ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
Titanium Nitri de  and Tiolu be  1175 coatin gTitanium Nitri de  and Tiolu be  1175 coatin g  Roller  (Tiolu be 11 75)  Spring BeamLockin g Pin  (Hard Chr ome  Plate )   

Figure 9  

Conclu sion 

It was foun d possibl e to d esign an effe ctive gimbal l aunch latch for a very rest ricted space. Rathe r than   maximizin g the radi us of action o r the length of th e lever arm s from the gimbal articulat ion point to the   points of fixity, the arm were kept tot a  minimum. T he restraints,  rather than  being simple  point restraints,  are m ulti-axis length s clamp point s with a hig her degree of rest raint. The  possibility of ge neratin g hig h  loads an d ov erstressing the p rotected stru cture is avoided by d esign of the  clampi ng m echanism to  accomm odate the strength and stiffne ss properties of the gimb al. A singl e relea se point fo r the multi-point  latch m echan ism m aximize s simpli city a nd reliability,  and al so mee ts operatio nal acce ss an d ergonomi cs  criteria. The concept ha s growth pote ntial to cover larg er diam eters and he avier p ayload s.  

Ackn owledgements 

Special  than ks to Mr. A kira Fukatsu of NEC To shiba Limited, Yokoh ama, Japa n for his continu ed support  and gui dance.  106
Example Procedure 

In the pro cedure to b e describ ed, a cran k and piston will illu strate cha nge of motion fro m rotation to  transl ation. A  cran k linkage will b e used, rather than a jackscrew,  to illu strate va riable mechani cal  advantag e depen ding on the position of the cran k. In Fi gure 1, a worm ge ar set, driven by an electri c  motor, drive s a spu r gear set and crank linkage. Th e crank drive s a pisto n having fluid pre ssure as the   resisting lo ad.      Figure 1 also  shows the coordi nates defining rotation  and tran slation. The drivin g point coo rdinate for the   rotation of the moto r shaft  and the atta ched worm pi nion i s θ1. The second coordinate  is the driven worm  gear and int ermediate sh aft rotation, θ2. The third c oordinate is  the rotation of the c ranks haft, θ3. The   rotational coordin ates fo r the linkage  bearin gs a re Φ4 and θ5. The piston  translatio n is ∆6. These  displacement s are refe renced to g round, except for Φ4, which i s the rotatio n of the lowe r (cranksh aft) link   relative to the upper (piston) link. 

Figure 1 Displacement Coordinates θ1θ2θ3 θ5 Piston and nkage       Electric Motor∆6 Crank Li Crank Li φ4 Figure 1 Displacement Coordinates θ1θ1θ2θ2θ3θ3 θ5θ5 Piston and nkage       Electric Motorφ4φ4∆6

The d riving t orque and resistin g torque s and fo rces are shown in  Figu res 2 th rough  4 as external fo rces  on the shafts, gea rs, lin kage, and pisto n. The exceptio n is th e resi sting torque, T 4B, at the cran k bearing,  Coordinate 4, which rep resents a relati ve displa cement, Φ4. This resi sting torque, T 4B, is an interface  torque b etween the upp er and lo wer crank links.  

These figures represent po rtions of Figu re 1, and a re not free bod y diagram s showi ng re action force s in  oppo sition  between  the diagrams.  It is that type of more complex representatio n and analysi s procedure  that this meth od bein g presented en deav ors to avoid.  

Referen ce Point, Coordi nate 1, ,Motor Dri ve Shaft Loads (Fi g.2)  The reference poi nt for th e calculation  of equival ent loads will be  chosen arbit rarily as the motor pinio n  drive shaft, θ1. The drivin g torqu e applied to this coordin ate (point) is p rovide d by the ele ctromag netic  torque, T 1M, on the motor armature.   110
θ1T1Μ T1W T11BT12B Figure 2 Drive  Torques and Resisti ng  Torques on Driv e Shaft  θ1θ1T1ΜT1Μ T1W T11BT12BT12B Figure 2 Drive  Torques and Resisti ng  Torques on Driv e Shaft 

The re sisting friction torque s, T 11B and T 12B, from each  of the two drive shaft bea rings, a ct in the dire ction  oppo site to  the drive  torqu e. The drag f orces from  friction at the worm and  gear tooth conta ct point will be  represented as a re sisting  torque, T 1W, acting on the driveshaft. Thus far, we  have the friction torque load   on the drive shaft as the su m of three co mpone nts. 

