ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
502  Approved for public release. OTR 2020- 00294  For stepper motor torque margin, engineers are given a choice to use either a step stability analysis or a  pull-in torque margin analysis . The step stability analysis is stated as preferred, but the pull -in torque  method is also acceptable, only when certain conditions are met . Equation 2  shows  the pull -in torque margin  calculation method.  

Pull-in torque margin  = �� Pull−in torque  at drive  rate Kvar  ∗ Total  friction  load  seen  by motor  �−1�         (2)  

When choosing the step stability analysis method instead, Equation 2 can be re- written to take the form of  Equation 3  

           Pull-in torque at drive rate =[1+Pull-in Torque  Margin ]∗[Total  friction  load  seen  by motor ]         (3)  

Step stability is achieved when the left side of Equation 3 is great er than the right side. In the step stability  analysis, the value of the [1+ Pull -in Torque Margin] term is increased until the motor goes unstable. The  value from the last stable case is then used to calculate the stepper motor margin . 

Summary and Path F orward  

A multi -year effort has culminated with a finished draft of a newly updated AIAA Moving Mechanical  Assemblies standard. The most significant changes have been discussed herein. These include the  elimination of the “shall, where practi cal” requireme nt weighting level, a completely new testing section that  mirrors other industry testing standards, and a more realistic approach to calculating torque/force margins .  There are a host of other changes which were not highlighted in this paper, but which the authors and  industry committee members believe will make a more robust and meaningful set of MMA requirements  for  space and launch vehicle programs in the future.  

As of the submission of this paper (January 2020), the draft document is making its way thr ough at least  two approval processes, one by The Aerospace Corporation to replace the Mission Assurance Baseline  callout of the previous MMA standard, and the other by the AIAA. It is anticipated that  these  will be  completed sometime in 2020.  

References  

1. SMC -S-016, Air Force Space Command, Space and Missile Syst ems Center Standard, “Test  Requirements for Launch, Upper Stage, and Space Vehicles, ” September  2014.   2. TR-RS-2014- 00016, The Aerospace Corporation, Technical Report, “Test Requirements for Launch,  Upper -Stage, and Space Vehicles ,” June 2014.   3. MIL-STD-1540 C, Department of Defense, Military Standard, “ Test Requirements for Launch, Upper - Stage, and Space Vehicles ,” September 1994.   4. GSFC -STD-7000, NASA Technical Standard, “General  Environmental  Verificati on Standard (GEVS) ,”  April 2013.   5. NASA- STD-5017A, NASA Technical Standard, “Design and Development Requirements for  Mechanisms,” July 2015.  

Acknowledgements  

The authors wish to acknowledge Rebecca McKenna of The Aerospace Corporation’s Enterprise Mission  Engineering Department, whose unwavering positive support allowed a long- term, low -level effort to  complete this work despite continually shifting and competing priorities.
503 Micro -Vibration Attenuation Using Novel Flexible Pivot Design  

Luc Blecha*, Yoël Puyol*, Simon Hayoz *, Martin Humphries** and Fabrice Rottmeier * 

Abstract  

Flexible pivots present numerous advantages such as no wear, no particle generation and predictable  torque. In addition, the patented design presented in this paper adds high stiffness tunability, large angle ,  nearly constant radial stiffness over the enti re range of motion , and infinite life capability. A design  optimization software has been developed to generate within a few hours  custom flexible pivot designs   matching specific application requirements such as pivot angle, torsional, radial, axial , bendi ng stiffness ,  maximal stress, and buckling factors. The flexible pivot design is an  enabling technology for many  applications  and in particular for ultra- stable pointing mechanisms . A novel concept of an ultra- stable  pointing mechanism using a flexible piv ot is presented.  It is shown with a simple Nastran model  that the  micro -vibration impact on pointing mirror  stability  can be theoretically decreased by 3 to 8 orders of  magnitude in the 50- 200 Hz frequency range, and by more than 9 orders of magnitude above 200 Hz  in  comparison with a design using ball bearings . The achieved pointing accuracy makes the need of a fine  pointing mechanism unnecessary. The total mass, volume and costs can thus be drastically reduced in  comparison to the existing s olution today on the market that uses coarse and fine pointing mechanisms . A  fully functional and motorized breadboard has been built and showed full hemispherical pointing range.  

