ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
272   Figure 3.  ‘HIMast ’ Drivetrain Design  

NASA Cube Sat Magnetometer   This effort  is currently under development with the NASA Goddard Space Flight Center in  Greenbelt,  Maryland. This project builds upon Roccor’s previous ex periences in fabricating high precision, thermally  stable booms with a new focus of miniaturization into the CubeSat form factor, use of magnetically clean  materials and need for low -cost hardware. This boom is 0.75” (1.9 cm) in diameter, has an included angle  of 350º  and a deployed length of 50”  (1.3 m) . This boom utilizes a thermally stable laminate design  consisting of both carbon and glass fibers . Unique to this design are a series of roller -free boom support  boundary conditions to reduce the number of  moving parts and to maximize the available volume. In  addition to meet precision,  this system contains a highly geared- up drive train to ensure fine deployment  resolution as well as a pin- latch  mechanism and a composite insert to lock the boom at the desi red deployed  length. This boom also contains a hybrid elastic friction wheel and mechanical toothed interface to improve  deployment length knowledge.  

NASA Asteroid Redirect Mission   This boom system was developed in conjunction with a commercial group working to fabricate ground  demonstration hardware in support of NASA’s Asteroid Redirect Mission. This system closely resembles  the ‘DARPA Phoenix  Camera Boom ’ deployer design outlined above however utilizes a higher fidelity  laminate design, contains an internal motor and utilizes a new edge roller constraint  scheme. The laminate  design consists of a 1.4” (3.6 -cm) diameter boom with a 400º  overlap and a deployed length of 80”  (2 m) .  The overlap strengthens the boom along the generally weaker bending direction where the open portion of the slit -tube is in compression. The internal motor is directly connected to the boom shaft and is capable of  supplying an axial deployment force in excess of 20 lbf (89 N) . The edge supports depart from earlier  approaches where a wheeled interface is replaced with a hard metallic interface. Here the composite rubs  against the surface enabling a stout boundary condition while eliminating additional moving components . 

Lessons Learned  in High Strain Composite  Boom Deployer  Design    During the development of the four boom systems outlined above, several best practices and lessons learned were established by the Roccor team . In this section several of these details are outlined and design  features that incorporate these best practices are discussed.  

Designing  HSC  Slit-Tubes  to be Neutrally Stable   The utilization of  neutrally stable HSC materials offers an opportunity to fabricate unique structures with a  wide range of performance properties . The design space ranges from  one extreme where the  neutrally
274 Distal End   The distal end, (i.e. the boom end fitting) is a complex component of any deployer system as its attachment  method plays a large role in ensuring boom rigidity . Perhaps the most challenging aspect to this component  is an attachment method that ensures boom torsional rigidity . Additional complexities arise for deployer  systems that do not exit the box with a fully formed cross section. For these cases, the distal end must  accommodate changes in the cross section geometry and lock into place once the boom reaches beyond  the 9x envelope form factor . An example of this case is illustrated in Figure 5 and shows the closeout feature  utilized for the ‘DARPA Phoenix  HIMast  Boom ’ system . Here as the numbers  in the figure ascend, the boom  is deployed out and the cross sect ional geometry  wraps  and closes  around the distal plate.  

Figure 5.  Distal End Closeout, Roccor ‘ DARPA Phoenix  HIMast  Boom ’ System  

For this case, it was found that the best distal closeout method was to use a series of kinematic mount  interfac es that preloaded boom front edge against the distal plate to enable torsional rigidity . Other practices  were trialed for additional improvement including the use of magnets, springs , etc., however with the large  closeout length for this architecture, significant benefits  for these added features were not realized. For  Roccor’s other deployers,  the ‘NASA ARM  Boom ’ system (with an envelope form factor of 4x), a distal plate   was adhered and fastened to the end of the boom , as shown in Figure 6, and worked very well however  minor,  non-destructive edge buckling was noticed upon full retraction. Further design changes to t he front  roller supports  relieved this effect . For the ‘DARPA Phoenix  Camera Boom ’ deployer (envelope length of  x6), a system utilizing a long, thin sheet metal plate adhered to the composite surface was  incorporated   without any observed issues.  

