann, ?Multiple chatter frequencies inmilling processes,? Journal of Sound and Vibration, vol. 262, pp. 333?345, Apr. 2003.[8] S. Y. Tsai and K. F. Eman, ?Chatter suppression in turning,? emu, vol. 1, p. 1, 1983.[9] S. Tsai, K. Eman, and S. Wu, ?Chatter Suppression in Turning,? in Proceedings of theNAMCR Conference, pp. 399?402, 1983.78Bibliography[10] E. G. Kubica and F. Ismail, ?Active Suppression of Chatter in peripheral milling. PartII. Application of Fuzzy Control,? pp. 236?245, 1996.[11] E. Rivi?re and V. Stalon, ?Chatter detection techniques using a microphone,? Seventhnational congress on theoretical and applied mechanics, 2006.[12] N.-C. Tsai, D.-C. Chen, and R.-M. Lee, ?Chatter prevention and improved finish ofworkpiece for a milling process,? Proceedings of the Institution of Mechanical En-gineers, Part B: Journal of Engineering Manufacture, vol. 224, pp. 579?588, Apr.2010.[13] T. L. Schmitz, K. Medicus, and B. Dutterer, ?Exploring Once-Per-Revolution AudioSignal Variance As a Chatter Indicator,? Machining Science and Technology, vol. 6,pp. 215?233, Oct. 2002.[14] Y. Altintas and P. K. Chan, ?In-process detection and suppression of chatter inmilling,? International Journal of Machine Tools and Manufacture, vol. 32, pp. 329?347, June 1992.[15] I. Bediaga, J. Mu?oa, J. Hern?ndez, and L. L?pez de Lacalle, ?An automatic spin-dle speed selection strategy to obtain stability in high-speed milling,? InternationalJournal of Machine Tools and Manufacture, vol. 49, pp. 384?394, Apr. 2009.[16] S. Smith and T. Delio, ?Sensor-based control for chatter-free milling by spindle speedselection,? in Symposium on Control Issues in Manufacturing, DSC, vol. 18, 1989.[17] S. Smith and J. Tlusty, ?Stabilizing Chatter by Automatic Spindle Speed Regulation,?CIRP Annals - Manufacturing Technology, vol. 41, pp. 433?436, Jan. 1992.[18] T. Takemura, T. Kitamura, T. Hoshi, and K. Okushima, ?Active suppression of chat-ter by programmed variation of spindle speed,? Annals of the CIRP, vol. 23, no. 1,pp. 121?122, 1974.79Bibliography[19] T. Inamura and T. Sata, ?Stability analysis of cutting under varying spindle speed,? J.Fac. Eng. Univ. Tokyo, vol. 33, no. 1, pp. 13?29, 1975.[20] J. D. Canniere, ?A contribution to the mathematical analysis of variable spindle speedmachining,? vol. 5, no. June, pp. 158?164, 1981.[21] J. S. Sexton, R. D. Milne, and B. J. Stone, ?A stability analysis of single- point ma-chining,? vol. 1, 1977.[22] K. Jemielniak and a. Widota, ?Suppression of self-excited vibration by the spindlespeed variation method,? International Journal of Machine Tool Design and Research,vol. 24, pp. 207?214, Jan. 1984.[23] E. Al-Regib, J. Ni, and S.-H. Lee, ?Programming spindle speed variation for machinetool chatter suppression,? International Journal of Machine Tools and Manufacture,vol. 43, pp. 1229?1240, Sept. 2003.[24] C. Brecher, R. Hermes, a. Epple, and S. B?umler, ?Simulative Parameterization ofDead Time Variable Rotation Speed Behavior to Improve Process Stability in HighPerformance Cutting,? Procedia CIRP, vol. 4, pp. 2?10, Jan. 2012.[25] S. Seguy, T. Insperger, L. Arnaud, G. Dessein, and G. Peign?, ?On the stability ofhigh-speed milling with spindle speed variation,? The International Journal of Ad-vanced Manufacturing Technology, vol. 48, pp. 883?895, Oct. 2009.[26] J. Tlusty and S. Smith, ?Use of Audio Signals for Chatter Detection and Control,?vol. 114, no. May, 1992.[27] A. Matsubara and S. Ibaraki, ?Monitoring and Control of Cutting Forces in MachiningProcesses : A Review,? pp. 445?456, 2009.80Bibliography[28] T. Kim and J. Kim, ?Adaptive cutting force control for a machining center by usingindirect cutting force measurements,? International Journal of Machine Tools and . . . ,vol. 36, no. 8, pp. 925?937, 1996.[29] B. Lee, H. Liu, and Y. Tarng, ?Monitoring of tool fracture in end milling using induc-tion motor current,? Journal of Materials Processing Technology, vol. 70, pp. 279?284, Oct. 1997.[30] G. Kim and C. Chu, ?In-Process Tool Fracture monitoring in Face Milling Using Spin-dle Motor Current and Tool Fracture Index,? The International Journal of AdvancedManufacturing Technology, vol. 18, pp. 383?389, Sept. 2001.[31] T.