Experimental Study of the Vibration Characteristics of an Electric Machine

P. T. Maltsev, Yu. V. Gorst

(Presented by the scientific seminar of the Department of Applied and Theoretical Mechanics)

The development of modern electrical-machine engineering is characterized by an increase in rotor speeds and a decrease in weight per unit of product power. In connection with this, the probability increases of a coincidence between the natural frequencies of individual structural elements and the frequencies of the exciting forces, which are caused by mechanical and electromagnetic sources during operation of the machine. Under the action of exciting forces, the electric machine and its individual elements undergo complex vibrational motions. In this case, a close coincidence of the natural frequencies of the structure, its individual units or elements, with the frequencies contained in the excitation spectrum may have a significant effect on the vibration level.

Vibration characteristics are one of the principal indicators of the quality of the electric machines being produced. If electric machines are manufactured with unsatisfactory vibration characteristics, the levels of structural and airborne noise emitted by the product naturally increase; as a rule, high requirements are imposed on these.

The determination of the natural frequencies of a system may be carried out either by calculation or experimentally. When designing an electric machine, the designer must calculate the natural frequencies of the structure and of its individual parts. Certain recommendations are available for such calculations [1, 2, 3]. However, the analytical determination of natural frequencies, taking into account all the features inherent in a given structure, presents considerable difficulties. It should be borne in mind that, for a complex structure, by adopting one or another calculation scheme that reflects the true picture only approximately, one may obtain results that differ substantially from experimental data. In a number of cases, even with the most careful manufacture of an electric machine, it is not possible to obtain satisfactory vibration characteristics. Therefore, prototypes are subjected to testing and adjustment. To carry out the tests and identify the causes of increased vibration of the product, it is necessary to outline an appropriate methodology.

In the present work, a converter was subjected to investigation (Fig. 1). The rated rotational speed of the armature of this converter ...

is equal to 15,000 rpm. A characteristic feature of the converter under study is the complexity of its design. Despite very careful manufacture, tests of the products being produced show increased vibration of the housing, premature failure of the bearing assemblies, and, in many products, increased power consumption in comparison with the rated value.

Fig. 1. Diagram of the converter installation for vibration measurement. EM—the converter under study; 1—platform; 2—shock absorbers; D—piezoelectric sensor; IVPSh—vibration meter; AG—harmonic analyzer; GMK—mechanical-vibration generator; ZG—audio-frequency generator.

In carrying out the work, the following tasks were set: to refine the method for measuring vibrations; to determine the dependence of the vibration of the product housing at the rotational frequency on the unbalance of the armature; to identify the resonance zones of structural oscillations; and to give recommendations for design changes aimed at increasing the reliability of operation of the converter.

It is known that the method of installing and fastening a product substantially affects its vibration level. Therefore, in conducting the experiments, vibration was measured with the product rigidly fastened on a platform mounted on soft shock absorbers; with the product installed directly on soft shock absorbers; with the converter rigidly fastened on a slab whose weight was 80 times greater than the weight of the converter; and with the converter housing rigidly fastened without a stand on a cushioned platform. The weight of the platform \(Q_{\mathrm{p}}\) was chosen equal to \(Q_{\mathrm{m}}, 2Q_{\mathrm{m}}, 8Q_{\mathrm{m}}\) (where \(Q_{\mathrm{m}}\) is the weight of the converter).

The resonance zones of the frequencies of forced oscillations of the housing were determined by measuring vibrations at various armature speeds and with various methods of fastening the product, and also by exciting oscillations of the structure in the frequency range from 50 to 10,000 Hz by means of a mechanical-vibration generator (GMK-1), powered by alternating current from an audio-frequency generator of type ZG-12M.

The vibration level at the rotational frequency can be calculated analytically, and for most electric machines the calculated data agree with the experimental data. But for some electric machines, because of their design features, the calculated data differ considerably from the experimental results. If it is assumed that the product is a rigid body and undergoes oscillations

as a single whole and that there is no clearance in the bearings, the vibration level at the rotational frequency, depending on the unbalance of the armature, can be calculated [4, 5] by the following formula:

\[ A=\mu \beta \varepsilon, \]

where \(A\) is the amplitude of the vibrational displacement;
\(\beta\) is the dynamic coefficient;
\(\varepsilon\) is the unbalance of the armature, expressed as the conventional displacement of the center of gravity of the armature masses;
\(\mu\) is the ratio of the armature mass to the entire damped mass.

