Non-linear mathematical modeling of gear rotor bearing systems including bearing clearance

Gürkan, Niyazi Ersan
In this study, a non-linear mathematical model of gear-rotor systems which consists of elastic shafts on elastic bearings with clearance and coupled by a non-linear gear mesh interface is developed. The mathematical model and the software (NLGRD 2.0) developed in a previous study is extended to include the non-linear effects due to bearing clearances by using non-linear bearing models. The model developed combines the versatility of using finite element method and the rigorous treatment of non-linear effect of backlash and bearing clearances on the dynamics of the system. The software uses the output of Load Distribution Program (LDP), which computes loaded static transmission error and mesh compliance for the contact points of a typical mesh cycle, as input. Although non-varying mesh compliance is assumed in the model, the excitation effect of time varying mesh stiffness is indirectly included through the loaded static transmission error, which is taken as a displacement input into the system. Previous computer program which was written in Fortran 77 is rewritten by using MatLAB 7.0 and named as NLGRD (Non-Linear Geared Rotor Dynamics) Version 3.0. The program is highly flexible and open to further developments. The program calculates dynamic to static load ratio, dynamic transmission error, forces and displacements at bearings. The mathematical model suggested and the code (NLGRD version 3.0) are validated by comparing the numerical results obtained from the model suggested with experimental data available in literature. The results are also compared with those of previously developed non-linear models. The effects of different system parameters such as bearing stiffness, bearing clearance and backlash on the gears are investigated. The emphasis is placed on the interaction of clearances in bearings with other system parameters.


Fracture mechanical behaviour of visco-elastic materials: application to the so-called dwell-effect
NAESER, Bastian; KALISKE, Michael; Dal, Hüsnü; NETZKER, Christiane (Wiley, 2009-08-01)
The material force approach is an efficient, elegant, and accepted means to compute the J-integral as a fracture mechanical parameter for elastic and inelastic materials. With the formulation of a multiplicative split of the deformation gradient at hand, rate-dependent (visco-elastic) materials described for example by the physically based Bergstrom-Boyce model can be investigated. For these investigations, the so-called material volume forces have to be computed in order to separate the driving forces acti...
Analytical and numerical solutions to rotating orthotropic disk problems
Kaya, Yasemin; Eraslan, Ahmet Nedim; Department of Engineering Sciences (2007)
Analytical and numerical models are developed to investigate the effect of orthotropy on the stress distribution in variable thickness solid and annular rotating disks. The plastic treatment is based on Hill’s quadratic yield criterion, total deformation theory, and Swift’s hardening law. The elastic-plastic stress distributions, residual stresses and radial displacement distributions are obtained after having analysed the cases of rotating solid disk, annular disk with rigid inclusion, annular disk subject...
Nonlinear time-varying dynamic analysis of a spiral bevel geared system
Yavuz, Siar Deniz; Sarıbay, Zihni Burcay; Ciğeroğlu, Ender (Springer Science and Business Media LLC, 2018-06-01)
In this paper, a nonlinear time-varying dynamic model of a drivetrain composed of a spiral bevel gear pair, shafts and bearings is developed. Gear shafts are modeled by utilizing Timoshenko beam finite elements, and the mesh model of a spiral bevel gear pair is used to couple them. The dynamic model includes the flexibilities of shaft bearings as well. Gear backlash and time variation of mesh stiffness are incorporated into the dynamic model. Clearance nonlinearity of bearings is assumed to be negligible, w...
Separation at the interface of non-linearly elastic spinning tube-rigid shaft subjected to circumferential shear
Akyüz, Uğurhan (Elsevier BV, 2004-10-01)
Separation at the interface of homogeneous, isotropic, compressible, hyperelastic, spinning cylindrical tube-rigid shaft subjected to circumferential shear is investigated within the context of the finite elasticity theory. The compressible, hyperelastic spinning tube with a uniform wall thickness is assumed to be tautly fitted to a rigid shaft along its inner curved surface. The outer surface of the tube is subjected to a constant uniformly distributed circumferential shearing stress while the rigid shaft ...
Stress distributions in elastic-plastic rotating disks with elliptical thickness profiles using Tresca and von Mises criteria
Eraslan, Ahmet Nedim (Wiley, 2005-04-01)
Analytical and numerical solutions for the elastic-plastic stress distribution in rotating variable thickness solid and annular disks are obtained under plane stress assumption. The thickness of the disk is assumed to vary radially in elliptic form which represents a wide range of continuously variable nonlinear cross-sectional profiles. Tresca's yield criterion and its associated flow rule are used to obtain analytical solutions for a linear hardening material. A computational model is developed to obtain ...
Citation Formats
N. E. Gürkan, “Non-linear mathematical modeling of gear rotor bearing systems including bearing clearance,” M.S. - Master of Science, Middle East Technical University, 2005.