A mixed formulation for frictional contact problems prone to Newton like solution methods
Computer Methods in Applied Mechanics and Engineering
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Rigid-Body Dynamics with Friction and Impact
SIAM Review
Stability and Convergence of Mechanical Systems with Unilateral Constraints
Stability and Convergence of Mechanical Systems with Unilateral Constraints
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With a pushbelt continuously variable transmission the whole drivetrain including the engine of a passenger car can operate in an optimal state at any time. For further improvements with respect to fuel consumption, dynamic simulations of the system were investigated by Bosch and the Institute of Applied Mechanics of the Technische Universitat Munchen in the last years. The underlying mathematical models are characterised by numerous contacts and a large degree of freedom. To avoid high numerical stiffnesses due to springs and to encourage an efficient as well as stable and robust numerical treatment, a nonsmooth contact description is chosen. Time-stepping schemes integrate the resulting measure differential inclusions. This paper deals with a spatial transient mathematical model of pushbelt continuously variable transmissions to consider also out-of-plane effects, for instance pushbelt misalignment. The equations of motion are derived using methods of multibody theory and nonlinear mechanics. Thereby, the bodies themselves are described using rigid and large deflection elastic mechanical models. In-between the bodies, all possible flexible or rigid contact descriptions namely frictionless unilateral contacts, bilateral contacts with 2D-friction and even unilateral contacts with 3D-friction occur. In comparison with the planar case the calculation time increases significantly mainly because of the large degree of freedom and the number of contact possibilities. Initial value problems are solved and parallelisation is used to reduce the computational effort.