Handbook of Small Electric Motors MAZ Part 10 docx

CHAPTER 4 DIRECT-CURRENT MOTORS Chapter Contributors Andrew E. Miller Earl F. Richards Alan W. Yeadon William H. Yeadon 4.1 This chapter covers methods of calculating performance for direct-current (dc) mechanically commutated motors. Section 4.1 discusses the electromagnetic circuit for dc motors and series ac motors. Sections 4.2 and 4.3 establish some common geometry and symbols and discuss commutation for dc motors. Section 4.4 presents permanent-magnet direct-current (PMDC) calculation methods. Section 4.5 pre- sents series dc and universal ac/dc performance calculations.Sections 4.6 and 4.7 dis- cuss methods for calculating the performance of shunt- and compound-connected dc motors. Finally, Secs. 4.8 and 4.9 discuss dc motor windings and automatic armature winding. 4.1 THEORY OF DC MOTORS* 4.1.1 DC Series Motors A series motor operating on direct current has characteristics similar to those when it is operated on ac current at power-system frequencies. However, it is best to describe dc and ac operation separately so that comparisons can be made. The general equivalent electrical circuit of the series dc motor and its physical construction is shown in Figs. 4.1 and 4.2.The motor consists of a stator having a con- centrated field winding (Fig. 4.3) connected in series by way of a commutator to a * Section contributed by Earl F. Richards. wound armature (Fig. 4.4). One of the first things to be considered in the operation of the motor are the motor and generator action, which exist simultaneously in the armature circuit of the motor. These two principles are (1) the instantaneous elec- tromotive force (emf), which is induced in the armature conductors when moving with a velocity v within a magnetic field, and (2) the force produced on the conduc- tors as the result of carrying an electric current in this same magnetic field. 4.2 CHAPTER FOUR FIGURE 4.1 Series motor diagram: r a = armature resis- tance measured at brushes, r f = main field resistance, and v = applied voltage. FIGURE 4.2 Series motor. It is known that the instantaneous force on a conductor of length ᐉ carrying a cur- rent i in a magnetic field B is: f = Bi ᐉ sin θ N (4.1) Or, in vector notation: f = ᐉ (i × B) (4.2) where θ is the angle between the direction of the magnetic field and the direction of current flow in the conductor, B is in webers per square meter (teslas), i is in DIRECT-CURRENT MOTORS 4.3 FIGURE 4.3 One pole of a series motor field winding. FIGURE 4.4 Wound armature. amperes, and ᐉ is in meters. Motors, by design, have the armature conductors and magnetic flux at quadrature to one another.Therefore, the force becomes: f = Biᐉ (4.3) Assume a situation in Fig. 4.5 where a conductor of length ᐉ is located in a mag- netic field and is free to move in the x direction perpendicular to the field. From the preceding discussion, a force is produced on the conductor, causing it to move in the x direction.Then: V − ir = e or Vi − i 2 r = ei (4.4) So, differential electrical energy into the conductor less differential i 2 r loss equals differential mechanical output energy: dW elect = dW mech (4.5) ei dt = f dx where f = Biᐉ (4.6) ei dt = Biᐉ dx (4.7) e = Bᐉ = Bᐉv (4.8) This force causes movement in the conductor, which in turn causes a volt- age to be induced into that conductor which is opposite to the direction of the original current. This is an important concept in the operation of motors in general and one which is used to discuss the operation of the series motor. This induced voltage is usually called a counter-emf (cemf) voltage because of its opposi- tion to the applied voltage. This example also indicates that a reversible energy or power exchange is possi- ble (i.e., between the mechanical and electrical systems). Therefore, the same machine may operate as a motor or a generator, depending on the flow of energy in the armature. In the motor mode, the field and armature of a dc series motor are supplied with the same current by an applied voltage, and a magnetic field (flux) is produced in the magnetic circuit. Since the armature conductors (coils) are located in this field,each of the conductors in the field experiences a force (torque) tending to make it move (rotate), and as we have just indicated, a countervoltage (cemf) is produced oppos- ing the applied voltage. Other than the cemf which the armature produces, we must recognize that the armature circuit (coils) also produces a magnetic field of its own. The armature, because of its commutator and brush construction, has a unidirec- tional current and therefore produces a fixed-direction magnetomotive force (mmf), measured in ampere-turns.This mmf is the product of the effective coil turns on the armature and the current through those turns. It must be understood here that the armature winding must be considered in developing those ampere-turns (i.e., there may be parallel paths through the armature, with the possibility of the armature coils being wound in series or parallel arrangements; hence, there will also be a division of the total armature current in each of the windings).This topic is addressed later.The following is a discussion of the action of the mmf produced by