数控机床伺服系统振动特性研究
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摘要
随着数控机床加工精度要求的提高,其结构也越来越复杂,随之引起的机床振动问题愈加严重,引起了人们的普遍关注。机床振动对工件加工质量、加工速度及刀具与机床的寿命都有很大的影响。本文主要针对数控机床伺服系统振动特性进行研究。
首先,利用有限元软件对永磁同步电动机进行了电磁场分析,计算电动机空载和加载后的磁场,并对其进行了对比,得到了电磁场中随位置变化径向磁密、切向磁密、径向力密度以及切向力密度的波形图。利用编程控制转子旋转,得到永磁同步电动机瞬念磁场的变化规律,绘制出径向磁密、切向磁密、径向力密度和切向力密度随时问变化的波形。电动机转矩脉动的主要来源是电动机的切向磁密。通过前面的分析可以计算电动机转矩脉动并绘制出转矩脉动波形图。在此基础上,提出了一种有效抑制电动机转矩脉动的方法,即改变电动机定子槽槽口参数,降低电动机的转矩脉动。通过多组数据的计算对比得出该型号电动机的最佳参数及对应的转矩脉动的数值。以上计算分析为优化永磁同步电动机设计提供了参考。
其次,对机床的切削振动进行了研究。基于切削振动的产生机理,利用解析法求出不同转速下数控机床的极限切削宽度,对机床实际加工生产有一定的参考意义。运用有限元软件对刀架系统进行模态分析并提取出各阶固有频率,计算了切削力作用下的刀架变形。
最后,分析了丝杠系统的刚度和变形对数控机床振动特性的影响。根据计算公式算出丝杠系统的刚度,考虑丝杠的变形因素主要来自切削力和电动机转矩脉动的综合作用,为了更加直观的观察丝杠的变形情况,采用有限元软件进行瞬态动力学分析,得到了电动机旋转一周的时间内丝杠受力变形的变化规律。
The structure of NC Machine Tool is more complicated as high accuracy requirements. The problem of machine vibration causes serious concern. Machine vibration affects machining quality and cutting speed, furthermore, it makes a shorter life of tool and machine. Therefore, this paper foci on the study of vibration characteristics of the NC machine tool servo-system.
First, Permanent Magnet Synchronous Motor is analyzed with the finite element software.The magnetic fields with no load and load are calculated and compared. The wave figures of radial flux density, tangential flux density, radial force density and tangential force density varied with position are gotten. Rotor of rotation is controlled by the program for a better research on the changes of motor magnetic field. The wave figures of radial flux density, tangential flux density, radial force density and tangential force density varied with time was drawn. Then the changing regulations of transient magnetic field were derived. Motor torque ripple resulted from motor tangential flux density, so the motor torque ripple and the torque waveform figure are got basing on the analysis of magnetic field of motor. On this basis, an effective method of suppressing motor torque ripple is proposed. The motor torque ripple is reduced by changing the parameters of motor stator slots The Optimal parameters are obtained from multiple results comparison. The calculation and analysis provide the basic design reference for the permanent magnet synchronous motor.
Secondly, cutting vibration of machine tool is calculated. According on the generating mechanism of cutting vibration, the limits of cutting width are calculated by analytical method in different speed. It provides references for actual machining. Natural frequencies are extracted through modal analysis of cutter system with the finite element software. The cutting system deformation is also analyzed.
Finally, the influence of stiffness and deformation of ball lead screw system on the vibration characteristics of NC machine is explored. The stiffness of ball lead screw system is calculated according to the calculation formula. The ball lead screw deformation results from cutting force and motor torque ripple. The figures of the screw deformation changing in one cycle are drawn by transient dynamic analysis with the finite element software, which shows more directly the ball lead screw deformation.
