基于后验误差拟合的角位移测量误差补偿
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摘要
在航天、军事、工业这些对器件的体积有着严格要求的领域,光电编码器不仅要求减小外径尺寸和重量,更要提高其测量精度。本文以光电编码器误差补偿方法为研究对象,基于后验误差拟合方法确定误差模型参数,从而实现对小型光电编码器的深度误差补偿。分析了影响光电编码器测角误差的主要因素,建立了长周期误差和短周期误差模型。然后,采用后验误差拟合算法实现了对误差模型参数的确定,提出误差补偿算法;最后,对某一小型光电编码器进行实验,验证了所提出误差补偿算法的性能。某型号光电编码器补偿前的精度为22.48″,补偿后的精度为5.82″。实验表明,采用后验误差补偿方法可以不考虑误差影响因素的大小,直接对编码器进行误差补偿,具有效率高、补偿准确等优点,极大地提高了批量生产时光电编码器产品的精度。
In the aerospace,military,and industrial fields,which have strict requirements on the volumes of devices,photoelectric encoders require not only a reduction in the size and weight of the outer diameter,but also improvements in the measurement accuracy.In this study,an error compensation method for photoelectric encoders was investigated.The error model parameters were determined based on a posteriori error-fitting method,and then depth error compensation was performed for a small photoelectric encoder.First,the main factors that affect the angle measurement error of the photoelectric encoder were analyzed,and the long-and short-period error models were established.Then,aposteriori error-fitting error compensation algorithm was proposed.Finally,a small photoelectric encoder was tested to verify the performance of the proposed error compensation algorithm.The test results demonstrate that the proposed posteriori error-fitting compensation method can significantly reduce the angle measurement error of the photoelectric encoder.We utilized an encoder toverify this method.The accuracy before compensation is 22.48″,and that after compensation is 5.82″.This approach employs a posteriori error compensation method,which can directly compensate the encoder error without considering the sizes of the error factors,and possesses the advantages of high efficiency and accurate compensation.The product precision is considerably improved when the photoelectric encoder is mass produced.
In the aerospace,military,and industrial fields,which have strict requirements on the volumes of devices,photoelectric encoders require not only a reduction in the size and weight of the outer diameter,but also improvements in the measurement accuracy.In this study,an error compensation method for photoelectric encoders was investigated.The error model parameters were determined based on a posteriori error-fitting method,and then depth error compensation was performed for a small photoelectric encoder.First,the main factors that affect the angle measurement error of the photoelectric encoder were analyzed,and the long-and short-period error models were established.Then,aposteriori error-fitting error compensation algorithm was proposed.Finally,a small photoelectric encoder was tested to verify the performance of the proposed error compensation algorithm.The test results demonstrate that the proposed posteriori error-fitting compensation method can significantly reduce the angle measurement error of the photoelectric encoder.We utilized an encoder toverify this method.The accuracy before compensation is 22.48″,and that after compensation is 5.82″.This approach employs a posteriori error compensation method,which can directly compensate the encoder error without considering the sizes of the error factors,and possesses the advantages of high efficiency and accurate compensation.The product precision is considerably improved when the photoelectric encoder is mass produced.
引文
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[12]WARNER M,KRABBENDAM V,SCHUMACHER G.Adaptive periodic error correction for Heidenhain tape encoders[C].Ground-based and Airborne Telescopes II.International Society for Optics and Photonics,2008:70123N-70123N-8.
[13] TAN K K,TANG K Z.Adaptive online correction and interpolation of quadrature encoder signals using radial basis functions[J].Control Systems Technology,IEEE Transactions on,2005,13(3):370-377.
[14] LU X D,TRUMPER D L.Self-calibration of onaxis rotary encoders[J].CIRP Annals-Manufacturing Technology,2007,56(1):499-504.
[15] WATANABE T,FUJIMOTO H,NAKAYAMA K,et al.Automatic high-precision calibration system for angle encoder[J].Recent Developments in Traceable Dimensional Measurements,2001:267-274.
