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The conventional resonance conditions are derived based on the conventionally designed impellers without splitter blades. This paper proposes the resonance conditions for impellers under the excitation from the impeller–diffuser interaction with attention paid on the influence of splitter blades. A lumped parameter model is established and the modal analysis is carried out. The blade-based representative modal vector (RMV) is defined. The influence of splitter blades on the impeller’s traits of modes is investigated by analyzing the spatial harmonic contents of the RMV. Then, given the specific form of the diffuser-induced engine order excitation acting on the main and splitter blades, the resonance conditions are derived. Tuned and mistuned cases are provided for a practical impeller. The resonance conditions are verified by harmonic response calculations. The applications of the proposed resonance conditions in resonance identification and hazard evaluation of different excitations are given. The differences between the proposed resonance conditions and the conventional ones are discussed. The research indicates that even the RMV of the tuned impeller contains two harmonic components due to the existence of splitter blades. When the excitation frequency equals the natural frequency of the impeller and the excitation order matches with either harmonic index of the two harmonics, the resonance occurs. The results of case studies show that the harmfulness of various engine orders of excitation can be exactly evaluated by the joint use of the spatial harmonic contents analysis result and the proposed resonance conditions; however, analyzing based on the conventional resonance conditions may lead to the misjudgment of the harmfulness of the excitations.

Investigation of the Influence of Splitter Blades on the Resonance Conditions of Impellers