Stepper฀Motor฀Basics Introduction - Programming the PIC microcontroller in c.pdf

Let’s฀start฀by฀considering฀the฀pluses฀and฀minuses฀of฀stepper฀motors:

Stepper฀Advantages Stepper฀Disadvantages

•฀฀Precise฀control฀of฀position-one฀pulse฀advances฀one฀step,฀

permitting฀open฀loop฀control.

•฀฀Full฀torque฀from฀zero฀RPM.

•฀฀ Step฀accuracy฀typically฀5%฀of฀step฀size,฀but฀errors฀are฀non-cumulative.

•฀฀No฀brushes฀or฀other฀current฀carrying฀moving฀parts;฀lifetime฀

is฀therefore฀limited฀only฀by฀the฀bearing฀life.

•฀฀Easy฀to฀interface฀with฀microcontrollers.

•฀฀The฀motor฀is฀self-locking฀if฀the฀windings฀are฀powered฀

while฀not฀rotating;฀even฀if฀unpowered,฀most฀designs฀have฀

appreciable฀residual฀torque.

•฀฀Limited฀speed.

•฀฀Certain฀step฀rates฀may฀mechanically฀resonate฀with฀the฀

motor฀causing฀loss฀of฀torque฀and฀undesired฀vibration.

•฀฀Large฀steppers฀are฀not฀readily฀available.฀Most฀steppers฀

are฀in฀the฀0.0001฀HP฀to฀0.05฀HP฀range.

•฀฀Torque฀decreases฀as฀rotational฀speed฀increases;฀if฀the฀

motor฀stalls,฀position฀location฀is฀lost.

Operation

Let’s฀see฀how฀a฀stepper฀motor฀works.฀We’ll฀consider฀a฀highly฀simpliﬁed฀

motor฀that฀doesn’t฀match฀real฀motor฀designs฀but฀provides฀a฀useful฀mental฀

model฀of฀how฀a฀stepper฀functions.฀Figure฀8-1฀illustrates฀our฀simple฀motor฀

model.฀At฀the฀center฀is฀a฀bar฀magnet,฀free฀to฀rotate,฀surrounded฀by฀four฀

electromagnets,฀spaced฀90฀degrees฀to฀each฀other.฀The฀electromagnets฀are฀

wound฀over฀soft฀iron฀poles.฀In฀motor฀terminology,฀the฀bar฀magnet฀is฀the฀

rotor฀and฀the฀surrounding฀electromagnets฀form฀the฀stator.฀In฀Figure฀8-1,฀

the฀motor฀is฀un-powered฀and฀the฀rotor฀has฀automatically฀rotated฀to฀the฀

position฀of฀minimum฀magnetic฀energy;฀that฀is,฀the฀permanent฀magnet฀ro-tor฀positions฀itself฀so฀that฀its฀ﬂux฀has฀the฀shortest฀air฀path฀and฀the฀longest฀

iron฀path.฀If฀you฀try฀to฀rotate฀the฀rotor฀by฀twisting฀the฀shaft,฀you฀will฀note฀

resistance;฀you฀have฀to฀supply฀the฀energy฀required฀to฀break฀the฀magnetic฀

attraction฀between฀the฀stator฀and฀the฀nearest฀pole.฀You฀should฀feel฀the฀same฀

resistance,฀followed฀by฀the฀motor฀snapping฀into฀a฀new฀stable฀position,฀if฀

you฀twist฀the฀shaft฀of฀a฀real฀stepper฀motor.฀(One฀uncommon฀type฀of฀step-per,฀the฀variable฀reluctance฀motor,฀doesn’t฀exhibit฀this฀behavior,฀as฀we’ll฀

note฀later.)฀In฀an฀unpowered฀motor฀the฀torque฀required฀to฀break฀the฀rotor฀

free฀from฀its฀rest฀position฀is฀called฀the฀detent฀torque.

