Modelling and Simulation of Brake Booster Vacuum Pumps 2013-01-9016
Aim of this work is the development of a lumped parameters simulation model of single-vane vacuum pumps for pneumatically actuated brake boosters. Kinematic and fluid-dynamic models are integrated in a simulation environment to create a tool aimed at evaluating the vacuum pump performance and at guiding the designer during the prototype development. The paper describes extensively the mathematical model, the time domain simulation and experimental analyses performed on a camshaft mounted unit. Great emphasis is placed on the evaluation of the geometric quantities of the control volumes into which the vacuum pump has been divided. For each control volume the mass and energy conservation equations lead to the determination of the instantaneous pressure. The volume of each variable chamber and the respective angular derivative are calculated as function of the shaft position starting from the stator track profile supplied as a generic closed polyline. Flow areas between each chamber and the inlet/outlet volumes during a complete shaft revolution are evaluated directly from a data file containing the x-y coordinates of the passage area contour. Different leakage paths are also taken into account. Specific attention is dedicated to the simulation of the lubricating fluid throughout the vacuum pump in order to take into account possible overpressures due to the presence of a trapped volume of oil, above all during cold starts. To achieve this target the equations describing the behavior of the liquid and gaseous phases are applied simultaneously and the current fraction of oil is evaluated for each variable volume chamber. The model is able to work with an oil fraction ranging from 0% to 100% without introducing discontinuities in the differential equations. Experimental tests have confirmed a good matching with the simulation results in terms of pressure vs. time characteristics and absorbed torque.