一种回转基准径向误差分离方法研究
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摘要
纳米精度误差补偿技术是伴随纳米技术的发展而提出,并继承了传统误差补偿技术的合理成分而发展起来的一项技术。它可以用较小的代价达到许多“硬技术”难以达到的精度水平,因而具有重要的研究价值和巨大的应用潜力。误差分离技术是误差补偿技术的一个重要组成部分,在多次定位法误差分离技术中,由于谐波抑制的影响,致使其分离精度并不够高。
本文首先对现有的圆度误差分离方法进行了比较,具体分析了这些方法的原理误差,在总结了这些方法的优点和不足的基础上,通过仿真分析了“多重多步法”误差分离技术,该技术将不同转位的多步法混合,分别进行谐波分析,将产生谐波抑制的项剔除,最后进行谐波合成实现主轴系统回转误差的分离,“多重多步法”大大扩展了无谐波抑制范围。本文主要完成的工作如下:
1、分析了多步法误差分离方法的原理,指出了其中存在的谐波抑制问题,并以本文构造的误差函数为例,对10转位法进行了仿真分析,结果表明,分离精度并不高,在本次分离中,主轴系统回转误差和工件圆度误差的最大分离误差,在归一化之后(除以构造信号的振幅最大值)分别为0.305和0.346;
2、在多步法的基础上,分析了多重多步法原理及数据处理过程,并对以3、4、5步法为基础的多重多步法进行了仿真分析。仿真结果表明多重多步法能在需求范围内很好的解决谐波抑制问题,达到较高的分离精度,在采样点数为512时,对主轴系统回转误差和工件圆度误差的最大分离误差分别为0.041和0.046左右;
3、分析了采样点数对多重多步法分离精度的影响。当采样点数增加到1024时,主轴系统回转误差和工件圆度误差的最大分离误差分别为0.027和0.031左右,与采样点数为512时的分离误差相比,分别减小34.1%和32.6%;
4、分析了在不同滤波范围内多重多步法的分离精度,结果表明,随着滤波范围的扩大,基于3、4、5步法的多重多步法分离误差不断增大;
5、对多重多步法进行了实验验证,结果表明,本文介绍的三种不同转位的多重多步法有较高的分离精度,最高误差可达到4.2nm。
理论分析及仿真结果表明本文研究的多重多步法误差分离技术有良好的可操作性及较高的分离精度,适合所设计的误差分离系统。
Nanometric error compensation technique is proposed with the development of nanotechnogy, which inherits the advantages of the traditional error compensation technique. This technique has important values of research and application for higher accuracy measurement. Error separation technique is an essential part of error compensation technique, due to harmonic suppression, the separation precision is very limited.
In this paper, theoretical error analysis of several error separation methods is performed, based on the advantages and disadvantages of these methods, a multi-series multi-step method is proposed. This method synthesizes several multi-step methods, analyzes the corresponding harmonic one by one and eliminates the items that bring harmonic suppression. Multi-series multi-step method enlarges the range without harmonic suppression by synthesis of harmonic to separate the main shaft circumgyration error.
The following works was finished in this thesis:
1. Analyzes the principle of multi-step error separation technique and the harmonic suppression problem. The emulation result for 10 steps indexing method indicates that error of separation is 0.305 and 0.346;
2. Analyzes the principle of multi-series multi-step method. Make simulation of multi-series multi-step method based on 3, 4, 5 multi-step method, which indicates that multi-series multi-step method could resolve harmonic suppression problem in a certain range with a higher precision. When the sample number is 512, the error of separation is about 0.041 and 0.046;
3. Analyzes the effect of sample number to the precision of error separation. The precision can be improved by increasing the sample number. When the sample number is 1024, the error of separation is up to 0.027 and 0.031;
4. Analyzes the separation precision in different filtering range, which indicates that large filtering range results in low precision;
5. Experiment certification on multi-series multi-step error separation is performed. Experiment data indicates that this technique has very high separation precision. The separation precision is up to 4.2nm.
Both the theoretical analysis and the experiment strongly suggest that multi-series multi-step error separation technique has good maneuverability and high separation precision.