Large -Angle Flexible Pivot Design   

The principle of the Large- Angle Flexib le Pivot is based on controlled deformation of structures  in pure  bending within their elastic limit. The flexible pivot  consists of two interface rings connected by flexible  elements  (Figure 1) . The first ring is the stator and the second is the rotor. A first set of flexible elements   connect the stator ring to a central cylinder. These  spokes  are composed of a thin elongated blade  connected to another smaller blade  called T -bars as they are forming a T -shape . The T -bars are  connected  to the stator. From the central  cylinder, connecting members  connect the first central cylinder  to an outer  ring by means of another set of T -bars. From the outer ring, the structure is symmetrical . The outer ring is  thus connected to another central ring on the rotor side by connecting members  and T -bars. Finally, the  second central ring is connected to the rotor ring by a set of spokes  and a f ourth set of T -bars. This is a so - called two -stage design that can achieve a rotation of ±70° for infin ite life conditions and higher angular  range with reduced life.   

* Almatech SA, Lausanne, Switzerland; luc.blecha@almatech.ch   ** SpaceMech Ltd., Bristol, UK  

Proceedings of the 45th Aerospace Mechanisms Symposium, NASA Johnson Space Center, 20 20
504   Figure 1. Design Overview of the Almaflex  

The number of spokes, connecting members  and T -bars can be adjusted to the need of the application. For  example, if a larger rotation angle is needed, the blade can be positioned at 120 degrees instead of   90 degrees. The number of spokes and connecting members  would thus be 3 instead of 4.  

The number of stages can also be increased which will increase the range of rotation al angle. The number  of thin blades, and spokes can also be increased to raise the torsional stiffness. This is used in oscillating  applications  to reach high natural rotational eigenfrequencies. All these applications  are documented in a  world  patent1.  

   A) B)  Figure 2: A) View of a 3 stage outside- inside design with parallel spokes and connecting members  to  increase stiffness B) a 3 stage outside- outside design for very large rotational angles.
505 The advantage of this unique flexible element configuration is that the sti ffness in each degree of freedom  can be tuned almost independently from the other direction. In particular, the T -bars drive the radial stiffness  whereas the total height of the blades drives the axial one. The rotation of the flexure is driven by spokes  for approximately one half of the full range while the other half is provided by the connecting members. This  decoupling feature is particularly useful for stiffness optimization considering in -orbit operations, launch  locking, gravity sag adjustments and c an easily be verified via non- linear Finite Element analysis. The fully  symmetrical design guarantees no geometrical center shift and, combined with T -bars compliance, a  smooth thermo- elastic behavior.  

Custom Design for E ach Application  

The Almaflex design is a family of designs  that can be optimized to specific performances. The Large Angle  Flexible Pivot (LAFP) is the result of an optimization in response to the European Space Agency (ESA)  CTP specifications.  

A software tool called FlexOptim has been developed to efficiently find an optimized design within the  Almaflex design family that matches best the application requirements.  

Rotational  angle, applied loads , and launch configuration are given as input to FlexOptim as well as stiffness  requirements for radial, axial, torsional and bending cases. The optimization process starts with a baseline  set of variables and associated boundaries def ining the initial geometry. A set of constants defining material  properties and weighting factors are also input. Depending on the configuration during launch: locked or  not, a set of design forces is retained for the optimization process. According to the  requirements, variables  and constants given as input, constraints are generated and cover geometry consistency, targeted stiffness ,  angle, stress limit and buckling factors. T he optimization process starts from the initial set of variables . The  optimizati on process is done in two steps. Optimization loops are performed using analytical formulas that  calculate axial, radial, bending and torsional stiffness as well as the stresses  and buckling factors .  Consistency of these formulas has been correlated with f inite element analysis during process  development. The optimization aims at minimizing torsional stiffness, volume,  and the deviation between  targeted and computed rotation angles while maximizing buckling factors and stress performances. In a  second step,  a complete finite element loop is performed to evaluate the requirements. Correction factors  between FE analysis and analytical approach are then computed and considered in the next analytical  iterations. The optimal solution is reached when convergence of these correction factors is met.  The generic  flow logic of the optimization algorithm is shown in Figure 3. 

