METHOD FOR THE VENTILATION CALCULATION OF LOW-POWER DIRECT-CURRENT MACHINES

V. A. Zhadan, D. I. Sannikov, M. A. Sannikova

(Presented by the scientific seminar of the Department of General Electrical Engineering and Electrical Machines)

The calculation of the flow rate of cooling air from the specified dimensions of the air duct and fan is of great importance for checking the correctness of the selection of these dimensions, for determining the heat-transfer coefficients from the cooled surfaces of the machine, and for calculating the heating of the air stream as it passes through the machine.

Existing universal methods of ventilation calculation in many cases give an impermissibly large error. In particular, when calculating the air flow through protected-design low-power machines of the P series, a discrepancy with experimental data by a factor of 1.7–2.4 is obtained. Thus, it becomes necessary to develop special methods for each structural type of machine.

On the basis of experimental investigations of more than 50 varieties of ventilation systems, differing both in design features and in dimensions, several variants of a method for the ventilation calculation of low-power direct-current machines of the P series, frame sizes 1–6, of protected and enclosed externally ventilated construction have been developed.

a) Calculation by the similarity method

As is known, for geometrically similar ventilation systems, with sufficiently small frictional resistance, the following relations are valid:

\[ zL^{4}=\mathrm{const}; \qquad \frac{H}{L^{2}n^{2}}=\mathrm{const}; \qquad \frac{V}{L^{3}n}=\mathrm{const}; \]

where
\(L\) — defining dimension;
\(n\) — fan rotational speed;
\(H\) — fan pressure;
\(V\) — air flow rate;
\(z\) — hydraulic resistance of the air duct.

Taking as the defining dimension for electrical machines the outside diameter of the frame \(D_c\), expressed in meters, we obtain:

\[ z=C_z \cdot D_c^{-4}; \tag{1} \]

\[ H=C_H \cdot D_c^{2}\left(\frac{n}{1500}\right)^2; \tag{2} \]

\[ V=\sqrt{\frac{H}{z}}; \tag{3} \]

or directly

\[ V=C_V \cdot D_c^3 \frac{n}{1500}, \tag{4} \]

The coefficients \(C\) are given in Table 1.

Table 1.

The accuracy of the calculation is determined by the degree of deviation of the machine dimensions from strict similarity. The discrepancy with experimental data amounts to up to 10 percent for the existing design and up to 25 percent for the improved design of the ventilation system.

b) Calculation by the static pressure of the fan

On the basis of experimental data it may be assumed that the working pressure of the fan constitutes some constant part of the theoretical value of its static pressure:

\[ H_{\mathrm{st}}=\frac{\rho}{2}\cdot\left(u_2^2-u_1^2\right) \tag{5} \]

(without taking into account the diffuser effect in the interblade channels). Here \(u_2\) and \(u_1\) are the peripheral velocities at the outer and inner blade diameters, and \(\rho\) is the air density.

Thus, the operating head is

\[ H=\eta_{pc}\rho\,(u_2^2-u_1^2), \tag{6} \]

where \(\eta_{pc}\) is the hydraulic efficiency referred to the static head.

To determine the efficiency of protected machines, the following empirical formula was found:

\[ \eta_{pc}=0.10+0.017N+\Delta\eta, \tag{7} \]

where \(N\) is the number of fan blades;

\(\Delta\eta\) is the increase in efficiency as a result of improvements: for the first (Table 1), \(0.10\); for the second, \(0.34\); for both, \(0.44\). For enclosed blown machines \(\eta_{pc}=0.80\).

The flow rate is calculated by formula (3). The hydraulic resistance is calculated by the method of [1] with an error not exceeding 10 percent. However, it should be specified that when calculating the cross section of the fan chamber ([1], p. 220), the following formula should be used:

\[ S_g=\frac{\pi}{4}\,(D_\delta^2-D_a^2), \tag{8} \]

where \(D_a\) is the armature diameter;

\(D_\delta\) is the inner diameter of the front fan disk.

When calculating the area of the openings of the outlet grille, it should be borne in mind that in some machines part of the openings is obscured by the widened rim of the front disk and therefore should not be taken into account.

The error in calculating the flow rate by this method does not exceed 15 percent.

c) Calculation by the total fan head

The magnitude of the inner diameter of the fan, as has been established from experience, affects the head to a lesser degree than follows from formula (6). In this connection the following formula is proposed:

\[ H=\eta_{pn}\cdot \delta \cdot u_2^2, \tag{9} \]

where

\[ \eta_{pn}=0.041+0.0037N+\Delta\eta'— \tag{10} \]

the hydraulic efficiency referred to the total theoretical head.

For enclosed machines \(\eta_{pn}=0.25\).

The increase in efficiency as a result of improvements is respectively \(0.028\), \(0.093\), and \(0.132\). The flow rate is calculated in the same way as

Table 2

in the preceding case. The calculation error is within ±10 percent.

It should be noted that the calculation of enclosed blown direct-current machines can also be performed by the method of [2], although it was developed for induction motors. In this case, the error in calculating the air flow rate for direct-current machines does not exceed 10 percent.

Table 2 gives the results of calculating several machines both in the existing and in the proposed design. The calculation was carried out according to the second variant of the method. For comparison, experimental data and the result of calculating the flow rate by the general method [1] are given, and for the enclosed machine, by the method of [2]. The results presented indicate the sufficiently high accuracy of the proposed method.

REFERENCES

1. Ya. S. Gurin, M. N. Kurochkin. Design of Direct-Current Machines, GEI, 1961.

2. V. V. Malyshev, L. L. Pantyukhov. Ventilation calculation of enclosed induction motors with a power of 0.6–100 kW, VEP, No. 3, 1962.