                              Figure 6.  ‘NASA ARM  Boom ’ Deployer, Distal End  

Boundary Conditions : The root boundary conditions, along with the distal end, define the structural  performance of the entire system . Within the Roccor boom deployer family, a myriad of boundary  constraints mechanisms have been incorporated in an attempt t o maximize rigidity while minimizing cost
277    Figure 9.  ‘NASA ARM  Boom ’ Deployer Drive Wheel  

Modeling the Formation Region   The geometry of the laminate formation region is a function of the material properties, laminate design,  thickness, cross -sectional geometry and fabrication processes . These interconnected design features  ultimately leads to a cross section that is hard to predict without empirical measurements . As such, it is  important to fabricate a fully functional boom prior to initiating detailed deployer design. In addition, the  formation region can change over time due to boom degradation, creep and thermal effects and should be fully understood prior to fabrication.  

Conclusion    In this paper, the design traits of four unique deployer systems developed by Roccor was presented with the goal to inform the reader of the wide range of design features  and applications for High Strain Composite  slit-tube deployable booms . In addition, common design practices were presented to provide a flavor for  how the designs converged when developing these boom deployers as well as to provide lessons learned and fut ure recommendations for new systems . The use of High Strain Composite structures in spacecraft  deployables is an emerging field that offers the opportunity to develop simplistic, low cost systems that can supplant and reduce complexities of e stablished deployable systems .
278 References  

1. Storable Tubular Extensional Member Device, US Patent # 3434674 A, 1969   2. Annon, “ Tubular Spacecraft Booms (Extendible, Reel Stored)," Tech. Rep. SP -8065, NASA, Feb  1971  3. Wikipedia page on “High Strain Composite Structure”, authored by Davis, B.  https://en.wikipedia.org/wiki/High_strain_composite_structure   4. Murphey, T., Franci s, W., Davis B., Mejia -Ariza, J., Santer, M., Footdale, J., Schmid, K., Soykasap, O.,  Guidanean, K.,  Warren , P., “High Strain Composites”, Proceedings of the 2015 AIAA SciTech  Conference,  2nd AIAA Spacecraft Structures Conference, AIAA- 2015- 0942, [Pg 1- 53], Kissimmee,  Florida, 5 -9 January 2015.   5. Francis, W. H., & Hulse, M. (2015). High Strain Composite Sl it Tubes for Roll -Out Structures. In 2nd  AIAA Spacecraft Structures Conference (pp. 1 –12). Kissimmee, FL.   6. NASA Website on the International Space Station Solar Arrays:    https://www.nasa.gov/mission_pages/station/structure/elements/solar_arrays.html   7. Im, E., Thompson, M., Fang, H., Pearson, J., Moore, J., Lin, J., “Prospects of Large Deployable Reflector Antennas for a New Generation of Geostationary Doppler Weather Radar Satellites”, Proceedings of the 2007 AIAA Space Conference & Exposition, AIAA 2007- 9917, Long Beach,  California, 18- 20 September 2007   8. Davis, B., Francis, W., Goff, J., Cross, M., Copel, D., “Big Deployables in Small Satellites” 28th Annual AIAA/USU Conference on Small Satellites , [SSC14 -VII-4, pp. 1- 8], Logan, Utah, 2014.   9. Davis, B., Francis W., “High Performance Electrical Conductors in Composite Slit -Tube Booms”,  Proceedings of the 2015 AIAA SciTech Conference,  2nd AIAA Spacecraft Structures Conference ,  AIAA- 2015- 0226, [Pg 1- 9], Kissimmee, Florida, 5- 9 January 2015.   10. Murphe y, T. W. and Pelligrino, S., “A Novel Actuated Composite Tape- Spring for Deployable  Structures,” Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics,  and Materials Conference, April 2004, AIAA- 2004- 1528.   11. Shultz, M., Hulse, M., and Keller, P., “Neutrally Stable Composite Tape Springs,” Proceedings of the  47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, April 2006, AIAA- 2006- 1810.   12. Rimrott, F.P.J, “Storable Tubular Extendible Member –  A Unique Machine Element,” Machine Design,  December 9, 1965.
279 James W ebb Space Telescope Deployment Brushless DC Motor    Characteristics Analysis  

Anh N. Tran* 

Abstract  

A DC motor’s performance is usually characterized by a series of tests, which are conducted by pass/fail  criteri a. In most cases, these tests are adequate to address the performance characteristics under  environmental and loading effects with some uncertainties and decent power/torque margins. However, if  the motor performance requirement is very stringent , a better understanding of the motor characteristics is  required.    The purpose of this paper is to establish a standard way to extract the torque components of the brushless motor and gear box characteristics of a high gear ratio geared motor from the composite geared motor  testing  and motor parameter measurement . These torque components include motor magnetic detent   torque, Coulomb torque, viscous torque, windage torque, and gear tooth sliding torque.    The Aerospace Corp bearing torque model  [1] and MPB torque models [ 2] are used to predict the Coulomb  torque of the motor rotor bearings and to model the viscous components . Gear tooth sliding friction torque  is derived from the dynamo geared motor test data.  With these torque data, the gear ed motor mechanical  efficiency can be estimated and provide the overall performance of the geared motor versus several motor  operating parameters such as speed, temperature, applied current, and transmitted power.  

