ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
The onset of cage instability will be detectable in the frequency domain (by the presence of the cage whirl  frequency and other easily detectable frequency domain changes) or in the time domain by assessing the  dependency of torque on speed (if unstable the mean torque may show a dependency on rotational speedsquared since torque becomes more directly related to cage energy rather than load-dependent  (Coulombic) ball/raceway friction (essentially fixed independent of speed).  In principle therefore, the validation of an accelerated test of a solid or self-lubricating bearing seems  achievable, on the basis of tribometer tests of primary and secondary lubricant behavior and the monitoring  of cage stability throughout the test. However more proof, in the form of a substantial number of bearing  tests of the validity of this kind of approach would be needed and the existing evidence for this is now  explored.  For MoS 2 Lubricated Bearings  ESTL’s Space Tribology Handbook [17] summarizes data for MoS 2 bearing lifetime from [29]. Whilst strictly  relating to the legacy PTFE/Glass-fiber MoS 2 material RT Duroid 5813 (rather than PGM-HT), in this  program the end-of-life of the MoS 2 film was defined by the onset of a mean torque equivalent to a friction  coefficient of 0.3 between ball and raceway. This data, shown in Figure 16, therefore relates to the MoS 2 “film lifetime” within the bearing and not specifically to the cage material performance.  For Self-lubricating Bearings   Data taken from [30] has been used as survey of the lifetime of self-lubricating bearings using PTFE/glassfiber/MoS 2 cages. It should be noted that the data from this survey contains both tests which completed  end-of-life (according to some undefined criterion) and those for which the end of test may have been due  to completion of the test target revolutions (with or without failure). Furthermore, this data relates to a range  of different bearing sizes and types as well as to the legacy Duroid material and to the currently used  PGM-HT.  If these two populations are combined, a power-law trend-line seems to provide an appropriate fit to the  data. The fit could likely be improved if the data were expressed in terms of ball passes (rather than  revolutions), nevertheless, this seems a reasonable “first approximation” guide to lifetime to be expected.  Figure 16. In-vacuum bearing life or test duration v ball/raceway Hertzian contact stress for MoS 2 films  and self-lubricating bearings  In summary, even if the behavior of the lubricant is known at tribometer level, the extrapolation of such test  results to bearing level is difficult due to differences in the definition of end-of-life torque for different  applications. A moderately well-defined relationship exists between bearing life and contact stress as shown  above. This kind of relationship has been used in the past to substantiate highly accelerated tests based  on increasing speed AND load for low cost and mission of opportunity applications. The observation that  products developed from an original mission of opportunity qualification carried out under accelerated load  NASA/CP—2018-219887 523
23. Buttery, M., Wardzinski, B., Houton, K., Modern Self-Lubricating Composites For Space Applications: PGM-HT & Sintimid 15M” Proc. 14th European Space Mechanisms & Tribology Symposium (ESMATS), Constance, Germany, 87, (2011) 24. Buttery, M., Cropper, M., Roberts, E.W., “Thermally Conditioned PGM-HT”, ESA-ESTL-TM-0069 01- (2011). 25. Buttery, M., “Fundamentals of Transfer Film Lubrication”, ESA-ESTL-TM-0206 01- (2018) 26. Merstallinger,A., Simon, Z., Nuss, G., Paul, C.E., Palladino, M., Buttery, M., “New Self Lubricating Polymer Matrix Composites for Journal and Ball Bearing Applications in Space (SLPMC2)”, Proc. 17th European Space Mechanisms and Tribology Symposium (ESMATS), Hatfield, U.K. (2017) 27. Buttery, M., Kent, A. “Validity of Accelerated Testing for Self-Lubricating Materials”, ESA-ESTL-TM0197 01- (2018) 28. Vortselas, A., “Cage Stability Study Using High-Speed Video”, ESA-ESTL-TM-0227 01- (2018) 29. Cunningham, J., Swales, G., “Assessment Of The Influence Of Contact Stress On The In-Vacuo Torque Performance & Lifetime Of MoS 2-Lubricated Bearings Fitted With Duroid Cages” ESTL/TM/208 (2001). 30. Lewis, S.D., Anderson, M.J. & Haslehurst, A., “Recent Developments In Performance And Life Testing Of Self-lubricating Bearings For Long-Life Applications”, Proc. 12th European Space Mechanisms and Tribology Symposium (ESMATS) , Liverpool, UK, (ESA SP-653) (2007). 31. Wade, A., “In-orbit Health Monitoring of PGM-HT Lubricated Reaction Wheels”, ESA Workshop on Mechanisms Testing and Health Monitoring  (2017) 32. Ward, P., Leveille, A., Frantz, P., “Measuring the EHD Film Thickness in a Rotating Ball Bearing”, Proc. 39th Aerospace Mechanisms Symposium , 107, (2008) NASA/CP—2018-219887 527
