A Refined Technique for the Automated Determination of Friction Losses in the Toothing of Multithreaded Transmissions with Differential Mechanisms and Planetary Gears

Multithreaded transmissions, which using differential mechanisms for separating and summing up power flows, have been widely used in the transmissions of transport vehicles and special drives. The quality of such transmissions and the magnitude of frictional losses in the toothing significantly depend on the adopted kinematic scheme and the ratio of powers passing through the corresponding links of the differential mechanisms. With the existing automated analysis and synthesis of such transmissions, a matrix approach has recently been widely used. The proposed work provides a refined technique for the automated determination of friction losses in the toothing of multithreaded transmissions which containing differential mechanisms and planetary gears. It makes it possible to more accurately determine friction losses in the toothing and at the same time preserves the linear structure of the system of equations, which permit to continue using the matrix approach to analyze and synthesize such transmissions. Examples are given for the formation of equations systems describing the force interaction between the elements of the scheme for all variants of the links commutation of planetary rows operating as three-link differential mechanisms and planetary gears with one stopped link. The work is based on the analysis of existing methods for determining friction losses in the toothing and personal practical experience in the design and study of multithreaded stepped and stepless transmissions. The received results allow to apply the offered technique in the modern program complexes focused on the automated analysis and synthesis of multithread transmissions with use of the matrix approach. This makes it possible to significantly reduce the time to develop new multithreaded transmissions and increase their technical characteristics.