Applying the law of conservation of angular momentum in the analysis of switching in automatic transmissions

Abstract

The solution of problems of the dynamics of mechanisms is based either on a differential principles of theoretical mechanics, or integrated principles. The first involves the drawing up of the Lagrange equations of the dynamics that characterize the state of the mechanism at any given time, and the analysis of their solutions. The second are related to the conservation laws (the law of conservation of energy, momentum conservation law) and allow making an integrated assessment of the results of movements for any interval. The differential principle is used for the analysis of dynamic processes in the switching at gearboxes of vehicles, and is acquitted in the analysis of switching at manual control gearboxes. In this case, the switching process takes seconds and all phases of the process are described mathematically correct. The use of this approach in the analysis of the dynamics of switching at automatic transmissions, lasting 0.2 ... 0.5 s, is connected with the involvement of a large number of assumptions. They relate to the description of alleged interactions of switched on and switched off mechanisms of gearbox control and are carried out on a fairly simple model of a two-stage gearbox. In the analysis of more complex models, such as the gearbox with dual switching (2 clutches off, 2 on) the application of differential principle becomes significantly difficult. Reducing (or increasing) of velocity of the inertial elements of transmission at a gear change in a short time is possible only under the action on switching on clutch of large forces. Therefore, considering the model of automatic transmission on a small time interval as a closed system, it is possible to apply the theorem of conservation of angular momentum. Using this integral principle in the article the velocity calculation is given in the input and output of the gearbox after the switch; the evaluation of the limit torque acting on the units of gears at switching was made; criteria for clutch selection corresponding to the required switch settings is proposed; and also the problem of controlling the process of double-shifting is solved. The approach complements the known methods of research and can greatly simplify calculations of dynamic loads.