the armature. dx ᎏ dt 4.4 CHAPTER FOUR FIGURE 4.5 Conductor moving in a magnetic field. Armature Reaction. The conductors in the armature carry a current proportional to the load. The magnetic field produced by this current reacts with the main field produced by the same current flowing in the field coils. Figure 4.6 indicates two so- called belts of armature conductors (coil sides) under each pole face. Each of the conductors comprising these belts carries current in the same direction and hence produces additive mmf. In addition, there are conductors which also carry unidirec- tional currents but are not under the pole arcs. The important consideration here is the effect of the presence of magnetic material in the pole pieces, armature core, and armature teeth. The flux paths through the armature are influenced by the reluc- tances of the paths. It is obvious that the reluctance of the flux paths under the pole pieces is less than that of the paths adjacent to the brush area, which constitute a material of much greater reluctance, namely air. DIRECT-CURRENT MOTORS 4.5 FIGURE 4.6 Armature magnetic field. Figure 4.6 indicates that the brushes are on the mechanical neutral axis (i.e., halfway between the poles).The general direction of the armature mmf is along the brush axis at quadrature to the main field.The armature conductors adjacent to the poles produce flux densities in the air gap which are equal and opposite at the pole tips. Keep in mind that the flux density produced by the armature is directly related to the armature current. (Also, a uniformly distributed flux density in the air gap is attributed to the main field and is directly related to this same armature current.) Now the net mmf (or flux in the air gap) is the result of both the main field mmf and the armature field mmf. The resultant air gap flux is now increased at one pole tip and reduced at the other pole tip because of the armature reaction. The flux distor- tion in the air gap is illustrated in Fig. 4.7. In this figure, two poles and the armature conductors beneath the poles have been unfolded to illustrate the distortion more clearly. Ampere’s circuital law is useful here in determining the armature mmf. The resulting air gap mmf is the result of the superposition of the field and armature mmfs. MMF drops in the poles and armature iron are considered negligible com- pared to the air gap mmf. For reference, positive direction for the mmfs is assumed to be a flux out of a north pole. The armature mmf is shown as a linear relationship, but actually, because the armature slots are discrete, this relationship is actually made up of small discrete stair-step transitions. However, it is shown as a smooth curve here for easier analysis. It is obvious that the air gap flux varies along the pole face.Another observation from the distortion mmf pattern is that harmonics are very present in the air gap mmf. Also, because of symmetry, only odd harmonics can exist in an analysis of the air gap mmf. It must also be remembered that in the case of a series ac motor, the variation of flux distortion would be approximately the same, only pulsating. The results of a Fourier analysis of the air gap flux harmonics for the case when (N f I f )/(N a I a ) = 7/5 are given in Figs. 4.8 to 4.10.The figures show the fundamental,the fundamental plus third and fifth harmonics, and finally the fundamental and odd harmonics, up to and including the fifteenth harmonic. The magnitudes of the odd harmonics beginning with the fundamental are 8.94, 0.467, 1.41, 0.924, −0.028, −0.02, 0.523, and 0.0094.That is, the series can be represented as follows: φ air gap = 8.94 cos θ+0.467 cos 3θ+1.41 cos 5θ+0.924 cos 7θ − 0.028 cos 9θ−0.02 cos 11θ+0.523 cos 13θ+0.0094 cos 15θ+иии (4.9) Of course, changing the pole arc or magnitudes of the armature and field mmfs will change the harmonic content.The change in flux density across the air gap pro- duces two effects: (1) a reduction in the total flux emanating from each pole,and (2) 4.6 CHAPTER FOUR FIGURE 4.7 Flux distortion in the air gap. a shift in the electrical neutral axis, lending to commutation problems due to the flux distortion. The flux distortion which the armature produces has been called a cross- magnetizing armature reaction, and rightly so.The net effect is illustrated in Fig. 4.11, showing the resultant field where the armature cross field is at right angles to the main field. The result is a distortion of the net flux in the motor; the second effect, which was indicated previously, is a reduction in the total main field flux.This reduc- tion of flux is not too obvious; in fact, it would almost appear from Fig. 4.8 that the vector addition of these two mmfs would lead to an increase in flux which would occur with the brushes on the mechanical neutral axis. DIRECT-CURRENT MOTORS 4.7 FIGURE 4.8 Fundamental frequency of air gap flux. FIGURE 4.9 Air gap flux due to fundamental plus third and fifth harmonics. This resulting decrease in flux can be attributed to magnetic saturation. Figure 4.12 illustrates how this comes about when one operates the motor at the knee of the saturation curve. The area ABC is proportional to the reduction in flux at the pole tip with a decrease in flux