Figure 3: Optim ization methodology
506   Manufacturing constraints are considered by the specification maximal blade length, minimal blade  thickness , and allowable range for blade length to height ratio. In addition, specified allowable stress and  elastic modulus shall repres ent achievable values by the end product. To this end, a fatigue test campaign  has been set up. Establishment of Wohler curve for titanium grade 5 is currently underway for  an ESA CTP  project.  The preliminary results have shown that the LAFP maximal number of cycles is highly dependent  on the manufacturing process (see reference 5  for further details). By selecting the adequate process,   309 million  cycles could be achieved without failure. Once the fatigue test s are finis hed, failure probability   analysis will be carried out based on the Wohler  curves to identify the maximal safe operation of the LAFP.  

The optimization tool used in FlexOptim to minimize or maximize the objective functions is MIDACO2,3,4  (Mixed Integer Dis tributed Ant Colony Optimization). MIDACO is a metaheuristic optimizer developed by  ESA based on the behavior  of ants looking for food around their hill, so its basis of functioning is the  exploration of the available space for the variables and the storage of the current best solution. The  constraints are handled by using an oracle penalty method. As shown on Figure 4, different levels of  exploration can be observed and finally a smaller area around the optimal solution is investigated.  

Figure 4: Example of optimization results from MIDACO  

Once the optimum geometry fulfils the customer’s requirements , the new set of geometry variables are sent  automatically to a 3D design software that updates the design.  

A Large Family  of Design s 

Based on the optimization method described above, different designs  have been established for a variety  of applications. Some of them have been selected to show the different possible design and their main  characteristics are shown in Table 1 .
507 Table 1: Main characteristics of some selected applications   Design identification  D1 D2 D3 D4  Characteristics  Unit      Application   Pointing  Pointing  Slow Scan  Rapid scan   Payload configuration   Supported on  both ends  Supported on  both ends  Supported on  both ends  Supported on  both ends   Launch configuration   Launch lock  Launch lock  Launch lock  Launch lock   Payload mass  kg 2 4 1.2 3.0  Flex material   Titanium  PEEK  Titanium  Stainless  Steel   Rotation angle  Degrees  ±8.5 ±45 ±70 ±45  Torsional  stiffness  Nm/rad  0.33 0.45 0.98 27.3  Axial stiffness  N/m 160000  103000  580000  592000   Radial stiffness  N/m 160000  114000  132000  422000   Radial to torsional  stiffness ratio  Rad/m2 474800  252400  134000  15500   External diameter  mm 47 52 100 172  Overall height  mm 10 23 45 40  Flex mass  kg 0.080  0.027  0.269  0.627  

The different designs are shown in the Figure 5. 

   Design D1  Design D2     

Design D3  Design D4   Figure 5: Different achievable design listed in Table 1, represented respecting their relative size
509   Figure 6: Example of micro -vibration  noise  specification  of reaction wheels  for MTG  

On the other hand, c ryo-coolers generate most of their micro -vibration  noise at frequencies around 50 Hz   and less at higher frequencies . Note that the level of micro -vibration  from cryo -coolers is generally smaller  than those of r eaction wheel s, even at 50 Hz.  

Figure 7: Example of micro -vibration  noise  spectrum for cryo-coolers  on MTG  

The different  sources of micro- vibration  add up at the pointing mechanism interface. The micro -vibrations  are then transmitted to the mirror  by the pointing mechanism which disturb the pointing stability. Translation  vibration of the mirror are generally not a concern as it does not affect  pointing stability. On the other hand,  rotational vibration of the mirror has a direct  effect on the pointing stability . The transfer function between  the pointing mirror and the pointing mechanism’s interface to the spacecraft is thus key.  

In case of a stiff pointing mechanism using ball bearings, the structure  trans fer function has a first  amplification peak at its first structural eigenfrequency , which  is typically between 140 Hz for spacecraft  decoupling requirement and below 1000 Hz. Bel ow the first eigenfrequency, micro- vibration s are either  transmitted to the mirror integrally for frequencies far below the peak or amplified for the ones near
510 resonance. Thus, cryo- cooler s micro -vibrations  that have the highest excitation at frequencies between 50  and 100  Hz are integrally transmitted to the pointing mirror. In addition, high level micro -vibration  noise from  reaction wheel s may well coincide with the first structural eigenmode of the pointing mechanism, leading to  huge amplification. The f irst eigenfrequency of the pointing mechanism shall thus be tuned  to match the  reaction wheel s quiet area.      To illustrate this phenomenon on a classical series az imuth- elevation pointing mechanism, a simplified  Nastran model was built  (see Figure 8).  

