Dynamic Modeling for Spur Planetary Gear Transmission with Flexible Ring Gear

Abstract

An elasto-dynamic model for spur planetary gear transmission(SPGT) is presented,in which the flexibility of ring gear,time-varying mesh stiffness,bearing stiffness,gyroscopic effect are accounted in.The continuous flexible ring gear is discreted into a serial of rigid ring gear segments connected with each other through equivalent virtual springs.The flexibility of ring gear is represented by the stiffness of proposed virtual springs.The mesh condition between ring gear segments and planetary gear is derived and the relative displacements among each component are analyzed.By combining the motion equations of each component,the governing equations of the planetary system are obtained.By solving the eigenvalue problem of system governing equations,the natural frequencies and corresponding mode shapes can be classified.Finally,the effects of ring gear flexibility as well as mounting conditions on system inherent characteristics are discussed.The simulation results reveal that there are two categories of vibration modes in SPGT,i.e.the rotational mode and the translational mode,in which the ring gear and the planetary gears undergo complex planar vibrations.In addition,the system lower natural frequencies are affected by ring gear flexibility and mounting conditions.The flexibility of ring gear will decrease the lower natural frequencies and this effect is more obvious when ring gear is floating radially or circumferentially rather than it is fixed.