ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
440 angular axis of rotation errors of an assembled, preloaded, duplex bearing pair. The test setup was  originally developed to determine whether ABEC 3 bearings would have sufficiently low angular runout to be used in a prototype precision pointing gimbal.   This paper will present measured angular runout data for preloaded ball bearing pairs of a unique diameter and cross section, but three separate ABEC ratings. The goal of this testing is to provide a correlation between assembled bearing runout and ABEC rating. This data will be presented in several forms, including repeatable or synchronous runout as well as non-repeatable or asynchronous runout.  [1-3]   Of particular interest to the authors are the repeatability of the angular runout errors and frequency content in terms of mechanical harmonics. The data presented will be useful for estimating angular runout during the design process and the test setup presented allows for bearing-level screening and selection based on minimizing angular runout in bearing applications.   

Figure 1. Test Setup Overview 

Test Fixture Overview   Each bearing tested was of the same diameter and cross section, so that a single fixture could be used for all testing. The test fixture consists of an aluminum housing and shaft, an integral, direct drive brushless DC motor, and an encoder for motor control purposes. The outer housing is mounted to the bench with the rotation axis parallel to gravity. Figure 2 shows both a photograph and schematic of the test fixture. The features of the housing and shaft that contact the bearing races were diamond turned in order to obtain appropriately precision bearing fits. The diameter tolerancing method is ±5 µm (0.0002 in) from the basic diameter, which permits a line-to-line contact under maximum material conditions. A benign thermal soak allows installation or removal of the bearings without applying excessive force. A mirror with a micrometer adjustable tip-tilt stage is mounted to the shaft. Bearing angular runout is measured using an electronic autocollimator.
441   Figure 2. Test Setup Description  The test setup procedure begins with aligning the mirror roughly perpendicular to the bearing axis (see  Figure 3). The autocollimator launches a reference beam, which reflects off the mirror and returns to a detector. When perfectly aligned, the reflected beam follows the same path as the reference beam upon return and has no angular difference between beams. However, introducing an angular displacement between the bearing axis and mirror normal or shaft axis will cause the reflected beam to sweep a conical path during shaft rotation, which will project a circular profile on the autocollimator detector. The nominally aligned case and an angular perturbation case are depicted in Figure 3. Recognize that if the bearing set were geometrically perfect then the trace recorded by the autocollimator would remain circular. The deviation from this perfect circle is therefore a direct measure of the bearing angular error.    

Figure 3. Measurement Method Overview
444  SN 3 (ABEC 3) SN 4 (ABEC 7)      Figure 9. Elevation vs. Azimuth Test Data Figure 10. Elevation vs. Azimuth Test Data   SN 5 (ABEC 7) SN 6 (ABEC 5, Super-Duplex)  Data Processing  It was conservatively assumed that the radial runouts of the two bearings in the duplex pair act in  opposite directions, using worst-case runout data from the ABMA standard. These predicted angular runouts are shown in Table 2. A summary of the actual runouts measured from each bearing pair is shown in Table 3. Each bearing pair significantly out-performed the expected angular runout based on this calculation method, most likely due to the fact that the bearings were installed in the test fixture with the high spot markings on each race aligned. The data presented shows that even the ABEC 3 bearings tested offer a very low level of asynchronous angular runout. It is important to emphasize that the angular runout estimation method presented in table is by no means an established approach. In fact, the data from this testing show that this estimation approach provides excessive conservatism and that the best way to determine angular runout is to perform testing on the bearings to be used. The angular runout performance of a given bearing set will depend on workmanship factors, including machining tolerances and ball size matching, but the results presented are also indicative of the order of magnitude one can expect with different ABEC rated bearings of the size range presented.  Table 2. Predicted Angular Runouts Using Different Methods 

   Angular  Runout  Summation  Method Angular  Runout RSS  Method Pitch Diameter Bearing Width Radial Runout  Inner Radial Runout  Outer  (in) (mm) (in) (mm) (in) (µm) (in) (µm) (microradian) (microradian)  ABEC 3 3.25 82.6 0.25 6.35 0.00040 10 0.0006 15 4000 2884  ABEC 5 3.25 82.6 0.25 6.35 0.00020 5.1 0.0004 10 2400 1789  ABEC 7 3.25 82.6 0.25 6.35 0.00015 3.8 0.0002 5.1 1400 1000
445 Table 3. Measured Angular Runouts  Synchronous  Error AmplitudeAsynchronous  Error AmplitudeSynchronous  Error RMSAsynchronous  Error RMS (microradian) (microradian) (microradian) (microradian) SN 1 3 116 13.0 52 3.0 SN 2 3 74 11.4 38 2.6 SN 3 3 90 8.4 38 2.0 SN 4 7 30 11.0 22 2.8 SN 5 7 88 12.6 36 3.0 SN 6 5 28 12.0 18 2.6ABEC

