Multibody simulation of vehicles equipped with an automatic transmission

Abstract

Abstract. Nowadays automotive vehicles remain as one of the most used modes of transportation. Furthermore automatic transmissions are increasingly used to provide a better driving comfort and a potential optimization of the engine performances (by placing the gear shifts at specific engine and vehicle speeds). This paper presents an effective modeling of the vehicle using the multibody methodology (numerically computed under EasyDyn, an open source and in-house library dedicated to multibody simulations). However, the transmission part of the vehicle is described by the usual equations of motion computed using a systematic matrix approach: del Castillo's methodology for planetary gear trains. By coupling the analytic equations of the transmission and the equations computed by the multibody methodology, the performances of any vehicle can be obtained if the characteristics of each element in the vehicle are known. The multibody methodology offers the possibilities to develop the vehicle modeling from 1D-motion to 3D-motion by taking into account the rotations and implementing tire models. The modeling presented in this paper remains very efficient and provides an easy and quick vehicle simulation tool which could be used in order to calibrate the automatic transmission. IntroductionLike any computer-aided design tool, the purpose of a numerical simulation is to provide information about a physical system without having to physically build it. Practically, simulation replaces the physical prototype with a numerical (or virtual) one on which the dynamic behavior can be investigated. As a virtual prototype is far cheaper than a physical one, the use of simulations is rapidly increasing. This paper investigates the dynamic simulations used in automotive engineering and, more specifically, the modeling and simulation of an automatic gearbox. This powertrain element has one of the highest impacts on vehicle driving. To simulate gear shifts, one option consists in building a series of models for each gear ratios and the simulation jumps from model to model according to some continuity conditions [1]. Another option is to build a complete mechanical system, including the actuators [2]. Several commercial software packages offer an efficient way to assess the dynamic performances of such models. On the other hand, industry needs only simple models which are sufficiently versatile and easy to use in order to to evaluate the efficiency of a powertrain during the design stage. This offers the possibility for industry to evaluate, in real-time, the gear transmissions [3]. In contrast to these approaches, Kouroussis et al. proposed an intermediate model which allows for the simulation of the complete acceleration process of a vehicle based on an analytical theory of gearbox kinematics [4]. Other models are more specific, focusing only on internal elements such