作者：杨继森, 牟智铭, 李路建, 邵争光, 李明

作者单位：重庆理工大学 机械检测技术与装备教育部工程研究中心，重庆 400054

关键词：位移传感器;时栅传感;激励信号;误差分析;误差修正

摘要：

针对在时栅位移传感器测量过程中激励信号所引入的误差问题，提出一种基于激励信号误差分析的误差模型，以及针对该误差模型的修正方法。通过对传感器感应信号进行建模分析，确定激励信号引入幅值误差、正交误差和相移误差，并分别建立3类误差模型。采用数值分析法研究3类误差的特性、来源及相互关系，基于误差之间相关性低这一特性，采用基于加窗函数的误差修正方法处理幅值误差，按误差源分步补偿正交误差，结合迭代最小二乘拟合法修正相移误差。实验结果表明：经误差修正，72对极圆型场式时栅位移传感器的整周测量误差由±119.6″降低至±1.84″，单对极范围内的测量误差由±117.7″降低至±1.54″，所提出的误差修正法可大幅度地降低测量误差，有效提高传感器的测量精度。

Analysis and correction of errors induced by excitation signal in time grating displacement sensor
YANG Jisen, MOU Zhiming, LI Lujian, SHAO Zhengguang, LI Ming
Engineering Research Center of Mechanical Testing Technology and Equipment Ministry of Education, Chongqing University of Technology, Chongqing 400054, China
Abstract: Aiming at the error caused by the excitation signal during the time grid displacement sensor measurement, an error model based on the error analysis of the excitation signal is proposed, and a correction method for the error model is proposed. By modeling and analyzing the sensor induced signals, it is determined that the excitation signal introduces amplitude error, quadrature error, and phase shift error, and three types of error models are established respectively. The characteristics, sources, and interrelationships of the three types of errors are studied using numerical analysis methods. Based on the low correlation between the errors, a method for processing the three types of errors is proposed separately. The error correction method based on the windowing function is used to deal with the amplitude errors. According to the error source, the quadrature error is compensated step by step, and the iterative least squares fitting method is used to correct the phase shift error. The experimental results show that after error correction, the measurement error of 72 pairs of polar field-type time-grid displacement sensors has been reduced from ±119.6″ to ±1.84″, and the measurement error in the single-pole range has been reduced from ±117.7″ to ±1.54″. The proposed error correction method greatly reduces the measurement error and effectively improves the measurement accuracy of the sensor.
Keywords: displacement sensor;time-grating sensor;excitation signal;error analysis;error correction
2020, 46(8):80-86  收稿日期: 2019-07-25;收到修改稿日期: 2019-09-16
基金项目: 国家自然科学基金重大科研仪器研制项目（51827805）；重庆市科技计划项目（cstc2017jcyjAX0400）；重庆市巴南区科技计划项目（2019TJ14）；重庆市高校优秀人才支持计划项目资助(2017-17) ；重庆理工大学研究生创新基金（ycx2018217）
作者简介: 杨继森（1977-），男，四川成都市人，教授，硕士生导师，主要从事精密测量与智能传感器方面的研究
参考文献
[1] 彭东林. 时栅位移传感器与新型机床动态检测系统[M]. 北京: 科学出版社, 2010:19-30.
[2] 彭东林, 刘小康, 张兴红, 等. 时栅位移传感器原理与发展历程[J]. 重庆理工大学学报(自然科学), 2010, 24(10): 40-45
[3] 彭东林, 刘小康, 张兴红, 等. 高精度时栅位移传感器研究[J]. 机械工程学报, 2005, 41(12): 126-129
[4] 王伟, 石照耀, 彭东林, 等. 基于d-q变换的时栅位移传感器补偿算法研究[J]. 仪器仪表学报, 2017(10): 2453-2460
[5] 王合文, 吴玉梅, 郑方燕, 等. 基于纳米时栅传感器安装偏差的测量精度分析研究[J]. 传感技术学报, 2017, 30(2): 230-235
[6] PENG K, LIU X, CHEN Z, et al. Sensing mechanism and error analysis of a capacitive long-range displacement nanometer sensor based on time grating[J]. IEEE Sensors Journal, 2017, 99: 1596-1607
[7] 鲁进, 陈锡侯, 武亮, 等. 变耦型时栅位移传感器理论模型与误差研究[J]. 仪器仪表学报, 2016, 37(3): 561-569
[8] MIRANDA D L, SCHWARTZ J B, LOOMIS A C, et al. Static and dynamic error of a biplanar videoradiography system using marker-based and markerless tracking techniques[J]. Journal of Biomechanical Engineering, 2011, 133(12): 121002
[9] HOTAIT M A, KAHRAMAN A. Experiments on the relationship between the dynamic transmission error and the dynamic stress factor of spur gear pairs[J]. Mechanism & Machine Theory, 2013, 70(6): 116-128
[10] 孙世政, 彭东林, 郑方燕, 等. 时栅传感器动态测量误差补偿[J]. 光学精密工程, 2015, 23(4): 1114-1121
[11] 杨继森, 李小雨, 张静, 等. 时栅位移传感器动态误差模型及修正算法研究[J]. 仪器仪表学报, 2015, 36(11): 2548-2555
[12] 杨继森, 张静, 江中伟, 等. 时栅位移传感器的动态特性研究[J]. 中国机械工程, 2016, 27(13): 1790-1795
[13] 彭东林, 孙世政, 高忠华, 等. 时栅位移传感器的误差分离与补偿方法研究[J]. 自动化仪表, 2012, 33(1): 15-17
[14] 张瀚潇,郑方燕,吴玉梅,等. 纳米时栅位移传感器误差模型建立与分析[J]. 仪表技术与传感器, 2018(4): 1-5
[15] LU J, CHEN X H, WU L, et al. Study on the theoretical model and error characteristics of variable coupling time grating displacement sensor[J]. Chinese Journal of Scientific Instrument, 2016, 27(3): 561-569
[16] 彭东林, 张兴红, 刘小康, 等. 场式时栅位移传感器研究[J]. 仪器仪表学报, 2003, 24(3): 321-323
[17] 董良浩, 汤其富, 彭东林, 等. 一种平面超薄型电磁感应式角位移传感器[J]. 仪表技术与传感器, 2018(3): 6-9
[18] 张俊敏, 刘开培, 汪立, 等. 基于乘法窗函数的插值FFT的谐波分析方法[J]. 电力系统保护与控制, 2016(13): 1-5
[19] 徐清华, 武亮, 彭东林, 等. 平面线圈型直线时栅参数优化方法[J]. 重庆理工大学学报(自然科学), 2018(2): 105-112