As shown in Table 3 & Figure 11, one of the ABEC 7 bearings exhibited unusually high angular runout.  This ABEC 7 bearing actually had higher angular runout than some of the ABEC 3 bearings. Of course the angular runout measured for this bearing does not necessarily mean that the bearing would be rejectable per the ABMA raceway groove runout requirements. It does however, demonstrate the variation that can be seen from bearing to bearing, even at higher ABEC ratings. Interestingly, the one ABEC 5 sample outperformed both ABEC 7 samples in terms of angular runout. However, the SN 6 ABEC 5 bearing had a one piece outer race which assured that the radial runout high point of the bearing set was perfectly matched eliminating any deleterious scissoring action. The inconsistency of angular runout performance serves to illustrate the importance of “cherry picking” of bearings for high-precision applications. If “cherry picking” is performed on a sample of bearings, it is important to mark the relative clocking between both adjacent inner and adjacent outer races respectively within a given duplex pair, as the race-to-race clocking can influence the angular runout performance. The cherry-picking approach may also be used to screen for linear runouts and drag torque properties. In this case, only one relative clocking between corresponding races was tested. However, it is conceivable that relative clocking could play an influential role in the angular runout performance, such that re-clocking of the inner or outer races relative to each other could increase or decrease the measured angular runout, depending on the relative orientation of the high spots between the two races. 

Figure 11. Maximum Synchronous Error Data  020406080100120140 SN 1 (ABEC 3)SN 2 (ABEC 3)SN 3 (ABEC 3)SN 4 (ABEC 7)SN 5 (ABEC 7)SN 6 (ABEC 5)Error Amplitude (microradian)
446 As shown in Figure 12, the asynchronous error was very low, and was nearly the same magnitude for  each bearing pair, regardless of ABEC rating. The asynchronous error is most likely a manifestation of the ball accuracy (sphericity) and ball-to-ball diameter matching. The later in conjunction with raceway geometry errors dictates preload variations as the balls orbit the bearing. This is one example where the performance of the bearing pair is workmanship dependant and could vary greatly from one manufacturer to another, or even lot to lot. The repeatability of the test setup is another factor. Figure 19 shows the Asynchronous error versus angle plot for SN3. 

Figure 12. Maximum Asynchronous Error Data      Figure 13. Synchronous Error Versus Angle Figure 14. Synchronous Error Versus Angle   SN 1 (ABEC 3) SN 2 (ABEC 3)   0.02.04.06.08.010.012.014.0 SN 1 (ABEC 3)SN 2 (ABEC 3)SN 3 (ABEC 3)SN 4 (ABEC 7)SN 5 (ABEC 7)SN 6 (ABEC 5)Error Amplitude (microradian)
447     Figure 15. Synchronous Error Versus Angle Figure 16. Synchronous Error Versus Angle   SN 3 (ABEC 3) SN 4 (ABEC 7) 

    Figure 17. Synchronous Error Versus Angle Figure 18. Synchronous Error Versus Angle   SN 5 (ABEC 7) SN 6 (ABEC 5) 

Figure 19. Asynchronous Error Versus Angle
448 SN 1 (ABEC 3) 

A Fast Fourier Transform (FFT) analysis of the data reveals dominate spikes at 1, 2, 3, and 4 cycles per revolution. The largest and most consistent spikes occur at 3 cycles per revolution. The ball pass frequency and ball spin frequency for the bearings tested are all above 10 cycles per revolution. The large spikes at 2, 3, and 4 cycles per revolution and absence of any significant spikes above 10 cycles per revolution indicate that the angular runout of the bearings is dominated by race machining tolerances rather than ball out-of-roundness. Typically, when bearing raceways are machined, a tri-lobing of the race is the largest source of machining error. This is consistent with the dominance of the 3 cycles per revolution FFT spikes.                 