首先,利用有限元软件对永磁同步电动机进行了电磁场分析,计算电动机空载和加载后的磁场,并对其进行了对比,得到了电磁场中随位置变化径向磁密、切向磁密、径向力密度以及切向力密度的波形图。利用编程控制转子旋转,得到永磁同步电动机瞬念磁场的变化规律,绘制出径向磁密、切向磁密、径向力密度和切向力密度随时问变化的波形。电动机转矩脉动的主要来源是电动机的切向磁密。通过前面的分析可以计算电动机转矩脉动并绘制出转矩脉动波形图。在此基础上,提出了一种有效抑制电动机转矩脉动的方法,即改变电动机定子槽槽口参数,降低电动机的转矩脉动。通过多组数据的计算对比得出该型号电动机的最佳参数及对应的转矩脉动的数值。以上计算分析为优化永磁同步电动机设计提供了参考。
其次,对机床的切削振动进行了研究。基于切削振动的产生机理,利用解析法求出不同转速下数控机床的极限切削宽度,对机床实际加工生产有一定的参考意义。运用有限元软件对刀架系统进行模态分析并提取出各阶固有频率,计算了切削力作用下的刀架变形。
最后,分析了丝杠系统的刚度和变形对数控机床振动特性的影响。根据计算公式算出丝杠系统的刚度,考虑丝杠的变形因素主要来自切削力和电动机转矩脉动的综合作用,为了更加直观的观察丝杠的变形情况,采用有限元软件进行瞬态动力学分析,得到了电动机旋转一周的时间内丝杠受力变形的变化规律。
The structure of NC Machine Tool is more complicated as high accuracy requirements. The problem of machine vibration causes serious concern. Machine vibration affects machining quality and cutting speed, furthermore, it makes a shorter life of tool and machine. Therefore, this paper foci on the study of vibration characteristics of the NC machine tool servo-system.
First, Permanent Magnet Synchronous Motor is analyzed with the finite element software.The magnetic fields with no load and load are calculated and compared. The wave figures of radial flux density, tangential flux density, radial force density and tangential force density varied with position are gotten. Rotor of rotation is controlled by the program for a better research on the changes of motor magnetic field. The wave figures of radial flux density, tangential flux density, radial force density and tangential force density varied with time was drawn. Then the changing regulations of transient magnetic field were derived. Motor torque ripple resulted from motor tangential flux density, so the motor torque ripple and the torque waveform figure are got basing on the analysis of magnetic field of motor. On this basis, an effective method of suppressing motor torque ripple is proposed. The motor torque ripple is reduced by changing the parameters of motor stator slots The Optimal parameters are obtained from multiple results comparison. The calculation and analysis provide the basic design reference for the permanent magnet synchronous motor.
Secondly, cutting vibration of machine tool is calculated. According on the generating mechanism of cutting vibration, the limits of cutting width are calculated by analytical method in different speed. It provides references for actual machining. Natural frequencies are extracted through modal analysis of cutter system with the finite element software. The cutting system deformation is also analyzed.
Finally, the influence of stiffness and deformation of ball lead screw system on the vibration characteristics of NC machine is explored. The stiffness of ball lead screw system is calculated according to the calculation formula. The ball lead screw deformation results from cutting force and motor torque ripple. The figures of the screw deformation changing in one cycle are drawn by transient dynamic analysis with the finite element software, which shows more directly the ball lead screw deformation.
引文
[1]Holtz J., Springob L. Identification and compensation of torque ripple in high-precision permanent magnet motor drives, IEEE Transactions on Industrial Electronics,1996,43:309-320.
[2]Favre E., Cardoletti L., Jufer M. Permanent-magnet synchronous Motors:a comprehensive approach to cogging torque suppression, Industry Applications, IEEE Transactions on,1993, 29:1141-1149.
[3]Hwang S. M., Lieu D. K. Reduction of Torque Ripple in Brushless DC Motors, IEEE Transactions on Magnetics,1995,31:3737-3739.
[4]Zhu Z. Q., Howe D. Influence of design parameters on cogging torque in permanent magnet machines. IEEE Transactions on Energy Conversion,2005,15:407-412.
[5]Islam M. S., S. Sebastian. USA Issues in reducing the cogging torque of mass-produced permanent-magnet brushless DC motor. Industry Applications Conference,2003,1:393-400.