T1R = T 11B + T12B + T1W      (4) 

(Beari ng drag torque is partially a fun ction of the  reaction force  at the bearing, which  is in tu rn, a fun ction  of the drive torqu e. Thu s, the values of beari ng drag torque would need to b e consistent with the moto r  drive torque, and would be calculate d as the solutio n to simulta neous equation s. This also applie s to the   worm ge ar fri ction torque, which likewise dep ends on the drive t orque and can be rep resented by the   efficien cy of the gea r set times the torq ue on the wo rm pinion. Th is friction torq ue is in effect applied to   the worm but not to the gea r).  

Coordinate 2, Intermediate Shaft Loads (Fig. 3)   Coordinate 2 is represented by θ2 at the interm ediate gear shaft. As shown in Fi gure 3, thi s coordi nate i s  also comm on to the spur g ear pini on.  

θ2Τ2G Τ22Β Figure  3 Resist ing T orques on Intermediate ShaftΤ21Β θ2 θ2Τ2GΤ2G Τ22ΒΤ22Β Figure  3 Resist ing T orques on Intermediate ShaftΤ21ΒΤ21Β

Accordi ng to this methodol ogy, the torques on this second shaft will be referenced to the selected drive  point coo rdinate by the displa cement ratio, θ2/θ1. There a re two friction torq ues from the shaft bearin gs,  T21B and T 22B. The d rag to rque from sliding fri ction at the spur gear te eth will  be in cluded with the d rag  111
torque on thi s shaft as T2G. (The fri ction torqu e on a spur gear varies with th e relative p osition s of the  conta cting ge ar teeth, and  is ze ro whe n conta ct is at the pitch li ne. Howeve r, since this friction i s small   comp ared to beari ng fri ction, it can  be represented as a constant efficien cy time s the torq ue on the pini on.  The fri ction t orques at the  two bea rings are li kewise a functio n of the torqu e on the interme diate sh aft).  The thre e friction torque s on this sh aft are summ ed to give the resi sting torque at Coordinate θ2. 

T2R = T 21B + T 22B + T 2G         (5) 

To reference this net drag torque summa tion at Coordinate 2 to the drive  point at Co ordin ate 1, it is  multiplied by the displa cement ratio θ2/θ1.  

T2/1R = T 2R (θ2/θ1)       (6) 

The qua ntity T2/1R constitutes an e quiva lent or virtual  load at the drive point. T he term “virt ual” he re is  based on the diction ary def inition, "being  in effect, but not in fact". (This ge neral definition of “virtual” ha s a  more  restricted me aning later when we apply it to  virtual work a nd virtual di splaceme nts). In other words,  the effect on  the accele ration of the mech anism i s the same as if the ori ginal d rag lo ads at the   interme diate shaft we re replaced by their equivale nt load T 2/1R at the drive shaft. The k ey to t he definition  of the equivalent loads i s that they  must do the same  amount of positiv e or neg ative mecha nical wo rk as  the origi nal lo ads. By this p rocess, the lo ads from t he interme diate shaft are referenced to the drive shaft,   so that the de finition of torque margin for a single rotating co ordinate can b e used. 

θ3 T31Bθ5T5B∆6 P Figure 4 Resisting Forces and Torques on Crank Shaft and  Pistonφ4 T32BT4Bφ4T4Bθ5T5B θ3θ3 T31BT31BT31Bθ5θ5T5BT5B∆6∆6 PP Figure 4 Resisting Forces and Torques on Crank Shaft and  Pistonφ4φ4 T32BT32BT4BT4Bφ4T4Bθ5T5B φ4T4Bθ5T5B φ4T4Bθ5T5B φ4φ4T4BT4Bθ5θ5T5BT5B

112
Becau se of the varying displacement  ratios, it is  important t hat the displacem ents be taken ove r  sufficie ntly small in crements such th at any e rrors i ntrodu ced are ne gligible. If exact form ulas for th e  kinem atic rel ationship bet ween the piston motion a nd the cran kshaft are u sed, the deriv atives of the   individual di splacement s to the referen ce displacement θ1 can b e used as the d isplacement ratios. 

