Controlling contour errors in CNC machines

CONTROLLING CONTOUR ERRORS IN CNC MACHINES HUO FENG (B.Eng, M.Eng, USTB) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2012 i Declaration I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Huo Feng 16 August 2012 ii Acknowledgements First and foremost, I sincerely thank Prof. Poo Aun-Neow, my supervisor, for his enthusiastic and continuous support and guidance. His suggestions, ideas and critical comments have been crucial for the progress of this PhD project. During my PhD studies, he provided me not only with the technical guidance, but also strong encouragement and kind affection. I also thank Mr. Sakthi, Mrs. Ooi, Ms. Tshin and Mdm. Hamidah in the Control and Mechatronics Lab for their help. I am grateful to Dr. Xi Xuecheng, Dr. Yu Deping, Mr. Lou Liang and many other friends for their invaluable friendship, advice and help during the project. Without their help and encouragement, I would not have carried out this study smoothly. Finally, I thank my dear parents and wife for their unwavering support and encouragement. Their love gives me the power to move forward. iii Table of Contents Declaration i Acknowledgements ii Table of Contents iii Summary vii List of Tables ix List of Figures xiii List of Symbols xv Introduction 1.1 An introduction to CNC machine tools . . . . . . . . . . . . . . . 1.2 Contour error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Aim and scope of the thesis . . . . . . . . . . . . . . . . . . . . . Review of Methodologies in controlling contour errors 10 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Reducing axial tracking errors . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Feedback controllers . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Feedforward controllers . . . . . . . . . . . . . . . . . . . . 13 iv 2.3 2.4 2.2.3 Sliding mode controllers . . . . . . . . . . . . . . . . . . . 15 2.2.4 Compensating the effects of friction and backlash . . . . . 16 Coordinating axial tracking errors . . . . . . . . . . . . . . . . . . 18 2.3.1 Matching axial dynamics . . . . . . . . . . . . . . . . . . . 19 2.3.2 Cross-coupled controllers . . . . . . . . . . . . . . . . . . . 22 Contour error compensation by reference input adjustment . . . . 25 2.4.1 Repetitive control . . . . . . . . . . . . . . . . . . . . . . . 25 2.4.2 Path compensation . . . . . . . . . . . . . . . . . . . . . . 27 2.4.3 Taylor series expansion error compensation . . . . . . . . . 28 Effect of servo control frequency on contour errors 29 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Contour errors of Type systems . . . . . . . . . . . . . . . . . . 31 3.2.1 Tracking errors for ramp inputs . . . . . . . . . . . . . . . 32 3.2.2 Stability analysis . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.3 Linear contours . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2.4 Circular contours . . . . . . . . . . . . . . . . . . . . . . . 38 3.3 Experimental evaluation . . . . . . . . . . . . . . . . . . . . . . . 41 3.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Generalized Taylor series expansion for free-form contour error compensation 48 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 Contour error estimation . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.1 Determination of contour error . . . . . . . . . . . . . . . 50 4.2.2 Contour error estimation for a free-form contour . . . . . . 52 Generalized error compensation based on Taylor series expansion . 54 4.3 v 4.4 4.5 4.6 4.3.1 Approach of TSEEC . . . . . . . . . . . . . . . . . . . . . 54 4.3.2 Extending TSEEC to GTSEEC . . . . . . . . . . . . . . . 56 Simulation experiments . . . . . . . . . . . . . . . . . . . . . . . . 59 4.4.1 Generation of reference inputs . . . . . . . . . . . . . . . . 59 4.4.2 Compensation with perfect models . . . . . . . . . . . . . 61 Experimental evaluation on a small CNC machine . . . . . . . . . 65 4.5.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . 65 4.5.2 Compensation gain . . . . . . . . . . . . . . . . . . . . . . 66 4.5.3 Performance of GTSEEC . . . . . . . . . . . . . . . . . . . 66 4.5.4 Performance of ZPETC . . . . . . . . . . . . . . . . . . . 71 4.5.5 Performance of CCC . . . . . . . . . . . . . . . . . . . . . 72 4.5.6 Comparison among GTSEEC, ZPETC and CCC . . . . . 73 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Generalized cross-coupled control 75 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.2 Generalized cross-coupled controller . . . . . . . . . . . . . . . . . 77 5.2.1 Cross-coupled controller . . . . . . . . . . . . . . . . . . . 77 5.2.2 Extending CCC to GCCC . . . . . . . . . . . . . . . . . . 79 Contour error estimation based on NURBS interpolation . . . . . 82 5.3.1 NURBS curve from reference input positions . . . . . . . . 82 5.3.2 Contour error estimation with NURBS . . . . . . . . . . . 84 5.3.3 Performance of CEEBNI . . . . . . . . . . . . . . . . . . . 