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2 Machine Dynamics Problems

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A Pivoting Solver for Dynamic Planar Multi-Contact Friction Problems

100%

Funk K. , Pfeiffer F.

tom Vol. 24, No. 1

87-99

An important application of complementarity theory is the determination of the contact forces in multi-body systems with rigid contacts. As long as the contacts are friction-free the formulation of the multi-contact problem results in a well posed linear complementarity problem (LPC). But once a friction force-depending on the normal contact force - is introduced the problem gets a lot more complicated, and the resulting LPC gets ill posed for many solving algorithms. The paper addresses a linear complementarity formulation in a generalised form, which is appropriate to handle planar friction problems. In addition, a direct solving method based on Lemke's method is presented, that can handle the generalised linear complementarity problem.

Optimisation of the Joint Geometry of a Rocker Pin Chain

80%

Neumann L. , Ulbrich H. , Pfeiffer F.

tom Vol. 29, No. 4

97-108

Continuous variable chain drives have to satisfy high requirements to compete with common gears and therefore an improvement of certain properties of the CVT (Continuously Variable Transmission) is desired. In this contribution the important goal to reduce the noise emission of the gear is realised by optimising the geometry of the rocker pin chain. Applying numerical simulation techniques and an optimisation algorithm carries out this optimisation. For this purpose a detailed dynamical model of the CVT is introduced which includes an exact treatment of the rocker pin kinematics of the chain. The geometry of the rocker pin joints, which shall be optimised, is defined by the optimisation parameters. A good choice for a measure of the noise emission is the amplitudes of the forces in the bearings in a certain frequency domain. They are used to form the target function. A numerical simulation provides a connection between the optimisation parameters and the objective function, which is not given analytically and takes high simulation effort. Therefore the optimisation algorithm implicit filtering is applied to solve the optimisation problem. The presented approach is applied to minimise the gear vibrations of a CVT by finding optimal geometry parameters. A significant reduction of the noise emission is gained.