ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
132 Table 2.  Stowed natural frequencies 

Mode  Frequency (Hz)  Mode  Frequency (Hz)    1 37.88  6  62.92   2 48.69  7  69.23   3 51.83  8  76.58   4 52.68  9  82.42   5 57.46  10  85.28  

Deployed Stiffness Analysis and Test 

A deployed nonlinear FEM was created to determine the deployed stiffness, natural frequencies, and its load capability. The nonlinear FEM was used to determine the deployed stiffness under different load conditions and was validated by test. Measurements were performed on the deployed TTM to characterize its stiffness under different loading conditions. The test setup consisted of the deployed mast offloaded with a total of 17 helium balloons. Each balloon was attached to the tip end of their respective tubes as shown in Figure 7. The lift of the individual balloons was adjusted to the mass of the supported tube sections. The tip load was applied with a motorized slide mechanism that had a load cell and  position transducer attached.  

Figure 7.  Deployed stiffness test configuration 

 Baseline Tip Load – No Preload  A baseline tip load test was performed with no preload. For this test, the mast was loaded in shear only at the tip to the levels shown in the plot in Figure 8. The blue curve in the figure shows the load-deflection characteristics of the mast with zero preload. The red line represents the predicted performance of the mast. The TTM measured stiffness correlates well with predictions, however it is lower at low amplitude and is higher at high amplitude compared to the predictions.
133   Figure 8.  Plot of tip displacement versus load for the no preload load case 

 Deployed Preload Condition  The deflection of the fully deployed mast due to the application of a tip preload was also characterized. This type of loading generally relates to typical flexible solar panels or sun-shields under tension. The test configuration is shown in Figure 9. A typical 55.6-N (12.5-lb) load was applied in the direction shown at the tip and the resulting deflection was measured at the tip.  

Figure 9.  Deployed preload condition 

The results of the preloaded test are shown in Figure 10. For this test, the mast was loaded with a 55.6-N (12.5-lb) tethered load, which creates an axial, shear, and moment load, and then an additional shear load was added at the tip to the levels shown in the plot. In this plot, zero deflection corresponds to the deflected shape under the tethered load, which was 13.8 cm (5.45 in).    -4-3-2-101234 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 - 1 8 - 1 6 - 1 4 - 1 2 - 1 0 - 8 - 6 - 4 - 2 02468 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8Load (N) Deflection (cm)
134 Figure 11.  First eight deployed modes The red line represents the predicted performance of the mast. This line shows the predicted tip  deflection of 12.7 cm (5.0 in) under the tethered load versus the 13.8 cm (5.45 in) observed in the test. It was observed from this test that lower than predicted stiffness occurred at lower loads while higher than predicted stiffness occurred at higher loads.   Figure 10.  Plot of tip displacement versus load for th e preload condition     Deployed Natural Frequency Analysis 

A linear FEM was created from the nonlinear model with applied tethered loads to compute the natural frequencies. The fundamental computed natural frequency is 0.1 Hz which meets the 0.1 Hz requirement. Note the mode shape is orthogonal to the plane of load application where the boom stiffness is at minimum stiffness region. The first eight deployed natural frequencies are listed in Table 3 and the mode shapes are shown in Figure 11. Note that these frequency results have not been validated by a modal test. A detailed view of the deployed FEM is shown in Figure 12.  

-3-2-101234 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25Load (N) Deflection (cm) Figure 12.  Deployed FEM
135   Table 3.  Deployed natural frequencies 

Mode  Frequency (Hz)  Mode  Frequency (Hz)    1 0.10 5  1.56  2 0.15 6  2.09  3 0.56 7  3.09  4 0.77 8  4.09 

Deployment Characteristics and Control   The goal was that the TTM should be deployed within 15 minutes. It is desirable to have a constant velocity during the deployment or retraction; however, due to friction, external tip loads, and latch up loads the velocity fluctuates. Also, the friction and latch up forces fluctuate during the deployment/retraction depending on the individual segments. A typical resistive force during a segment latch up is show in Figure 13.  