Now,฀let’s฀energize฀winding฀A,฀as฀shown฀

in฀Figure฀8-2.฀We’ll฀set฀the฀polarity฀of฀

the฀current฀through฀A฀so฀that฀the฀inward฀

facing฀pole฀is฀a฀magnetic฀south฀pole,฀

which฀attracts฀the฀rotor’s฀north฀pole.฀As฀

long฀as฀winding฀A฀is฀energized,฀the฀rotor฀

is฀held฀in฀place.฀The฀external฀torque฀nec-essary฀to฀override฀the฀magnetic฀attraction฀

and฀move฀the฀rotor฀is฀known฀as฀the฀

holding฀torque฀or฀static฀torque.฀For฀most฀

motors฀the฀holding฀torque฀when฀operated฀

at฀rated฀current฀is฀about฀10฀times฀the฀

detent฀torque.

What฀happens฀if฀we฀energize฀the฀wind-ings฀in฀sequence?฀Suppose฀we฀apply฀

current฀to฀windings฀A,฀B฀and฀C,฀in฀that฀

order,฀with฀the฀polarity฀so฀that฀the฀inside฀

of฀each฀winding฀is฀a฀magnetic฀south฀

Figure฀ 8-1:฀ Simple฀ stepper฀ model:฀

unpowered.

Figure฀8-2:฀Winding฀A฀energized.

Figure฀8-3:฀Sequential฀current฀ﬂow฀

in฀A,฀B฀and฀C฀causes฀rotation.

pole.฀Figure฀8-3฀shows฀the฀result;฀the฀rotor฀rotates฀clockwise,฀as฀its฀north฀pole฀is฀sequentially฀attracted฀by฀

the฀south฀poles฀temporarily฀created฀by฀energizing฀A,฀B฀and฀C.฀Of฀course,฀we฀may฀keep฀this฀up฀and฀energize฀

D,฀then฀A,฀B,฀C,฀D…฀so฀long฀as฀we฀desire฀the฀rotor฀to฀continue฀stepping฀clockwise.฀Should฀we฀wish฀to฀stop฀

the฀motor,฀we฀may฀either฀de-energize฀all฀windings฀or,฀if฀we฀need฀additional฀rest฀torque,฀we฀may฀keep฀one฀

winding฀energized.฀If฀we฀wish฀to฀rotate฀the฀rotor฀counter-clockwise,฀we฀energize฀the฀windings฀in฀the฀reverse฀

order:฀D,฀C,฀B,฀A.฀

As฀we’ll฀see฀later,฀there฀are฀several฀variations฀on฀the฀order฀of฀energizing฀windings,฀including฀energizing฀

more฀than฀one฀winding฀at฀once.

Unipolar฀and฀Bipolar

The฀windings฀in฀our฀stepper฀may฀be฀internally฀connected฀in฀several฀conﬁgurations.฀Two,฀however,฀two฀are฀of฀

interest,฀the฀unipolar฀and฀bipolar฀connection.฀We’ll฀start฀with฀the฀bipolar฀motor,฀sometimes฀called฀a฀two-phase฀stepper฀motor.

Figure฀8-4฀shows฀our฀simple฀model฀motor฀connected฀in฀the฀

bipolar฀conﬁguration.฀The฀motor฀has฀four฀terminals฀acces-sible฀to฀the฀user,฀1฀through฀4.฀The฀upper฀diagram฀shows฀

our฀motor฀in฀the฀starting฀position,฀with฀current฀ﬂowing฀

through฀both฀windings฀A฀and฀C.฀Note฀that฀windings฀A฀and฀

C฀are฀wound฀so฀as฀to฀produce฀opposite฀ﬁeld฀polarity;฀when฀

current฀ﬂows฀in฀the฀direction฀of฀the฀arrows,฀winding฀A฀

presents฀a฀south฀pole฀to฀the฀rotor฀while฀winding฀C฀pres-ents฀a฀north฀pole.฀This฀polarity฀is฀represented฀by฀terminal฀