results do not guarantee success for alternate mission parameters, nor do they summarize the limits of  these components; rather, they provide a handful of data points for which successful operation has been  demonstrated.  Planet Support Load Within a Planetary Gearbox  Planetary gearboxes are a power-dense option for translating high-speed, low-torque motor shaft outputs  into more useable lower-speed, higher-torque outputs. The planet gears that operate within these  gearboxes must be supported by and rotate upon carrier posts. Friction losses at the interface between  the planet gears and carrier posts are typically minimized through the use of bushings or rolling element  bearings. Rolling element bearings are generally selected in the faster moving, more lightly loaded initial  stages of a planetary gearbox. By contrast, bushings may be effectively used in the latter planetary  gearbox stages, where their additional drag is counterbalanced by their ability to withstand higher loads  with less volume. A well-designed bushing can successfully operate at higher radial loads than a rollingelement bearing of the same proportions. Bushings have also proven to be far more tolerant of slight  imperfections or contamination than plain steel bearings. Figure 1 shows the typical construction of a  planetary gearbox.   Figure 1 . Generic Planetary Gearbox Components and Planet Support Load  Figure 1 also shows the radial load, FRadial, to which the bushing or bearing is subjected as a result of the  torque transmission through the gearbox. This radial load  is generated as torque and is  transferred from  the torque input, Tin, to the resistive load at the output, TResistive . The severity of this radial load is related in  terms  of pressure  for a bushing  and  Hertzian  contact  stress  for a rolling  element  bearing.  It is these  © 2018 Sierra Nevada Corporation  NASA/CP—2018-219887 530
bushin g pressures , bearing stresses, and th e associate d effects on the lubrican t which this  developmental testing was designed to evaluate.  The bushing  pressures  and distances  are calculated  from  the bushing  inner  diameter  and assume  that  the outer  diameter  does  not rotate  relative  to the planet  gear.  Ball  bearing  Hertzian  stresses  were  calculated  with  COBRA  AHS ™ software,  using  radial  play  and  raceway  curvatures  provided  by the  bearing vendor for each serialized bearing.   Component-Level Testing  Because high stresses in ball bearings and bushings presented one of the largest gearbox program risks,  component level life tests were expediently developed in order to demonstrate that the final design could  meet the 2X life requirement set forth by NASA JPL.   Materials and Lubrication  All materials and lubrication were base d on the designed fligh t configuration a t the time of the Detailed  Design Reviews. For test expediency , commercially available 440 C bearings of th e sam e basic bearing  size as th e fligh t configuration were procured to undergo component-level testing. These bearings  contained stainless steel crown retainers equivalen t to the fligh t configuration. They were delivered with  serialized inspection data for radial play and inner/outer raceway curvature tha t allowed loads to be  tailored t o achiev e the require d max mean Hertzian stresses . The bearings were lubricated with grease  plate and a 5-10% free volume fill of 50/50 slurry containing Braycot e Micronic 600 EF grease an d Brayco  815Z oil. This lubrication fill was selected on the basis of prior published research [6]. Braycote Micronic  600 EF greas e was selected over the very similar 601 EF greas e because the use of stainless steel  components lessened the need for the corrosion inhibiting additives found in 601 EF.  SAE 841 bronze  alloy  bushings  (now  procured  to material  specification  CT-1000-K26)  were  also  readily  available.  This  bushing  material,  in combination  with  hardened  440C  posts,  was  shown  to be most  effective  in the NASA  Phase  II SBIR  Lightweight  Gearbox  Technology  Program  [4]. For lubrication,  the  bushings  were impregnated with  Brayco  Micronic 815Z oil and the surrounding  parts were grease plated  with Braycote 600 EF grease.  Component-Level Bushing Testing  The test rig shown in Figure 2 was available from the Lightweigh t Gearbox program and repurposed to  allow for expedient component-level testing on bushings and bearings. This tes t setup involved a  stationary gear blank to hold the outer diameter of the bushing under tes t with a rotating shaft interfacing  with its bore . The radial load was applied with a Radial Load bar, having its fulcrum on the far side of the  component under tes t, and a mass was hung on th e near side to generate the radial loads experienced  within a planetary gearbox. Finally , the rotating shaft was driven by a motor through a rotary torque  sensor via an opening in the thermal chamber wall.  © 2018 Sierra Nevada Corporation  NASA/CP—2018-219887 531
© 2018 Sierra Nevada Corporation Figure 2. Component Test Fixture  At this point in the program, design reviews were complete and procurement was underway. Table 1  shows the two enveloping design points to which a single bushing would need to successfully operate in  order to satisfy the cumulative 2X life requirement. Figure 3 shows the cumulative required operating  pressures and durations for each of the five gearbox designs utilizing bushings, along with the enveloping  component test points. Some of these design points later changed due to revisions JPL made to the  design specifications, further supporting the need for this initial developmental testing.  The test temperature was the final, crucial variable which needed to be defined for this developmental  test. The required operational temperature range was -70°C to +70°C. For simplicity and conservatism,  the team decided to run the entire test at the worst-case temperature. Elevated temperatures were  assumed in design reviews to be worst-case because of PFPE’s propensity to chemically break down in  high stress environments. Hot environments lower the viscosity of PFPE lubricants, resulting in thinner  lubricant film thicknesses for the otherwise same speed and load conditions. When sufficiently thin, the  lubricant regime will be near or in boundary contact, which accelerates the breakdown of the lubricant due  to the high stresses occurring at the molecular level, shearing apart molecules. Broken down, the  lubricant can no longer effectively protect the bushing from more rapid wear.   Table 1. Initial Bushing Operational Requirements  Load Case Load Duration Speed  High Load /   Short Duration 8.49 MPa  (1,231 psi) 1.78 km   (5,895 ft) 39.6-77.2 mm/s  (7.8-15.2 ft/min)  Low Load /  Long Duration 2.59 MPa  (376 psi) 122 km  (400,170 ft) 127-249 mm/s (25-49 ft/min) NASA/CP—2018-219887 532
