Dynamic characteristics of the lost motion of the reducer
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摘要:
基于传动误差对回差的动态特性展开研究,综合考虑转矩、加载速率和转速的影响,解析了回差与传动误差的关系,论证了回差的动态特性,研究发现可通过正反向传动误差相减得到回差。探讨了回差的分类,可分为动态回差、准静态回差和静态回差。给出了回差的测试方法,动态回差可通过双向传动误差法得到,准静态回差和静态回差可以通过滞回曲线法获得。以小型减速器和大型减速器为例,进行了回差的试验研究,验证了回差的动态特性;研究发现动态回差和准静态回差是动态变化的,而静态回差不受加载速率依赖性的影响,试验结果与理论分析一致。最后指出了该研究在理论和工程应用方面的价值。
Abstract:The dynamic characteristics of lost motion based on transmission errors were explored. By considering the influences of torque, loading rate, and rotational speed, the relationship between lost motion and transmission errors was analytically derived. The dynamic characteristics of lost motion were substantiated, revealing that lost motion can be obtained by subtracting reverse transmission errors. The classification of lost motion was examined, and lost motion was divided into dynamic lost motion, quasi-static lost motion, and static lost motion. The testing methods for lost motion were provided, by which dynamic lost motion can be obtained through bidirectional transmission error analysis, and quasi-static lost motion and static lost motion can be acquired through hysteresis loop analysis. Experimental investigations on lost motion were conducted using examples of small and large reducers, confirming the dynamic characteristics of lost motion. It was observed that dynamic lost motion and quasi-static lost motion exhibited dynamic variations, while static lost motion was kept unaffected by loading rate dependence, aligning with theoretical analyses. In conclusion, the theoretical and engineering values of the research were highlighted.
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Key words:
- reducer /
- lost motion /
- bidirectional transmission error /
- dynamic characteristics /
- hysteresis curve
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表 2 减速器参数
Table 2. Parameters of the two types of reducers used in the experiments
类型 额定转矩/(N·m) 最大转速/(r/min) 设计回差 小型减速器 1.0 70 3.6° 大型减速器 380.0 70 7′ 表 1 测试设备参数
Table 1. Test equipment parameters
指标 小型减速器 大型精密减速器 转矩范围 0~10 N·m 0~ 1500 N·m转矩测量精度 ±0.1%F.S ±0.1%F.S 角度测量精度 ±1.44″ ±1″ 表 3 动态回差测试条件
Table 3. Dynamic lost motion experiment conditions
类型 负载转矩/
(N·m)转速/(r/min) 条件1 条件2 条件3 小型减速器 1.0 1 5 10 大型精密减速器 380.0 1 5 10 表 4 动态回差试验结果
Table 4. Dynamic lost motion experiment result
类型 结果1 结果2 结果3 小型减速器/(°) 4.0638 3.9938 3.9314 大型精密减速器/(′) 7.9829 7.9913 7.9675 表 5 准静态回差测试条件
Table 5. Quasi static lost motion experiment conditions
类型 位置/(°) 转矩时间/( N·m/s) 条件1 条件2 条件3 小型减速器 180 0.02 0.05 0.1 大型精密减速器 180 1 2.5 5 表 6 准静态回差测试结果
Table 6. Quasi static lost motion experiment results
类型 结果1 结果2 结果3 小型减速器/(°) 4.0126 3.9032 3.8521 大型精密减速器/(′) 7.9971 7.4678 7.2631 表 7 静态回差测试结果
Table 7. Static lost motion experiment results
类型 结果1 结果2 结果3 小型减速器/(°) 2.8258 2.7971 2.8012 大型精密减速器/(′) 3.6253 3.6229 3.6193 -