Figure 8: Description of the simplified  Nastran model  

The interface of the mechanism to the spacecraft is model ed by a single node and a CBUSH element. The  CBUSH has the stiffness properties of the az imuth ball bearing with low rotational stiffness around Z axis.  The azimuth fork connects the az imuth ball bearing to the upper frame. The elevation axis is connected to  the upper frame by two CBUSH s representing the elevation axis ball bearings. The mirror Co G is located  at the intersection of the azimuth and elevation axis.  

The beam section has been tuned to obtain a first frequency above 140 Hz, and near the quiet reaction  wheel zone that is below 200 Hz  and the CBUSH spring constant has been chosen to represent  ball  bearings  stiffness . The total mass of the modeled mechanism is about 7 kg.  

The eigenfrequencies and modal effective mass of the simplified model  of a pointing mechanism using ball  bearing is shown in Table 2. The participating mass and inertia that are dominant for each mode has been  highlighted in Table 2. 

Table 2: Ball bearing pointing mechanism eigenfrequencies and participating mass   ID Freq TX TY TZ RX RY RZ   Hz kg kg kg kg m2 kg m2 kg m2  1 0.2 -2.74E -05 -1.33E -05 1.95E -16 1.10E -08 1.46E -10 -2.13E -01  2 4.3 1.62E -15 -3.55E -05 -8.11E -10 .521E-01 -2.45E -17 -.116E-12  3 163.4  -3.29E -10 2.59E+00  .278E-05 -4.09E -03 -.242E-10 -2.54E -12  4 179.9  1.15E+00  3.98E -10 -2.81E -05 1.23E -11 1.68E -01 -1.78E -12  5 499.6  -2.33E+00  6.44E -12 -2.46E -05 2.31E -11 .845E-01 .544E-12  6 779.9  -.974E-05 -1.54E -05 2.57E+00  -1.54E -05 1.51E -06 9.89E -18
511 The first two modes are the ones associated with the az imuth and elevation rotation ax es. As these modes  are controlled  by the elevation and azimuth motors, they are not a  concern in the micro -vibration analysis.   The 3rd mode is a translational mode in Y direction and takes  place at 163 Hz. The 4th and 5th modes are  due to the bending of the azimuth fork and combine a translation in X and a rotation around Y. Finally, the  6th mode is a translational mode in Z direction.  

A frequency response (SOL111) analysis is carried out with a unit acceleration excitation in each  translational and rotational direction. The X, Y, Z displacements and angles of the mirror center of gravity  are monitored giving 36 transfer functions of the mechanism.  The responses  that are the most detrimental  to the pointing stability are the Y rotation (elevation) due to X -translation excitation, and Y rotation due to  Y-rotation excitation (see Figure 9). 

Figure 9: Ball bearing pointing mechanism response on elevation axis  rotation (Y-rotation) for a X - translational (left) and a Y -rotational (right) unit acceleration excitation  

Figure 9 shows that even though the mirror is perfectly balance d, micro -vibration  at the base of a stiff  pointing mechanism will be amplified by the structural mode and lead to rotation of the mirror around  elevation axis. These perturbations cannot be compensated by drive electronics as they are taking place  above the control frequency bandwidth. In addition, the prediction of the induced movement can be dif ficult,  as the mode shape is playing a key role. In an optimistic approach,  where the mirror is perfectly balanced   and the first main mode located in a rather quiet micro -vibration frequency range where acceleration is   0.001 m/s2, the micro -vibration -induc ed motion around the elevation axis is o n the order of 1 µrad for   X translation excitation. On top of this, the motion due to Y rotation excitation shall be added as well as all   the noise coming from the mechanism ball bearings and the induced motion  from unbalanced mass . In  these conditions, it is difficult to reach the stability requirement of 0.1 µ rad or smaller.  