[6]杨玉波,王秀和,丁婷婷等.极弧系数组合优化的永磁电动机齿槽转矩削弱方法.中国电动机工程学报,2007,27(6)：7－11.
[7]Li Zhu, Jiang S. Z, Zhu Z. Q. et al. Analytical Methods for Minimizing Cogging Torque in Permanent-Magnet Machines. IEEE Transactions on Magnetics,2009,4(45):2023-2031.
[8]J. Tlusty, F. Ismail. Basic Nonlinearity in Machining Chatter, Anna. CIPP,1981,30(1):299-304.
[9]丁俊一.工艺系统刚度主轴方位对切削过程稳定性影响的研究.振动工程学报,1988,1(4)：36-43.
[10]Gasparetto, Alessandro. Journal of Dynamic Systems Measurement and Control. Transactions of the ASME,1998,120(4):545-547.
[11]陈花玲.机床切削颤振的非线性理论研究.振动工程学报,1992,5(4)：335－342.
[12]刘习军.机床速度型切削颤振的非线性研究.振动与冲击,1999,18(2)：5－9.
[13]Neter Stelter. Nonlinear Vibrations of Structures Induced by Dry Friction. Nonlinear Dynamics, 1992,3:329-345.
[14]丁骏一.切削过程再生颤振的模糊稳定性分析.振动工程学报,1998,11(1)：106－109.
[15]Kondo Eiji, Ota Hiroshi. Effects of tool flank wear on occurrences of regenerative chatter(lst report, A model of dynamic undercutting forces caused by tool flank wear), C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C,1995,61(584):1279-1285.
[16]Marui E, Hashimoto M., Kato S. Regenerative chatter vibration occurring in turning with different side cutting edge angles. Journal of Engineering for Industry. Transactions of the ASME,1995, 117(4):551-558.
[17]Davies M A, Dutterer B. On the dynamics of high-speed milling withlong, slender endmills. CIRP Annals-Manufacturing Technolgy,1998,47(1):55-60.
[18]David E Gilsinn. Estimating Critical Hopf Bifurcation Parameters for a Second-Order Delay Differential Equation with Application to Machine Tool Chatter. Nonlinear dynamics,2002, 30(2):103-154.
[19]师汉民等.影响机床颤振的几个非线性因素及其数学模型.华中工学院学报,1984,12(6)：101－112.
[20]吴雅.金属切削机床切削噪声的动力学研究.机械工程学报,1995,31(5)：76-85.
[21]鲁宏伟,杨叔子.基于非线性模型的切削过程的混沌研究.振动工程学报,1996,9(2)：169－172.
[22]Lee B Y, Tarng Y S, Ma S C. Modeling of the process damping force in chatter vibration. International Journal of Machine Tools & Manufacture,1995,35(7):951-962.
[23]Fu J C, Troy C A, Mori K. Chatter classification by entropy functions and morphological processing in cylindrical traverse grinding. Precision Engineering,1996,18(2-3):110-117.
[24]Pakdemirli M, Ulsoy A G. Perturbation analysis of spindle speed vibration in machine tool chatter, Journal of Vibration and Control,1997,3(3):261-278.
[25]Yuan Ning, M Rahman, Y S Wong. Investigation of chip formation in high speed end milling. Journal of material processing technology,2001,113(1-3):360-367.
[26]SP TIMOSHENKO. On the correction for shear of differential equation for transverse vibrations of prismatic beams. Philosophical Magazine,1921,41:744-746.
[27]SP TIMOSHENKO. On the transverse vibration of bars with uniform cross-section. Philosophical Magazine,1922,43:125-131.
[28]Nelson H. M. Transverse vibration of a moving strip. Journal of Sound and Vibration,1979, 65(3):381-389.
[29]Mote C D Jr. A study of band saw vibrations. Journal of the Franklin Institute,1965,279(6): 430-444.
[30]Wu W Z, Mote C D Jr. Parametric excitation of an axially moving band by periodic edge loading. Journal of Sound and Vibration,1986,110:27-39.
