大导程滚珠丝杠副螺母成型磨削加工建模与仿真
|
摘要
滚珠丝杠副由于具有高效率、高精度、高刚度、低成本等特点,被广泛应用于机械、航天、航空、核工业等领域。高速精密滚珠丝杠副是发展高档数控机床的关键部件,传统结构的滚珠丝杠副已不能适应现代高速高精数控机床的发展需求。因此,研究提高滚珠丝杠副驱动速度的技术具有重大的经济意义和战略意义。基于高速精密滚珠丝杠副的发展要求,本文以昆山市科技局KC0720:大导程滚珠丝杠副螺母成型磨削加工建模与仿真为背景,围绕解决精密滚珠丝杠副高速化的关键技术──大导程滚珠丝杠副螺母成型磨削加工展开讨论,主要研究大导程滚珠丝杠副螺母成型磨削加工理论,大导程滚珠丝杠副螺母成型磨削砂轮截形计算和加工仿真动画设计。
提高滚珠丝杠驱动速度的途径有两条:其一是提高丝杠的转速N,其二是增大丝杠导程Ph。因用提高转速办法来解决是不可取的。于是,大导程滚珠丝杠副在进给驱动的高速化中得到发展。但是大导程使加工制造的难度增大。本文介绍了大导程滚珠丝杠副螺母磨削加工方法,分析了各种加工大导程滚珠丝杠副螺母方法的优缺点,阐述了大导程滚珠丝杠副螺母磨削加工的研究现状和理论分析。
本文提出一种新的加工方法,该方法在改变砂轮安装角的同时,也改变磨削砂轮的截形,对螺母进行磨削加工。
根据螺旋面滚道曲面加工原理、齿轮啮合原理以及回转面砂轮加工螺母工艺建立了相应的数学模型,建立螺旋曲面的数学模型和砂轮磨削加工螺母螺旋滚道面的数学模型。以螺旋滚道的法向截形为初始已知条件,根据螺旋滚道面与砂轮回转面在接触点处法向矢量相同的原理,推导出接触线方程,由坐标转换得出接触线与砂轮轴截形之间的数学关系。使用Matlab数学编程软件进行计算求解接触点。根据实例求解砂轮截形,并研究在不同条件下砂轮截形的求解及它们之间的比较,对求解结果进行分析误差。
使用SolidWorks中的COSMOSMotion插件对大导程滚珠丝杠副螺母进行磨削加工仿真动画。根据汉江机床厂昆山分厂的设备条件进行大导程滚珠螺母加工实验,并对加工好的大导程滚珠螺母进行运行调试检测。实验结果表明,本文提出的大导程滚珠丝杠副螺母成型磨削加工方法是可行的。
Ball screw mechanisms have been widely used in Machinery, Aviation, Aerospace, Nuclear industry and other fields, due to its performance such as its high efficiency, high precision , high rigidity, low-cost, etc. High-speed precision ball screws is key components of development of high-end CNC machine tools, the traditional structure of the ball screw can not meet the modern high-speed high-precision numerical control machine tool development needs. Therefore, it is of great economic significance and strategic significance to study the technology of increasing the driven-speed of the ball screw. Based on the requirements of the high-speed precision ball screw development, this thesis comes from the program: Modeling and Simulation of Large Pitch Ball Screw Nut Formation Grinding, which was sponsored by the city of Kunshan Technology KC0720. Around the settlement of the key technology of high speed of precision ball screw——the formation grinding of large pitch ball screw nut to discuss, the major researches: formation grinding theory of large pitch ball screw nut, calculation of wheel’s section and simulation design of grinding of large pitch ball screw nut formation grinding.
To increase of feed speed of ball screw mechanism there are two ways: one is to increase the speed of the screw N, the other is to enlarge the lead Ph of the screw. The way of increasing of screw speed is undesirable. As a result, ball screws are developed in the high-speed feed drive. But the large pitch makes the manufacturing process more difficult. This thesis describes the large pitch ball screw nut grinding method, analyzes the advantages and disadvantages of a variety of large pitch ball screw nut processing method, and describes the research and theoretical analysis of the big pitch ball screw nut grinding.
A new processing method is proposed in this thesis. In the method, we change the installation wheel angle, and also change the grinding wheel section, then grinding the nut.