Figure 20. Magnitude vs. Cycles Per Rev Figure 21. Magnitude vs. Cycles Per Rev   SN 1 (ABEC 3) SN 2 (ABEC 3) 

Figure 22. Magnitude vs. Cycles Per Rev Figure 23. Magnitude vs. Cycles Per Rev   SN 3 (ABEC 3) SN 4 (ABEC 7)
449               

Figure 24. Magnitude vs. Cycles Per Rev Figure 25. Magnitude vs. Cycles Per Rev   SN 5 (ABEC 7) SN 6 (ABEC 5) 

Lessons Learned 

An economical bearing fixture was initially fabricated using standard lathe tolerances, in order to determine if exotic feature grinding was necessary. After processing the initial test data, it was determined that the fixture diametral clearance to bearing race was excessive, which was made evident by a cycle-to-cycle trace precession and large asynchronous error. The error trace precession reversed directions, corresponding to the bearing rotation direction. It was concluded that the economical fixture did not provide adequate relative concentricity control between the duplex pair races. The second bearing fixture, which is the one presented in this paper, had decreased the asynchronous error substantially over the economical fixture and proved that bearing mount tolerances have a large influence over the shaft runout performance to levels similar to the bearings themselves. It can be concluded that it is imperative that bearing mount features be precision machined and ground even when using ABEC 3 bearings and especially for slim section angular contact pairs. Test results showing relatively low asynchronous error of all three ABEC 3 bearings came as a pleasant surprise. Testing additional quantities beyond those presented is, of course, desirable for statistical data processing. From a design standpoint, the data gathered from this testing may allow much more economical ABEC 3 bearings to be used, while still meeting the same design requirements that based on the predicted angular runout, would have required ABEC 7 bearings. This serves to illustrate the development testing benefits, which lead to the relaxation of requirements and ultimately cost savings. Although designing for the worst-case predicted angular runout would have resulted in a conservative design, it would have unnecessarily driven the design to excessively tight tolerances and excessively expensive bearings.    Conclusions   Three ABEC qualities were measured for synchronous and asynchronous runouts. Although bearings with a higher ABEC rating did correlate with lower measured synchronous runout, it was also observed that asynchronous runout was relatively consistent, independent of the ABEC rating. Also bearings had significantly lower angular runout than estimated using ABMA individual race tolerances. This confirms that such analytical estimates are not a viable substitute for actual runout measurements of the assembled bearing set. Finally, in the case of ABEC 7 bearings, the behavior of two bearings acquired at the same time, from the same vendor and to the same part number did not show consistent performance. For this reason, it is recommended that for critical applications, all bearings be tested prior to assembly and that appropriate spares are procured, if the application demands superior performance consistency.
450 Acknowledgements  The authors would like to thank their Lockheed Martin colleagues, including Kyle Brookes for his role in  the design of the bearing test fixture and for the technical review provided by Dr. Jean-Noel Aubrun and Dr. Ken Lorell.   References   1. ISO-230-7,  “Geometric accuracy of axes of rotation” and ASME  B89.3.4-1985,  “Axes of Rotation,  Methods for Specifying and Testing.”  2. Marsh Eric and Grejda, Robert “Experiences with the Master Axis Method for Measuring Spindle Error Motions,  Precision Engineering 24 (2000) 50–57 

3. "Bearing Runout Measurements" Agilent Technologies, Applications Note 243-7. 

4. Harris, Tedric A. and Kotzalas, Michael N.  "Advanced Concepts of Bearing Technology" CRC Press,  5th edition (2007), p182 .   5. Weiss, Jeffrey R. "Rolling Element Bearing Metrology" Penn State University Thesis, May 2005 .
451 LightSail-1 Solar Sail Design and Qualification 

