大型数控滚齿机伺服系统同步控制研究
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摘要
在数控滚齿加工过程中,为了保证齿轮加工的精度,滚刀主轴和回转工作台的转速必须保证线性比例关系,两轴间的速度匹配关系到滚齿加工精度。在传统数控同步控制方法中,一直采用数控系统的电子齿轮功能。电子齿轮的实现方式主要有主从式、并行式、基于硬件控制式和基于软件插补控制四种。不论电子齿轮采用哪种模式,都存在着控制系统只关注单轴的运行情况,而不综合考虑多轴之间的运动同步信息,因此,虽然保证了单轴的跟踪精度,但在遇到负载突变或持续变化时,各运动轴间的运动同步便无法得到有力保证,从而降低数控滚齿机床最终的加工的精度。交叉耦合同步控制策略在轮廓成形精度控制方面具有较大优势,它由交叉耦合轮廓误差模型及轮廓误差补偿分配器组成,通过综合考虑各轴间的同步误差,利用一定的分配补偿规律,对机床各运动轴进行同步误差补偿,从而提高机床整体加工精度。
本文在传统数控滚齿机给定同步控制策略基础上,结合交叉耦合控制,误差分配器选择PI补偿器,建立了滚齿机滚刀主轴和回转工作台的联系;通过分析研究永磁同步电动机的控制原理和机床伺服系统的控制系统,建立了简化的永磁电动机数学模型,对速度和电流控制器控制规律进行了数学描述,并由此导出了运动系统的速度和同步误差的数学公式。
在得到数控机床运动控制系统的数学模型后,利用仿真软件建立起整个系统的仿真模型。对系统在空载和负载突变两种工况下进行仿真研究,从仿真结果得到了采用PI型交叉耦合控制器的机床同步控制策略的效果,仿真结果表明了所提出和控制策略可以有效降低机床的同步误差,从而提高机床加工精度。
最后,对本文的工作进行了总结,并对今后下一步的研究工作提供了建议和设想。
In the process of CNC gear hobbing machining, both the rotation speeds of the hob and rotating table have to be maintained in a linear relationship to guarantee the precision of gear machining. So the degree of speed match between the hob and rotating table is closely related to the gear machining precision. In the traditional synchronization method of CNC machines, the electronic gearbox is usually adopted to maintain this linear relationship. There are four ways to realize the function of electronic gearbox, which are master-slave electronic gearbox, parallel electronic gearbox, hardware-based electronic gearbox and software-based electronic gearbox. Whichever way the electronic gearbox is implemented, they are all only focused on the operation of single axis, without consideration of synchronization information among multiple axes. Thus, the tracing precision of single axis can be maintained, but the precision of synchronization motion can not be guaranteed under situation of the abrupt or constant change of load, which will deteriorate the performance of CNC hobbing machines. Cross-coupled synchronization control strategy has great advantage on the aspect of contour forming precision. It is consisted of a contour error model and a contour error compensation distributor. Through integration and synthesis of synchronization information among multiple axes, the motion of each axis in the machine will be compensated using a kind of compensation distribution law, which will then improve the whole precision of machining.
On the basis of conventional set-point synchronization control strategy, the connection between the hob and rotation table is established in this thesis, with the introduction of cross-coupled control consisted of PI type compensation distributor. With the analysis of control principle of permanent magnet synchronous motors (PMSM) and control structure of servo system of machine, a simplified PMSM mathematical model is created, the speed and current controller are described mathematically, thus the formulas of output speed and synchronization error are deduced.
With the mathematical models of control system in CNC machines, the simulation model for the whole motion system is created. The working condition of both no load and load abrupt change are simulated and researched. Conclusion can be obtained from simulation results that the proposed PI type cross-coupled control strategy have better effect, which can significantly reduce the synchronization error and improve the precision of hobbing machining.
In the end, the achievement of this paper is summarized, and the suggestions and plans for the further work are proposed.