According to the principles of manufacturing helicoids, tooth meshing and rotary wheel processing nut technology, a mathematics model is constructed to reflect the manufacture process of nut,and the formula of the grinding wheel section is developed. The thread normal section as the initial conditions, the contact line equation is derived, according to the same normal vector of the spiral rolling pavement surface and rotary wheel in the contact point, the mathematics relationship between the contact line and the wheel shaft-shaped section is obtained from the coordinate transformation. The contact points of the section are obtained through the use of numerical calculation and Matlab mathematical software. through examples,the section of wheel is solved and the section's errors are analyzed.
Use the COSMOSMotion of SolidWorks plug-in software to make grinding simulation animation of the big pitch ball screw nut. According to equipment conditions of the Hanjiang machine tool factory’s subsidiary factory in Kunshan, tests the large pitch ball nut processing, and then running the processed large lead ball nut for debugging testing. Test results show that the large pitch ball screw nut forming grinding method is feasible.
提高滚珠丝杠驱动速度的途径有两条:其一是提高丝杠的转速N,其二是增大丝杠导程Ph。因用提高转速办法来解决是不可取的。于是,大导程滚珠丝杠副在进给驱动的高速化中得到发展。但是大导程使加工制造的难度增大。本文介绍了大导程滚珠丝杠副螺母磨削加工方法,分析了各种加工大导程滚珠丝杠副螺母方法的优缺点,阐述了大导程滚珠丝杠副螺母磨削加工的研究现状和理论分析。
本文提出一种新的加工方法,该方法在改变砂轮安装角的同时,也改变磨削砂轮的截形,对螺母进行磨削加工。
根据螺旋面滚道曲面加工原理、齿轮啮合原理以及回转面砂轮加工螺母工艺建立了相应的数学模型,建立螺旋曲面的数学模型和砂轮磨削加工螺母螺旋滚道面的数学模型。以螺旋滚道的法向截形为初始已知条件,根据螺旋滚道面与砂轮回转面在接触点处法向矢量相同的原理,推导出接触线方程,由坐标转换得出接触线与砂轮轴截形之间的数学关系。使用Matlab数学编程软件进行计算求解接触点。根据实例求解砂轮截形,并研究在不同条件下砂轮截形的求解及它们之间的比较,对求解结果进行分析误差。
使用SolidWorks中的COSMOSMotion插件对大导程滚珠丝杠副螺母进行磨削加工仿真动画。根据汉江机床厂昆山分厂的设备条件进行大导程滚珠螺母加工实验,并对加工好的大导程滚珠螺母进行运行调试检测。实验结果表明,本文提出的大导程滚珠丝杠副螺母成型磨削加工方法是可行的。
Ball screw mechanisms have been widely used in Machinery, Aviation, Aerospace, Nuclear industry and other fields, due to its performance such as its high efficiency, high precision , high rigidity, low-cost, etc. High-speed precision ball screws is key components of development of high-end CNC machine tools, the traditional structure of the ball screw can not meet the modern high-speed high-precision numerical control machine tool development needs. Therefore, it is of great economic significance and strategic significance to study the technology of increasing the driven-speed of the ball screw. Based on the requirements of the high-speed precision ball screw development, this thesis comes from the program: Modeling and Simulation of Large Pitch Ball Screw Nut Formation Grinding, which was sponsored by the city of Kunshan Technology KC0720. Around the settlement of the key technology of high speed of precision ball screw——the formation grinding of large pitch ball screw nut to discuss, the major researches: formation grinding theory of large pitch ball screw nut, calculation of wheel’s section and simulation design of grinding of large pitch ball screw nut formation grinding.
To increase of feed speed of ball screw mechanism there are two ways: one is to increase the speed of the screw N, the other is to enlarge the lead Ph of the screw. The way of increasing of screw speed is undesirable. As a result, ball screws are developed in the high-speed feed drive. But the large pitch makes the manufacturing process more difficult. This thesis describes the large pitch ball screw nut grinding method, analyzes the advantages and disadvantages of a variety of large pitch ball screw nut processing method, and describes the research and theoretical analysis of the big pitch ball screw nut grinding.
A new processing method is proposed in this thesis. In the method, we change the installation wheel angle, and also change the grinding wheel section, then grinding the nut.
