圆柱蜗杆测量及误差评定技术研究
摘要
蜗杆传动装置在工业自动化发展中具有重要的地位,广泛应用在机床、汽车、仪器、冶金机械等仪器设备中,为了确保在使用中的安全性、稳定性和可靠性,必须要求蜗杆传动正确,所以对蜗杆精度进行检测和分析是非常必要的。本文首先建立了蜗杆的理论模型,然后根据国标对各项误差定义推导出相应误差计算的函数表达式并设计出误差测量运动轨迹,使用VS.NET编程软件开发系统软件在CNC齿轮测量中心上实现蜗杆误差自动检测功能,最后对精度已知蜗杆进行了测量和误差评定实验,对系统的正确性进行验证。下面是本文完成的主要工作内容。
圆柱蜗杆造型包括ZA、ZI、ZN、ZK等多种。本文在查阅大量与蜗杆和CNC齿轮测量中心有关的国内外科技文献的基础上,利用微分几何和空间立体几何的相关知识建立了多种常用圆柱蜗杆的理论模型。根据圆柱蜗杆各项误差项的定义,结合蜗杆的理论模型,推导出蜗杆各项误差计算的方程,由此设计了相应的误差测量运动轨迹。采用测球半径的补偿方法对采集数据进行补偿处理,以保证误差计算前数据的准确性。
基于VS.NET开发系统测量软件和误差评定软件,能够实现在对蜗杆各项误差的自动测量和误差计算、评定、曲线显示、打印报表。把开发的系统软件在CNC齿轮测量中心进行系统联调实验,对已知精度等级的蜗杆进行测量来评价系统的性能,测量误差项包括:螺旋线误差、齿形误差、齿距误差、齿厚误差和啮合误差,并对测得结果进行了分析。
Worm-gearing device have an important position in the development of industrial automation, widely used in machine tools, automobiles, equipment, metallurgical machinery and other equipment. In order to ensure the safety, stability and reliability of use, the worm-gearing must carry out precisely, so to test and analyze the precision of the worm is very necessary . In this paper, firstly establish a theoretical model of the worm; and then according to the national standard of worm error definition, derive the formula for calculating the worm error and design the measuring trajectory, develop the system software based on the VS.NET programming software, which is used in CNC Gear Measurement Center to achieve automatic detection of worm; finally, measure each error of the worm that the precision rank is known to verify the system correctness.
The type of cylindrical worm includes ZA, ZI, ZN and ZK and so on. In this paper, referring to great lot of scientific and technical literatures about worm and CNC, establish mathematical model of cylindrical worm on the basis of the differential geometry and three-dimensional geometry of space-related knowledge. Derive the formula of worm error items from the standard for worm error, and also design measuring trajectory based on the geometry model of worm. To ensuring data accuracy, use the compensation for the radius of probe to process the data from probe before being used to calculate the deviation.
Develop the measurement and error assessment software based on VS.NET, which used in CNC Gear Measurement Center for worm, can achieve the automatic measurement of the error, error calculation, assessment, curve display band, print statements. On the CNC Gear Measurement Center, the measure system is evaluated by measuring the helix, profile, pitch, mesh error of the worm that the precision rank is known, and Analyze of measured results.
圆柱蜗杆造型包括ZA、ZI、ZN、ZK等多种。本文在查阅大量与蜗杆和CNC齿轮测量中心有关的国内外科技文献的基础上,利用微分几何和空间立体几何的相关知识建立了多种常用圆柱蜗杆的理论模型。根据圆柱蜗杆各项误差项的定义,结合蜗杆的理论模型,推导出蜗杆各项误差计算的方程,由此设计了相应的误差测量运动轨迹。采用测球半径的补偿方法对采集数据进行补偿处理,以保证误差计算前数据的准确性。
基于VS.NET开发系统测量软件和误差评定软件,能够实现在对蜗杆各项误差的自动测量和误差计算、评定、曲线显示、打印报表。把开发的系统软件在CNC齿轮测量中心进行系统联调实验,对已知精度等级的蜗杆进行测量来评价系统的性能,测量误差项包括:螺旋线误差、齿形误差、齿距误差、齿厚误差和啮合误差,并对测得结果进行了分析。
Worm-gearing device have an important position in the development of industrial automation, widely used in machine tools, automobiles, equipment, metallurgical machinery and other equipment. In order to ensure the safety, stability and reliability of use, the worm-gearing must carry out precisely, so to test and analyze the precision of the worm is very necessary . In this paper, firstly establish a theoretical model of the worm; and then according to the national standard of worm error definition, derive the formula for calculating the worm error and design the measuring trajectory, develop the system software based on the VS.NET programming software, which is used in CNC Gear Measurement Center to achieve automatic detection of worm; finally, measure each error of the worm that the precision rank is known to verify the system correctness.
