单、双径向轴承安装时三叉式万向联轴器的附加弯矩分析
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摘要
为找出三叉式万向联轴器在安装和使用过程中出现振动、噪声的原因,分析采用单、双径向轴承安装三叉式万向联轴器输出轴时联轴器附加弯矩随输入轴转角及偏转角的分布规律。首先建立2种安装方式下联轴器的运动简图,应用空间机构坐标变换技术建立输入轴与输出轴的关系方程,推导出系统存在偏转角时输出轴的运动方程,表明输出轴采用单径向轴承安装时三叉式万向联轴器为准等角速传动,采用双径向轴承安装时其具有等角速传动特性。其次分析这2种安装方式下作用在输入轴和输出轴上的附加弯矩分量,根据虚位移原理确定三叉式万向联轴器输出轴在2种安装方式下系统均出现附加弯矩。通过分析发现:采用单径向轴承安装时,存在偏转弯矩,且一个运动周期内附加弯矩的波动频率是输入轴的3倍,呈正弦曲线变化,且附加弯矩的变化趋势为随偏转角的增大呈直线上升;双径向轴承安装时,偏转弯矩为零,附加弯矩随偏转角的增大而逐渐增大,未出现波动。结果表明:2种安装方式下三叉式万向联轴器上均产生附加弯矩,从而使系统产生振动效应。该结果对研究系统产生振动的原因、确定系统非线性动力学行为具有重要的意义。
To find out the causes of vibration and noise of the trigeminal universal joint which appeared in the installation and use process,the additional moment distribution with the varies of the input shaft angular and the deflection angle was analyzed.Kinematics diagrams of the trigeminal universal joint when the output shaft installed by single radial bearing or twin radial bearing were established.The system coordinates were established under the two installation ways,and the motion equations were established by the direction cosine matrix tools.It indicated that the trigeminal universal joint installed by the single radial bearing was an approximately isometric speed transmission,and was a constant velocity transmission with twin radial bearing installed.Furthermore,the additional moment component on the input shaft and the output shaft was analyzed under the two installation ways.According to the virtual displacement principle,the additional moment on the tripod universal joint when the output shaft installed by twin radial bearing and single radial bearing were determined.When installed by single radial bearing,the deflection moment exists and the vibration frequency of additional moment was three times of the input shaft as a sine curve.The variation trend of the additional moment was straight up with the in-crease of deflection angle.When installed by twin radial bearing,the deflection moment was zero and the additional moment increased gradually with the increase of deflection angle but did not fluctuate.The analysis revealed that additional moment existed in the trigeminal universal joint system under both installation ways would produce bending vibration.This study is of great significance to study the causes of vibration and determine the nonlinear dynamics of the system.
To find out the causes of vibration and noise of the trigeminal universal joint which appeared in the installation and use process,the additional moment distribution with the varies of the input shaft angular and the deflection angle was analyzed.Kinematics diagrams of the trigeminal universal joint when the output shaft installed by single radial bearing or twin radial bearing were established.The system coordinates were established under the two installation ways,and the motion equations were established by the direction cosine matrix tools.It indicated that the trigeminal universal joint installed by the single radial bearing was an approximately isometric speed transmission,and was a constant velocity transmission with twin radial bearing installed.Furthermore,the additional moment component on the input shaft and the output shaft was analyzed under the two installation ways.According to the virtual displacement principle,the additional moment on the tripod universal joint when the output shaft installed by twin radial bearing and single radial bearing were determined.When installed by single radial bearing,the deflection moment exists and the vibration frequency of additional moment was three times of the input shaft as a sine curve.The variation trend of the additional moment was straight up with the in-crease of deflection angle.When installed by twin radial bearing,the deflection moment was zero and the additional moment increased gradually with the increase of deflection angle but did not fluctuate.The analysis revealed that additional moment existed in the trigeminal universal joint system under both installation ways would produce bending vibration.This study is of great significance to study the causes of vibration and determine the nonlinear dynamics of the system.
引文
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[11]李松梅,常德功,杨福芹.三叉杆滑块式万向联轴器的传输能力分析[J].青岛科技大学学报(自然科学版),2016,37(2):105-109.LI Song-mei,CHANG De-gong,YANG Fu-qin.Transmission capacity analysis of the tripod sliding universal joint[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2016,37(2):105-109.
[12]常德功,邵晨,李松梅.一种减振型三叉杆倾斜滑块式等角速万向联轴器:ZL201320595302.9[P].2014-03-12.CHANG De-gong,SHAO Chen,LI Song-mei.A damping type of the tripod sliding constant universal joint:ZL201320595302.9[P].2014-03-12.
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[14]张启先.空间机构的分析与综合[M].北京:机械工业出版社,1984:77-80.ZHANG Qi-xian.Analysis and synthesis of space agencies[M].Beijing:China Machine Press,1984:77-80.
[15]王鸿恩,罗义艮,贺明.三维空间多节万向传动轴扭振的分析计算[J].机械工程学报,2000,36(6):37-41.WANG Hong-en,LUO Yi-gen,HE Ming.The torsional vibration of the three-dimensional multi-section propeller shaft[J].Journal of Mechanical Engineering,2000,36(6):37-41.
[16]杨福芹.三叉杆滑块式等角速万向联轴联轴器的理论研究[D].上海:上海大学机电工程学院,2010:14-17.YANG Fu-qian.Theory research of tripod constant velocity joints[D].Shanghai:Shanghai University,College of Electromechanical Engineering,2010:14-17.
