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2. Machine vibration measurements

The laboratory stand consists of: a set of accelerometers, preamplifiers and measuring

amplifiers with instrumentation (personal computers equipped with measurement cards), two

standard vibration sources and four fans of the same type in different technical condition.

The exercise consists of three parts (all parts are performed individually by each student).

The first part consists in completing the equipment, compiling the complete track for measuring

the effective value of the amplitude of vibration acceleration and calibrating the measuring track.

Complete measurement paths can be calibrated using a reference vibration signal with a known

amplitude. The discrepancy between the amplitude of the reference signal and the value indicated

by the meter can be treated as the result of calibration, each time improving the obtained

measurement results. If we do not have a reference source of vibrations, and the voltage

sensitivity of the measuring transducer with the matching circuit is known, the calibration element

is to synchronize the meter indications with the value of the reference voltage signal. During the

measurements, the voltage amplitude will be read, which gives the acceleration divided by the

sensitivity

First, attach the accelerometer to a selected point on the body of the tested

machine (the mounting method should be justified). Then, in the measurement protocol,

we note the results of ten readings of the amplitude of vibration acceleration with the

averaging time constant "fast”; and ten with the constant "slow".

The last and third step is to develop and interpret the results. You should:

• Calculate the average measured value of the vibration acceleration amplitude

separately for each time averaging method;

• Interpret discrepancies between results;

• Report the amplitude range for the 95% confidence level of the results;

• Estimate the maximum measurement error and justify the estimation made;

• Calculate the effective and peak values of vibration velocity and displacement for the

measured amplitude of the harmonic vibration acceleration with the given frequencies.

The report documents the performance of the exercise and is prepared in full

during the classes. The completion of the measurement track and the method of

conducting are assessed measurements, formulating conclusions and understanding

the issues related to the conducted research. The degree of mastering the material is

reflected in the proficiency in performing tasks.

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The exercise requires a good knowledge of the issues presented in the first part of the

manual (without chapter 4) and in the further part of the exercise description.

Background information

According to the standard definition (PN-82/N-01350), vibration is a process in which

certain characteristic quantities are functions of time, usually alternately increasing and

decreasing in successive time intervals.

Mechanical vibrations - these are vibrations in which the change of any kinematic or

dynamic quantity characterizing the state of the system is a function of time. The studied

motion parameters are usually: displacement, velocity, acceleration. As you know, integrating

acceleration over time gives velocity; displacement is obtained by reintegration. The mutual

relations of these three parameters are shown in Figure II.2.1, where both axes (frequency and

amplitude) are presented on a logarithmic scale.

Fig. II.2.1 Dependence between acceleration and speed and vibration displacement

as a function of frequency.

The choice of the measured parameter depends primarily on the frequency of the

significant vibrations from the point of view of the conducted research. For low-frequency

vibrations, the amplitude of displacements gives the most information. The vibration speed is

a good parameter in a fairly wide range because it is proportional to the energy of the

vibrating motion dissipated as a side effect of the machine operation.

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Vibration acceleration allows you to extend the analysis range also to higher

frequencies. It is often used in vibroacoustic diagnostics, for example in detecting short-term

damage to rolling bearings.

The set of apparatus for measuring vibrations follows the general scheme of the

measuring path. Various types of measuring transducers are used, including:

- electrodynamic,

- piezo-electric

- piezoresistive,

- Induction

- Capacitive

- using Foucault currents,

- optical (including laser),

- using an electromagnetic field.

Piezoelectric accelerometers are used in the exercise. Their main strengths below:

- Resistance to environmental factors

- wide frequency response,

- good linearity,

- low dependence of sensitivity on temperature,

- low interference impact,

- Size and weight

The drawback is relatively low sensitivity and high impedance, which makes it

necessary to use charge amplifiers or matching preamplifiers.

Charge preamplifiers practically make the sensitivity of the measurement path

independent of the length of the test lead. In voltage preamplifiers, on the other hand, the electric

capacity of the cable significantly changes the voltage sensitivity of the accelerometer. If we

consider a substitute diagram of such a converter (generating charge q) with a wire as shown in

the figure, then voltage will be applied to the input of the preamplifier V e according to the

relationship:

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where:

Ve - preamplifier input voltage,

Ce - capacity of electric cable,

Ca - internal capacity of accelerometer.

Fig. II.2.2 Equivalent diagram of an accelerometer with a wire.

Currently, quite common use is made of converters equipped with a miniature,

integrally placed preamplifier. Sometimes, when using piezoelectric accelerometers, it is

necessary to consider the influence of transverse vibrations on the measurement result. In

modern accelerometers, transverse vibrations have a small share (usually it does not exceed

3%). In higher-class accelerometers, the direction of the highest sensitivity axis deviation

from the vertical is often indicated by a red dot on the transducer body (Figure II.2.3

When selecting a transducer, consider its dynamic range (the size of the processed

amplitudes) and the frequency response. The usual rule of thumb is that measurements are

made in a linear region. The useful measuring bandwidth of piezoelectric transducers is well

below the accelerometer resonance (after considering the mounting effect).

The influence of different mounting methods on the frequency response is illustrated

in the following figures. It can be seen that the best properties have rigid connections, and at

higher temperatures, almost exclusively threaded connections are used. The results of

measurements with a hand-held probe are not very repeatable, and such a set is only suitable

for low-frequency vibration measurements.

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Fig. II.2.3 Illustration of the position of the axis of highest sensitivity of the accelerometer.

Fig. II.2.4 Resonance curve for mounting the accelerometer with a centrally located screw .

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Fig. II.2.5 Resonance curve for fixing an accelerometer with beeswax.

Fig. II.2.6 Resonance curve for accelerometer mount screw through the washer ceramic.

Fig. II.2.7 Resonance curve for mounting an accelerometer using a sticky threaded washer.

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Fig. II.2.8 Resonance curve for attaching the accelerometer with adhesive discs.

Fig. II.2.9 Resonance curve for mounting an accelerometer with a magnet.

Fig. II.2.10 Resonance curve illustrating the range of applications hand probe.