本文在传统数控滚齿机给定同步控制策略基础上,结合交叉耦合控制,误差分配器选择PI补偿器,建立了滚齿机滚刀主轴和回转工作台的联系;通过分析研究永磁同步电动机的控制原理和机床伺服系统的控制系统,建立了简化的永磁电动机数学模型,对速度和电流控制器控制规律进行了数学描述,并由此导出了运动系统的速度和同步误差的数学公式。
在得到数控机床运动控制系统的数学模型后,利用仿真软件建立起整个系统的仿真模型。对系统在空载和负载突变两种工况下进行仿真研究,从仿真结果得到了采用PI型交叉耦合控制器的机床同步控制策略的效果,仿真结果表明了所提出和控制策略可以有效降低机床的同步误差,从而提高机床加工精度。
最后,对本文的工作进行了总结,并对今后下一步的研究工作提供了建议和设想。
In the process of CNC gear hobbing machining, both the rotation speeds of the hob and rotating table have to be maintained in a linear relationship to guarantee the precision of gear machining. So the degree of speed match between the hob and rotating table is closely related to the gear machining precision. In the traditional synchronization method of CNC machines, the electronic gearbox is usually adopted to maintain this linear relationship. There are four ways to realize the function of electronic gearbox, which are master-slave electronic gearbox, parallel electronic gearbox, hardware-based electronic gearbox and software-based electronic gearbox. Whichever way the electronic gearbox is implemented, they are all only focused on the operation of single axis, without consideration of synchronization information among multiple axes. Thus, the tracing precision of single axis can be maintained, but the precision of synchronization motion can not be guaranteed under situation of the abrupt or constant change of load, which will deteriorate the performance of CNC hobbing machines. Cross-coupled synchronization control strategy has great advantage on the aspect of contour forming precision. It is consisted of a contour error model and a contour error compensation distributor. Through integration and synthesis of synchronization information among multiple axes, the motion of each axis in the machine will be compensated using a kind of compensation distribution law, which will then improve the whole precision of machining.
On the basis of conventional set-point synchronization control strategy, the connection between the hob and rotation table is established in this thesis, with the introduction of cross-coupled control consisted of PI type compensation distributor. With the analysis of control principle of permanent magnet synchronous motors (PMSM) and control structure of servo system of machine, a simplified PMSM mathematical model is created, the speed and current controller are described mathematically, thus the formulas of output speed and synchronization error are deduced.
With the mathematical models of control system in CNC machines, the simulation model for the whole motion system is created. The working condition of both no load and load abrupt change are simulated and researched. Conclusion can be obtained from simulation results that the proposed PI type cross-coupled control strategy have better effect, which can significantly reduce the synchronization error and improve the precision of hobbing machining.
In the end, the achievement of this paper is summarized, and the suggestions and plans for the further work are proposed.
引文
[1]《齿轮制造工艺手册:滚、插、磨、剃、刨》编委会.齿轮制造工艺手册:滚、插、磨、剃、刨[M].北京:机械工业出版社, 2010, 2
[2]吴其华,徐邦荃.多电机同步传动控制系统分析[J].自动控制技术, 2003, I22(1): 20-24
[3] Tomizuka M., Hu J, Chiu, Kamano T.. Synchronization of Two Motion Control Axes Under Adaptive Feedforward Control[J], ASME Journal of Dynamic Systems. Measurement and Control, 1992, 114: 3234-3245
[4]刘福才,刘学莲,刘立伟.多级电机传动系统同步控制理论与应用研究[J].控制工程, 2002, 9(4): 78-82
[5] Anderson R. G., Lorenz R.. Web Machine Coordinated Motion Control via Electronic Line-Shfating[J]. IEEE, IAS Annual Tech. Conf., 1999, (10): 3-7
[6] Y. Koren. Cross-coupled Biaxial Computer Controls for Manufacturing Systems[J]. ASME Journal of Dynamic System. Measurement and Control, 1980, 102(12): 1324-1330
[7] Y. Koren and C. C. Lo, Variable-gain cross-coupling controller for contouring[J]. Ann. CIRP, vol. 40, no. 1, 1991, 371–374.
