Tooth Surface Contact Analysis Of Secondary Internal Gear Pairs Of Involute RV Reducer

As a key component of industrial robots,precision reducer is mainly dependent on imports,the improvement of our country's industrial automation level has been severely restricted.It is more and more urgent to develop our own high-precision reducer.In this paper,taking an involute RV reducer as the research object,the contact analysis of its' secondary internal gear pairs is carried out by using the finite element-linear programming method,which provides the basis for involute RV reducer's structure design and improvement.The main research content as follows:The deformation compatibility relationship of the general contact object under external normal force and the single secondary internal gear pairs of involute RV reducer under torque is been deduced.By transforming the deformation compatibility formula into a linear programming form,a mathematical model is established to deal with the tooth surface contact problem of the single secondary internal gear pairs of involute RV reducer.The improved simplex method is used to solve the linear programming problem,and the calculation steps are modified according to the additional constraint.The MATLAB calculation program is written.In reduce to the calculation,the two-dimensional calculation method for number of involute internal meshing with small tooth number difference and MATLAB mapping method are used to determine the contact area of the single secondary internal gear pairs of RV reducer.The partial finite element model of internal and external gears is established in ANSYS by APDL.By the cyclic loading method,the gear pairs' flexibility matrix is obtained,and the initial gap is obtained according to the coordinate position of the gear pairs' contact points.After substituting the flexibility matrix,initial gap and torque into the linear programming problem,the contact tooth number,tooth load distribution and tooth surface contact force distribution of the internal gear pairs are calculated.To verify the accuracy and effectiveness of the finite element-linear programming method,the calculation results are compared with the ANSYS simulation from the three dimensions of contact tooth number,tooth load and tooth surface contact force.The comparison results using two methods are shown almost the same on the contact tooth number and tooth load,and the contact area calculated by the finite element-linear programming method is slightly smaller than that calculated by ANSYS.But most of points' error is less than 12%,so it shows that the tooth surface contact conditions obtained by the two calculation methods are basically the same.