A variational approach to the calculation of bearing load distribution
Abstract
Accurate design of bearing systems, essential for long, reliable life, requires that the stress imposed on the rotating bearing elements be acceptable. This requires accurate calculation of the forces developed in the bearing elements due to the applied load. This is commonly referred to as the bearing load distribution. Calculation of the bearing load distribution has historically been achieved through Classical Bearing Theory. This method was developed through a combination of theoretical and experimental analysis. While results obtained through Classical Bearing Theory are generally acceptable for simple bearing systems, use of this method in "real life" designs can lead to substantial error. Use of Finite Element Analysis (FEA) is now being employed to analyze bearing systems too complicated for the Classical approach. While accurate results are obtainable for complex systems, FEA generally requires expensive computer system hardware and software, extensive model generation and modification time, and specialized training in the software. Complexity of most FEA software and inaccurate modeling can result in significant solution error. Therefore, a need exists to span the gap between the limited Classical Bearing Theory and the expensive, time consuming Finite Element Analysis. This "bridge" is the Variational Method here presented. This method possesses the best components of each of the previous procedures. The Variational Method is based on the minimization of potential energy of the bearing system using the Ritz Method. Load distributions for various general and specific bearing systems will be made using both Classical Bearing Theory and the Variational Method. Results demonstrate excellent agreement between the Variational Method and Classical Bearing Theory for the range of bearing systems where Classical Bearing Theory can be appropriately be applied. Solutions for more complex bearing systems will be obtained by use of the Variational Method. A computer program has been written to implement the Variational Method and obtain solutions. The computer program is designed to run on an ordinary PC.
This paper has been withdrawn.