The sixth chapter of Rolling Bearing Analysis by Tedric Harris is entitled Distribution of Load in Statically Loaded Bearings. In this section of the book the forces and deflections of bearings under axial, radial, and moment loading are calculated while neglecting dynamic effects. These equations are applicable for most of the time because many applications involve steady state operation, moderate speeds and insignificant friction. At moderate speeds the centrifugal force and gyroscopic moment can be neglected.
The chapter begins by reviewing the force-deflection relationships developed earlier. For point contacts force is equal to a spring constant multiplied by overlap raised to the 3/2 power. For line contacts force is proportional to overlap raised to the 10/9 power. These relationships are used for all contacts between bearing elements.
The derivations for loaded bearings are quite complex. However, they are accompanied by figures and tables to aid in calculations. Many steps of the derivations are shown as well as the final solution.
Harris begins with derivations for bearings under either a radial or thrust load. These systems are relatively simple and lead to closed form solutions. For the angular contact bearings the solution is a little more complex because the contact angle changes with the axial deflection.
Next combined loading is analyzed. Combined radial and thrust loads have a simple solution, but a combined radial, thrust, and moment loading require the solution of simultaneous equations using the Newton-Raphson method.
Finally some complex situations are studied. The effect of misalignment on the loading, the roller crown, and non-rigid housings are all studied. Non-rigid housings become important when the outer race of the bearing is only supported at a few points or when the shaft is hollow. The flexible housing problem is solved using the energy method.
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