Friction induced dynamics of ball joints : instability and post bifurcation behavior

It is well known that ball joints may be subject to friction induced oscillations. In the present analysis the stability behavior of a ball joint model with Coulomb and Stribeck-type friction is studied and the post bifurcation behavior of the resulting limit cycles is determined. The bifurcating limit cycles can be followed for both types of friction, and velocity dependent friction is not necessary to yield vibrations, as was proposed in the literature before. The linear instability is found to be of the whirl or flutter type. The results suggest that, depending on the ball joint and friction parameters, a complicated variety of nonlinear periodic solutions exists. It is shown that the previously often used approach of computing parameter values where stable sliding turns unstable can not even serve as a first rough indicator for the existence of friction induced oscillations. Instead, existence areas for stable/unstable sliding and co-existing stable limit cycles give a far better impression of the system characteristics, and can even give hints on measures that can help to eliminate friction whirl vibrations from ball joints. The analysis yields that a low friction coefficient, low loads and high system or interface damping seem promising to calm squeaking joints, as is physically plausible. Furthermore, the combination of the momentary speed of rotation and the relative component kinematics has a huge impact on the existence of limit cycles - hence the human gait is likely to influence the occurrence of squeaking in total hip arthroplasty.

Subjects

Ball joint

Friction

Vibration

DDC Class

610: Medicine, Health

620: Engineering

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Friction induced dynamics of ball joints : instability and post bifurcation behavior