INVESTIGATION OF FRICTION LOSSES

IN THE CYLINDRICAL SURFACES OF THE ROTOR

OF AN OIL-FILLED ELECTRIC MOTOR

OF A HYDRAULIC THRUSTER

E. M. GUSEL'NIKOV, V. A. ZHADAN

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

The desire to create compact electrohydraulic thrusters (EHT) and pumps makes it necessary to bring the electric motor directly up to the impeller and to make the electric motors oil-filled, i.e., submerged. In designing submersible electric motors for EHT and pumps, it is important to determine the mechanical losses correctly, since they may exceed the sum of all other losses in the machine. Friction losses at the rotor end faces are considered as disk losses and can be determined according to [4].

The flow of liquid in the gap between the stator and the rotor can be represented schematically as plane motion between two concentric cylinders, when the inner cylinder rotates and the outer one is stationary.

As is known, the friction moment of a rotating cylindrical surface against a liquid can be represented in the form

\[ M = 2\pi r^{2}\tau l, \tag{1} \]

where

\(l\) and \(r\) are, respectively, the length and radius of the cylindrical surface;

\(\tau\) is the shear stress at the wall, equal to

\[ \tau = \lambda \frac{jv^{2}}{2g} = \frac{\omega^{2} r^{2} j}{2g}, \tag{2} \]

where

\(v\) is the mean velocity of the liquid in the gap;

\(\lambda\) is the dimensionless resistance coefficient, which is a similarity criterion;

\(j\) is the specific weight of the liquid.

To calculate the value of the resistance coefficient \(\lambda\) and the cylindrical losses, the authors of [1–3] proposed several formulas. Calculation of cylindrical losses in an EHT by the proposed formulas does not provide sufficient accuracy for practice. Therefore, on the basis of an analysis of these formulas and of experimental investigations, the results of which are given in Table 1, we established the value of the resistance coefficient for rubbing cylindrical surfaces in an EHT as equal to

\[ \lambda = 0.46 k_{\delta}\left(\frac{\delta}{r}\right)^{0.25}\mathrm{Re}^{-5} \quad \text{for } \quad 10 < \mathrm{Re} < 10^{4}, \tag{3} \]

Table 1

\[ \lambda = 0.073 \cdot k_{\delta}\left(\frac{\delta}{r}\right)^{0.25} Re^{-0.3} \quad \text{for } 10^{4} < Re < 2.5 \cdot 10^{4}, \tag{4} \]

where

\[ k_{\delta}=\frac{t_{1}+1.5\delta}{t_{1}+10\delta-b_{s}} \]

is a coefficient taking into account the increase in hydraulic resistance caused by additional swirling of the fluid in the open or semi-closed slots of the stator; for smooth cylindrical surfaces \(k_{\delta}=1\);

\[ Re=\frac{\omega \cdot r \cdot \delta}{\nu} =\frac{\pi \cdot n \cdot r \cdot \delta}{30\nu} \]

is the Reynolds number;

\(\delta\) — radial clearance between the rotating cylindrical surface and the stationary wall;
\(\nu\) — viscosity of the working fluid;
\(t_{1}\) — pitch of the stator slots;
\(b_{s}\) — stator-slot opening.

Using equations (1–4), we find the friction power of the cylindrical surfaces:

\[ N=\omega M=\frac{1.65\cdot 10^{-6}}{\sqrt{Re}}\cdot k_{\delta}\cdot j\cdot l\cdot n^{3}\cdot r^{4}\cdot \sqrt[4]{\frac{\delta}{r}} \]

for \(10^{2}<Re<10^{4}\);

\[ N=0.26\cdot 10^{-6}\cdot k_{\delta}\cdot j\cdot n^{3}\cdot r^{4}\cdot Re^{-0.3}\cdot \sqrt[4]{\frac{\delta}{r}} \]

for \(10^{4}<Re<2.5\cdot 10^{4}\).

The investigation of the influence on the magnitude of losses of the viscosity of the working fluid, the radial clearance \(\delta\) between the rotating and stationary cylinders, the stator tooth geometry, etc., was carried out on the experimental setup shown in Fig. 1. The results of the experimental investigation and calculations are given in Table 1. They show that the formulas proposed for calculating cylindrical losses in EHT make it possible, with accuracy sufficient for practice, to take into account the influence of various factors on the magnitude of these losses.

REFERENCES

1. A. A. Lomakin. Centrifugal and Propeller Pumps. Mashgiz, 1950.
2. M. D. Aizenshtein. Centrifugal Pumps for the Petroleum Industry. Gostoptekhizdat, 1957.
3. E. I. Yantovskii. Mechanical losses in the clearance of an electric motor filled with liquid. — Vestnik elektropromyshlennosti, 1957, No. 9.
4. E. M. Guselnikov, V. F. Rott. Electrohydraulic Thrusters. “Energiya,” 1968.