indexfingerandthumbapplyingpressuretothemotorshaft).Thereducedacceleration signalequatesto about54krad/sec2.Byrearranging Equation1,andsolvingforFLU,wecandetermine thatmyfinger frictional torqueisapproximately 0.034Nm,bythereduction inacceleration signalfromFigure3A. System Characterization through Acceleration Analysis Withthebackground information and characterization presented, wemayexpand onthisknowledge toanalyze motor performance insystems. Bystudying the acceleration profileofastepper motor,itis possible todetermine anumber ofimportant aspects oftorque margin andresonant frequencies. Itiseasiest toaccomplish this goalbyfirsttestingthestepper motoractuator outside thesystem, atthedesired pulse rates.Fromhereonoutweassume the stepper motor alsoincorporates gearing whichserves tomultiply torqueandreduce reflected loadinertiatothemotor. Viewinq theResonant Frequency: Figure4A shows ageared stepper motor with acceleration transducer providing the acceleration signalshownwithnoloadinertia orfrictional torque, running atarelatively low pulserateof20pulsespersecond. Figure4B isthesameactuator installed inasystem with reflected loadinertiaapproximately twotimes themotorinertia. Therewasalsoanominal frictional torqueapplied tothissystem. The apparent increase innoiseonthisscope traceisactually aresultofthenaturalcircular resonant frequency ofthesystem. Insome geared stepper motorapplications youmay findthattheresonant frequency changes very littlewithdifferent loadinertias. ThisisduetoI----F-- - i ,_E:!fi:42:25 ,.',  ......................i.....J,,t.......!.............i---ii......./ i--!J_i.......i?........fiI_ii_I." ,i( ii/'.i!;__: ti:I:_;-4-i...'..:...._........:.......:__.... ;:i_:!ii!,!!'di Figure4A-Sample Actuator Acceleration underNo Load ,__._ Ei-'J:7._'?.,mU 32.5SGms ......:................... :................................... _!....:.',, ,_{ :•l: i [_::_ _i.......................... _!.......t.......!............................... .. _:: iTi : ....2....,......._........_......._........_........:......._......._........... 4', ; i : i._._-Hi:2_-';_r''r-i:_:_rr's Figure4B-Sample Actuator Acceleration under InertialLoad gearmeshing andhunting toothratiosthatmaycauselowerresonant frequencies thanastraight calculation oftheResonant Frequency willindicate. However, thesefrequencies aretypically muchhigher thanstepper motors aredriven. Intheexample showninfigure4B,weobserve aresonant frequency of approximately 600Hz. Torque Margin: Itiseasytodetermine the operational Torque Margin ofastepper motor withanacceleration signal.Withthestepper motor installed inasystem, monitor the accelerometer outputsignalwhileoperating underdesired conditions (nominal orworst case).Thenloadthesystem withfrictional torque (fingers donicely) untilthestepper motormisses steps,orisunable topullin fromrest.Thetorquemargin maysimplybe calculated astheratiooftheoperational acceleration signalatdesired conditions, to themagnitude ofacceleration signaljustCH]: [_....5(;!m'. ":"_•.5S_,rr,s L!F_7_:£,.2.: 2:i/;:_] :-T ...... _ 'i'iE:i_:T__':1!9,..i............. ....................... ;......:.......•........,................ :i I'..; :ii/ ,-'-............._.......!......,.................... :.......i.......:I• ;i : !: _!;.....i _J..................... .i......../,/" 'f,.: ,''-.', /:'1 /;i . _,, ,] I ,-.....i....!......i............i........!........i............i.......................... !......i........................ Figure4C-Sample Actuator Acceleration under Maximum Frictional Load NASA/C P--2002-211506 144