The type of cylindrical worm includes ZA, ZI, ZN and ZK and so on. In this paper, referring to great lot of scientific and technical literatures about worm and CNC, establish mathematical model of cylindrical worm on the basis of the differential geometry and three-dimensional geometry of space-related knowledge. Derive the formula of worm error items from the standard for worm error, and also design measuring trajectory based on the geometry model of worm. To ensuring data accuracy, use the compensation for the radius of probe to process the data from probe before being used to calculate the deviation.
Develop the measurement and error assessment software based on VS.NET, which used in CNC Gear Measurement Center for worm, can achieve the automatic measurement of the error, error calculation, assessment, curve display band, print statements. On the CNC Gear Measurement Center, the measure system is evaluated by measuring the helix, profile, pitch, mesh error of the worm that the precision rank is known, and Analyze of measured results.
引文
1傅则绍,赵松年,杨春兰等.新型蜗杆传动.陕西科学技术出版社. 1990
2谢华锟.齿轮测量仪的近况与和展望.工具技术. 1996, 30(6): 39~41
3石照耀,费业泰,谢华锟.齿轮测量技术100年——回顾与展望.中国工程科学. 2003,5(9):13~17
4吴玉梅.基于电子展成与坐标结合原理自动测量圆柱齿轮的研究.宇航计测技术. 2002, (8): 17~ 21
5 E. Joseph Shigley, R. Charles Mischke, H. Thomas Brown, Jr. Standard Handbook of Machine Design. New York:McGraw-Hill,2004:11~12
6国家公差与配合标委会秘书处.坐标测量机在国内外标准化及生产技术概况:1997:37~38
7赵丹阳,宋满仓.三坐标测量机技术改造关键技术.计量技术.2004.No 3:49~52
8谢华锟.近年来齿轮测量技术与仪器的发展.工具技术. 2004, 38(9):27~33
9 G. Mikoleizig. CNC Gear Inspection Technology and New Software Solutions Adapted To Individual Industry Needs. Laser Metrology and Machine Performance IV,WIT Press, 1999: 237~251
10 JA. Bosch. Coordinate Measuring Machines and Systems. Marcel Decker. Inc, 1995:367~374
11 D. C. Thompson. The Design of an Ultra-Precision CNC Measuring Machine. Annals of the CIRP. 1989, 38(1)501~504
12 J. Ni. CNC Machine Accuracy Enhancement through Real-time Error Compensation , ASME Journal of Manufacturing Science an Engineering, 1997,119:717~725
13 J. Mou, C .R. Liu. An Innovative Approach to Increase the Accuracy of Multi-Axis Machines for Process-Intermittent Inspection , ASME Journal of Manufacturing Science and Engineering, 1996,118:585~594
14 Yi Hu; Dong Yu, Shaohua Du, Xiaohui Zhang, Yaodong Tao, Zhicheng Wang .Design and Implementation of Reconfigurable CNC System Based on Fieldbus. Information and Automation. 2008: 794-799
15 C. K. Chen , S. W. Lin. The Study of a Ball Plate to Calibrate a CNC Tool and aCoordinate Measuring Machine,Proceedings of APSI’97. 1997:206~216
16魏华亮.我国CNC齿轮测量中心的发展现状.计量技术. 2004, 10:33~34
