ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
where K is a generalized stiffness term considering the nonlinear load-deflection characteristic of a bearing  system as described in Figure 2 and Figure 3, and L is a generalized loss term catering for viscous damping,  contact interface friction and other dissipative effects. Thus, the loss term manifests itself in the form of  hysteresis between the load-deflection curves for the two motion directions.  Figure 7. Output acceleration PSD for the hard preload unit (left) and soft preload unit #3 (right)  Figure 8. Quality factor and resonance frequency vs. excitation magnitude  The corresponding results are presented in Figure 10, including the modelled load-deflection curves. The  hard preload unit reacts in an almost perfectly linearly form (also acknowledging the rather high preload).  The hysteresis and, hence, the corresponding loss term is very small. The dummy mass and shaft load  reaches ~1200 N, which is about 7.5 times the bearing preload. Therefore, considerable gapping is  occurring in the bearings, however the transition to and from the gapping state appears entirely smooth.  Only one of the soft preload units (#3) is presented for brevity. As the main difference compared to the hard  preload case, the load (and, hence, the stiffness) evolves in a much more nonlinear way over the entire  deflection range, as expected. The bearing system enters the gapping state (= “compliant range” in spring  compression direction) at approximately 50 N, which is around 2.5 times the preload. However, in the spring  relaxation direction, the gapping state is left at around 20 N, i.e. at the preload. Such discrepancy may be  explained by a combination of elastic spring force and viscous damping and interface friction forces at the  Belleville washers. Evidently, a considerable amount of energy is dissipated in the gapping process and  the interaction with the preload spring. 700 800 900 1000 1100 1200 1300 1400 1500 1600 Frequency [Hz]10-410-310-210-1100101102Dummy mass acceleration PSD [g2/Hz]1.113 grms 1.574 grms 2.226 grms 4.452 grms 6.296 grms 8.904 grmsInput levels 100 1000 Frequency [Hz]10-610-510-410-310-210-1100101Dummy mass acceleration PSD [g2/Hz]1.113 grms 1.574 grms 2.226 grms 3.148 grms 4.452 grms 6.296 grms 8.904 grmsInput levels 1 2 3 4 5 6 7 8 9 Input excitation magnitude [grms]260280300320340360380400420Resonance frequency [Hz] 3.544.555.56 Quality factor [-]Test unit #3 resonance frequency Test unit #6 resonance frequency Test unit #3 quality factor Test unit #6 quality factor NASA/CP—2018-219887 89
Figure 9. Steady-state response of the hard preload unit (left) and soft preload unit #3 (right), constant  frequency excitation with increasing amplitude  Figure 10. Quasi-static force vs. deflection for hard preload (left) and soft preload (#3, right)  Time Domain (for random vibration input)  For the random vibration tests, the histograms of the input and output accelerations have been analyzed to  infer on the underlying statistics. Figure 11 shows the histograms for the hard preload unit and increasing  levels of excitation. The hard preload unit maintains a normally distributed output (no skewness) across all  excitation levels applied, even when high peak amplitudes (and therefore gapping) are reached. The red  curve represents a best-fit analytical model of a normal distribution.  Figure 12 shows the histograms for one of the soft preload test units. For low levels of excitation, any  distortions (as identified via skewness) remain small. However, the response gets more and more skewed  (asymmetric) with increasing input power. In this context, the left side of the histogram corresponds to the  gapping state. For high-level excitation (see right histogram), two modes become evident as spiky features.  They correspond to the compression and relaxation processes of the preload spring. Furthermore, when  the shaft hits the snubber, the load increases rapidly, which may be noticed as the elevated left-side tail of  the histogram. The right-side tail of the distribution corresponds to the stiff range of bearing compression.  In fact, the highest bearing loads are reached in that region.   A common practice to approximate the response RMS level can be found with the Miles formula [7]. Using  the resulting RMS value (standard deviation), a 3σ value can be calculated and used to size the bearings.  