# Torque Slip Characteristics

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18-Nov-2014Category

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### Transcript of Torque Slip Characteristics

TORQUE SLIP CHARACTERISTICS OF INDUCTION MOTORBy Avinash SrivastavaRavi Kumar(MTECH CAID MSRIT)Basic Induction Motor ConceptsThe Development of Induced Torque in an Induction Motorind R SkB B If the induction motors rotor were turning at synchronous speedthe rotor bars would be stationary relative to the magnetic fieldno induced voltage no rotor currentno rotor magnetic field Induced torque = 0Rotor will slow down due to friction Slip of induction motorThe speed of induction motor must always be less than the synchronous speed and as the load increased the spree of the motor will decrease. The difference between the speed of the stator and the actual speed of the rotor is known as the slip speed of induction motor.Where nslip = slip speed of the machinensync = speed of the magnetic field.nm = mechanical shaft speed of the motorThe slip can be expressed in rpm and radians per second, but usually it is expressed as a fraction or percentage of synchronous speedSlip may also be described in terms of angular velocity, . slip sync mn n n , 100% 100%slip sync msync syncn n nSlip sn n % 100 x ssyncm sync The Electrical Frequency on the RotorWhen the rotor is stationary, rotor conductor are being cut by the rotating flux at the synchronous speed , the frequency of rotorcurrent (or emf) is the same as that of supply frequency.And rotor frequency may be expressed as:since slip is given by

And since nsync=120fe/ P,This shows that the relative difference between synchronous speed and the rotor speed will determine the rotor frequency.sync msyncn nSn r ef sf ( )m sync rn nPf 120The Equivalent Circuit of an Induction MotorThe Transformer Model of an Induction MotorThe transformer model or an induction motor, with rotor and stator connected by an ideal transformer of turns ratio aeff.The Rotor Circuit ModelThe reactance of an induction motor rotor depends on the inductance of the rotor and the frequency of the voltage and current in the rotor.With a rotor inductance of LR, the rotor reactance is: The rotor current flow is02,2R r R r Rr eR e R RX L fLSincef sfX s fL sX000R R RRRR R R RRE E EIRR jX R jsXjXs + ++The Final Equivalent CircuitTo produce the final per-phase equivalent circuit for an induction motor, it is necessary to refer the rotor part of the model over to the stator side.If the effective turns ratio of an induction motor is aeff , then the transformed rotor voltage becomesThe rotor currentAnd the rotor impedanceIf we make the following definitions:R2 = a2eff RR;X2 = a2eff XR0The final per-phase equivalent circuit is as shown below'1 0 R eff RE E a E 2ReffIIa22 0Reff RRZ a jXs| ` + . ,The Derivation of the Induction Motor Induced-Torque EquationThe Derivation of the Induction Motor Induced-Torque EquationTorque speed equation based upon the power flow diagram of an induction motor. We know that,By definition, air gap power is the power transferred from the stator to the rotor via the air gap in the induction machine. Based upon the induction motor equivalent circuit, the air gap power may be defined as:Our next task is to find I2 (current flow in the rotor circuit). The easiest way is via the construction of the Thevenin equivalent circuit.conv AGind indm syncP Por 2 222 22, :3AGperphaseAGRP IshencetotalairgappowerRP IsCalculation via thevenin equivalent method 1. Derive the thevenin voltage (potential divider rule):Hence the magnitude of thevenin voltage: Since Xm >> X1 , Xm >> R1, therefore the magnitude may be approximated to:2. Find the thevenin impedanceTake out the source and replace it with a short circuit, and derive the equivalent impedances.Since Xm >> X1, Xm >> R1,1 1mTHmjXV VR jX jX+ +( ) 221 1mTHmXV VR X X+ +1mTHmXV VX X+( )1 11 1mTHmjX R jXZR jX jX++ +2111mTHmTHXR RX XX X| ` +. , Representing the stator circuit by the thevenin equivalent, and adding back the rotor circuit, we can derive I2, Hence the magnitude will be, Hence air gap power,Hence, induced torque,222( )THTH THVIRR j X Xs+ + +( )( )22222THTH THVIRR X Xs+ + +( )( )2222223THAGTH THV RPsRR X Xs| ` + + + . ,( )( )2222223THTH THindsyncV RsRR X Xs| ` + + + . ,If a graph of Torque and speed were plotted based upon changes in slipComments on the Induction Motor Torque Speed Curve Induced Torque is zero at synchronous speed. The graph is nearly linear between no load and full load (at near synchronous speeds). Max torque is known as pull out torque or breakdown torque Starting torque is very large. Torque for a given slip value would change to the square of the applied voltage. If the rotor were driven faster than synchronous speed, the motor would then become a generator.If we reverse the direction of the stator magnetic field, it would act as a braking action to the rotor plugging.To be continued by AvinashMaximum (Pullout) Torque in an Induction MotorBased upon the maximum power transfer theorem, maximum power transfer will be achieved when the magnitude of source impedance matches the load impedance. Since the source impedance is as follows:Hence maximum power transfer occurs duringHence max power transfer is possible when slip is as follows:Put in the value of Smax into the torque equation,2 source TH THZ R jX jX + +( )2222 TH THRR X Xs++( )2max222 TH THRsR X X+ +( )2max22232THsync TH TH THVR R X X ]+ + + ] ] From above equation we conclude that:1. Torque is related to the square of the applied voltage2. Torque is also inversely proportional to the machine impedances3. Slip during maximum torque is dependent upon rotor resistance4. Torque is also independent to rotor resistance as shown in the maximum torque equation By adding more resistance to the machine impedances, we can vary:1. Starting torque2. Max pull out speedVariations in Induction Motor Torque-Speed CharactericticsA torque-speed characteristic curve combininghigh-resistance effects at low speeds (high slip) with low resistance effects at high speed (low slip). Effect of rotor resistance on torque-slip or torque-speed relationEffect of change in supply voltage on the torque and slip (or speed)Effectof varyingsupply voltage and supply frequency Current speed characteristics Torque speed curve and operating region