双输入面齿轮分流-并车传动系统固有特性分析

Analysis of natural characteristics of double input face gear split-parallel transmission system

以双输入面齿轮分流-并车传动系统为研究对象,基于集中参数法建立包含传动误差、啮合阻尼和支撑刚度等参数的平移-扭转耦合动力学模型,通过分析各齿轮副间的相对位移关系及其受力情况,依据牛顿第二定律建立各齿轮运动微分方程,利用动力学方程的特征值计算得到系统的固有频率和模态振型,并研究啮合刚度和支撑刚度对固有频率的影响规律。通过求解系统模态应变能和动能,揭示各齿轮模态能较大时所对应的频率阶次。研究结果表明:在7种重根对应的固有频率中,1重根对应的固有频率个数最多,多包含高阶频率;系统包含多个振型,每一传动级齿轮均存在独特的平移振动模式和扭转振动模式,在重根数相同的固有频率对应的振型矢量中,多种振动模式并存;对于总的系统模态能,第46阶频率下的总应变能最大,此时系统整体变形最大,第60阶频率下的总动能最大,此时系统振动最剧烈;高阶固有频率对啮合刚度和支撑刚度的变化更敏感,且敏感性随刚度的增大而依次增加;同时,系统刚度的变化会使固有频率在遇到相近频率时产生模态跃迁现象,振动模式发生交换,之后维持不变,直至再次遇到频率接近的情况才会再次发生模态跃迁,故在系统动态设计中尽可能避开模态跃迁点。

The double input face gear split-parallel transmission system was taken as the research object,and the translation-torsion coupling dynamic model including transmission errors,meshing damping and support stiffness was established based on the lumped parameter method.In addition,by analyzing the relative displacement relationship and force situation of each gear pair,the motion differential equations of each gear were established according to Newton's second law.Meanwhile,the natural frequencies and mode shapes of the system were obtained through utilizing the eigenvalue of the dynamic equation,and the influence laws of the meshing stiffness and support stiffness on the natural frequencies were also studied.By solving the modal strain energy and kinetic energy of the system,the frequency order corresponding to the larger modal energy of each gear was revealed.The results show that among the natural frequencies corresponding to the 7 multiple roots,1 multiple root has the largest number of natural frequency,most of which contains high-order frequencies.The system contains many vibration modes,and there are unique translational vibration modes and torsional vibration modes of each drive stage gear.Similarly,in the vibration mode vector corresponding to the natural frequency with the same number of multiple roots,multiple vibration modes coexist.For the total system modal energy,the total strain energy at the 46th order frequency is the largest,and the system overall deformation is the largest,and the total kinetic energy at the 60th order frequency is the largest,and the system vibration is the most intense.The higher-order natural frequencies are more sensitive to changes in meshing stiffness and support stiffness,and the sensitivity increases sequentially with the increase of stiffness.Meanwhile,the change of the system stiffness will lead to modal transition when the natural frequencies encounter similar frequencies,and the vibration modes will be exchanged suddenly,and then it will remain unchanged until the frequencies are close again.Therefore,The mode transition points should be avoided as far as possible in the dynamic design.