66 J.M. Liu et al. A B Fig. 6.8 Exciting point and response point 0 0 0.25 0.5 0.75 1.0 -180 -90 0 90 180 0 0.50 1 1.50 2 2.50 3 3.50 (e+1)m/s2/NName:test Test No.:1 Input:f1 Output:1 4 200 400 600 800 1k 1200(Hz) FRF(H1) SF= 12800.000Hz Ave. times: 1 Df= 3.1250Hz Tot points: 401 cursor: 108 f = 334.3750Hz H = 2.9029e+001 Ph.= 90.675 Co.=1.000 NewCo.=1.000 FitIndex=96.078% m/s2/N Fig. 6.9 FRF and new coherence function with one time averaging Exciting point is A, for harmer to knock in vertical direction. Accelerometer is fixed in point B for measuring vertical direction. Five times impacting are recorded. The sampling frequency is 12,800 Hz, FFT point number is 4,096. The analyzing frequency range is 0 to 1,250 Hz. The analysis result is illustrated as Figs. 6.9, 6.10, 6.11, 6.12, and 6.13 with different averaging times. In the figure, the above part is FRF amplitude with log style, middle part is FRF phase, below part is coherence function and new coherence function (green color). With new coherence function definition, only one impact will obtain the stable coherence function, so the impact times can be greatly reduced. Furthermore, the new coherence function has clearer engineering meaning than tradition coherence function. Let’s assume in one test, the sampling length is too short in one impact, which will cause serious leakage in FRF calculation. But in the traditional coherence function, the serious leakage can’t be reflected. With new coherence function, only by one time averaging, the serious leakage will be reflected. The traditional coherence function can’t reflect the leakage caused by too short of sampling length of one impact, the leakage is reduced by adding negative exponent window, the exponent window index is decided according to analyzer’s experience.
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