A9AEngineering ReferenceM o to r Te c h n o lo g ie sThe forcer is equipped w ith 4 pole pieces eachhaving 3 teeth. The teeth are staggered in pitchw ith respect to those on the platen, so thatsw itching the current in the coils w ill bring the nextset of teeth into alignm ent. A com plete sw itchingcycle (4 full steps) is equivalent to one tooth pitchon the platen. Like the rotary stepper, the linearm otor can be driven froma m icrostep drive.In thiscase, a typical linear resolution w ill be 12,500 stepsper inch.The linear m otor is best suited for applications thatrequire a lowm ass to be m oved at high speed. In aleadscrew -driven system , the predom inant inertia isusually the leadscrewrather than the load to bem oved.H ence, m ost of the m otor torque goes toaccelerate the leadscrew , and this problembecom es m ore severe the longer the travelrequired. U sing a linear m otor, all the developedforce is applied directly to the load and theperform ance achieved is independent of the lengthof the m ove. A screw -driven systemcan developgreater linear force and better stiffness; how ever,the m axim umspeed m ay be as m uch as ten tim eshigher w ith the equivalent linear m otor. Forexam ple, a typical m axim umspeed for a linearm otor is 100 in/sec.To achieve this w ith a 10-pitchballscreww ould require a rotary speed of 6,000rpm . In addition, the linear m otor can travel up to12 feet using a standard platen.How t he Li near Mot or WorksThe forcer consists of tw o electrom agnets (A and B )and a strong rare earth perm anent m agnet. Thetw o pole faces of each electrom agnet are toothedto concentrate the m agnetic flux. Four sets of teethon the forcer are spaced in quadrature so that onlyone set at a tim e can be aligned w ith the platenteeth.The m agnetic flux passing betw een the forcer andthe platen gives rise to a very strong force ofattraction betw een the tw o pieces. The attractiveforce can be up to 10 tim es the peak holding forceof the m otor, requiring a bearing arrangem ent tom aintain precise clearance betw een the pole facesand platen teeth. Either m echanical roller bearingsor air bearings are usedto m aintain the requiredclearance.W hen current is established in a field w inding, theresulting m agnetic field tends to reinforceperm anent m agnetic flux at one pole face andcancel it at the other. B y reversing the current, thereinforcem ent and cancellation are exchanged.R em oving current divides the perm anent m agneticflux equally betw een the pole faces.B y selectivelyapplying current to phase A and B , it is possible toconcentrate flux at any of the forcers four polefaces. The face receiving the highest fluxconcentration w ill attem pt to align its teeth w ith theplaten.Fig. 1.17 show s the four prim ary states orfull steps of the forcer. The four steps result inm otion of one tooth interval to the right. R eversingthe sequence m oves the forcer to the left.adding further m agnet sections or stacksto thesam e shaft (Fig. 1.15). A second stack w ill enabletw ice the torque to be produced and w ill double theinertia, so the torque-to-inertia ratio rem ains thesam e. H ence, stepper m otors are produced insingle-, tw o- and three-stack versions in eachfram e size.Fig. 1.15 Three-stack hybrid stepping motorAs a guideline, the torque-to-inertia ratio reduces bya factor of tw o w ith each increase in fram e size(diam eter). So an unloaded 34-size m otor canaccelerate tw ice as rapidly as a 42-size, regardlessof the num ber of stacks.Li near St eppi ng Mot orsFig. 1.16 Linear stepping motorPlaten TeethField WindingsPlatenPhaseAElectromagnetForcerPermanentMagnetB B A APoleFacesS N{1 2 1 2{{{AirGapPhaseBElectromagnetThe linear stepper is essentially a conventionalrotary stepper that has been unw rappedso that itoperates in a straight line. The m oving com ponentis referred to as the forcer and it travels along afixed elem ent or platen. For operational purposes,the platen is equivalent to the rotor in a norm alstepper, although it is an entirely passive deviceand has no perm anent m agnet. The m agnet isincorporated in the m oving forcer together w ith thecoils (see Fig. 1.16).A10M o to r Te c h n o lo g ie sSt ep Mot or Charact eri st i csThere are num erous step m otor perform ancecharacteristics that w arrant discussion. H ow ever,w ell confine ourselves to those traits w ith thegreatest practical significance.Fig. 1.18 illustrates the static torque curve of thehybrid step m otor. This relates to a m otor that isenergized but stationary. It show s us howtherestoring torque varies w ith rotor position as it isdeflected fromits stable point. W ere assum ing thatthere are no frictional or other static loads on them otor. As the rotor m oves aw ay fromthe stableposition, the torque steadily increases until itreaches a m axim umafter one full step (1.8).Thism axim umvalue is called the holding torque and itrepresents the largest static load that can beapplied to the shaft w ithout causing continuousrotation. H ow ever, it doesnt tell us the m axim umrunning torque of the m otor this is alw ays lessthan the holding torque (typically about 70% ).Fig. 1.18Static torque-displacementcharacteristicR epeating the sequence in the exam ple w ill causethe forcer to continue its m ovem ent. W hen thesequence is stopped, the forcer stops w ith theappropriate tooth set aligned. At rest, the forcerdevelops a holding force that opposes any attem ptto displace it. As the resting m otor is displaced fromequilibrium , the restoring force increases until thedisplacem ent reaches one-quarter of a