Constrained Lagrangian Formulation for Modelling and Analysis of Transmission Synchronizers
An engineering model of a generic synchronizer is considered. The generic synchronizer
is modeled consisting of the selector sleeve with engaging teeth and frictional cone, the
synchronizing ring with blocker and the gearwheel with engaging teeth. It is assumed that
for the sleeve and synchronizing ring translational and rotational motions are feasible, for
the gearwheel only rotational motion is feasible. The motion of the generic synchronizer is
performed under the external and internal loads. The external loads comprise the vehicle
resistance torque and the control force applied to the sleeve and the drag torque due to the
clutch. The internal loads comprise the forces and torques arises due to interaction
between the sleeve, the synchronizing ring, the gearwheel as well as oil splash during the
synchronization process. A feasible synchronization process of a generic synchronizer is
divided into four main phases: pre-synchronization, main synchronization, blocker
transition (indexing for the ring), and engagement. Pre-synchronization and blocker
transition are further divided into several sub-phases. The generic synchronizer is fully
parametrized and together with description of all phases constitutes kinematics of
synchronization process in question.
Due to the nature of synchronization process in transmission system a motion of a
synchronizer mechanism is subjected to unilateral or/and bilateral constraints imposed on
generalized coordinates or/and generalized velocities of the synchronizer. Constrained
Lagrangian Formalism (CLF) has been proposed as an approach for developing
mathematical and computational models of a generic synchronizer dynamics. The CLF
gives possibility to formulate direct dynamics, semi-inverse dynamics and inverse
dynamics problems for a generic synchronizer in unified and efficient way. It is shown that
CLF can be promising and useful for advanced dynamic analysis of the existing
synchronizer mechanisms and to design novel optimized ones.
In the present report mathematical and computational models of a generic synchronizer
with five degrees of freedom have been developed using CLF. Application of CLF on the
modelling of the synchronization process gives system of differential-algebraic equations
(DAE). Analysis of the generic synchronizer performance diagrams has shown that the CLF
based model is able to predict the synchronization process characteristics reasonably well.
The developed model has been validated by using measurement data from test rig at CV
AB Scania. Performance of the generic synchronizer is also analyzed in case of driveline
vibrations. Sensitivity analysis of the synchronizer mechanism performance with respect to
cone angle, coefficient of friction, maximum value of shift force and rate of applying shift
force has been done.
Next, the developed models will be used to get further insight into synchronizer design and
its performance diagrams with aid of global sensitivity analysis and Pareto optimization.
Force Control and Kinematic Control
Constrained Lagrangian Formulation