JWST  Deployment Mechanism General Description    There are fourteen brushless DC motors  that are used for the James Webb Space Telescope d eployment  mechanisms . Three of these motors are used in the Optical Telescope Elements  deployment, which is the  study of this paper. Most of these motors demonstrate excellent performance during flight tests. In order to  assess the deploying margin on these systems, the geared motor performance characteristics, particularly  the power losses, need to be estimated. Unfor tunately, most of the tests  for these motors are performed at  the geared motor level. Therefore, the losses at the motor and the gearbox levels are not available. In order to extract these individual components, a geared motor model is developed. The model, then, is matched   with the composite measured data to derive the individual torque components.  The overview of the geared  motor is  shown in Figure 1.   

Figure 1.  JWST  Deployment Brushless DC Geared Motor Overview  

                                                               * Northrop Grumman Aerospace Systems, Redondo Beach, CA  

Proceedings of the 43rd Aerospace Mechanisms Symposium, NASA Ames Research Center, May 4-6, 2016
280 JWST  Deployment Brushless DC Motor Parameters  

The geared motor consists of a 3- phase, 4- pole, permanent -magnet brushless DC  motor with an add- on  resolver for position, and a 4608 :1 planetary gearbox  (4-stage) . The detailed geared motor parameters are  shown in Figure 2.  

Number of Poles  4  Number of Phases  3  Motor Rotor Inertia  1.E-4 oz-in-s2  (0.77 µN -m-s2)  Back EMF Constant (ambient), kb  2.11 mV/rpm   Winding Resistance (leg -to-leg) (ambient)  1.64 ohm   Winding Inductance (leg -to-leg) (ambient)  605 µhenry   Motor Torque Constant, kb  2.85 in -oz/A  (0.020 N -m/A)   Operating Gearbox Shaft Speed  0.1 rpm   Gearbox Speed Reduction Ratio  4608   Maximum Applied Current  2 A  Figure 2.  PMSA Geared Motor Parameter s 

Brushless DC Motor General Equations    The simplified brushless DC motor torque governing equations are expressed as follows:  

 𝑉𝑉=𝐿𝐿𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑+𝑅𝑅𝑑𝑑+𝑘𝑘𝑏𝑏𝜃𝜃̇ (1)   𝑀𝑀𝜃𝜃̈=�𝑘𝑘𝑇𝑇𝑑𝑑−𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667−𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667−𝑘𝑘𝑤𝑤𝜃𝜃̇2−𝑇𝑇𝑐𝑐𝑣𝑣 −𝑇𝑇𝑐𝑐𝑣𝑣−𝑇𝑇𝑑𝑑�∗�1−𝑘𝑘𝑠𝑠𝑣𝑣�−𝑇𝑇𝑙𝑙∗16 𝐺𝐺𝑅𝑅   (2)   where   V = voltage applied to the motor , volt  L = motor inductance, henry  I = net current through the motor windings , ampere  k T = motor torque constant, in- oz/A  kb = motor back emf constant, V/( rpm)  kvm = motor rotor bearing viscous torque constant, in -oz/(rpm)(2/3)  kw = motor rotor  windage torque constant, in- oz/(rpm)2  kvg = gearbox  viscous  torque constant, in- oz/(rpm)(2/3)  Tl = geared motor output torque, in -lb  Tcm = motor rotor bearing Coulomb torque, in- oz  Tcg = gearbox Coulomb torque, in- oz  ksg = gear tooth sliding coefficient   M = motor rotor moment of inertia, oz-in-sec2  Td = motor magnetic cogging or detent torque, in- oz  GR = gearbox gear ratio    In this equation, the motor and the gear box viscous torques are modelled using the MPB ball bearing viscous torque equation. This non- linear viscous torque model showed a remarkabl e comparison with the  measurement data on geared motor spin- down tests reported by Tran and Halpin [3].
281 There are seven unknowns in the geared motor torque equations, which are listed as follows:  

kvm = motor rotor bearing viscous torque constant, in- oz/(rpm)(2/3)  kw = motor rotor  windage torque constant, in- oz/(rpm)2  kvg = gearbox  viscous torque constant, in- oz/(rpm)(2/3)  Tcm = motor rotor bearing Coulomb torque, in- oz  Tcg = gearbox Coulomb torque, in- oz  ksg = gear tooth sliding coefficient   Td = motor magnetic cogging or detent torque, in- oz 

There are only five usable sets of motor torque test data available. Two unknowns need to be estimated.  Among these unknowns, for this particular application, the motor windage torque appears to be small  and  is predicted using the model developed by James E.  Vkzncik [ 4] as shown Equation 3.  

