Static and Dynamic Analysis of a Planetary Gearbox Working Process

Abstract

Present paper focuses on the power circuits within planetary gearboxes, providing an original mathematical model. This model is an excellent instrument to analyze and determine the torque, angular speed, power factors, global gear ratios and efficiency distribution. The analysis itself has been developed for the second-gear, forward-motion of the gearbox. The analysis provides the mathematical model of the gearboxs way of working both in the static and dynamic modes. The method starts with issuing the equivalent graph (network structure) of the gearbox. Using this model, the gearbox is associated to a power driveline network that both transforms and guides the power flow to the final transmission of the vehicle. Using the network structural model, the gearbox turns into a general nodal diagram (graph). Our study concerned both the static and dynamic modes. It consists in a mathematical determination of the cinematic (angular speed) and dynamic (torque) factors that charge the gearboxs components. The mathematical model takes into account the power losses and the inertia occurring within the entire network and their influences upon the general power distribution. Using the model, we could get accurate results of the torque and power distribution. Moreover, the model provides the map of the power distribution when the gearbox works in its second gear, emphasizing the difference between the analysis performed for the two above mentioned working regimes (static and dynamic). The results can be further used as entry points for a much more complex mathematical model that describes the dynamic features of the vehicle.