基于接触应力均化的摆线轮修形方法
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摘要
在传统组合修形的基础上,综合分析摆线轮传动精度和齿面接触应力,提出一种基于接触应力均化的摆线轮修形方法。将摆线针轮齿廓传动压力角最小的工作段作为修形量优化的区间,分析所需齿侧间隙,选定合理的转角修形量范围;以转角修形齿廓为目标齿廓,用等距和移距组合修形逼近方法确定相应的等距和移距修形量,并将其代入摆线轮传动受力方程,得到优化区间内同时啮合各齿之间接触应力分布方差;以同时啮合各齿之间接触应力分布方差最小为优化目标,在转角修形量范围内,搜索出最佳的转角修形量以及对应的组合修形量。仿真和试验结果表明,相较于传统方法,该方法能够提高传动精度,并显著改善齿面受力状况,延长摆线轮使用寿命。
Based on the traditional combination modification methods, a cycloid gear modification method involving with contact stress equalization was proposed after comprehensively analyzing the transmission accuracy and tooth surface contact stress. Firstly, the working sections with the minimum pressure angle of the cycloidal gear transmission were used as the intervals for the shaping amount modification. Secondly, required backlashes were analyzed and a reasonable range of corner modification was selected; Then, with the angle modification as the target profile, approximation was made by combinion of equidistant and displacement modification, and finally was used to determine the corresponding equidistant and distance modification amount. The variances of contact stress distribution among teeth meshing at the same time in the optimum interval were obtained after the modification amounts were brought into the equation of the cycloidal transmission. Finally, with the objective of minimizing the variance of contact stress distribution among teeth meshing at the same time, the optimum angular modification and corresponding combined modification were searched within the range of angular modification. The simulation and test results show that this method may improve the transmission accuracy, the forced conditions of the tooth surfaces and prolong the services life of cycloidal gears, compared with the traditional methods.
Based on the traditional combination modification methods, a cycloid gear modification method involving with contact stress equalization was proposed after comprehensively analyzing the transmission accuracy and tooth surface contact stress. Firstly, the working sections with the minimum pressure angle of the cycloidal gear transmission were used as the intervals for the shaping amount modification. Secondly, required backlashes were analyzed and a reasonable range of corner modification was selected; Then, with the angle modification as the target profile, approximation was made by combinion of equidistant and displacement modification, and finally was used to determine the corresponding equidistant and distance modification amount. The variances of contact stress distribution among teeth meshing at the same time in the optimum interval were obtained after the modification amounts were brought into the equation of the cycloidal transmission. Finally, with the objective of minimizing the variance of contact stress distribution among teeth meshing at the same time, the optimum angular modification and corresponding combined modification were searched within the range of angular modification. The simulation and test results show that this method may improve the transmission accuracy, the forced conditions of the tooth surfaces and prolong the services life of cycloidal gears, compared with the traditional methods.
引文
[1] CHMURAWA M,LOKIEC A.Distribution of Loads in Cycloidal Planetary Gear Cycloid including Modification of Equidistant[C]//Proceedings of the 16th European ADAMS User Conference.Berchtesgaden,2001:14-15.
[2] 库特略夫采 В Н.齿轮减速器的结构与计算[M].江耕华,顾永寿,泽.上海:上海科学技术出版社,1982.KUTLOVSCHE B Н.Structure and Calculation of Gear Reducer [M].JIANG Genghua,GU Yongshou,Trans.Shanghai:Shanghai Science and Technology Press,1982.
[3] LEHMANN M.Die Berechnung der Kr?fteim Trochoiden-Getriebe[J].Antriebstechnik,1979,18(2):613-616.
[4] 关天民.FA型摆线针轮行星传动齿形优化方法与相关理论的研究[D].大连:大连交通大学,2005.GUAN Tianmin.Research on Optimization Method and Related Theory of FA Type Cycloid Pinwheel Planetary Transmission[D].Dalian:Dalian Jiaotong University,2005.
[5] 王秋成.摆线轮齿形修整的优化[J].浙江工业大学学报,1989(1):7-16.WANG Qiucheng.Optimization of Tooth Profile Trimming of Cycloid[J].Journal of Zhejiang University of Technology,1989(1):7-16.
[6] 严勇,汤子琳.摆线齿轮最佳复合修正齿形的研究[J].重庆大学学报(自然科学版),1993,16(5):137-140.YAN Yong,TANG Zilin.Research on the Best Composite Modified Tooth Profile of Cycloidal Gear[J].Journal of Chongqing University(Natural Science Edition),1993,16(5):137-140.