[1] 国家市场监督管理总局,国家标准化管理委员会. 精密减速器回差测试与评价方法: GB/T 40731-2021[S]. 北京: 中国标准出版社,2021. State Administration for Market Regulation,Standardization Administration of the People’s Republic of China. Method of test and evaluation for lost motion of precision reducer: GB/T 40731-2021[S]. Beijing: Standards Press of China,2021. (in ChineseState Administration for Market Regulation, Standardization Administration of the People’s Republic of China. Method of test and evaluation for lost motion of precision reducer: GB/T 40731-2021[S]. Beijing: Standards Press of China, 2021. (in Chinese) [2] 石照耀,徐航,韩方旭,等. 精密减速器回差测量的现状与趋势[J]. 光学 精密工程,2018,26(9): 2150-2158. SHI Zhaoyao,XU Hang,HAN Fangxu,et al. Current status and trends in precision reducer lost motion measurement[J]. Optics and Precision Engineering,2018,26(9): 2150-2158. (in Chinese doi: 10.3788/OPE.20182609.2150SHI Zhaoyao, XU Hang, HAN Fangxu, et al. Current status and trends in precision reducer lost motion measurement[J]. Optics and Precision Engineering, 2018, 26(9): 2150-2158. (in Chinese) doi: 10.3788/OPE.20182609.2150 [3] 石照耀,徐航,林家春,等. 精密减速器回差测量与评价体系研究[J]. 仪器仪表学报,2018,39(6): 56-63. SHI Zhaoyao,XU Hang,LIN Jiachun,et al. Research on measurement and evaluation system of precision reducer lost motion[J]. Chinese Journal of Scientific Instrument,2018,39(6): 56-63. (in ChineseSHI Zhaoyao, XU Hang, LIN Jiachun, et al. Research on measurement and evaluation system of precision reducer lost motion[J]. Chinese Journal of Scientific Instrument, 2018, 39(6): 56-63. (in Chinese) [4] SHI Zhaoyao,CHENG Huiming,YU Bo,et al. Loading rate dependence of reducer hysteresis and its influence on lost motion test[J]. Machines,2022,10(9): 765. doi: 10.3390/machines10090765 [5] XU Hang,SHI Zhaoyao,YU Bo,et al. Dynamic measurement of the lost motion of precision reducers in robots and the determination of optimal measurement speed[J]. Journal of Advanced Mechanical Design,Systems,and Manufacturing,2019,13(3): 2146. [6] 程慧明,石照耀. 减速器滞回模型及其应用[EB/OL]. 北京航空航天大学学报,(2023-05-10) [2024-03-05]. https://doi.org/10.13700/j.bh.1001-5965.2023.0055. CHENG Huiming, SHI Zhaoyao. Hysteresis model of reducer and its application[EB/OL]. Journal of Beijing University of Aeronautics and Astronautics,(2023-05-10) [2024-03-05]. https://doi.org/10.13700/j.bh.1001-5965.2023.0055. (in ChineseCHENG Huiming, SHI Zhaoyao. Hysteresis model of reducer and its application[EB/OL]. Journal of Beijing University of Aeronautics and Astronautics, (2023-05-10) [2024-03-05]. https://doi.org/10.13700/j.bh.1001-5965.2023.0055. (in Chinese) [7] CHENG Huiming,SHI Zhaoyao,YU Zhiyong,et al. Dynamic torsional stiffness of reducers and its testing method[J]. Applied Sciences,2023,13(16): 9277. doi: 10.3390/app13169277 [8] 程慧明,石照耀,于渤,等. 服务机器人小型关节回差测量的实验研究[J]. 仪器仪表学报,2020,41(5): 48-57. CHENG Huiming,SHI Zhaoyao,YU Bo,et al. Experiment research on hysteresis measurement of the small-size joint of service robot[J]. Chinese Journal of Scientific Instrument,2020,41(5): 48-57. (in ChineseCHENG Huiming, SHI Zhaoyao, YU Bo, et al. Experiment research on hysteresis measurement of the small-size joint of service robot[J]. Chinese Journal of Scientific Instrument, 2020, 41(5): 48-57. (in Chinese) [9] 徐航. 精密减速器回差测量与评价体系研究[D]. 北京: 北京工业大学,2018: 27-44. XU Hang. Research on mearsurement and evaluation sysytem of precision reducer lost motion[D]. Beijing: Beijing University of Technology,2018: 27-44. (in ChineseXU Hang. Research on mearsurement and evaluation sysytem of precision reducer lost motion[D]. Beijing: Beijing University of Technology, 2018: 27-44. (in Chinese) [10] YUE Huijun,WU Xiangkai,SHI Zhaoyao,et al. A comprehensive cycloid pin-wheel precision reducer test platform integrated with a new dynamic measurement method of lost motion[J]. Metrology and Measurement Systems,2021: 207-229. [11] 俞志勇,石照耀,程慧明,等. 