86 5.4 Simulation performance of GCCC . . . . . . . . . . . . . . . . . . 89 5.5 Experimental evaluation . . . . . . . . . . . . . . . . . . . . . . . 91 5.5.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . 91 5.5.2 Performance of GCCC . . . . . . . . . . . . . . . . . . . . 93 5.3 vi 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 NARX-network based contour error reduction (NCER) 102 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.2 NARX-based contour error reduction (NCER) . . . . . . . . . . . 106 6.3 6.4 6.5 6.2.1 Nonlinear autoregressive network with exogenous inputs (NARX) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.2.2 Structure of NCER . . . . . . . . . . . . . . . . . . . . . . 108 Simulation experiments . . . . . . . . . . . . . . . . . . . . . . . . 111 6.3.1 NARX network and training . . . . . . . . . . . . . . . . . 111 6.3.2 Simulation evaluation of NCER performance . . . . . . . . 113 Experimental evaluation . . . . . . . . . . . . . . . . . . . . . . . 115 6.4.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . 115 6.4.2 Performance of NCER . . . . . . . . . . . . . . . . . . . . 117 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Conclusions 123 7.1 Conclusions of this thesis . . . . . . . . . . . . . . . . . . . . . . . 123 7.2 Possible future research issues . . . . . . . . . . . . . . . . . . . . 126 Bibliography 128 Author’s Publications 136 vii Summary Computer numerical control (CNC) machines are now widely used in the manufacturing industry. To achieve high precision machining, the motions of the axes of these machine tools need to be controlled precisely so that they follow a desired path, or contour, accurately. Contouring accuracy in terms of contour error has been, and continues to be, a big concern in the design and control of continuous-path CNC machines. Several approaches are explored and developed in this thesis to control the contour errors of CNC machines. The relation between servo control frequency and contour error is first studied in a bi-axis CNC machine. The objective is to determine the effect of servo control sampling frequency on the contouring accuracy thereby allowing a proper selection of this frequency depending upon the accuracy required. The results show that while the servo control sampling frequency affects contouring errors these are not significant except when very high accuracies, in the sub-micron range, are required. The model-based Taylor series expansion error compensation (TSEEC) method, which is capable of eliminating contour errors when used with a perfect dynamic model of the machine, is extended to a generalized TSEEC or GTSEEC. GTSEEC is applicable to any contour, including free-form contours, and thus removes the viii limitation of TSEEC’s applicability to only linear and circular contours. Simulation results show that, with perfect knowledge of the axial dynamics, GTSEEC can perfectly eliminate the contour errors for any contour. Experiments on a small computer-controlled machine also showed the excellent performance of GTSEEC in reducing contour errors, with performance better than the Zero Phase Error Tracking Controller (ZPETC) or the Cross-Coupled Controller. A generalized cross-coupled control (GCCC) approach is also proposed which can be applied for any free-form contour. For the linear, circular and parabolic contours that CCC can also be applied to, GCCC achieved the same level of performance, which is better than that achieved with ZPETC. In addition, GCCC achieved similar levels of contour error reductions for free-form contours. Without the need for a knowledge of the mathematical expressions defining the contours, GCCC can be used on contours defined by the series of reference input axial positions which are available for all CNC systems. Finally, a NARX (nonlinear autoregressive network with exogenous inputs) based contour error reduction (NCER) approach is developed and evaluated for reducing contour errors. This approach can be used for systems where the dynamic models of the systems are either not accurately known or when they change during machine operation. In this approach, NARX networks are first trained, using experimentally obtained input-output data, to model the system. The trained NARX networks are then used to predict the outputs in the next time instant for the X-axis and the Y-axis respectively. Based on the predicted contour error in the next time instant, compensation terms are added to the reference position inputs to correct for this error. Experiments conducted show the effectiveness of the proposed method which performed better than ZPETC. ix List of Tables 1.1 Methods of controlling contour errors . . . . . . . . . . . . . . . . 3.1 Radial contour errors at different sampling frequencies . . . . . . 40 4.1 Coefficients for the X and Y model [61] . . . . . . . . . . . . . . . 