Final Static T orque Margin   The static torque margin e quation for th is example now compri ses the drive torqu e at the drive pinio n  divided by the resi sting to rques on the motor shaft, plus the other resisting l oads from  the intermedi ate  shaft and crankshaft refe renced to Coo rdinate 1 a s equivalent loa ds.  1001 T  T TT  Margin Force Static  3/1R 2/1R 1R1M⋅   −++=     ( 12) 

Gener al For ce and Torq ue Margin F ormulas 

The static margin derive d for this exam ple can b e stated in general as th e sums of drive fo rces divide d by  the sum s of resi sting loa ds. Each drive f orce or to rque and resi sting load is m ultiplied by its di splacement  ratio, and ea ch is refere nced to one a rbitrarily cho sen co ordinate, sho wn in the followin g equatio n as  Coordinate j. The di splacement ratio s can be  called i nfluen ce coefficients, kij. Using F to represent either  driving force or torq ue an d L to repre sent either re sisting force o r torqu e, the sta tic margi n is defined a s:  

1001Lk ........ LkLkFk ....... FkFk Margin Torque or Force Static  nnj 22j 11jmmj 22j 11j⋅     −++++++ =    ( 13) 

   where m eq uals the num ber of driving p oints,     n equal s the numbe r of re sistin g point s, 

The F i and L i terms represent the sums of driving fo rces and torq ues or resisting loa ds at the re spective   coordinates, or al ready re feren ced to t hose coordinates from other co ordinat es by related influe nce  coeffici ents. The influ ence coefficient s, k1j, k2j, k3j, etc., are the  displacement ratios referenced to el ement  Coordinate j. Usi ng the letter u to rep resent small di splacem ents, ei ther rotatio nal or tran slation al,  

kij = u i/uj      (14) 

where i is the  coordinate of  interest, and j is the refere nce coordinate.  .  One of the coordinates (i = 1,2,3,....etc) will be at  the reference point  j. Thus, that particular influence  coeffici ent wil l be equal to unity.     kij = 1 for i = j      (15) 

As a gene ral note, the referen ce coordinate j can b e a totally fic titious or virtual coo rdinate (i.e., j=0,  having an arbitrarily ch osen influence coefficient k 10 relative to  Coordinate 1), a s long as th e oth er  influen ce coe fficients a re consi stently re feren ced to th is coordinate (j= 0). 

Expressin g the summ ation of Equation 1 0 in a more g eneral form gi ves:  

1001.LkFk   Margin Torque or Force Static  n1,iiijm1,iiij ⋅     − ∑∑ = ==    ( 16)  114
Force an d Torque Requi red for Accel eration  

In the Reference 3 revisi on of the MMA spe cification, (198 8), the drive torq ue and force  requi red fo r  accele ration  were a dded to the fo rmulas fo r static torque  and force m argins. The requirement for the   margi n to be 100 pe rcent o r greater rem ained the same as befo re. 

1001Torque Resistingion  Acceleratfor Required Torque - Torque Drive  Margin Torque Static ⋅   − =        (17) 

Formul as for Kinetic F orce and  Torque Margin were also in cluded. The  requireme nt specified wa s 25  percent. 

1001ion  Acceleratfor Required Torque Torque Resisting - Torque Drive   Margin Torque Kinetic ⋅   − =    ( 18) 

In these  form ulas, the  drive force a nd torque requi red for a cceleration a re part of the requi rement rathe r  than bei ng in herent in the mech anism. Acco rdingly, the meth odolo gy for tran slating the d rive and resistin g  force s and torques to a  common point would not necessarily b e need ed fo r these specified accel eration  torque s.  One  example of d rive torqu e require d for a cceleratio n is th e torqu e required for a ste pper m otor  to overcome  detent torq ue and acce lerate the rotor past each individual step. Thi s torque can be   calculate d by a dyn amic a nalysi s or determin ed from  test d ata. Si nce this ad ditional resistin g torq ue is  considered to be a spe cification, it can be inse rted into the formula s already dev elope d (Eqn s.12 throug h  16). Ge nerall y, this detent torque would be relatively small. 

Force an d Torque Mar gins as Energ y and Po wer Margins 

The g eneral force a nd to rque ma rgin equation can be restated as an en ergy m argin. Taking Equation  13  and re stating it terms of the displa cement ratios, we h ave:  

1001 Luu........ LuuLuuFuu.......FuuFuu   Margin Torque or Force Static  n jn 2 j2 1 j1m jm 2 j2 1 j1 ⋅     − ++++++ =    ( 19) 

This exp ression ca n be converted to an  incremental energy margin (or virtu al work ma rgin) by can celing  out the refere nce di splacement u j, giving:  

1001Lu ........ LuLuFu ....... FuFu  Margin Energy  nn 22 11mm 22 11⋅   −++++++=     ( 20) 

Or, re stated:  1001Energy  Resisting  Energy Drive  Margin Energy ⋅   − =      ( 21) 

