Abstract:

The dynamic model which describes the torsional vibration behaviors of gear system was introduced accurately in this paper. The differential equation of gear system nonlinear dynamics exhibiting combined nonlinearity influence such as timevarying stiffness, tooth backlash and dynamic transmission error (DTE) was proposed. The theory of multiple scales method was used to solve nonlinear differential equations of gear systems and the frequency response equation was obtained. The fact that the approximate analytical solution by using the method of multiple scales is in good agreement with the exact solutions by numerically integrating differential equations and it proved that the method of multiple scales is one of the most frequently used methods in solving differential equations, especially for large and complicated differential equations.

Key words: mechanical design, gear systems, nonlinear oscillations, method of multiple scales