EFFECT OF THE STIFFNESS OF STRUCTURAL ELEMENTS ON THE VIBRATION AND AIRBORNE NOISE LEVELS OF AN ELECTRIC MACHINE

A. T. MOLODYKH, Yu. V. GORST, P. T. MAL’TSEV

(Presented by the scientific seminar of the departments of electric machines and general electrical engineering)

The increase in power, the rise in the speed of electric machines, and the associated increase in dynamic forces, vibration intensity, and noise pose urgent problems in reducing the latter. The vibration and noise level of an electric machine can be substantially affected by its structural design, the shape, dimensions, and material of the individual parts of the product. In this connection it is necessary to know the influence of the stiffness of the structure on the vibroacoustic characteristics of an electric machine.

To investigate the dependence of vibration and noise on the above-mentioned factors, a single-armature converter having four versions was taken.

In machines of versions 1 and 2, two main units can be distinguished structurally: the single-armature converter proper and the filter box. The converter is mounted on the filter box by means of rubber shock absorbers. The difference between them is that the converter of the first version is supplied by a voltage of 110 V, while the converter of the second version is supplied by a voltage of 220 V. Their output parameters are the same.

Machines of versions 3 and 4 are a modification of machines of versions 1 and 2; they have a filter box of larger dimensions and are equipped with noise suppressors. In order to determine the influence of individual structural elements on vibration and noise, it is necessary to have a clear idea of the natural frequencies of the machine’s structural elements and of the frequencies of the main sources of vibration.

Frequencies of the Main Sources of Vibration and Noise of the Product

Sources of vibration and noise can be divided into sources of magnetic, mechanical, and aerodynamic origin.

The single-armature converter under investigation has clearly expressed poles and provides a single-phase output voltage with frequency \(f = 50\) Hz. This accounts for the presence of an asymmetrical magnetic field that creates a pulsating flux, which can be decomposed into two components. The first component rotates synchronously with the ar-

… and the second with double speed relative to the poles and is called the asynchronous or counter-rotating m.m.f. The action of the second component is reduced to the creation of an asynchronous field which, crossing the pole and the armature at a frequency equal to twice the frequency of the generated voltage, causes vibration at a frequency \(2f = 100\) Hz.

The tooth frequency of vibration and noise is found from formula (1).

\[ f_M=\frac{K_1 \cdot Z \cdot n}{60},\ \text{Hz}. \]

The frequency of ventilation noise is

\[ f_{\text{sh}}=\frac{k_2 n}{60},\ \text{Hz}. \]

The frequencies of the components of vibration of mechanical origin are determined by the following formulas:

1. From the action of armature unbalance

\[ f_d=\frac{n}{60},\ \text{Hz}. \]

1. From the operation of the brush-commutator assembly

\[ f_{\text{shch}}=\frac{k_3 n}{60},\ \text{Hz}, \]

1. Caused by the operation of rolling bearings:

a) from rotation of the cage

\[ f_1=\frac{r_1}{r_1+r_2}\cdot\frac{n}{60},\ \text{Hz}, \]

b) determined by rotation of the balls

\[ f_2=\frac{r_2}{r_{\text{sh}}}\cdot\frac{r_1}{r_1+r_2},\ \text{Hz}, \]

c) from defects on the raceway of the inner ring

\[ f_3=\frac{r_1}{r_1+r_2}\cdot\frac{n}{60} z_{\text{sh}},\ \text{Hz}, \]

d) from defects on the raceway of the outer ring

\[ f_4=\frac{r_2}{r_1+r_2}\cdot\frac{n}{60}\cdot z_{\text{sh}},\ \text{Hz}. \]

In these formulas

\(n\) — number of revolutions (rpm);
\(K_1 = 1.2\);
\(K_2\) — number of fan blades;
\(K_3\) — number of commutator segments;
\(Z\) — number of armature teeth;
\(r_1\) — radius of the raceway of the inner ring (mm);
\(r_2\) — radius of the raceway of the outer ring (mm);
\(r_{\text{sh}}\) — radius of the balls (mm);
\(z_{\text{sh}}\) — number of balls in the bearing.

The results of the calculations are given in Table 1.

Table 1

Method and results of determining the natural frequencies of individual parts and structural elements

To determine the natural frequencies, the part (assembly), with a piezoelectric sensor fastened to it, was suspended on elastic elements that ensured a low frequency of the system’s free vibrations. The signal from the sensor was fed through an IVPSh to an analyzer manufactured by “Dawe.” The vibrations of the part were excited by means of a mechanical-vibration generator of the GMK-1 type, to which voltage was supplied from a ZG-10 audio-frequency generator. As the frequency of the disturbing force was varied, resonance was found. For complex assemblies, such as the silencer and the filter box, the natural vibration frequencies were found with the sensor fastened at various points of the structure.