[8] P. Moore and C. Chen, Fuzzy logic coupling and synchronized control of multiple independent servo-drives[J]. Contr. Eng. Practice vol. 3, no.12, 1995, 1697–1708.
[9] G. J. Wang and T. J. Lee, Neural-network cross-coupled control system with application on circular tracking of linear motor X-Y table[J]. in Proc. Int. Joint Conf. Digital Object Identifier, 1999, 2194–2199.
[10] M. T. Yan, M. H. Lee, and P. L. Yen, Theory and application of a combined self-tuning adaptive control and cross coupling control in a retrofit milling machine[J]. IEEE/ASME Trans. Mechatronics, vol. 15, no. 2, Mar. 2005, 193–211
[11] Dong Sun, Xiaoyin Shao, and Gang Feng, A Model-Free Cross-Coupled Control for Position Synchronization of Multi-Axis Motions: Theory and Experiments[J]. IEEE Contr. Syst. Technol., vol. 13, no. 6, vol. 15, no. 2, Mar. 2007, 306-314.
[12] Loxham. J. British Patent No. 10011538. Manufacture of Gear (1961)
[13] Loxham. J. British Patent No. 1015662. Improvement in or Relating to Drivefor Gear Grinding Machines (1961)
[14]庄磊.电子齿轮箱关键控制技术及其应用研究[博士学位论文].南京:南京航空航天大学, 2001
[15]吴焱明.齿轮加工数控技术的研究[博士学位论文].合肥:合肥工业大学, 2000, 10
[16] J. Dinsdale, P. F. Iones, M. Thorneycroft. The Electronic Gearbox-Computer Software Replace Mechanical Coupling[J]. Annals of CIRP, 1982, 31(1): 247-249
[17]刘润爱.零传动滚齿机关键技术研究与应用[博士学位论文].重庆:重庆大学, 2006
[18]郭庆鼎,孙宜标,王丽梅.现代永磁电动机交流伺服系统[M].北京:中国电力出版社, 2006
[19] T. Low, M. A. Jabbar, and M. Rahman, Permanent-Magnet Motors for Brushless Operation[J]. IEEE Transaction on Industry Application, 26(1), 1990, 2,124 - 129
[20]马志源.电力拖动控制系统[M].北京:科学出版社, 2004
[21] Solsona J, Valla M I. Muravchik C. A Nonlinear Reduced Order Observer for Permanent Magnet Synchronous Motors[J]. IEEE. Trans Ind. Electron. 1996, 43(4): 492-497
[22]卢绍青.数控机床通用误差补偿技术研究[硕士学位论文].北京:北京工业大学, 2001.
[23]张志飞.多轴数控机床热误差与集合误差建模及补偿技术的研究[博士学位论文].天津:天津大学, 2000.
[24]刘金棍.先进PID控制MATLAB仿真(第二版)[M].北京:电子工业出版社, 2004: 153-165.
[25]李佳特.数控机床进给伺服系统的性能评估与改进[J].制造技术与机床, 2004(10): 112一115.
[26] David Alan Smith. Wide Bandwidth Control of High-Speed Milling Machine Feed Drives. PH.D. Thesis, University of Florida, 1999.
[27]廖效果,刘又午,朱剑英.数控技术[M].湖北科学技术出版社, 2000: 171-254.
[28]肖本贤.多轴运动下轮廓跟踪误差控制与补偿方法的研究[博士学位论文].合肥:合肥工业大学, 2004.
[29] Syn-Shiuh Yeh, Pau-Lo Hsu. Estimation of the Contouring Error Vector for theCross-Coupled Control Design[J]. IEEE/ASME, 2002, Vo1.7 (1): 44-51.
