A Mathematical Model of a Differential Drive with a Limited Gear Ratio

Abstract

Nowadays, there are a lot of types of self-locking differentials used in transmissions of all-wheel-drive vehicles, which proves that the problem of all-wheel drive has not been fully solved yet. The problem is that when the car is moving, often at the same time, there are factors that are making conflicting demands on the drive of the drive wheels. The impacting factors are the kinematic mismatch between the driving wheels, and a decrease in traction on one of the wheels. One of the existing types of limited slip differentials is a limited gear differential. The paper presents a mathematical model of an interaxle drive with a limited gear ratio. The previously developed mathematical model describing the movement of an all-wheel drive vehicle has been supplemented by the mathematical model described in this research. As a result, there was obtained a mathematical model of an all-wheel drive vehicle equipped with a differential with a limited gear ratio. The research investigates dynamics of changes in the power and kinematic parameters of the movement of a car equipped with a differential with a limited gear ratio. In particular, the response time of the differential lock mechanism has been determined. This mathematical model allows determining the dynamic loads acting on the locking mechanism and other parameters necessary for the design of the locking mechanism. Using the efficiency, which estimates slip losses of a wheeled vehicle, as a single criterion for the energy efficiency of a wheeled vehicle, one can investigate and conclude that a differential with a limited gear ratio should be used in the transmission of a given vehicle in case of its operation in a given range of road conditions.