In real-life applications, multi-disk-rotor systems are supported on bearings with nonlinear flexibility. The balancing of such systems at high speeds is a challenging task. This work presents a method of balancing such systems. The dynamic equations of motion for a nonlinear system are derived first using the influence coefficient method and then Lagrangian equations. An equivalent linear system is found using the optimization principles. Finally, the correct balance weights for the nonlinear system are obtained based on the equivalent linear system. The results thus obtained establish the utility of such a method of balancing nonlinear systems.
Balancing of Rotors Supported on Bearings Having Nonlinear Stiffness Characteristics
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Turpin, A., and Sharan, A. M. (July 1, 1994). "Balancing of Rotors Supported on Bearings Having Nonlinear Stiffness Characteristics." ASME. J. Eng. Gas Turbines Power. July 1994; 116(3): 718–726. https://doi.org/10.1115/1.2906878
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