The results of the experimental determination of the natural frequencies of individual parts and assemblies are given in Table 2.

Table 2

Study of the influence of individual structural elements on the overall level and frequency composition of vibration

According to the technical specifications, control measurements of the vibration level of the products are made on the filter box. In Fig. 1, curves 1 and 2 represent the envelopes of the vibration spectra of, respectively, the converter housing and the filter box at rated load. Curve 1 shows that the principal frequencies in the vibration spectrum are 50, 100, 280, and 800 Hz. The determining component in this spectrum is the compo-

component at a frequency of 800 Hz. On the filter box (curve 2), the vibration level at frequencies of 70, 100, and 140 Hz is considerably higher than the vibration level at these frequencies on the converter housing. In the frequency range above 200 Hz, the level of the high-frequency components on the filter box proves to be considerably lower than on the converter.

Since one of the natural vibration frequencies of the filter box (100 Hz) coincides with one of the frequencies present in the spectrum of the excitation, a considerable amplification of the oscillations at a frequency of 100 Hz is observed. At the same time, the high frequencies are well damped by the shock absorbers installed in the path of wave propagation from the converter housing. For vibrations with frequencies of 50, 70, 100, and 140 Hz, the low-frequency shock absorbers are a weak obstacle in the path of their propagation.

Fig. 1. Vibration spectra of a single-arm converter of design 1.
1 — envelope of the frequency components of vibration of the converter housing at rated load;
2—3 — envelopes of the frequency components of vibration of the filter box at rated load and at no load, respectively.

Since the component at a frequency of 100 Hz determines the overall vibration level on the filter box, it is first of all necessary to reduce the vibration level at this frequency. This can be achieved in the following ways:

to eliminate the coincidence of the natural vibration frequencies of the filter box with the frequency of the exciting force;

to change the elastic coupling between the filter box and the converter housing;

to eliminate the primary cause of oscillations with a frequency of 100 Hz, i.e., to reduce the intensity of the counter-rotating magnetic field.

From the graph (curves 2 and 3 in Fig. 1) it is evident that, when the converter operates at no load, the vibration level of the filter box at frequencies of 70, 100, and 140 Hz decreases by 9–24 dB in comparison with the vibration at rated load. It follows from this that the most effective measure would be to eliminate the harmful effect of the counter-rotating m.m.f. of the magnetic field. This magnetic flux is usually damped by special damping devices.

As the calculations showed, in order to install damper windings it is necessary to increase the overall dimensions of the converter housing, which is undesirable for well-known reasons. Therefore, an attempt was made first of all to reduce the vibration level by changing the natural frequency of the filter box and the stiffness of the elastic connection between the filter box and the converter housing.

To eliminate resonance at a frequency of 100 Hz, it is obviously necessary to change the stiffness of the filter box so that the frequency of its natural oscillations is either above or below the component in the disturbance spectrum at a frequency of 100 Hz. This can be achieved by changing the design of the filter box or by using another material.

The natural frequencies of production filter boxes made of material grade A1M lie within the range of 85–92 Hz, while those of experimental boxes made of AMT material of the same thickness lie within the range of 92–103 Hz.

It proved possible to raise the natural frequency to 105–109 Hz by reducing the height of the filter box by 35%. Raising the natural frequency of the filter box to 108–109 Hz, or lowering it to 83 Hz, as experiments showed, makes it possible to reduce the overall vibration level and the component at a frequency of 100 Hz by 4–7 dB; at the same time, the vibration level at frequencies of 70 and 140 dB is reduced by only 3–5 dB.

A cast box was also made, whose natural frequency turned out to be 134 Hz, which made it possible to reduce the vibration level by 9 dB. But because the rubber shock absorbers used represent a weak obstacle to low-frequency components, in the vibration spectrum of the cast filter box the component at a frequency of 100 Hz still remains predominant.

The degree of damping of mechanical oscillations by rubber shock absorbers increases with increasing oscillation frequency of the object and with increasing thickness of the rubber layer. On the basis of these considerations, studies were carried out to reduce the vibration level by changing the stiffness of the connection between the filter box and the converter housing. Experiments showed that by reducing the stiffness of the connections between the filter box and the converter housing and simultaneously increasing the stiffness of the box itself, the vibration level can be reduced by 12–15 dB.

