Simplification of the rolling contact-related lifetime calculation of profiled rail guides with a polynomial regression

The calculation of the lifespan of profile rail guides is an essential part in the design process of machines. Conventional lifespan models yield good results when calculating lifespan values under a homogeneous distribution of individual rolling contact forces on the raceways. In the case of an uneven load distribution, significantly too low lifespan values are calculated, resulting in a considerable loss of lifetime potential. The novel and experimentally validated rolling contact-based lifespan calculation (RCBL) takes the transferred force on each rolling element into account, resulting in more realistic lifespan values that can be up to 4 times higher than those obtained through the classical method. The disadvantage lies in the complex calculation of the necessary individual rolling contact forces, which until now has been done by using extensive finite element models, along with the computationally intensive optimization problem of the RCBL. To overcome these disadvantages, a method is introduced that efficiently calculates the individual rolling contact forces, taking into account all relevant system elasticities, and pre-solves the RCBL for a variety of potential superimposed load combinations. The results are subsequently approximated through an analytical multiparametric polynomial function and can be utilized with the conventional lifespan formula for rolling bearings.