density, while the area CDE is proportional to the increase in flux at the other pole tip. Note that the reduction in flux exceeds the increase in 4.8 CHAPTER FOUR FIGURE 4.10 Air gap flux due to odd harmonics through fifteenth. FIGURE 4.11 Field of armature with and without brush shift. flux because of the saturation effect. This is sometimes called the demagnetizing effect of armature reaction. This demagnetization effect can be on the order of about 4 percent. Both armature reaction distortion and flux can be reduced or eliminated by com- pensation windings in the pole face or by increasing the reluctance at the pole tips; the latter by either lamination design or a nonuniform air gap. DIRECT-CURRENT MOTORS 4.9 FIGURE 4.12 Armature reaction resulting in main pole flux reduction. Because the purpose of the commutator and brushes is to change the current in a short-circuited coil from, say, a current of +I to −I in the length of time the coil is short-circuited by the brushes,some arcing at the brushes is expected. One desires to keep any voltage induced into the coil to a minimum in order to keep this arcing as small as possible. When the brushes are on the mechanical neutral position and the main field becomes distorted, the coils being commutated will have an induced voltage from the distorted air gap flux. A shifting of the brushes to a new neutral position is sug- gested to keep the induced voltage to a minimum and keep the brush arcing low. It should be recognized that the amount of distortion of the field is a function of the ampere-turns of the armature and hence is dependent on the motor load. One then realizes that the electrical neutral position is a function of the load and that shifting brushes to an electrically neutral position is therefore not a matter of shifting them to a unique point in space. Brush shifting causes another effect—that is, a demagnetization effect on the air gap flux. This effect is in addition to the demagnetizing effect which occurs because of saturation. When the brushes are shifted, the pole axis of the armature is shifted. The result is that the angle between the main field and the armature field is greater than 90°.This process is also illustrated in Fig. 4.11. In summary, there are two processes which cause reduction of the air gap flux:(1) reduction due to cross-magnetization when the brushes are on the mechanical neu- tral position, which changes the flux distribution across the pole face and the net flux because of saturation effects, and (2) demagnetization resulting from a brush shift and change of the armature pole orientation with respect to the main field, resulting in the armature field mmf having a component in direct opposition to the main field mmf. Reactance Voltage and Commutation. It was indicated previously that during commutation the current in the shorted coil(s) under a brush must reverse and change direction. The self-inductance of the shorted winding by Lenz’s law induces an emf in the shorted winding to oppose the change in coil current. This voltage is sometimes called the reactance voltage. (Actually, it may be only a portion of the reactance voltage, as is shown later.) This voltage slows down the reversal of current and tends to produce sparks or arcing as the trailing commutator bar leaves a brush. The reactance voltage hinders good commutation. The magnitude of this voltage depends directly on the square of the number of coil turns, the current flowing, and the armature velocity; it is inversely proportional to the reluctance of the magnetic path. When shifting brushes to seek an electrical neutral position on a motor, the shift- ing is done in the opposite direction of armature rotation. It must be remembered that the reactance voltage is an e = L(di/dt) voltage and is simply due to the current change during commutation. It has nothing to do with induced voltage from air gap flux. Shifting the brushes really does not help the reactance voltage. Theoretically, there is no induced voltage on the neutral axis from the motor flux (in fact, dλ/dt should be zero here since the coil sides are moving parallel to the flux). In order to counteract the reactance voltage and induce a voltage opposite to the reactance voltage, the brushes must be shifted further backward than the magnetic neutral axis. At this point a dλ/dt voltage is induced into the commutated coil by the field flux, which counteracts the reactance voltage.The result is that two voltages in oppo- site polarities are induced into the shorted coil, thereby reducing brush arcing. An important consideration is that there can be another component of the reac- tance voltage which can occur when two coil sides are in the same slot and both are undergoing commutation.There is then the following self-inductance term: Reactance voltage = L 11 + M 12 (4.10) where the coil being considered is the coil carrying current i 1 and the coil in the same slot undergoing commutation is carrying current i 2 . If there is more coupling between coils, more mutual terms can exist. Brushes are a very important consideration, and contrary to normal electrical principles, one would assume that keeping the brush resistance low would assist in reducing arcing at the brush commutator bar interface. This is far from the truth. In fact, resistance commutation is now an accepted technology. Brushes normally have a graphite or carbon formulation and hence introduce, by their characteristics, resis- tance into the interface. If constant current density could be achieved at a brush for all loads and speeds, an ideal condition would exist for commutation. Figure 4.13 illustrates what would occur if ideal conditions are assumed.The assumptions are as follows: di 2 ᎏ dt di 1 ᎏ dt 4.10 CHAPTER FOUR [...]