According to the principles of manufacturing helicoids, tooth meshing and rotary wheel processing nut technology, a mathematics model is constructed to reflect the manufacture process of nut,and the formula of the grinding wheel section is developed. The thread normal section as the initial conditions, the contact line equation is derived, according to the same normal vector of the spiral rolling pavement surface and rotary wheel in the contact point, the mathematics relationship between the contact line and the wheel shaft-shaped section is obtained from the coordinate transformation. The contact points of the section are obtained through the use of numerical calculation and Matlab mathematical software. through examples,the section of wheel is solved and the section's errors are analyzed.
Use the COSMOSMotion of SolidWorks plug-in software to make grinding simulation animation of the big pitch ball screw nut. According to equipment conditions of the Hanjiang machine tool factory’s subsidiary factory in Kunshan, tests the large pitch ball nut processing, and then running the processed large lead ball nut for debugging testing. Test results show that the large pitch ball screw nut forming grinding method is feasible.
引文
[1]黄祖尧.精密高速滚珠丝杠副的最新发展及其应用.航空制造技术.2003(4):36-40.
[2]王恒敏.值得关注的“直线电动机驱动”技术. GM通用机械.2005.5:14-15
[3]肖正义.滚珠丝杠副的发展趋势.制造技术与机床.2000(4):11-13
[4]肖正义,焦洁.高速滚珠丝杠副的研发和测试技术.制造技术与机床.2004(4):95-98.
[5]曹建国,陈世平.实现滚珠丝杠螺母副高速化的技术措施.机床与液压.2005(5):54-55.
[6]赵仲琪.浅谈我国滚动功能部件的现状及发展对策.世界制造技术与装备市场.2006(4):75-77
[7]程光仁,施祖康,张起鹏.滚珠螺旋传动设计基础.北京:机械工业出版社. 1987.8:1-35
[8]黄祖尧.实现高速驱动的大导程滚珠丝杠副.机床. 1990.2: 21-22
[9]闫笃政,严虎勤.大导程滚珠丝杠副加工探讨.滚动功能部件科技论文集.2007.10:89-90
[10] T. Murakami, Developmental situations of recent direct acting rolling guides. High-precision, low-priced precision ball screw. Machine Design 44 15 (2000):45 - 45
[11] T. Nishimoto, Newest technologies of grinding and polishing. Grinder and polishing machine for high-level grinding. Internal grinder,“GI-20N”for grinding of high-lead female thread. Tool Eng. 42 5 ( 1998):27-32
[12] D.S. Guevarra, A. Kyusojin, H. Isobe and Y. Kaneko, Development of a new lapping method for high precision balls crew (1st report) feasibility study of a prototyped lapping tool for automatic lapping process. Prec. Eng. 25 1 (2001):63-69
[13] T. Kagiwada and H. Harada, Method for ball screw generation without form-dressing. Mechanical systems machine elements and manufacturing. JSME Int. J .Ser. C 39 4(1996):871-877
[14]孟德平.加工螺旋面用盘形刀具廓形的理论计算.石油机械, 1994,第9期,18-24
[15]饶振刚,王勇卫.滚珠丝杠副及自锁装置.国防工业出版社. 1990.2:1-87
[16]黄祖尧.从我国滚珠丝杠副标准的演变看其技术发展,制造技术与机床,1995, (09)
[17]周祖德.数字制造的现状与发展.中国机械工程, 2002, 13(6)
[18]黄祖尧.国外滚珠丝杠副技术发展动向.新技术新工艺. 1991.4:16-17
[19]黄育全,喻忠志.我国滚珠丝杠副发展历程及未来趋势.数控机床市场2008.1:59-61
[20]宋现春等.高速滚珠丝杠副综合性能试验台的研制开发.工具技术. 2005.3
[21]姜洪奎.大导程滚珠丝杠副动力学性能及加工方法研究[博士论文].山东:山东大学. 2007.04
[22] Tamaki,A.,Elements for ultra-high speed/low noise linear motion table, Mechanical Automation, Vol.25, No.3(1993),43.[in Japanese]
