Improved inverse filter for the correction of distorted measured cutting forces

- Improved inverse filter to correct the distorted cutting forces is proposed.
- Failure behaviors of traditional methods are analyzed and discussed in-depth.
- Scheme for achieving the point-to-point frequency correspondence between the measured forces and FRFs is developed.
- Correction reliability and efficiency of the proposed method are analyzed deeply.

The cutting forces sampled from machining processes may be distorted by the dynamic response of measuring system. Traditional methods, whether discrete inverse filter or Kalman filter, may result in accuracy loss due to inaccurate approximation of transfer function. This paper proposes an improved inverse filter to achieve accurate and efficient correction of the distorted cutting forces. Failure behaviors of traditional methods are analyzed in-depth first, and then, a spline curve-based interpolation scheme is proposed to approximate the transfer function of the measuring system. The transfer function corresponding to the frequencies of the measured cutting forces obtained by this method can be close to the actual response of the cutting system to the most degree. As a result, the corrected cutting forces can well reflect the actual physical response of the machining processes. To show the advantage of the proposed method, both the improved inverse filter and traditional Kalman filter are utilized to correct the cutting forces measured from three tests. Thorough comparison implies that both methods can give good and consistent corrected results in most cases, while Kalman filter will lose correction accuracy if the transfer function cannot be fitted so well to be sufficiently close to the measured result. Especially, calculation procedure turns out that the improved inverse filter is better in efficiency than Kalman filter.