Improved calculation method for dry modal analysis of four-stage centrifugal-pump rotor system based on concentrated-mass method

To improve the accuracy of modal analysis for a four-stage centrifugal-pump rotor system with a balancing disc based on the concentrated-mass analytical method, a simplified concentrated mass mathematical model and an ANSYS simulation model are established. The results from these two models are compared to determine factors that cause significant differences in the mode shapes. Subsequently, an optimized mathematical model based on the corrected mass moment of an inertia matrix and stiffness correction coefficients is proposed, and the effectiveness of this optimized mathematical model is validated using a four-stage centrifugal pump with back blades. The results show that the natural frequencies obtained from the ANSYS simulations are consistently higher than those obtained using the analytical method. The simplification of the moment of inertia at the impeller and balancing disc contributes primarily to the calculated errors. The optimized mathematical model reduces the errors in the natural frequencies from 12.96%, 12.13%, 9.96%, 5.85%, and 8.74% to 2.45%, 1.56%, 0.65%, 5.34%, and 2.28%, respectively. The optimization of natural frequencies offers better performance at lower-order modes, whereas its effects on higher-order modes are less significant. The optimization method is applicable to centrifugal pumps with back blades and reduces the error in theoretical calculations, based on reductions in the concentrated mass from 13.11%, 12.85%, 9.91%, and 7.2% to 3.7%, 3.86%, 0.57%, and 2.87%, respectively, thus further confirming the feasibility of the optimized model design.