The IVPSh instrument used indicates the effective value of the vibration level in terms of acceleration; therefore the calculated effective value of the vibration-acceleration level is determined by the formula

\[ L_f=20\lg \frac{a}{a_0}-3, \]

where \(a=A(2\pi f)^2\) is the amplitude value of the vibration acceleration at the rotational frequency, \(\text{cm}/\text{s}^2\);
\(a_0=3\cdot 10^{-2}\), \(\text{cm}/\text{s}^2\), is a constant corresponding to the zero level and taken as the origin; \(f\) is the rotational frequency of the armature, cps.

The calculation results are given in Tables 1 and 2. In this case the value of the dynamic coefficient \(\beta\) was taken equal to 1 [5], assuming that the machine under study has normal dynamic characteristics. When the machine under study was installed during the experiments on a damped platform or directly on shock absorbers, the latter provided a natural-oscillation frequency of the system of no more than 5–6 Hz.

Table 1

Calculated values of the vibration level of the frame as a function of armature unbalance for various methods of installing the converter

Table 2

Calculated values of the housing vibration level as a function of armature unbalance at various rotational speeds of the converter, \(\gamma = 0.096\)

Comparison of the calculated and experimental data makes it possible to give a certain judgment about the vibration characteristics of the electrical machine under study.

In the case where the machine is mounted on a cushioned platform whose weight is equal to the weight of the machine, the experimental values of the housing vibration level at nominal speed are 17–20 dB higher than the calculated values; i.e., the measured values of vibration acceleration are 7–10 times higher than the calculated values (see Fig. 2).

Fig. 2. Dependence of the vibration level on armature unbalance. 1—calculated, 2—experimental.

Investigation of the vibration of the converter housing, mounted on vibration isolators without a platform, \(\gamma = 0.2\), \(\varepsilon = 4\) μm, showed that the greatest oscillation energy occurs at high frequencies (Fig. 3, curve 1). The vibration level at the rotational frequency is only slightly higher than the calculated one. It should be noted that, as the armature unbalance of the converter under study increases, the vibration level rises not only at the rotational frequency, but also at higher frequencies.

When the machine is mounted on a foundation slab weighing \(80Q_m\), the vibration frequency spectrum (Fig. 3, curve 4) is analogous to the vibration spectrum when the converter is installed on vibration isolators without a platform (curve 1); however, here the vibration level at the rotational frequency is higher than

when the converter is mounted on shock absorbers without a platform, with the same armature unbalance.

Thus, the experiments established that, with a certain residual unbalance, much smaller than the permissible value, a significant amplification of oscillations occurs.

Fig. 3. Vibration spectrum under different conditions of installation of the converter, \(\varepsilon = 4\ \mu\). 1 — on shock absorbers without a platform; 2 — on a cushioned platform of weight \(Q_m\); \(2'\) — on a cushioned platform of weight \(Q_m\) with the wedge installed; 3 — on a cushioned platform of weight \(Q_m\), converter without a support; 4 — with rigid fastening on a foundation slab of weight \(80Q_m\).

It has been established that each weight of the platform on which the converter was fastened corresponds to a certain rotational speed of the armature at which amplification of oscillations occurs and an elevated level of vibration of the housing at the rotational frequency is observed (Fig. 4).

In the case of installing the converter on shock absorbers without a platform, when the armature rotational speed is varied within the range from 10,000 to 16,500 rpm (Fig. 4, curve 1), a more or less smooth increase in the vibration level of the housing at the armature rotational frequency is observed. At the same time, the vibration level differs only slightly from the calculated value.

Thus, the resonance zones of oscillations of the converter when it is installed on a platform weighing from \(Q_m\) to \(80Q_m\) lie within the range from 255 cps \((n = 15300\ \text{rpm})\) to 180 cps \((n = 10800\ \text{rpm})\).

Measurements of the vibration level of the converter housing when oscillations were excited by means of a generator of mechanical oscillations (Fig. 5), under various fastening conditions of the product under investigation, made it possible to determine the natural frequencies of oscillation of the system.

As the experiments carried out showed, the frequency limits of the system’s natural oscillations range from 180 cps—when the converter is rigidly fastened to a foundation slab weighing \(80Q_m\)—to 380 cps—when the converter is installed on soft shock absorbers providing a free-oscillation frequency of the system of about 6 cps.

An analysis of the converter design and of the results of the experiments performed shows that the causes of the amplification of oscillations of the converter under investigation are the close coincidence of the frequencies of the natural oscilla-

Fig. 5. Graph of the natural-vibration frequencies of the structure under various installation conditions of the converter:

• ● — rigidly on a foundation slab weighing \(80Q\);
• ▲ — on a platform weighing \(80Q\);
• △ — on a platform weighing \(20Q\);
• □ — on a platform weighing \(2Q\);
• ○ — on shock absorbers without a platform.

