Enhancing the multi-encoder-based cutting force estimation along the stationary axis of a machine tool with multiple inertia dynamics

Wideband cutting force sensing is a key technology for process monitoring. Sensorless cutting force estimation using the internal servo information of a machine tool with ball-screw-driven stages has been studied owing to its high maintainability and ease of introduction. In the motor current-based method, the cutting force estimation along the stationary axis is challenging, and the estimation bandwidth is significantly limited owing to the low sensitivity of the motor current in the high-frequency range. The dual-inertia model-based load-side disturbance observer (LDOB) can estimate the cutting force along the stationary axis using the relative position obtained from the rotary encoder and linear encoder, which is installed relatively near the cutting point and has a high sensitivity in the high-frequency range. However, this approach is not applicable to machine tools with complicated structural dynamics. To address this challenge, we propose a cutting force estimation method along the stationary axis using the Kalman filter (KF) based on a multiple inertia model derived solely from the relative position signal. The dynamics, depending on the stage position of the feed drive, were modeled using linear interpolation. Through end milling tests, we confirmed that the cutting force estimation accuracy along the stationary axis of a machine tool with multiple inertia dynamics was significantly improved by the proposed method compared to the current and LDOB-based methods. Additionally, the wideband cutting force could be estimated using the proposed method for bandwidths up to 1000 Hz.