Figure 3 . Initial Gearbox Bushing Pressure v. Duration Requirements and Test Plan  To confirm the assumption that the hot operational temperature limit was the more stressing environment,  two bushings  were  tested:  Bushing  A at the hot extreme  (+65°C  to +70°C)  and  Bushing  B at the cold  extreme  (-65°C  to -70°C).  The  two bushings  were  exposed  to the identical  loads  and  life of the High  Load/Short  Duration  load  case  of Table  1: 8.487  MPa  (1,231  psi) load  at a speed  of 40.1  mm/s  (7.89  ft/min)  for a total  duration  of 1.78  km (5,895  ft). Direction  was  alternated  every  five minutes  as a rough  replication of the change in direction to which the gearboxes would be subjected. After this exposure, the  bushings were removed from the test fixture and visually evaluated.  Unexpectedly, the wear on Bushing B from the cold test was more severe than on Bushing A from the hot  test, as shown in Figure 4. This was likely due to lubricant starvation from sub-optimum oil replenishment  at the wear  interface  due to such  cold  operating  temperatures.  The  pour  point  of Braycote  815Z  oil is   -72°C.  Operation  between  -65°C  and  -70°C,  so close  to the -72°C  pour  point,  likely  reduced  the oil’s  ability  to flow  within  the pores  of the impregnated  sintered  bushing,  hampering  its ability  to protect  the  bushing from more rapid wear. © 2018 Sierra Nevada Corporation  NASA/CP—2018-219887 533
© 2018 Sierra Nevada Corporation Component-Level Bearing Testing  A representative radial ball bearing was tested in the fixture shown in Figure 2, understanding that it  would be more tolerant of fixture shortcomings. The bearing was tested at loads, speeds, and durations  representative of and encompassing all Mars 2020 gearbox designs, including the newly-planned  2nd Stage applications in the GB7 and GB8 gearboxes.   Ball bearing testing was completed successfully. The max mean Hertzian contact stress, number of stress  cycles, and inner race speed of the tested bearing are shown in Figure 7. Although the speed was  uniform at each stress level, the lambda factor varied with temperature. The final condition of the bearing  grease is shown in Figure 8. The bearing completed approximately 32 million stress cycles at stresses  exceeding 1.31 GPa (190 ksi), including 29 million over 1.517 GPa (220 ksi) and nearly 390,000 at 2.179  GPa (316 ksi). Historically available PFPE curves are also shown in Figure 7 for reference:  •The Cumulative Degradation Factor (CDF) curves (“CDF = 2” and “CDF = 8”) indicate greater concern for long life usage of PFPE lubricants without directly cautioning against high stresses at a lower number of stress cycles [3]. The CDF is calculated as the product of max mean stress times the number of stress cycles and is typically expressed in units of 1012 psi-cycles (e.g. CDF = 2 is shorthand for 2 x 1012 psi-cycles). •Conversely, curves from other test data (“Upper Limit Line” and “Lower Limit Line”), based on NASA CP-3062 [1], indicate a greater concern for high stresses which accelerate the polymerization and breakdown of PFPE lubricants, but suggest very long life is possible at low stresses. Stress cycles are the number of times a ball passes across a given spot on the raceway. The conversion  from bearing revolutions to stress cycles is a function of bearing geometry as shown in Eq. 1:  #		 = #		 ×1− ( ) ( )⁄ (1)  Where N  is the number of balls, d is the pitch diameter, and D is the diameter of the balls.  It is worth noting that the bearing under test was exposed to all of these stress cycles while running  continuously in a thermal chamber cycled to achieve a distribution of 25% hot (+65°C to +70°C), 25%  cold (-65°C to -70°C) and the remainder between -65°C and +65°C. Each thermal cycle was  approximately 400 minutes with the average test temperature of approximately 0°C. The thermal chamber  ramp time made it impractical to include the additional temperature plateau for 25% of cycles at the  nominal temperature, -55°C.   NASA/CP—2018-219887 536
Table 2. As-Tested Flight-Like Gearbox Bushing Exposure  Test  Step Bushing  Pressure  (MPa) Total  Duration  (m) Bushing  Speed  (mm/s)  Run-In 0.625 61 17.042X  Ground  Test  Cycles 1.258 3,301 2.499 157 2.954 1,555 3.583 16 5.155 52 5.332 42 7.858 100 2X  Mission  Life  Cycles 0.625 6,788 1.375 74 2.766 5,533 1.886 444 0.625 6,728 30.971.375 74 2.766 15,670 1.886 10,605 Figure 9 . Bushing Wear Exposures  © 2018 Sierra Nevada Corporation  NASA/CP—2018-219887 539
© 2018 Sierra Nevada Corporation Disassembly and inspection of the bronze alloy bushings and 440C posts at the conclusion of testing are  shown in Figure 10. The results of surface roughness measurements along the axial length of the bushing  outer diameters are shown in Figure 11. A visual comparison and these roughness measurements  indicate the Brayco 814 oil provided superior wear protection to the bushings for this predominately cold  operational test. The 814 oiled bushings displayed a surface condition more similar to the virgin bushing  pulled from stock for comparison. The improvement seen from the Brayco 814 oil is most likely due to the  lower viscosity of 814 at cold temperature versus the 815Z oil allowing improved lubricant flow and  replenishment.  Figure 10. Bushings (Left) and Posts (Right) at the Conclusion of Wear Testing  Figure 11. Bushing OD Surface Roughness Measurements  NASA/CP—2018-219887 540
Fi gure 1. Bearing Test Fixture ’s Thermal Sub- System  

