Wavelet Time Series ARMA Prediction on Cutting Vibration in Diamond Turning

It is a critical step to control the cutting vibration during diamond turning in order to obtain super smooth surface. Both the wavelet transformation method and the autoregressive moving average (ARMA) model are combined utilized to predict and fit the cutting vibration signals in diamond turning. Firstly, by means of the wavelet transform, the cutting vibration series have been decomposed at multi-levels so as to get their scale decomposition series and wavelet decomposition series. Further, the scale decomposition series have been forecasted by intercepting segments from sine wave at each level. And the wavelet decomposition series have been predicted based on the ARMA model at each level. Finally, the forecasted scale decomposition series and wavelet decomposition series have been reconstructed and fitted into the predicting vibration series. In addition, the cutting vibration series have been extracted from the scanned AFM digital images of diamond turning surface, where the valley signals exhibit the serial vibrating information of each cutting edge profile along cutting direction.