Vertical axis: \(L\), dB. Horizontal axis: \(f\), Hz.

of the structural elements with the frequency of the exciting force, caused by the residual unbalance of the armature. Attention is drawn to the presence of a cantilevered part on the motor side, of the breaker unit, and of a support of low rigidity.

Fig. 4. Dependence of the vibration level of the frame on the armature rotation speed under different installation conditions of the converter.
1 — on shock absorbers without a platform; 2 — on a platform of weight \(Q_{\mathrm{m}}\); 3 — on a platform of weight \(1.7Q_{\mathrm{m}}\); 4 — on a platform of weight \(2Q_{\mathrm{m}}\); 5 — on a platform of weight \(8Q_{\mathrm{m}}\); 6 — rigidly on a foundation slab of weight \(80Q_{\mathrm{m}}\).

To determine the influence of the cantilevered part on the motor side on the amplification of oscillations, the following experiment was performed. A wedge was inserted between the support and the cantilevered part, and the vibration level was measured. When the wedge was installed, an additional support was created, thereby increasing the rigidity of the system. The results of these experiments (Fig. 3, curve 2) show that, for the case in which the converter is installed on a platform of weight \(Q_{\mathrm{m}}\), the vibration level decreases by 5–6 dB in comparison with the vibration level without the wedge installed (Fig. 3, curve 2). The absolute value of the vibration acceleration in this case decreases by a factor of 1.8.

The vibration level at the armature rotation frequency of the converter, fixed without a support on a shock-mounted platform of weight \(Q_{\mathrm{m}}\) (Fig. 3, curve 3), proved to be 12–13 dB lower than the vibration level in the presence of the support (Fig. 3, curve 2). The absolute value of the vibration acceleration in this case decreased approximately fourfold. But even in this case, installing a wedge under the cantilevered part of the converter gives a reduction in the vibration level at the rotation frequency by 3–4 dB. These experiments show that the presence of the support, together with the cantilevered part, is one of the causes of amplification of the frame oscillations of the converter under study.

As a result of an approximate calculation of the lowest natural frequency of oscillations of the cantilevered part, carried out according to the scheme proposed by B. B. Voronetskii [3], a frequency of 465 Hz was determined. However, as is evident from experiments under different conditions of fixing the converter, the natural frequency of the system proved to be considerably lower than the calculated one.

Therefore, calculation of the natural frequencies of the elements of an electric machine without taking into account the conditions of its mounting may lead to erroneous conclusions that the natural frequencies of the system elements will not coincide with the frequencies of forced vibrations and that, in this way, resonance phenomena during machine operation will be excluded.

As a result of the investigations carried out, the following conclusions were drawn.

When the converter is installed on a platform weighing from \(Q_{\mathrm{m}}\) to \(80Q_{\mathrm{m}}\), the absolute value of the vibration acceleration of the housing under the action of armature unbalance is 7–10 times greater than the calculated value.

The main cause of the amplified vibrations of the converter housing is the insufficient rigidity of the structure, the presence of a cantilever on the motor side, of the interrupter unit, and the insufficient rigidity of the pedestal.

In the case where the converter is installed on a base weighing from \(Q_{\mathrm{m}}\) to \(80Q_{\mathrm{m}}\), one of the natural frequencies of the system lies within the range from 0.76 to 1.1 of the frequency of the disturbing force caused by armature unbalance at the rated rotational speed.

As a result of the work performed, a research methodology has been outlined that can serve as the basis for bringing newly designed or modernized electric machines to satisfactory vibration characteristics.

In order to eliminate resonance phenomena at low frequencies and to obtain satisfactory vibration characteristics of the converter under study during operation, the following design changes are recommended:

a) design the housing structure so that the cantilevered part on the motor side is eliminated;

b) make the converter pedestal more rigid or, if the installation conditions at the operating site permit, remove it and combine it into a single unit with the frequency regulator.

REFERENCES

1. Ponomarev S. D., Biderman V. L., Likharev K. K., Makushin V. M., Malinin N. N., Feodos’ev V. I. Strength Calculations in Mechanical Engineering, Vol. III, Mashgiz, 1959.

2. Kryukov K. A. The influence of design parameters on the critical speeds of the rotor—housing—suspension system of an aviation GDT. Proceedings of MAI, issue 136, Oboroniz, 1961.

3. Voronetskii B. B. On the natural frequencies of certain units of aviation electric machines. Proceedings of MAI, issue 110, Oboroniz, 1951.

4. Klochkov Yu. S. Vibrations of shipboard mechanisms under the action of rotor unbalance. Proceedings of the Central Research Institute named after Academician A. N. Krylov, Sudpromgiz, 1959.

5. Mal’tsev P. T. A method for checking the quality of balancing rotors in assembled electric machines. Izvestiya TPI, Vol. 117, 1963.