distribution on the end face of two types of solid cylindrical rotors for different currents ... useful as in eddy current brakes, clutches, relays, squirrel cage rotor of ...
Distribution of eddy current and power loss density on the end face of solid cylindrical rotor Amer M. Kado, B.Sc. Engg,M.Sc Technical college /Mosul Mosul- Iraq
Mohammed Y. Suliman, Bsc. Engg,M.Sc Technical college /Mosul Mosul-Iraq
Abstract: This paper investigates the analyze of eddy current and power loss density distribution on the end face of two types of solid cylindrical rotors for different currents and variables frequency. The first rotor is made of aluminum, while the second rotor is made of mild steel. These eddy currents are in peripheral and radial directions. Small pins are used to measure eddy currents and then the power loss density distributions can be calculated. Areas of hot sports are noticed on different parts on rotor surface. Introduction: In the design of modern electric machines, a plan is usually made to take full advantage of the active materials in order to raise the efficiency and decrease the weight. This policy is connected with many difficulties, one of, which is the problem of circulating eddy currents. Therefore, the developments in modern highly rated electrical machines, transformers and other low frequency electromagnetic devices have led to an increasing interest in eddy current problems. Two reasons account for the importance of the subject. First, there are the losses – usually undesirable –caused by the eddy currents. Secondly, there is the influence of the eddy currents on the magnetic field in their neighborhood. Moreover, the eddy currents generate hot spots in various parts of the machine during normal running and on the secondary surface during short circuit or unbalanced loading. Eddy current originates in any magnetic or non-magnetic conducting material when it is subjected to a time varying magnetic field. The pronounced nonlinearly of magnetic materials makes it necessary to distinguish between the eddy current phenomena in magnetic and non-magnetic conductors. These currents are sometimes useful as in eddy current brakes, clutches, relays, squirrel cage rotor of synchronous machines and in induction furnaces, where in the latter equipment the heat produced by the eddy currents is used to melt materials. On the other hand, eddy currents, in most electrical machines, are not desired because of their associated I2R losses. Eddy currents give rise to a power loss in the resistance of the eddy current path. To minimize the loss, only the cross sectional area and the resistively can be varied. The area can be divided into smaller sections by making the core of a number of thin sheets, called laminations, which are lightly insulated from one another by an oxide. This
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reduces the area of each section and hence the induced e.m.f. It also increases the resistance of the eddy current path since the area through which the currents can pass is smaller. Both effects combined to reduce the current and hence the power loss. To decrease the effect of eddy currents the rotor and stator core materials are laminated as much as possible. The eddy current brakes are used now to produce a force opposite to the direction of rotation. The brake used consists of four poles, d.c. Stator winding with 282 turn/pole. The stator length is 12 cm and 13 cm in diameter. These four poles were connected in series or concentric {chain} making alternate polarities. Two solid rotors were made; each of them was 12 cm long with a 12.2 cm diameter allowing 0.4 cm airgap. The eddy current brake used is 1.3 kw with 3000 r.p.m. as a maximum allowed speed. In conventional eddy current brakes, eddy current is induced on the surface of the rotor when there is an mmf rotating with respect to the rotor. To simulate the situation in the laboratory, the rotor was kept stationary, while the stator was excited by a singlephase a.c. supply of variable frequency, producing pulsating mmf, which pulsates at the supply frequency. Eddy currents at supply frequency will be induced on the rotor surface producing power loss and hot spots in some places on the rotor surface. This locked test of the rotor can give general idea of the current density and its distribution on the rotor surface. Experimental Work: The objective of the investigation is to measure the current density and power loss density on the surface of two types of current brakes. Current probe method was used for the measurement of the eddy current density on the surface of a rectangular conductor. This method consists basically of measuring the voltage drop between two points on the surface of the rotor. For this purpose a fine wire is connected to the sample surface by using small pins. The diameter of the pin used is 1mm. The pin is driven into a hole about 2mm deep. To obtain a good contact between the inner surface of the hole and the pin, the diameter of the hole is made less than 1mm. A sufficient length of the pin {3mm} is left above the rotor surface to enable the wire to be soldered to the top of the pin without the heat being conducted a way down to the rotor. The wire is then spiraled down the first pin and taken along the surface to meet the wire attached to the second pin, as shown in figure (1). The first wire is kept as near as possible to the surface to reduce the effect of any stray fields. This method depends upon the distance between the two pins. As far as the distance is small, the accuracy is better. Therefore, an error can be produced due to the distance, loose connection between pins and surface, and holes themselves can cause distortion to the eddy current flow if they are deep enough. Despite the errors, this method is considered as a reliable method and more efficient than other methods for measuring eddy current on solid conducting materials,
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since it is cheaper and easier. After measuring the voltage drop {v} between the two pins, the current density J can be obtained by applying this formula. J
V L
Where is the material conductivity { υ / m } and
L is the distance between the pins {m} The power loss density at any point on the surface can be found as follows: J A2 J C2 P 2
Where JA is the radial and JC is the peripheral current density as shown in fig.(2). Discussion of results: In figure (3), the peripheral current density has maximum value at rotor end and decreases rapidly toward the shaft. The radial current at the rotor end is zero and slightly increases towards the rotor shaft. It is shown also that all current densities increase as stator current increases. All current densities at I=3A stator excitation are three times greater than that at 1 A , this is due to the rotor being of nonmagnetic alloys of 0.579* 106 υ/m electrical conductivity. Due to the above current distribution the power loss density increases in its direction to the shaft, as shown in figure (4). The power loss density increases with supply frequency; this is due to the smaller skin depth of the currents near the surface as supply frequency increases. As currents go nearer to surface, probes compared to the lower frequency can measure higher current densities. Concerning the mild steel rotor of 0.815* 104 υ/m, it is shown in figure (5), that the peripheral current is strong at the rotor end and then decrease towards the shaft. On the other hand the radial current density has a minimum value at the end and goes to a maximum value at the mid- point between the shaft and rotor end. The power loss density distribution is shown in figure (6). It is found that the current density flowing on the aluminum rotor is greater than that of mild steel rotor, as shown in figure (7). This can be referred to the greater conductivity of aluminum alloy made compared to the mild steel alloy used in the experiments.
