Directionally independent failure prediction of end-mill cutting tools: An investigation of noise reduction using higher dimensional real fourier analysis

Accurate on-line forecasting of a tool's condition during end-milling operations is advantageous to the functionality and reliability of automated industrial processes. The ability to disengage the tool prior to catastrophic failure reduces manufacturing costs, excessive machine deterioration, and personnel hazards. Rapid computational feedback describing the system's state is critical for realizing a practical failure forecasting model. To this end, spectral analysis by fast Fourier type algorithms allows a rapid computational response. The research described herein explores the development of non-traditional real FFT (Discrete Cosine Transform) based algorithms performed in unique higher-dimensional states of observed datasets. The developed Fourier algorithm is novel since it quantifies chaotic noise rather than relying on the more traditional observation of system energy. By increasing the vector dimensionality of the DCT, the respective linear transform basis will more effectively cross-correlate the transform data into fewer (more significant) transform coefficients. Thus, a single vector in orthogonally higher-dimensional space is observed instead of multiple orthogonal vectors in single-dimensional space. More specifically, a novel noise reduction technique is utilized to track trends measured from tri-axial force dynamometer signals. This transformation effectively achieves both system noise reduction and directional independence by observing the chaotic noise instead of system energy. Algorithm output trends from six end-milling life-tests are tracked from both linear and pocketing maneuvers in order to demonstrate the technique's capabilities. In all six tests, the algorithm predicts impending tool failure with sufficient time for tool removal.