Nonlinear dynamic analysis of a drivetrain composed of cylindrical gears, straight and spiral bevel gears

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2018
Yavuz, Şiar Deniz
A nonlinear dynamic model of a drivetrain composed of spur, helical and spiral bevel gears is proposed. Gear shafts are modeled by using Timoshenko beam finite element method and mesh models of gear pairs are used to couple them. Dynamic model includes the flexibilities of bearings as well. Gear backlash and time variation of mesh stiffness are incorporated into the mesh model. Harmonic Balance Method (HBM) with multiple harmonics is applied on the system of nonlinear differential equations in order to obtain a system of nonlinear algebraic equations. Since finite element modelling results in large number of nonlinear equations, receptance method and modal superposition method are introduced to forced response analysis of geared systems with nonlinearities in order to reduce computational effort. This makes it possible to use finite element models for gear shafts. In the calculation of Fourier coefficients, continuous-time Fourier transform, as opposed to the gear dynamics studies that utilize discrete Fourier transform, is used. Thus, convergence problems that arise when the number of nonlinear DOFs is large are avoided. Moreover, analytical integration is employed for the calculation of Fourier coefficients rather than numerical integration in order to further reduce the computational time required. Nonlinear algebraic equations obtained are solved by utilizing Newton’s method with arc-length continuation. The results obtained by HBM are verified by comparing them with those obtained by direct numerical integration, which are computationally demanding. Several parametric studies are performed and response of the system is investigated to demonstrate the effects of system parameters.

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Citation Formats
Ş. D. Yavuz, “Nonlinear dynamic analysis of a drivetrain composed of cylindrical gears, straight and spiral bevel gears,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.