Electric Motors, Part I
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Electric motors, part I Introduction The basic laws that govern the operation of the electric machines are Faraday's law of induction, Kirchoff's law of the electric circuit, Ampere's law of the magnetic field, Biot Savart law of force on a conductor in a magnetic field and the law that governs the force exerted between two current carrying conductors. Electric motors are classified into single phase or threephase ones, also into low voltage and medium voltage (7.2KV for example). They are also classified according to principle of operation i.e. d.c. motors, induction and synchronous motors, the first can further be classified according to its type of excitation; series, shunt or compound, the second into squirrel cage or wound rotor, the latter either with salient pole rotor or cylindrical one. All motors are classified into integral or fractional horsepower motors. From the energy consumption view, motors will have standard efficiency or high efficiency. The Nema standard classifies induction motors into Nema A, B, C, D and F each classification defines the following parameters of an induction motor: starting toque, pullout torque, starting current and rated slip. For the synchronous motors the classification is accordingly: general purpose motors (unity power factor and .8 p.f.), large high speed motors (unity p.f. and 0.8 p.f.) and low speed motors (unity and .8 p.f.). The parameters expressed for each of these motor types are: the speed, the starting torque, the pullin torque, the pullout torque and the starting current at full voltage. The enclosure of the motor can be used to classify motors: open drip proof (ODP), totally enclosed fan cooled (TEFC), splash proof, explosion proof,..etc. The major components of any motor are the windings (field and armature), the rotor, the stator, the shaft/bearing, the enclosure, the connection box and the base plate. The classification of the insulation system as used with the windings of electrical motors are: class A (105 deg C), class B (130 C), class F (155 C), class H (180 C), N (200C), R (220), S (240 C) and C (>240 C). The insulation material is given any of the above designations when by test or experience, it is proven that the material can endure the limiting temperature specified (for each type) without failure. A.C. armature windings can be single or polyphase. Polyphase armature windings are usually 2 layer. The rotors of small wound rotor induction motors are of the single layer type, the stator is of the 2layer. The armature winding is of the lap or wave type. D.C. armature windings have the same classification as above. D.C. windings are wound continuously and closed (due to the use of the commutatorto transform the a.c. inside the machine to d.c. outside the machine). Polyphase armature windings are arranged in groups of two or more single coils (the number of groups is function of the number of poles and number of phases). Medium and large size wound rotor induction motors use wave type polyphase windings on the rotors. The winding The definition of pole pitch is given by T=3.14D/P; where T is the pole pitch, D is the diameter of the armature, P is the number of poles. In order that both sides of a coil to lie in flux densities of the same strength, the coil span as measured by an arc must be equal to the pole pitch. The two conductors of each turn has to lie under poles of different polarities, so that the induced emf in the two conductors add. The number of single coils in a group is determined by the number of slots per pole per phase. The number of groups in a winding are determined by the product of the number of poles and the number of phases. An example, if the motor is 3 phase with 2 poles, the number of groups in an armature winding
is 6, 2 groups per phase. If the total slots are 12, the number of coils in a group = the number of slots per pole per phase = 2. For polyphase lap windings, the beginning's (as well as the ends) of the three phases must be displaced from each other by 120 electrical degrees. A 2pole machine corresponds to 360 electrical degrees. If the number of slots in an armature is 12 the slot pitch is 360/12=30 electrical degrees. The beginnings of the three phases must be displaced from each other by (120/30=) 4 slots. If slot 1 is taken as the part of phase I, then phase II should start in slot (1+4=) 5 and phase III at (5+4=) 9. If in the above example the armature is wound in 2 layers, phase 1 will occupy slot 1,2,7 and 8, phase II 5,6,11 and 12 and phase III 3,4,9 and 10. The upper coil side in slot one will have its lower coil side in slot 7, the distance between both coil sides the coil span is (71=) 6 slot pitches. The coil span is equal the pole pitch and this is termed full pitch (not chorded). In a 2layer windings, all coils have the same coil span. The coil may consist of one or more turns. The distance between the beginnings of two consecutive turns is called the winding pitch. The distance which correspond to the two steps necessary to follow from the beginning of a turn to