# The Bivariate Empirical Mode Decomposition and Its Contribution to Grinding Chatter Detection
## 4 Grinding Experiments Validation  
### Grinding Experiments  
In order to further validate the feasibility of BEMD for grinding chatter detection, an experimental method was designed to acquire various vibration signals from different grinding parameters for a CNC guideway grinder (KD4020X16, Hangzhou Hangji Machine Tool Co., Ltd., Hangzhou, China). An integral electronic piezoelectric (IEPE) accelerometer sensor with a supporting dynamic signal test and analysis system (TST5912) were used to collect grinding vibration signals (Figure 11).  
In practice, the grinder is more sensitive to rotational speed, feeding speed and grinding depth of the grinding wheel, which actually contribute to imbalances in grinding vibration. Thus, this experiment was carried out with the following steps:  
* Keeping the workpiece feeding speed and grinding wheel depth constant while gradually increasing the rotational speed;
* Keeping the feeding speed and rotational speed constant while gradually increasing the grinding depth;
* Keeping the rotational speed and depth of grinding constant while gradually increasing the feeding speed.  
Thus, the parameters are listed in Table 3.  
According to the experimental conditions shown in Table 3, eight piezoelectric acceleration sensors were used to test vibration acceleration signals from the grinding wheel spindle, motor and machine column in various directions [34]. The position of the sensors and their corresponding sensitivities are given in Table 4.  
As per the above steps, 80 groups of grinding signals were obtained, of which 45 were in a stable grinding state, while 35 were in a chatter state. Based upon practical experience and considerable experimental data, it has been demonstrated that the chatter of wheel spindles occurs more in the \(x\)- and \(z\)-directions than in the y-direction. Thus, for convenience of this presentation, this paper selects parts of \(x\)- and \(z\)-direction chatter data as an original complex-valued signal. However, in the signal acquisition stage, the disturbing noise will inevitably be mixed in grinding vibration signal duo to the influence of many random factors, directly affecting detection accuracy of grinding chatter. It is reasonable to carry out pre-processing to eliminate noise for signals. Moreover, the wavelet de-noising technique, which has the characteristics of time domain localization, multi-resolution and flexibility of selecting wavelet basis, has been widely employed in signal processing [35; 36]. Thus, in this paper, the noise is removed from the original complex-valued signal based on wavelet de-noising. Meanwhile, we resample the complex-valued signal based on Nyquist sampling theory [37]. The new, reconstructed complex-valued signal is shown in Figure 12.  
From Figure 12, it is found that grinding chatter emerges at about 5-14 s and the transitional phase lasts almost 9 s. It is clearly seen that the amplitude of the vibration signal rapidly expands when the grinder starts chattering, then the amplitude becomes steady when the grinder enters stable chatter. However, the signal vibrates more markedly compared with the stable grinding state. Moreover, note that the abnormal signals derived from the joints of the workpiece will not greatly affect the overall signal analysis.