Vehicle and powertrain dynamics analysis with an automatic gearbox

• A powertrain/vehicle dynamic model developed including the automatic gearbox.
• Del Castillo's method is preferred for the gearbox modelling.
• A set of penalty functions are associated with the clutches and brakes.
• Two real automatic gearboxes are analysed.
• The simple and effective formulation serves at the beginning of design process.

This paper presents an effective formulation to model an automatic transmission for evaluating the vehicle performance in the early development stage of a powertrain design. The corresponding equations of motion are obtained with the help of the virtual power principle, involving all rotating parts of the gearbox. Del Castillo's method is used to efficiently establish the analytical expression of partial gear ratios. A set of penalty functions are associated with the clutches and brakes allowing a continuous simulation of the gear shift. The acceleration of the vehicle is calculated by including the gearbox model in the equations governing the longitudinal behaviour of a passenger car, including the motor, a realistic model of the tire and classical road loads. This formulation offers a powertrain/vehicle dynamic model developed for the sake of simplicity (rigid interconnected bodies with kinematic constraints), and sufficiently efficient to simulate continuously the gear shifts. Two realistic cases are presented, namely Chrysler 45RFE and Aisin Warner 55-50 SN powertrains. For the latter, a validation is made through a comparison with measured data. The developed model reveals itself as a valuable tool for simulating the implementation of different control laws governing the gear shifts.