the beginning of the next (following) turn are termed back pitch and front pitch. In a lap winding, the winding pitch = back pitch front pitch; in a wave winding, it is equal back pitch + front one. Chording (fraction pitch) has an advantage that the shape of the emf induced in the winding and the mmf produced by the winding is closer in shape to a sinusoidal one than with full pitch winding. When wave windings are compared to lap ones, the following differences will be obvious: fewer end connections for the first, the diamond lap winding has loops on both ends of the coil and the wave has one loop on the end with no connections. The single phase windings will be covered in a later issue. The stator & the rotor The stator is made up of a stack of laminations with slots, the same for the rotor, the primary winding (armature) of the induction motor is connected to a source of power and is placed in the stator slots. It is completely insulated (function of the supply voltage eg. 600 V, 2.4KV, etc.). The secondary winding is placed in the slots of the rotor. This winding is not connected to any source, but it gets its power by induction from the flux produced by the stator winding. The squirrel cage winding consists of bare bars put in the slots and connected together at each end by a ring. The slots can be shallow and semiopen (the definite speed torque characteristics are produced). If the slots and bars are narrow and located much deeper, the characteristics will change. Skewing the slots will reduce the noise and produce better starting performance. Double cage induction motors i.e. two squirrel cages in the same rotor, are used to achieve certain operating characteristics. The performance The six parameters of the induction motors are: r1, x1, r2',x2', rm (or gm) and Xm (or bm), the stator winding resistance, the leakage reactance, the rotor winding resistance which is function of the slip, the rotor leakage reactance, the main flux resistance (or main flux conductance), the main flux reactance (or susceptance). These parameters are determined by the two tests: no load and the locked rotor. The performance of an induction motor is determined by the following: heating of the windings and iron, efficiency, power factor, pullout torque, inrush starting current and the starting torque. The heating of the windings and iron depends on the I2r and the iron losses. The current (I) is function of the load, if the maximum possible winding material is used in the available space, r1 and r2' will be as low as
possible and this will reduce the copper losses. To produce a high starting torque r2' has to be high (large enough). The iron losses due to the main flux can be maintained low by reducing the main flux. The torque is function of the rotor current and the main flux, thus to achieve the required pullout (maximum) torque the main flux cannot be reduced below a certain level, the rotational iron losses are to be kept to absolute minimum. The efficiency is determined by the total losses of the motor. The lower the losses at a given load, the higher is the efficiency. For high power factor, a low reactive current is necessary ie. small leakage reactances and low reactive component of magnetizing current. The small air gap and the low flux achieve a low reactive component of magnetizing current. Reducing the leakage reactances increase the inrush current and reducing the flux too much will affect the pull
out torque beyond acceptable limits. The lower the primary losses I12r1 (copper), the higher the pull out torque. The torque is determined by the power transferred by the rotating flux to the rotor and the higher the primary losses for a given power input, the smaller is the power transferred by the rotating flux. At large slips, the magnitude of the primary current is determined mainly by the stator and rotor leakage reactances, slip=(speed of rotating flux i.e.synchronous speed rotor speed)/synchronous speed The lower the leakage reactances of the rotor and stator the higher the pullout torque. The secondary resistance r2' has no influence on the magnitude of the pullout torque. A high starting current is not desirable because of voltage drop caused on the supply lines (limits are established for starting currents in appropriate standards). This means that leakage reactances have to be maintained at certain levels, to achieve an acceptable inrush currents, but this will affect negatively the power factor and the pullout torque (reduce them). At standstill the torque is directly proportional to M1I2'2r2'. This means it is