Figure 13.  Typical latch loads during deployment 

 The drive system is a STEM deployer powered by either a brushless dc motor or a stepper motor which pushes against the tip plate. The STEM deployer inherently has large dead band due to the winding/unwinding of its STEM element around the spool, therefore each time the motor changes its direction it can not affect the deployment/retraction for while. Hence the feedback control system (required for brushless dc motor application) should minimize the motor reversal during the deployment operation. Finally, it is desirable to limit the average velocity.      -0.20.00.20.40.60.81.01.2 05 0 1 0 0 1 5 0Normalized Load Time (sec)
136 Deployment Drive Feedback Control System  To achieve the deployment criteria, a feedback control system containing the following is considered (see  Figure 14):   Position loop  Velocity loop inside the position loop  Feed forward time dependent velocity profile - trapezoidal   Time dependent reference position – integral of velocity profile  Both velocity and position loops should be:  o Stable for minimum inertia due to the backlash (motor inertia only) as well as maximum  inertia  o Open loop frequency bands should be less than 70% of the structural natural frequency  o Nonlinear gains used in both position and velocity loops  o Gain and phase margins should be greater than 10 dB and 40 degrees respectively   Current limit is required to prevent high deployment force    

Figure 14.  Control system block diagram     In Figure 14, V tr is the translational drive reference velocity, Td is the approximate differentiator time  constant, L is the motor inductance, R is the motor resistance, τe is equal to L/R, kT is the motor torque  constant, and kb is the back emf constant.   The gains for the control system are: k p is the position loop gain, kv is the velocity loop gain, and kR is the  resolver gain. It is desirable to have nonlinear gains in both the position and velocity loops in order to  prevent the motor reversal caused by back winding in the STEM. A possible nonlinear control gain that can be implemented is a piece-wise linear gain that is high gain for lag and low gain for lead.  The TTM is a time variant system and, because of this, there are non-conservative forces during the deployment. These forces become significant as the deployment velocity and acceleration increases
137 [2,4]. A similar feedback control system was designed and tested for the Space Station Freedom Mobile  Transporter [2,3]. For the Mobile Transporter, an avionics control breadboard simulator was designed to simulate and verify the operation of the Mobile Transporter control system.  The following dynamic models are used to derive the TTM system state space matrix [A,B,C,D]. Note that during deployment the length of the TTM is changing causing a change in natural frequencies.  Primary Dynamic Model  The primary dynamic model used for the design of the control system is shown in Figure 15. This model  represents the deployment and axial vibration of the TTM. The moving mass M is the mass of the  deploying tubes plus the mass of the payload and fresistive  are loads due to friction, tube latching, and any  external loads such as sun-shields tension and/ or space craft attitude control. For the STEM deployer, k STEM is the axial stiffness of the partially deployed STEM and varies by length, θm and θs are the rotation  of the motor and spooler, respectively, Jm and J s are the inertias of the motor and spooler, respectively,  and n is the gear ratio. 

Figure 15.  Dynamic model for control system    The equations of motion for the STEM deployer and the system of deploying tubes shown in Figure 15 are   resistive STEM f x x k x M   0 1 1                                                     (1)   The axial natural frequency changes as the STEM deploys and the boom length changes. A plot showing the change in axial natural frequency as the system deploys and the length increases and moving mass of the tubes decreases is shown in Figure 16.
138  

Figure 16.  Plot of axial frequency versus deployed tube bays 

 Secondary Dynamic Model  The secondary dynamic model used for the design of the control system represents the lateral vibrations of the TTM during the deployment. This can be represented by an axially moving cantilever beam with a tip mass as shown in Figure 17.   

Figure 17.  Cantilever beam with tip mass and time dependent length 

 The equation of motion for the system shown in Figure 17 for a cantilever beam whose length changes with time is given by [2]   0) (6857 . 0) (8 . 4 028 . 1 ) (12 35334 ) (35332 3                ut Lmat LM m t LEImu M t mLtip tip          (2) 

where u is the velocity of the moving beam, a is the acceleration of the moving beam, EI is the bending  stiffness of the beam, m is the mass of the beam, L(t) is the instantaneous length of the beam, Mtip is the  tip mass and η  is the normal coordinate representing the lateral displacement y. Note that equation (2)  has non-conservative forces which could become important depending on the deployment velocity and  acceleration.  00.20.40.60.811.2 0123456789 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7Normalized Frequency Deployed Bay
139 If the velocity and accelerations are small, equation (2) reduces to 

0 ) (124 ) (3533 3     t LEIM t mLtip                                                (3) 

Control System Simulation  A simulation of the control system was performed using Simulink. A resistive force representative of the one shown in Figure 13 is used to simulate latching loads. Non-linear control gains are used for the position and velocity loop gains and a deadband of ±7.6 cm (3 in) is used.  Simulation results for the TTM deployment are shown in Figures 18 and 19. Figure 18 is a plot of velocity versus time and includes deadband in the system. Figure 19 is also a plot of velocity versus time, but does not include deadband in the system. In both plots, time is in seconds and velocity is in meters per second.   

