内啮合锥齿轮章动传动的运动学分析
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摘要
章动传动的实质为陀螺运动,即刚体绕定点转动。通过以图解的形式描述章动传动的三个欧拉角及用其描述的刚体绕定点转动运动学方程的建立过程,推导出章动轮角速度在定坐标系及动坐标系上的投影表达式。再结合空间共轭曲线锥齿轮啮合原理知识,构建传动坐标系统,利用齐次坐标变换及齿轮运动学原理,推导出两锥齿轮的相对运动速度。分析表明,此理论推导的计算方法在一定程度上将抽象、繁难、复杂的运动学问题得到简化分步,转变为立体直观的空间描述,推导过程简单清晰,并且数式转换准确易见。
The essence of the nutation drive is the gyro's motion, that is, the rigid body with a fixed point. The three Euler angles of the nutation drive are described in the graphical form and described in the process of the establishment of the kinematics equation of the rigid body around the fixed point rotation. The projection expression of angular velocity of the nutation gear is deduced in the fixed coordinate system and of the dynamic coordinate system. Combined with the spatial conjugate curve bevel gear meshing theory knowledge, the system of transmission coordinates is constructed, and the relative motion velocity of two bevel gears is deduced by using homogeneous coordinate transformation and the principle of gear kinematics. The analysis shows that, to a certain extent,abstract, complicated and complex kinematics problems are simplified and calculated step by step with the calculation method. The analysis process is transformed into a three-dimensional intuitive space description, the derivation process is simple and clear, and the numerical conversion is accurate and easy to see.
The essence of the nutation drive is the gyro's motion, that is, the rigid body with a fixed point. The three Euler angles of the nutation drive are described in the graphical form and described in the process of the establishment of the kinematics equation of the rigid body around the fixed point rotation. The projection expression of angular velocity of the nutation gear is deduced in the fixed coordinate system and of the dynamic coordinate system. Combined with the spatial conjugate curve bevel gear meshing theory knowledge, the system of transmission coordinates is constructed, and the relative motion velocity of two bevel gears is deduced by using homogeneous coordinate transformation and the principle of gear kinematics. The analysis shows that, to a certain extent,abstract, complicated and complex kinematics problems are simplified and calculated step by step with the calculation method. The analysis process is transformed into a three-dimensional intuitive space description, the derivation process is simple and clear, and the numerical conversion is accurate and easy to see.
引文
[ 1 ] 张展.齿轮减速器现状及发展趋势[J].水利电力机械,2001(1):58-59.
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[ 8 ] 林铮,姚立纲,姚琢,等.章动内啮合渐开线螺旋锥齿轮齿面接触分析[J].武夷学院学报,2014,33(2):70-74.
[ 9 ] 蔡英杰,姚立纲,顾炳.双圆弧螺旋锥齿轮章动传动运动和动力学仿真[J].传动技术,2007(4):22-25.
[10] JINLONG H,LIGANG Y,WENTAO J,et al.Kinematic modeling for the nutation drive based on screw theory [J].Procedia CIRP,2015,36.
[11] 姜玉明,蔡敏.欧拉运动学方程[J].辽宁教育学院学报,1999(5):38.
[12] 张立杰,潘存云,李明宇,等.全方位偏摆关节机构运动分析及仿真[J].机械设计与研究,2007,23(4):27-31.
[13] 梁栋.共轭曲线齿轮啮合理论研究[D].重庆:重庆大学,2015:17-23.
[14] RULONG T,BINGKUI C,CHANGYAN P.General mathematical model of spiral bevel gears of continuous pure-rolling contact [J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2015,229(15):2810-2826.
[15] 杨东超,刘莉,汪劲松,等.利用奇次变换矩阵进行运动学正问题分析[J].机械设计与研究,2002,18(2):20-22.
[ 2 ] 李智刚,金成哲.章动理论在降速传动中的应用[J].机械传动,1996(1):57-58.
[ 3 ] 何文杰.滚锥齿章动活齿传动装置的有限元分析[D].大连:大连交通大学,2015.
[ 4 ] UZUKA K,ENOMOTO I,SUZUMORI K.Development of nutation motors (4th report,development of small-sized and high torque pneumatic nutation motor by the OFW type bevel gears and principle of lever) [J].Nihon Kikai Gakkai Ronbunshu,Hen/Transactions of the Japan Society of Mechanical Engineers (Part C),2007,73(6):1731-1737.
[ 5 ] SARIBAY Z B,BILL R C.Design analysis of pericyclic mechanical transmission system [J].Mechanism and Machine Theory,2013,61:102-122.
[ 6 ] 赵建衡,张根保.章动轮系及其传动比计算[J].机械科学与技术,1996(5):21-23.
[ 7 ] 刘顺淑.章动齿轮减速装置传动比的计算[J].渝州大学学报:自然科学版,1997(4):30-34.
[ 8 ] 林铮,姚立纲,姚琢,等.章动内啮合渐开线螺旋锥齿轮齿面接触分析[J].武夷学院学报,2014,33(2):70-74.
[ 9 ] 蔡英杰,姚立纲,顾炳.双圆弧螺旋锥齿轮章动传动运动和动力学仿真[J].传动技术,2007(4):22-25.
[10] JINLONG H,LIGANG Y,WENTAO J,et al.Kinematic modeling for the nutation drive based on screw theory [J].Procedia CIRP,2015,36.
[11] 姜玉明,蔡敏.欧拉运动学方程[J].辽宁教育学院学报,1999(5):38.
[12] 张立杰,潘存云,李明宇,等.全方位偏摆关节机构运动分析及仿真[J].机械设计与研究,2007,23(4):27-31.
[13] 梁栋.共轭曲线齿轮啮合理论研究[D].重庆:重庆大学,2015:17-23.
[14] RULONG T,BINGKUI C,CHANGYAN P.General mathematical model of spiral bevel gears of continuous pure-rolling contact [J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2015,229(15):2810-2826.
[15] 杨东超,刘莉,汪劲松,等.利用奇次变换矩阵进行运动学正问题分析[J].机械设计与研究,2002,18(2):20-22.