It is well known that presence of backlash in the timing gear train of modern internal combustion engines leads to significant increase in dynamic loads and noise. Accounting for the backlash introduces non-linearity in the numerical model. Traditionally such a system is solved as an initial value problem using multi-cycle numerical integration of the equation of motion in time domain. Present work offers an efficient method for analysis of periodic oscillations of multi-mass system of complex structure by converting it into a chainlike system. At first, the method is applied to a linear system. It is also shown that this method is applicable to a nonlinear system offering significant improvement in the simulation time as compared to the traditional approach. The developed method is applied to studying dynamics of timing gear train of a high power density diesel engine.

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