PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE
NAMED AFTER S. M. KIROV
AWARDED THE ORDER OF THE OCTOBER REVOLUTION AND THE ORDER OF THE RED BANNER OF LABOR

Volume 200

1974

STUDY OF BEARING WEAR IN ASYNCHRONOUS MOTORS DURING OPERATION AND DETERMINATION OF THE TIME FOR THEIR PREVENTIVE REPLACEMENT

A. G. Vereshch, O. P. Muravlev

Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering

The reliability and durability of asynchronous motors is determined mainly by the reliability and durability of the windings and bearing assemblies. The principal work in the field of calculating, ensuring, and improving reliability is being carried out with respect to windings, while insufficient attention is paid to bearing assemblies. At plants and institutes of the bearing industry, mechanical comparative tests of bearings for durability and tests of consistent greases are conducted. The main type of investigation of bearing operability is bench testing according to the method [1] developed by VNIIPP.

The testing method has a number of significant shortcomings:

— rolling bearings are tested outside the working mechanisms into which they are built;

— on the test bench it is impossible to imitate the variety of influences to which the bearing assemblies of asynchronous motors are subjected in operation;

— in order to reduce the time of bearing tests to 200–500 hours, very large loads are selected; therefore the tests take place in the zone of plastic deformation \((\sigma_{\text{test}}>400\ \text{kg}/\text{mm}^2)\).

The test results are subsequently extended to the region of elastic deformations. The indicated shortcomings of the bench-test method emphasize its limited character. Therefore, in order to determine the reliability and durability of bearings, tests of bearing assemblies on actual motors are necessary. As a criterion characterizing the condition of a bearing assembly, it is most expedient to adopt the value of the radial clearance of the bearing, which determines the nonuniformity of the air gap in operation.

To determine the operability of bearing assemblies under real conditions, in the reliability laboratory of the Special Design Bureau of the Sibelektromotor plant, 24 motors of the AO2 series of frame sizes 3 and 4 were put on test. The motors were manufactured with class P and N ball bearings and filled with greases 1-13 and CIATIM-203. The following amount of grease was placed in each motor bearing assembly: for AO2-32, 14 g; for AO2-42, 24 g; moreover, 50% of the grease was uniformly placed in the bearings and 50% in the chamber of the bearing cover. The temperature of the bearings was measured with thermocouples. In the event that the bearing temperature rose above the allowable—

permissible value, the bearing covers were removed and the causes of the excess were eliminated.

A radial load was created on the working end of the shaft by means of rods, with the force indicated in Table 1. The switching frequency of the motor was equal to 2 starts/hour.

Table 1

According to the established regulations, after 1000 hours of operation the bearing assemblies were replenished with grease.

After the motors had operated for 10,000 hours, they were removed from the tests. Of the 24 motors placed under test, 22 completed the accepted operating life. Two motors were removed from the tests because of separator failure: one after 1100 hours, and the other after 9000 hours of operation. Radial clearances were measured for all bearings; these are presented in Table 1. The measurement results showed an increase in the magnitude of the radial clearance, which indicates wear of the raceways. In connection with this, the nonuniformity of the air gap also increased, and the probability of rotor rubbing against the stator in the tested motors rose. The proportion of motors in which the rotor rubs against the stator can be found on the basis of the distribution law of eccentricity [2]:

\[ f(\varepsilon)=\frac{\varepsilon}{\sigma_{\varepsilon}^{2}} \exp\left(-\frac{\varepsilon^{2}}{2\sigma_{\varepsilon}^{2}}\right), \tag{1} \]

where \(\varepsilon\) is the eccentricity of the motor,

\(\sigma_{\varepsilon}\) is the distribution parameter.

The parameter \(\sigma_{\varepsilon}\) of the eccentricity distribution can be determined from the number (fraction) of cases of rotor rubbing against the stator during factory acceptance tests:

\[ \sigma_{\varepsilon}= \sqrt{-\frac{\varepsilon_{\mathrm{allow}}^{2}}{2\ln q}}, \tag{2} \]

where \(\varepsilon_{\mathrm{dop}}\) is the smallest value of the eccentricity at which the rotor begins to strike the stator;

\(q\) is the fraction of rotor strikes against the stator according to the data of the Technical Control Department.

Fig. 1

The distribution curve of the eccentricity of AO2-32-4 motors is presented in Fig. 1.

The probability of the rotor striking the stator after the tests have been carried out is

\[ q(\varepsilon) = \exp\left(-\frac{\varepsilon_{\mathrm{dop}}^{\prime\,2}}{2\sigma_{\varepsilon}^{2}}\right)=0.022, \tag{3} \]

where \(\varepsilon'_{\mathrm{dop}}\) is the smallest value of the eccentricity at which the rotor strikes the stator after the tests have been carried out.