toothinterval. (See Fig. 1.18.)B eyond this point, therestoring force drops.If the m otor is pushed overthe crest of its holding force, it slips or jum ps rathersharply and com es to rest at an integral num ber oftooth intervals aw ay fromits original location. If thisoccurs w hile the forcer is travelling along the platen,it is referred to as a stall condition.Fig. 1.17The four cardinal states or full steps ofthe forcerS NS NS NBAlignedA AlignedB AlignedS NFlux LinesDirection of MMF due to electromagnetA AlignedPhase BPhase A1221TorqueClockwiseCounter Clockwise4 Motor StepsMaxTorqueUnstable Stable StableAngleAs the shaft is deflected beyond one full step, thetorque w ill fall until it is again at zero after tw o fullsteps. H ow ever, this zero point is unstable and thetorque reverses im m ediately beyond it. The nextstable point is found four full steps aw ay fromthefirst, equivalent to one tooth pitch on the rotor or1/50 of a revolution.Although this static torque characteristic isnt agreat deal of use on its ow n, it does help explainsom e of the effects w e observe. For exam ple, itindicates the static stiffness of the system , (i.e.,howthe shaft position changes w hen a torque loadis applied to a stationary m otor). C learly the shaftm ust deflect until the generated torque m atches theapplied load. If the load varies, so too w ill the staticposition. N on-cum ulative position errors w illtherefore result fromeffects such as friction or out-of-balance torque loads. It is im portant torem em ber that the static stiffness is not im provedby using a m icrostepping drivea given load on theshaft w ill produce the sam e angular deflection.Sow hile m icrostepping increases resolution andsm oothness, it m ay not necessarily im provepositioning accuracy.A11AEngineering ReferenceM o to r Te c h n o lo g ie sU nder dynam ic conditions w ith the m otor running,the rotor m ust be lagging behind the stator field if itis producing torque. Sim ilarly, there w ill be a leadsituation w hen the torque reverses duringdeceleration. N ote that the lag and lead relate onlyto position and not to speed.Fromthe statictorque curve (Fig. 1.18), clearly this lag or leadcannot exceed tw o full steps (3.6) if the m otor is toretain synchronism . This lim it to the position errorcan m ake the stepper an attractive option insystem s w here dynam ic position accuracy isim portant.W hen the stepper perform s a single step, thenature of the response is oscillatory as show n inFig. 1.19. The systemcan be likened to a m ass thatis located by a m agnetic spring, so the behaviorresem bles the classic m ass-spring characteristic.Looking at it in sim ple term s, the static torque curveindicates that during the step, the torque is positiveduring the full forw ard m ovem ent and so isaccelerating the rotor until the newstable point isreached. B y this tim e, the m om entumcarries therotor past the stable position and the torque nowreverses, slow ing the rotor dow n and bringing itback in the opposite direction. The am plitude,frequency and decay rate of this oscillation w illdepend on the friction and inertia in the systemasw ell as the electrical characteristics of the m otorand drive. The initial overshoot also depends onstep am plitude, so half-stepping produces lessovershoot than full stepping and m icrostepping w illbe better still.Fig. 1.19 Single step responseAttem pting to step the m otor at its naturaloscillation frequency can cause an exaggeratedresponse know n as resonance.In severe cases,this can lead to the m otor desynchronizing orstalling. It is seldoma problemw ith half-stepdrives and even less so w ith a m icrostepper.Thenatural resonant speed is typically 100-200 fullsteps/sec. (0.5-1 rev/sec).AngleTimeU nder full dynam ic conditions, the perform ance ofthe m otor is described by the torque-speed curve asshow n in Fig. 1.20. There are tw o operating ranges,the start/stop (or pull in) range and the slew(or pullout) range. W ithin the start/stop range, the m otor canbe started or stopped by applying index pulses atconstant frequency to the drive. At speeds w ithin thisrange, the m otor has sufficient torque to accelerateits ow n inertia up to synchronous speed w ithout theposition lag exceeding 3.6.C learly, if an inertial loadis added, this speed range is reduced.So the start/stop speed range depends on the load inertia. Theupper lim it to the start/stop range is typically betw een200 and 500 full steps/sec (1-2.5 revs/sec).Fig. 1.20Start/stop and slew curvesTo operate the m otor at faster speeds, it isnecessary to start at a speed w ithin the start/stoprange and then accelerate the m otor into the slewregion. Sim ilarly, w hen stopping the m otor, it m ustbe decelerated back into the start/stop rangebefore the clock pulses are term inated.U singacceleration and deceleration ram pingallow sm uch higher speeds to be achieved, and inindustrial applications the useful speed rangeextends to about 3000 rpm(10,000 full steps/sec).N ote that continuous operation at high speeds isnot norm ally possible w ith a stepper due to rotorheating, but high speeds can be used successfullyin positioning applications.The torque available in the slewrange does notdepend on load inertia. The torque-speed curve isnorm ally m easured by accelerating the m otor up tospeed and then increasing the load until the m otorstalls. W ith a higher load inertia, a low eracceleration rate m ust be used but the availabletorque at the final speed is unaffected.TorqueSteps per secondStart/StopRangeSlewRangeSlew CurveStart/Stop CurveHoldingTorque