[23] Kajita, T., Ishikawa, A., Noise level of precision ball screw, Motion & Control, NSK Ltd., No.1, (1996),37
[24] Ninomiya, M., Temperature rise and its countermeasures of ball screw, Machine Tool & Machine Technology, Vo1.28, No.4(1987),98.[in Japanese]
[25] Jan Braasch, Dr. Ing.海德汉进给传动精度系列讲座第1讲进给传动系统的结构.机械工人(冷加工),2004,(01)
[26] Jan Braasch, Dr. Ing.海德汉进给传动精度系列讲座第2讲进给系统的受力变形.机械工人(冷加工),2004,(02)
[27] Jan Braasch, Dr. Ing.海德汉进给传动精度系列讲座第3讲滚珠丝杠轴承对定位精度的影响.机械工人(冷加工),2004,(03)
[28] Jan Braasch, Dr. Ing.海德汉进给传动精度系列讲座第4讲滚珠丝杠长度方向温度分布的影响.机械工人.冷加工,2004,(04)
[29] Won Soo Yun, Soo Kwang Kim, Dong Woo Cho. Thermal error analysis for a CNC lathe feed drive system. International Journal of Machine Tools and Manufacture, Vol.39, Issue7, July 1999:1087-1101
[30] J-Y Ahn and S-C Chung. Real-time estimation of the temperature distribution and expansion of a ball screw system using an observer. Proc. Instn Mech. EngrsVo1.219 Part B:J. Engineering Manufacture,2004
[31] Dominic S. Guevarra. Development of a new lapping method for high precision ball screw. Journal of the International Societies for Precision Engineering and Nanotechnology. 26(2002):389-395
[32] Xuesong Mei. Study on the load distribution of ball screw with errors. Mechanism and Machine Theory 38(2003:1257-1269
[33] M.C. Lin, B. Ravani and S.A. Velinsky, Kinematics of the ball screw mechanism. Journal of Mechanical Design, Transactions of the ASME116 3(1994):849-855
[34] 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 vol.119(1997):8-14
[35]孙健利.关于滚动直线导轨摩擦力与预紧力关系的研究.华中理工大学学报,1997.3
[36]黄祖尧.从CCMT2004看滚动功能部件产品的发展.制造技术与机床, 2004,7
[37]赵训贵,平舜娣.滚珠丝杠副产生弹性接触变形时实际接触角的计算[J].制造技术与机床,1989, (10)
[38]袭著燕,路长厚,郭涛,张建川.滚珠丝杠螺距误差前馈补偿法提高X-Y工作台定位精度的研究.机械科学与技术,2004,(07)
[39]柔顺性课题组.初论滚珠丝杠副的柔顺性(上).机械工人.冷加工. 2006,(01)
[40]深圳市威远精密技术有限公司柔顺性课题组.初论滚珠丝杠副的柔顺性(下).机械工人冷加工,2006, (02)
[41]宋现春等.高速滚珠丝杠副综合性能试验台的研制开发,工具技术,2005, 3
[42]刘晓初,黄运尧.滚动轴承新的额定静载荷的研究.中国机械工程,2001, (09)
[43]焦洁,梅景登,刘若华,勾清泉.滚珠丝杠副动态预紧转矩的测量技术,制造技术与机床,1998,(11)
[44]曹建国,陈世平.实现滚珠丝杠螺母副高速化的技术措施.机床与液压. 2005. No.5: 54-55
[45]黄租尧.精密滚珠丝杠副实现高速化的前景.制造技术与机床. 2001(3):5-7
[46]杨晓峰.大导程圆弧滚道的拉削加工.工具技术. 1996年第30卷,No5:6-9
[47]许舜,吴元徽.高速硬体旋风铣削在滚珠螺母滚道加工中的应用.新技术新工艺. 2005.11:59-60
[48]黄祖尧. CNC螺纹旋风硬铣削——高效绿色制造技术.机械工人(冷加工). 2004.9:26-28
[49] T. Nishimoto.Newest technologies of grinding and polishing. Grinder and polishing machine for high-level grinding. Internal grinder,“GI-20N”for grinding of high-lead female thread. Tool Eng.42 5 (1998):27-32.
[50] H. Harada, T. Kagiwada and T. Uraike, Method for ball-nut generation without form dressing. Trans. JSME Ser. C 65 639 (1999):4521-4526.
[51] T. Kagiwada and H. Harada. Method for ball screw generation without form-dressing. Mechanical systems machine elements and manufacturing. JSME Int. J. Ser. C 39 4(1996):871-877.
[52]孟德平.加工螺旋面用盘形刀具廓形的理论计算[J].石油机械,1994.9:18-24.
[53]姜洪奎,宋现春.大导程滚珠丝杠副螺母的截形计算与加工仿真[J].工具技术,2006.40(4):47-50.
[54]吴序堂.齿轮啮合原理[M].机械工业出版社,1985:114-123.
[55]王沫然编著.Matlab与科学计算[M].电子工业出版社,2003.9:257-265.