-Y. Kim, J. Woo, D. Shin, and J. Kim, ?Indirect cutting force measurement in multi-axis simultaneous NC milling processes,? International Journal of Machine Tools andManufacture, vol. 39, pp. 1717?1731, Nov. 1999.[32] Y.-H. Jeong and D.-W. Cho, ?Estimating cutting force from rotating and stationaryfeed motor currents on a milling machine,? International Journal of Machine Toolsand Manufacture, vol. 42, pp. 1559?1566, Nov. 2002.[33] X. Li, ?Real-Time Prediction of Workpiece Errors for a CNC Turning Centre, Part3. Cutting Force Estimation Using Current Sensors,? The International Journal ofAdvanced Manufacturing Technology, vol. 17, pp. 659?664, May 2001.[34] J. Stein, ?Current monitoring of field controlled DC spindle drives,? Journal of dy-namic systems, measurement, and control, pp. 1?7, 1986.[35] P. C. Krause, O. Wasynczuk, and S. D. Sudhoff, Analysis of Electric Machinery andDrive Systems, Second Edition. IEEE Series on Power Engineering, 2002.81Bibliography[36] T. Kamigochi and Y. Kakinuma, ?Development of an Intelligent Stage with Sensor-Less Cutting Force and Torque Monitoring Function,? International Journal of Au-tomation Technology, vol. 6, no. 6, pp. 6?11, 2012.[37] S. Kawaji and Y. Suenaga, ?Control of cutting torque in the drilling process usingdisturbance observer,? American Control . . . , pp. 723?728, 1995.[38] G. Kim, W. Kwon, and C. Chu, ?Indirect cutting force measurement and cutting forceregulation using spindle motor current,? Int J Manufact Sci Technol, vol. 1, pp. 46?54,1999.[39] Y. T. Oh, W. T. Kwon, and C. N. Chu, ?Drilling torque control using spindle motorcurrent and its effect on tool wear,? The International Journal of Advanced Manufac-turing Technology, vol. 24, pp. 327?334, July 2004.[40] X. Li, ?Development of Current Sensor for Cutting Force Measurement in Turning,?IEEE Transactions on Instrumentation and Measurement, vol. 54, pp. 289?296, Feb.2005.[41] W. Kwon and I. jun Hong, ?Estimation of the cutting torque without a speed sensorduring CNC turning,? Journal of mechanical science and technology, no. C, 2005.[42] A. Spence and Y. Altintas, ?CAD assisted adaptive control for milling.,? TRANS.ASME J. DYN. SYST. MEAS. CONTROL., vol. 113, no. September 1991, 1991.[43] M. Kim, M. Cho, and K. Kim, ?Application of the fuzzy control strategy to adaptiveforce control of non-minimum phase end milling operations,? International Journalof Machine Tools and . . . , vol. 34, no. 5, pp. 677?696, 1994.[44] J. Stein and C.-h. Wang, ?Analysis of power monitoring on AC induction drive sys-tems,? Journal of dynamic systems, measurement, and . . . , vol. 112, no. June 1990,pp. 239?248, 1990.82Bibliography[45] C. Ma and Y. Altintas, ?Direct adaptive cutting force control of milling processes,?Automatica, vol. 26, no. 5, pp. 899?902, 1990.[46] G. Sekhon, K. Ahmadi, and Y. Altintas, ?Automatic Chatter Detection and Suppres-sion in Milling,? in MTTRF Annual Meeting, 2013.[47] J. O. Smith, ?Physical audio signal processing: For virtual musical instruments anddigital audio effects,? 2006.[48] A. Yilmaz, E. AL-Regib, and J. Ni, ?Machine Tool Chatter Suppression by Multi-Level Random Spindle Speed Variation,? Journal of Manufacturing Science and En-gineering, vol. 124, no. 2, p. 208, 2002.[49] R. Radulescu, S. Kapoor, and R. DeVor, ?An investigation of variable spindle speedface milling for tool-work structures with complex dynamics, part 1: simulation re-sults,? Journal of manufacturing science . . . , vol. 119, no. August 1997, 1997.[50] R. Radulescu, S. Kapoor, and R. DeVor, ?An investigation of variable spindle speedface milling for tool-work structures with complex dynamics, Part 2: physical ex-planation,? Journal of manufacturing science . . . , vol. 1, no. August 1997, pp. 3?10,1997.[51] I. Kioskeridis and N. Margaris, ?Loss minimization in scalar-controlled induction mo-tor drives with search controllers,? IEEE Transactions on Power Electronics, vol. 11,pp. 213?220, Mar. 1996.[52] B. Quinn and J. Fernandes, ?A fast efficient technique for the estimation of fre-quency,? Biometrika, 1991.[53] G. Goodwin and K. Sin, ?Adaptive filtering prediction and control,? 2013.83

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.24.1-0074258/manifest

Comment

Related Items