Non-sticking oscillation formulae for Coulomb friction under harmonic loading

In this paper, a new estimate for periodic non-sticking (i.e., zero stop pe r cycle) solutions is presented for the steady state responses of the Coulo mb friction oscillator subjected to harmonic loading. Compared with the Den Hartog (1931 Transactions of the American Society of Mechanical Engineers 53, 107-115 [1]) estimate, the new estimate leads to the same formulae for the maximum displacement and its time lag, but only the new estimate offers the closed-form formulae for the maximum velocity and its time lag. More i mportantly, a simple formula is derived for estimating the minimum driving force amplitude needed to prevent an oscillating object From sticking to th e friction surface on which it slides. The validity of the assumptions made for the new estimate and the accuracy of the formulae developed are confir med by comparing with the exact solutions (Hong and Liu 2000 Journal of Sou nd and Vibration 229, 1171- 1192 [2]). It is also Found that there exists t he best driving force amplitude for maximum dissipation efficiency. (C) 200 1 Academic Press.