High frequency bandwidth cutting force measurement in milling using capacitance displacement sensors

This article presents a method of measuring cutting forces from the displacements of rotating spindle shafts. A capacitance displacement sensor is integrated into the spindle and measures static and dynamic variations of the gap between the sensor head and the rotating spindle shaft under cutting load. To calibrate the sensing system, the tool is loaded statically while the deflection of the tool is measured with the capacitance probe. With this calibration, the displacement sensor can be used as an indirect force sensor. However, the measurement bandwidth is limited by the natural modes of the spindle structure. If cutting force frequency contents are within the range of the natural modes of the spindle structure or higher, the measurements are distorted due to the dynamic characteristics of the spindle system. In order to increase the bandwidth of the indirect force sensor by compensating for the spindle dynamics, the design of a Kalman filter scheme, which is based on the frequency response function (FRF) of the displacement sensor system to the cutting force, is presented in this paper. With the suggested sensing and signal processing method, the frequency bandwidth of the sensor system is increased significantly, from 350 to approximately 1000 Hz. The proposed indirect force sensor system is tested experimentally by conducting cutting tests up to 12,000 rpm with a five-fluted end mill. Besides cutting forces, the measured displacements can also be affected by factors such as roundness errors, unbalance at different speeds, or dilatation of the spindle shaft due to temperature variations. Methods to compensate for these disturbing effects are also described in the paper.