Each  of the  term s in the numerator of Equation  20 represents the  increm ental work do ne by ea ch of the  driving fo rces over ea ch of their re spective sm all displacements.  The term s in the denomin ator represent  the increme ntal wo rk or energy di ssipated by friction  force s and the increm ental potential e nergy g ained  by items su ch as the compressed fluid  implied in th e illustratio ns. (Sometimes  the resi sting  energy ca n  turn p ositive: for exampl e, depe nding  on the po sition of the cran k and pi ston. Li kewise, cable  stiffness can  assist rather t han resi st mo tion duri ng a portion of the cycle. In so me ca ses, the deci sion has to be ma de  as to wh ether such term s belong in the n umerator o r denomin ator).   115
The form ula for kin etic torq ue or force m argin (Eqn. 2 0) can like wise be stated a s a kin etic en ergy margin. 

1001Energy Kinetic  Required  Energy Resisting - Energy  Drive   Margin Energy Kinetic ⋅   − =     ( 22) 

One exampl e of required kineti c ene rgy would be t he ene rgy n eede d to en sure ade quate sep aration  velocity durin g vehicle sta ging. The dri ve energy woul d be the e nergy sto red in the kickoff spri ngs, and   the re sisting energy would  be th e energy required to extra ct the electri cal interface  conn ector pins fro m  their sockets,  or any oth er sources of frictional  losse s.  In thi s case th e displaceme nts would be the full   displacement  requi red for compl ete se paration. 

If each of the terms in Equ ation 20 is di vided by the time increme nt for these small displ acements u i, the  expre ssion re presents the time avera ge power ma rgin over the increment.  

1001Power  Resisting  Power Drive  Margin Power ⋅   − =      ( 23) 

The fact that Equation 20 can b e altere d to give Equation 19 by d ividing nume rator an d den ominato r by  any on e of t he small displacement s uj sho ws tha t the sele ction of referen ce poi nt is a rbitrary. T he  nume rical re sult is the sam e rega rdless wheth er an e nergy ma rgin, a power ma rgin, a force margi n, or a  torque m argin is cal culated.  

When restat ed a s an e nergy m argin, the force  or torqu e margin is a m easure of the kinetic energy  acquired by the syste m as it a ccelerate s fro m rest over a small displa cement u j at some arbitrary  coordinate j. The ki netic energy in crem ent over thi s small di splaceme nt is e qual to the nu merato r of  Equation 20  minus the denomin ator. (Equation 22  for kineti c energy  margin shows thi s relation ship  explicitly for l arge displacements). Sin ce the  torque or force m argins are n umerically  equal to the energy  margi ns, this restatem ent of the torque or force margin a s an energy margi n is an arg ument for the  validity of thi s method. Thus, th e “net force” avail able fo r accelerating  the system from rest u sing the  equivalent fo rce system, referen ced to one coordinate location, is the same as fo r the original fo rce  system. The validity of this method is di scusse d furth er und er the subject of virtual wo rk. 

Mecha nical Efficiency  

The efficien cy of a mecha nical tra nsmission sy stem  is defined a s the ratio of the output wo rk divide d by  the inp ut work. Me chanical efficien cy is typically illu strated  in tex tbooks by an  example  of a rel atively  inefficient de vice, su ch as a jackscre w or wo rm driv e. This usage  has simil arities to the force and ene rgy  formula s as develope d here, except th at for me chanical efficien cy the work o utput to the d riven devi ce is  exclud ed fro m the resi sting energy. Re vising Equati on 21 to incl ude only the e nergy di ssipated as fri ction: 

100Energy  FrictionEnergy  Friction - Energy  Drive  Margin Energy ⋅   =    ( 24) 

100Energy  DriveEnergy  Friction - Energy  Drive   Efficiency  Mechanical ⋅   =    ( 25) 

116
displacement . Using the letter “v” to re present di splacements th at are not ne cessarily sm all or startin g  from ze ro, Eq uation 14 d efining the influ ence co efficients ca n be re presented in derivative not ation. 

     jiijdvvd     =k        ( 27) 

This a pproach wo uld b e particula rly u seful where the di splacement ratio s are not con stant, and a re  descri bable by a mathematical fun ction, su ch as for th e cra nk linkage of the example. 

Concludin g Comments 

The p resentation of this energy-b ased method has proceed ed from an illu strative exa mple to mo re  gene ral form s of the formulas for fo rce a nd torq ue margi ns. The obje ct has bee n to adapt these   comm only used formul as to compl ex mech anical systems h aving element s interconn ected by gears,   jackscrews, b elts, and linkage s. In exte nding the forc e and torq ue margi n formu las to inclu de energy an d  power ma rgins, the relati onship bet ween force and  torque ma rgins and mech anical efficie ncy ha s bee n  shown. It is believed that this metho d is intuitively recognizable to  those in the aca demi c field and othe rs  who do mechani cal analy sis. The method i s believ ed to  be theoretically correct a nd consistent with th e  method of virtual work. It i s hoped that the comm ents regarding the validity of the method a re convinci ng  and that this presentatio n will be helpful  to those faced with the types of analy ses discu ssed.  

