Wave Generator-Flexible Wheel Contact Mechanical Properties And Fatigue Life Analysis

Harmonic gear drive is widely used in high-end fields such as industrial robots,aerospace,medical and optical fields.It has the ability to work normally in the vacuum,strong radiation and large temperature difference environment.The failure of harmonic gear drive is mainly caused by the fatigue fracture of flexible wheel and the fatigue damage of flexible bearing.Therefore,it is of practical significance to analyze the contact mechanical characteristics and the fatigue life characteristics of flexible wheel and flexible bearing of thin-walled vulnerable components.In this paper,the finite element model of wave generator-flexible wheel contact mechanics is established.The contact mechanics analysis and fatigue life of thin-wall vulnerable members of flexible gears and flexible bearings are studied.The main contents are as follows:(1)The influence of structural parameters on the stress characteristics of flexible wheels is analyzed.The three-dimensional finite element models of the three basic components of harmonic gear reducer,i.e.flexible wheel,rigid wheel and wave generator,are established respectively.Then,the meshing force of the flexible wheel teeth is calculated.By changing the cylinder length,the wall thickness of the cylinder bottom,the wall thickness of the smooth cylinder and the load value,the maximum stress change curve of the flexible wheel ring,the smooth cylinder and the flexible wheel bottom is obtained,and its stress to the flexible wheel is analyzed.(2)The internal load distribution of flexible bearing is analyzed.Based on the theory of thin-walled ring and hertz contact,considering the contact deformation of ball and ferrule of flexible bearing and the deflection deformation of ferrule,according to the condition of deformation coordination,the mathematical model of internal load distribution of flexible bearing is established,which is solved by Newton-Raphon iteration method,and the internal load distribution law of flexible bearing is obtained.(3)The kinematic characteristics of the nodes at the center of the ball and at the contact between the sphere and the inner and outer rings of the flexible bearing before and after assembly deformation are analyzed by using explicit dynamic finite element method.Through the simulation,the time-domain curves of the displacement,velocity and acceleration of the joint are obtained.The finite element simulation results are compared with the theoretical analytical results.It is found that the error values of each physical quantity are within 5%,which proves the use of finite element software.(4)The differential equations of free vibration of flexible wheel shell expressed by displacement components are established.By changing the values of the axial half wave number m and the circumferential total wave number n,the ratio of the axial displacement amplitude to the normal displacement amplitude and the ratio of the tangential displacement amplitude to the normal displacement amplitude of the flexible wheel shell under different dimensionless frequency coefficients are calculated.The contour map and the vibration mode curve of the three displacement directions are obtained respectively,and the correspondence between the external excitation frequency and the vibration mode curve of the flexible wheel shell is analyzed.(5)The influence of assembly accuracy on the contact mechanical characteristics of wave generator flexible wheel is analyzed.By changing the offset of the cosine cam wave generator along the positive direction of the x-axis and the y-axis,and then performing dynamic simulation on the wave generator-rubber contact mechanics finite element model respectively,the neutral layer cross section of the flexible ring gear at different times is obtained.The radial displacement,the circumferential displacement and the maximum equivalent stress value are plotted with the polar angle,and the influence of different offsets in the radial plane on the mechanical properties of the wave generator-flexible wheel is analyzed.(6)The fatigue life characteristics of flexible bearings and flexible wheels are analyzed.According to the statistical contact fatigue index equation,combined with the structural characteristics of the flexible bearing and the actual working conditions,the mathematical model of the fatigue life of the flexible bearing involving structural parameters,force transfer coefficient,load coefficient and temperature coefficient is established.On this basis,Using the mathematical model as the objective function,the sensitivity and response surface analysis and the genetic algorithm optimization process were carried out.By changing the length,bottom thickness and smooth thickness of the cylinder,the fatigue life curves of flexible wheels under different loading ratios are obtained,and the influence of structural parameters on the fatigue life characteristics of flexible wheels is obtained.(7)A flexible wheel deformation test-bed is designed and built to measure the shape variables of the flexible wheel.According to the purpose and principle of the experiment,the required equipment was prepared to build a flexible wheel deformation experiment platform.With the help of high-precision foil type full bridge resistance strain gauge,strain gauge tester,USB to TTL serial port module,notebook computer and other major experimental equipment,the shape variables of the flexible wheel were measured,and the correctness of the simulation results was verified by experiments.It is found that the structural parameters,load torque and assembly accuracy of the flexible wheel can change the mechanical characteristics of the neutral layer section of the ring gear,and then affect its fatigue life.Among them,the increase of the length of the cylinder can significantly improve the stress situation of the flexible wheel and extend its service life.Compared with the common bearing,the flexible bearing is more prone to failure.When the geometry size of the flexible bearing is the same as that of the common bearing,theservice reliability of the flexible bearing is less than that of the common bearing.With the reduction of the curvature radius of the inner and outer ring grooves,the inner ring wallthickness and the outer ring raceway depth,the fatigue life value will increase,but with the decrease of the inner and outer ring raceway depth,the fatigue life value will increase Withthe decrease of the thickness of outer ring and the depth of inner ring raceway,the value of fatigue life will decrease.