proportional to the copper losses in the rotor. At standstill the rotor current as referred to the stator is equal the locked rotor current, approximately. This current is limited by the leakage reactances, which must be high to limit the inrush current, thus for a high starting torque the rotor resistance must be high. A high rotor resistance (under normal running conditions) contradicts the requirements for a high efficiency. There are certain slot arrangements for the rotor that help achieving a high resistance during starting and a low resistance during running. These rotor slot arrangements are: deepbar rotors and double cage (boucherot) rotors. The operation of these rotors is based upon the skineffect phenomena. At higher frequencies current is allowed to flow only at the top part of the conductor (in the case of the deep bar designs) and in the upper conductor (with the double cage rotors). At stand still, in relation to running at full load, the frequency is considered higher (is equal to the line frequency), the rotor current flows only in one part of the rotor conductor and the resistance of the rotor, r2', appears high. At full load, the whole crosssection of the rotor conductor is effective and the rotor resistance is small. The rotor leakage reactance varies from the lowest at high slips (starting) to highest at full speed its change with slip is opposites to that of the resistance. The leakage reactances x1 and x2 are practically constant between noload and overload, as long as the stator and rotor currents are not too high. At larger slips and specially at standstill, these currents are high and saturation of the leakage flux path is possible. Leakage reactance at starting is 75 to 85% that of running with full load. The balance of power in a polyphase induction motor can be expressed as follows: the input power to the stator is equal the sum of the following: the stator copper loss, the iron loss due
to the main flux, the rotating field power transferred to the rotor. The rotating field power transferred to the rotor is divided into power consumed by the rotor (copper loss), and the mechanical power developed which further divided into mechanical power delivered at the shaft plus mechanical losses (bearing friction and windage losses, losses due to the slot openings and losses due to the flux harmonics). The developed torque of the polyphase induction motor is given by (7.04 M1I2'2r2')/n
is 6, 2 groups per phase. If the total slots are 12, the number of coils in a group = the number of slots per pole per phase = 2. For polyphase lap windings, the beginning's (as well as the ends) of the three phases must be displaced from each other by 120 electrical degrees. A 2pole machine corresponds to 360 electrical degrees. If the number of slots in an armature is 12 the slot pitch is 360/12=30 electrical degrees. The beginnings of the three phases must be displaced from each other by (120/30=) 4 slots. If slot 1 is taken as the part of phase I, then phase II should start in slot (1+4=) 5 and phase III at (5+4=) 9. If in the above example the armature is wound in 2 layers, phase 1 will occupy slot 1,2,7 and 8, phase II 5,6,11 and 12 and phase III 3,4,9 and 10. The upper coil side in slot one will have its lower coil side in slot 7, the distance between both coil sides the coil span is (71=) 6 slot pitches. The coil span is equal the pole pitch and this is termed full pitch (not chorded). In a 2layer windings, all coils have the same coil span. The coil may consist of one or more turns. The distance between the beginnings of two consecutive turns is called the winding pitch. The distance which correspond to the two steps necessary to follow from the beginning of a turn to the beginning of the next (following) turn are termed back pitch and front pitch. In a lap winding, the winding pitch = back pitch front pitch; in a wave winding, it is equal back pitch + front one. Chording (fraction pitch) has an advantage that the shape of the emf induced in the winding and the mmf produced by the winding is closer in shape to a sinusoidal one than with full pitch winding. When wave windings are compared to lap ones, the following differences will be obvious: fewer end connections for the first, the diamond lap winding has loops on both ends of the coil and the wave has one loop on the end with no connections. The single phase windings will be covered in a later issue. The stator & the rotor The stator is made up of a stack of laminations with slots, the same for the rotor, the primary winding (armature) of the induction motor is connected to a source of power and is placed in the stator slots. It is completely insulated (function of the supply voltage eg. 600 V, 2.4KV, etc.). The secondary winding is placed in the slots of the rotor. This winding is not connected to any source, but it gets its power by induction from the flux produced by the stator winding. The squirrel cage winding consists of bare bars put in the slots and connected together at each end by a ring. The slots can be shallow and semiopen (the definite speed torque characteristics are produced). If the slots and bars are narrow and located much deeper, the characteristics will change. Skewing the slots will reduce the noise and produce better starting performance. Double cage induction motors i.e. two squirrel cages in the same rotor, are used to achieve certain operating characteristics. The performance The six parameters of the induction motors are: r1, x1, r2',x2', rm (or gm) and Xm (or bm), the stator winding resistance, the leakage reactance, the rotor winding resistance which is function of the slip, the rotor leakage reactance, the main flux resistance (or main flux conductance), the main flux reactance (or susceptance). These parameters are determined by the two tests: no load and the locked rotor. The performance of an induction motor is determined by the following: heating of the windings and iron, efficiency, power factor, pullout torque, inrush starting current and the starting torque. The heating of the windings and iron depends on the I2r and the iron losses. The current (I) is function of the load, if the maximum possible winding material is used in the available space, r1 and r2' will be as low as