Since the bearing temperatures are not controlled, a test matrix is needed to allow the results to be processed by interpolation. If, for instance, LQF is desired for a given temperature, it can be determined by  selecting data points near the desired temperature and using linear interpolation.     Non- contact pyrometers are used to measure temperatures of rotational components, while thermocouples  measure temperatures of stationary components . Sensors include two pyrometer measurements on the  shaft, determining the heat entering the bearing, and two thermocouple measurements on the Outer Heat  Meter that determine the heat exiting the bearing. The difference between the heat leaving and entering  the test bearing determines the heat generated by the bearing. The inner race temperature is measured  with a pyrometer and the outer race with a thermocouple (Figure 1) .    To calculate heat entering the shaft, Q in, we have:  

 𝑄𝑄𝑖𝑖𝑖𝑖=𝜋𝜋𝑑𝑑2𝑘𝑘𝑠𝑠 4𝐿𝐿𝑠𝑠(𝑇𝑇𝑠𝑠1−𝑇𝑇𝑠𝑠2) (1)  where   Q in  Heat entering the bearing from the shaft [W]    d  Diameter of the shaft [m]    k s  Conductivity of the shaft [W/m -°C]   L s  Pyrometer measurement separation distance [m]    T s1  Temperature of the shaft at pyrometer location 1 [°C]    T s2  Temperature of the shaft at pyrometer location 2 [°C]   To calculate the heat leaving the test bearing, we  have :  NASA/CP—2018-219887 545
𝑄𝑄𝑜𝑜𝑜𝑜𝑜𝑜=2𝜋𝜋 ℎ 𝑘𝑘ℎ𝑚𝑚 𝑙𝑙𝑖𝑖(𝑟𝑟2 𝑟𝑟1)∙(𝑇𝑇ℎ𝑚𝑚1−𝑇𝑇ℎ𝑚𝑚2) (2)  where    Q out  Heat exiting the bearing and entering the heat sink [W]    h  Thickness of the Outer Heat Meter [m]    k hm  Conductivity of the Outer Heat Meter [W/m -°C]   r 1  Location of thermocouple c lose to bearing [m]    r 2  Location of thermocouple furthest from bearing [m]    T hm1  Temperature of the shaft at thermocouple location close to bearing [°C]    T hm2  Temperature of the shaft at thermocouple location furthest from bearing [°C]   Thus, the calculation of the heat generated by the bearing, Qint, is as follows:    𝑄𝑄𝑖𝑖𝑖𝑖𝑜𝑜=𝑄𝑄𝑜𝑜𝑜𝑜𝑜𝑜− 𝑄𝑄𝑖𝑖𝑖𝑖 (3)  Fr om test measurements , we know the following quantities:   1. Test rig thermal boundary conditions   a. Q in – heat entering into the bearing from the shaft   b. T sink – temperature sink along the outer rim of the Outer Heat Meter   2. Bearing thermal variables   a. Q int – Heat generated by the test bearing   b. T bin – Bearing inner race temperature  c. T bout – Bearing outer race temperature 

