STUDY OF THE MAGNETIC FIELD IN THE AIR GAP OF A DC MACHINE

K. A. KHOR'KOV, V. N. DMITRIEV, E. E. DUTLOV

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

The operation of rotating electrical machines is inevitably accompanied by vibrations, which may be subdivided into vibrations of mechanical, aerodynamic, and magnetic origin. The cause of the latter is variable magnetic forces arising on the pole shoes as a result of the periodic change in the magnetic permeance of the air gap during rotation of the toothed armature. Taking into account the ever-increasing requirements imposed on the vibration level of DC machines, the study of the variable component of the magnetic field in the air gap of the machine becomes an urgent task.

For the purpose of studying changes in the distribution of the magnetic field under the pole shoe during motion of a toothed armature, an experimental setup was created on the basis of a P-40 DC motor.

The machine under test has several interchangeable armatures with different numbers of teeth. The present work gives the results of investigations of the magnetic field in the machine gap for armatures having a tooth pitch with straight teeth, a tooth skew by one tooth pitch, and a “herringbone” tooth skew, as well as for an armature with 27 teeth skewed by one tooth pitch.

EMF sensors were placed on the teeth of the armatures according to Fig. 1. The arrangement of the sensors along the armature teeth and along the circumference of the armature makes it possible to analyze the change in flux linkages of the sensors with the pole winding and, consequently, the corresponding fluxes between the sections of the armature teeth and the machine poles. A typical oscillogram of the sensor EMF is presented in Fig. 2.

Fig. 1. Diagram of the arrangement of EMF sensors on armature teeth made: a) without tooth skew; b) with linear tooth skew; c) with “herringbone” tooth skew.

Fig. 2. Curve of the sensor emf

The curve of the sensor emf as the armature passes under a pole has two peaks: the first peak corresponds to the appearance of magnetic linkage between a section of an armature tooth and the pole as this section of the tooth enters under the pole; the second peak corresponds to the breaking of the magnetic linkage between them as the tooth leaves from under the pole. During the motion of the tooth under the pole, the magnetic flux passing through the sensor frame remains practically constant. The small pulsations in the emf curve in this region are caused by a certain change in the total magnetic flux under the pole due to the fractional number of tooth pitches falling within the width of the pole shoe, as teeth lying ahead of the tooth with the sensor leave from under the pole and the following teeth enter under the pole. With skewed armature teeth, the indicated phenomenon is insignificant.

Attention is drawn to the fact that the inner front of the emf pulses of the sensors is steeper. This corresponds to a greater rate of change of the flux under the pole edge in comparison with the change of flux in the interpolar space.

a                    b

Fig. 3. Emf of sensors located: a) along an armature tooth, b) on adjacent teeth around the armature circumference

In Fig. 3 the emf curves are plotted for sensors located on the teeth of an armature having 27 slots. The width of the armature tooth pitch is 16 mm. The width of the pole arc is 66 mm, that is, 4.12 tooth pitches fit within the width of the pole arc. The width of the armature slot opening is 3.5 mm. The sensors placed on the armature teeth were preliminarily calibrated.

The oscillograms presented show quite clearly that, when an armature tooth leaves the pole, the magnetic flux is intercepted by the tooth entering under the pole.

With an integral number of tooth pitches under the pole shoe, the approaching and receding zones of the teeth will be arranged symmetrically, and two equal, symmetrically located magnetic-attraction forces will act on the pole.

As the armature rotates, the line of action of the forces moves smoothly from one end of the pole to the other, for example, from zone 1a to zone 1d; then, when tooth 1 has completely emerged from under the pole, the forces arise in zone 2a and move toward zone 2d, and so on. The tangential components of the forces are directed in opposite directions and balance one another. The radial and axial components of the forces add in pairs.

The axial components of the magnetic-attraction forces create a continuously acting torque, whose point of application shifts along the horizontal axis of the pole as the armature rotates. The radial components of the magnetic-attraction forces are directed to one side and move along the horizontal axis of the pole, thereby producing, even in an ideally manufactured machine, forces that rock the pole.

With a fractional number of tooth pitches under the pole shoe, the approaching and receding zones of the teeth will be arranged asymmetrically, and the points of application of the forces will be displaced relative to one another. This causes the appearance of pairs of forces acting in the tangential and radial directions. The appearance of an additional torque leads to oscillations of the pole about its vertical axis and to diagonal rocking of the pole from corner to corner.

When the air gaps under the approaching and receding edges of the pole are asymmetric, the equality of the forces acting on both sides of the pole is disturbed, which leads to a sharp increase in the vibrations of the machine.

Figure 4 presents the e.m.f. curves of sensors located on the teeth of armatures having \(Z_{\mathrm{a}} = 31\) and differing from one another in tooth skew.

Fig. 4. E.m.f. of sensors located on the armature teeth: a) without tooth skew, b) with linear tooth skew, c) with “herringbone” tooth skew.

teeth. With straight armature teeth, the emf curves of all sensors are in phase; that is, forces act on the pole edges that are the arithmetic sum of individual unit forces acting on sections of the pole edge along the length of the active part of the machine. It is obvious that the width of the pole shoe can be selected so that the forces at the trailing and leading edges will balance one another. In this case there will be no alternating forces. In practice, however, it is very difficult to obtain uniform gaps under the leading and trailing edges of the poles because of large manufacturing tolerances, in particular for the pole-fastening elements. Taking into account that the force acting on the pole edges is considerable, linear deviations in the gaps cause significant vibrations. The vibrations of the machine under test with an armature having straight slots are 2–3 times greater than the vibrations of a machine with an armature having skewed teeth.

When the armature teeth are skewed, the emf curves of the sensors are shifted in phase. The time for a tooth to enter under a pole, with a skew of one tooth pitch, is doubled in comparison with the first case. As a result, the attractive forces at the entry and exit of the teeth from under the pole are distributed in time, and the magnitude of the resultant force becomes several times smaller. An analysis of the phenomena accompanying rotation of an armature with skewed slots was described above. In contrast to an armature with straight slots, where forces pulsating at tooth frequency act on the pole edges, in an armature with a skew of the teeth by one tooth pitch there act forces that are constant in magnitude, with moving points of application.

From the standpoint of flux distribution and, consequently, of the magnetic-attraction forces under the pole edges, the best arrangement is an armature with a “herringbone” tooth skew. From Fig. 4 it is evident that the emf of the sensors is shifted in phase symmetrically with respect to the center line of the pole. That is, during armature rotation, magnetic-attraction forces act at four points simultaneously, moving from the center line of the pole to its ends synchronously with one another. This leads to the fact that, in an ideally manufactured machine, all forces—tangential, radial, and axial—mutually balance one another. At the same time, the presence of tooth skew leads to the magnitude of the resultant forces acting on the pole edges being significantly lower than with straight teeth. In a real machine, which has certain inequalities of the air gaps under the pole edges, vibrations do occur when the armature teeth are arranged in a “herringbone” pattern; however, they are considerably lower than with straight armature slots and with linear slot skew.