精密减速器回差试验台的精度特性[J]. 光学 精密工程,2023,31(16): 2372-2382. YU Zhiyong,SHI Zhaoyao,CHENG Huiming,et al. Accuracy characteristic of test bench of lost motion of precision reducer[J]. Optics and Precision Engineering,2023,31(16): 2372-2382. (in Chinese doi: 10.37188/OPE.20233116.2372YU Zhiyong, SHI Zhaoyao, CHENG Huiming, et al. Accuracy characteristic of test bench of lost motion of precision reducer[J]. Optics and Precision Engineering, 2023, 31(16): 2372-2382. (in Chinese) doi: 10.37188/OPE.20233116.2372 [12] HAN Linshan,GUO Fei. Global sensitivity analysis of transmission accuracy for RV-type cycloid-pin drive[J]. Journal of Mechanical Science and Technology,2016,30(3): 1225-1231. doi: 10.1007/s12206-016-0226-2 [13] 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 and Machine Theory,2013,70: 116-128. doi: 10.1016/j.mechmachtheory.2013.07.006 [14] LIN Ken,CHAN K Y,LEE J. Kinematic error analysis and tolerance allocation of cycloidal gear reducers[J]. Mechanism and Machine Theory,2018,124: 73-91. doi: 10.1016/j.mechmachtheory.2017.12.028 [15] 石照耀,康焱,林家春. 基于齿轮副整体误差的齿轮动力学模型及其动态特性[J]. 机械工程学报,2010,46(17): 55-61. SHI Zhaoyao,KANG Yan,LIN Jiachun. Comprehensive dynamics model and dynamic response analysis of a spur gear pair based on gear pair integrated error[J]. Journal of Mechanical Engineering,2010,46(17): 55-61. (in Chinese doi: 10.3901/JME.2010.17.055SHI Zhaoyao, KANG Yan, LIN Jiachun. Comprehensive dynamics model and dynamic response analysis of a spur gear pair based on gear pair integrated error[J]. Journal of Mechanical Engineering, 2010, 46(17): 55-61. (in Chinese) doi: 10.3901/JME.2010.17.055 [16] 秦树人,高大启,何玮. 高速小型传动链动态精度测量系统的研究[J]. 重庆大学学报(自然科学版),1994,17(4): 1-5. QIN Shuren,GAO Daqi,HE Wei. The high speed and miniature system for measuring dynamic accuracy of drive chain[J]. Journal of Chongqing University,1994,17(4): 1-5. (in ChineseQIN Shuren, GAO Daqi, HE Wei. The high speed and miniature system for measuring dynamic accuracy of drive chain[J]. Journal of Chongqing University, 1994, 17(4): 1-5. (in Chinese) [17] 彭东林,张光辉,郭松涛,等. 全微机化传动误差检测分析系统的研制[J]. 重庆大学学报(自然科学版),1993,16(6): 70-74. PENG Donglin,ZHANG Guanghui,GUO Songtao,et al. Full microcomputerized testing and analysing system for transmission error[J]. Journal of Chongqing University (Natural Science Edition),1993,16(6): 70-74. (in ChinesePENG Donglin, ZHANG Guanghui, GUO Songtao, et al. Full microcomputerized testing and analysing system for transmission error[J]. Journal of Chongqing University (Natural Science Edition), 1993, 16(6): 70-74. (in Chinese) [18] 彭东林,郑永,陈自然,等. 基于误差传递理论及误差修正技术的高精度蜗轮母机研制[J]. 机械工程学报,2011,47(9): 157-163. PENG Donglin,ZHENG Yong,CHEN Ziran,et al. Research of high-precision worm gear machine tool based on error transmission theory and error correction technique[J]. Journal of Mechanical Engineering,2011,47(9): 157-163. (in Chinese doi: 10.3901/JME.2011.09.157PENG Donglin, ZHENG Yong, CHEN Ziran, et al. Research of high-precision worm gear machine tool based on error transmission theory and error correction technique[J]. Journal of Mechanical Engineering, 2011, 47(9): 157-163. (in Chinese) doi: 10.3901/JME.2011.09.157