EXPERIMENTAL STUDY OF THE ELECTROMAGNETIC FIELD IN THE REGION OF THE STATOR WINDING END TURNS IN THE PRESENCE OF CONDUCTIVE SHIELDS

L. O. OGANYAN

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

The electromagnetic field in the region of the end turns of the stator winding of electrical machines has a complex distribution. It is determined by many factors, the main ones being: the type of winding used in the electrical machine, the configuration of the end turns and their spatial distribution, the angle of inclination of the end turns to the axis of the machine, and the presence of surfaces surrounding the end portion with different magnetic and electrical permeabilities. Knowledge of the field pattern is necessary for determining the electrodynamic forces acting on the stator winding end turns and the structures surrounding them, for determining the inductive reactance of the end turns, and for determining losses in the end portions of the stator core and in the massive structural elements of the machine end region.

Among all possible design solutions for obtaining optimal parameters of the end region of a pulsed generator, shields made of nonmagnetic conducting material occupy a special place. On the one hand, the shields serve as an element for fastening the end turns and protect them from deformation by electrodynamic forces. On the other hand, owing to the induction of eddy currents in the body of the shield, the magnetic field in the region of the end turns is weakened, which leads to a reduction in inductance, a reduction in electrodynamic forces, and a reduction in losses in the end region [1]. Therefore, the study of the influence of shields on the field distribution in the region of the end turns is of great practical interest.

An attempt to calculate electromagnetic fields in order to obtain formulas convenient for practical calculations, while simultaneously taking into account the above-listed factors affecting the field distribution pattern, leads to cumbersome analytical expressions that are of little use in practice. Therefore, when solving calculation problems, assumptions are adopted that accelerate the solution of the problem and simplify it as a whole for a specific case, without grossly distorting the physics of the phenomena, and that give satisfactory results. However, in connection with the increase in the pulse power of pulsed generators, there arises a need for a more accurate calculation of the parameters of the end region and, consequently, for a more accurate determination of the field pattern. Studies [2] have shown that the experimental method of determining the field pattern is the most effective.

In the present work, the influence was investigated experimentally

electromagnetic shields on the field distribution in the end-winding zone of the stator winding of a pulsed generator under steady-state short-circuit conditions.

The studies were carried out on a static model of the end portion of the stator of a two-pole pulsed generator with a single-phase concentric winding, the end parts of which form an angle of 90° with the machine axis (Fig. 1). This type of winding makes it possible to shield the end-winding zone with shields of simple configuration and to ensure sufficient rigidity in fastening the end parts.

Fig. 1. Model of the end portion of a pulsed generator

A static model for studying the magnetic field in the end portion of the stator of a pulsed generator was made with allowance for the requirements for obtaining physical similarity of the phenomena [3]. This made it possible to simplify the model considerably; namely, all conducting and ferromagnetic structures whose influence in the region being modeled is insignificant were made of dielectric material, and the length of the model was also substantially reduced. The modeling winding consisted of two series-connected coil groups, with six coils in each group. The coils were wound with copper wire of rectangular cross section measuring \(10 \times 2.5\) mm and had one turn each. Depending on the formulation of the experimental problem, the model provided for the possibility of changing the distance between the end jumpers and the end iron. Power was supplied by an alternating voltage with a frequency of 50 Hz.

The program for studying the influence of shields on the field distribution was carried out in two stages. In the first stage, the magnetic field in the end-winding zone was studied with their ferromagnetic surroundings (on the surface of the pressure plate and the end shield); in the second stage, these studies were performed with the end parts enclosed in copper shields 10 mm thick.

The experiments in the first and second cases were carried out under identical conditions, with the current in the winding equal to 80 A. The similarity in carrying out the experiments made it possible to compare the results obtained without large error.

For convenience of measurements and subsequent processing of the experimental results, a special probe was made with three Hall sensors oriented along three mutually perpendicular directions:

a) axial—parallel to the axis of the model \((z)\),

b) radial—along the radius of the machine \((x)\),

c) tangential—along the tangent to a circumference centered on the machine axis \((y)\).

During installation of the probe, attention was paid to the accuracy with which the normals of the sensors coincided with the selected axes.

The use of Hall sensors as magnetic-field measuring devices is due to their simplicity and reliability in operation, the possibility of obtaining at the sensor output an electrical signal that accurately reproduces the shape of the magnetic field, and their relatively small dimensions, which makes it possible to measure magnetic fields in small volumes and narrow gaps. In addition, the voltage at the sensor output is proportional to the induction of the measured field, and not to the time derivative of the induction, as is the case in induction methods.

