Forces in the End Windings of the Stator Winding of a Shock Generator
Abstract Generated abstract
This paper addresses the calculation of electromechanical forces in the stator end windings of shock generators, where short-circuit currents can greatly exceed rated values and impose severe mechanical stresses. It divides the force system into radial and tangential forces on straight end sections, axial forces on bent sections, and attraction forces between bent sections and the stator core end face, with calculations expressed through geometric factors obtained using computer analysis for machines of varying bore diameter, overhang, and slot number. The resulting curves and example calculation for a single-phase, single-layer concentric winding show that the largest forces occur on the first bar near the edge of the phase zone and especially on bent end-winding sections. The derived relationships are intended for estimating insulation strength requirements and stresses in end-winding fastening structures.
Full Text
FORCES IN THE END PARTS OF THE STATOR WINDING OF A SHOCK GENERATOR
A. I. Verkhoturov, G. A. Sipaĭlov, K. A. Khor’kov
(Presented by the scientific seminar of the Department of Electrical Machines and General Electrical Engineering)
In connection with the growth in the power of alternating-current machines, much attention in their design is devoted to calculating the forces arising in individual structural elements. Especially great attention has recently been given to calculating the mechanical forces experienced by the end parts of the stator winding during a short circuit. These forces present a great danger for a shock generator, whose normal operating mode is a sudden short circuit or a sudden closing onto a load with a small resistance for the period of one maximum half-wave of current.
It is known that the shock current of synchronous generators can reach values 20–30 times, or more, greater than the rated current. Consequently, the forces experienced by the conductors of the generator stator will exceed by 400–900 times the forces acting during normal operation of the machine. In this connection, the problems of fastening the end parts of the stator winding of a shock generator and calculating their mechanical strength require special investigation. The calculation of forces in the end parts of a stator winding can be performed only approximately. This is explained by the very complex spatial distribution of a large number of winding bars in the zone of the end parts and by the influence exerted on the end parts by the ferromagnetic surfaces surrounding them: the end of the stator, the frame, the end shields, and the rotor. Investigations have shown that the greatest part of the leakage flux (about 20% of the total leakage flux) links the end part with the end of the stator core. The leakage fluxes of the end part with respect to the frame and the end shields amount, respectively, to approximately 3% and 10% of the total leakage flux [1]. Consequently, first of all the forces between the end part and the end of the stator core must be taken into account.
The method for calculating the forces in the zone of the end parts of the stator winding of an electrical machine is based on the method for calculating the forces between separate sections of different length [2]. For the purpose of simplifying the calculations, the forces arising in sections of the end parts of the stator winding are divided into separate components:
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Radial and tangential forces arising between the rectilinear sections of the end parts of the winding.
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Axial forces arising between the bent sections of the end parts of the winding.
- Forces arising between the sections of the end part and the ferromagnetic surfaces. In this case, only the forces between the curved sections of the end parts, parallel to the end face of the stator iron, and the end face of the stator are considered.
Investigations of the mechanical forces in the end parts of a single-phase, single-layer concentric stator winding were carried out with the aid of the ETsVM-Minsk-1. Calculations of the mechanical forces were performed for a number of machines with different stator-bore diameters, different overhangs of the end parts, and different numbers of stator slots. The algorithm for calculating the forces and the calculation formulas were set forth earlier [2], and therefore are not given here. To determine the mechanical forces per unit length of conductor we use the relation
\[ F_x = k_x \cdot 10^{-8} I_{\mathrm{ud}}^{2}, \ \text{kg/m}, \]
where \(I_{\mathrm{ud}}\) is the peak short-circuit current in amperes,
\(k_{\mathrm{g}}\) is the geometric factor that takes into account the spatial position of an individual section of the end part and the configuration of the entire end part as a whole.
Fig. 1. For calculating the forces on straight sections of the end parts:
a) geometric factor for calculating tangential forces,
b) geometric factor for calculating radial forces.
