STUDY OF TEMPERATURE FIELDS IN LOW-POWER DIRECT-CURRENT MOTORS

R. Ya. Klyain, D. I. Sannikov

(Presented by the joint seminar of the Departments of Electrical Machines and General Electrical Engineering)

The temperature field in the windings of electrical machines under steady nominal operating conditions is nonuniform, due to two causes:

1) the regularities of heat-transfer and heat-conduction phenomena in different parts of the machine in the absence of random deviations of the thermophysical conditions,

2) random deviations of the conditions of heat generation and heat removal in different machines of one type, in different coils of one machine, etc.

The first cause produces a definite temperature distribution along the length of the machine and over the cross section of the coils. Although considerable research experience exists in this area and methods have been developed for approximate calculation of the temperature field, the difficulties of preliminarily determining the thermophysical conditions and other causes lead to the necessity of continuing experimental investigations.

The second cause produces scatter in the heating of machines of the same type and of identical parts within a machine. This scatter in low-power direct-current machines has practically not been investigated; however, the need for such a study is obvious, since the scatter must be taken into account when assigning temperature allowances.

To obtain a sufficient volume of information in the study of temperature fields, modifications of the P32 and P52 motors, intended for operation in the three nominal modes indicated in Table 1, were selected as the test objects.

Table 1

For the tests, four P32 motors and two P52 motors were manufactured with embedded copper-constantan thermocouples, up to 250 in each motor. In the armature of the P32 there were 47 thermocouples, in the P52—71 thermocouples; in the pole coils, respectively, 64 and 128; in the pole cores and the frame—52 each.

The tests were carried out in the three indicated nominal modes; the thermo-emf was measured at steady heating by means of potentiometer P2/1; in addition, the average temperature of the windings was determined by the resistance method. The modes were repeated 3–5 times, after which the measurement data were averaged.

Temperature field of the armature

The thermocouples of one position were arranged around the circumference of the armature at 4–8 points for machine P32 and at 4–12 points for P52. The ends of the thermocouples were led out through a channel in the motor shaft to an attached current collector.

Figure 1 gives the positions of the thermocouples in the armature winding and shows the distribution of the temperature rise along the length of the winding in three P32 motors in the 2nd mode; in this case the readings of the thermocouples of one position were averaged. The measurement data for the temperature rise above ambient temperature for both types of motors in the three nominal modes are collected in Table 2, and the data for machines of the same type have likewise been averaged.

Fig. 1. Temperature distribution along the length of the armature winding in motor P32

Table 2

From the curves in Fig. 1 and analogous curves obtained in other conditions, it is evident that the character of the temperature distribution for different machines of the same type is not the same, that is, it is subject to the influence of random factors; however, the nonuniformity of the temperature distribution along the length and height of the winding is approximately the same for all machines, and when the data for machines of the same type are averaged, the nonuniformity decreases.

The rms scatter of heating \(d\Theta_{\mathrm{ym}}\) between motors of the same type, P32, at individual positions under different conditions lies within the range 1.8–5%; the scatter of the mean winding overheating in the 2nd condition is 2.8% according to thermocouples and 1.8% according to the resistance method; in the other conditions the scatter has similar values and does not exceed 4%. For the P52 motors, because only two prototypes were available, this scatter was not determined.

The rms deviation of the temperature \(d\Theta_{\mathrm{yo}}\) around the circumference of the armature in one position is no more than 2.5% for P32 and up to 12.5% for P52.

The resulting rms deviation

\[ d\Theta_{\mathrm{yo}} = \sqrt{d\Theta_{\mathrm{ym}}^{2} + d\Theta_{\mathrm{yo}}^{2}} \tag{1} \]

is, for P32 in the 2nd condition, 3.8% on average for all positions and 6.0% for the position with the maximum scatter (position 12). For the P52 machine this deviation is estimated at 13%.

The temperature distribution along the length of the winding is characterized by the excess of the temperature of the hottest point over the mean, \(\Delta\Theta_{\mathrm{yg}}\). For P32 machines, \(\Delta\Theta_{\mathrm{yg}}\) is: in the 1st condition 2.9%, in the 2nd, 1.5%, and in the 3rd condition 1.7%; for P52, respectively, 19, 10, and 17.5%.