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Fig. (1) Eddy current probe for bi-directional flows.
Fig. (2) Location of current probe s on the rotor face and end face of solid cylindrical rotor. All distance in cm. 4
18 16
CURRENT DENSITY(A/M2)
14
END FACE
12 10 8 6
PERIPHERAL
4
RADIAL I = 3A
2
I = 1A
0 0
1
2 3 DISTANCE FORM ROTOR END (CM)
4
5
Fig. (3) Current density distribution for the aluminum rotor. Rotor position=Under pole center.Frequency=50Hz.
POWER LOSS ROTOR DENSITY (w /m 3)
12
10
8
END FACE 6
4
40 HZ
2
20 HZ 0 0
0.5
1
1.5
2
2.5
3
3.5
4
DISTANCE FROM ROTOR END (cm )
Fig. (4)Power loss density distribution for the aluminum rotor . Rotor position =in between poles. Excitation current =2A
5
4.5
35
CURRENT DENSITY (A/m2)
30 25
END FACE I = 1A
20 PERIPHERAL
15
I = 0.5
10 5
RADIAL
0 0
1
2 3 DISTANCE FROM ROTOR END (cm)
4
5
FIG. (5) Current desity distribution for the mild steel rotor. Rotor position = Under pole center. Frequency
POWER LOSS DENSITY(W/m3)
7 6 5 50 HZ
4 END FACE
3 2
30 HZ
1 0 0
1
2
3
4
DISTANCE FROM ROTOR END (cm)
FIG. (6) Power loss desity distribution for the mild steel rotor . Rotor posision = Under pole center.Exactation current= 0.7 A
6 4
5
2.5
2
CURRENT DENSITY(A/m 2)
END FACE 1.5
1
PERIPHERAL 0.5
ALUMINUM MILD STEEL
RADIAL 0 0
1
2
3
4
DISTANCE FROM ROTOM END (cm )
FIG. (7) Current desity distribution for the rotor. Rotor posision = Under pole center. Excitation current =1 A . Frequency =50Hz.
7
5
Conclusion: The distribution of eddy current and power loss density on the end face of the solid cylindrical rotors has been found under the influence of a single-phase winding. It is observed that eddy current is concentrating near the edge and decreases towards the shaft on the end. This eddy current concentration can cause a rise of temperature during the excitation of such kinds of brakes. This rise of temperature depends on the material conductivity, degree of saturation and speed of the machine to be stopped. Eddy current magnitudes are directly proportional with stator current and with supply frequency. The type of material used in manufacturing the rotor is effective on the magnitude of eddy current. Since the aluminum has conductivity greater than that of mild steel, the eddy current flow on the aluminum surface rotor is greater than that of mild steel. But the aluminum is considered as a nonmagnetic material, while mild steel is a magnetic material, which means that saturation can affect the eddy current magnitudes and their positions of concentration.
References 1. Kado, Amer M., "Eddy current problems in linear induction motors". M.SC. Thesis (1988). University of Mosul. Iraq. 2. Venkataratnan, K., "Analysis of eddy current brakes with non magnetic rotor", IEEE proc., Vol.124, No.1, (1977). 3. Stoll, R. I.,The analysis of eddy current, Oxford University Press, London,(1974). 4. Kado, Amer M., ''Simulation of eddy current braking force used with induction motor'', the sixth scientific conference for foundation of technical institutes, (1998). 5. Kado, Amer M., ''Eddy current problems in sold cylindrical rotors'', Al-taqani Journal,Vol., 7th, No.2, (2004).
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