Aerospace and Mechanical Engineering by Qi Luo

By Qi Luo

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Any increase in the spectral energy of the first harmonic corresponds to an increase in the degree of wear; nevertheless we noticed the important influence of the tool position on the spectral energy of this harmonics. The sensor which is fixed (Fig. 10-a) on the spindle provides the best results, it is less sensitive to the variations of the direction of machining because the position of the sensor compared to the point of contact tool-workpiece is constant. 10 Evolutions of the first Harmonics a) Accelerometer fixed at Spindle b) Accelerometer fixed at pallet Discrete wavelet transform (dwt) analysis DWT is a signal processing technique in the time–frequency domain.

In contrast to the variance plot, the harmonic's evolution has certain characteristics only on the fifteenth pass (t=300sec), representing the change of the machining cycle of the workpiece but not on the thirtieth one (t=600sec). Consequently, we deduce that any change of the cutting conditions or the tool performance leads to changes in the amounts of flank wear and then in the significant cutting forces harmonics. Stimate of Flank Wear vb by Neural Network. By definition a neural network is an assembly of elements or nodes “processors” where an under group makes an independent treatment and passes the result to the second under group.

Given a time-varying signal x[n], DWT consists of computing coefficients which are inner products of the signal and a family of scaling and wavelet functions. It is defined as : h j  n − 2 j k  = 2 −j 2  t − 2jk   j  2  φ . With φ as the scaling function defined together with c j , k = ∑ x [ n ]h j  ¨n − 2 j k  . (3) (4) Cjk are called the approximation coefficients, which are the low-frequency maps of the original discrete time signal x[n]. [10, 11, 12] A multiresolution analysis approach is used in which a discrete wavelet (ψ ) function is used to compute the details (dj,k) coefficients, which are the sampled versions of the original signal and are the high frequency representations of it.

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