1st ICAI 2020

International Conference on Automotive Industry 2020

Mladá Boleslav, Czech Republic

The model of radial roller bearing, is based on the standard ISO/TS 16281. It uses parameters of internal geometry to compute load supported by individual elements. From illustration depicted in Figure 1 a) relation between radial displacement of internal ring δ r and compression of individual rollers δ i is derived in equation (1). Very important aspect of this relationship (and even more important for bearing itself) is an internal radial clearance P d which is a parameter directly driving the load distribution. The condition stated in equation (1) addresses the unloaded elements, of which deformation results in a negative value. Due to these elements do not contribute to bearing stiffness, the negative value of displacement is substituted by zero.

Figure 1: Schemes defining the models: a) radial roller bearing, b) EHL line contact

Source: Own elaboration (2020)

(1)

Then, a balance between external load and reaction forces of individual elements per equation (2) is defined. A stiffness of the roller K b could be calculated by Finite Element Method (FEM) or per the standard, estimated with sufficient accuracy by using relation where L w is a length of rolling element. The equation (2) is then solved iteratively for δ r which minimizes it with acceptable numerical error. (2) Result of this calculation is radial displacement of inner ring with respect to outer ring and vector of radial loads transferred by individual rolling elements. The other model describes EHL lubrication film for line contact between roller and race. Solution follows approach described by Venner in (Venner, 1991). The model is defined by Reynolds’ equation in the form per (3) and equation of lubrication film thickness per (4). The Reynolds’ equation describes the pressure profile p(x) in the contact which forms due to varying thickness h(x) of the thin channel in the direction of the fluid velocity u s . Sometimes this is referred as wedge effect.

(3)

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