By Cornelius Leondes, Cornelius T. Leondes
Within the aggressive company enviornment businesses needs to always try to create new and higher items speedier, extra successfully, and extra cheaply than their rivals to realize and preserve the aggressive virtue. Computer-aided layout (CAD), computer-aided engineering (CAE), and computer-aided production (CAM) are actually the regular. those seven volumes provide the reader a entire remedy of the ideas and functions of CAD, CAE, and CAM.
Read or Download Computer-Aided Design, Engineering, and Manufacturing: Systems Techniques and Applications, Volume VI, Manufacturing Systems Processes PDF
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Additional info for Computer-Aided Design, Engineering, and Manufacturing: Systems Techniques and Applications, Volume VI, Manufacturing Systems Processes
Sample text
For example, if a third frequency component is introduced, it would appear as an additional eigenfunction pair. This might, for example, correspond to the appearance of harmonics due to a bearing misalignment in the manufacturing machine. Its immediate identification is crucial for the diagnosis of the fault mechanism. The coefficient vectors corresponding to each of the fundamental eigenfunctions are shown in Fig. 12. Note that the first coefficient vector shows the change in slope of the linear trend isolated in the form of eigenfunction #1 (Fig.
T 1 2 The covariance matrix is computed using: Sˆ ϭ --2 ⌺ iϭ1 Z i Z i , which becomes: 1 Sˆ ϭ -2 Ϫ ␦ 11 Ϫ ␦ 21 [ Ϫ ␦ 11 Ϫ ␦ 21 ] ϩ ␦ 11 ␦ ␦ 11 ␦ 21 [ ␦ 11 ␦ 21 ] ϭ 11 . 28) The solution of this characteristic polynomial in is 1 ϭ 0 or 2 ϭ ␦ 11 ϩ ␦ 21, resulting in only one dominant eigenvalue. 29) which is the equation for a straight line. Since the eigenvector has to be orthonormal, the orthonormality ␦ 11 ␦ 21 T 2 2 - and 1 ϭ -------------------------- , as the condition ⌽ ⌽ ϭ I implies 1 ϩ 2 ϭ 1, which results in 2 ϭ -------------------------2 2 2 2 ␦ ϩ ␦ ␦ 11 21 11 ϩ ␦ 21 normalized linear vector ⌽.
This might, for example, correspond to the appearance of harmonics due to a bearing misalignment in the manufacturing machine. Its immediate identification is crucial for the diagnosis of the fault mechanism. The coefficient vectors corresponding to each of the fundamental eigenfunctions are shown in Fig. 12. Note that the first coefficient vector shows the change in slope of the linear trend isolated in the form of eigenfunction #1 (Fig. 11). Using the eigenfunction and the corresponding coefficient vector, the introduction of linear trends can be monitored separately from the rest of the significant components.