Statistical Analysis of Contact Stiffness for Shaft-Bearing Assembly with Tolerancing and Fit

Abstract

Abstract Tolerance and fit (T&F) are crucial as it affects the performance of mechanical system. Fitting condition between shaft and bearing is the most typical one that affects the pressure distribution between the them that, in turn, determines its contact stiffness. This paper is aimed to explore a method to analyze the statistical distribution of the contact pressure and stiffness between the shaft and the bearing based on the size distribution of the T&F specification. We analyzed the pressure distribution corresponding to the T&F specifications of the shaft and the bearing by the probability density function and convolution. Contact pressures and stiffness of the mating surface are analyzed according to the amount of interference. A roller bearing with diameter 50 mm is taken as an example to illustrate this analysis. The contact pressure and stiffness are analyzed under a transition fitting condition o50H6/k5, as recommended by many bearing makers and design handbooks. The results showed that there is a high possibility to become clearance fit in this case and the expectation is a gap of 0.5μm, which implies loss of the contact stiffness thus far from the original design intention. Two approaches, either using tighter tolerance of bearing inner ring or higher dimensional deviation of the shaft diameter, are further investigated to overcome this problem. The results showed that probability and expectation of contact stiffness increase by employing either approach. The main contribution of this paper is to develop a methodology for analyzing statistical distribution of contact stiffness between the shaft-bearing assembly based on the T&F specification. It also shows tighter tolerance for the bearing inner ring or higher dimensional deviation of the shaft diameter will improve contact stiffness, if the T&F specification does not meet stiffness requirement.