Motor Torque, Load Torque And Selection Of Motors

2/46 Electrical Power Engineering Reference & Applications Handbookharmonics and slot losses. The angle of twist (skew) is amatter of experience, by results obtained over the years.The most common skew angles, for various combinationsof stator and rotor slots in practice, are given in Table2.1.ForTst3Ist2st2Numberof statorslotsÏ 18Ì 24Ó 362Numberof rotorslotsSkew angle(degrees)1416282620164Ï 24Ì 36Ó18282013 to 146363311 to 14For TIst1Typical angles of skew for cage rotorsNumberof polesFor Tst1CurrentTable 2.1Ist3Tst3 Tst2 Tst1IrSSpeedSlipNr2.4 Effect of starting current on torqueIgnoring the friction and core losses, the torque developedin synchronous watts,Tr 3 I rr2 R2 1 – SSor 3 i.e. Tr µcorroborating this statement.) The Tst and Ist are, therefore,a matter of compromise to achieve a good Tpo, a betterpower factor and a lower slip. Figure 2.9 shows fordifferent starting torques the corresponding pull-outtorques and their occurrence of slip, maintaining the samefull-load slip.I rr2 R2SI rr2 R2SFigure 2.8 Starting (locked rotor) currents corresponding todifferent starting torques(2.1)Since the stator current is a function of the rotor current,the motor torque is proportional to the square of thestator current. Generalizing,Tpo12Tst1ÊI ˆ Á st1 Tst2Ë I st2 S (slip at start 1)(2.2)(for the same rotor resistance R2)(2.3)Tst1ÊI ˆ Á st1 Tst2Ë I st2 2R2(for different rotor resistances)R2 (2.4)Analyzing Equation (2.2), the higher the starting torque,the higher will be the starting current for the same motorparameters (Figure 2.8). An attempt to keep the startingcurrent low and yet achieve a higher starting torque maybe feasible, but only up to a certain extent, by suitablyredesigning the rotor with a higher resistance (Equation(2.1)). However, the results of such an attempt mayadversely affect the other performance of the motor. Forexample, the Tpo will be reduced due to a higher rotorresistance and may occur at a higher slip, even if thefull-load slip is the same. The increased slot leakage,due to the skin effect, will also diminish the full-loadpower factor. (See the circle diagram, Figure 1.16,orTpo3Tpo2S3S2 S1Tst32Tst2TorqueTstÊI ˆ Á st TrË Ir Tst1 TrSpeedSlipSNrTst3 Tst2 Tst1Tpo1 Tpo2 Tpo3S3 S 2 S1Figure 2.9Effect of starting torque on Tpo and slip

Motor torque, load torque and selection of motors 2/472.4.1 NEMA recommendations on startingcurrents2.5 Load torque or opposing torqueWith a view to achieve yet more standardization in motordesign, NEMA Standard MG-1 has also recommended themaximum locked rotor current of single-speed three-phasemotors for the various rotor designs A, B, C, and D, forvarious recommended torque values. These have been derivedfor a 415 V a.c. system and are shown in Table 2.2.For smaller loads, say up to 20/30 kW, it may not beessential to pre-check the load curve with that of themotor. But one should ensure that working conditions orthe load demand are not so stringent that they may causea lock-up of rotor during pick-up due to a very low appliedvoltage or accelerating torque, or a prolonged startingtime as a consequence or due to a very large inertia ofrotating masses etc. For critical applications and for largermotors it is essential to check the speed–torque requirementof the load with that of the motor. Loads can generallybe classified into four groups. Table 2.3 indicates themore common of these and their normal torquerequirements, during start-up and variation with speed.The corresponding curves are also drawn in Figures 2.10–2.13. To ascertain the output requirement of a motor, fordifferent applications a few useful formulae are given inAppendix I at the end of Part I of this book.Table 2.2 Recommended maximum locked rotor currents forvarious rotor designsHPApprox. maximumlocked rotor currentRotor .B.C.2.6 Selection of motorsThe recommended practice would require that at eachpoint on the motor speed–torque curve there should be aminimum 15–20% surplus torque available, over andabove the load torque, for a safe start (Figure 2.14). Thetorque thus available is known as the accelerating torque.NoteFor motors beyond 200 h.p., NEMA has not covered these data. Itis, however, recommended that larger motors may be designed tohave even lower locked rotor currents than the above to reduce thestarting transient effects on the distribution system as well as onthe motor windings.Table 2.32.7 Time of start-up and its effect onmotor performanceThis depends upon the applied voltage, i.e. type ofswitching, starting torque of the motor, counter-torqueof the load and the inertia of the rotating masses etc. It isexpressed byTypes of loads and their characteristicsSerial Loadno.Characteristics ofloadStarting torqueOpposing torque withspeedFigure no.1Presses, punches, latchesand drilling machines–Light duty 20–30%Torque remains constantand at a very low value,since the load is appliedwhen the motor has run tospeed2.102Fans, blowers, centrifugalpumps and compressorsThe power isproportional to thethird power of thespeed (P µ N3)Medium duty 10–40%Torque rises with square ofthe speed (T µ N2)2.113Rolling mills, ball mills,hammer mills, calendardrives and sugarcentrifugesThe power isproportional to thesquare of the speed(P µ N2)Heavy duty 30–40%.May be more and have toaccelerate large massesof heavy moment ofinertia, requiring aprolonged time of start-upNear full-load torque2.124Conveyors and hoistsThe power isproportional to thespeed (P µ N)Heavy duty 100–110%Torque remains constantthroughout the speed rangeand at almost the full-loadtorque2.13