𝑇𝑇𝑤𝑤=𝜋𝜋𝐶𝐶𝑑𝑑𝜌𝜌𝑅𝑅4𝜔𝜔2𝐿𝐿           (3) 

where  

Cd = skin friction coefficient. It can be determined by solving the below equation with a known Reynold s  number   1 �𝐶𝐶𝑑𝑑=2.04 +1.768 ln (𝑅𝑅𝑅𝑅�𝐶𝐶𝑑𝑑 )     Re = Reynolds number = 𝑅𝑅𝑅𝑅𝑅𝑅 𝜗𝜗  ω = rotor speed, rad/sec   υ = kinematic viscosity of air = 1.36e- 4 ft2/s (12.6 mm2/s)  ρ = air density = 0.0765 lbm/ft3  (1.225 kg/m3)  t = rotor/stat or radial gap thickness = 0.002 in (0.05 mm)   R= rotor radius = 0.5 in   (13 mm)   L= rotor length = 1 in (25 mm)                                Figure 3.  Motor Rotor Parameters  

The skin friction coefficient and the windage torque versus rotor speed in air at room temperature and 70%  relative humidity are plotted in Figure 4. From Figure 4, it is observed that the windage torque for this  particular motor application is very small and can be ignored in the subsequent calculat ion.    The other unknown, k sg, gear tooth sliding coefficient is derived from the geared motor stalled torque vs.  current test and the geared motor dynamo test, which are shown later.
282   Figure 4.  Motor Skin Friction Coefficient and Windage Torque as a Function of Rotor Speed  

The rest of the five unknowns are extracted from the series of motor and geared motor tested conducted  at the motor vendors  and NGC listed as follows:  

1. Motor No- Load Synchronous Test   Parameters:   Speed = 1800 rpm; no load; motor only; a pplied voltage, V: 3. 0 volts; motor inductance, L=605  µHenry; commutation frequency, f = 1000 Hz; motor winding resistance, R = 1.64 Ω; kt = 2. 85 inoz/A (2.01 N -cm/A) ; kb=0.0021 V/rpm   Torque governing equation:   �𝑘𝑘𝑇𝑇𝑑𝑑−𝑇𝑇𝑐𝑐𝑣𝑣 −𝑇𝑇𝑑𝑑−𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667�=(𝑘𝑘𝑇𝑇𝑉𝑉−𝑘𝑘𝑏𝑏𝜃𝜃̇ �𝑅𝑅2+(𝐿𝐿∗𝑓𝑓∗2∗𝜋𝜋)2−𝑇𝑇𝑐𝑐𝑣𝑣 −𝑇𝑇𝑑𝑑−𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667)=0   (4)  2. Motor Dynamo Test   Parameters:   Speed = 461 rpm; motor load torque, T ml = 3.0 in-oz (2. 1 N-cm); applied current, I = 1. 2 A  Torque governing equation:   �𝑘𝑘𝑇𝑇𝑑𝑑−𝑇𝑇𝑐𝑐𝑣𝑣 −𝑇𝑇𝑑𝑑−𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667�=𝑇𝑇𝑣𝑣𝑙𝑙        (5)  3. Geared Motor No- Load Synchronous Test   Parameters:   Speed = 1797 rpm; no load; geared motor; applied voltage, V: 3.58 volts; motor inductance, L=605  µHenry; commutation frequency, f = 1000 Hz; motor winding resistance, R = 1.64 Ω; kt = 2.85 inozf/A  (2.01 N -cm/A) ; kb=0.0021  V/rpm   Torque governing equation:   �𝑘𝑘𝑇𝑇𝑑𝑑−𝑇𝑇𝑐𝑐𝑣𝑣 −𝑇𝑇𝑐𝑐𝑣𝑣−𝑇𝑇𝑑𝑑−𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667−𝑘𝑘𝑤𝑤𝜃𝜃̇2−𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667�=(𝑘𝑘𝑇𝑇𝑉𝑉−𝑘𝑘𝑏𝑏𝜃𝜃̇ �𝑅𝑅2+(𝐿𝐿∗𝑓𝑓∗2∗𝜋𝜋)2−𝑇𝑇𝑐𝑐𝑣𝑣 −𝑇𝑇𝑐𝑐𝑣𝑣−𝑇𝑇𝑑𝑑− 𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667−𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667)=0         (6)
283 4. Geared Motor Stalled Torque from the Stalled Torque vs Current Test in Figure 8  Parameters:   Speed = 0 rpm; free current, I = 0.161  A; motor winding resistance, R = 1.64 Ω; kt = 2.85 in-oz/A  (2.01 N -cm/A)   Torque governing equation:   �𝑘𝑘𝑇𝑇𝑑𝑑−𝑇𝑇𝑐𝑐𝑣𝑣 −𝑇𝑇𝑐𝑐𝑣𝑣−𝑇𝑇𝑑𝑑�=0         (7)  5. The motor bearing Coulomb torque is predicted based on the Aerospace Corporation B RGS 10C  with the friction coefficient selected to be 0.15 for this bearing size and precision class with the  measured preload of 2.5 lb (11 N) . The bearing parameters and the output are shown in Figure 5.  The predicted motor bearing Coulomb torque of 0.028 in- oz (0.20 mN -m) is comparable with the  reported range of this motor Coulomb torque of 0.02 to 0.05 in- oz (0.14 to 0.35 mN -m) by the motor  vendor [ 5] 

