Finite Element Analysis And Structural Optimization Design Of Ultra-short Flexible Wheel Of Harmonic Gear Transmission

With rapid development of robot technology,especially the application of industrial robots,the performance and cost of harmonic reducer are becoming more and more important.Ultra-short harmonic drive is widely used in small joints of industrial robots because it can better adapt to the robot joint requirement.Shorter axial size of the flexspline,much higher stress is produced in the bottom of flexspline.Therefore,the bottom stress analysis and the structural optimization of flexspline bottom are the key problems for the ultra-short harmonic drive.At present,no theoretical method is found to accurately calculate the assembly stress and transmission stress of flexspline,and the finite element method is the main method to calculate the deformation and stress of flexspline in assembly state and transmission state.Based on analysis of cup-shaped and hat-shaped characteristic of flexspline and their parameters relation,parametric models of cup-shaped and hat-shaped flexspline are established.According to the radial deformation of standard elliptical wave generator,the radial displacement constraint is applied to the neutral surface of the tooth ring,and the deformation and stress of flexspline are obtained.According to the distribution of meshing force given by an empirical formula in reference,the transmission stress in transmission state is obtained by applying the circumferential meshing forces on neutral surface and corresponding displacement constraints on the flexspline.Secondly,based on cup-shaped and hat-shaped parametric models,the ratio of length to diameter,fillet radius at the bottom,fillet radius near the diaphragm plate and the thickness of cup bottom are selected to discuss the stress sensitivity in the assembly state and transmission state,respectively,in order to find the key geometric parameter to decrease the maximum assembling stress and maximum transmission stress,respectively.Three different variations of the bottom thickness are selected and their parametric models are established.Finally,the assembly stress and transmission stress are reduced by optimizing the variation of the thickness of bottom.Cubic spline curve is introduced to express the variation of bottom thickness with APDL language,a program of complex method is built to optimize to the maximum assembly stress and the transmission stress,respectively,and the optimization results is verified with the application of zero order and first order optimization procedure.The research found that the maximum stress in the flexspline bottom is much higher than that of the tooth ring.The maximum assembly stress and maximum transmission stress can be reduced by reducing the fillet radius of flexspline bottom.The maximum assembly stress and the maximum transmission stress increases with increase of the fillet radius near the diaphragm plate,but the transmission stress of cup-shaped flexspline will decrease.Increasing the width of diaphragm plate reduces the assembly stress and transmission stress of cup-shaped flexspline and hat-shaped flexspline.Wider diaphragm plate leads to lower assembly stress and transmission stress in the bottom.Increasing wall thickness increases the maximum assembly stress and maximum transmission stress of hat-shaped flexspline and the maximum assembly stress of cup-shaped flexspline,but reduce the maximum transmission stress of cup-shaped flexspline.Monotonous increase inward the flexspline bottom thickness reduces the maximum stress of the flexspline bottom.Compared with hat-shaped flexspline,higher stress in the bottom of cup-shaped flexspline is produced by transmission load.