As a result of the investigations carried out, dependences of the geometric factor on various machine parameters were found. These dependences are presented in the form of curves in Figs. 1, 2, and 3. From the curves in Fig. 1 one can determine the geometric factors \(k_r\) and \(k_t\) for calculating the radial \(F_r\) and tangential \(F_t\) forces acting on straight sections of the end part. From the curves in Fig. 2 one can determine the geometric factors \(k_a\) and \(k_c\) for calculating the axial forces acting on individual curved sections of the end part, \(F_a\), and the forces of attraction of these sections to the end face of the stator iron stack, \(F_c\).
As follows from the curves in Figs. 1 and 2, the greatest forces act on the first bar, taken to be the bar lying at the edge of the phase zone on the side of the slots free from the winding. The greatest
forces act on the bent segment of the rod of the frontal part. Calculations show that the geometric factor depends to a very high degree on the diameter of the stator bore of the machine. Using a series of curves analogous to the dependences presented in Figs. 1, 2 for \(D = 110\) cm, one can construct dependences of the geometric factor on the number of slots for various diameters of the stator bore. Such dependences are presented in Fig. 3. Using the curves for determi-
Fig. 2. For the calculation of forces on the bent segments of frontal parts:
a) geometric factor for calculating the forces of attraction to the stator steel, b) geometric factor for calculating axial forces.
Table 1
| \(n\) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| \(F_r \dfrac{m}{M}\) | 9,78 | 8,74 | 7,83 | 6,94 | 6,02 | 5,07 | 4,07 | 3,00 | 1,87 | 0,65 |
| \(F_l \dfrac{m}{M}\) | 52,0 | 35,8 | 29,6 | 25,6 | 22,3 | 19,2 | 16,0 | 12,7 | 8,78 | 3,50 |
| \(F_a \dfrac{m}{M}\) | 135,7 | 89,7 | 65,4 | 47,0 | 30,4 | 13,8 | 4,1 | −25,4 | −54,4 | −107,8 |
| \(F_c \dfrac{m}{M}\) | 3,44 | 2,80 | 2,35 | 2,03 | 1,79 | 1,60 | 1,45 | 1,33 | 1,22 | 1,14 |
| \(\sum F_r = 801,6\) | \(\sum F_r = 801,6\) | \(\sum F_r = 801,6\) | \(\sum F_r = 801,6\) | \(\sum F_a = 190,45\) | \(\sum F_a = 190,45\) | \(\sum F_a = 190,45\) | \(\sum F_a = 190,45\) | \(\sum F_c = 19,17\) | \(\sum F_c = 19,17\) | \(\sum F_c = 19,17\) |
Fig. 3. For the calculation of the resultant forces acting on the end portions:
a) geometric factor for calculating radial forces;
b) geometric factor for calculating axial forces;
c) geometric factor for calculating the forces of attraction to the stator steel.
...the values \(k_{xr}\), \(k_{xa}\), \(k_{xc}\) (Fig. 3), one can calculate the total forces acting on any part of the stator winding in the radial \(F_r\) and axial \(F_a\) directions, as well as the forces of attraction to the steel \(F_c\).
As an example, using the obtained relationships, the forces acting on any part of a generator with a single-phase, single-layer, concentric, subdivided winding were calculated for a stator bore diameter \(D = 110\) cm, with the number of stator slots \(z'_1 = 60\), when a current \(I_{\mathrm{sh}} = 300000\) A flows through the winding. The calculations are presented in Table 1.
The forces found may be used for calculating the mechanical strength of the insulation, and also for calculating the mechanical stresses in the fastening nodes of any parts.
LITERATURE
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G. A. Sipailov, K. A. Khorkov. On methods for calculating the leakage of frontal parts of single-phase windings. Izvestiya TPI, vol. 138, 1965.
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A. I. Verkhoturov, G. A. Sipailov, K. A. Khorkov. Method for calculating mechanical forces. Izvestiya TPI, vol. 139, 1965.