本文首先对现有的圆度误差分离方法进行了比较,具体分析了这些方法的原理误差,在总结了这些方法的优点和不足的基础上,通过仿真分析了“多重多步法”误差分离技术,该技术将不同转位的多步法混合,分别进行谐波分析,将产生谐波抑制的项剔除,最后进行谐波合成实现主轴系统回转误差的分离,“多重多步法”大大扩展了无谐波抑制范围。本文主要完成的工作如下:
1、分析了多步法误差分离方法的原理,指出了其中存在的谐波抑制问题,并以本文构造的误差函数为例,对10转位法进行了仿真分析,结果表明,分离精度并不高,在本次分离中,主轴系统回转误差和工件圆度误差的最大分离误差,在归一化之后(除以构造信号的振幅最大值)分别为0.305和0.346;
2、在多步法的基础上,分析了多重多步法原理及数据处理过程,并对以3、4、5步法为基础的多重多步法进行了仿真分析。仿真结果表明多重多步法能在需求范围内很好的解决谐波抑制问题,达到较高的分离精度,在采样点数为512时,对主轴系统回转误差和工件圆度误差的最大分离误差分别为0.041和0.046左右;
3、分析了采样点数对多重多步法分离精度的影响。当采样点数增加到1024时,主轴系统回转误差和工件圆度误差的最大分离误差分别为0.027和0.031左右,与采样点数为512时的分离误差相比,分别减小34.1%和32.6%;
4、分析了在不同滤波范围内多重多步法的分离精度,结果表明,随着滤波范围的扩大,基于3、4、5步法的多重多步法分离误差不断增大;
5、对多重多步法进行了实验验证,结果表明,本文介绍的三种不同转位的多重多步法有较高的分离精度,最高误差可达到4.2nm。
理论分析及仿真结果表明本文研究的多重多步法误差分离技术有良好的可操作性及较高的分离精度,适合所设计的误差分离系统。
Nanometric error compensation technique is proposed with the development of nanotechnogy, which inherits the advantages of the traditional error compensation technique. This technique has important values of research and application for higher accuracy measurement. Error separation technique is an essential part of error compensation technique, due to harmonic suppression, the separation precision is very limited.
In this paper, theoretical error analysis of several error separation methods is performed, based on the advantages and disadvantages of these methods, a multi-series multi-step method is proposed. This method synthesizes several multi-step methods, analyzes the corresponding harmonic one by one and eliminates the items that bring harmonic suppression. Multi-series multi-step method enlarges the range without harmonic suppression by synthesis of harmonic to separate the main shaft circumgyration error.
The following works was finished in this thesis:
1. Analyzes the principle of multi-step error separation technique and the harmonic suppression problem. The emulation result for 10 steps indexing method indicates that error of separation is 0.305 and 0.346;
2. Analyzes the principle of multi-series multi-step method. Make simulation of multi-series multi-step method based on 3, 4, 5 multi-step method, which indicates that multi-series multi-step method could resolve harmonic suppression problem in a certain range with a higher precision. When the sample number is 512, the error of separation is about 0.041 and 0.046;
3. Analyzes the effect of sample number to the precision of error separation. The precision can be improved by increasing the sample number. When the sample number is 1024, the error of separation is up to 0.027 and 0.031;
4. Analyzes the separation precision in different filtering range, which indicates that large filtering range results in low precision;
5. Experiment certification on multi-series multi-step error separation is performed. Experiment data indicates that this technique has very high separation precision. The separation precision is up to 4.2nm.
Both the theoretical analysis and the experiment strongly suggest that multi-series multi-step error separation technique has good maneuverability and high separation precision.