Table 2 summarizes the number of dummy mass acceleration samples (and indirectly, the bearing forces) 0 1 2 3 4 5 6 Time [ms]-80-60-40-20020406080Dummy mass acceleration [g]2.4 g 3.6 g 4.8 g 7.2 g 9.7 g 14.5 g 19.3 g 29 g 38 g 58 g 0 2 4 6 8 10 Time [ms]-15-10-50510Dummy mass acceleration [g]0.2 g 0.3 g 0.4 g 0.6 g 0.8 g 1.2 g 1.6 g 2.4 g -15 -10 -5 0 5 10 15 Deflection [ m]-1000-800-600-400-20002004006008001000Dummy mass load [N]Static load deflection curve (K) 58 g 38 g 29 g 19.3 g 14.5 g 9.7 g 7.2 g 4.8 g 3.6 g 2.4 g -20 -15 -10 -5 0 5 10 15 20 Deflection [ m]-200-150-100-50050100150200Dummy mass load [N]Static load deflection curve (K) 2.4 g 1.6 g 1.2 g 0.8 g 0.6 g 0.4 g 0.3 g 0.2 g NASA/CP—2018-219887 90
that are greater than the related 3σ value. For this purpose, the natural frequencies and quality factors for  small levels of excitation have been applied in Miles formula. Because the 3σ rule is based on the fact that  only 0.27% of the samples will be higher (normally distributed samples), it becomes evident that this rule is  only valid for the hard preload unit, for the specific cases investigated.  The dummy mass acceleration can be related to the dummy mass load and, hence, to the bearing loads.  On this basis, using the bearing design parameters, the model can deliver the Hertzian contact stress in  the ball-race contacts (equal load distribution among all balls in axial direction). The maximum Hertzian  contact pressure reached during in the tests (estimated via the maximum output acceleration) are compared  to those obtained via the predicted 3σ values in Table 3. It can be seen that the extreme value events are  significantly higher than what would be predicted with the Miles formula (even for the hard preload unit,  although the predictions are closer).   Figure 11. Histograms of the output acceleration for random excitation 2.2, 4.5 and 8.9 g rms (hard preload unit)  Figure 12. Histograms of the output acceleration for random excitation 1.1, 2.2 and 4.5 g rms (soft preload unit #3) -2000 -1000 0 1000 2000 Dummy mass load [N]00.511.522.5310-3 Input level 2.2 grms -2000 -1000 0 1000 2000 Dummy mass load [N]00.511.522.5310-3 Input level 4.5 grms -2000 -1000 0 1000 2000 Dummy mass load [N]00.511.522.5310-3 Input level 8.9 grms Input level 1.1 grms -400 -200 0 200 400 Dummy mass load [N]00.0050.010.015Input level 2.2 grms -400 -200 0 200 400 Dummy mass load [N]00.0050.010.015Input level 4.5 grms -400 -200 0 200 400 Dummy mass load [N]00.0050.010.015 NASA/CP—2018-219887 91
Table 2. Percentage of output acceleration samples exceeding the related 3σ value  Test unit  ID 1.1 g rms 1.6 g rms 2.2 g rms 4.5 g rms 6.3 g rms 8.9 g rms #3  (soft) 1.04% 0.62% 0.78% 1.54% 3.07% 5.51%  #6  (soft) 1.41% 1.92% 1.21% 1.70% 2.88% 2.64%  #22 (hard) 0.37% 0.37% 0.57% 0.26% 0.15% 0.29%  Table 3. Comparison of maximum contact pressures with 3σ equivalent values  Model Correlation  Ball Bearing Stiffness  Around the preload point and for low levels of vibration, the stiffness of the bearing cartridges can be  linearized. This “tangential” or “differential” stiffness (slope of the load-deflection curve around the origin)  relates to the resonance frequency.   The load-deflection curves of a single bearing, as predicted using the model equations in [5] and derived  from the test results, are compared in Figure 13 for the soft preload units (left) and for the hard preload unit  (right). Several geometry parameters are used to compute the load-deflection characteristics. The one with  the highest uncertainty (and the strongest effect on the stiffness) is the contact angle, linked to the radial  clearance in deep groove bearings. A range from 5 to 20 degrees is indicated in Figure 13. As stated before,  single bearings of the soft preload units can be represented and compared directly, just by plotting the nongapping range and shifting it by the preload magnitude. Indeed, the stiffness of the single bearing dominates  that range. The stiffness of a single bearing in a hard preload configuration is more difficult to extract from  the test results. Nevertheless, a linearized approximation may be obtained by dividing the stiffness by two  and shifting it by the preload magnitude and corresponding deflection.  Via above approach, the free contact angle of test unit #3 and #6 is estimated with approximately  13 degrees. The stiffness of the hard preload test unit is higher than expected with such free contact angle.  