65 4.2 Comparison of contour errors at different feedrates (IAE(mm)) . . 71 4.3 Contouring performance comparison (IAE(mm)) . . . . . . . . . . 74 5.1 Comparison of contour errors at different feedrates (IAE(mm)) . . 99 6.1 Comparison of contour errors at different feedrates (IAE(mm)) . . 120 7.1 Comparison of different approaches at the feedrate of 2400 mm/min (IAE(mm)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 123 Chapter Conclusions 7.1 Conclusions of this thesis The main objective of this research was to study factors affecting contour errors in CNC machines, existing approaches to reducing these and to explore how higher contouring accuracies can be achieved. The first investigation was into how the servo control loop sampling frequency affects system performance and contouring accuracy. The results obtained, through both simulations and actual experimentation on a small CNC machine show that while sampling frequency has an affect on both system response and stability, for the bandwidths of typical CNC machines, above about a few hundred Hertz sampling frequency does not have any significant effect on contouring accuracies unless accuracies in the sub-microns range is required. Three new approaches for achieving higher contouring accuracies were proposed and evaluated in this work. The experimental results with these three and the other two well-known approaches were shown in Table 7.1. Among these three, 124 Table 7.1: Comparison of different approaches at the feedrate of 2400 mm/min (IAE(mm)) Contour type Linear Circular Parabolic Goggles GTSEEC 4.8236e-4 7.6800e-4 4.2464e-4 0.0011 GCCC 8.3316e-4 0.0012 7.8473e-4 0.0016 NCER CCC ZPETC 3.3782e-3 8.1353e-4 0.0112 2.9095e-3 0.0013 0.0079 1.6644e-3 7.5811e-4 0.0044 2.7826e-3 N.A. 0.0073 the Generalized Taylor Series Expansion Error Compensation (GTSEEC) approach provides the best performance in terms of achieving the smallest contour errors on the same small not-so-well build CNC machine that was used in all the experiments. Theoretically, TSEEC can achieve perfect contouring with perfect knowledge of the dynamics of the CNC system even when the axial dynamics of the machine are not matched. Unfortunately TSEEC is limited in its applicability to only linear and circular contours. GTSEEC extends TSEEC so that the same approach can be applied to any general free-form contours, including those specified by only the series of reference axial position inputs from the interpolators that are present in all CNC machines. When used for linear and circular contours, GTSEEC has similar level of performance in contour error reduction as TSEEC. The main disadvantage of GTSEEC is that it is model-based and requires an accurate model of the machine for good contouring performance. Otherwise, contouring performance will be degraded. Experiments performed on a small CNC machine with unmatched axial dynamics using linear, circular and parabolic contours, GTSEEC outperformed the well-known Zero Phase Error Tracking Controller (ZPETC) approach, which is also model-based, by an order of magnitude. 125 The second proposed new approach, Generalized Cross-Coupled Control (GCCC), makes use of the same principles as used in the cross-coupled controller (CCC) removed some of the limitations associated with CCC. With GCCC, there requirement that the contour being generated needs to have a differentiable describing function is no longer needed. GCCC thus can be used with any contour, including free-form contours and those which are represented by just the series of reference axial position inputs which are available in all CNC machines. Unlike for CCC for which different algorithms are required to determine the cross-couple gains, for GCCC, the same algorithm is used. On weakness of GCCC, if it can be called that, is that the contouring performance is dependent upon the values of the PI gains used and some efforts, e.g. by trial and error, is necessary to determine near optimal gains for best performance. A third approach has been proposed and investigated here using a non-linear autoregressive network with exogenous inputs (NARX) for contour error reduction (NCER). As with the other two approaches, GTSEEC and GCCC, proposed in this work, the NCER approach is also not limited to only linear and circular contours or only contours with known describing functions. It can be applied for any free-form contour including those described by only the series of reference position input points that are found in all CNC machines. With NCER, no changes is required of the hardware of the CNC system and there is also no need for any PI gain tuning as is required in GCCC. Unlike GTSEEC, there is no need for an accurate a priori knowledge of the machine’s dynamics for good contouring tracking performance. While the performance in terms of contour error of NCER is not as good as that for both GTSEEC and GCCC, in the experiments that were performed with a linear, a circular, a parabolic and a goggles contour, it 126 easily outperforms the well-known ZPETC approach. The NCER approach has another advantage as compared with other model-based approaches, including GTSEEC and ZPETC. When the dynamics of the machine changes during operation, e.g. due to chances in temperature or changes in the weight of workpiece, online retraining of the NARX networks using input-output data obtained during operation can be introduced. In this way, the NCER approach can be made to adapt and to continue to maintain good performance even when there are changes in the dynamics of the machine during operation. 