Taking into account the special features of the measurement process and the properties of Hall sensors, which predetermine the presence of interference affecting the accuracy of measurement, the circuit was installed using shielded wire. In addition, parasitic induced voltages arising in the loops formed by the control-current and voltage conductors were reduced by noninductive laying (bifilar) of the conductors when mounting the measuring probe. Compensation of the resistive voltage was carried out according to the circuit of [4]. Thermostating of the Hall sensors was not performed because of the comparatively small temperature drop (of the order of 1–2°) in the measurement zone. The nonlinearity of the sensor characteristic was 1–3%. The sensors were calibrated on a special setup. The above measures made it possible to minimize measurement error and to obtain a stable signal at the output.

To measure the components of the magnetic induction at any point of interest, a device was used that made it possible to move the sensors in both the radial and tangential directions. A step switch made it possible to connect the sensors into the measuring circuit in a definite sequence. Measurement of the emf values at the sensor output, after preliminary amplification, was carried out with a multirange average-reading voltmeter of type F564. When two signals were simultaneously applied to the oscilloscope—one from the Hall sensor and the other from the current of the phase feeding the model—it was possible to determine the phase shift between them.

The points at which measurements of the induction components were made covered the surface of the pressure plate and the end shield, bounded by the slot pitch. In the present work an analysis is given of the results of experiments at 12 points located on the geometrical axis of the model with a spacing of 10 mm. Figure 1 shows the position of the probe corresponding to these points. The choice of points for analysis is due to the fact that in this part of the winding the field may be regarded as plane-parallel, and, when calculating the field analytically, \(n\) elementary conductors carrying current \(I\) may be replaced by one conductor carrying current \(nI\). Figure 2 shows the lines of displacement of the sensors in the radial direction of the model. The measured values of the induction components and their distribution in the main parts of the end region are shown in Figs. 3, 4, and 5. The magnitude of the induction is expressed in relative units, with the axial component of induction measured at point A along line \(1—1'\), in the absence of shields and of the end shield, taken as unity; moreover, in the figures the position of this point is taken as the origin of the coordinates along the \(x\) and \(z\) axes.

In Figs. 3 and 4 the curves \(B_a\), \(B_R\), \(B_\tau\) correspond to the initial data, with which the remaining variants will subsequently be compared for a qualitative analysis of the influence of the structural elements of the end region on the distribution of the electromagnetic field.

As is evident from Fig. 3, the nature of the induction distribution on the surface of the pressure plate for the type of winding under consideration is determined by the magnitude of its axial component, \(B_a\). The radial \(B_R\) and tan—

Fig. 2. Sketch of the end part of the model:
I — pressure plate; II, III — shields;
IV — end shield; 1—1′, 2—2′,
3—3′ — lines of sensor displacement

Fig. 3. Distribution of induction components along line 1—1′ at \(\Delta_1=\Delta_2=20\) mm. \(B_a\), \(B_R\), \(B_T\) — without taking into account the end shield (IV) and the shields (II) and (III). \(B_a'\), \(B_R'\), \(B_T'\) — taking into account the end shield (IV). \(B_a''\), \(B_R''\), \(B_T''\) — induction components taking into account the end shield (IV) and shield (II)

The tangential \(B_T\) components are insignificant and in this case may be disregarded. The value of the angle \(\varphi\) at which the magnetic-induction vector enters the boundary surface is different:

\[ \varphi = \operatorname{arc\,tg}\frac{B_a}{B_R}. \tag{1} \]

The angle \(\varphi\) has its smallest value directly under the conductors; in the remaining cases its value tends to \(90^\circ\). It should be noted that the induction increases when passing from the outer surfaces of the end-winding ...

jumpers to the internal ones. The presence of the end shield leads to an increase in the induction in the end-winding zone, in particular in the zone of the pressure plate of the stator core adjoining the air gap. The curves \(B_a'\), \(B_R'\), \(B_T'\) are given for the case when \(\Delta_1=\Delta_2=20\) mm. As the investigations showed, for \(\Delta_1<\Delta_2\) the effect of the end shield on the distribution of induction in the zone of the pressure plate decreases, and at \(\Delta_2=5\div 6\Delta_1\) it disappears completely.

The effectiveness of shielding the pressure plate of the stator core is shown by the curves \(B_a''\), \(B_R''\), \(B_T''\) (Fig. 3).

Owing to the presence of the shield, the induction penetrating to the pressure plate of the stator core is noticeably weakened. This action of the shield can be evaluated by the shielding coefficient

\[ k_{\mathrm{sh}}=\frac{B_{\mathrm{sh}}}{B_{\mathrm{Fe}}}, \tag{2} \]

where

\(B_{\mathrm{sh}}\) is the value of the induction after the shield,

\(B_{\mathrm{Fe}}\) is the value of the induction before the shield.

