Nonlinear dynamic modeling and analysis of spur gears considering uncertain interval shaft misalignment with multiple degrees of freedom

Shaft misalignment is regarded as a deterministic parameter in traditional dynamics analysis of gear system, but due to design tolerance and assembly accuracy, shaft misalignment is unavoidably uncertain and this kind of uncertainty exhibits interval attribute. To evaluate the dynamic characteristics of gear system more reasonably, a new nonlinear dynamic model of spur gears considering the uncertainty of shaft misalignment with multiple degrees of freedom (DOFs) is proposed and studied in this paper. First, the meshing analysis of spur gears under shaft misalignment is completed based on tooth contact theory. Then a nonlinear interval dynamic model of gear system is established and an interval analysis approach based on Chebyshev inclusion function and optimization method is used to obtain the upper and lower bounds of the dynamic response. Afterwards, the effectiveness of proposed dynamic model and interval algorithm is validated by comparison with the existing experiments and simulations respectively. Finally, parameter studies are carried out in detail and the result shows that the uncertainty of shaft misalignment will significantly change the internal excitation of gear system and thus enormously enhancing the system vibration, this will bring valuable guidance for the tolerance allocation in gearbox design.