7.2 Possible future research issues While significant reduction in contour errors have been achieved with the three approaches proposed and evaluated in this thesis, there are still work that can be done to achieve improvements to these approaches. Theoretically, the TSEEC, and by extension GTSEEC approaches should be able to achieve perfect contour tracking if a perfect model of the machine’s dynamics is used in implementation. This was demonstrated in the simulation experiments for which perfect models can be assumed and used. In practice, however, obtaining a good dynamic model is already a challenge, not to mention a perfect model. Furthermore, the dynamics of the machine can change, and change, during operation either due to the changing weights of workpieces during operation, changes in the temperature of the machine structure during operation and as the workday progress, or due to aging over a longer period. An approach which can potentially overcome the problem of using an inaccurate dynamic model for GTSEEC implementation is the incorporation of neural networks into the GTSEEC 127 scheme. If this can be accomplished and the neural networks can be trained using actual machine input-output data to accurately model the machine’s dynamics, then good performance can be assured. Online retraining of the neural network can also be introduced to accommodate situations when the dynamics of the machine changes during operation. The NCER approach also has potential to be further investigated so that it can achieve better contour tracking control performance. Areas of investigation could include, but not restricted to, the use of neural network other than multilayer perceptrons such as radial basis function networks, the effect of neural network structure and size. The reason why the NCER approach is not able to perform better and to reduce the contour error further can also be investigated so that once these are known, the NCER approach can be improved. The work done in this thesis focussed only on the two-dimensional contour errors resulting form imperfect control and coordination of the machine’s axial drive systems. There are many other sources of errors which limits the ability of CNC machines to produce ever more accurate parts. These include the effect of cutting forces, deflections and vibrations [3] during machining and imperfections in the drivers of the servo motors used for the machine drives. 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Feng Huo, Xue-Cheng Xi and Aun-Neow Poo, Generalized Taylor series expansion for free-form two-dimensional contour error compensation (2012), International Journal of Machines Tools & Manufacture, vol. 53, no. 1, pp. 91-99. 2. Feng Huo and Aun-Neow Poo, Free-form two-dimensional contour error estimation based on NURBS interpolation (2012), Applied Mechanics and Materials, vol. 157-158, pp. 236-240. 3. Feng Huo and Aun-Neow Poo, Precision contouring control of machine tools (2012), International Journal of Advanced Manufacturing Technology, http://dx.doi.org/10.1007/s00170-012-4015-5. 4. Xue-Cheng Xi, Aun-Neow Poo, Geok-Soon Hong, Feng Huo (2011). Experimental implementation of Taylor series expansion error compensation on a bi-axial CNC Machine, International Journal of Advanced Manufacturing Technology, vol. 53, pp. 285-299. 5. Feng Huo and Aun-Neow Poo, Improving contouring accuracy by using generalized cross-coupled control (2012), International Journal of Machines Tools & Manufacture, vol. 63, pp. 49-57. 138 6. Feng Huo and Aun-Neow Poo, Nonlinear autoregressive network with exogenous inputs based contour error reduction in CNC machines, accepted by International Journal of Machines Tools & Manufacture, 2012. Conference Papers 1. Feng Huo, Xue-Cheng Xi and Aun-Neow Poo, Effect of servo control frequency on contour errors in a bi-axial CNC machine. In: Proceedings of 2010 IEEE International Conference on Mechatronics and Automation (ICMA 2010). Xi’an, China. pp. 1132-1136. 2. Feng Huo and Aun-Neow Poo, Generalized Taylor series expansion for contour error compensation. In: Proceedings of the 4th Asia International Symposium on Mechatronics (AISM 2010). Singapore. pp. 33-37. 3. Feng Huo and Aun-Neow Poo, Generalized cross-coupled control for contour error reduction. In: Proceedings of the 16th International Conference on Mechatronics Technology (ICMT 2012). Tianjin, China. pp. 322-326. 