[56]江洪,陆利锋,魏峥等编著. SolidWorks动画演示与运动分析实例解析[M].北京:机械工业出版社. 2006.5:144-193
[57]曾翠华,廖海平.转向螺母的精确三维造型设计.计算机应用汽车科技2007.1: 38-40
[58]范铭,傅嘉乐.外循环滚珠螺母的加工工艺.机械制造. 1990.9:17-18
[2]王恒敏.值得关注的“直线电动机驱动”技术. GM通用机械.2005.5:14-15
[3]肖正义.滚珠丝杠副的发展趋势.制造技术与机床.2000(4):11-13
[4]肖正义,焦洁.高速滚珠丝杠副的研发和测试技术.制造技术与机床.2004(4):95-98.
[5]曹建国,陈世平.实现滚珠丝杠螺母副高速化的技术措施.机床与液压.2005(5):54-55.
[6]赵仲琪.浅谈我国滚动功能部件的现状及发展对策.世界制造技术与装备市场.2006(4):75-77
[7]程光仁,施祖康,张起鹏.滚珠螺旋传动设计基础.北京:机械工业出版社. 1987.8:1-35
[8]黄祖尧.实现高速驱动的大导程滚珠丝杠副.机床. 1990.2: 21-22
[9]闫笃政,严虎勤.大导程滚珠丝杠副加工探讨.滚动功能部件科技论文集.2007.10:89-90
[10] T. Murakami, Developmental situations of recent direct acting rolling guides. High-precision, low-priced precision ball screw. Machine Design 44 15 (2000):45 - 45
[11] T. Nishimoto, Newest technologies of grinding and polishing. Grinder and polishing machine for high-level grinding. Internal grinder,“GI-20N”for grinding of high-lead female thread. Tool Eng. 42 5 ( 1998):27-32
[12] D.S. Guevarra, A. Kyusojin, H. Isobe and Y. Kaneko, Development of a new lapping method for high precision balls crew (1st report) feasibility study of a prototyped lapping tool for automatic lapping process. Prec. Eng. 25 1 (2001):63-69
[13] T. Kagiwada and H. Harada, Method for ball screw generation without form-dressing. Mechanical systems machine elements and manufacturing. JSME Int. J .Ser. C 39 4(1996):871-877
[14]孟德平.加工螺旋面用盘形刀具廓形的理论计算.石油机械, 1994,第9期,18-24
[15]饶振刚,王勇卫.滚珠丝杠副及自锁装置.国防工业出版社. 1990.2:1-87
[16]黄祖尧.从我国滚珠丝杠副标准的演变看其技术发展,制造技术与机床,1995, (09)
[17]周祖德.数字制造的现状与发展.中国机械工程, 2002, 13(6)
[18]黄祖尧.国外滚珠丝杠副技术发展动向.新技术新工艺. 1991.4:16-17
[19]黄育全,喻忠志.我国滚珠丝杠副发展历程及未来趋势.数控机床市场2008.1:59-61
[20]宋现春等.高速滚珠丝杠副综合性能试验台的研制开发.工具技术. 2005.3
[21]姜洪奎.大导程滚珠丝杠副动力学性能及加工方法研究[博士论文].山东:山东大学. 2007.04
[22] Tamaki,A.,Elements for ultra-high speed/low noise linear motion table, Mechanical Automation, Vol.25, No.3(1993),43.[in Japanese]
[23] Kajita, T., Ishikawa, A., Noise level of precision ball screw, Motion & Control, NSK Ltd., No.1, (1996),37
[24] Ninomiya, M., Temperature rise and its countermeasures of ball screw, Machine Tool & Machine Technology, Vo1.28, No.4(1987),98.[in Japanese]
[25] Jan Braasch, Dr. Ing.海德汉进给传动精度系列讲座第1讲进给传动系统的结构.机械工人(冷加工),2004,(01)
[26] Jan Braasch, Dr. Ing.海德汉进给传动精度系列讲座第2讲进给系统的受力变形.机械工人(冷加工),2004,(02)
[27] Jan Braasch, Dr. Ing.海德汉进给传动精度系列讲座第3讲滚珠丝杠轴承对定位精度的影响.机械工人(冷加工),2004,(03)
[28] Jan Braasch, Dr. Ing.海德汉进给传动精度系列讲座第4讲滚珠丝杠长度方向温度分布的影响.机械工人.冷加工,2004,(04)