2/48 Electrical Power Engineering Reference & Applications HandbookGDT2 N r375 Tats (2.5)wherets time of start-up in secondsGDT2 total weight moment of inertia of all the rotatingmasses, referred to the motor speed in kg.m2 GDM2 GDL2(GDM2 is motor and GDL2 is load weight momentof inertia referred to the motor speed)whereGD2 4 · g · M · K2g 9.81 m/s2M mass andg · M W (weight in kg)K radius of gyration in mTa average accelerating torque in mkg (Figure 2.14),i.e. average (Tst – TL) in mkgTL opposing torque (load torque)GD L2 at motor speedIf the load is driven through belts or gears at a speeddifferent from that of the motor, the effective value ofGD2 of the load, as referred to the motor speed, will bedifferent. Equating the work done at the two speeds:GDL2 N r2 GD12 N L28080% Torque100% Torque1006040Load torque6040rqueL o ad t o202000% SpeedFigure 2.10% SpeedLight dutyFigure 2.12Heavy-duty start10010080ue1. Load torq801.Lo602.Powequired40eq20wePo2.rr0200% Speed% Speed1. Torque µ (speed)22. Power µ (speed)3Figure 2.111. Torque constant2. Power µ speedMedium dutyFigure 2.13Heavy dutyLoad% TorqueadurqtoLoade40erruired% Torque60

Motor torque, load torque and selection of motors 2/493H W ·d · qorq (2.8)H CW dwhereW weight of heated portion in kgd specific heat of the material of windings, in watt · s/kg/ Cq temperature rise in C (Table 11.1)2Minimum15–20% of TrTorquealsoAccelerating torque, Ta1TrMotor torqueA possible way to restrict the temperature rise is theuse of a material having a high specific heat. An increasein the weight would require more material and prove tobe a costly proposition. A motor’s constructional featuresshould be such as to provide good heat dissipation throughits body. Motors for high inertia will be longer.Load torqueSharing of heatSpeedFigure 2.14NrAccelerating torque (Ta)Nor GDL2 GD12 Ê L ˆË Nr IfHr the heat of rotor in W · s.andHs the heat of stator in W · s.ThenHsR 1HrR2 2(2.6)whereGD12 weight moment of inertia of load at a speed NL.Example 2.1A 100 kW, 750 r.p.m. motor drives a coal mill, having GD 12 as600 kg.m2 through belts, at a speed of 500 r.p.m. Then itseffective GD L2 at motor speed will beÊ 500 ˆGD L2 600 Á Ë 750 The rotor and stator heats, during start-up and run, areinterrelated and vary in the same proportion as theirrespective resistances. (See circle diagram Figure 1.16in Section 1.10.)2 600 0.445 267 kg m2NoteFor simplicity, the synchronous speed of the motor is considered, which will make only a marginal difference in calculations.(2.9)While the total heat generated in the rotor iscomparatively higher than the stator, there is a significantdifference in the temperature rise of the respective partsas a result of the bulk of their active parts and area ofheat dissipation. For the same material, the rotor willhave a much higher temperature rise compared to thestator, in view of its weight, which may be several timesless than the stator. During start-up, therefore, the rotorwill become heated quickly and much more than thestator. Repeated start-ups may even be disastrous. Duringa run, however, when the temperature has stabilized, anoverload will render the stator more vulnerable to damagethan the rotor. The rotors, as standard can withstand muchhigher temperature rises (200–300 C) and may be suitableto withstand such marginal overloads.Corollary2.7.1 Motor heating during start-upIrrespective of the type of switching adopted or the loaddriven by the motor, each time it is switched it generatesheat, in both the rotor and the stator components. Themagnitude of the start-up heat will depend upon the inertiaof the rotating masses, the type of switching, the torquedeveloped by the motor and the opposing (load) torqueetc., as can be inferred from Equation (2.5). The higherthe time of start-up, the higher will be the heat generated.The corresponding temperature rise of the stator or therotor windings can be measured as below:Heat generated:H I st2 R t swatt · s · (W · s.)(2.7)During start-up the rotor, due to its lighter weight comparedto the stator, and during a run, the stator, due to overloadare more vulnerable to damage through excessive heat.Example 2.2A rotor fails during start-up, possibly due to a lower supplyvoltage than desired or a smaller accelerating torque thanrequired or reasons leading to similar conditions. In suchcases the rotor fails first, due to higher rotor currents and aprolonged acceleration time or a locked rotor. At this instant,unless the motor controlgear trips, the stator may also faildue to excessive heat. Instances can be cited where eventhe short-circuit end rings of a squirrel cage rotor melted, andthe molten metal, through its centrifugal force, hit the statoroverhangs and damaged that also through its insulation, causing an inter-turn fault.