[30] Doo-Jin Shin et al. Fuzzy Logic Control For the Contouring Accuracy of XY Positioning System[J]. IEEE, 2001:1248一1252.
[31] Crispin A.J. et al. High Performance Trajectory Control using a Neural Network Cross-Coupled Gin Scheduler[J]. IEEE, 1998: 333-336.
[32] Hua Qiu, Kai Cheng, Yan Li. Optimal Circular Arc Interpolation for NC tool-path Generation in Curve Contour Manufacturing[J]. Computer-Aided Design, 1997, Vo1.29, (11): 751-760.
[33] Lingyun Ye, Kaichen Song, Ying Chen. Precise Motion Control for Multi-axis System Using Real Time Forecast Cross-coupling Controller[J]. IEEE, 2004: 2139-2144.
[34] Hyun C.Lee, Gi J.Jeon. Real-time Compensation of Two-Dimensional Contour Error in CNC Machine Tools[J]. IEEE/ASME, 1999: 623-628.
[35] Ming-yang Cheng, Cheng-Chien Lee. On Real-time Contour Error Estimation for Contour Following Task[J]. Proceeding of the 2005, IEEE, 2005: 1047-1-52.
[36]德赖斯著;金爱娟,李少龙,李航天译.线性控制系统工程[M].北京:清华大学出版社, 2005.6
[37]梅雪松,陶涛,堤正臣等.高速、高精度数控伺服工作台摩擦误差的研究[J].机械工程学报, 2001, 37(6): 76-81
[2]吴其华,徐邦荃.多电机同步传动控制系统分析[J].自动控制技术, 2003, I22(1): 20-24
[3] Tomizuka M., Hu J, Chiu, Kamano T.. Synchronization of Two Motion Control Axes Under Adaptive Feedforward Control[J], ASME Journal of Dynamic Systems. Measurement and Control, 1992, 114: 3234-3245
[4]刘福才,刘学莲,刘立伟.多级电机传动系统同步控制理论与应用研究[J].控制工程, 2002, 9(4): 78-82
[5] Anderson R. G., Lorenz R.. Web Machine Coordinated Motion Control via Electronic Line-Shfating[J]. IEEE, IAS Annual Tech. Conf., 1999, (10): 3-7
[6] Y. Koren. Cross-coupled Biaxial Computer Controls for Manufacturing Systems[J]. ASME Journal of Dynamic System. Measurement and Control, 1980, 102(12): 1324-1330
[7] Y. Koren and C. C. Lo, Variable-gain cross-coupling controller for contouring[J]. Ann. CIRP, vol. 40, no. 1, 1991, 371–374.
[8] P. Moore and C. Chen, Fuzzy logic coupling and synchronized control of multiple independent servo-drives[J]. Contr. Eng. Practice vol. 3, no.12, 1995, 1697–1708.
[9] G. J. Wang and T. J. Lee, Neural-network cross-coupled control system with application on circular tracking of linear motor X-Y table[J]. in Proc. Int. Joint Conf. Digital Object Identifier, 1999, 2194–2199.
[10] M. T. Yan, M. H. Lee, and P. L. Yen, Theory and application of a combined self-tuning adaptive control and cross coupling control in a retrofit milling machine[J]. IEEE/ASME Trans. Mechatronics, vol. 15, no. 2, Mar. 2005, 193–211
[11] Dong Sun, Xiaoyin Shao, and Gang Feng, A Model-Free Cross-Coupled Control for Position Synchronization of Multi-Axis Motions: Theory and Experiments[J]. IEEE Contr. Syst. Technol., vol. 13, no. 6, vol. 15, no. 2, Mar. 2007, 306-314.