... response of the series motor can be calculated 4.1.3 Permanent-Magnet DC Motors (Shunt PM Field Motors) The general equivalent electrical circuit of a PMDC motor and its physical construction are shown in Figs 4.24 and 4.25 The motor consists of a stator (Fig 4.26) having permanent magnets attached to a soft steel housing and a commutator connected through brushes to a wound armature (Fig 4.27) One of the... electrical input (4.31) Sometimes both electrical and mechanical efficiencies are of interest in order to determine where improvements can be made useful mechanical output Mechanical efficiency = ᎏᎏᎏᎏᎏ mechanical output + rotational losses electrical power output Electrical efficiency = ᎏᎏᎏᎏᎏ electrical power output + electrical losses (4.32) (4.33) DIRECT-CURRENT MOTORS FIGURE 4.17 4.17 Losses in a series... losses must be equal to those that vary as the square of the armature current This is typical for all different pieces of rotational electrical equipment.The constant losses usually are considered to be the core losses, friction, and windage Usually the brush loss is small 4.1.2 AC Series Motors One of the first considerations when considering ac operation of a series-wound motor is: Does the motor develop... subject coil of turns N1, and self-inductance L11, and the current i1 which is being commutated 1 The voltage of self inductance (reactance voltage) of the commutated coil is di1 eL1 = L11 ᎏ dt (4.11) where i1 is the current being commutated and L11 is the self-inductance of the coil being commutated DIRECT-CURRENT MOTORS FIGURE 4.15 4.13 Commutation voltages 2 The voltage of mutual inductance of an adjacent... (4.8) 4.15 DIRECT-CURRENT MOTORS It is necessary to modify this and express e in terms of the motor parameters Beginning with Faraday’s law: ∆φ Eg = Ecemf = N ᎏ V (4.16) ∆t where N is the number of conductors per armature path when Z is the total number of conductors (coil sides) on the armature Then: Z = number of slots × coils/slot × turns/coil × 2 (conductors/turn) a = number of parallel paths through... brush and the copper commutator is extremely important This interface is formed of copper oxide and free particles of graphite film; it provides a general resistance commutation and supplies lubricant to reduce surface friction and heat between the commutator and the brush Torque-Speed Characteristics of DC Series Motors The electrical equivalent steady-state circuit is the most appropriate method for... important concept in the operation of motors in general and one which is used to discuss the operation of the dc motor This induced voltage is usually called a counter-emf (cemf) voltage because of its opposition to the applied voltage DIRECT-CURRENT MOTORS 4.27 This example also indicates that a reversible energy or power exchange is possible (i.e., between the mechanical and electrical systems) Therefore... should be recognized that the amount of distortion of the field is a function of the ampere-turns of the armature and hence is dependent on the motor load One then realizes that the electrical neutral position is a function of the load and that shifting brushes to an electrically neutral position is therefore not a matter of shifting them to a unique point in space Brush shifting causes another effect—that... voltage hinders good commutation The magnitude of this voltage depends directly on the square of the number of coil turns, the current flowing, and the armature velocity; it is inversely proportional to the reluctance of the magnetic path When shifting brushes to seek an electrical neutral position on a motor, the shifting is done in the opposite direction of armature rotation It must be remembered that... effect of this armature reaction In addition to the normal design demagnetization curve shown in Fig 4.39, a set of intrinsic curves is also indicated These curves are extremely important because they represent limits on the amount of demagnetization which can be tolerated The value of −H required to remove the magnetization is given the value Hci The PM of the motor normally does not span 180° electrical; . performance of shunt- and compound-connected dc motors. Finally, Secs. 4.8 and 4.9 discuss dc motor windings and automatic armature winding. 4.1 THEORY OF DC MOTORS* 4.1.1 DC Series Motors A series. commutated motors. Section 4.1 discusses the electromagnetic circuit for dc motors and series ac motors. Sections 4.2 and 4.3 establish some common geometry and symbols and discuss commutation for dc motors. . opposite to the direction of the original current. This is an important concept in the operation of motors in general and one which is used to discuss the operation of the series motor. This induced