Analysis of an Arched Outer-Race Ball Bearing Considering Centrifugal Forces

Abstract

A thrust load analysis of an arched outer-race ball bearing which considers centrifugal forces but which neglects gyroscopics, elastohydrodynamics, and thermal effects was performed. A Newton-Raphson method of iteration was used in evaluating the radial and axial projection of the distance between the ball center and the outer raceway groove curvature center (V and W). Fatigue life evaluations were made. The similar analysis of a conventional bearing can be directly obtained from the arched bearing analysis by simply letting the amount of arching be zero (g = 0) and not considering equations related to the unloaded half of the outer race. The analysis was applied to a 150-mm angular contact ball bearing. Results for life, contact loads, and angles are shown for a conventional bearing (g = 0) and two arched bearings (g = 0.127 mm (0.005 in.), and 0.254 mm (0.010 in.)). The results indicate that an arched bearing is highly desirable for high speed applications. In particular, for a DN value of 3 million (20000 rpm) and an applied axial load of 4448 N (1000 lb), an arched bearing shows an improvement in life of 306 percent over that of a conventional bearing. At 4.2 million DN (28000 rpm), the corresponding improvement is 340 percent. It was also found for low speeds, the arched bearing does not offer the advantages that it does for high speed applications.