17王建华,刘波,劳奇成. CNC齿轮测量中心的需求与发展.工具技术. 1996, 30(4):42~43
18 Ya-Bo Luo, He Ling, Han Yuan. The Automatic Scheduling Algorithm Based on the Correlated Analysis for Share-Oriented CNC Tasks. Digital Object Identifier
10.1109/ICMLC.2007.4370689
19 Moosavian, S.MohammadiAsl, E. Robotics,Backlash. Detection in CNC Machines Based on Experimental Vibration Analysis. Automation and Mechatronics, Sept. 2008, 21-24 : 393-398
20张国雄.三坐标测量机的发展趋势.中国机械工程. 2000, (11): 222~226
21谢华锟.现代精密量仪现状和发展趋势.成都工具研究所.2005
22 F. Calabrese, G. Celentano. Design and realization of a STEP-NC compliant CNC embedded controller.Emerging Technologies and Factory Automation, 2007, 25-28: 1010-1017
23 Dong Yu,Yi Hu,Xu, X.W,Yan Huang, Shaohua Du .An Open CNC System Based on Component Technology. Automation Science and Engineering. IEEE Transactions on.April 2009 : 302-310
24杨春兰.齿轮工程词典.机械工业出版社. 1994
25 Rida, T. Farouki, Sagar Shah. Real time CNC interpolators for Pythagorean- hodograph curves. Computer Aided Geometer Design. 1996, 13:583~600
26 M. Anjanappa, D K. Anand, J A. Kirk. Error Correction Methodologies and Control Strategiesfor Numerical Control Machines. Control Methods for Manufacturing Process.1988,7:41~49
27石照耀.复杂螺旋曲面特征线测量的理论与技术研究.博士生毕业论文.2000.11
28费业泰等.复杂曲面测量模式与关键技术.工具技术. 2000, 34(11):31~34
29石照耀.论齿轮滚刀的啮合误差测量.机械. 1999,26(1):45~47
30王建华,劳其成,刘波等.CNC齿轮测量中心的原理、特点及关键技术[J] .工具技术,1996(3):41
31林慎旺三坐标测量机精度检测评定及虚拟坐标系统研究.合肥工业大学博士学位论文. 2004:44~45
32宋艳霞,陆伯印.三坐标测量机误差补偿方法的研究.计量技术.1997No.12:9~11
33卢红.测头半径补偿的方法,组合机床与自动化加工技术. 2001, (9):39~41
34王红敏,石沛林.三坐标测量机测头的测球半径补偿误差的计算.工具技术.2003,7:63~65
35 M. C. Malburg, D. G. Chetwynd, etal. The Robust Detection and Removal of Unwanted Asperities in Applied Surface Metrology. Int. J. Mach. Tools Manufact, 1998, 38(3):134~153
36国家机械工业委员会质量安全监督司.齿轮和蜗轮蜗杆的检查与测量.机械工业出版社. 1991
37王伯平,曾建潮.一种自调整的空间面轮廓度误差的评定方法.计量学报. 2002, 23(2):106~108
38陈海燕.三维坐标中测量曲面的定位.光学仪器. 2000, 22(6):1~7
39徐惊雷.径向运动方程在绝对相对坐标系下的相互转换.力学与实践. 2007,29(6):67~69
40谢竹铭.齿轮检测.中国计量出版社. 1991
41 Wang Jun, Wang Xiao-chun, Jiang Hong,Feng Wen-jun. Measurement and Compensationof Deviations of Real Tooth Surface of Spiral Bevel Gear. Chinese Journal of Aeronautics,Aug 2003:89~101
42李蔚,劳奇成等.在CNC上实现蜗轮齿形误差自动检测.西安工业学院学报,2002.12.22(4)
43 Marria Pia Sammartini. Development and Validation of A New Reference Cylindrical Gear for Pitch Measurement. Precision Engineering. 2000, (1):28~34
44王安. CNC齿轮测量中心总体设计和软件设计.计量技术. 2004, (5):36~38
45 Hua Qiu, etal. A Practical Evaluation Approach Towards form Deviation for Two dimensional Contours Based on Coordinate Measurement Data. International Journal of Machine Tools & Manufacture. 2000,40(1):259~275