4. Feng Huo, Peter Chao-Yu Chen and Aun-Neow Poo, An application of NARX-network to reduce contour errors. In: Proceedings of the IASTED International Conference on Engineering and Applied Science (EAS 2012). Colombo, Sri Lanka. pp. 209-215. [...]... approaches to control contour errors in CNC machines is presented Efforts to eliminate contour errors have been made mainly through (1) reducing axial tracking errors (2) coordinating axial tracking errors and (3) compensation for the errors by reference input adjustment In Chapter 1 the relationship between the tracking error and the contour error was discussed All these methods reduce the contour error either... systems controlling the machine axes resulting in non-zero axial tracking errors In this thesis, the focus is on reducing contouring errors which are caused by these non-zero tracking errors Much work has been done to improve accuracies in machine tools These previous works have helped in developing greater understanding and have led to improved machine accuracies The need to extract even higher contouring... contributing to contouring errors in CNC machines In this thesis, the focus will be on reducing contour errors resulting from imperfect control or in imperfect coordination of the motions of the machine’s different axis Other aspects such like contour errors due to thermal expansion and inaccuracies of transducers are not considered in this thesis The specific objectives of this research are to: 9 • investigate... of CNC machines according to the type of machining process required, namely, point-to-point systems and contouring systems In point-topoint systems, only the accuracy of the cutting tool’s final positions relative to the workpiece are important In contouring systems, on the other hand, the accuracy of the paths traveled by the cutting tool is important as machining operations are carried out during... presents how the tracking errors can be coordinated 11 and made to cancel the effect of each other on the contouring error Section 2.4 introduces the different kinds of compensation techniques for reducing contour errors through reference input adjustments 2.2 Reducing axial tracking errors If the axial following, or tracking, errors can be reduced or eliminated, then the resulting contour errors will similarly... for the manufacturing industry It is hope that the work done here can contribute to a better understanding of errors in CNC machines and how they can be controlled, thereby leading to lower-cost and better performing machines 10 Chapter 2 Review of Methodologies in controlling contour errors 2.1 Introduction In the previous chapter, a general background of this research was given In this chapter, a... the contours generated by these machines The demand for accuracy has led to much work which have been done in reducing errors in these machine tool These past works have led to a greater understanding and to improved accuracy 8 Table 1.1: Methods of controlling contour errors reducing axial tracking errors coordinating axial tracking errors compensation by reference input adjustment feedback controller... determine the factors contributing to contouring errors and how the errors can be reduced Factors contributing to contouring errors can broadly be classified as quasi-static or dynamic [44] In the first category are the geometrical inaccuracies in the machine tool structure including straightness and alignment of sliding surfaces, inaccuracies in the position feedback transducers, deflections of the machine... build machines, and for free-form contours, motivates the work described here in this thesis The subsequent sections provide a background of CNC machines tools, further exploration of the contour error and the factors which affect this A more detailed discussion of the methods of controlling contour errors and on-going research will be presented in Chapter 2 1.1 An introduction to CNC machine tools Controlling. .. xi 3.6 Tracking errors for linear contour 44 3.7 Contour errors for linear contour 44 3.8 circular contour errors for R=5mm 45 3.9 circular contour errors for R=20mm 45 3.10 circular contour errors for R=50mm 45 3.11 Tracking errors for circular contour 46 4.1 Schematic illustration of contour error . types of CNC machines according to the type of machining process required, namely, point-to-point systems and contouring systems. In point-to- point systems, only the accuracy of the cutting tool’s. systems controlling the machine axes resulting in non-zero axial tracking errors. In this thesis, the focus is on reducing contouring errors which are caused by these non-zero tracking errors. . Trackingerrorsforlinearcontour 44 3.7 Contourerrorsforlinearcontour 44 3.8 circularcontourerrorsforR=5mm 45 3.9 circularcontourerrorsforR=20mm 45 3.10circularcontourerrorsforR=50mm 45 3.11Trackingerrorsforcircularcontour