Section 1 Vibration

1.1  Narrowband analysis

Narrowband frequency analysis is the recommended method of interpreting vibration measurements in relation to the guidance limits or for investigation purposes.

Narrowband frequency analysis should be capable of resolving the frequency of individual components of interest over the relevant frequency range.

1.2  Broadband limits

Some guidance values based on broadband measurements of the overall amplitude of composite frequency vibration are suggested in later sections to simplify routine survey procedures.

Broadband measurements should cover the specified range of vibration frequencies for each particular application.

If the acceptability of vibration severity is marginal from the results of broadband measurements, narrow band frequency analysis should be used. Records of the vibration measurements should be taken in such cases.

1.3  Orders of vibration

Vibration frequencies can conveniently be related to a known fundamental excitation frequency by the use of order numbers. In cases where shaft rotational frequency is an appropriate reference, then:

Order numbers are typically integer numbers, 1, 2, 3,......,n. Vibration at four cycles per shaft revolution arising from a four-bladed propeller, for example, can either be described as occurring at shaft fourth order or at blade order. Half orders (½, 1½, ...) may typically occur with 4-stroke diesel engines where the working cycle takes place over two shaft revolutions.

1.4  Analysis methods

Vibration data can be divided into two categories: steady and transient. Some data with minimal transient characteristics can be considered in a quasi-steady sense. The available analysis methods are summarized in Figure 3.1.1 Summary of available analysis methods .

1.5  Fast Fourier Transform analysis

Analysis of steady and quasi-steady signals is usually carried out using the Fast Fourier Transform (FFT) function found on most vibration analysers.

An FFT analysis transforms consecutive samples (typically 1024, 2048, or 4096) from the time domain to the same number of lines in the frequency domain. The algorithm used to calculate the FFT is finite and discrete. This has a number of effects.

The first is that aliasing might occur, when because of a limited number of samples, high frequencies might appear as false lower frequencies. This is avoided by lowpass “anti-aliasing” filters. A sampling frequency higher than the maximum frequency of interest, f_max , is used. This is determined by:

The frequency resolution is thus dependent on the frequency range used, but most analysers have band- selectable analysis which gives increased resolution or “zoom” at frequencies of interest.

The second effect of a finite sample record is that discontinuities can arise at the ends of the sample, giving rise to false results when the signal is not periodic in the time record. This causes leakage of energy from one resolution line of the FFT into other lines. The amplitude at the start and end of each block of samples is therefore reduced to zero, a technique known as windowing. The Hanning window is a good, general purpose compromise for continuous signals. A transient signal, such as from an impact, is self-windowing and a Uniform (Rectangular) window should be used.

The third effect is known as the picket fence effect. It arises from the discrete sampling of the spectrum in the frequency domain in which the FFT acts like a series of parallel filters. The results are similar to viewing the results through slits in a picket fence.

The shape or response of the filters is determined by the window function used. The amplitude of a frequency which is in the middle of a filter using a Hanning window will be measured accurately. A frequency midway between filters could be attenuated by up to 1.5 dB (18%). The use of a Flat-top window will reduce the possible attenuation to less than 0.1 dB (1%). However, the increase in accuracy comes at the expense of frequency resolution of small components.

1.6  Time domain signal

It is desirable to view the “raw” vibration signal (signal amplitude displayed against time) during analysis. Signal characteristics such as beating, transients and irregularities can be readily detected in the time domain. Approximate inspection methods of analysis are recommended as a check on the results derived from analytical techniques.

1.7  Averaging

Averaging is not always appropriate and its use may destroy or disguise the original signal characteristics. This includes, for example, signals arising from intermittent defects or averaging of non-steady signals. It may be possible to use non-steady signal techniques to give a better understanding of the signal characteristics. Root mean square (r.m.s.) averaging will give a better estimate of the value of a signal, but it will not improve the signal-to-noise ratio. Linear averaging will improve the signal-to-noise ratio if a trigger signal is available which is synchronous with the periodic part of the signal.

1.8  Modulation

Modulation describes a time dependant variation, either random or repetitive, in a vibration signal, Figure 3.1.2 Vibration modulation .

• Amplitude modulation arises, for example, in an eccentrically mounted gear where the tooth meshing frequency is constant but the amplitude varies, typically at once per revolution of the gear.
• Frequency modulation occurs, for example, in gears with tooth spacing errors or the passing signal from torsionally vibrating gear teeth.
• Phase modulation occurs, for example, onboard a twin screw ship where the excitation varies in time.

These types of modulation can occur in the same signal, for example in heavy weather where the speed and load of a ship’s main engine may vary simultaneously or in the hunting of a governor of an alternator set. Frequency analysis cannot describe the varying amplitude and frequency. The information is interpreted as steady sine waves which appear as side bands about the fundamental frequency. The amplitude of the fundamental frequency may be significantly diminished in cases of very heavy modulation.

One side effect of modulation is that the ear may detect frequencies that do not exist or may be outside the normal range of audible frequencies.

1.9  Rolling element envelope analysis

Incipient defects in rolling element bearings produce sharp pulses which may produce measurable frequencies up to 20 kHz. Identification of the source cannot be carried out using simple FFT analysis and a technique known as envelope analysis is used to extract useful information from the vibration signal as follows. First the time domain signal is band-pass filtered around the region of high frequency energy. This leaves a signal containing bursts of energy at the defect frequency, which is then rectified and low-pass-filtered. An FFT analysis of the resultant signal will allow the defect frequency to be identified. Calculation of the impact rates is given in Table 3.1.1 Calculation of rolling element impact frequencies .

1.10  Calibration

Analysis methods should be verified using known input data. Any software used in calibration, measurement or analysis should be part of an appropriate Quality Assurance system.