Influence of individual structural elements of the products under investigation on the overall level and frequency composition of airborne noise

Airborne-noise measurements were made at a distance of 0.5 m from the product with the successive removal of certain structural elements: covers, fans, and the filter box. Measurement of the overall level and frequency composition of the noise at rated load and at no load made it possible to identify the noise component caused by pulsations of the magnetic field.

For measuring the noise, a Sh-52 sound-level meter and a PF-1 octave-band filter were used.

Tests of converters of versions 1 and 2 on the filter box at rated load showed that the principal frequencies of the noise components are 100, 280, 1600, and 3200 Hz, as well as 4800 and 6400 Hz. The sources of the noise components at the indicated frequencies are the operation of the bearing units (280 Hz), pulsations of the magnetic field (100 and 800 Hz), operation of the brush-commutator unit (3200 Hz), and their har—

harmonic components. Analysis of the noise spectra shows that, at no load, in all cases the component at a frequency of 100 Hz almost completely disappears. Since one of the natural-vibration frequencies of the filter box lies in the 100 Hz region, resonance is observed at rated load.

When the end caps are removed, the noise component at a frequency of 800 Hz decreases, since in this case the dimensions of the vibrating surface are reduced. Experiments showed that the intensity of the noise produced by the end caps can be reduced by 3–4 dB if these same end caps are installed with damping gaskets or if the end caps are made of a softer material.

Fig. 2. Spectra of airborne noise of single-armature converters.
1–2 — envelopes of the frequency components of the noise of products of designs 1 and 2 at rated load and at no load, respectively; 3, 4 — envelopes of the frequency components of the noise of products of designs 3 and 4 at rated load and at no load, respectively.

Comparing curves 3 and 4 (Fig. 2) of the noise spectrum of products of designs 1 and 2 with curves 1 and 2 of the noise spectrum of products of designs 3 and 4 (with muffler), we see that, with the aid of the noise muffler, the level of the components can be reduced beginning at a frequency of 800 Hz and above. The levels of the noise components at frequencies below 800 Hz for products of designs 3 and 4 prove to be higher than for products of designs 1 and 2. The use of a casing-muffler in products of designs 3 and 4 in the presence of the filter box gives a reduction in the overall level by 5–8 dB. In this case the noise components at frequencies above 800 Hz are well muffled, while the noise components at low frequencies (50, 100, and 140 Hz) are not only not muffled but, on the contrary, are amplified because the fundamental natural-vibration frequencies of the elements of the filter box and of the casing walls prove to be close to the frequency of 100 Hz.

The overall level of airborne noise of all the tested products without the filter box, and also of products of designs 3 and 4 without the muffler, proves to be of the same order as during operation with the filter box of products of designs 1 and 2, since the noise of these products is determined by the noise level at a frequency of 800 Hz (magnetic), and also at frequencies of 1600–3200 Hz, caused by operation of the brush gear and quality bearings.

The influence of individual structural elements on the overall noise level of products of designs 1–4 is shown in Figs. 3 and 4.

Fig. 3. Influence of structural elements on the overall noise level of converters.

c — version 1; d — version 2;
a — with hoods and fan;
б — without hoods, but with fan;
в — with hoods and without fan;
г — without hoods and without fan.

Conclusions

1. Amplification of vibration and an increase in the noise of an electrical machine occur as a result of the coincidence of the natural frequencies of vibration of assemblies and structural elements with the frequencies of the exciting forces.

2. When creating new machines, even at the design stage it is necessary, by calculation, to assess both the natural frequencies of vibration of assemblies and structural elements and the frequencies of the principal exciting forces. In doing so, the greatest possible difference should be ensured between the natural frequencies of vibration and the frequencies of the exciting forces in the machine. In the course of refinement and testing of prototypes, corrections should be introduced aimed at improving the vibration characteristics of the machine.

3. In electrical machines in which elastic elements are used to connect individual assemblies, a rational selection of the stiffness of these elements can ensure a significant reduction in the level of vibrations and noise.

Fig. 4. Effect of structural elements on the overall noise level of converter 3 design:

a — normal design (with caps and both fans);
б — without the external fan, but with the internal fan and with caps;
в — without both fans and with caps;
г — without the internal fan, but with the external fan and with caps;
д — without caps, but with both fans;
е — without caps, without the external fan, but with the internal fan;
ж — without caps and without both fans;
з — without caps, without the internal fan, but with the external fan.

References

1. V. G. Shpringman. Magnetic Noise of Electrical Machines. In: Noises of Electrical Machines, Publishing House of the USSR Academy of Sciences, 1939.
2. V. Tseller. Techniques for Combating Noise, Gosstroiizdat, 1958.
3. E. T. Grigor’ev. Calculation and Design of Rubber Shock Absorbers, Mashgiz, 1960.