Assuming exponential decay by incorporating viscous damping improves the prediction of the coeffcient of friction in pendulum tests of whole articular joints

Abstract

A pendulum test with a whole articular joint serving as the fulcrum is commonly used to measure the bulk coefficient of friction (COF). In such tests it is universally assumed that energy loss is due to frictional damping only, and accordingly the decay of pendulum amplitude is linear with time. The purpose of this work was to determine whether the measurement of the COF is improved when viscous damping and exponential decay of pendulum amplitude are incorporated into a lumped-parameter model. Various pendulum models with a range of values for COF and for viscous damping were constructed. The resulting decay was fitted with an exponential function (including both frictional and viscous damping) and with a linear decay function (frictional damping only). The values predicted from the fit of each function were then compared to the known values. It was found that the exponential decay function was able to predict the COF values within 2 per cent error. This error increased for models in which the damping coefficient was relatively small and the COF was relatively large. On the other hand, the linear decay function resulted in large errors in the prediction of the COF, even for small values of viscous damping. The exponential decay function including both frictional and constant viscous damping presented herein dramatically increased the accuracy of measuring the COF in a pendulum test of modelled whole articular joints.