CAJ | 학술논문

考虑摩擦与参数激励影响建立摆线锥齿轮副啮合模型。以齿轮副啮合点间沿啮合线相对位移为广义坐标，用 Lagrange 原理建立主、从动齿轮扭转振动平衡方程，通过降阶、解耦及归一化获得系统动力学方程。采用四五阶Runge-Kutta 法对动力学方程求解，给出摩擦因子对轮齿啮合点位移响应关系曲线；基于系统参数激励，对比分析有无摩擦时阻尼水平、外载荷、传递误差、刚度及激励频率对振动特性影响规律，给出相应参数激励下位移响应关系曲线。仿真结果表明，摩擦能有效抑制轮齿啮合点参数激励位移响应幅值，使峰值频率发生漂移；摩擦、激励频率均能改变系统运动状态、增加系统运动的复杂性。
고필마찰여삼수격려영향건립파선추치륜부교합모형。이치륜부교합점간연교합선상대위이위엄의좌표，용 Lagrange 원리건립주、종동치륜뉴전진동평형방정，통과강계、해우급귀일화획득계통동역학방정。채용사오계Runge-Kutta 법대동역학방정구해，급출마찰인자대륜치교합점위이향응관계곡선；기우계통삼수격려，대비분석유무마찰시조니수평、외재하、전체오차、강도급격려빈솔대진동특성영향규률，급출상응삼수격려하위이향응관계곡선。방진결과표명，마찰능유효억제륜치교합점삼수격려위이향응폭치，사봉치빈솔발생표이；마찰、격려빈솔균능개변계통운동상태、증가계통운동적복잡성。
A meshing model of cycloid bevel gear was established,considering the effect of friction and parameter excitation.The relative displacements along the line of action of gear meshing point was taken as generalized coordinates, the torsional vibration equation of pinion and gear was obtained by using Lagrange principle,and then the system dynamics equation was derived through order reduction,decoupling and normalization.Adopting fourth-fifth order Runge-Kutta method to solve the dynamic equation,the curve of the displacement response at tooth meshing point versus friction factor was given.Under system parameter excitation,the influences of damping level,external load,transmission error,stiffness and excitation frequency on vibration characteristics of meshing point were analysed with and without consideration of friction effect respectively.The displacement response curves corresponding to parameter excitation were also presented. The simulation results show that:the displacement response amplitude at meshing point under parametric excitation is effectively restrained by friction,the peak frequency drifts and the excitation frequency and the friction can both change the motion behavior and increase the complexity of system movement.