Chatter is generally defined as self-generated vibrations from the interaction between tool and workpiece. It is the most critical vibration in machining operations and can decrease the surface quality and cause the premature tool wear. Chatter creates erroneous vibrations on the workpiece surface.
Methodology
:
Ching-Chih Wei, Meng-Kun Liu, and Guo-Hua Huang
This mathcad worksheet is a signal processing technique of chatter detection for bar boring based on the hilbert–Huang Transform (HHT). HHT is suitable for the analysis of non-stationary and non-linear signals. The signals are decomposed into several intrinsic mode functions (IMFs) using empirical mode decomposition (EMD). Dominant IMFs, which best represent the occurance of chatter can be identified and combined to give the best chatter indicator. The hilbert transform is then applied to the chatter indicator IMF to obtain the instantaneous frequencies with time and their amplitudes. Finally, the marginal and the hilbert spectrums of strain signals were produced using selected IMFs.
The Reference Worksheets listed below are used in the Signal Processing of the Chatter data.
Note: The Array Origin in the referenced worksheets below is set to 1
Read Two Sets of Data (A and B having Different depths of Cut ) in 4 Columns (Time-microsec, Vibration-mv)
Sample times in μs:
NOTE: The Array Origin of the worksheets is 1. HHT<1> is just the original signal.
Index n starts with 2 so that the original EMD HHT function (n=1) output is excluded from the Ratio
Comparison of Energy Ratios of
Spectrum Content of B to A
Note: Below value of the Normalized Energy Ratio of Sample B to A of Intrinsic Mode 4 (HHT<5>, Z5) is 2.235.
See Graph of Z5 and ZB5 at bottom of next page.
Normalized S pectral Energy Content
Above ERatios show IMFs 3, 4, 5 have the greatest discrimination and are added for our chatter detector, IMFD.
Find the discrete Fourier transform spectrum CFFT of the complex signals in the frequency domain:
Compute the transform for Modes 1 to 5:
Build the complex signal:
Data set A
Data set B
Sampling time,
Ts in seconds: