Planetary Gears Dynamic Model of Road Machine Drives for Calculating Forced Vibrations

Abstract

The paper proposes an experimental technique for finding the uneven distribution of torque between the gears of a planetary gear and, at the same time, the distribution of the load along the tooth based on five load sensors on the shaft of each planetary gear. The object of study is the rigidity and inertial parameters of the planetary gear elements. The purpose of the study is to create a dynamic model of a planetary gear to calculate forced vibrations caused by time-varying gaps - tensions arising in gears. The paper provides an analysis of the problem for the developed model and factors that complicate its creation. Recommendations based on the results of theoretical studies are highlighted. Such recommendations necessitate the obligatory identification of the satellite axes in the model as separate masses. Also, each satellite is represented in the model by a separate mass, which includes its moment of inertia in rotational motion and the mass reduced to it in translational motion together with the carrier. All connections between moving and stationary masses are represented in the model in the form of elastic massless elements with corresponding stiffness values. A mathematical model has been constructed that analytically depicts the movement of masses in the proposed dynamic model. The model consists of ten inhomogeneous second-order differential equations with constant coefficients. To check the adequacy of the resulting model, the parameters of rigidity and inertia of the planetary gear elements were determined. The results obtained indicate that the rigidity of elastic connections between the masses introduced into the mathematical model does not differ from the real ones. The conducted studies indicate the possibility of using this mathematical model to calculate forced vibrations caused by time-varying gaps - tensions arising in gears.