46候宇,张竞,崔晨阳.复杂线轮廓度误差坐标测量的数据处理方法.计量学报, 2002, 23(1):13~20
47何菊明,王芙.实验数据的线性拟合及计算机处理.武汉工程大学学报. 2008,30(1):117~124
48 M. Moreau. A CNC model well-suited for the requirements of CNC software construction environment .Computers in Design, Manufacturing and Production.1993, 24-27: 176-181
49 Y. Cao, Z. Shao, M. Wang, C.J. Xue, Y. Chen, H. Wei, T.A. Wang. Formal Specification and Verification Framework for Designing and Verifying Reliable and Dependable Software for Computerized Numerical Control (CNC) Systems. Machine Tools & Manufacture. 2008.7 :269– 276
2谢华锟.齿轮测量仪的近况与和展望.工具技术. 1996, 30(6): 39~41
3石照耀,费业泰,谢华锟.齿轮测量技术100年——回顾与展望.中国工程科学. 2003,5(9):13~17
4吴玉梅.基于电子展成与坐标结合原理自动测量圆柱齿轮的研究.宇航计测技术. 2002, (8): 17~ 21
5 E. Joseph Shigley, R. Charles Mischke, H. Thomas Brown, Jr. Standard Handbook of Machine Design. New York:McGraw-Hill,2004:11~12
6国家公差与配合标委会秘书处.坐标测量机在国内外标准化及生产技术概况:1997:37~38
7赵丹阳,宋满仓.三坐标测量机技术改造关键技术.计量技术.2004.No 3:49~52
8谢华锟.近年来齿轮测量技术与仪器的发展.工具技术. 2004, 38(9):27~33
9 G. Mikoleizig. CNC Gear Inspection Technology and New Software Solutions Adapted To Individual Industry Needs. Laser Metrology and Machine Performance IV,WIT Press, 1999: 237~251
10 JA. Bosch. Coordinate Measuring Machines and Systems. Marcel Decker. Inc, 1995:367~374
11 D. C. Thompson. The Design of an Ultra-Precision CNC Measuring Machine. Annals of the CIRP. 1989, 38(1)501~504
12 J. Ni. CNC Machine Accuracy Enhancement through Real-time Error Compensation , ASME Journal of Manufacturing Science an Engineering, 1997,119:717~725
13 J. Mou, C .R. Liu. An Innovative Approach to Increase the Accuracy of Multi-Axis Machines for Process-Intermittent Inspection , ASME Journal of Manufacturing Science and Engineering, 1996,118:585~594
14 Yi Hu; Dong Yu, Shaohua Du, Xiaohui Zhang, Yaodong Tao, Zhicheng Wang .Design and Implementation of Reconfigurable CNC System Based on Fieldbus. Information and Automation. 2008: 794-799
15 C. K. Chen , S. W. Lin. The Study of a Ball Plate to Calibrate a CNC Tool and aCoordinate Measuring Machine,Proceedings of APSI’97. 1997:206~216
16魏华亮.我国CNC齿轮测量中心的发展现状.计量技术. 2004, 10:33~34
17王建华,刘波,劳奇成. CNC齿轮测量中心的需求与发展.工具技术. 1996, 30(4):42~43
18 Ya-Bo Luo, He Ling, Han Yuan. The Automatic Scheduling Algorithm Based on the Correlated Analysis for Share-Oriented CNC Tasks. Digital Object Identifier
10.1109/ICMLC.2007.4370689
19 Moosavian, S.MohammadiAsl, E. Robotics,Backlash. Detection in CNC Machines Based on Experimental Vibration Analysis. Automation and Mechatronics, Sept. 2008, 21-24 : 393-398
20张国雄.三坐标测量机的发展趋势.中国机械工程. 2000, (11): 222~226
21谢华锟.现代精密量仪现状和发展趋势.成都工具研究所.2005
