Graph-theoretic Modeling and Dynamic Simulation of an Automotive Torque Converter ⋆ Joydeep M. Banerjee and John J. McPhee Department of Systems Design Engineering University of Waterloo, Waterloo, Ontario N2L3G1, Canada (e-mail: jbanerjee83@gmail.com) Abstract: A linear graph based model of an automotive torque converter is presented in this paper. The linear graph is used to represent the topology of the system and the connectivity of its components. The model accounts for the dynamic behavior of the hydraulic fluid and that of the mechanical components, i.e. the pump, the turbine and the stator. The governing equations in symbolic form are generated from the model in an automated fashion and are used to simulate the operation of the torque converter under specified input conditions. The model is capable of simulating both forward and backward flow modes. The simulation results are compared and validated using data available from existing literature. Keywords: Graph-theoretic Models, Computer Simulation, Symbolic Equations, Torque Converter, Powertrain. 1. INTRODUCTION Torque converters are used as coupling devices in au- tomobile powertrains involving automatic transmissions. Efficient modeling of torque converters capturing various modes of operation is important for powertrain design and simulation, Hrovat and Tobler (1985), Ishihara and Emori (1966), Lucas and Rayner (1970). In this paper a linear graph model of a torque converter is presented and analyzed. The presented model accounts for the dynamic behavior of the mechanical components, i.e. the pump, the turbine and the stator, and that of the hydraulic fluid used in a torque converter. Conventional modeling methods require manual derivation of equations, which can be tedious and prone to errors, Hrovat and Tobler (1985). By employing linear graph theory to model the behavior of the torque converter, it is possible to generate the governing equations in an automated fashion. Also, using graph-theoretic methods makes it easier to extend the model to include other pow- ertrain components from different physical domains. Our ultimate goal is to develop tools for automated generation of real time simulation codes for complete automotive systems. Currently, very efficient methods are available that can perform accurate simulations of multibody vehic- ular systems, Schmitke et al. (2008) . These methods are based on graph-theoretic modeling techniques. However, graph-theoretic models of certain key components of the transmission system are not available at this point. This is precisely the motivation behind the current research. Also, from the stand point of system analysis, a linear graph model of a torque converter would enable us to perform ⋆ Financial support for this work has been provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), Toyota, and Maplesoft. graph-theoretic sensitivity analysis of the torque converter, Banerjee and McPhee (2011). Fig. 1. Schematic diagram of a typical torque converter Figure 1 shows the schematic diagram of a typical torque converter. The mechanical components and the path followed by the hydraulic fluid during the forward flow mode are shown in the diagram. The operation of a torque converter can be described as that of a hydraulic pump driving a hydraulic turbine. The torque from the engine drives the pump which imparts energy to the hydraulic fluid in the system, the hydraulic fluid flows through the vaned construction of the turbine and makes it rotate thereby transmitting the torque com- ing from the engine towards the rest of the transmission system. From the standpoint of energy transmission, the pump converts mechanical energy into hydraulic energy and the turbine converts it back to the mechanical domain. A linear graph can be used to represent the flow of power across different domains of the system and account for the storage and losses incurred in the process.