1฀being฀positive฀with฀respect฀to฀terminal฀3.฀Unlike฀our฀

earlier฀examination,฀the฀rotor฀is฀thus฀held฀in฀place฀by฀two฀

energized฀windings,฀not฀one.฀Suppose฀we฀then฀de-energize฀

windings฀A฀and฀C,฀energize฀windings฀B฀and฀D฀to฀rotate฀

the฀rotor฀90฀degrees฀clockwise,฀de-energize฀B฀and฀D฀and฀

then฀re-energize฀windings฀A฀and฀C.฀We฀now฀desire฀the฀

magnetic฀polarity฀to฀match฀that฀of฀the฀lower฀illustration฀in฀

Figure฀8-4;฀the฀magnetic฀polarity฀of฀windings฀A฀and฀C฀are฀

reversed฀from฀the฀upper฀illustration.฀We฀accomplish฀this฀

magnetic฀polarity฀reversal฀by฀reversing฀the฀direction฀of฀

current฀ﬂow฀through฀windings฀A฀and฀C;฀we฀make฀terminal฀

3฀positive฀with฀respect฀to฀terminal฀1.฀Let’s฀see฀how฀the฀po-larity฀changes฀for฀one฀complete฀clockwise฀rotation฀cycle.

Step Terminal฀1 Terminal฀3 Terminal฀2 Terminal฀4

1 + – None None

2 None None + –

3 – + None None

4 None None – +

The฀reason฀we฀term฀this฀connection฀“bipolar”฀is฀that฀the฀

current฀polarity฀in฀the฀windings฀reverses—that฀is,฀it฀has฀two฀possible฀polarities,฀depending฀on฀the฀step.฀We’ll฀

consider฀how฀to฀accomplish฀reversing฀the฀winding฀current฀ﬂow฀when฀examining฀drive฀circuits.

Figure฀8-4:฀Bipolar฀conﬁguration฀of฀simple฀stepper.

Figure฀8-5฀shows฀our฀simple฀stepper฀connected฀as฀a฀

unipolar฀motor.฀(Unipolar฀motors฀are฀also฀known฀as฀four฀

phase฀stepper฀motors.)฀The฀windings฀A-C฀and฀B-D฀remain฀

in฀series,฀but฀the฀center฀taps,฀X฀and฀Y,฀respectively฀are฀also฀

available,฀thus฀giving฀us฀six฀connections฀to฀the฀windings.฀

(In฀some฀unipolar฀motors,฀both฀center฀taps฀are฀connected฀

together฀and฀only฀ﬁve฀wires฀are฀brought฀out,฀as฀shown฀by฀

the฀dashed฀connection฀line฀between฀terminals฀X฀and฀Y฀in฀

Figure฀8-5.)฀In฀the฀normal฀mode฀of฀operation,฀the฀center฀

tap฀is฀always฀connected฀to฀the฀positive฀supply฀and฀we฀cause฀

current฀to฀ﬂow฀in฀the฀windings฀by฀connecting฀their฀free฀

ends฀to฀the฀negative฀return,฀ground฀in฀most฀designs.

In฀the฀upper฀illustration฀in฀Figure฀8-5,฀winding฀A฀is฀

energized฀by฀placing฀positive฀voltage฀on฀terminal฀X฀and฀

grounding฀terminal฀1.฀From฀this฀is฀the฀starting฀point฀we’ll฀

assume฀that฀winding฀A฀is฀then฀been฀de-energized,฀winding฀

B฀energized฀to฀pull฀the฀rotor฀90฀degrees฀clockwise฀and฀then฀

winding฀B฀is฀de-energized฀and฀now฀winding฀C฀is฀ener-gized฀by฀connecting฀terminal฀3฀to฀ground,฀as฀shown฀in฀the฀

lower฀illustration฀in฀Figure฀8-5.฀Current฀ﬂow฀through฀the฀

windings฀is฀always฀in฀the฀same฀direction;฀hence฀the฀name฀

“unipolar”฀for฀this฀connection.฀Note฀that฀since฀windings฀A-C฀and฀B-D฀are฀in฀series฀just฀as฀in฀our฀bipolar฀conﬁguration,฀

we฀may฀take฀this฀unipolar฀motor฀and฀connect฀it฀to฀a฀bipolar฀

drive฀circuit฀(making฀no฀connections฀to฀the฀center฀taps฀X฀

and฀Y)฀and฀it฀will฀work.฀(This฀is฀true฀for฀real฀unipolar฀mo-tors,฀not฀just฀for฀our฀simple฀model.)

Figure฀8-5:฀Unipolar฀conﬁguration฀of฀simple฀stepper.