引文
1 Donaldson, R. A simple Method for Separating Spindle Error from Test Ball Roundness Error. Annals of the CIRP .1972 , 21(1): 125~126
2梁建成.误差补偿-提高机械加工精度的重要途径.机械工程. 1987,3:46~48
3谭久彬.精密测量中的误差补偿技术:哈尔滨工业大学出版社,1995,52~108
4 Whitehouse.D.J. Some Theoretical Aspects of Error Separation Techniques in Surface Metrology. J.phys.E:Sci.Instru 1976,(9):531~536
5谭久彬.圆和圆柱轮廓的超精密测量技术与特征分析理论的研究.哈尔滨工业大学博士论文. 1991:28~8
6 D.G.Chetwynd and G.J.Siddall. Improving the Accuracy of Roundness Measurement. J.Phys.E,Sci.Instru. 1976,9(7): 537~545
7 A.Sacconi. Intercomparison of High Accuracy Roundness Measurements. Report EUR 14662 EN,ECSC-EEC-EAEC,Brussels. 1993: 32
8 A,Sacconi and W.Pasin. An Intercomparison of Roundness Measurements between ten-Europen National Standards Laboratories. Measurement. 1994, 13: 119~128
9 Donaldson R.R. A Simple Method for Separating Spindle Error from Test Ball Roundness Error. CIRP Ann . 1976 ,21: 125~126
10 O.Horikawa, N.Maruyama, M.Shimada. A low cost, high accuracy roundness measuring system. Precision Engineering. 2001, 25(3):200~205
11 Grejda Robert, Marsh Eric, Vallance Ryan. Techniques for calibrating spindles with nanometer error motion. Precision Engineering. 2005, 29(1):113~123
12赵维谦,谭久彬,常承,孙彤.超精密圆度仪全自动误差分离装置的研制.仪器仪表学报. 2000,21(2):203~205
13曹麟祥,王丙甲.圆度检测技术.国防工业出版社,1998:192~215
14谭久彬,赵维谦,杨文国.改善多步法谐波抑制的新方法——鉴相法.中国机械工程增刊. 2001:(12):161~162
15 P.L.Holsteretal. Measuring the radial error of precision air bearing. Philips Tech.Rev. 1984, 41:334~337
16 Wei Gao, Satoshi Kiyono and Tadatoshi Nomrua. A new multiprobe method of roundness measurements. Precision Engineering. 1996,19(1):37~44
17 H.Haitjema, H.Bosse,M.Frennberg, A.Sacconi and R.Thalmann. International Comparison of Roundness Profiles with Nanometric Accuracy. Metrologia. 1996, 33: 67~73
18韩正桐,洪迈生,李自军.三点法圆度误差分离及演化形式与精度分析.上海交通大学学报. 2002,36(9):1225~1227
19刘越.基于误差分离技术的圆度误差检测方法.计量与测试技术. 2004,(1):6~7
20 D S Suen,C N Chang. Application of neutral network interval regression method for minimum. zone circle roundness. Technol.1997,8:245~252.
21 Wen-Yuh Jywe,Chen-Hong Liu,Cha’o-Kuang Chen. The min-max problem for evaluating the form error of a circle. Measurement. 1999,26:273~282
22 Tong Sun and J.B.Tan. Compensation Harmonics in Muti-Step Error Separation with Comprehensive Method. Journal of Chinese Society of Mechanical Engineers.1996,17(6):549~553
23洪迈生,蔡萍.多步法误差分离技术的比较分析.上海交通大学学报. 2004,38(6):877~881
24 D.G.Chetwynd. High-precision Measurement of Small Balls. J.phys.E:Sci. Instrum.1987,(20):1179~1187
25谭久彬,李柱.精密仪器设计理论与方法(资料).附录8~15
26 Cao Linxiang. Full-harmonic error separation technique. Meas.Sci.Technol. 1992,(3):1129~1132
27张梅,金施群.圆度测量误差分离技术解决ICA的不确定性问题.黑龙江科技学院学报. 2004,14(5):290~303
28 M.Weck and M.Schmidt. A new method for detemining geometric accuracy in the axis of movement of machine tools. Precision Engineering. 1986, 8(2):97~103
29小泽则光等.精密工学会志.1990,56(2):147~153
30莴小键,颜景平.机床主轴回转误差补偿信号的测量理论和方法.计量学报. 1994, 4:116~120
31 Whitehouse.D.J, Modern Trends in the Measurement of Surfaces. Rev.M.mec.1975,21:19~28
32王红,曹麟祥.混合多步法误差分离技术.计量学报. 1994,15(3):223~225
33雷贤卿,李言,李济顺,周彦伟,潘为民.多步法圆度误差分离的演化形式及其谐波抑制分析.工业仪表与自动化装置. 2006,(1):45~46