Hence the maximum possible excess of the temperature of the hot spot over the mean temperature of the armature winding can be found with 96% probability as

\[ \Delta\theta_{\mathrm{ymax}} = 2d\theta_{\mathrm{y}} + \Delta\theta_{\mathrm{yg}}. \tag{2} \]

In the first condition, that is, at the greatest load, \(\Delta\Theta_{\mathrm{ymax}}\) is 15%, or \(8^\circ\)C, for the P32 motors, and 45%, or \(38.5^\circ\)C, for the P52 motors.

The temperature distribution over the height of the winding in the slot, determined in the P52 motor, is shown in Fig. 2a and is characterized by relative uniformity.

Temperature field of the windings of the main and auxiliary poles

Thermocouples were embedded in each coil in four sections located at the middle of its sides: I, on the commutator side; III, on the opposite side; II and IV, in the lateral sides of the coil. The location of the thermocouples in the section is indicated in Fig. 2b by positions A, B, C, D, E. When considering the temperature distribution along the length of a half-turn, the thermocouple readings in each section were averaged on the basis of the assumption that the temperature distribution in the section follows the law of an elliptic paraboloid.

Fig. 2. Temperature distribution over the height of the winding in the slot and in the pole coils

\[ \theta_{\mathrm{av}}=\frac{4\theta_A+\theta_B+\theta_C+\theta_D+\theta_F}{8}. \tag{3} \]

In addition, the temperature of sections II and IV was averaged. The values of the averaged temperature rises are presented in Table 3. The nonuniformity of the distribution along the length for both motors is insignificant; the deviation from the mean does not exceed \(2^\circ\mathrm{C}\), and in relative terms is \(3.5\%\) for the shunt coils and \(5\%\) for the interpole coils.

Table 3

A considerably greater nonuniformity of the temperature distribution is observed in the transverse section of the coils, as is evident from the graphs in Fig. 3, where the temperature distribution is shown for motor P32 in the 2nd mode. The thermocouple readings are averaged by positions in all coils. Summary data for both motors and all three modes are given in Table 4. The nonuniformity of the temperature distribution over the section is characterized by the coefficient of maximum temperature rise

\[ k_M=\frac{\theta_A}{\theta_{\mathrm{av}}}. \tag{4} \]

Table 4

The nature of the temperature field in the coils is determined by the low thermal conductivity of the bundle of round insulated conductors in the transverse direction and by the high conductivity in the longitudinal direction, and indicates a comparatively uniform distribution of heat-flux density over the surface of the coils.

The scatter in the heating of the coils among individual machines and among positions in each machine, according to the available experimental data, does not exceed the scatter characteristic of the armature winding.

Main Conclusions

In a machine of the third size, the temperature field of the armature is characterized by weakly expressed nonuniformity and by a small scatter both around the circumference of the armature and between machines of the same type. The indicated deviations do not exceed 3–6%. However, the resulting maximum deviation can reach a considerable value ($\Delta \Theta_{\max}=15\%$).

As the dimensions of the machine increase, all the listed deviations increase substantially; in a machine of the fifth size, $\Delta \Theta_{\max}$ reaches 45%. The hottest point of the armature winding is located in the lower layer of the end parts on the side opposite the commutator, or near the middle of the armature.

In the pole coils the hottest point is located near the center of the cross section, and its temperature excess over the average coil overheating is 12–35%, with the larger values applying to the shunt coils and to machines of larger size. The temperature distribution along the length of a turn is uniform. The maximum possible excess of the temperature of the hot spot over the average temperature, taking random deviations into account, may be estimated as 25% for P32 and 50% for P52 in the mode with the greatest load.

Reducing the nonuniformity of heating and the scatter is, therefore, one of the reserves for increasing the utilization of machines.

REFERENCES

1. A. K. Mitropolsky, Technique of Statistical Computations. Fizmatgiz, 1961.

2. M. N. Ulyanitsky, Analysis of temperature fields of direct-current machines of the P series. “Izv. TPI,” vol. 132, 1965.