Figure 18.  Velocity versus time plot with deadband 

Figure 19.  Velocity versus time plot with no deadband
140 Summary  

A deployable and retractable telescoping boom that contains large-diameter, thin-walled composite tubes  has been developed that is capable of high deployed stiffness. Tapered pins are used to control the deployment and retraction between the tubular sections and create a stable extended structure when deployed. The latch design and STEM work together to eliminate the need for segments to overlap when deployed giving a lightweight design.    The key parameters and requirements for the TTM study are given, and it is shown by analysis and test that the requirements are met. Frequency analysis on the deployed and stowed configurations was performed using FEA software to show that the frequency requirements are met. Testing was also performed on the deployed TTM to characterize the stiffness under different loading conditions. In all the load conditions, lower than predicted stiffness occurred at lower bending loads and higher than predicted stiffness occurred at higher loads.  Control of the deployment drive for the TTM presents several challenges due to the design of the STEM actuator and the latching loads during deployment. To analyze the system, a dynamic model was developed that includes the deploying tubes and the STEM motor and spooler. The equations of motion for the system were derived and a feedback control system was designed. The work done to date and the progress made on the TTM system are presented here.    References   1. Thomson, M.W. “Deployable and Retractable Telescoping Tubular Structure Development.”  Proceedings of the 28 th Aerospace Mechanisms Symposium  (May 1994).   2. Mobrem, Mehran and Mark Thomson. “Control Design of Space Station Mobile Transporter with  Multiple Constraints.” First Joint U.S./Japan Conference on Adaptive Structures , (November 1990),  pp. 87-116.   3. Mobrem, M., Paden, B., Bayo, E., Devasia, S., “Optimal Output-Trajectory Tracking: Application to  Mobile Transporter Avionic Breadboard.,” AIAA Guidance, Navigation, and Control Conference and Exhibit, (August 2000) 

4. Taborrok, B., Leech, C.M., Kim Y.I., “On the Dynamics of an Axially Moving Beam,” Journal of the  Franklin Institute , Vol. 297, No. 3, (1974), pp. 201-220.
141 Development of Variable Reluctance Resolver for Position Feedback  

Greg Leibovich* and Sara Senanian* 

Abstract 

The variable reluctance resolver (VRR) is commonly used in the automotive industry as a rotor position sensor. Its use in the Aerospace and Defense Industries has been limited due to inadequate accuracy performance. However, recent interest in the Aerospace Industry for VRRs as a viable alternative to conventional resolvers has driven the development of higher accuracy VRRs for use in angular position feedback applications. This paper presents the progression in the development of the VRR and provides information on the lessons learned during the completion of the first generation of single speed and multi-speed engineering units of VRRs. This first generation of engineering units was evaluated to identify potential design and manufacturing process improvements. Incorporating the lessons learned from the development of the first generation units resulted in an improvement in performance and manufacturability in the second generation of VRRs, making it a desirable option for future use in commutation of brushless DC motors.    Figure 1. Single-speed (left) and multi-speed (right) variable reluctance resolvers     Introduction   Resolvers are rotary motion feedback sensors used to provide angular position detection in a wide variety of environments; space, defense, automotive and oil exploration. For decades, conventional resolvers have been used for high precision mechanism position feedback and commutation in a range of adjustable speed drives; vector control induction motor, switched reluctance motor and brushless DC motor drives. Besides resolvers, optical incremental encoders and potentiometers offer an alternative solution for position sensing by producing precise incremental position information. However, optical encoders are susceptible to vibration, debris and high temperatures. Potentiometers are easy to use; however the potentiometer contains an electrically conductive wiper that slides across a fixed resistive element causing the possibility of considerable wear. Hence the life cycle of a potentiometer is limited and its sensitivity to vibration is of significance. Resolvers do not depend on moving electrical contacts for signal reliability and do not exhibit significant aging or changes to performance due to extreme temperatures or vibration.                                                                * Ducommun LaBarge Technologies, Carson CA 

