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Advanced Sensors in Precision Manufacturing
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FIGURE 6.19
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Data ow for an automatic bearing fault detection system.
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to a lower frequency band to simplify processing by use of a Fourier transformation. This transformation would then be applied to compute the power spectrum. The output of the tachometer would be processed in parallel with the spectral calculations so that the frequency bins of the power spectrum could be normalized on the basis of the speed of rotation of the machine. The power spectrum would be averaged with a selected number of previous spectra and presented graphically as a waterfall display; this is similar to a sonar display with which technicians can detect a discrete frequency before an automatic system can. The bearing frequencies would be calculated from the measured speed and the known parameters of the bearings, with allowances for slip. The power spectrum levels would be read for each bearing frequency; a moving average of the amplitude at each bearing
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frequency and harmonic would be maintained, and trends representing statistically significant increases would be identified by threshold detection and indicated graphically. By using algorithms based partly on analyses of data from prior tests, the results of both keratosis and power spectrum calculations would be processed onto predictions of the remaining operating time until failure. All the results would then be processed by an expert system. The final output would be a graphical display and text that would describe the condition of the bearings.
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Sensors for Vibration Measurement of a Structure
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An advanced sensor was developed to gauge structure excitations and measurements that yield data for design of robust stabilizing control systems (Fig. 6.20). An automated method for characterizing the dynamic properties of a large flexible structure estimates model parameters that can be used by a robust control system to stabilize the structure and minimize undesired motions. Although it was developed for the control of large flexible structures in outer space, the method is also applicable to terrestrial structures in which vibrations are important especially aircraft, buildings, bridges, cranes, and drill rigs.
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FIGURE 6.20
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Automated characterization of vibrations of a structure.
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Advanced Sensors in Precision Manufacturing
The method was developed for use under the following practical constraints: The structure cannot be characterized in advance with enough accuracy for purposes of control. The dynamics of the structure can change in service. The numbers, types, placements, and frequency responses of sensors that measure the motions and actuators that control them are limited. Time available during service for characterization of the dynamics is limited. The dynamics are dominated by a resonant mode at low frequency. In-service measurements of the dynamics are supervised by a digital computer and are taken at a low rate of sampling, consistent with the low characteristic frequencies of the control system. The system must operate under little or no human supervision. The method is based on extracting the desired model and controldesign data from the response of the structure to known vibrational excitations (Fig. 6.20). Initially, wideband stochastic excitations are used to obtain the general characteristics of the structure. Narrowband stochastic and piece-wise-constant (consistent with sampleand-hold discretizations) approximations to sinusoidal excitations are used to investigate specific frequency bands in more detail. The relationships between the responses and excitations are first computed nonparametrically by spectral estimation in the case of stochastic excitations and by estimation of gains and phases in the case of approximately sinusoidal excitations. In anticipation of the parametric curve fitting to follow, the order of a mathematical model of the dynamics of the structure is estimated by use of a product moment matrix (PMM). Next, the parameters of this model are identified by a least-squares fit of transfer-function coefficients to the nonparametric data. The fit is performed by an iterative reweighting technique to remove high-frequency emphasis and assure minimumvariance estimation of the transfer-function coefficient. The order of the model starts at the PMM estimate and is determined more precisely thereafter by successively adjusting a number of modes in the fit at each iteration until an adequately small output-error profile is observed. In the analysis of the output error, the additive uncertainty is estimated to characterize the quality of the parametric estimate of the transfer function and for later use in the analysis and design of
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