摆线针轮行星传动机构的设计参数对压力角的影响机理
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摘要
为了研究摆线针轮传动机构设计参数与压力角之间的关系,对摆线轮与针轮之间的压力角及其影响因素进行了分析.基于齿轮啮合原理,建立摆线轮齿廓的数学模型,根据摆线针轮传动机构的多齿啮合特点,推导了压力角的数学表达式,并仿真了特殊位置处摆线轮与针轮之间的啮合关系.以工业机器人用RV减速器中的摆线针轮传动机构为例,应用VC++软件编程和AutoCAD软件仿真,详细论述了机构的偏心距、针轮分布圆半径以及针轮半径等机构设计参数对压力角的影响.通过对摆线轮与针轮不同啮合状态的仿真,揭示机构设计参数对压力角的影响机理.结果表明:偏心距对机构压力角的影响显著,针轮分布圆半径次之,而针轮半径的影响可以忽略不计.该研究为摆线针轮机构的参数设计和分析提供了理论依据.
To study the relationship between the design variables and the pressure angle of cycloid-pin gear transmission mechanism,the pressure angle between the cycloidal gear and the pin tooth and its influencing factors were analyzed. The mathematical model of the cycloidal gear was established using the conjugate theory. According to the characteristics of multi-teeth meshing in the cycloid-pin gear transmission mechanism,the expression of the pressure angle was derived,and the meshing state between the cycloidal gear and the pin tooth was simulated. By applying VC++ and AutoCAD software for calculation and simulation,the cycloid-pin gear mechanism of the RV reducer used in the industrial robot joints was applied as an example to clarify the influence of design variables on the pressure angle,such as eccentricity,radius of the pin position and the radius of the pin tooth. Based on the meshing simulation between the cycloidal gear and the pin tooth,the cause of the influence on the pressure angle was revealed. Results show that eccentricity has a great effect on the pressure angle,the radius of the pin tooth position is moderate,and the effect of the radius of pin tooth can be neglected. The research provides a theoretical basis for the parameter design and analysis of cycloid-pin gear mechanism.
To study the relationship between the design variables and the pressure angle of cycloid-pin gear transmission mechanism,the pressure angle between the cycloidal gear and the pin tooth and its influencing factors were analyzed. The mathematical model of the cycloidal gear was established using the conjugate theory. According to the characteristics of multi-teeth meshing in the cycloid-pin gear transmission mechanism,the expression of the pressure angle was derived,and the meshing state between the cycloidal gear and the pin tooth was simulated. By applying VC++ and AutoCAD software for calculation and simulation,the cycloid-pin gear mechanism of the RV reducer used in the industrial robot joints was applied as an example to clarify the influence of design variables on the pressure angle,such as eccentricity,radius of the pin position and the radius of the pin tooth. Based on the meshing simulation between the cycloidal gear and the pin tooth,the cause of the influence on the pressure angle was revealed. Results show that eccentricity has a great effect on the pressure angle,the radius of the pin tooth position is moderate,and the effect of the radius of pin tooth can be neglected. The research provides a theoretical basis for the parameter design and analysis of cycloid-pin gear mechanism.
引文
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[14]叶福民,朱如鹏,靳广虎,等.考虑齿侧间隙的非等模数非等压力角行星齿轮系统的均载特性研究[J].振动与冲击,2015,34(11):206-211.YE F M,ZHU R P,JIN G H,et al.Load sharing characteristics of a planetary gear train system with nonequivalent modulus and pressure angle considering backlashes[J].Journal of Vibration and Shock,2015,34(11):206-211.(in Chinese)
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[2]陈兵奎,梁栋,高艳娥.齿轮传动共轭曲线原理[J].机械工程学报,2014,50(1):130-136.CHEN B K,LIANG D,GAO Y E.The principle of conjugate curves for gear transmission[J].Chinese Journal of Mechanical Engineering,2014,50(1):130-136.(in Chinese)
[3]LITVIN F L,FENG P H.Computerized design and generation of cycloidal gearings[J].Mechanism and Machine Theory,1996,31(7):891-911.
[4]LIN W S,SHIH Y P,LEE J J.Design of a two-stage cycloidal gear reducer with tooth modifications[J].Mechanism and Machine Theory,2014,79:184-197.
[5]纪姝婷,张跃明,赵京.弧面凸轮专用加工机床中心距误差对凸轮廓面误差的影响[J].北京工业大学学报,2014,40(6):825-830.JI S T,ZHANG Y M,ZHAO J.Influence of the center distance error of machine tool on the profile error in machining globoidal cam[J].Journal of Beijing University of Technology,2014,40(6):825-830.(in Chinese)
[6]JI S T,ZHAO J,ZHANG Y M.An application of geodesics to the calculation of the rib-thickness of globoidal cam mechanisms[J].Mechanism and Machine Theory,2015,87:163-176.
[7]ZHANG Y M,JI S T,ZHAO J.Study on the geometric characteristics of mating surfaces of globoidal cam mechanisms[J].Mechanism and Machine Theory,2016,100:44-62.
[8]WEI B,WANG J X,ZHOU G W,et al.Mixed lubrication analysis of modified cycloidal gear used in the RV reducer[J].Proceedings of the Institution of Mechanical Engineers Part J:Journal of Engineering Tribology,2015,230(2):121-134.
[9]MIHAILIDIS A,EMMANOUIL A,KONSTANTINOS A.EHL film thickness and load dependent power loss of cycloid reducers[J].Proceedings of the Institution of Mechanical Engineers Part C:Journal of Mechanical Engineering Science,2016,230(7/8):1303-1317.
[10]XU L,YANG Y.Dynamic modeling and contact analysis of a cycloid-pin gear mechanism with a turning arm cylindrical roller bearing[J].Mechanism and Machine Theory,2016,104:327-349.
[11]GUAN T,SHI X.Force analysis considering manufacture error of pin-hole-output mechanism in cycloid drive.Chinese Journal of Mechanical Engineering,2002,15(2):142-144.
[12]DEMENEGO A,VECCHIATO D,LITVIN F L,et al.Design and simulation of meshing of a cycloidal pump[J].Mechanism and Machine Theory,2002,37(3):311-332.
[13]陈兵奎,梁栋,彭帅,等.共轭曲线齿轮啮合管齿面的几何及接触特性分析[J].西安交通大学学报,2015,49(3):85-94.CHEN B K,LIANG D,PENG S,et al.Analysis on geometric and contact characteristics of tubular meshing tooth surfaces for conjugate-curve gears[J].Journal of Xi'an Jiaotong University,2015,49(3):85-94.(in Chinese)
[14]叶福民,朱如鹏,靳广虎,等.考虑齿侧间隙的非等模数非等压力角行星齿轮系统的均载特性研究[J].振动与冲击,2015,34(11):206-211.YE F M,ZHU R P,JIN G H,et al.Load sharing characteristics of a planetary gear train system with nonequivalent modulus and pressure angle considering backlashes[J].Journal of Vibration and Shock,2015,34(11):206-211.(in Chinese)
[15]陈振宇,沈兆光,杨玉虎.摆线针轮行星传动机构啮合特性分析[J].机械设计,2015,32(10):9-14.CHEN Z Y,SHEN Z G,YANG Y H.Meshing characteristics analysis of cycloid pin gear planetary transmission mechanism[J].Journal of Machine Design,2015,32(10):9-14.(in Chinese)