Abstract: A new modeling method of shaft-bearing stiffness coupling and an iterative method for calculating the deformation of multi-bearing shafting system are presented for the typical complex multi-bearing shafting system used in driving system. The bearing stiffness matrix is created by Newton-Raphson method through the following steps: calculation of contact stress and deformation, calculation of internal load distribution, and solution of rolling elements mechanics equilibrium equations, which is based on the theory of bearing geometry and contact mechanics. The shafting system stiffness matrix is constructed by coupling the Timoshenko beam and bearings. The deformation of system can be solved by iterative matrix displacement method of variable bearing stiffness, which is applied to SSOR iterative matrix. It is proven that the method has better convergence, lower demand to initial data, and higher accuracy, which is more convenient to use for engineering design.

Key words: solid mechanics, matrix displacement method, Timoshenko beam, bearing stiffness, SSOR iterative matrix, Newton-Raphson method