[31]M. C. Lin, B. Ravan and S. A. Velinsky. Kinematics of the ball screw mechanism. Journal of Mechanical Design, Transactions of the ASME,1994,116(3):849-555.
[32]M. C. Lin. Design and mechanics of the ball screw mechanism. The University of Wisconsin-Madison,1989.
[33]Hual-Te T., Huang. B. Ravani. Contact stress analysis in ball screw mechanism using the tubular medial axis representation of contacting surfaces. Transactions of the ASME,1997(11):8-14
[34]Belyaev V. G., Malyuga. Force transfer factor in the return channel of a ball and screw mechanism. Soviet Engineering Research,1983,3 (2):78-80.
[35]Belyaev V. G., Kogan A. I. Effect of geometrical errors on contact angle in ball lead screw transmission. Machines & Tooling (English translation of Stanki 1 Instrument),1973,44(5): 25-29.
[36]Yoshida T, Tozaki Y, Matsumoto S. Study on load distribution and ball motion of ball lead screw. Journal of Japanese Society of Tribologists,2003,48(8):659-666.
[37]Shimoda. H. Stiffness analysis of ball lead screw. International Journal of the Japan Society for precision Engineering,1999,33(3):168-172.
[38]Nakashima Katuhiro, Takafuji Kazuki. Stiffness of a ball screw including the deformation of screw, nut and screw thread(lst report, single nut). Transactions of the Japan Society of Mechanical Engineers, Part C,1988,54(505):2181-2187.
[39]Takafuji Kazuki, Nakashima Katuhiro. Stiffness of a ball screw including with consideration to deformation of the screw, nut and screw thread(2nd Report:Preloaded double nuts). Transactions of the Japan Society of Mechanical Engineers, Part C,1989,55(515):1734-1740.
[40]Pillay P, Krishnan R. Modeling, simulation, and analysis of perma-nent-magnet motor drives, Part I:The permanent-magnet synchronous motor drive. IEEE Trans, on Industry Applica-tions, 1989,25(2):265-273.
[41]Pillay P, Krishnan R. Modeling, simulation, and analysis of perma-nent- magnet motor drives, PartⅡ:The brushless DC motor drive. IEEE Trans, on Industry Applications,1989,25(2): 274-279.
[42]陈永校,诸自成,应善成.电动机噪声的分析和控制.杭州：浙江大学出版社,1987.
[43]唐任远.现代永磁电动机理论与设计.北京：机械工业出版社,1997.
[44]Koen Delaere, Ward Heylen, Ronnie Belmans et al. Comparison of Induction Machine Stator Vibration Spectra Induced by Reluctance Forces and Magnetostriction. IEEE Transactions On Magnetics,2002,38(2):969-972
[45]Kyung-Tae Kim, Kwang-Suk Kim, Sang-Moon Hwang et al. Comparison of Magnetic Forces for IPM and SPM Motor with Rotor Eccentricity, IEEE Transactions On Magnetics,2001,37(5): 3448-3451.
[46]张洪信,赵清海. Ansys有限元分析完全自学手册.北京：机械工业出版社.2008.
[47]于骏一,邹青.机械制造技术基础.北京：机械工业出版社,2007.
[48]师汉民.机械振动系统.武汉：华中科技大学出版社,2004.
[49]许向荣,宋现春,姜洪奎.提高数控机床滚珠丝杠进给系统机械刚度的措施.设计与研究,2008(8)：1－4.
[50]尹汉桥,尹明,张高平.丝杠刚度受支撑方式影响的变化规律研究.机械研究与应用,2010(01)：45-46.
[51]许实章.电机学.北京：机械工业出版社,1996.
[2]Favre E., Cardoletti L., Jufer M. Permanent-magnet synchronous Motors:a comprehensive approach to cogging torque suppression, Industry Applications, IEEE Transactions on,1993, 29:1141-1149.
[3]Hwang S. M., Lieu D. K. Reduction of Torque Ripple in Brushless DC Motors, IEEE Transactions on Magnetics,1995,31:3737-3739.