We฀can฀summarize฀the฀beneﬁts฀and฀drawbacks฀of฀unipolar฀and฀bipolar฀connections฀as:

Conﬁguration Advantages Disadvantages

Unipolar •฀฀Simplest฀drive฀circuit. •฀฀Less฀efﬁcient฀use฀of฀motor฀windings.

Bipolar

•฀฀Efﬁcient฀use฀of฀motor฀windings.

•฀฀Greater฀torque฀than฀for฀same฀size฀unipolar฀

motor.

•฀฀Requires฀special฀drive฀circuitry;฀most฀

commonly฀an฀H-bridge฀arrangement.

Types฀of฀Stepper฀Motors

Figure฀8-6฀shows฀four฀typical฀stepper฀motors.฀The฀smaller฀two฀

motors฀at฀the฀left฀of฀the฀ﬁgure฀are฀known฀as฀tin฀can฀or฀can฀

stack฀or฀permanent฀magnet฀motors,฀while฀the฀two฀larger฀mo-tors฀are฀hybrid฀constructed.

Tin฀can฀motors฀are฀inexpensive,฀constructed฀from฀a฀pressed฀

or฀stamped฀case฀and฀with฀a฀smooth฀permanent฀magnet฀rotor฀

magnetized฀with฀alternating฀north฀and฀south฀poles.฀Usually฀tin฀

can฀motors฀have฀relatively฀coarse฀step฀sizes,฀with฀24฀and฀48฀ Figure฀8-6:฀Typical฀stepper฀motors.

steps/rev฀(15฀and฀7.5฀degrees/step)฀being฀typical฀values.฀Tin฀can฀motors฀use฀sleeve฀bearings฀and฀are฀typically฀

found฀in฀inexpensive฀electronic฀products,฀such฀as฀ink฀jet฀printers฀and฀fax฀machines.฀Most฀manufacturers฀use฀

the฀case฀diameter฀(in฀millimeters)฀and฀number฀of฀steps฀as฀part฀of฀the฀model฀number.฀For฀example,฀the฀small-est฀motor฀in฀Figure฀8-6฀is฀a฀Nippon฀Pulse฀Motor฀model฀PF35-48L4฀stepper.฀The฀case฀diameter฀is฀35฀mm฀

(about฀1-3/8")฀and฀it฀has฀48฀steps฀per฀revolution.฀The฀L4฀sufﬁx฀indicates฀the฀coil฀voltage฀(nonstandard)฀and฀

rotor฀magnet฀type฀(Neodymium).฀Other฀manufacturers฀use฀different฀identiﬁers,฀of฀course,฀but฀case฀diameter฀

and฀number฀of฀steps/revolution฀are฀commonly฀incorporated฀into฀the฀model฀identiﬁcation.

The฀two฀larger฀motors฀in฀Figure฀8-6฀are฀of฀hybrid฀construction.฀Figures฀8-7฀through฀8-9฀show฀a฀partially฀

disassembled฀hybrid฀motor.฀(I฀don’t฀recommend฀disassembling฀a฀stepper฀motor฀unless฀absolutely฀essential,฀

as฀some฀high฀performance฀rotors฀will฀be฀partially฀demagnetized฀if฀the฀rotor฀is฀removed฀from฀the฀motor฀case.)฀

Figure฀8-8฀shows฀the฀toothed฀permanent฀magnet฀rotor.฀The฀rotor฀is฀constructed฀of฀two฀toothed฀segments,฀

with฀one฀segment฀offset฀by฀one-half฀tooth฀width฀from฀the฀other,฀thereby฀effectively฀halving฀the฀step฀size.฀

(The฀objects฀at฀the฀end฀of฀the฀rotor฀shaft฀are฀a฀ball฀bearing฀and฀a฀Belleville฀washer.)฀Figure฀8-9฀shows฀the฀

stator,฀which฀has฀several฀noteworthy฀features.฀First,฀the฀four฀windings฀are฀clearly฀visible,฀just฀like฀our฀mental฀

motor฀model.฀However,฀the฀poles฀are฀segmented,฀with฀each฀pole฀having฀four฀projecting฀pieces.฀(In฀motor฀

terminology,฀these฀are฀salient฀poles.)฀It฀isn’t฀necessary—or฀even฀desirable—for฀the฀poles฀to฀be฀continuous฀

around฀the฀inner฀periphery฀of฀the฀motor;฀the฀rotor฀is฀continuous,฀which฀is฀sufﬁcient.

