【作者】 张鹏；

【导师】 安子军；

【作者基本信息】 燕山大学 ， 机械设计及理论， 2010， 博士

【摘要】 摆线钢球行星传动作为一种精密行星传动机构,其工作过程中所产生的振动,影响了机械设备的精度、生产效率和使用寿命,使得人们对其动态性能提出了更高的要求。研究摆线钢球行星传动系统的动力学问题,对其动态性能优化具有重要的意义,同时对工程中应用的其它行星传动系统也具有普遍的科学意义。首先,利用超静定方法建立了摆线钢球啮合副的非线性力学模型,通过求解能量平衡方程得到啮合副的载荷关系式。利用赫兹公式计算出啮合副接触区中心变形和中心压强等参数,并求出传动过程中各参数极值对应的啮合位置。利用叠加法积分求出半椭球状分布载荷作用下啮合副的接触区变形挠曲面方程、接触区表面以下不同深度处的应力分布,以及最大切应力的深度位置。建立了摆线钢球啮合副的有限元模型,根据啮合副的载荷分布状态对有限元模型进行加载,通过对啮合过程的有限元仿真,得到啮合副的应力分布状态,并对啮合过程中承载接触对的交替变化规律和啮合点的应力变化规律进行了分析。其次,综合考虑时变啮合刚度、轴承支承刚度和陀螺效应等影响因素,建立了摆线钢球行星传动系统在偏心轴随动坐标系下的多自由度平移—扭转耦合动力学模型,并推导出系统的运动微分方程和动力学方程,以揭示其固有特性。对系统的啮合刚度激励进行时域分析和频域分析,得到其频谱成分,并分析了不同系统参数对啮合刚度激励的影响。通过求解系统的特征值和特征向量问题,得到系统的各阶固有频率和主振型。对系统的固有频率进行灵敏度分析,进而探讨了系统参数和传动结构对各阶固有频率的影响。然后,通过对摆线钢球行星传动系统动力学方程的变换和解耦,构建了系统的参数振动分析模型。利用多尺度法计算出系统的组合共振频率,并分析了系统的动力稳定性。利用林滋泰德-庞加莱摄动方法推导出内共振状态下系统的各特征函数,得到系统的稳定区边界曲线,绘制出稳定图,并分析了系统的广义质量和啮合刚度对动力稳定性的影响。在系统的动力学方程内增加线性阻尼项,分析了系统阻尼对动力稳定性的影响。利用摄动法求解了系统的参数振动的稳态响应。最后,利用三维设计软件Pro/E对摆线钢球行星传动机构进行参数化造型,并进行虚拟装配。根据摆线钢球啮合副的正确啮合条件,研究了摆线槽的截面齿形、槽形角和槽深的设计准则,并推导出钢球密排结构对应的摆线短幅系数设计公式。利用Pro/E的Pro/NC模块设计了摆线槽的数控加工工序,通过轨迹加工方法模拟摆线槽的加工过程,并编制出摆线槽的数控铣削程序。总结了摆线钢球行星传动机构的设计步骤,并成功的加工制造出样机。更多还原

【Abstract】 The cycloid ball planetary transmission is a precise planetary transmission mechanism, and the vibration caused in working process will influence the precision, the production efficiency and the operating life of mechanical devices, so the higher requirements are present to improve the dynamic characteristics. By investigating the dynamic problems of the cycloid ball planetary transmission system, it has an important significance to the dynamic characteristics optimization, and offers a general scientific reference to the other planetary transmission systems in practical engineering applications.Firstly, the nonlinear mechanical model of the cycloid ball engagement pair is established using the hyperstatic method. The load of the engagement pair is present by solving the energy equilibrium equation. The central deformation and the central pressure of the engagement pair in contact zone are calculated by the Hertz contact formula, and the engagement positions of the parameter extremes in transmission process are obtained. The deformed deflection surface equation of contact zone, the stress distribution under contact surface, and the depth of the maximum shear stress are presented using the superposition method. The finite element models of the engagement pair are established, and the loads are applied to the models according to the load distribution of the engagement pair. The stress distribution states are present by the finite element simulation of the engagement process, and the alternate variation regularity of the loading contact pairs as well as the stress variation regularity of the engagement points is analyzed.Secondly, the translational-torsional coupling dynamic model of the cycloid ball planetary transmission system is established in the following coordinate system of the eccentric shaft, and the model includes some key factors such as the time-variant engagement rigidity, the bearing rigidity and the gyroscopic effect. The governing differential equations and the dynamic equations of system are derived to investigate the natural characteristics. The engagement rigidity excitation is analyzed in time-domain and frequency-domain. The frequency spectrum components of the engagement rigidity excitation are present, and the influences of the different system parameters to the engagement rigidity excitation are analyzed. The natural frequencies and the principal modes of system are present by solving the eigenvalues and the eigenvectors. The sensitivities of the natural frequencies are analyzed, and the influence of the system parameters as well as the transmission structures to the natural frequencies is discussed.Thirdly, the parametric vibration analytic model of the cycloid ball planetary transmission system is established by transformation and uncoupling of the dynamic equations. The combination resonance frequencies of system are calculated using the multi-scale method, and the dynamic stability of system is analyzed. The characteristic functions of system of the internal resonance are derived using the Lindstedt-Poincaréperturbation method, the boundary curves of the stability zones are obtained, the stability diagrams are drawn, and the influence of the generalized mass and the engagement rigidity to the dynamic stability is analyzed. The linear damping is added in the dynamic equations, and the influence of the damping to the dynamic stability is analyzed. The steady-state response of the parametric vibration of system is solved using the perturbation method.Finally, the parametric models and the simulated assembly of the cycloid ball planetary transmission mechanism are completed using the three-dimensional design software Pro/E. According to the accurate engagement conditions of the cycloid ball engagement pair, the design criterions for the sectional profile, the angle and the depth of the cycloid groove are present, and the design formula for the cycloid curtate coefficient of the compact arrangement structure of balls is also present. The numerical control manufacture process is designed using the module of Pro/NC. The manufacture process of the cycloid groove is simulated by the locus manufacture method, and the procedure of the numerical control milling is programmed. The design process of the cycloid ball planetary transmission mechanism is summarized, and the prototype is manufactured successfully.更多还原