[29] Won Soo Yun, Soo Kwang Kim, Dong Woo Cho. Thermal error analysis for a CNC lathe feed drive system. International Journal of Machine Tools and Manufacture, Vol.39, Issue7, July 1999:1087-1101
[30] J-Y Ahn and S-C Chung. Real-time estimation of the temperature distribution and expansion of a ball screw system using an observer. Proc. Instn Mech. EngrsVo1.219 Part B:J. Engineering Manufacture,2004
[31] Dominic S. Guevarra. Development of a new lapping method for high precision ball screw. Journal of the International Societies for Precision Engineering and Nanotechnology. 26(2002):389-395
[32] Xuesong Mei. Study on the load distribution of ball screw with errors. Mechanism and Machine Theory 38(2003:1257-1269
[33] M.C. Lin, B. Ravani and S.A. Velinsky, Kinematics of the ball screw mechanism. Journal of Mechanical Design, Transactions of the ASME116 3(1994):849-855
[34] 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 vol.119(1997):8-14
[35]孙健利.关于滚动直线导轨摩擦力与预紧力关系的研究.华中理工大学学报,1997.3
[36]黄祖尧.从CCMT2004看滚动功能部件产品的发展.制造技术与机床, 2004,7
[37]赵训贵,平舜娣.滚珠丝杠副产生弹性接触变形时实际接触角的计算[J].制造技术与机床,1989, (10)
[38]袭著燕,路长厚,郭涛,张建川.滚珠丝杠螺距误差前馈补偿法提高X-Y工作台定位精度的研究.机械科学与技术,2004,(07)
[39]柔顺性课题组.初论滚珠丝杠副的柔顺性(上).机械工人.冷加工. 2006,(01)
[40]深圳市威远精密技术有限公司柔顺性课题组.初论滚珠丝杠副的柔顺性(下).机械工人冷加工,2006, (02)
[41]宋现春等.高速滚珠丝杠副综合性能试验台的研制开发,工具技术,2005, 3
[42]刘晓初,黄运尧.滚动轴承新的额定静载荷的研究.中国机械工程,2001, (09)
[43]焦洁,梅景登,刘若华,勾清泉.滚珠丝杠副动态预紧转矩的测量技术,制造技术与机床,1998,(11)
[44]曹建国,陈世平.实现滚珠丝杠螺母副高速化的技术措施.机床与液压. 2005. No.5: 54-55
[45]黄租尧.精密滚珠丝杠副实现高速化的前景.制造技术与机床. 2001(3):5-7
[46]杨晓峰.大导程圆弧滚道的拉削加工.工具技术. 1996年第30卷,No5:6-9
[47]许舜,吴元徽.高速硬体旋风铣削在滚珠螺母滚道加工中的应用.新技术新工艺. 2005.11:59-60
[48]黄祖尧. CNC螺纹旋风硬铣削——高效绿色制造技术.机械工人(冷加工). 2004.9:26-28
[49] T. Nishimoto.Newest technologies of grinding and polishing. Grinder and polishing machine for high-level grinding. Internal grinder,“GI-20N”for grinding of high-lead female thread. Tool Eng.42 5 (1998):27-32.
[50] H. Harada, T. Kagiwada and T. Uraike, Method for ball-nut generation without form dressing. Trans. JSME Ser. C 65 639 (1999):4521-4526.
[51] T. Kagiwada and H. Harada. Method for ball screw generation without form-dressing. Mechanical systems machine elements and manufacturing. JSME Int. J. Ser. C 39 4(1996):871-877.
[52]孟德平.加工螺旋面用盘形刀具廓形的理论计算[J].石油机械,1994.9:18-24.
[53]姜洪奎,宋现春.大导程滚珠丝杠副螺母的截形计算与加工仿真[J].工具技术,2006.40(4):47-50.
[54]吴序堂.齿轮啮合原理[M].机械工业出版社,1985:114-123.
[55]王沫然编著.Matlab与科学计算[M].电子工业出版社,2003.9:257-265.
[56]江洪,陆利锋,魏峥等编著. SolidWorks动画演示与运动分析实例解析[M].北京:机械工业出版社. 2006.5:144-193
[57]曾翠华,廖海平.转向螺母的精确三维造型设计.计算机应用汽车科技2007.1: 38-40
[58]范铭,傅嘉乐.外循环滚珠螺母的加工工艺.机械制造. 1990.9:17-18