Parametrical Fluctuations of Epicycle in Wheel Gearboxes
Victor Yaglinskiy
Odessa National Polytechnic University, Odessa, Ukraine
Sergiy Gutyrya *
Odessa National Polytechnic University, Odessa, Ukraine
Andriy Chanchin
Odessa National Polytechnic University, Odessa, Ukraine
*Author to whom correspondence should be addressed.
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 an elimination of parametrical fluctuations of an epicycle by means of an arrangement of axes of planets, uneven on a circle.
Conclusion: The positive effect of influence of an arrangement of axes of planets, uneven on a circle, on depth of a pulsation of rigidity of multiline gearing and narrowing of area of instability of parametrical fluctuations of an epicycle is confirmed.
Keywords: Planetary gear, mesh rigidity cyclic function, model of parametrical fluctuations