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The orbit shape responded from each concerned section of anisotropic rotating machinery varies along with the axial position of unbalance force, especially its parameters like the inclination angle and the major to minor axis ratio. Considering the axial position difference between the original unbalance mass existed and the balancing planes adopted, vibration reduction with balancing could be disturbed by the anisotropy of rotating machinery. Through in-depth analysis on these mechanisms, a method for anisotropy evaluation is presented based on the dispersion characteristics estimation of system difference coefficients. Balancing experiments under different degrees of system difference coefficients dispersion and different unbalance mass distribution are implemented to show the effectiveness of this method. Essentially, the unbalance response of each concerned section is a synthesis of system difference coefficients and unbalance mass. Therefore, as weight coefficients of unbalance mass, the dispersion evaluation indexes of system difference coefficients can be used in distributing the original unbalance mass to further reduce the disturbance of system anisotropy to vibration reduction.

The vibration responses of different linear faults all possess some common features, which make fault diagnosis very difficult. Based on the multi-sensor information fusion theory, this paper presents a new qualitative identification method for the diagnosis of linear faults. The excitation–response dynamic equation is constructed and system balancing response with full consideration of system anisotropy is analyzed. Through discussion of the precession orbit shape difference and its dispersive situation, the orbit shape average difference coefficient and the corresponding dispersion term are estimated to obtain the theoretical balancing effect. Finally, the qualitative identification of linear fault can be done according to whether the calculated balancing effect meets the safe operation requirement or not. The dynamic characteristic of the system difference coefficients is verified by a simulation experiment and the case study further testifies the capability and reliability of the proposed method.

In this paper, the holospectrum technique based balancing method has been improved by reselection of the balancing object. Current holospectrum based balancing technique uses the initial phase vector (IPV) as the balancing object. Theoretical analysis of the precession behavior of an unbalanced rotor with anisotropic stiffness shows that, compared with the IPV, its forward precession component vector is much better in describing the rotor balance state and is more suitable to be used as the measurement of unbalance response. After the backward precession component is removed, the impact of probe orientation on the balancing analysis and calculation is completely eliminated and the computational procedure is greatly simplified without sacrificing the balancing precision. The experiments and field application cases verify the accuracy and effectiveness of this method.