A number of experiments on a physical system with clearance having combined parametric and external forcing excitation are presented. The data demonstrate several nonlinear phenomena that exist in periodically excited oscillators subject to clearance at a contact interface. Jump discontinuities in forced response curves are shown to exist and subharmonic resonances which are formed by period-n (nT) motions with n ≥ 2 are demonstrated. Long-period subharmonic motions with periods as long as nine times the excitation period are reported. Finally, several cases of measured chaotic motions are also illustrated through time-traces, phase portraits, Fourier spectra, and Poincare plots which form strange attractors.

A mechanical system exhibiting combined parametric excitation and clearance type non-linearity is examined analytically and experimentally in an effort to explain complex behavior that is commonly observed in the steady state forced response of rotating machines. The specific case of a preloaded mechanical oscillator having a periodically time-varying stiffness function and subject to a symmetric backlash condition is considered. A generalized solution methodology is proposed based on the harmonic balance method. The resulting non-linear algebraic equations are solved by using a direct Newton-Raphson technique, in which a closed form Jacobian matrix is computed using frequency domain methods. Analytical solutions are validated by comparison with numerical integration results and experimental measurements obtained from a gear dynamics test rig. 7 1995 Academic Press Limited 743 0022-460X/95/350743+23 $12.00/0

The influence of involute contact ratio on the torsional vibration behavior of a spur gear pair is investigated experimentally by measuring the dynamic transmission error of several gear pairs using a specially designed gear test rig. Measured forced response curves are presented, and harmonic amplitudes of dynamic transmission error are compared above and below gear mesh resonances for both unmodified and modified gears having various involute contact ratio values. The influence of involute contact ratio on dynamic transmission error is quantified and a set of generalized, experimentally validated design guidelines for the proper selection of involute contact ratio to achieve quite gear systems is presented. A simplified analytical model is also proposed which accurately describes the effects of involute contact ratio on dynamic transmission error.

The influence of gear tooth flank modifications in the form of linear involute tip relief on the torsional vibration behavior of a spur gear pair is investigated by using an experimental test stand. Measured dynamic transmission error (DTE) values are compared and a family of forced response curves is presented. Guidelines for the design of quiet spur gear sets are also given.

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