Parametrical Fluctuations of Epicycle in Wheel Gearboxes

Abstract

Purpose: To develop mathematical model of the parametrical fluctuations, conditions of its emergence and development caused by cyclically variable in time rigidity of gearings. Methodology: Modeling of structural parametrical fluctuations of an epicycle is executed on the basis of the differential equation of Mathieu-Hill with variable periodic coefficients and diagnosing of instability of oscillatory system is carried out according to Ains-Strett’s chart. Results: It is established that width of area of instability of parametrical fluctuations of an epicycle for a 2k-h gear depends on coefficient μ pulsations of mesh rigidity and the relation of frequency of own fluctuations k0 of an epicycle to the angular frequency ω of parametrical excitement. Calculations for the given algorithm on the example of wheel gearbox Raba designs 118.77 and 318.78, which are widely applied as a part of transmissions of car and electrical wheel transport, confirmed possibility of