According to the experimental data, the value of \(k_{\mathrm{sh}}\) lies within the range \(0.3\div 0.6\).

Shielding of the pressure plate of the stator core leads to a weakening of the field also on the surface of the end shield (Fig. 4, curves \(B_a'\), \(B_R'\), \(B_T'\)). In addition, weakening of the field on the surface of the end shield can be achieved by shielding it from the leakage fluxes of the end parts. The curves \(B_a''\), \(B_R''\), \(B_T''\) (Fig. 4) give the character of the field distribution on the surface of the end shield in the presence of shields (II) and (III). Since shield (III) of the model had a smaller surface than the shielding zone of the end parts and, moreover, there was a 5 mm gap between the shield and the end shield, the effect occurred of the flux bending around the lower edge of shield (III) and being forced into the gap. This led only to a shielding effect in the outer part of the end shield.

Fig. 4. Distribution of induction components along line \(3—3'\) at \(\Delta_1=\Delta_2=20\) mm. \(B_a\), \(B_R\), \(B_T\)—without taking into account the influence of shields (I) and (II). \(B_a'\), \(B_R'\), \(B_T'\)—taking into account the influence of shield (I). \(B_a''\), \(B_R''\), \(B_T''\)—taking into account the influence of shields (I) and (II).

Eddy currents induced in the body of the shield not only weaken the flux in the end-winding zone, but also cause its redistribution, leading to the displacement of part of the flux into the tooth zone. This leads to an increase in losses and heating of the teeth of the end packets of the stator iron. Therefore, to reduce this effect it is necessary to shield the tooth zone.

The alternating magnetic field of the stator-winding end portions induces currents in the shields that damp this field. This leads to a redistribution of the magnitudes of the components of the induction of the end-leakage field. The field lines, as it were, slide along the surface of the shield. In this case the electromagnetic-induction vector enters the body of the shield at an angle considerably smaller than in a ferromagnetic environment. This leads to a sharp increase in the radial component and to a decrease in the axial component of the induction. The character of the field distribution in front of shield (II) is represented by the curves \(B_a\), \(B_R\), \(B_T\) in Fig. 5. The curves \(B_a'\), \(B_R'\), \(B_T'\) show the slight change in the components in the presence of the end shield (IV), and \(B_a''\), \(B_R''\), \(B_T''\)—in the presence of shield (III).

Fig. 5. Distribution of the induction components along line \(2—2'\) at \(\Lambda_1=\Lambda_2=25\) mm. \(B_a\); \(B_R\); \(B_T\)—without the end shield (IV) and shield (III). \(B_a'\); \(B_R'\); \(B_T'\)—with allowance for the end shield (IV). \(B_a''\); \(B_R''\); \(B_T''\)—with allowance for the end shield (IV) and shields (II) and (III).

The effectiveness of the use of shields depends on the distance between the end jumpers and the surface of the shield \((\Delta)\). The greater this distance, the lower the effectiveness of shielding the elements of the end zone from the leakage fields of the end portions. Figure 6 shows the change in the induction components along the \(z\) axis. As \(\Delta\) increases, the induction components \(B_{R\varphi}\) and \(B_\theta\) tend toward the magnitude of the induction components in the end-winding zone without the influence of the surrounding medium.

Fig. 6. Variation of the components of induction as a function of the distance \(\Delta\), without taking into account the end shield. \(B_a, B_R, B_T\)—at a point on the surface of the clamping plate (I), without shield (I). \(B_{a\mathrm{e}}, B_{R\mathrm{e}}, B_{T\mathrm{e}}\)—at the same point with shield (I).

Thus, enclosing the end-winding parts in shields made of materials with high electrical conductivity substantially reduces the magnitude of the induction in the end region of impulse generators. The experimental data obtained generally confirm the general physical concepts concerning the distribution of the field in the space surrounding the end-winding parts.

REFERENCES

1. P. A. Sipaylov, V. F. Kulakov, V. I. Popov. On the influence of shielding of the end-winding parts of an impulse generator. Izv. TPI, vol. 212, 1971.

2. A. S. Moizhes. On methods for determining the magnetic field in the end region of a turbogenerator. Elektrotekhnika, 1971, No. 11.

3. A. V. Ivan-Smolenskii. Electromagnetic Fields and Processes in Electrical Machines and Their Physical Modeling. Moscow, “Energiya,” 1969.

4. A. Kobus, Ya. Tushinskii. Hall Sensors and Magnetoresistors. Moscow, “Energiya,” 1971.