Analysis of nonlinear oscillations in spur gear pairs with approximated modelling of backlash nonlinearity

Due to international competition and strict limitations of standards regarding the noise level, investigation of gear vibration is of great importance. In this paper, nonlinear oscillations of spur gear pairs including the backlash nonlinearity is studied. Dynamic system is described through the classical single degree of freedom (SDOF) model in terms of dynamic transmission error (DTE). Using multiple scale method, forced vibration responses of the gear system including primary, super-harmonic and sub-harmonic resonances are investigated. In each case, the jump phenomenon and stability analysis are studied. In addition, the effect of dynamic and manufacturing parameters of the gear system on the DTE amplitude and consequently time responses are analyzed and interpreted physically. Results show interesting behaviors of the DTE amplitude under super/sub-harmonic resonances in comparison with the primary resonance.