376 S. Richardson et al. Fig. 35.1 Rotating machine with accelerometers attached 35.1.1 Output-Only Frequency Spectra In operating machinery where the excitation forces cannot be measured, three types of output-only frequency spectra can be calculated from acquired time waveforms. The three types are Fourier spectra, Cross spectra, and ODSFRFs. AFourier spectrumis simply the Digital Fourier Spectrum (DFT) of a response digital time waveform. It is calculated with the FFT algorithm. ACross spectrumis calculated between two simultaneously acquired responses. It is the DFT on one signal multiplied by the complex conjugate of the other. An ODSFRF is the Auto spectrum of a roving response combined with the phase of the Cross spectrum between the roving response and a (fixed) reference response. 35.1.2 Operating Deflection Shape When a vibration response is measured at two or more points and directions on a machine, this data can be assembled into what is called anOperating Deflection Shape(or ODS) [5]. Three different types of ODS’s are possible; time-basedODS’s, frequency-basedODS’s, and order-basedODS’s. 35.1.3 Time-Based ODS A time-based ODS is simply the values for the same time sample of two or more simultaneously acquired or calculated time waveforms. A time-based ODS contains the responses that were simultaneously acquired at a moment of time from the machine.
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