[16]齐永岳,赵美蓉,林玉池.提高激光干涉测量系统精度的方法与途径[J].天津大学学报,2006,39(8):989-993.QI Y Y,ZHAO M R,LIN Y CH.Methods of improving accuracy of laser interferometry system[J].Journal of Tianjin University,2006,39(8):989-993.(in Chinese)
[17]王选择,郭军,谢铁邦.精密衍射光栅信号的椭圆拟合与细分校正算法[J].工具技术,2003,37(12):47-49.WANG X Z,GUO J,XIE T J.Ellipse fit algorithm and subdivision revision method of precision diffraction grating[J].Tool Engineering,2003,37(12):47-49.(in Chinese)
[18]刘文文,费业泰.高精度的光栅信号细分算法[J].应用科学学报,1999,17(1):70-74.LIU W W,FEI Y T.High precision subdivision algorithm for grating signal[J].Journal of Applied Sciences,1999,17(1):70-74.(in Chinese)
[19]洪喜,续志军,杨宁.基于径向基函数网络的光电编码器误差补偿法[J].光学精密工程,2008,16(4):598-604.HONG X,XU ZH J,YANG N.Error compensation of optical encoder based on RBF network[J].Opt.Precision Eng.,2008,16(4):598-604.(in Chinese)
[20]杨进堂.“角度基准”中系统误差的修正[J].光学精密工程,1997,5(1):142-146.YANG J T.Revision of systematic error of angle standard[J].Opt.Precision Eng.,1997,5(1):142-146.(in Chinese)
[21]朱帆,吴易明,刘长春.四读头法消除码盘偏心和振动对叠栅条纹相位测量的影响[J].光学学报,2011,31(4):0412008.ZHU F,WU Y M,LIU CH CH.Eliminating influence of grating encoder′s eccentricity and vibration to Moiréfringes signal by four reading heads[J].Acta Optica Sinica,2011,31(4):0412008.(in Chinese)
[22]于海,万秋华,王树洁,等.小型绝对式光电编码器动态误差分析[J].中国激光,2013,40(8):0808004.YU H,WAN Q H,WANG SH J,et al..Dynamic errors analysis of small absolute photoelectric encoder[J].Chinese Journal of Lasers,2013,40(8):0808004.(in Chinese)
[23]于海,万秋华,赵长海,等.图像式光电编码器高分辨率细分算法及误差分析[J].光学学报,2017,37(3):0312001.YU H,WAN Q H,ZHAO CH H,et al..Highresolution subdivision arithmetic and error analyses of photographic encoder[J].Acta Optica Sinica,2017,37(3):0312001.(in Chinese)
[2]吕强,李文昊,巴音贺希格,等.基于衍射光栅的干涉式精密位移测量系统[J].中国光学,2017,10(1):39-50.LQ,LI W H,BAYINHESHIG,et al..Interferometric precision displacement measurement system based on diffraction grating[J].Chinese Optics,2017,10(1):39-50.(in Chinese)
[3]董静,万秋华,于海,等.小型绝对式光电编码器误码自动检测系统[J].中国光学,2016,9(6):695-703.DONG J,WAN Q H,YU H,et al..Automatic detection system of fault code for small size absolute photoelectric encoder[J].Chinese Optics,2016,9(6):695-703.(in Chinese)
[4]张洪波,万秋华,王树洁,等.小型编码器动态精度检测的安装误差控制[J].光学精密工程,2016,24(7):1655-1660.ZHANG H B,WAN Q H,WANG SH J,et al..Installation error control of dynamic measurement for small photoelectric encoder[J].Opt.Precision Eng.,2016,24(7):1655-1660.(in Chinese)
[5]于海,万秋华,卢新然,等.光电编码器误差检测转台的动态精度标定[J].光学精密工程,2016,24(11):2699-2704.YU H,WAN Q H,LU X R,et al..Calibration of dynamic precision for measurement platform of photoelectric encoder[J].Opt.Precision Eng.,2016,24(11):2699-2704.(in Chinese)
[6] YU H,WAN Q H,LU X R,et al.Small-size,high-resolution angular displacement measurement technology based on an imaging detector[J].Applied Optics,2017,56(3):755-760.
[7] YU H,WAN Q H,LU X R,et al..A robust subpixel subdivision algorithm for image-type angular displacement measurement[J],Optics and Lasers in Engineering,2018.100:234-238.