22 F. Calabrese, G. Celentano. Design and realization of a STEP-NC compliant CNC embedded controller.Emerging Technologies and Factory Automation, 2007, 25-28: 1010-1017
23 Dong Yu,Yi Hu,Xu, X.W,Yan Huang, Shaohua Du .An Open CNC System Based on Component Technology. Automation Science and Engineering. IEEE Transactions on.April 2009 : 302-310
24杨春兰.齿轮工程词典.机械工业出版社. 1994
25 Rida, T. Farouki, Sagar Shah. Real time CNC interpolators for Pythagorean- hodograph curves. Computer Aided Geometer Design. 1996, 13:583~600
26 M. Anjanappa, D K. Anand, J A. Kirk. Error Correction Methodologies and Control Strategiesfor Numerical Control Machines. Control Methods for Manufacturing Process.1988,7:41~49
27石照耀.复杂螺旋曲面特征线测量的理论与技术研究.博士生毕业论文.2000.11
28费业泰等.复杂曲面测量模式与关键技术.工具技术. 2000, 34(11):31~34
29石照耀.论齿轮滚刀的啮合误差测量.机械. 1999,26(1):45~47
30王建华,劳其成,刘波等.CNC齿轮测量中心的原理、特点及关键技术[J] .工具技术,1996(3):41
31林慎旺三坐标测量机精度检测评定及虚拟坐标系统研究.合肥工业大学博士学位论文. 2004:44~45
32宋艳霞,陆伯印.三坐标测量机误差补偿方法的研究.计量技术.1997No.12:9~11
33卢红.测头半径补偿的方法,组合机床与自动化加工技术. 2001, (9):39~41
34王红敏,石沛林.三坐标测量机测头的测球半径补偿误差的计算.工具技术.2003,7:63~65
35 M. C. Malburg, D. G. Chetwynd, etal. The Robust Detection and Removal of Unwanted Asperities in Applied Surface Metrology. Int. J. Mach. Tools Manufact, 1998, 38(3):134~153
36国家机械工业委员会质量安全监督司.齿轮和蜗轮蜗杆的检查与测量.机械工业出版社. 1991
37王伯平,曾建潮.一种自调整的空间面轮廓度误差的评定方法.计量学报. 2002, 23(2):106~108
38陈海燕.三维坐标中测量曲面的定位.光学仪器. 2000, 22(6):1~7
39徐惊雷.径向运动方程在绝对相对坐标系下的相互转换.力学与实践. 2007,29(6):67~69
40谢竹铭.齿轮检测.中国计量出版社. 1991
41 Wang Jun, Wang Xiao-chun, Jiang Hong,Feng Wen-jun. Measurement and Compensationof Deviations of Real Tooth Surface of Spiral Bevel Gear. Chinese Journal of Aeronautics,Aug 2003:89~101
42李蔚,劳奇成等.在CNC上实现蜗轮齿形误差自动检测.西安工业学院学报,2002.12.22(4)
43 Marria Pia Sammartini. Development and Validation of A New Reference Cylindrical Gear for Pitch Measurement. Precision Engineering. 2000, (1):28~34
44王安. CNC齿轮测量中心总体设计和软件设计.计量技术. 2004, (5):36~38
45 Hua Qiu, etal. A Practical Evaluation Approach Towards form Deviation for Two dimensional Contours Based on Coordinate Measurement Data. International Journal of Machine Tools & Manufacture. 2000,40(1):259~275
46候宇,张竞,崔晨阳.复杂线轮廓度误差坐标测量的数据处理方法.计量学报, 2002, 23(1):13~20
47何菊明,王芙.实验数据的线性拟合及计算机处理.武汉工程大学学报. 2008,30(1):117~124
48 M. Moreau. A CNC model well-suited for the requirements of CNC software construction environment .Computers in Design, Manufacturing and Production.1993, 24-27: 176-181
49 Y. Cao, Z. Shao, M. Wang, C.J. Xue, Y. Chen, H. Wei, T.A. Wang. Formal Specification and Verification Framework for Designing and Verifying Reliable and Dependable Software for Computerized Numerical Control (CNC) Systems. Machine Tools & Manufacture. 2008.7 :269– 276