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Multi-point substructure coupling method to compensate multi-accelerometer masses in measuring rotation-related FRFs


 Tool-tip Frequency Response Functions (FRFs) are often required in milling vibration analysis. Receptance coupling substructures analysis (RCSA) affords an efficient analytical way for different tool-tip FRFs prediction with only one modal test. The coupling theory includes both translational and rotational degrees of freedom, so rotation-related FRFs are essential to know in the test. The finite-differential technique is generally used to measure these special FRFs due to the avoidance of specialist equipment. The technique uses several translational accelerometers spatially placed close to each other to approximate the rotational vibration. However, the added sensor masses lead to the frequency shift of the test structure, and the phenomenon would aggravate as the sensors increase. The polluted measurement data would subsequently decrease the tool-tip FRFs prediction accuracy. Addressing this problem, this paper introduces a multi-point substructure coupling method to simultaneously compensate the multi-accelerometer masses in a single experimental setup. The proposed method considers the installed accelerators as multiple point masses and then uses inverse coupling calculation to isolate their effect. The compensation procedure is first effectively validated in simulation and experiment, and then it is integrated into an RCSA-based application of predicting different tool-tip dynamics. Experimental results show that the compensated FRF data can improve prediction accuracy, especially when predicting tools shorter than the tested tool.