Chris Biddy* and Tomas Svitek* 

Abstract 

LightSail-1, a project of The Planetary Society, is a Solar Sail Demonstration mission built on the CubeSat platform. Stellar Exploration Inc. designed, built and fully qualified the Solar Sail module for LightSail-1 which includes a boom deployer mechanism that stows a total boom length of 16 meters (4 x 4 meter booms) which are used to deploy a 32-m 2 sail membrane in a 2U package. This design utilizes the rigid  TRAC boom developed by AFRL (Air Force Research Laboratory) for deploying and tensioning the membrane that makes up the sail. In order to maximize the size of the solar sail, the boom deployer took on a unique shape to maximize packaging efficiency and achieve an 80:1 deployed to pre-deployed ratio. This paper will discuss the design challenges, unique design features as well system verification for LightSail-1.    Introduction  LightSail-1 is a project of The Planetary Society and is privately funded by members of the organization (Figure 1). The Planetary Society has been a proponent of solar sails for many years and the LightSail program is dedicated to advancing solar sail technology.   The main objective of LightSail-1 is to demonstrate the viability of solar sails by demonstrating a positive  change in orbit energy, the ability to manage the orbit energy, and to control the spacecraft under solar sail power. These objectives will be achieved by developing and demonstrating key technologies such as sail deployment and sail material management during flight as well as the control of the spacecraft's attitude. 

Figure 1. Artist rendering of LightSail-1 (The Planetary Society).  LightSail-1 follows work done for The Planetary Society on another program called COSMOS-1 which was also a solar sail demonstration mission. Unfortunately COSMOS-1 failed to reach orbit due to launch vehicle failure. COSMOS-1 was ~100 kg and had a total sail area of ~600 m 2. This gives COSMOS-1 a  solar sail characteristic acceleration (a common metric for evaluating solar sail performance) of  0.047  mm/s2.                                                              * Stellar Exploration, San Luis Obispo, CA 

Proceedings of the 41st Aerospace Mechanisms Symposium, Jet Propulsion Laboratory, May 16-18, 2012
453   Figure 2. TRAC boom.  The TRAC boom collapses and is then rolled around a drum so it can be stored in an annular space. The  TRAC boom has a self-deploying feature due to the stored strain energy in the boom while collapsed and rolled around the drum. This collapsible and rollable feature of the TRAC boom allows it to be stored in a very compact fashion. Due to the constraint imposed on the individual metal strips by the weld bead, the minimum bend radius is driven by the maximum strain of the material.  The sail storage section consists of a section with a wedge shaped cavity cut on each of the four faces.  Also included is a hole passed through the center of the section for the routing of the wire harness to connect the avionics board in the top of the spacecraft to the sensors and deployer motor housed in the payload section. This configuration was driven somewhat by the requirement to have P-POD interface rails at least 75% of the overall length of the spacecraft (Figure 3). 

Figure 3. LightSail-1 layout.  The sail folding concept consisted of z-folding the sail in two directions while varying the fold widths from the center to the outside tips to take a wedge shaped cross-section matching the sail storage cavity (Figure 4).
454   Figure 4. Sail Folding Procedure.  Prototype sails were built to empirically determine the magnitude of the fold height and width tolerances  that were required, (and reasonable from a manufacturing standpoint) for the proper fitment into the sail storage cavity.  

Figure 5. Sail test-fit in engineering structure.  The design of the sail was such that it had a slight interference fit in the sail storage cavity for sail management purposes during deployment. The idea being that each fold would be pulled out of the sail storage cavity one by one as the booms were deployed while the rest of the folded sail material was held in place. This would insure that the sail material would not billow from the cavity and potentially tangle around a deploying boom or get caught in the deployer and fail to deploy properly (Figure 6).  

Figure 6. Sail behavior during deployment.
455 The sail-to-boom connection is made using metal grommets in the sails and booms with split rings and  extension springs in series as shown in Figure 7. The extension springs are required to maintain an appropriate tension in the sail during thermal cycling. 

Figure 7. Sail to Boom connection feature.  Deployer Design  The deployer has four main functions: (1) Provide an attachment point to the boom to react all deployment loads (2) Protect the booms from yield due to strain (3) Store the 4m TRAC booms within the CubeSat allowable cross-section, (4) Provide smooth unrestrained deployment of the TRAC booms and Sail material.   The deployer is made up of a simply supported spindle mounted between two plates that the booms are  attached to. The booms are clamped to the spindle and held with two stainless steel #4-40 bolts. This feature provides the attachment point for the booms and takes all the boom reaction loads. The spindle and clamp are machined with a flare at the bottom so as to not completely pinch the booms while mounted to the spindle. This increases the area moment of inertia of the boom over the pinched configuration providing a better boom root condition. The spindle flanges constrain and protect the booms from contacting any non-moving surfaces during deployment. The spindle with flanges and clamps are shown in Figure 8.   

