Abstract
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 a load torque is derived. By transforming the deformation coordination relationship into a linear programming form, a mathematical model for the analysis of the single secondary internal gear pairs with the tooth surface contact of the involute RV reducer is established. An improved simplex method is used to solve the linear programming problem. The calculation results are compared with the ANSYS simulation values from the three aspects of contact tooth pairs, gear tooth load and tooth surface contact force. The results show that the values obtained by the two methods are almost the same on the contact tooth pairs and the tooth load. In terms of tooth surface contact force, the contact area calculated using the finite element linear programming method is slightly smaller than the ANSYS results, but most of the errors are below 12%, indicating that the tooth surface contact conditions obtained using the two calculation methods are consistent. The accuracy and effectiveness of the finite element-linear programming method are thus verified.
Highlights
With the increased research on the involute transmission with small tooth number differences and the improvement of manufacturing processes, the performance of involute small tooth number difference planetary reducers has reached that of cycloidal pin gear reducers, which makes the development of involute rotate vector (RV) reducers possible [4]–[6]
Based on linear programming method that was proposed by Conry, Li derived the mathematical model of the small tooth number difference transmission contact problem under the condition of internal gear pair mesh, taking into account the pin and bearing effects [16], [17]
The finite element-linear programming method was used to calculate the number of the contact tooth pairs of the small tooth number difference gear pairs, the tooth surface load distribution, the pin shaft and the bearing ball force
Summary
Based on linear programming method that was proposed by Conry, Li derived the mathematical model of the small tooth number difference transmission contact problem under the condition of internal gear pair mesh, taking into account the pin and bearing effects [16], [17]. The finite element-linear programming method was used to calculate the number of the contact tooth pairs of the small tooth number difference gear pairs, the tooth surface load distribution, the pin shaft and the bearing ball force.
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