Series solution of symmetric dry frictional stick-slip motion and stick-slip boundary characteristics

To study frictional vibration problems in areo-engine, piecewise expression of frictional force in symmetric stick-slip motion was presented. Analytical series solution of symmetric stick-slip motion with even stops was derived by using harmonic balance method. Stick-slip boundary function in parameter plane was derived based on the series solution. Stick-slip response contained only odd harmonic components and super-harmonic resonances existed at odd fractional frequency ratios. When frequency ratio was less than 0.4, the stick-slip boundary curve had the feature of concave-convex alternation and its local minimums located at the super-harmonic resonant frequencies. Increase in viscous damping reduced the non-sticking parameter range at most frequency ratio ranges except near super-harmonic resonant frequencies, where larger viscous damping led to larger non-sticking parameter range.