[4]Zhu Z. Q., Howe D. Influence of design parameters on cogging torque in permanent magnet machines. IEEE Transactions on Energy Conversion,2005,15:407-412.
[5]Islam M. S., S. Sebastian. USA Issues in reducing the cogging torque of mass-produced permanent-magnet brushless DC motor. Industry Applications Conference,2003,1:393-400.
[6]杨玉波,王秀和,丁婷婷等.极弧系数组合优化的永磁电动机齿槽转矩削弱方法.中国电动机工程学报,2007,27(6)：7－11.
[7]Li Zhu, Jiang S. Z, Zhu Z. Q. et al. Analytical Methods for Minimizing Cogging Torque in Permanent-Magnet Machines. IEEE Transactions on Magnetics,2009,4(45):2023-2031.
[8]J. Tlusty, F. Ismail. Basic Nonlinearity in Machining Chatter, Anna. CIPP,1981,30(1):299-304.
[9]丁俊一.工艺系统刚度主轴方位对切削过程稳定性影响的研究.振动工程学报,1988,1(4)：36-43.
[10]Gasparetto, Alessandro. Journal of Dynamic Systems Measurement and Control. Transactions of the ASME,1998,120(4):545-547.
[11]陈花玲.机床切削颤振的非线性理论研究.振动工程学报,1992,5(4)：335－342.
[12]刘习军.机床速度型切削颤振的非线性研究.振动与冲击,1999,18(2)：5－9.
[13]Neter Stelter. Nonlinear Vibrations of Structures Induced by Dry Friction. Nonlinear Dynamics, 1992,3:329-345.
[14]丁骏一.切削过程再生颤振的模糊稳定性分析.振动工程学报,1998,11(1)：106－109.
[15]Kondo Eiji, Ota Hiroshi. Effects of tool flank wear on occurrences of regenerative chatter(lst report, A model of dynamic undercutting forces caused by tool flank wear), C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C,1995,61(584):1279-1285.
[16]Marui E, Hashimoto M., Kato S. Regenerative chatter vibration occurring in turning with different side cutting edge angles. Journal of Engineering for Industry. Transactions of the ASME,1995, 117(4):551-558.
[17]Davies M A, Dutterer B. On the dynamics of high-speed milling withlong, slender endmills. CIRP Annals-Manufacturing Technolgy,1998,47(1):55-60.
[18]David E Gilsinn. Estimating Critical Hopf Bifurcation Parameters for a Second-Order Delay Differential Equation with Application to Machine Tool Chatter. Nonlinear dynamics,2002, 30(2):103-154.
[19]师汉民等.影响机床颤振的几个非线性因素及其数学模型.华中工学院学报,1984,12(6)：101－112.
[20]吴雅.金属切削机床切削噪声的动力学研究.机械工程学报,1995,31(5)：76-85.
[21]鲁宏伟,杨叔子.基于非线性模型的切削过程的混沌研究.振动工程学报,1996,9(2)：169－172.
[22]Lee B Y, Tarng Y S, Ma S C. Modeling of the process damping force in chatter vibration. International Journal of Machine Tools & Manufacture,1995,35(7):951-962.
[23]Fu J C, Troy C A, Mori K. Chatter classification by entropy functions and morphological processing in cylindrical traverse grinding. Precision Engineering,1996,18(2-3):110-117.
[24]Pakdemirli M, Ulsoy A G. Perturbation analysis of spindle speed vibration in machine tool chatter, Journal of Vibration and Control,1997,3(3):261-278.
[25]Yuan Ning, M Rahman, Y S Wong. Investigation of chip formation in high speed end milling. Journal of material processing technology,2001,113(1-3):360-367.
[26]SP TIMOSHENKO. On the correction for shear of differential equation for transverse vibrations of prismatic beams. Philosophical Magazine,1921,41:744-746.
[27]SP TIMOSHENKO. On the transverse vibration of bars with uniform cross-section. Philosophical Magazine,1922,43:125-131.
