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This paper describes the classification and analysis of lateral torque-vectoring differentials using velocity diagrams, which are frequently used for the gear-shifting analysis of an automatic transmission. A lateral torque-vectoring differential is composed of the mechanism of torque vectoring from the right wheel to the left wheel, and the similar mechanism of torque vectoring from the left to the right. The analysis shows that, when only the mechanism part of one-way torque vectoring is considered, then the smallest number of the rotational elements composing the one-way torque-vectoring mechanism is four. This is the simplest mechanism. The mechanism is classified into seven kinds of mechanism, namely six clutch-type mechanisms and one brake-type mechanism. The expressions for the clutch torque for torque vectoring, the clutch slip speed, and the energy loss generated by clutch are presented for these mechanisms. As a result, the theoretical value of energy loss is completely the same in these seven kinds of mechanism in the ideal state, in which the transmission efficiency of gears, agitation loss, etc., are assumed to be neglected. Finally, from an actual mechanism design point of view, the best mechanism is evaluated.

A lateral torque-vectoring differential consists of a slip clutch for torque vectoring from right to left, another slip clutch for torque vectoring from left to right, differential gears, and some planetary gears which generate the differential speeds of the slip clutches. The present authors introduced a design parameter, namely the maximum acceptable differential speed ratio, and showed that the design parameter is very useful to analyse the lateral torquevectoring differentials. The minimum of the design parameter is determined by the vehicle driving condition in which the torque-vectoring differential should be activated. In order to find the most appropriate value of the design parameter, this paper studies possible influences -namely the vehicle track, vehicle cornering radius, dynamic tyre radius difference between right and left wheels, lateral torque vectoring, and tyre-road friction characteristic -on the maximum acceptable differential speed ratio. As a result, the lateral torque vectoring and tyreroad friction characteristic should be considered as much as the vehicle track or cornering radius; meanwhile the dynamic tyre radius variation is negligible. Finally, a determination method for the maximum acceptable differential speed ratio is proposed.