工程科学学报.第42卷，第8期：1055-1064.2020年8月 Chinese Journal of Engineering,Vol.42,No.8:1055-1064,August 2020 https://doi.org/10.13374/j.issn2095-9389.2019.10.18.004;http://cje.ustb.edu.cn 基于双齿面传动误差的侧隙连续测量与预测 王光建12区，周磊3)，邹帅东13) 1)重庆大学机械传动国家重点实验室，重庆4000442)重庆大学汽车工程学院.重庆4000443)重庆大学机械工程学院，重庆400044 ☒通信作者，E-mail:gjwang@cqu.edu.cn 摘要提出了基于双偏心误差齿轮副的驱动齿面与齿背面（双齿面）无负载传动误差计算模型，建立与时变侧隙计算公式 的等价关系，从理论上证明了基于双齿面传动误差的侧隙测量方法.通过实验方法测量不同负载力矩、不同初始啮合面的双 面传动误差并获得相应载荷下的初始回差.基于双齿面传动误差实验曲线，实现了对齿轮副整个大周期侧隙的连续测量与 预测.结果表明，连续侧隙曲线与机械滞后回差法测量结果吻合良好，而侧隙预测较好地反应了侧隙值变化范围和变化趋势 司时，侧隙连续测量方法及侧隙预测均证明了理论模型的正确性，提高了侧隙测量效率并获得了更全面的侧隙数据，对齿轮 传动的非线性研究、消隙控制以及齿轮精度研究等均具有指导意义和参考价值. 关键词时变侧隙：双齿面传动误差；连续测量：侧隙预测：偏心误差 分类号TH132.4 Measurement and prediction of backlash based on two-sided transmission error WANG Guang-jian,ZHOU Lei,ZOU Shuai-dong 1)State Key Laboratory of Mechanical Transmissions,Chongqing University,Chongqing 400044,China 2)School of Automotive Engineering.Chongqing University,Chongqing 400044,China 3)College of Mechanical Engineering,Chongqing University,Chongqing 400044,China Corresponding author,E-mail:gjwang@cqu.edu.cn ABSTRACT Transmission error in gear system and backlash are important factors that affect the accuracy of precision transmission systems.The main sources of the complete cycle transmission errors and periodic backlash are eccentric errors due to imperfections in machining and assembling.Therefore,analyzing the transmission error in gear system and backlash under the effect of eccentricity error is necessary.Scholars from around the world have conducted extensive research on the transmission error of the gear system.They observed that the back-side contact of the gear tooth generally happens in high-speed light-load conditions,or when alternate load torque occurs or anti-backlash gear has been used.However,the existing literature does not evidently show the calculation method of the transmission error of the back-side tooth mesh.Therefore,analyzing the transmission error of the back-side tooth mesh is of great significance.The present work develops a calculation model of drive-and back-side(two-sided)transmission error of an involute gear pair with eccentricities to construct the equivalence of time-varying backlash calculation formula to demonstrate the continuous measurement of gear backlash based on two-sided transmission error that can also be realized in theory.The experimental transmission error and the corresponding hysteresis were acquired under various load torques and different initial conditions,such as initial position of the gear unit.The continuous backlash curve of the gear pair was obtained from the two-sided transmission curves,and the backlash of the whole cycle could be predicted.The result of the experiment shows that the continuous measurement curve agrees with the mechanical hysteresis method,and the prediction of backlash perfectly reflects the variation range and trend of backlash.Moreover,both the continuous measurement method of backlash and prediction of backlash demonstrate that the model is practicable and have higher 收稿日期：2019-10-18 基金项目：国家自然科学基金资助项目(51275538)：上海市空间飞行器机构重点实验室开放课题(SM2014D101)基于双齿面传动误差的侧隙连续测量与预测 王光建1,2) 苣，周    磊1,3)，邹帅东1,3) 1) 重庆大学机械传动国家重点实验室，重庆 400044    2) 重庆大学汽车工程学院，重庆 400044    3) 重庆大学机械工程学院，重庆 400044 苣通信作者，E-mail：gjwang@cqu.edu.cn 摘    要    提出了基于双偏心误差齿轮副的驱动齿面与齿背面（双齿面）无负载传动误差计算模型，建立与时变侧隙计算公式 的等价关系，从理论上证明了基于双齿面传动误差的侧隙测量方法. 通过实验方法测量不同负载力矩、不同初始啮合面的双 面传动误差并获得相应载荷下的初始回差. 基于双齿面传动误差实验曲线，实现了对齿轮副整个大周期侧隙的连续测量与 预测. 结果表明，连续侧隙曲线与机械滞后回差法测量结果吻合良好，而侧隙预测较好地反应了侧隙值变化范围和变化趋势. 同时，侧隙连续测量方法及侧隙预测均证明了理论模型的正确性，提高了侧隙测量效率并获得了更全面的侧隙数据，对齿轮 传动的非线性研究、消隙控制以及齿轮精度研究等均具有指导意义和参考价值. 关键词    时变侧隙；双齿面传动误差；连续测量；侧隙预测；偏心误差 分类号    TH132.4 Measurement and prediction of backlash based on two-sided transmission error WANG Guang-jian1,2) 苣 ，ZHOU Lei1,3) ，ZOU Shuai-dong1,3) 1) State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China 2) School of Automotive Engineering, Chongqing University, Chongqing 400044, China 3) College of Mechanical Engineering, Chongqing University, Chongqing 400044, China 苣 Corresponding author, E-mail: gjwang@cqu.edu.cn ABSTRACT    Transmission error in gear system and backlash are important factors that affect the accuracy of precision transmission systems. The main sources of the complete cycle transmission errors and periodic backlash are eccentric errors due to imperfections in machining and assembling. Therefore, analyzing the transmission error in gear system and backlash under the effect of eccentricity error is  necessary.  Scholars  from  around  the  world  have  conducted  extensive  research  on  the  transmission  error  of  the  gear  system.  They observed that the back-side contact of the gear tooth generally happens in high-speed light-load conditions, or when alternate load torque occurs  or  anti-backlash  gear  has  been  used.  However,  the  existing  literature  does  not  evidently  show  the  calculation  method  of  the transmission  error  of  the  back-side  tooth  mesh.  Therefore,  analyzing  the  transmission  error  of  the  back-side  tooth  mesh  is  of  great significance. The present work develops a calculation model of drive- and back-side (two-sided) transmission error of an involute gear pair  with  eccentricities  to  construct  the  equivalence  of  time-varying  backlash  calculation  formula  to  demonstrate  the  continuous measurement of gear backlash based on two-sided transmission error that can also be realized in theory. The experimental transmission error and the corresponding hysteresis were acquired under various load torques and different initial conditions, such as initial position of the gear unit. The continuous backlash curve of the gear pair was obtained from the two-sided transmission curves, and the backlash of the  whole  cycle  could  be  predicted.  The  result  of  the  experiment  shows  that  the  continuous  measurement  curve  agrees  with  the mechanical hysteresis method, and the prediction of backlash perfectly reflects the variation range and trend of backlash. Moreover, both the continuous measurement method of backlash and prediction of backlash demonstrate that the model is practicable and have higher 收稿日期: 2019−10−18 基金项目: 国家自然科学基金资助项目 (51275538)；上海市空间飞行器机构重点实验室开放课题 (SM2014D101) 工程科学学报，第 42 卷，第 8 期：1055−1064，2020 年 8 月 Chinese Journal of Engineering, Vol. 42, No. 8: 1055−1064, August 2020 https://doi.org/10.13374/j.issn2095-9389.2019.10.18.004; http://cje.ustb.edu.cn