Estimation of FRFs of machine tools in output-only modal analysis

Output-only (or operational) modal analysis (OMA) has proven to be a desirable tool for a wide range of applications for identifying dynamic modal parameters while structures are in service. It is especially useful for machine tools because evident changes will occur in dynamic properties between the working state and the static condition. However, the absence of input measurements obstructs OMA from assembling the frequency response function (FRF), which is necessary for many applications. Recently, a random cutting technique was proposed to excite the machine tools in order to extract the dynamic parameters through OMA. The present study is an extension of that work to estimate the FRF of machine tools. In this paper, the random cutting process is modeled to predict the cutting forces according to available information, such as the cutting parameters, the tool geometry, and the workpiece material, which are all known before machining. A function is introduced into the model to evaluate the influence of the variation of spindle speed on the cutting forces. Then, the calculated cutting forces are employed to replace the missing input measurement to estimate the FRF. The proposed method was experimentally validated and showed satisfactory agreement between the measured and estimated results in magnitude, although the phase is not that desirable. Finally, the approximation error of the method was analyzed and some error reduction strategies were presented.