Negative stiffness in gear contact

Abstract

The tooth contact stiffness is very often included in dynamic mathematical models of gear drives. It is an important value for calculation of torsion eigenfrequencies as w ell as the dynamic properties of the whole transmission systems. Planetary gear drives have several advantages over simple parallel axis gears, especially due to theirs compact design and great torque-to-weight ratio caused by multiple parallel paths. However, the dimensional or mounting errors can cause that some planets have the tendency to take more load than the others. One of the ways how to improve load sharing is the application of flexible planetary pins or by using a free central wheel. However in such cases, the wheels motion is defined in one rotation coordinate and two translation coordinates — tangential and radial. The reaction force at radial change of axis distance is usually neglected. The focus of this contribution is to derive the stiffness of this radial connection and to analyse the influence of radial stiffness on planetary gear dynamics.