Considerations of a Simplified Analysis of Transducer Dynamics for Measuring Friction

In many tribological investigations, the measurement of friction is complicated by the vibrational characteristics of the transducer. In particular, when a mechanical force transducer is excited, the static calibration factor no longer provides the friction force in the interface. In a recent study (Streator and Bogy, 1992), the problem of determining the friction force from a measurement of the periodic bending strain in a cantilever-mass transducer was solved using the equations of Euler-Bernoulli beam theory. The method showed that modelling the transducer as a single degree-of-freedom (DOF) system could lead to inaccuracies depending on the frequency content of the friction force, and depending on whether a measurement of beam strain or mass displacement was available. Employing the Euler-Bernoulli analysis, however, requires substantially greater analytical and computational effort. In the present work a two DOF model is considered which represents a compromise between the simplicity of the single DOF model and the accuracy of the more thorough analysis. Force computations are made for a simulated slider/disk tribological contact at different frequencies of disk rotation. One set of computations is performed based on knowledge of the beam strain and the other based on knowledge of the mass displacement. It is found that the friction force computed from the two DOF model compares well with that of the Euler-Bernoulli analysis for an extended range of frequencies as against the single DOF model, but loses accuracy at high frequencies. Nevertheless, if used in a careful manner, the two DOF model offers an improved method of determining dynamic friction forces for certain applications.