Figure฀8-7:฀Hybrid฀motor฀disassembly. Figure฀8-8:฀Hybrid฀motor฀

toothed฀rotor. Figure฀ 8-9:฀ Hybrid฀ motor฀

interrupted฀toothed฀stator.

Hybrid฀motors฀are฀often฀manufactured฀in฀industry-standard฀case฀sizes,฀as฀deﬁned฀by฀the฀National฀Electrical฀

Manufacturers฀Association฀(NEMA).฀A฀motor฀manufactured฀by฀Company฀X฀in฀NEMA฀style฀34฀is฀mechani-cally฀interchangeable฀with฀another฀NEMA฀34฀case฀size฀motor฀manufactured฀by฀Company฀Y.฀The฀largest฀

motor฀in฀Figure฀8-6฀is฀a฀NEMA฀34฀motor,฀while฀the฀one฀next฀to฀it฀is฀a฀NEMA฀23฀motor.฀Of฀course,฀the฀

electrical฀and฀performance฀speciﬁcations฀of฀two฀motors฀with฀identical฀NEMA฀case฀sizes฀are฀not฀necessarily฀

(or฀even฀usually)฀the฀same.

Hybrid฀motors฀are฀more฀expensive฀than฀tin฀can฀motors฀and฀feature฀higher฀quality฀construction,฀such฀as฀ball฀

bearings฀instead฀of฀sleeve฀bearings,฀and฀cast฀or฀machined฀cases฀instead฀of฀pressed฀case.฀Additionally,฀the฀

toothed฀construction฀permits฀much฀ﬁner฀steps,฀with฀180฀and฀200฀step/rev฀being฀common฀values.

A฀third฀type฀of฀motor฀is฀the฀variable฀reluctance,฀resembling฀the฀hybrid฀in฀construction,฀but฀with฀a฀nonpermanent฀

magnet฀toothed฀rotor.฀Variable฀reluctance฀motors฀are฀relatively฀uncommon฀and฀will฀not฀be฀further฀discussed.

There฀are฀other฀much฀less฀common฀stepper฀motor฀types,฀such฀as฀three-phase฀unipolar.฀These฀require฀special-ized฀driving฀circuits฀and฀are฀beyond฀the฀scope฀of฀this฀text.

Identifying฀Stepper฀Motors

To฀identify฀a฀stepper฀motor฀that฀has฀no฀nameplate฀or฀for฀which฀a฀data฀sheet฀is฀not฀available,฀we฀may฀use฀the฀

following฀steps.

1.฀ Turn฀the฀motor฀shaft฀by฀hand.฀You฀should฀feel฀the฀detents;฀if฀you฀feel฀no฀detents฀the฀motor฀is฀not฀a฀step-per฀of฀the฀type฀considered฀in฀this฀chapter.฀Turn฀the฀motor฀shaft฀one฀complete฀revolution฀and฀count฀the฀

number฀of฀detents฀you฀encounter.฀This฀gives฀the฀steps/rev฀value฀for฀the฀motor.฀Common฀step/rev฀values฀

are฀24,฀48,฀72,฀100,฀180,฀200,฀400฀and฀800,฀although฀the฀later฀two฀values฀are฀relatively฀unusual.฀Your฀

count฀should฀be฀close฀to฀a฀multiple฀of฀10฀or฀12.฀If฀you฀count฀197,฀it฀almost฀certainly฀means฀you฀missed฀a฀

count฀here฀or฀there฀and฀have฀a฀200฀step/rev฀motor.

2.฀ How฀many฀wires฀or฀a฀connection฀does฀the฀motor฀have?฀

a.฀ Four—you฀likely฀have฀a฀bipolar฀motor.

b.฀ Five฀or฀six—you฀likely฀have฀a฀unipolar฀motor.