2/50 Electrical Power Engineering Reference & Applications HandbookDuring a no-load start-up, i.e. when the motor shaft isfree, half the energy drawn from the supply appears asheat in the rotor and the stator windings. In slip-ringmotors the bulk of the rotor heat is shared by the externalresistance, a feature which makes it a better choice forfrequent starts and stops, and for driving loads that possesslarge inertia. It has been seen that most of the stringentload requirements can also be met with high torque squirrelcage motors, manufactured with a judicious design ofstator and rotor resistances, an efficient means of heatdissipation and a proper choice of active material. Theheat generated during a no-load start-up can be expressedby:2 N r2GDMW·s(2.10)H nl 730This expression, except for the mechanical design, istotally independent of the type of start and the electricaldesign of the motor. Electrically also, this is demonstratedin the subsequent example. The expression, however,does not hold good for an ON-LOAD start. On load, theaccelerating torque diminishes substantially with the typeof load and the method of start, as can be seen fromFigure 2.14, and so diminishes the denominator ofEquation (2.5), raising the time of start.Example 2.3A squirrel cage motor is started through an auto-transformerstarter with a tapping of 40%. Compare the starting heat witha DOL starting when the motor shaft is free.With DOL Ta 100%With an auto-transformer Ta (0.4)2 or 16%Starting time with DOL, t s and with auto-transformer, t s1 GD M2N r375TaGD M2Nr 3750.16T ai.e. 6.25 times of DOLSince the heat during start-up µ (I st)2 · t\ Heat during start on a DOL µ (I st)2 · tsand on an auto-transformerµ (0.4I st)2 · ts1orµ 0.16(I st)2 6.25tsi.e.µ (I st)2 · tsThus at no-load, irrespective of the motor torque and the typeof switching, the starting heat would remain the same.2.7.3 Heating during an on-load start-upAgainst an opposing torque, the accelerating torque ofthe motor, which hitherto had varied in proportion to thetype of switching, will now diminish disproportionatelywith a switching other than DOL (Figure 2.15). Thestarting time rises disproportionately and so does the300%Motor to r quneo‘ DOL’200%Ta on ‘DOL’Torque2.7.2 Heating during a no-load start-up100%Motor torque on YTa on YLoad curve0SpeedFigure 2.15NrVariation in Ta with Y / D switchingstarting heat. Care should therefore be taken when selectinga motor for a particular type of switching and magnitudeof the opposing torque. This is to avert possible damageto the motor due to prolonged starting time, as aconsequence of an inadequate accelerating torque.Maintaining a minimum accelerating torque at eachpoint, during the pick-up may also not be adequatesometimes. In which case the starting time may exceedthe locked rotor or thermal withstand time of the motor,as discussed below.2.8 Thermal withstand timeThis is also known as safe stall time or the locked rotorwithstand capacity of the motor. This is the time duringwhich the motor can safely withstand electromagneticeffects and consequent heating in a locked condition.These are drawn for the cold and hot conditions of themotor in Figure 2.16. Evidently, the motor must come tospeed within this time, irrespective of type of load ormethod of switching. In a reduced voltage start-up orslip-ring motors the starting current would be low andthese curves would signify that for any reason if therotor becomes locked during start or run, or takes aprolonged time to come up to speed, the protective devicemust operate within the safe stall time. Generally, thesecurves are drawn for the stator to monitor the actualrunning condition and not the condition during start-up.The rotor can withstand much higher temperatures duringa run. With the help of these curves, knowing the startingtime and the starting current of the motor, one can ascertainthe number of starts and stops the motor would be capableof undertaking. These curves also help in the selection ofthe protective relays and their setting as discussed inChapter 12.