possible and this will reduce the copper losses. To produce a high starting torque r2' has to be high (large enough). The iron losses due to the main flux can be maintained low by reducing the main flux. The torque is function of the rotor current and the main flux, thus to achieve the required pullout (maximum) torque the main flux cannot be reduced below a certain level, the rotational iron losses are to be kept to absolute minimum. The efficiency is determined by the total losses of the motor. The lower the losses at a given load, the higher is the efficiency. For high power factor, a low reactive current is necessary ie. small leakage reactances and low reactive component of magnetizing current. The small air gap and the low flux achieve a low reactive component of magnetizing current. Reducing the leakage reactances increase the inrush current and reducing the flux too much will affect the pull
out torque beyond acceptable limits. The lower the primary losses I12r1 (copper), the higher the pull out torque. The torque is determined by the power transferred by the rotating flux to the rotor and the higher the primary losses for a given power input, the smaller is the power transferred by the rotating flux. At large slips, the magnitude of the primary current is determined mainly by the stator and rotor leakage reactances, slip=(speed of rotating flux i.e.synchronous speed rotor speed)/synchronous speed The lower the leakage reactances of the rotor and stator the higher the pullout torque. The secondary resistance r2' has no influence on the magnitude of the pullout torque. A high starting current is not desirable because of voltage drop caused on the supply lines (limits are established for starting currents in appropriate standards). This means that leakage reactances have to be maintained at certain levels, to achieve an acceptable inrush currents, but this will affect negatively the power factor and the pullout torque (reduce them). At standstill the torque is directly proportional to M1I2'2r2'. This means it is
proportional to the copper losses in the rotor. At standstill the rotor current as referred to the stator is equal the locked rotor current, approximately. This current is limited by the leakage reactances, which must be high to limit the inrush current, thus for a high starting torque the rotor resistance must be high. A high rotor resistance (under normal running conditions) contradicts the requirements for a high efficiency. There are certain slot arrangements for the rotor that help achieving a high resistance during starting and a low resistance during running. These rotor slot arrangements are: deepbar rotors and double cage (boucherot) rotors. The operation of these rotors is based upon the skineffect phenomena. At higher frequencies current is allowed to flow only at the top part of the conductor (in the case of the deep bar designs) and in the upper conductor (with the double cage rotors). At stand still, in relation to running at full load, the frequency is considered higher (is equal to the line frequency), the rotor current flows only in one part of the rotor conductor and the resistance of the rotor, r2', appears high. At full load, the whole crosssection of the rotor conductor is effective and the rotor resistance is small. The rotor leakage reactance varies from the lowest at high slips (starting) to highest at full speed its change with slip is opposites to that of the resistance. The leakage reactances x1 and x2 are practically constant between noload and overload, as long as the stator and rotor currents are not too high. At larger slips and specially at standstill, these currents are high and saturation of the leakage flux path is possible. Leakage reactance at starting is 75 to 85% that of running with full load. The balance of power in a polyphase induction motor can be expressed as follows: the input power to the stator is equal the sum of the following: the stator copper loss, the iron loss due
to the main flux, the rotating field power transferred to the rotor. The rotating field power transferred to the rotor is divided into power consumed by the rotor (copper loss), and the mechanical power developed which further divided into mechanical power delivered at the shaft plus mechanical losses (bearing friction and windage losses, losses due to the slot openings and losses due to the flux harmonics). The developed torque of the polyphase induction motor is given by (7.04 M1I2'2r2')/n
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