Modelling of Heavy Vehicle Transmission Synchronizer using Constrained Lagrangian Formalism
Paper in proceedings, 2015
Robust and efficient synchronizers are keys elements to ensure good gear shift in heavy vehicles. In order to improve existing as well as develop new synchronizers, efficient simulation tools are needed. In this contribution, a mechanical system with 5 degrees of freedom modelling a generic synchronizer consisting of engaging sleeve, synchronizer ring and gearwheel are considered.
Due to the design of the different components and their interactions the synchronizing process is described in terms of different steps or phases; presynchronization, main synchronization, blocker transition and engagement. The four main phases are further divided into sub-phases.
To study the whole process in a unified manner, Constrained Lagrangian Formalism (CLF) turns out to be a suitable method in which the interactions between components (sleeve,
synchronizer ring and gearwheel) are described by unilateral or/and bilateral constraints imposed on generalized coordinates of the system during different phases. Using CLF a mathematical model of a generic synchronizer is developed and represented by the system of differential-algebraic equations. Kinematics and kinetics of the generic synchronizer are modelled for each sub-phase. The sleeve is considered as a master and the
gearwheel is considered as a slave. The statement of the dynamics problem for a generic synchronizer is given and the numerical algorithm is implemented in Matlab for solving the differential-algebraic equations resulting from CLF. The generic synchronizer computational model is adapted to available experimental setup and validated using obtained measurement data. Sensitivity of the synchronization time is studied varying the cone angle, coefficient of dry friction and sleeve force. Effect of driveline vibrations on synchronization performance is
Constrained Lagrangian Formalism