The next section will explain how to determine the LQF based on test data and a detailed bearing- level  mechanical model.  

Modeling Method   The total bearing heat generation, Qint, may be related to the total bearing drag torque, t, based on the  model described here .    𝑄𝑄𝑖𝑖𝑖𝑖𝑜𝑜= 2𝜋𝜋 ∙𝑡𝑡 ∙𝑟𝑟𝑟𝑟𝑚𝑚 60 (4)  The total torque, t, is the sum of the mechanical components , tm, of torque and the viscous shear torque,  tvs, (lubricant torque) . The total mechanical torque, is due to the motion and mechanics of contact between  the ball, race and cage, while the viscous shear torque is due to the ball “plowing” through the lubricant.    𝑡𝑡=𝑡𝑡𝑚𝑚+𝑡𝑡𝑣𝑣𝑠𝑠 (5)  Mechanical Torque Modeling   The total mechanical torque has three components:   1. Ball spin friction torque [ 2-3] – a function of friction between ball and raceway, bearing  geometries, mechanical loads, and bearing speed   2. Interfacial slip friction torque [ 4-6] – a function of friction between ball and raceway, bearing  geometries, mechanical loads   3. Material hysteresis torque [ 7] – a function of mean contact stress, bearing geometries, and  mechanical loads  

