Developing the Power Model of a Roller Bearing

The paper proposes a new method for calculating the force vector and the stiffness matrix for all types of roller bearings. The derived bearing model has 12 degrees of freedom as each ring is considered as a rigid body. Local deformations of the ring due to the interaction with the rollers are accounted for through contact stiffness coefficients. The existing slicing technique is applied to split a roller into thin disks to calculate the total deformation energy of both individual rollers and the bearing itself. The components of the force vector and the stiffness matrix are computed through the first and the second order derivatives of the deformation energy. The equilibrium position of the roller between the bearing rings is determined by solving a nonlinear system of algebraic equations with the aid of the quasi-Newton method. The obtained relative displacements of the rollers and the rings are used to calculate the distribution of contact pressure between the rollers and the roller ways. The proposed method of calculating the force vector and the stiffness matrix can be used for studying load characteristics of bearings as well as solving rotor dynamics problems. The developed algorithm is much more efficient than a conventional 3D finite element analysis that can generate models with tens of thousands of degrees of freedom for only a single bearing. The model is verified using a numerical test, the results of which are compared with the solutions proposed by other researchers and with experimental data.

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