The use of  force m argins offers somewhat more v ersatility than  mechanical efficien cy, be cause force  margi ns can i nclude resisting lo ads where mechani cal work is done (i.e., moto r driven pump s) or potentia l  energy is g ained (i.e., a hydrauli c or m echanical jack). It is conceivabl e that a m ore general  unde rstanding coul d lead  to extended  usag e of force and torq ue margin criteria in the mech anical  engin eering comm unity, esp ecially for other critical  applicatio ns such as a ctuators for aircraft co ntrol  surfaces.  

Referen ces 

1. “Moving Mechani cal A ssemblies for S pace Vehi cles, Design and Testing Require ment s, Gene ral  Specification for”, MIL-A-8 3577 (USAF),  15 Jun e 1975.   2. “Moving  Mechani cal A ssemblies for S pace Vehi cles, Ge neral Specification  for”, DOD-A-835 77  (USAF ), 15 March 197 8.   3. “Moving  Mechani cal A ssemblies for Space Vehi cles, Ge neral Specification  for”, MIL-A-8357 7B  (USAF ), 01 Feb 198 8.   4.  “General E nvironmental Verification S pecif ication (GEVS) for S TS and ELV Payloads, Subsystems,  and Compo nents”, Rev. A, Godda rd Sp ace Flig ht Ce nter, 29 Augu st 2000.  

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is impo rtant t o have a n understan ding of stepp er perform ance specifi cation d evelopme nt, perfo rman ce  margi n and methodol ogy, steppe r sim ulation and a nalysi s, step per ha rdware testing, and  past lesson s  learn ed. 

Lesso ns le arned from stepper m otor usage on space me chani sms can be categori zed into four differe nt  areas that will be explain ed furth er. These Lesson s Learned  areas are: torque produ ction assumption s,  temperature effects, und er-margin and  over-ma rgin, and ele ctrical input effects on step stability. Critica l  motor ap plication errors ca n be avoide d if thes e are as of concern a re con sistently addre ssed. 

Backgrou nd 

A two-axi s steppe r moto r / harm onic drive rotary a ctuator typically applie d in such appli cations as a ntenna  pointing mechani sms is shown in Fi gure 1. M argin on ste pper motor requi rements is requi red, be cause  unlike simila r brushless dc motors, the st eppe r moto r runs in an op en loop mo de without any f eedb ack to   regul ate its commutation o r rotation oth er than the m otor input pul ses. 

Figure 1.  Stepper Mo tors with Ha rmonic Driv es for a T wo-Axis Antenna P ointing Mec hanism 

It is ne cessary in applying  a step per motor to care fully define rang es (minim ums or maximu ms) on m any  parameters, such as the  motor speed (pulse rate) to a ssure th at the m otor and  load rotation remai n  synchro nous over all con ditions of voltage variation , temperature  and  internal frictio nal drag chan ges,  load vari ations, etc. Syn chrono us operation i s the pre cise electro -mechanical inte raction re quired  betwe en the motor controll er, step per m otor, and o utput load so that every discrete m otor rotation (step)   that is commande d results in  the proper and  precise in cremental rotati on of th e load. Thi s is  accompli shed witho ut any  position fe edback devi ces for control (othe r than perhaps an end of t ravel  sensor or potentiomete r.) Ele ctrical pulses are sequenced, cou nted, a nd supplie d to the m otor.  Multiplying th e kno wn motor step angle by the p ulse count dete rmines the angular rot ation of the m otor  output, if the system rem ains syn chronous. Th e corresponding angle of the l oad rotation i s related by a ny  gear reduction that is pre sent betwe en the motor a nd the load. 

Since th e stepper moto r does not operate in a closed, servo l oop mod e of operation  (whi ch re sults in a  simple r, less expen sive op erating  system), the effe ctive torqu e production va ries according to a num ber  of facto rs, and so the  traditional d c motor meth od of determi ning torq ue as presented in Equation  1.0  does NO T apply: 

Touput = (Kt x I) -  Tloss           ( 1)  Where,  Touput is the net output torq ue of the motor  Kt is the motor torqu e sensitivity consta nt, torque outp ut per amp in put   120