Viscous Torque Modeling   Calculation of the viscous torque is based on a model by Palmgren and Snare [ 8]   𝑡𝑡𝑣𝑣𝑠𝑠= 1.42∙10−5∙𝐿𝐿𝑄𝑄𝐿𝐿∙𝐸𝐸3∙(𝑟𝑟𝑟𝑟𝑟𝑟∙𝑣𝑣)2/3 (6)  NASA/CP—2018-219887 546
Fi gure 2a.  Applied load of 89 N ( 20 lb) Figure 2b. Applied load of 133 N ( 30 lb )         Figure 2c . Applied load of 178 N ( 40 lb ) Figure 2d. Applied load of 222 N ( 50 lb ) 

Figure 2. Normalized LQF vs. average temperature (Tave)  for variable applied loads and constant  temperature gradient  (DT) for 305- size all -Steel Bearing 

Figure 3. Normalized LQF vs. average temperature for variable applied loads and constant temperature  gradient of 12°C for 305- size all -Steel Bearing  

Effect of Temperature Gradient on LQF   Figures 4 were generated from the same data set as those shown in the previous section. However, in this section, the normalized LQF is plotted against temperature gradient (DT) for the all steel 305- size bearing.  Each  graph in this series represents a different axial load. Each individual curve represents a particular  fixed average temperature. The trends show that there is an increase in LQF with increased temperature gradient, but the slope is strongly influenced by axial loads. This implies that there is a coupled relation between temperature gradient and axial loads.  

NASA/CP—2018-219887 549
Fi gure 4a. A pplied load of 89 N ( 20 lb) Figure 4b. A pplied load of 133 N ( 30 lb )  Figure 4c . Applied load of 178 N ( 40 lb ) Figure 4d. A pplied load of 222 N ( 50 lb ) 

Figure 4. Normalized LQF vs. temperature gradient for variable applied loads and constant average  temperature for 305- size all -Steel Bearing  

Figure 5 shows the coupled relation between temperature gradient and axial load on LQF in a more  condensed way. Here,  the normalized LQF is plotted as a function of temperature gradient for a constant  average temperature of 20°C for each of the applied loads . The data indicates that there is an approximately  linear relation between temperature gradient and LQF . But the slope of this relation is non- linearly  dependent on the axial load . 

Figure 5. Normalized LQF vs. temperature gradient for variable applied loads and constant average  temperature of 20°C for 305- size all -Steel Bearing  

Effect of Axial Load on LQF   In Figure 6, the data are plotted to show the dependence of axial load for the all -steel 305- size bearing. All  of the data in this plot were collected with  a temperature gradient of 12 °C. Each curve on this plot represents  a unique constant average temperature. The results show that the LQF generally increases with axial load.  And although the LQF is generally higher with greater T ave, the rate of increase with preload is not sensitively  dependent on T ave.  NASA/CP—2018-219887 550