Forces in the engagement of planetary-pinion gear with satellite having eccentricity

Abstract

Background. The forces acting in the engagement of the gear affect the resource of the engagement itself and the satellite supports. The number of factors on which the load distribution in the engagement depends is very large, including modification of tooth profiles, manufacturing inaccuracy of the gear and a change in the relative position of the satellite, the pinwheel and the output shaft during its operation. The existing methods of static gear calculation do not fully take into account this influence. The purpose of the study is to improve the static analysis of gear and increase the accuracy of calculation. Materials and methods. In this work, the displacements in the contact pairs of engagement are determined using the method of kinematic analysis. Next, classical Hertzian contact mechanics is used to determine the elasticity characteristics. The forces in the engagement are calculated using an iterative procedure for analyzing the state of the contacts. To obtain quantitative characteristics, computer modeling in the Mathcad system was used. Results. A mathematical model, algorithm and program for calculating the forces arising in the planetary-pinion gear with modification of the satellite teeth profile and satellite eccentricity have been created. Calculations are performed and it is shown how, in this case, the forces in the contact pairs change in the gear. Conclusions. The proposed solution makes it possible to take into account the combined influence of a uniform modification of the tooth profiles and the eccentricity of the satellite on the loads in the engagement. Research has shown that eccentricity can significantly change the load pattern of the gear engagement, which must be taken into account in engineering calculation.

Keywords

• planetary-pinion gears
• satellite eccentricity
• forces in contacts
• coefficient of maximum force increase