Motor torque, load torque and selection of motors 2/51C heat capacity of the motor heat required to raise the temperature of the windingsby 1 C in Joules W·dLocked rotor current6whereW weight of the stator windings in kg volume of stator windings specific gravity ofthe metal of the windings Lmt · Zs · Acu · dLmt length of a mean turn of the winding in metresZs number of stator turns per phaseAcu area of the whole windings in m2d specific gravity of the winding material in kg/m3d specific heat of winding metal in watt · s/kg/ C4ColdoncCurrent (Ist /Ir )53Ho2ditio ntconditionNote 1In Equation (2.11) it is presumed that the heating of the windings isadiabatic, i.e. whatever heat is generated during a stalled conditionis totally consumed in raising the temperature of the stator windingsby q. An adiabatic process means that there is no heat transfer fromthe system to the surroundings. This is also known as the heat sinkprocess. The presumption is logical, because the duration of heatingis too short to be able to dissipate a part of it to other parts of themachine or the surroundings.1ASafe stall time ‘tst’ (seconds)BCDA – Maximum withstand time under hot condition (on DOL)B – Maximum withstand time under cold condition (on DOL)C – Maximum withstand time under hot condition during YD – Maximum withstand time under cold condition during Y\ t st q C q 2 W dH st I st R Figure 2.16 Thermal withstand curvesq ( L mt Z s Acu d ) dI st2 R where R 2.8.1 Heating phenomenon in a motor during astalled conditionand (2.11)Hst heat generated during stalled condition per secondin watts power loss I st2 R Ist current at the point of stalling in AmpsR resistance of the stator windings per phase in Wtst time for which the stalling condition exists inseconds1 C234.5r40 resistivity of copper at 40 Ch is known as the middle temperature during the entire temperaturevariation in the locked rotor condition.IstMotor currentTpoMotor torque at VrCurrent IrHst · tst q · Cr r40(1 µ h)where µ temperature coefficient of resistivity(a) For the statorStalling is a condition in which the rotor becomes lockeddue to excessive load torque or opposing torque. Stallingis thus a replica of a locked rotor condition and canoccur at any speed below the Tpo region, as illustrated inFigure 2.17. The figure also shows that the stator currentduring stalling will generally correspond to Ist only, dueto the characteristic of the motor speed–current curve.Whenever the rotor becomes locked in a region that almostcorresponds to the Ist region of the motor (Figure 2.17) itwill mean a stalling condition.In such a condition, if the heat generated in the windingsraises the temperature of the windings by q above thetemperature, the motor was operating just before stalling.Then by a differential form of the heat equation:r L mt Z sAcuTstStarting torqueat reduced voltageTrIrLoad torqueSpeedStalling(Locked rotorcondition)Figure 2.17Stalled or locked rotor conditionNrTorque7

2/52 Electrical Power Engineering Reference & Applications Handbook\ t st I st2 Limiting temperature for rings100 COperating temperature for bars150 COperating temperature for rings70 CTherefore the permissible rise in temperature in a stalledcondition will be as follows:q L mt Z s Acu d dL Z r40 (1 µ h ) mt sAcuÊA ˆ Á cu Ë I st 2 q d dr40 (1 µh )qqqqIand st J ss current density during start in A/cm2 andAcur40 (1 µh ) kd dwherek material constant for the metal;(i) for aluminium 0.016(ii) for copper 0.0065(iii) for brass 0.0276forforforforbars in cold conditions bars in hot conditions rings in cold conditions rings in hot conditions Stalled current Ist as % of Irt st qJ ss2 0.0065 0.85J ss2(2.12)For safe stall conditions t st should be less than thethermal withstand time of the motor under locked orshort-circuit condition.(i) q is called the permissible rise in temperature in thestalled condition.(ii) For class B insulation, the maximum limitingtemperature is 185 C and for class F 210 C (shorttime permissible temperature). The permissible risein temperature in class B is 80 C above an ambientof 40 C.q 185 – (40 80)I st 3 (Area of windings/turn) Z sNoteJss is a design parameter and more details may be obtained from themotor manufacturer.Example 2.4A 250 kW motor has a cold thermal withstand time of 30seconds and a hot thermal withstand time of 25 seconds. Ifthe starting time is 7 seconds, determine the conse

Motor torque, load torque and selection of motors 2/43 2.1 Motor speed–torque curve Refer to Figure 2.1 where T st starting torque or breakaway torque. T m minimum, pull-in or pull-up torque. T po pull-out, breakdown or maximum torque, obtainable over the entire speed range.