At this stage of the investigation, two potential reasons are considered: The free contact angle might  actually be higher than 13 degrees, or the preload magnitude might be higher than expected, keeping in  mind that a hard preload is set by a small deflection with high precision, which is more sensitive to errors.  Another interesting observation comprises the load-deflection characteristic for the soft preload cases: It  can be fit with a function 	=∙, where the exponent ≈ 2.1, which is higher than the 1.5 used to derive  the rule of ≈ 2.83 ∙  . In order to correlate the hard preload results with the model, another  bearing model using a different contact angle and preload magnitude was assumed. Its characteristic  corresponds to a model function with an exponent of 1.79, closer to 1.5.  Test  unit ID Max. Hertzian  Pressure  [MPa] 1.1 g rms 1.6 g rms 2.2 g rms 4.5 g rms 6.3 g rms 8.9 g rms #3  (soft) 3σ 940 1120 1188 1569 1693 1830  peak 1382 1486 1772 2240 2478 2595  #6  (soft) 3σ 975 1102 1299 1386 1605 1739  peak 1534 1661 1902 2049 2171 2563  #22  (hard) 3σ 1300 1483 1651 2104 2308 2543  peak 1541 1762 1949 2457 2613 2899  NASA/CP—2018-219887 92
Figure 13. Load-deflection characteristics of the test bearings vs. model output  (left: hard preload unit, right: soft preload units)  Sine Sweeps Results  A comparison between the Simulink®model output and the test results is made using the output of the sine  sweeps runs. Figure 14  shows the resulting peak acceleration vs. excitation frequency. The peak amplitude  is presented for both motion directions acknowledging the strong asymmetry in the soft preload cases.  Figure 14. Output acceleration magnitude vs. excitation frequency  (left: hard preload unit, right: soft preload unit #3)  For both test units, the largest difference is found with the higher quality factor derived from the test data.  This may be due the fact that the input acceleration was somewhat disturbed during the test runs because  the shaker controller had some problems to keep the input level steady (possibly a sign of shaker  saturation). For the hard preload unit, the system acts in a fairly linear way (left plot in Figure 14). Also for  the soft preload unit, the overall evolution of the response is broadly similar. However, the nearly vertical  rise at about 380 Hz and the pronounced asymmetry around the resonance for the highest excitation level  (right plot in Figure 14) is typical of a non-linear transition in a vibrating system. In this particular case, it  happens when the dummy mass acceleration is high enough to create gapping and to reach the spring  compression range in the load-deflection characteristic.   In Figure 15, the deflection is plotted against the force on the shaft for the sine sweep with the highest  amplitude. In the test results, the gapping range appears stiffer than predicted by the model. This was  already found in Figure 10, and is probably caused by friction and other effects in the spring assembly. As 0 10 20 30 40 50 60 70 Axial deflection [ m]01002003004005006007008009001000Axial load [N]Free contact angle = 5 degrees Free contact angle = 13 degrees Free contact angle = 20 degrees Test unit 3 Test unit 6 0 10 20 30 40 50 60 70 Axial deflection [ m]01002003004005006007008009001000Axial load [N]Free contact angle = 5 degrees Free contact angle = 13 degrees Free contact angle = 20 degrees Test unit 22 200 400 600 800 1000 1200 1400 1600 1800 2000 Frequency of input acceleration [Hz]-200-150-100-50050100150200Peak acceleration [g]Experimental result Model output 200 400 600 800 1000 1200 Frequency of input acceleration [Hz]-4-2024681012Peak acceleration [g]Experiment results Model output NASA/CP—2018-219887 93
a major element of the continued investigation, it will be attempted to measure the static load-deflection  characteristic of the bearing cartridges with higher precision, for a more comprehensive model validation.   Figure 15. Load-deflection characteristics of the test units for the highest amplitude sine sweeps (left:  hard preload unit; right: soft preload unit #3)  Constant Frequency Sine Vibration Input and Snubber Interaction  In some of the constant frequency sine runs with the soft preload units, the deflection in the gapping range  was large enough to hit the snubber. This interaction is also represented in the Simulink®model. Figure 16  shows the model output compared to the experimental results for test units #3 and #6.  