Figure 5.  Motor Rotor Bearing Analysis Using the Aerospace Corporation BRGS10C  

With f ive equations and five unknowns, the system of l inear equations can be solved as shown in Figure 6 .  The result is summarized in Figure 7.    It is important to note that under high  speed running conditions, this cogging or detent torque, T d, has a  mean value of zero and, therefore, does not constitute a loss of torque. The variation in the instantaneous value can, however, cause an unacceptable increase in the percentage ripple torq ue.  

Figure 6.  System of Linear Equations for Motor Torque Test Data
284 Torque Component or Constant  Value   Tcm 2.800E -2 in-oz 197.7 µN -m  Tcg 1.560E -1 in-oz 1.102 mN -m  Td 2.780E -1 in-oz 1.963 mN -m  Kvm 1.911E -3 in-oz/rpm0.667 13.49 µN -m/rpm0.667  Kvg 2.777E -3 in-oz/rpm0.667 19.61 µN -m/rpm0.667  Kw 1.600E -10 in -oz/rpm2 1.130 pN-m/rpm2  Figure 7: Geared Motor Derived Torque Components  

The derived motor viscous torque of 0.001 911 in-oz/rpm.667 (13.49 µN -m/ rpm.667) is also comparable with  this motor viscous torque constant, Bv, of 1.33E -4 in-oz/rpm or 0.00 162 in-oz/rpm.667 reported by the motor  vendor [ 6]. 

The static gear tooth sliding coefficient is  derived based on the geared motor stalled torque versus applied  current test data. T he geared motor stalled torque versus applied current condition can be modelled as  follows:    𝑉𝑉=𝐿𝐿𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑+𝑅𝑅𝑑𝑑 (8)   𝑇𝑇𝑠𝑠=(𝑘𝑘𝑇𝑇𝑑𝑑−𝑇𝑇𝑐𝑐𝑣𝑣 −𝑇𝑇𝑐𝑐𝑣𝑣−𝑇𝑇𝑑𝑑)(1−𝑘𝑘𝑠𝑠𝑣𝑣) (9)   where k sg is the static gear tooth contact frictional torque loss coefficient, which is the only loss component  depending on the transmitted torque.    By applying a linear regression to the stalled torque versus applied current data as shown in Figure 8 , the  slope and the x -intercept are expressed as follows:  

k sg = 1-slope/kt = 1- 1.773/2.85 = 1- 0.622 =  0.38 or 38% gear tooth loss at static loaded condition.  