[12] Loxham. J. British Patent No. 10011538. Manufacture of Gear (1961)
[13] Loxham. J. British Patent No. 1015662. Improvement in or Relating to Drivefor Gear Grinding Machines (1961)
[14]庄磊.电子齿轮箱关键控制技术及其应用研究[博士学位论文].南京:南京航空航天大学, 2001
[15]吴焱明.齿轮加工数控技术的研究[博士学位论文].合肥:合肥工业大学, 2000, 10
[16] J. Dinsdale, P. F. Iones, M. Thorneycroft. The Electronic Gearbox-Computer Software Replace Mechanical Coupling[J]. Annals of CIRP, 1982, 31(1): 247-249
[17]刘润爱.零传动滚齿机关键技术研究与应用[博士学位论文].重庆:重庆大学, 2006
[18]郭庆鼎,孙宜标,王丽梅.现代永磁电动机交流伺服系统[M].北京:中国电力出版社, 2006
[19] T. Low, M. A. Jabbar, and M. Rahman, Permanent-Magnet Motors for Brushless Operation[J]. IEEE Transaction on Industry Application, 26(1), 1990, 2,124 - 129
[20]马志源.电力拖动控制系统[M].北京:科学出版社, 2004
[21] Solsona J, Valla M I. Muravchik C. A Nonlinear Reduced Order Observer for Permanent Magnet Synchronous Motors[J]. IEEE. Trans Ind. Electron. 1996, 43(4): 492-497
[22]卢绍青.数控机床通用误差补偿技术研究[硕士学位论文].北京:北京工业大学, 2001.
[23]张志飞.多轴数控机床热误差与集合误差建模及补偿技术的研究[博士学位论文].天津:天津大学, 2000.
[24]刘金棍.先进PID控制MATLAB仿真(第二版)[M].北京:电子工业出版社, 2004: 153-165.
[25]李佳特.数控机床进给伺服系统的性能评估与改进[J].制造技术与机床, 2004(10): 112一115.
[26] David Alan Smith. Wide Bandwidth Control of High-Speed Milling Machine Feed Drives. PH.D. Thesis, University of Florida, 1999.
[27]廖效果,刘又午,朱剑英.数控技术[M].湖北科学技术出版社, 2000: 171-254.
[28]肖本贤.多轴运动下轮廓跟踪误差控制与补偿方法的研究[博士学位论文].合肥:合肥工业大学, 2004.
[29] Syn-Shiuh Yeh, Pau-Lo Hsu. Estimation of the Contouring Error Vector for theCross-Coupled Control Design[J]. IEEE/ASME, 2002, Vo1.7 (1): 44-51.
[30] Doo-Jin Shin et al. Fuzzy Logic Control For the Contouring Accuracy of XY Positioning System[J]. IEEE, 2001:1248一1252.
[31] Crispin A.J. et al. High Performance Trajectory Control using a Neural Network Cross-Coupled Gin Scheduler[J]. IEEE, 1998: 333-336.
[32] Hua Qiu, Kai Cheng, Yan Li. Optimal Circular Arc Interpolation for NC tool-path Generation in Curve Contour Manufacturing[J]. Computer-Aided Design, 1997, Vo1.29, (11): 751-760.
[33] Lingyun Ye, Kaichen Song, Ying Chen. Precise Motion Control for Multi-axis System Using Real Time Forecast Cross-coupling Controller[J]. IEEE, 2004: 2139-2144.
[34] Hyun C.Lee, Gi J.Jeon. Real-time Compensation of Two-Dimensional Contour Error in CNC Machine Tools[J]. IEEE/ASME, 1999: 623-628.
[35] Ming-yang Cheng, Cheng-Chien Lee. On Real-time Contour Error Estimation for Contour Following Task[J]. Proceeding of the 2005, IEEE, 2005: 1047-1-52.
[36]德赖斯著;金爱娟,李少龙,李航天译.线性控制系统工程[M].北京:清华大学出版社, 2005.6
[37]梅雪松,陶涛,堤正臣等.高速、高精度数控伺服工作台摩擦误差的研究[J].机械工程学报, 2001, 37(6): 76-81