[28]Nelson H. M. Transverse vibration of a moving strip. Journal of Sound and Vibration,1979, 65(3):381-389.
[29]Mote C D Jr. A study of band saw vibrations. Journal of the Franklin Institute,1965,279(6): 430-444.
[30]Wu W Z, Mote C D Jr. Parametric excitation of an axially moving band by periodic edge loading. Journal of Sound and Vibration,1986,110:27-39.
[31]M. C. Lin, B. Ravan and S. A. Velinsky. Kinematics of the ball screw mechanism. Journal of Mechanical Design, Transactions of the ASME,1994,116(3):849-555.
[32]M. C. Lin. Design and mechanics of the ball screw mechanism. The University of Wisconsin-Madison,1989.
[33]Hual-Te T., Huang. B. Ravani. Contact stress analysis in ball screw mechanism using the tubular medial axis representation of contacting surfaces. Transactions of the ASME,1997(11):8-14
[34]Belyaev V. G., Malyuga. Force transfer factor in the return channel of a ball and screw mechanism. Soviet Engineering Research,1983,3 (2):78-80.
[35]Belyaev V. G., Kogan A. I. Effect of geometrical errors on contact angle in ball lead screw transmission. Machines & Tooling (English translation of Stanki 1 Instrument),1973,44(5): 25-29.
[36]Yoshida T, Tozaki Y, Matsumoto S. Study on load distribution and ball motion of ball lead screw. Journal of Japanese Society of Tribologists,2003,48(8):659-666.
[37]Shimoda. H. Stiffness analysis of ball lead screw. International Journal of the Japan Society for precision Engineering,1999,33(3):168-172.
[38]Nakashima Katuhiro, Takafuji Kazuki. Stiffness of a ball screw including the deformation of screw, nut and screw thread(lst report, single nut). Transactions of the Japan Society of Mechanical Engineers, Part C,1988,54(505):2181-2187.
[39]Takafuji Kazuki, Nakashima Katuhiro. Stiffness of a ball screw including with consideration to deformation of the screw, nut and screw thread(2nd Report:Preloaded double nuts). Transactions of the Japan Society of Mechanical Engineers, Part C,1989,55(515):1734-1740.
[40]Pillay P, Krishnan R. Modeling, simulation, and analysis of perma-nent-magnet motor drives, Part I:The permanent-magnet synchronous motor drive. IEEE Trans, on Industry Applica-tions, 1989,25(2):265-273.
[41]Pillay P, Krishnan R. Modeling, simulation, and analysis of perma-nent- magnet motor drives, PartⅡ:The brushless DC motor drive. IEEE Trans, on Industry Applications,1989,25(2): 274-279.
[42]陈永校,诸自成,应善成.电动机噪声的分析和控制.杭州：浙江大学出版社,1987.
[43]唐任远.现代永磁电动机理论与设计.北京：机械工业出版社,1997.
[44]Koen Delaere, Ward Heylen, Ronnie Belmans et al. Comparison of Induction Machine Stator Vibration Spectra Induced by Reluctance Forces and Magnetostriction. IEEE Transactions On Magnetics,2002,38(2):969-972
[45]Kyung-Tae Kim, Kwang-Suk Kim, Sang-Moon Hwang et al. Comparison of Magnetic Forces for IPM and SPM Motor with Rotor Eccentricity, IEEE Transactions On Magnetics,2001,37(5): 3448-3451.
[46]张洪信,赵清海. Ansys有限元分析完全自学手册.北京：机械工业出版社.2008.
[47]于骏一,邹青.机械制造技术基础.北京：机械工业出版社,2007.
[48]师汉民.机械振动系统.武汉：华中科技大学出版社,2004.
[49]许向荣,宋现春,姜洪奎.提高数控机床滚珠丝杠进给系统机械刚度的措施.设计与研究,2008(8)：1－4.
[50]尹汉桥,尹明,张高平.丝杠刚度受支撑方式影响的变化规律研究.机械研究与应用,2010(01)：45-46.
[51]许实章.电机学.北京：机械工业出版社,1996.