Nonlinear dynamic modelling and analysis for a spur gear system with time-varying pressure angle and gear backlash

Abstract

• This paper presents a new dynamic model for a spur gear system cosidering time-varying behaviors of pressure angle and baclash, together with the effecs of other factors. • The time-varying gear mesh stiffness is calculated by an improved potential energy method. • The differential equations of motion of the gear system are strictly derived using Lagrange’s equation. • The proposed model can more accurately estimate the dynamic responses in comparison to the traditional models. In the previous nonlinear dynamic models of spur gear system, when considering bearing deformation, the pressure angle and gear backlash are usually considered as constants to facilitate the modelling. In fact, bearing deformation will cause the gear translation motion, and then lead to the changes of a series of gear mesh parameters. In view of this, this paper presents a new nonlinear dynamic model for a spur gear system considering the time-varying behaviors of pressure angle and gear backlash, together with the effects of gear gravity, unbalance mass, and internal/external excitations, etc. The equations of motion of the system are strictly derived using Lagrange method and solved by the numerical integral method. The time-varying mesh stiffness is calculated by the potential energy method based on an improved mesh stiffness model. Afterwards, the new model is compared with the previous model and some dynamic characteristic differences between the two models are demonstrated using the rotating speed and backlash as control parameters. This results shows that due to the effects of the time-varying pressure angle and backlash, the system may enter into chaotic motion in advance and the tooth impact state will also alter. This research can provide a useful source of reference for dynamic design of gear transmission system and the further study of spur gear system.