Rolling bearing damping for dynamic analysis of multi-body systems—experimental and theoretical results

Abstract

The present paper deals with the measurement and calculation of the damping capability of rolling element bearings. Rolling bearing damping is strongly influenced by the lubricated contacts between rolling elements and raceways. A theoretical model for calculating lubricant film (elastohydrodynamic lubrication) damping is briefly described in the first part of this paper. Furthermore, a relationship for estimating damping due to other dissipative mechanisms in the bearing is suggested. In the second part, two experimental approaches for measuring rolling bearing damping are discussed. The first (more 'classical') approach is based on conventional frequency response measurements and was used to verify the developed damping model regarding the influence of bearing lubrication, speed and preload. Finally, a new experimental approach for identifying rolling bearing damping is presented, eliminating some of the drawbacks of the 'classical' approach.

Dynamics and efficiency of planetary gear sets for hybrid powertrains

“…In the present work the emphasis has been primarily placed on the examination of the effect of different driving power modes, thus it is assumed that there is no phase difference at different meshing points between the gear sets. During meshing, hysteretic material damping needs to be included [12]. The damping coefficient for the contact of a single meshing teeth pair can be obtained using:…”

Effect of tapered roller bearing supports on the dynamic behaviour of hypoid gear pair differentials

“…m is the number of rolling element and ( ) is the instantaneous angular position of the rolling element . is the instantaneous contact load of the i th rolling element, obtained using Hertzian contact theory also accounting for hysteretic damping [35]:…”

A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems

“…The exponent α is typically equal to 3/2, but can also assume other values [42,43]. The generalized parameter K is dependent on the material properties and the shape of the surfaces in contact and can be evaluated as [44] (23) in which σ j and σ b denote the material parameter for rigid journal and bearing, respectively, which are given by…”

“…The ANCF approach is used to model the flexible parts, while the NCF is considered to model the rigid elements. The equations of motion for constrained flexible multibody systems can be expressed in a compact form as a set of differential and algebraic equations as [64] Mq + T q λ + F(q) = Q(q) (q, t) = 0 (43) where M is the system mass matrix, (q, t) represents the vector that contains the system constraint equations, q is the derivative matrix of constraint equations with respect to the system generalized coordinates q, vector λ is the Lagrangian multipliers associated with the constraints, and Q(q) denotes the system external generalized forces. In this formulation, vector Q(q) includes the distributed gravitational forces as well as the contact-impact forces and the lubrication forces, and F(q) denotes the system elastic force vector.…”

“…As has already been mentioned, based on the mixed formulations (ANCF and NCF), the system mass matrix M will be constant and the constraint equations can be simplified. There are several methods for solving (43), namely those available in the specialized literature [65][66][67].…”