Experiment 1The DC MachineECEN 4517R. W. Erickson and D. MaksimovicThe purpose of this experiment is to become familiar with operating principles, equivalentcircuit models, and basic characteristics of a dc machine. Dc machines are most commonlyused in control and servomechanism, as well as industrial, applications. The applicationsrange from small permanent-magnet dc motors at a fraction of a Watt in consumerelectronics, to large industrial shunt dc machines having a separate field winding. Themachine used in this experiment is a representative of an industrial dc motor (or generator)with a rated power of tens of kilowatts.The basic dc machine with separate field winding contains three sets of input/outputterminals, represented schematically here as in Fig. 1.Field winding+Vf–If+Va–IaArmatureSpeedωTorqueTMechanical shaftFig. 1. Symbols used to represent the field winding, armature winding, andmechanical shaft of the dc machine.The purpose of the machine is to convert electrical energy to mechanical energy (motoraction), or vice-versa (generator action). When operated as a generator, it is usuallydesirable to regulate the dc output voltage Va. When operated as a motor, it is often desiredto control the shaft speed, position, or torque.In general, the mechanical power of a rotating system isPmech = Tω = (torque) (speed) (1)In MKS units, we have(Watts) = (Newton-meters) (radians/second) (2)In the US, we often measure shaft speed in revolutions per minute (rpm), and torque infoot-pounds or ounce-inches. Appropriate unit conversions must then be made.The “business winding” of any machine is called the armature. This is where thepower flows. In a dc machine, the electrical power flowing into the armature isPelec = VaIa(3)To the extent that losses within the machine can be ignored (i.e., by approximating theefficiency as 100%), this electrical power is converted into mechanical power:VaIa ≈ Tω(4)This is the objective of the machine. For the defined polarities of Va and Ia, and the defineddirections of T and ω shown in Fig. 1, the machine operates as a motor when Pmech andPelec are positive, and as a generator when Pmech and Pelec are negative.1 . Basic relationships in the dc machineThe basic parts of the dc machine are diagrammed in Fig. 2. The stationary part of themachine is called the stator. The field winding is normally placed on the stator. A dc currentthrough this field winding induces a flux φ in the machine, which flows through the statoriron, across the air gap, through the rotor iron, across the air gap, and back to the statoriron (Fig. 3). In small dc motors, the field winding is often replaced by permanent magnetson the stator. Such motors have only one electrical port (the armature); the relationships areexactly the same as described here, except that the field φ is a fixed value. In machines witha separate field winding, the field winding current If is an additional variable that can beused to adjust the machine operation, as discussed below.Fig. 2. Basic elements of a dc machine: stator with field winding, rotor witharmature winding and commutator.Fig. 3. Field current If induces flux φ in the machine.The relationship between the field winding current If and the total flux φ depends onthe B-H characteristics of the iron and air gaps. The actual relationship is sketched in Fig.4, and the following linear approximation, Fig. 5, is often useful: φ= IfNfℜ(5)Here, NfIf is the magnetomotive force due to the field winding current, and ℜ is theequivalent reluctance of the magnetic path for the flux φ. This approximation ignores thehysteresis and saturation of the stator and rotoriron, and it states that the flux φ is directlyproportional to the field current. Thisapproximation is useful for understanding thebehavior of the dc motor. However, it does notfully predict the machine operation, such as theobserved behavior of the self-excited generator.Dc machines can be constructed with thefield winding connected in series with thearmature, in parallel with the armature, oravailable separately. In cases where the fieldφNfIf1/ℜFig. 4. Relationship between fieldwinding current If and total flux φ.winding is connected in parallel (“shunt”) with thearmature (as in this lab experiment), the shuntfield windings typically consist of many turns ofrelatively small wire, and typically If << Ia. Sinceseries field windings must conduct the armaturecurrent, these windings consist of a few turns ofmuch larger wire. In any event, the purpose of thefield winding is only to create the flux φ in themachine; it does not participate in the electro-mechanical energy conversion.The armature winding consists of turns ofrelatively large wire on the rotor. It is connectedvia commutator brushes to the stationary frame ofreference. As sketched in Fig. 2, the commutator brushes connect to whichever turns ofwire are physically at the top and bottom of the rotor. As the rotor turns, the commutatorbrushes connect to different taps in the rotor armature winding. The effect of this is torectify the voltage, such that Va and Ia are dc.Whenever there is aflux φ and the shaft isturning, then a voltage isinduced in the armaturewinding. This voltage E iscalled the “back EMF,”“speed voltage,” or“generated voltage.” Itsorigin can be understood byconsidering Fig. 6.Let’s examine thetotal flux passing throughone of the turns of thearmature winding. Assketched in Fig. 6, there aretwo flux lines passingthrough the turn when theturn is near the top of therotor, position a. As the rotorφNfIf1/ℜFig. 5. Approximate linearrelationship between If and φ,which ignores hysteresis andsaturation of the stator and rotoriron: φ = NfIf/ℜ.Fig. 6. When the shaft rotates, the flux passing through thearmature winding turns changes.turns, the flux decreases to one line (position b), zero lines (position c), one line in theopposite direction (position d) or –1 line, and –2 lines (position e). Thus, as the rotor turnsthe flux through the armature windings changes.We know from Faraday’s law that when the flux φturn passing through a loop ofwire changes, then a voltage is induced: v =dφturndt(6)Hence, as illustrated in Fig. 7 there is a voltage E induced in the armature winding,proportional to the rate at which the flux in each turn changes. It can be seen that, if theshaft speed is increased, then φturn will change more quickly and E is increased. Also, if thetotal
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