The vibration of a helical geared shaft system is studied, considering the coupling between the torsional, flexural, rotational (about the diametral axis), and axial motions of the gear carrying shafts. The effects of the nonlinear backlash function and time varying tooth stiffness are also considered. The excitation to the geared shaft system is in the form of a static transmission error which has deterministic and filtered white noise components. The equations of motion are formulated in state space form and solved using matrix exponential approach. Piecewise linearization is used in the simulation and results for the mean and variance of the dynamic response are presented.

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