[17]常德功,庞峰,邹玉静.三叉杆滑移式万向联轴器的动力学分析[J].机械科学与技术,2004,23(3):284-285.CHANG De-gong,PANG Feng,ZOU Yu-jing.Dynamics analysis of the tripod sliding universal coupling[J].Mechanical Science and Technology,2004,23(3):284-285.
[18]WATANABE K,KAWAKASTU T,NAKAO S.Kinematic and static analyses of tripod constant velocity joints of the spherical end spider type[J].Journal of Mechanical Design,2005,127(6):1137-1144.
[2]SERVETO S,MARIOT J P,DIABY M.Modelling and measuring the axial force generated by tripod joint of automotive drive-shaft[J].Multibody System Dynamics,2008,19(3):209-226.
[3]DESMIDT H A,KANG W W.Stability of segmented supercritical driveline with non-constant velocity couplings subjected to misalignment and torque[J].Journal of Sound and Vibration,2004,277(4):895-918.
[4]CAI Q C,LEE K H,SONG W L,et al.Simplified dynamics model for axial force in tripod constant velocity joint[J].International Journal of Automotive Technology,2012,13(5):751-757.
[5]SAI J S,KANG T W,KIM C M.Experimental study of the characteristics of idle vibrations that result from axial forces and the spider positions of constant velocity joints[J].International Journal of Automotive Technology,2010,11(3):355-361.
[6]朱拥勇,王德石,冯昌林.万向铰驱动的偏斜转子系统传递力矩分析[J].海军工程大学学报,2010,22(5):5-9.ZHU Yong-yong,WANG De-shi,FENG Chang-lin.Analysis of transmitted moment of misaligned rotor system driven by universal joint[J].Journal of Naval Universal of Engineering,2010,22(5):5-9.
[7]王学锋,常德功,王江忠.滑移型三叉式联轴器运动学建模[J].农业机械学报,2009,40(9):7-11.WANG Xue-feng,CHANG De-gong,WANG Jiangzhong.Kinematic model of tripod sliding universal joints[J].Transactions of the Chinese Society for Agricultural Machinery,2009,40(9):7-11.
[8]王学锋,常德功.滑移型三叉式联轴器抗磨损结构及数学建模[J].中国机械工程,2009,20(5):538-541.WANG Xue-feng,CHANG De-gong.Anti-wear structure of tripod sliding universal joints and its mathematics modeling[J].China Mechanical Engineering,2009,20(5):538-541.
[9]WANG Xue-feng,CHANG De-gong.Kinematic and dynamic analyses of tripod sliding universal joints[J].Journal of Mechanical Design,2009,131(6):061011.
[10]常德功,李松梅.双径向轴承安装三叉杆滑块式万向联轴器机构的运动分析[J].机械工程学报,2015,51(13):218-226.CHANG De-gong,LI Song-mei.Kinematic analysis of the trigeminal sliding universal joint mechanism installed twin radial bearings[J].Journal of Mechanical Engineering,2015,51(13):218-226.
[11]李松梅,常德功,杨福芹.三叉杆滑块式万向联轴器的传输能力分析[J].青岛科技大学学报(自然科学版),2016,37(2):105-109.LI Song-mei,CHANG De-gong,YANG Fu-qin.Transmission capacity analysis of the tripod sliding universal joint[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2016,37(2):105-109.
[12]常德功,邵晨,李松梅.一种减振型三叉杆倾斜滑块式等角速万向联轴器:ZL201320595302.9[P].2014-03-12.CHANG De-gong,SHAO Chen,LI Song-mei.A damping type of the tripod sliding constant universal joint:ZL201320595302.9[P].2014-03-12.
[13]刘善增,余跃庆,侣国宁,等.3自由度并联机器人的运动学和动力学分析[J].机械工程学报,2009,45(8):11-17.LIU Shan-zeng,YU Yue-qing,SI Guo-ning,et al.Kinematic and dynamic analysis of a three-degree of freedom parallel manipulator[J].Journal of Mechanical Engineering,2009,45(8):11-17.
[14]张启先.空间机构的分析与综合[M].北京:机械工业出版社,1984:77-80.ZHANG Qi-xian.Analysis and synthesis of space agencies[M].Beijing:China Machine Press,1984:77-80.
[15]王鸿恩,罗义艮,贺明.三维空间多节万向传动轴扭振的分析计算[J].机械工程学报,2000,36(6):37-41.WANG Hong-en,LUO Yi-gen,HE Ming.The torsional vibration of the three-dimensional multi-section propeller shaft[J].Journal of Mechanical Engineering,2000,36(6):37-41.
[16]杨福芹.三叉杆滑块式等角速万向联轴联轴器的理论研究[D].上海:上海大学机电工程学院,2010:14-17.YANG Fu-qian.Theory research of tripod constant velocity joints[D].Shanghai:Shanghai University,College of Electromechanical Engineering,2010:14-17.
[17]常德功,庞峰,邹玉静.三叉杆滑移式万向联轴器的动力学分析[J].机械科学与技术,2004,23(3):284-285.CHANG De-gong,PANG Feng,ZOU Yu-jing.Dynamics analysis of the tripod sliding universal coupling[J].Mechanical Science and Technology,2004,23(3):284-285.
[18]WATANABE K,KAWAKASTU T,NAKAO S.Kinematic and static analyses of tripod constant velocity joints of the spherical end spider type[J].Journal of Mechanical Design,2005,127(6):1137-1144.