The change in the probability of failure-free operation of the motor \(P(t)\), from the condition of the rotor striking the stator, is shown in Fig. 2. The nature of the curve shows that the probability of failure-free operation of motors decreases with time, since the probability of the rotor striking the stator increases.

To increase the probability of failure-free operation of motors in service, it is advisable to replace the bearings after they have worked a certain service life \(t_{\mathrm{zamena}} < t_{\mathrm{tabl.}}\), where \(t_{\mathrm{tabl.}}\) is the calculated service life of the bearing. In particular, [3] pointed out the possibility of increasing the reliability of motors in service by periodic replacement of bearings.

Let us consider the determination of the time for preventive replacement of bearings.

Let \(C_{\mathrm{z.p}}\) be the costs of preventive replacement of bearings, including the cost of the bearing and the costs of disassembling and assembling the motor, rubles;

\(C_{\mathrm{e}}\) is the average value of operating costs attributable to one motor failure, rubles.

Fig. 2

The value \(C_\mathrm{e}\) can be determined by the expression

\[ C_\mathrm{e}=C_\mathrm{y}+C_\mathrm{pr}+C_\mathrm{v}, \tag{4} \]

where \(C_\mathrm{y}\) is the amount of damage caused by damage to equipment and mechanisms, tool breakage, defective products, and spoilage of raw materials and materials in the event of failure, rubles.

\(C_\mathrm{pr}\) is the amount of damage caused by downtime of equipment and machines in the event of failure, rubles.

\(C_\mathrm{v}\) is the amount of expenditures for restorative repair of the motor in the event of failure, rubles.

Then the costs in the event of motor failures are

\[ C_1=C_\mathrm{e}[1-P(t)]N, \tag{5} \]

where \(P(t)\) is the probability of failure-free operation of the motors over time \(t\) as a function of the probability of rotor rubbing;

\(N\) is the number of motors of a given type-size produced for the given consumer sector.

The optimal time for preventive replacement of bearings will be when the costs associated with replacing bearings \(C_{\mathrm{z.p}}\) are equal to the costs in the event of motor failures in operation \(C_1\)

\[ C_{\mathrm{z.p}}\cdot n_1=C_\mathrm{e}[1-P(t_\mathrm{z})]N. \tag{6} \]

Here

\(n_1\) is the number of bearings being replaced.

Statistical data on wear-related failures of bearing units in operation and [3, 4] indicate that, to describe failures, the Weibull distribution should be used

\[ P(t)=\exp\left(-\frac{t^\alpha}{t_0}\right), \tag{7} \]

where \(\alpha\) and \(t_0\) are the parameters of the Weibull law.

Then, substituting (7) into (6) and making minor transformations, we obtain

\[ t_\mathrm{z}=\left[-t_0\ln\left(1-\frac{n_1\cdot C_{\mathrm{z.p}}}{N\cdot C_\mathrm{e}}\right)\right]^{\frac{1}{\alpha}}. \tag{8} \]

On the basis of the obtained equation (8), let us determine, as an example, the time for preventive replacement of ball bearings No. 60306 in A02-32-4 motors.

The equation for failure-free operation of these motors under the condition of rotor contact with the stator has the form

\[ P(t)=\exp\left(-\frac{t^{1.483}}{3.98\cdot 10^{7}}\right); \tag{9} \]

The average value of operating costs attributable to one motor failure is \(C_\mathrm{e}=38.38\). The costs associated with preventive replacement of two motor bearings amount to \(C_{\mathrm{z.p}}=1.77\) rubles.

Then, substituting the parameters \(a=1.483\), \(t_0=3.98\cdot 10^7\) hours from equation (9) and the found cost values \(C_\mathrm{e}\) and \(C_{\mathrm{z.p}}\) into (8), we obtain \(t_\mathrm{z}=16600\) hours. That is, after the motors have accumulated 16,600 hours of operation, the bearings must be replaced, since with any increase in this time the costs due to motor failures caused by rotor contact with the stator will exceed the costs associated with bearing replacement.

The results of the investigations carried out make it possible to formulate the following conclusions:

1. When conducting tests of bearing assemblies of asynchronous motors for reliability and service life, it is proposed to use the radial clearance of the bearing as the criterion characterizing the degree of bearing wear.

2. A method has been developed for determining the optimal time for preventive replacement of bearings under the conditions of the tests performed.

REFERENCES

1. Methodology for life testing of rolling bearings. GP90-56, TsKB VNIIPP, Moscow, 1966.

2. Kh. B. Kordonskii. Applications of Probability Theory in Engineering. Moscow–Leningrad, Fizmat Publishing House, 1963.

3. T. A. Harris, S. F. Aaronson, R. Piante. The effect of partial replacement on the reliability of a closed group of rolling bearings. ASLE. Annual meet. Preprint, 1966, 31, No. 11.

4. Quality Assurance at U.S. Firms. Moscow, Standards Publishing House, 1970.