Calculation of the Stiffness Matrix of Angular Contact Ball Bearings by Using the Analytical Approach

Abstract

The stiffness matrix of angular contact ball bearings is calculated by using the analytical approach in which the summation of ball-race loads is replaced by an integration. The matrix connected to the conventional model in two degrees of freedom is first presented. A practical application of this formulation is illustrated through the common problem of sizing a two bearings-shaft arrangement. Variations of displacements, axial forces, and bearing fatigue life related to preload are shown to be easily obtained. Then, the matrix connected to the model in five degrees of freedom is given. This may be coupled with finite elements which are generally used to model the shaft or the housing. [S1050-0472(00)01801-8]

Stability analysis of machine tool spindle under uncertainty

“…The K c is an empirical coefficient which is dependent on the workpiece material and tool geometry. Both N Ã t and G(v) are related to the cutting geometry and can be determined using the formulas in equation (13) respectively, as depicted in Figure 5 for a down milling application…”

A catalogue capacity of slewing bearings

“…In the method of local displacements clamped rolling elements are replaced by tensioned non-linear springs as in the works [20,21]. These are springs with characteristics of similar course as in Fig.…”

Design and experimental study of the SPKM165, a five-axis serial-parallel kinematic milling machine

“…This is because stiffness greatly influences precision and the surface finish. The matrix stiffness method [28][29][30][31] and the finite-element method (FEM) are the most commonly used methods for stiffness analysis. The FEM is effective in evaluating the performance of a parallel or hybrid machine under actual working conditions.…”