Figure 8. Spindle with boom clamps and flanges.
456 The rest of the deployer assembly contains four Tensioner Assemblies that are arranged between the two  plates 90˚  from each other as well as multiple Delrin rollers mounted near the four corners, and four  flexure clamp assemblies mounted adjacent to the Delrin Boom Exit Guides. These components are shown in Figure 9. 

Figure 9. The deployer assembly with booms not shown.  As mentioned above, the booms require the application of a normal force to first collapse the boom into  its pinched configuration and then to force the boom to roll around the drum. This is accomplished with the tensioner which uses the reaction force of a deflected cantilever flat spring against the flexure contact pin. The force on the flexure contact pin produces a moment on the tensioner body which pivots around two shoulder screws with Delrin bushings. This moment is reacted at the Boom Roller causing a normal force against the boom wrap. The flexure spring passes though the space between the shoulder screws and contacts the contact pin mounted in the tensioner. Standoff rollers are used to isolate the boom wrap from the metal tensioner body and shoulder screw heads. The tensioner assembly is shown in Figure 10. 

Figure 10. Tensioner Assembly.  Figure 11 shows a top view of the deployer in the fully deployed configuration with the top plate and spindle flange transparent, and the booms not shown for clarity. This fully deployed configuration refers to the state when the booms are just beginning to be rolled around the spindle to be stowed, or at the end of deployment.
457   Figure 11. Tensioner orientation at  full boom deployment with the flexure springs in the relaxed  state (red arrows indicate the path of the booms).  As the booms are wound around the spindle, the increasing outside diameter of the boom wrap pushes  the contact roller on the tensioner outward increasing the deflection of the flexure spring. As the boom wrap thickness reaches its maximum outside diameter and the flexure spring reaches its maximum deflection, the tensioner assembly is stowed within the CubeSat allowable cross-section as shown in Figure 12.  

Figure 12. Tensioner orientation for stowed booms with flexure spring at maximum deflection (red  arrows indicate the path of the booms).  The “rocker-arm” configuration of the tensioner allows for very compact packaging by taking up area around the boom wrap and not protruding past the allowable CubeSat cross-sectional area while in the stowed configuration. The deployer and elegant design of the TRAC boom resulted in a deployed to pre-deployed ratio of 80:1 since the packaged cross-section is 0.1 m x 0.1 m and the deployed boom length, tip to tip, is 8 m.
458   Figure 13. Deployer with top plate and flanges transparent to show booms in fully deployed  configuration.  Development testing of the boom deployer assembly consisted of measuring the drive motor current  required to deploy the booms while varying parameters within the deployer including the flexure spring rate, and coefficient of friction between adjacent boom wraps. This testing revealed a strong correlation between the required motor drive current required to deploy the booms and (1) the coefficient of friction between the adjacent boom wraps, and (2) the flexure spring thickness. It was discovered that a large coefficient of friction was desired between adjacent boom wraps because a higher axial force could be transferred from the drive motor through the boom wrap to the deployed length of the boom. Since the sails had a slight interference fit with the sail storage cavity a small axial force was imparted on the booms in order to pull the sail material out of the cavity and unfold it. Initially this axial force would cause ballooning of the boom wrap inside of the deployer. This ballooning was controlled with a higher spring rate on the flexure spring which exerted a larger normal force on the boom wrap keeping it contained. This was critical for achieving reliable deployment of the sail. 

Figure 14. Flight deployer and payload as sembly in fully stowed configuration.
459 Figure 14 shows the deployer and payload section in the flight configuration with the booms fully stowed.  Figure 15 shows the spacecraft fully assembled (with engineering deployable solar cell panels). 

Figure 15. LightSail-1 fully assembled.  System Validation  System validation consisted of full-scale sail deployment tests before and after random vibration testing, and TVAC testing while monitoring the drive motor current as the performance metric. Cold full-scale sail deployment tests while monitoring motor drive current were conducted as well to verify cold deployment performance. In order to conduct sail deployment tests a method of off-loading was required to simulate a zero-g environment. This was accomplished by building a deployment table to support the weight of the booms and sail during testing. The table is shown in Figure 16 and features removable panels in order to access the spacecraft while the sail and/or booms are deployed.  

Figure 16. Sail deployment table.