34 D.G.Chetwynd. Roundness measurement using limacons. Precision Engineering. 1979, 1:137~141
35 G.X.Zhang. Four-point method of roundness and spindle error measurements. Annals of CIRP. 1993,42(1):593~596
36管炳良,陈晓怀.高精度圆度仪误差分离装置研制及测量不确定度分析.计测技术. 2005,25(1):37~39
37叶京生,顾启泰.圆度误差分离技术中若干问题的探讨.计量学报,1992,13(3):170~175
38崔绍良,钟家桢,孙荣平,宋涛.圆度测量的误差分离及数据处理.北京科技大学学报. 1995,17(6):543~546
39李济顺,洪迈生.提高圆度误差分离精度的措施.计量学报. 1999,20(2):92~95
40赵维谦,谭久彬,杨文国,张杰.基于两步法超精密圆度仪误差分离系统.中国机械工程. 2000,11(11):1206~1208
41 Y.Aoki and S.Ozono. A new method of roundness measurement based on the three point method. J.Japan.Soc.Precision Eng.1966:27~32
42张宇华,王晓琳.多点法圆度及轴系误差分离方法的若干问题.北京理工大学学报. 1999,19(3):309~312
43申博,王建华,劳奇成.圆度、直线度误差分离方法之比较.机械工程及自动化. 2004,(6):43~45
44洪迈生,邓宗煌,陈健强,大园成夫.精确的时域三点法圆度误差分离技术.上海交通大学学报. 2000,34(10):1318~1319
45 H.Shinno,K.Mitui,Y.Tatsue,N.Tanaka and T.Tabata. A new method for evaluating error motion of ultra precision spindle. Annals of CIRP. 1987,36:381~384
46雷贤卿,李言,周彦伟,李济顺,薛玉君. 3点法圆度误差分离技术的新算法.兵工学报. 2007,28(1):73~77
47洪迈生,蔡萍.多步法误差分离技术的比较分析.上海交通大学学报. 2004, 38(6):877~881
48史德卿.圆度仪数据采集处理系统.轴承. 2003,(6):31~33
49郑德星.基于圆度测量的误差分离技术的分析.诊断与检测.2007,(5):101~102
50刘越.基于误差分离技术的圆度误差检测方法.计测技术. 2004,(1):6~7
51李副来.高速圆度仪在轴承行业中的应用.机电信息. 2003,(15):24~25
2梁建成.误差补偿-提高机械加工精度的重要途径.机械工程. 1987,3:46~48
3谭久彬.精密测量中的误差补偿技术:哈尔滨工业大学出版社,1995,52~108
4 Whitehouse.D.J. Some Theoretical Aspects of Error Separation Techniques in Surface Metrology. J.phys.E:Sci.Instru 1976,(9):531~536
5谭久彬.圆和圆柱轮廓的超精密测量技术与特征分析理论的研究.哈尔滨工业大学博士论文. 1991:28~8
6 D.G.Chetwynd and G.J.Siddall. Improving the Accuracy of Roundness Measurement. J.Phys.E,Sci.Instru. 1976,9(7): 537~545
7 A.Sacconi. Intercomparison of High Accuracy Roundness Measurements. Report EUR 14662 EN,ECSC-EEC-EAEC,Brussels. 1993: 32
8 A,Sacconi and W.Pasin. An Intercomparison of Roundness Measurements between ten-Europen National Standards Laboratories. Measurement. 1994, 13: 119~128
9 Donaldson R.R. A Simple Method for Separating Spindle Error from Test Ball Roundness Error. CIRP Ann . 1976 ,21: 125~126
10 O.Horikawa, N.Maruyama, M.Shimada. A low cost, high accuracy roundness measuring system. Precision Engineering. 2001, 25(3):200~205
11 Grejda Robert, Marsh Eric, Vallance Ryan. Techniques for calibrating spindles with nanometer error motion. Precision Engineering. 2005, 29(1):113~123
12赵维谦,谭久彬,常承,孙彤.超精密圆度仪全自动误差分离装置的研制.仪器仪表学报. 2000,21(2):203~205
13曹麟祥,王丙甲.圆度检测技术.国防工业出版社,1998:192~215
14谭久彬,赵维谦,杨文国.改善多步法谐波抑制的新方法——鉴相法.中国机械工程增刊. 2001:(12):161~162
15 P.L.Holsteretal. Measuring the radial error of precision air bearing. Philips Tech.Rev. 1984, 41:334~337
16 Wei Gao, Satoshi Kiyono and Tadatoshi Nomrua. A new multiprobe method of roundness measurements. Precision Engineering. 1996,19(1):37~44
17 H.Haitjema, H.Bosse,M.Frennberg, A.Sacconi and R.Thalmann. International Comparison of Roundness Profiles with Nanometric Accuracy. Metrologia. 1996, 33: 67~73
18韩正桐,洪迈生,李自军.三点法圆度误差分离及演化形式与精度分析.上海交通大学学报. 2002,36(9):1225~1227
19刘越.基于误差分离技术的圆度误差检测方法.计量与测试技术. 2004,(1):6~7
20 D S Suen,C N Chang. Application of neutral network interval regression method for minimum. zone circle roundness. Technol.1997,8:245~252.