[8]董莉莉,熊经武,万秋华.光电轴角编码器的发展动态[J].光学精密工程,2000,8(2):198-202.DONG L L,XIONG J W,WAN Q H.Development of photoelectric rotary encoders[J].Opt.Precision Eng.,2000,8(2):198-202.(in Chinese)
[9] DARIO M,ENRICO C,GANLILEO P S.Highresolution encoder system[J].SPIE,1997,3112:328-334.
[10]汤天瑾,曹向群,林斌.光电轴角编码器发展现状分析及展望[J].光学仪器,2005,27(1):91-95.TANG T J,CAO X Q,LIN B.Developing current situation and the trend of photoelectric-angular encoder[J].Optical Instruments,2005,27(1):91-95.(in Chinese)
[11]熊经武,万秋华.二十三位绝对式光电轴角编码器[J].光学机械,1990(2):52-60.XIONG J W,WAN Q H.A 23-bit absolute photo-electric rotary encoder[J].Optical Mechnical,1990,2:52-60.(in Chinese)
[12]WARNER M,KRABBENDAM V,SCHUMACHER G.Adaptive periodic error correction for Heidenhain tape encoders[C].Ground-based and Airborne Telescopes II.International Society for Optics and Photonics,2008:70123N-70123N-8.
[13] TAN K K,TANG K Z.Adaptive online correction and interpolation of quadrature encoder signals using radial basis functions[J].Control Systems Technology,IEEE Transactions on,2005,13(3):370-377.
[14] LU X D,TRUMPER D L.Self-calibration of onaxis rotary encoders[J].CIRP Annals-Manufacturing Technology,2007,56(1):499-504.
[15] WATANABE T,FUJIMOTO H,NAKAYAMA K,et al.Automatic high-precision calibration system for angle encoder[J].Recent Developments in Traceable Dimensional Measurements,2001:267-274.
[16]齐永岳,赵美蓉,林玉池.提高激光干涉测量系统精度的方法与途径[J].天津大学学报,2006,39(8):989-993.QI Y Y,ZHAO M R,LIN Y CH.Methods of improving accuracy of laser interferometry system[J].Journal of Tianjin University,2006,39(8):989-993.(in Chinese)
[17]王选择,郭军,谢铁邦.精密衍射光栅信号的椭圆拟合与细分校正算法[J].工具技术,2003,37(12):47-49.WANG X Z,GUO J,XIE T J.Ellipse fit algorithm and subdivision revision method of precision diffraction grating[J].Tool Engineering,2003,37(12):47-49.(in Chinese)
[18]刘文文,费业泰.高精度的光栅信号细分算法[J].应用科学学报,1999,17(1):70-74.LIU W W,FEI Y T.High precision subdivision algorithm for grating signal[J].Journal of Applied Sciences,1999,17(1):70-74.(in Chinese)
[19]洪喜,续志军,杨宁.基于径向基函数网络的光电编码器误差补偿法[J].光学精密工程,2008,16(4):598-604.HONG X,XU ZH J,YANG N.Error compensation of optical encoder based on RBF network[J].Opt.Precision Eng.,2008,16(4):598-604.(in Chinese)
[20]杨进堂.“角度基准”中系统误差的修正[J].光学精密工程,1997,5(1):142-146.YANG J T.Revision of systematic error of angle standard[J].Opt.Precision Eng.,1997,5(1):142-146.(in Chinese)
[21]朱帆,吴易明,刘长春.四读头法消除码盘偏心和振动对叠栅条纹相位测量的影响[J].光学学报,2011,31(4):0412008.ZHU F,WU Y M,LIU CH CH.Eliminating influence of grating encoder′s eccentricity and vibration to Moiréfringes signal by four reading heads[J].Acta Optica Sinica,2011,31(4):0412008.(in Chinese)
[22]于海,万秋华,王树洁,等.小型绝对式光电编码器动态误差分析[J].中国激光,2013,40(8):0808004.YU H,WAN Q H,WANG SH J,et al..Dynamic errors analysis of small absolute photoelectric encoder[J].Chinese Journal of Lasers,2013,40(8):0808004.(in Chinese)
[23]于海,万秋华,赵长海,等.图像式光电编码器高分辨率细分算法及误差分析[J].光学学报,2017,37(3):0312001.YU H,WAN Q H,ZHAO CH H,et al..Highresolution subdivision arithmetic and error analyses of photographic encoder[J].Acta Optica Sinica,2017,37(3):0312001.(in Chinese)