3.฀ With฀an฀ohmmeter,฀identify฀the฀wire฀colors฀or฀terminal฀

numbers฀corresponding฀to฀your฀windings฀and฀label฀them฀

as฀in฀Figure฀8-10฀(bipolar)฀or฀Figure฀8-11฀(unipolar).฀Make฀

a฀note฀of฀your฀resistance฀measurements.฀The฀resistance฀of฀

windings฀A฀and฀B฀should฀measure฀

within฀5%฀or฀so฀of฀each฀other.฀

Likewise,฀in฀a฀unipolar฀motor,฀

the฀resistance฀from฀the฀common฀

center฀tap฀to฀each฀winding฀end฀

should฀be฀approximately฀equal฀

and฀the฀resistance฀across฀each฀

complete฀winding฀(A1฀to฀A2฀and฀

B1฀to฀B2)฀should฀be฀approximate-ly฀equal฀and฀twice฀the฀value฀from฀

the฀common฀to฀each฀end.฀

4.฀

If฀you฀have฀access฀to฀an฀induc-tance฀bridge,฀measure฀the฀inductance฀of฀the฀windings.฀If฀you฀don’t฀have฀a฀bridge,฀you฀may฀safely฀skip฀

this฀step.

5.฀ Now฀we฀will฀attempt฀to฀“guestimate”฀the฀motor’s฀voltage฀and฀current฀ratings.฀This฀step฀is฀necessary฀

only฀if฀your฀motor฀doesn’t฀have฀a฀nameplate฀or฀part฀number฀providing฀this฀information฀or฀if฀you฀can’t฀

ﬁnd฀a฀data฀sheet฀for฀the฀motor.฀There฀is฀no฀magic฀way฀to฀accomplish฀reverse฀engineering฀the฀motor’s฀

rating฀with฀complete฀accuracy,฀but฀we฀can฀come฀close฀enough฀for฀experimentation฀purposes.฀Measure฀

the฀physical฀size฀of฀the฀unknown฀motor฀and฀determine฀the฀construction฀type.฀Is฀it฀a฀tin฀can฀or฀a฀hybrid฀

motor?฀Next,฀search฀the฀manufacturer’s฀catalogs,฀either฀paper฀copies฀or฀on฀the฀internet,฀until฀you฀ﬁnd฀a฀

motor฀with฀the฀same฀physical฀size,฀construction฀type฀connection฀type฀(bipolar฀or฀unipolar)฀and฀num-ber฀of฀steps.฀See฀if฀you฀can฀ﬁnd฀a฀motor฀with฀similar฀coil฀resistance฀and฀(if฀you฀have฀measured฀it,฀coil฀

inductance).฀฀If฀you฀can’t฀ﬁnd฀a฀match,฀then฀calculate฀the฀power฀dissipation฀(in฀watts)฀for฀several฀motors฀

of฀the฀same฀case฀size฀as฀your฀motor฀using฀the฀formula฀P฀=฀I²R,฀where฀P฀is฀the฀power฀in฀watts,฀I฀is฀the฀

motor’s฀current฀rating฀in฀amperes฀and฀R฀is฀the฀motor’s฀winding฀resistance฀in฀ohms,฀with฀both฀I฀and฀R฀

from฀the฀catalog฀values.฀Your฀calculated฀P฀will฀likely฀differ฀among฀the฀matching฀motors,฀so฀calculate฀

an฀average฀value.฀Then,฀using฀the฀average฀power฀dissipation฀for฀the฀physically฀similar฀motors฀and฀your฀

measured฀resistance฀value,฀calculate฀the฀resulting฀I฀for฀your฀motor,฀using฀the฀formula฀ I P

= R.

6.฀ Now฀that฀we฀have฀determined฀the฀motor’s฀rated฀current,฀I,฀and฀the฀measured฀R,฀calculate฀the฀motor’s฀

nominal฀operating฀voltage฀V฀from฀Ohm’s฀law,฀V฀=฀IR.

7.฀ Note฀any฀other฀important฀parameters฀from฀the฀closest฀matching฀data฀sheet,฀such฀as฀the฀maximum฀speed฀

in฀steps/second฀or฀the฀maximum฀torque.

Figure฀ 8-10:฀ Winding฀

labels฀for฀bipolar฀stepper฀

motor.

Figure฀ 8-11:฀ Winding฀ labels฀ for฀ unipolar฀

stepper฀motor.