21 Wen-Yuh Jywe,Chen-Hong Liu,Cha’o-Kuang Chen. The min-max problem for evaluating the form error of a circle. Measurement. 1999,26:273~282
22 Tong Sun and J.B.Tan. Compensation Harmonics in Muti-Step Error Separation with Comprehensive Method. Journal of Chinese Society of Mechanical Engineers.1996,17(6):549~553
23洪迈生,蔡萍.多步法误差分离技术的比较分析.上海交通大学学报. 2004,38(6):877~881
24 D.G.Chetwynd. High-precision Measurement of Small Balls. J.phys.E:Sci. Instrum.1987,(20):1179~1187
25谭久彬,李柱.精密仪器设计理论与方法(资料).附录8~15
26 Cao Linxiang. Full-harmonic error separation technique. Meas.Sci.Technol. 1992,(3):1129~1132
27张梅,金施群.圆度测量误差分离技术解决ICA的不确定性问题.黑龙江科技学院学报. 2004,14(5):290~303
28 M.Weck and M.Schmidt. A new method for detemining geometric accuracy in the axis of movement of machine tools. Precision Engineering. 1986, 8(2):97~103
29小泽则光等.精密工学会志.1990,56(2):147~153
30莴小键,颜景平.机床主轴回转误差补偿信号的测量理论和方法.计量学报. 1994, 4:116~120
31 Whitehouse.D.J, Modern Trends in the Measurement of Surfaces. Rev.M.mec.1975,21:19~28
32王红,曹麟祥.混合多步法误差分离技术.计量学报. 1994,15(3):223~225
33雷贤卿,李言,李济顺,周彦伟,潘为民.多步法圆度误差分离的演化形式及其谐波抑制分析.工业仪表与自动化装置. 2006,(1):45~46
34 D.G.Chetwynd. Roundness measurement using limacons. Precision Engineering. 1979, 1:137~141
35 G.X.Zhang. Four-point method of roundness and spindle error measurements. Annals of CIRP. 1993,42(1):593~596
36管炳良,陈晓怀.高精度圆度仪误差分离装置研制及测量不确定度分析.计测技术. 2005,25(1):37~39
37叶京生,顾启泰.圆度误差分离技术中若干问题的探讨.计量学报,1992,13(3):170~175
38崔绍良,钟家桢,孙荣平,宋涛.圆度测量的误差分离及数据处理.北京科技大学学报. 1995,17(6):543~546
39李济顺,洪迈生.提高圆度误差分离精度的措施.计量学报. 1999,20(2):92~95
40赵维谦,谭久彬,杨文国,张杰.基于两步法超精密圆度仪误差分离系统.中国机械工程. 2000,11(11):1206~1208
41 Y.Aoki and S.Ozono. A new method of roundness measurement based on the three point method. J.Japan.Soc.Precision Eng.1966:27~32
42张宇华,王晓琳.多点法圆度及轴系误差分离方法的若干问题.北京理工大学学报. 1999,19(3):309~312
43申博,王建华,劳奇成.圆度、直线度误差分离方法之比较.机械工程及自动化. 2004,(6):43~45
44洪迈生,邓宗煌,陈健强,大园成夫.精确的时域三点法圆度误差分离技术.上海交通大学学报. 2000,34(10):1318~1319
45 H.Shinno,K.Mitui,Y.Tatsue,N.Tanaka and T.Tabata. A new method for evaluating error motion of ultra precision spindle. Annals of CIRP. 1987,36:381~384
46雷贤卿,李言,周彦伟,李济顺,薛玉君. 3点法圆度误差分离技术的新算法.兵工学报. 2007,28(1):73~77
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