Proceedings of the 41st Aerospace Mechanisms Symposium, Jet Propulsion Laboratory, May 16-18, 2012
142 In addition, conventional resolvers transmit high accuracy angular data electrically in the thousands of a  degree (arc-seconds) and consist of a stator, a rotor and a transformer assembly; each with its own winding as seen in Figure 2. Nonetheless, the conventional resolvers are intricate to manufacture and therefore labor intense and costly. Furthermore, in larger conventional resolvers, the transformers have been observed to delaminate and are difficult to rework or replace. The high cost and manufacturing complexity of conventional resolvers lead to the development of variable reluctance resolvers .   Unlike a conventional resolver, the VRR has no need for rotary transformer and it consists of a simpler design. All windings are located on its stator assembly whereas in conventional resolvers the stator core, rotor core, stator transformer and rotor transformer each contain windings as labeled in Figure 2.   Figure 2. Conventional resolver with transformer   Furthermore, the study and experiments conducted by the Ducommun Team resulted in an improvement in the accuracy of the VRR making them competitive to convention resolvers particularly for the commutation of brushless DC motor drives in the Space and Defense Industries. This paper documents the development and qualification of the VRR for use in commutation of brushless DC motors that minimizes envelope size, mass and increases reliability.   The purpose of development of VRR  1. Provide resolver architecture for continuous operation without rotary transformer 2. Reduce amount of magnetic components and windings 3. Decrease the manufacturing complexity and fabrication cost  4. Reduced envelope size and mass   The VRR was developed to meet the following accuracy requirements:  1. Single speed accuracy to be less than 30 arc-minutes  2. Multi-speed accuracy less than 6 arc-minutes   Background 

The VRR consists of stator core and a rotor core and is unique in that its rotor core is slot-less with no  windings. Unlike conventional resolvers, the VRR is based on variable reluctance between the stator and rotor segments. The voltages of the output windings of the resolver vary as sine and cosine functions of the rotor angular position. The VRR is structured to vary the reluctance of the magnetic path between the  stator and rotor core in accordance with equation (1) through the change in the length of the air gap ( l) or  the area of the air gap ( A). From equations (2) and (3) it is easily determined that the variation in  reluctance causes a change in the induced voltage in the sense windings. Therefore, varying the air gap
143  or coupling area will cause a variation in the reluctance and consequently cause a change in the voltage  outputs.    ൌ	௟ ఓ஺                                                                           (1) 

Φൌ	௠௠௙ ௠௔௚௡௘௧௜௖	௥௘௟௨௖௧௔௡௖௘ൌ	ே௜ ࣬2) 

ௗథ ௗ௧  (3)  Where 	࣬is the magnetic reluctance; ݈ is the length of the air gap; ܣis the area of the air gap; Φ is the  magnetic flux and ݁is the induced voltage.    For a multi-pole configuration, as seen in Figure 3, the structure is such that the variation in the length of the air gap between the stator and the rotor produces sinusoidal variations in the output voltages.            Figure 3. Structure of multi-speed variable reluctance resolver   For absolute position feedback a single speed variable reluctance resolver is used, which consists of a couple-pole configuration. The configuration of a couple-pole VRR varies the reluctance through the variation in the coupling area between the stator and rotor core segments. A unique circular rotor core is supported by two non-magnetic members, as seen in Figure 4. The rotor core provides a diametrical diagonal magnetic path from upper half of stator core to the lower half of stator core as illustrated below.    Figure 4. Structure of single-speed VRR     Development of Single Speed Variable Reluctance Resolver    Description of first generation single speed VRR  The architecture of the first generation single-speed VRR, as seen in Figure 5, consisted of two laminated stator cores and a single laminated rotor core. Each stator core, made of high permeability laminations, were stacked, bonded and insulated.
144   Figure 5. First generation single speed VRR  

The two stator cores were then inserted into the back iron and aligned and then bonded to the back iron. The excitation winding was placed between the two laminated stator half cores diametrically, as shown in Figure 6, and the sense winding was inserted through both cores axially.   Figure 6. Architecture of the single speed VRR 

The rotor core consisted of high permeability laminations, which were stacked and placed on a temporary hub against spacers on either side of the lamination stack and were bonded. The rotor core was designed as a laminated core in order to minimize rotor reluctance since a solid rotor has high reluctance due to eddy current losses. The laminated rotor core produced a high enough transformation ratio of the output voltage to the input voltage.   Shortcomings of first generation single speed VRR  During the manufacturing process and the functional testing, the following were issues which called for  design improvements:   The manufacturing process for the rotor core was extensive and consisted of several machining  steps. After the rotor laminations were bonded lamination-to-lamination and lamination-tospacers, the rotor assembly was machined on the outer diameter (O.D.), then removed from fixture and ground on the inner diameter (I.D.). Finally the rotor assembly was bonded to a hub and its O.D. ground to final dimension to improve concentricity.  The several machining processes introduced various stresses to the assembly and jeopardized the bonding adhesive; which introduced de-laminations of the rotor core.    The thickness of the insulation on the stator cores was inconsistent which contributed to the tolerance stack-up of the stator cores in the stator assembly. Furthermore, the insulation used which was Scotchcast Electrical Resin #260 (3M) was observed to chip off the stator teeth during testing and handling of the VRR.

 During accuracy testing, the accuracy of the single speed VRR was initially found to be  approximately 85 arc-minutes as highlighted in Table I, which was much greater than the design