Reading฀a฀Stepper฀Speciﬁcation฀Sheet

Let’s฀look฀at฀a฀typical฀speciﬁcation฀sheet฀for฀an฀inexpensive฀tin฀can฀motor,฀a฀Nippon฀Pulse฀Motor฀model฀

PF35-48.฀I’ve฀reproduced฀the฀data฀sheet฀parameters฀below.

Parameters

Units PF35-48

Drive฀Mode Unipolar Bipolar

Excitation฀Mode ฀ Full-step฀(2-2฀ex)

Step฀Angle ° 7.5

Step฀Angle฀Tolerance % ±฀5

Steps฀per฀Revolution ฀ 48

Voltage V 12 5 12 5

Winding฀Resistance ohm/Ø 90฀ 16฀ 100฀ 17฀

Winding฀Inductance mH/Ø 48฀ 8.9฀ 124฀ 19฀

Holding฀Torque mN•m 20 20 25 25

Rotor฀Inertia kg•m² 4.5฀x10^–7

Starting฀Pulse฀Rate,฀Max pps 500

Slewing฀Pulse฀Rate,฀Max pps 530

Ambient฀Temp.฀Range,฀Operating °C –10฀~฀+50฀

Temperature฀rise K 55

Mass g 80฀

What฀does฀each฀line฀mean?

Drive฀mode—The฀PF35-48฀is฀available฀in฀either฀a฀bipolar฀or฀a฀unipolar฀conﬁguration.฀

Excitation฀mode—As฀we฀will฀see฀later,฀a฀stepper฀may฀be฀operated฀in฀several฀modes,฀and฀certain฀parameters,฀

such฀as฀torque฀and฀step฀angle,฀are฀different฀for฀different฀modes.฀The฀data฀sheet’s฀statement฀“full-step฀

(2-2฀ex)”฀means฀that฀the฀performance฀data฀is฀based฀upon฀full฀step฀operation,฀with฀both฀coils฀energized.฀

If฀this฀sentence฀doesn’t฀mean฀much฀to฀you฀right฀now,฀put฀a฀star฀in฀the฀margin฀and฀come฀back฀to฀it฀after฀

reading฀the฀rest฀of฀this฀chapter.

Step฀angle—the฀angle฀in฀degrees฀through฀which฀the฀shaft฀rotates฀when฀it฀advances฀one฀step฀while฀in฀full฀step฀

mode.฀The฀value฀7.5°฀corresponds฀to฀48฀steps/rev.

Step฀angle฀tolerance—the฀tolerance,฀as฀applied฀to฀the฀step฀angle,฀that฀is,฀the฀angle฀the฀motor฀shaft฀advances฀

in฀one฀full฀step฀is฀7.5°฀±5%.฀It’s฀important฀to฀remember฀this฀tolerance฀applies฀on฀a฀step-by-step฀basis฀

and฀is฀not฀cumulative.฀After฀48฀steps,฀the฀motor฀will฀return฀to฀its฀original฀starting฀point฀with฀an฀accuracy฀

of฀±5%฀×฀7.5°฀or฀±0.375°.฀After฀48000฀steps฀(1000฀complete฀revolutions),฀the฀motor฀will฀be฀at฀its฀origi-nal฀starting฀angle฀±0.375฀degrees.฀The฀noncumulative฀error฀performance฀of฀a฀stepper฀is฀the฀key฀to฀its฀

ability฀to฀perform฀precision฀operations.฀If฀the฀error฀were฀cumulative,฀after฀being฀commanded฀to฀perform฀

48000฀steps,฀or฀1,000฀revolutions,฀the฀shaft฀angle฀would฀be฀unknown฀within฀±50฀revolutions,฀quite฀a฀dif-ference฀from฀the฀actual฀±0.375฀degrees!

Steps฀per฀revolution—the฀number฀of฀full฀steps฀required฀to฀return฀the฀motor฀shaft฀to฀its฀starting฀angle.฀Since฀

there฀are฀360°฀in฀one฀revolution,฀the฀step฀angle฀and฀steps฀per฀revolution฀are฀related฀by฀the฀formula:฀

θ =360

N ฀where฀θ฀is฀the฀step฀angle฀and฀N฀is฀the฀number฀of฀steps฀per฀revolution.