Figure 16. Snubber interaction for the soft preload units (left: #3, right: #6)  The blue lines represent the model output while the green lines are the experimental results. Within the  long and nearly horizontal stroke, it can be seen that the predicted stiffness of the spring matches the test  data rather well. At the right end of the stroke, the snubber interaction is evident. However, the stiffness  transition and evolution in the vibrations test results appears smoother than in the simulated output, an area  for future model refinement.  In general, it can be noticed that the behavior of the bearing system is more complex when the snubber is  hit. Concerning the maximum load reached for re-contact after gapping (left end of the graphs), the model  shows good correlation. However, the load and stroke reached when hitting the snubber is not well  predicted yet (right end of the graphs). -40 -30 -20 -10 0 10 20 30 40 Axial deflection [ m]-3000-2000-10000100020003000Axial load [N] Sine sweep experiment result (6.52g) Sine sweep model output (6.52g) -10 -5 0 5 10 15 Axial deflection [ m]-140-120-100-80-60-40-200204060Axial load [N] Sine sweep experimental result (0.8g) Sine sweep model output (0.8g) -30 -20 -10 0 10 20 30 40 50 Axial deflection [ m]-500-400-300-200-1000100200300400Axial load [N]Experimental result Model output -40 -20 0 20 40 60 80 Axial deflection [ m]-800-600-400-2000200400600Axial load [N]Experimental result Model output NASA/CP—2018-219887 94
Random Vibration Results  Since the model will also accept a random time series as input, the signal acquired from the input  accelerometer (on the shaker interface) can be directly used as model excitation for comparison of the  results. This avoids any differences in the input due to shaker control, etc. The histograms of the resulting  loads on the dummy mass are presented in Figure 17 and Figure 18.  For the hard preload case, the random vibration response of the model matches the test data rather closely,  see Figure 17. Due to the skewness and relatively complex shape of the histograms for soft preload (Figure  18) a statistical interpretation tends to be more difficult than for the hard preload case. Nevertheless, the overall shapes of the model response histograms follow those for the test response. For the highest excitation (right plot in Figure 18), the two statistical modes, i.e. the two clearly separated spikes, are represented by only a single peak in the model response. This is explained by the fact that the hysteresis of the spring preload system is not fully represented in the model yet. Figure 17. Histograms of the dummy mass loads for the hard preload unit  (blue: derived from vibration test data, green: model output)  Figure 18. Histograms of the dummy mass loads for the soft preload unit #3  (blue: derived from vibration test data, green: model output) -1000 -500 0 500 1000 Dummy mass load [N]012345678910-3 Input level 1.1 grms -1000 -500 0 500 1000 Dummy mass load [N]012345678910-3 Input level 2.2 grms -1000 -500 0 500 1000 Dummy mass load [N]012345678910-3 Input level 6.3 grms -400 -200 0 200 400 Dummy mass load [N]00.0050.010.015Input level 1.1 grms -400 -200 0 200 400 Dummy mass load [N]00.0050.010.015Input level 2.2 grms -400 -200 0 200 400 Dummy mass load [N]00.0050.010.015Input level 4.5 grms NASA/CP—2018-219887 95
The Design & Development of the Ocean Color Instrument  Precision Superduplex Hybrid Bearing Cartridge  Joseph Schepis∗, Timothy Woodard**, Claef Hakun*, Konrad Bergandy*, Joseph Church*,  Peter Ward∗∗, Michael Lee**, Alfred Conti+ and Jeffrey Guzek++ Abstract  A high-precision, high-resolution Ocean Color Imaging (OCI) instrument is under development for the  Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission which requires a pair of medium-speed  mechanisms to scan the ocean surface continuously. The design of the rotating telescope (RT) mechanism  operating at 360 RPM and the half-angle mirror (HAM) mechanism synchronized at 180 RPM was concern  for maintaining pointing precision over the required life and continuous operations. An effort was undertaken  with the manufacturer to design and analyze a special bearing configuration to minimize axial and radial  runout, minimize torque, and maintain nominal contact stresses and stiffness over the operating  temperature range and to maximize life. The bearing design, analysis, development and testing along with  the design-specific technical challenges imposed upon mechanism engineers will be discussed. Bearing  performance, runout as achieved and verified during encoder installation, and operating torque will be  described.  