Title: Improved models of vehicle differential mechanisms using various approaches

Authors: Maksym Diachuk; Said M. Easa

Addresses: Department of Civil Engineering, Toronto Metropolitan University, 350 Victoria Street, Toronto, Ontario, M5B2K3, Canada ' Department of Civil Engineering, Toronto Metropolitan University, 350 Victoria Street, Toronto, Ontario, M5B2K3, Canada

Abstract: The mathematical modelling of the branched automotive drivetrain is mainly based on various configurations of differential mechanisms (DM). This paper proposes variant math approaches for modelling DM's dynamics. The symmetric (open) DM is considered first. Two mathematical methods based on ordinary differential equation (ODE) and differential-algebraic equation (DEA) problems are applied. The asymmetric self-locking inter-axle differential with proportional friction moments is then considered. Three variants of the mathematical models for this DM type are represented. The linearised model uses the shortest description based on a previous step solution. Two other nonlinear models are formed by mixing with ODE and DAE approaches. The Simulink blocks for implementing developments were composed. The models were validated by comparing the results under the same conditions to prove their math coherence. The analysis of the proposed variants was carried out regarding structural complexity, usability, computational speed, and relative accuracy. Conclusions about their usability in drivetrain dynamics and active control were made.

Keywords: symmetric differential; self-locking differential; friction clutch; differential efficiency; differential simulink-model.

DOI: 10.1504/IJVSMT.2023.132931

International Journal of Vehicle Systems Modelling and Testing, 2023 Vol.17 No.2, pp.112 - 142

Received: 24 Nov 2021
Accepted: 05 Dec 2021
Published online: 20 Aug 2023 *