Passive Damping of Micro -vibration  

A simple way to reduce the micro -vibration effec ts on the mirror pointing stability is to introduce compliance  in the system. The goal is to control and lower the rotational eigenfrequencies of the pointing mechanism  below micro -vibration  excitation frequencies  from the spacecraft  but still above control loop frequenc ies. A  pointing mechanism with such low resonance frequency is passively damping the micro -vibration  thanks to  the natural transfer function decay observed above resonance frequency.  

Compliance is efficiently introduced in the mechanism using flexible pivots. A novel concept of a pointing  mechanism has been developed  to cover a full hemispherical pointing range . A fully functional, and  motorized breadboard has been built to verify the functional  and range requirement and  is shown in    Figure 10.  The beauty of this concept is that it replaces  the traditional coarse and fine pointing mechanism
512 used in high accuracy pointing mechanisms  by one unique ultra- stable pointing mechanism with micro - vibration isolation capability, bringing mass, volume and cost down.   

Figure 10: Novel concept of pointing mechanism  

The pointing mirror is supported by two large angle flexible pivot s similar to the D3 design presented earlier  and provides  the elevation rotation around X. The ir stators are connected to a frame structure by two small  angle flexible pivots  (3rd Axis)  to lower the Y rotation eigenmode of the elevation axis. The stator side of the  small angle 3rd axis pivot s is then connected t o the azimuth fork . The azimuth fork is then connected to the  azimuth ball bearing by a set of small angle flexible structures  for decoupling the azimuth rotation axis  from  azimuth motorization mode, azimuth ball bearing,  and spacecraft -born rotational micro-vibration . A flexible  pivot is used between the elevation stepper and elevation axis to filter out the high frequency micro -vibration   noise coming from the motor.  

The novel pointing mechanism dynamic behavior is studied using a simplified Nastran model  shown in  Figure 11.
513   Figure 11: Simplified Nastran model of the novel pointing mechanism  

The exact same structur al properties have been used for the novel concept using flexible pivot s as in the  ball bearing version presented previously . The notable difference is that the axial, radial, bending and  torsional stiffness of the flexible connection have been tuned to lower the first eigenmodes. Table 3 shows  the eigenfrequencies of the first 12 modes together with their participating mass and inertia.  

Table 3: Novel concept pointing mechanism using flexible pivots eigenfrequencies and participating mass   ID Freq TX TY TZ RX RY RZ   Hz kg kg kg kg m2 kg m2 kg m2  1 0.2 7.51E -10 1.78E -10 8.90E -29 1.21E -16 1.52E -20 4.53E -02  2 0.4 1.90E -11 2.13E -27 2.41E -10 2.62E -28 3.53E -02 7.38E -22  3 4.3 2.76E -28 1.28E -09 6.58E -19 .272E -02 3.35E -27 3.73E -26  4 20.6 7.84E -25 1.22E+00  1.51E -16 6.98E -10 5.15E -29 5.45E -25  5 20.6 1.01E -15 2.92E -17 1.19E+00  3.55E -19 7.84E -23 5.34E -30  6 29.2 1.20E+00  3.56E -25 1.16E -15 2.19E -27 6.93E -12 2.24E -25  7 46.9  7.46E -11 1.96E -11 1.71E -25 1.64E -17 9.07E -21 2.82E -12  8 47.6  3.96E -12 2.01E -28 3.08E -11 4.42E -28 1.81E -11 7.78E -31  9 180.6  5.94E -20 5.47E+00  9.60E -12 2.09E -05 5.75E -28 2.96E -24  10 362.4  5.51E+00  9.92E -21 2.97E -10 5.12E -22 6.80E -07 1.35E -24  11 839.4  2.97E -17 1.26E -02 5.11E -07 1.34E -02 7.56E -24 1.03E -24  12 870.8  3.06E -10 9.74E -10 5.44E+00  1.08E -09 8.22E -17 7.64E -32 

Modes  number 1 and 3 are the same ones as those of Table 2, and are rotational modes around azimuth  and elevation ax es. Mode number 2 is a new mode introduced by the 3rd axis which will greatly help to  damp Y rotations of the mirror under perturbations  coming from the spacecraft interface.  

Modes 4, 5 and 6 are translational modes of the elevation axis. Thanks to the low radial and axial stiffness  of the large- angle flexible pivot, it is possible to lower these modes  below the excitation frequencies of  cryocooler s while keeping them well above typical controller frequency and avoid control issues.