Introduction  PACE will extend the high-quality ocean ecological, ocean biogeochemical, cloud, and aerosol particle data  records begun by NASA in the 1990s, building on the heritage of the Sea-Viewing Wide Field-of-View  Sensor (SeaWiFS), the Moderate Resolution Imaging Spectroradiometer (MODIS), the Multi-angle Imaging  SpectroRadiometer (MISR), and the Visible Infrared Imaging Radiometer Suite (VIIRS). The mission will  be capable of collecting radiometric and polarimetric measurements of the ocean and atmosphere, from  which biological, biogeochemical, and physical properties will be determined.  The PACE observatory is comprised of two instruments, an  Ocean Color Instrument (OCI), Figure 1, and a Multi-Angle  Polarimeter. The OCI is the primary instrument on the  observatory and is being developed at GSFC. The OCI is a  hyper-spectral scanning radiometer designed to measure  spectral radiances from the ultraviolet to shortwave infrared  to enable advanced ocean color and heritage cloud and  aerosol particle science. OCI accomplishes its mission  objectives by implementing an RT mechanism, rotating at  360 RPM, and phase locked to the HAM mechanism  rotating at half the RT speed. These synchronized  mechanisms scan ocean surfaces with 1000-m resolution  and 20-m track-to-track overlap. The PACE satellite is  planned to be launched in 2022-2023. [1, 2]  ∗NASA Goddard Space Flight Center, Greenbelt, MD  ∗∗The Aerospace Corp, El Segundo, CA    +The Barden Corp, Danbury, CT ++ Design Interface, Columbia, MD Proceedings of the 44th Aerospace Mechanisms Symposium, NASA Glenn Research Center, May 16-18, 2018  Figure 1. OCI Configuration NASA/CP—2018-219887 97
Mechanism Operating Requirements  The RT and HAM are precision mechanisms spinning synchronously to scan the ocean surface and place  the optical image through the OCI slit. The requirements considered for these mechanism designs include:  •Speed: 360 & 180 RPM •Position: 40 arc-sec knowledge and 10 arc-sec maximum error (215 bits), sampling at 50 kHz •Life: ground testing + 3 months in-orbit commissioning + 3 years continuous on-orbit operations •Torque: minimize mechanical power to minimize thermal conditions at the bearing and for minimizing control electronics overhead •Mechanical Loads •Structural: worst-case launch vehicle mass acceleration curve (MAC), 42g, for mechanisms; sine vibration 10g from 5-100 Hz •Thermal: 10°C to 30°C qualification range, including self-generated heat Figure 2. RT and HAM Mounted on Main Optical Bench Runout: Challenges to Meet Requirements  Minimizing the axial and radial runouts were primarily driven by the optical system sensitivity estimates and  the need to meet challenging pointing requirements. Both synchronous runout and asynchronous runout  had to be minimized to keep the bearing cartridge runouts within the requirements. The RT and HAM, with  precision optical encoders mounted to the shaft flange end, runout requirements were most challenging  while the motor and encoder supported by the aft end have slightly relaxed requirements. The cartridge  total indicator runout (TIR) requirements are given in Table 1. As these were very challenging requirements,  the bearing vendor was taking all reasonable steps necessary within their capabilities to achieve these  values while operating in a “best effort” mode.  Table 1. TIR Runout Requirements  Shaft Flange End Aft End Outer Races (ea.)  Radial Runout 2.54 µm (100 µ-in) 2.54 µm (100 µ-in) 0.51 µm (20 µ-in)  Axial Runout 1.27 µm (50 µ-in) 5.08 µm (200 µ-in) NA  These challenging requirements meant that the best geometrical precision in bearing races, ball roundness  and their potential lobing was required. Additionally, the number of mating surfaces with their inherent errors  due to tolerance buildup had to be minimized. For these reasons, the mechanism designers decided not to  use commercial off-the-shelf bearing designs but rather to start with no preconception and design a system  that maximized the likelihood of success. The cartridge design demanded complete customization that led  to inner races ground on the same grinder setup. There were no shaft fit or concentricity errors because  NASA/CP—2018-219887 98