Tcm+Tcg+Td = 2.85*0.162 = 0.462 in- oz  (3.26 mN -m) 

The dynamic gear tooth sliding coefficient is derived from the geared motor dynamo test, which has the  operating parameters listed as follows:    Speed = 4608 r pm; load torque, Tl = 375 in- lb (42.4 N -m) at gear shaft; applied current, I = 1.2 A   Torque governing equation:  

�𝑘𝑘𝑇𝑇𝑑𝑑−𝑇𝑇𝑐𝑐𝑣𝑣 −𝑇𝑇𝑑𝑑−𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667−𝑇𝑇𝑐𝑐𝑣𝑣−𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667��1−𝑘𝑘𝑠𝑠𝑣𝑣�=𝑇𝑇𝑙𝑙∗16 𝐺𝐺𝑅𝑅               (10)  

From the data in Figure 7, the dynamic gear tooth sliding friction coefficient is derived to be 0.33, which is consistent with the static sliding friction coefficient of 0.38 extracted from the stalled torque vs current curve shown in Figure 8. The static and the dynamic gear tooth sliding coefficients are very close. To be  conservative, the static gear tooth sliding friction coefficient will be used for the subsequent analysis.    The motor bearing viscous torque model is well described analytically by the MPB torque equation [2] . It’s  assumed that the gearbox viscous torque is also modelled using the MPB torque equation (Equation 11).  

𝑇𝑇 𝑣𝑣𝑣𝑣𝑠𝑠𝑐𝑐 =𝑎𝑎∗2.4∗10−5𝑅𝑅𝑅𝑅𝑀𝑀0.67(10104.354−1.612∗𝑙𝑙𝑙𝑙𝑙𝑙10(𝑇𝑇)−0.6).67                                                               (11)  

where T is oil temperature in degree Kelvin, RPM is rotor speed in rev per minute, and a is a scaling factor to match with the measured data, which is derived to be 5.045 to match the derived composite geared motor torque constant. Figure 9 shows the geared motor viscous torque for different speeds and oil temperatures. This model uses the Brayco 815Z oil for both motor bearings and gearbox components.
285   Figure 8.  Geared Motor Stalled Torque vs Applied Current Curve  

Figure 9.  JWST Motor Viscous Torque versus Operating Temperature and Rotor Speed     y = 1.7726x -0.2865 R² = 0.9976 00.20.40.60.811.21.41.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1STALLED TORQUE, IN -OZ APPLIED CURRENT, AMPERESJWST BLDC 301 CDA -8124 Stalled Torque vs. Applied Current Primary Winding, Deploy Direction
286 To increase the fidelity of the geared motor model and its prediction, the model prediction is compared with  the no-load current versus motor rotor speed test data. The governing tor que model equation is expressed  as follows:  

 𝑉𝑉=𝑅𝑅𝑑𝑑+𝑘𝑘𝑏𝑏𝜃𝜃̇ (12)   𝑘𝑘𝑇𝑇𝑑𝑑=𝑇𝑇𝑐𝑐𝑣𝑣 +𝑇𝑇𝑐𝑐𝑣𝑣+𝑇𝑇𝑑𝑑+𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667+𝑘𝑘𝑤𝑤𝜃𝜃̇2+𝑘𝑘𝑣𝑣𝑣𝑣𝜃𝜃̇.667   (13)  By applying the linear regression analysis from E quation 13 on the measured no- load current versus motor  rotor speed as shown in Figure 10, the results from both the regression analysis and the model prediction  using system of equations are plotted in Figure 10. From Figure 10, these two curves show a remarkable  match.  

Figure 10.  No-Load Applied Current versus Rotor Speed for the Measured and Derived Data    For the deployment, the applied current and the motor rotor speed are controlled with a forward control fashion. There is no force/torque feedback control . The gearbox output torque is expected to responded   accordingly to the controlled input within a certain level of uncertainty under the imposed environmental conditions such as operating temperature, vibration induced load, humidity, etc. If the gear output  torque  exceeds a certain limit,  deployment mechanical failure will occur. On the other hand, the gear output torque  may not be sufficient to deploy the s ystem . The limit between these values sometime is small .  

The effect of motor parameter variation and environmental conditions on the geared motor output torque is  evaluated as follows.
287 Variation of Output Torque from a Given Applied Current  

The geared motor output torque equation is expressed as follows:  

   (14)  

Applying the above procedure to the rest of the motors, all motor parameters, test data, and the torque  components are calculated and shown in Figure 11. The geared motor output torque versus speed at room  temper ature and applied current of 1 ampere for three geared motors are plotted in Fi gure 12.  

From Figure 12, at the nominal operating motor rotor speed of 461 rpm, the gear motor output torque can  vary as much as 7%. The variation can be higher if the sample size becomes larger or both the primary and the redundant winding data are eval uated.   

Figure 11.  Geared Motor Parameters, Test Data, and Torque Component Values and Constants