[7] 关天民,张东生.摆线针轮行星传动中反弓齿廓研究及其优化设计[J].机械工程学报,2005,41(1):151-156.GUAN Tianmin,ZHANG Dongsheng.Research and Optimization Design of Anti-bow Profile in Cycloid Pinwheel Planetary Transmission[J].Journal of Mechanical Engineering,2005,41(1):151-156.
[8] 陈振宇.RV减速器的误差建模与摆线齿廓修形[D].天津:天津大学,2014.CHEN Zhenyu.Error Modeling and Cycloid Profile Reconstruction of RV Reducer [D].Tianjin:Tianjin University,2014.
[9] 王新春.摆线轮齿廓修形及RV减速器设计[D].哈尔滨:哈尔滨工业大学,2017.WANG Xinchun.Cycloidal Profile Modification and RV Reducer Design [D].Harbin:Harbin Institute of Technology,2017.
[10] 洪淳赫.关于修正摆线轮啮合初始间隙分布规律的探讨[J].机械传动,1991(1):31-34.HONG Chunhe.Discussion on Correcting the Distribution Law of Initial Clearance of Cycloidal Engagement[J].Mechanical Transmission,1991(1):31-34.
[11] 李力行.摆线针轮行星传动的齿形修正及受力分析[J].大连交通大学学报,1984,22(4):32-43.LI Lixing.Tooth Shape Correction and Force Analysis of Cycloidal Pinion Planetary Transmission[J].Journal of Dalian Jiaotong University,1984,22(4):32-43.
[12] GUAN T.Optimum Profile Modification on Cycloid Disks in the Cycloid Gearing Mechanism with Small Teeth Difference[J].China Mechanical Engineering,2002,13(10):805-811.
[2] 库特略夫采 В Н.齿轮减速器的结构与计算[M].江耕华,顾永寿,泽.上海:上海科学技术出版社,1982.KUTLOVSCHE B Н.Structure and Calculation of Gear Reducer [M].JIANG Genghua,GU Yongshou,Trans.Shanghai:Shanghai Science and Technology Press,1982.
[3] LEHMANN M.Die Berechnung der Kr?fteim Trochoiden-Getriebe[J].Antriebstechnik,1979,18(2):613-616.
[4] 关天民.FA型摆线针轮行星传动齿形优化方法与相关理论的研究[D].大连:大连交通大学,2005.GUAN Tianmin.Research on Optimization Method and Related Theory of FA Type Cycloid Pinwheel Planetary Transmission[D].Dalian:Dalian Jiaotong University,2005.
[5] 王秋成.摆线轮齿形修整的优化[J].浙江工业大学学报,1989(1):7-16.WANG Qiucheng.Optimization of Tooth Profile Trimming of Cycloid[J].Journal of Zhejiang University of Technology,1989(1):7-16.
[6] 严勇,汤子琳.摆线齿轮最佳复合修正齿形的研究[J].重庆大学学报(自然科学版),1993,16(5):137-140.YAN Yong,TANG Zilin.Research on the Best Composite Modified Tooth Profile of Cycloidal Gear[J].Journal of Chongqing University(Natural Science Edition),1993,16(5):137-140.
[7] 关天民,张东生.摆线针轮行星传动中反弓齿廓研究及其优化设计[J].机械工程学报,2005,41(1):151-156.GUAN Tianmin,ZHANG Dongsheng.Research and Optimization Design of Anti-bow Profile in Cycloid Pinwheel Planetary Transmission[J].Journal of Mechanical Engineering,2005,41(1):151-156.
[8] 陈振宇.RV减速器的误差建模与摆线齿廓修形[D].天津:天津大学,2014.CHEN Zhenyu.Error Modeling and Cycloid Profile Reconstruction of RV Reducer [D].Tianjin:Tianjin University,2014.
[9] 王新春.摆线轮齿廓修形及RV减速器设计[D].哈尔滨:哈尔滨工业大学,2017.WANG Xinchun.Cycloidal Profile Modification and RV Reducer Design [D].Harbin:Harbin Institute of Technology,2017.
[10] 洪淳赫.关于修正摆线轮啮合初始间隙分布规律的探讨[J].机械传动,1991(1):31-34.HONG Chunhe.Discussion on Correcting the Distribution Law of Initial Clearance of Cycloidal Engagement[J].Mechanical Transmission,1991(1):31-34.
[11] 李力行.摆线针轮行星传动的齿形修正及受力分析[J].大连交通大学学报,1984,22(4):32-43.LI Lixing.Tooth Shape Correction and Force Analysis of Cycloidal Pinion Planetary Transmission[J].Journal of Dalian Jiaotong University,1984,22(4):32-43.
[12] GUAN T.Optimum Profile Modification on Cycloid Disks in the Cycloid Gearing Mechanism with Small Teeth Difference[J].China Mechanical Engineering,2002,13(10):805-811.