A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions

A completely general solution is obtained whereby the elastic compliances of a system of any number of ball and radial roller bearings under any system of loads can be determined. Elastic yielding of the shaft and supporting structure are considered as well as centrifugal and gyroscopic loading of the rolling elements under high-speed operation. The solution defines the loading and attitude of each rolling element in each bearing of the system as well as the displacement of each inner ring with respect to its outer ring. For ball bearings the precise location of the load paths in each raceway are found. Life estimates can be more accurately made since the fatigue effects can be evaluated over known paths in the raceways. The solution, which is accomplished numerically by iterative techniques, has been programmed for an IBM-704 digital computer.