Voltage฀and฀winding฀resistance—We’ll฀consider฀these฀two฀parameters฀at฀the฀same฀time.฀You฀may฀recall฀

from฀high฀school฀physics฀that฀the฀magnetic฀ﬁeld฀of฀an฀electromagnet฀is฀proportional฀to฀the฀current฀in฀

the฀windings฀multiplied฀by฀the฀number฀of฀turns฀(ampere-turns)฀and฀that฀the฀attractive฀force฀between฀two฀

magnets฀is฀proportional฀to฀their฀magnetic฀ﬁelds.฀Hence,฀for฀a฀ﬁxed฀number฀of฀turns,฀the฀shaft฀torque฀

in฀the฀stepper฀motor฀is฀proportional฀to฀the฀current฀through฀the฀windings.฀If฀we฀double฀the฀current,฀we฀

double฀the฀torque.฀And,฀we฀know฀from฀elementary฀circuit฀theory฀that฀resistive฀power฀dissipation฀is฀

proportional฀to฀the฀square฀of฀the฀current;฀P฀=฀I²R.฀If฀we฀double฀the฀current,฀the฀power฀dissipated฀in฀the฀

motor฀goes฀up฀fourfold.

The฀motor฀designer฀must฀balance฀these฀two฀effects฀against฀each฀other;฀to฀make฀the฀motor฀more฀powerful฀for฀

its฀size,฀the฀designer฀wishes฀to฀maximize฀the฀current.฀However,฀more฀current฀causes฀more฀internal฀heating฀

and฀if฀the฀motor฀temperature฀exceeds฀a฀certain฀level฀the฀winding฀insulation฀may฀break฀down฀and฀the฀mo-tor฀will฀fail.฀Alternatively,฀to฀increase฀the฀stator’s฀magnetic฀ﬁeld,฀the฀designer฀may฀decide฀to฀use฀smaller฀

diameter฀wire,฀which฀allows฀more฀turns฀in฀a฀given฀space฀(increasing฀ampere฀turns),฀but฀the฀smaller฀diameter฀

wire฀has฀greater฀resistance฀which฀means฀we฀must฀apply฀higher฀voltage฀to฀the฀stator฀coil฀to฀obtain฀the฀desired฀

current.฀The฀trend฀is฀to฀lower฀voltage฀power฀supplies,฀and฀the฀motor฀manufacturers฀try฀to฀meet฀their฀custom-ers’฀needs฀with฀lower฀voltage฀motor฀designs.

The฀motor’s฀rated฀voltage฀and฀resistance฀allow฀us฀to฀calculate฀the฀nominal฀winding฀current฀using฀Ohm’s฀law:฀

I฀=฀V/R.฀As฀we฀will฀see฀when฀we฀look฀at฀driver฀circuits,฀usually฀we฀drive฀the฀motor฀through฀a฀quasi-constant฀

current฀arrangement.

In฀this฀case,฀the฀PF35-48฀motor฀has฀two฀winding฀options;฀a฀12฀V฀winding฀with฀100฀ohms฀resistance฀and฀a฀฀

5฀V฀winding฀with฀17฀ohms฀resistance.฀We฀can฀calculate฀the฀corresponding฀currents฀as฀120฀mA฀and฀294฀mA,฀

respectively.฀Since฀the฀torque฀speciﬁcations฀are฀identical฀for฀both฀winding฀options,฀we฀may฀safely฀assume฀

that฀the฀12฀V฀winding฀has฀close฀to฀2.45฀more฀turns฀than฀the฀5฀V฀version,฀thereby฀keeping฀the฀ampere฀turns—

and฀torque—identical.฀A฀quick฀check฀conﬁrms฀that฀the฀PF35-48฀is฀designed฀for฀identical฀power฀dissipation฀

for฀both฀12฀V฀and฀5฀V฀windings.฀The฀12฀V฀coil฀dissipates฀1.44฀watts฀at฀the฀rated฀voltage,฀while฀the฀5฀V฀coil฀

dissipates฀1.47฀watts.

The฀PF35-48฀motor฀I฀used฀in฀this฀chapter฀has฀an฀“L4”฀sufﬁx,฀meaning฀it฀is฀a฀“special”฀voltage฀rating.฀Since฀

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