Modal balancing for ball bearing-rotor system using nonlinear normal modes

•A new modal balancing method based on nonlinear normal modes (NNMs) is used to balance nonlinear rotor-bearing systems.•The complex Fourier expansion of the rotor responses and NNMs is utilized to obtain correction coefficients for each harmonic, considering the super and subharmonic components.•Hertz contact force and different sizes of radial internal clearances of the ball bearings are considered.•NNMs demonstrate the frequency energy dependence of the ball bearing rotor systems and the phenomena of harmonic resonance and internal resonance.•Compared to traditional methods, rotors balanced by the NNMs method have greater amplitude reduction, fewer and smaller harmonic components, and more stable vibrations. Rotor dynamic balancing procedure relies on the linearisation hypothesis of the rotor system. However, some mechanical elements constituting a rotor system behave in various nonlinearities, such as the contact force and radial internal clearance between rolling balls and races for a rotor-bearing system. To balance a nonlinear rotor system, the traditional modal balancing method must be extended. This paper investigates the modal balancing method for a rotor-bearing system based on nonlinear normal modes (NNMs). The proposed algorithm includes three main steps. First, compute the NNMs and express nonlinear modal shapes using complex Fourier series. Second, describe the unbalance response as a complex amplitude containing higher harmonics. Third, estimate the correction coefficient of each harmonic, then compute the unbalance correction of each mode of interest until the total unbalance corrections are obtained. Hertz contact force and two different sizes of radial internal clearances of the ball bearings are considered during the balancing simulation. The responses after balancing with NNMs are present and compared with the linear modal method to demonstrate the accuracy and effectiveness of the proposed method.