ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
(7)  (8)  (9)  (10)  (11)  (12) 𝜴𝜴 is the frequency ratio between excitation and natural frequencies 𝜴𝜴=𝒘𝒘 𝒘𝒘𝒏𝒏,  𝝃𝝃𝒇𝒇 is the damping ratio 𝝃𝝃𝒇𝒇=𝒄𝒄𝒇𝒇 𝟐𝟐�𝒌𝒌𝒇𝒇·𝒎𝒎𝒇𝒇 It can be useful to define a normalized displacement as  a relationship between the fast moving and the  input  stage displacements:   𝑵𝑵𝑵𝑵 =𝒙𝒙𝒇𝒇 𝒙𝒙=𝐧𝐧𝟏𝟏 (𝟏𝟏−𝜴𝜴𝟐𝟐)+𝟐𝟐𝝃𝝃𝒇𝒇𝜴𝜴  The m agnetic forces acting on the fast  mass (𝒎𝒎𝒇𝒇) will depend on the relative displacements between the  “virtual intermediate stage” and the inertial mass   𝑭𝑭𝒇𝒇𝒇𝒇𝒔𝒔𝒊𝒊=−𝒌𝒌𝒇𝒇(𝑿𝑿𝒇𝒇−𝒏𝒏𝑿𝑿)=𝒏𝒏𝒌𝒌𝒇𝒇𝑿𝑿·𝒎𝒎𝒇𝒇𝝎𝝎𝟐𝟐−𝒋𝒋𝑪𝑪𝒇𝒇𝝎𝝎 (𝒌𝒌𝒇𝒇−𝒎𝒎𝒇𝒇𝝎𝝎𝟐𝟐)+𝒋𝒋𝑪𝑪𝒇𝒇𝝎𝝎  By  hypothesis of the magnetic linear gearbox, the input reactive force exerted by the device when  connected to the main system mass ( m) is multiplied by the gearbox ratio:   𝑭𝑭𝒊𝒊𝒏𝒏𝒊𝒊𝒊𝒊𝒊𝒊 =−𝒏𝒏·𝑭𝑭𝒇𝒇𝒇𝒇𝒔𝒔𝒊𝒊  Therefore, combining Eq.7 and E q.8 and including a friction damping component to represent the friction  in the linear bearings observed during tests.   𝑭𝑭𝒊𝒊𝒏𝒏𝒊𝒊𝒊𝒊𝒊𝒊 =−𝒏𝒏𝟐𝟐𝒌𝒌𝒇𝒇𝑿𝑿�𝒎𝒎𝒇𝒇𝝎𝝎𝟐𝟐−𝒋𝒋𝑪𝑪𝒇𝒇𝝎𝝎 (𝒌𝒌𝒇𝒇−𝒎𝒎𝒇𝒇𝝎𝝎𝟐𝟐)+𝒋𝒋𝑪𝑪𝒇𝒇𝝎𝝎�+𝒋𝒋𝑭𝑭𝒄𝒄·𝒔𝒔𝒊𝒊𝒔𝒔𝒏𝒏(𝑿𝑿)  where  𝑭𝑭𝒄𝒄 is the Coulomb equivalent force,   𝒔𝒔𝒊𝒊𝒔𝒔𝒏𝒏(𝑿𝑿) repres ents the sign of the input displacement vector.   Two p otential advantages can be derived from previous equation. One is  that the enhancement of the input  force of the Z -Damper  is proportional to the square of the gear ratio and  the other is  the maximization of  the input force at the resonance of the Z -Damper .  Wh en connected to a vibrating mass, the overall system can be described as a two -mass system with a  motion equation of the shape:   �𝒎𝒎 𝟎𝟎 𝟎𝟎 𝒎𝒎𝒇𝒇�·�𝒙𝒙̈ 𝒙𝒙̈𝒇𝒇�+�𝒄𝒄+𝒄𝒄𝒇𝒇−𝒄𝒄𝒇𝒇 −𝒄𝒄𝒇𝒇𝒄𝒄𝒇𝒇�·�𝒙𝒙̇ 𝒙𝒙̇𝒇𝒇�+�𝒌𝒌+𝒏𝒏𝒌𝒌𝒇𝒇−𝒏𝒏𝒌𝒌𝒇𝒇 −𝒏𝒏𝒌𝒌𝒇𝒇𝒌𝒌𝒇𝒇�·�𝒙𝒙 𝒙𝒙𝒇𝒇�=�𝑭𝑭𝒆𝒆����⃗ 𝟎𝟎�  In order to represent the effectiveness of the vibration isolation performance, the normalized displacement   amplitude  of the vibrating mass  (𝑵𝑵𝑵𝑵 =�𝒙𝒙𝒌𝒌 𝑭𝑭𝒆𝒆�) is frequently used:  �𝒙𝒙𝒌𝒌 𝑭𝑭𝒆𝒆�= ⎷⃓⃓⃓⃓⃓⃓⃓⃓� �𝟏𝟏−𝜴𝜴𝟐𝟐 𝜷𝜷𝟐𝟐�𝟐𝟐 +�𝟐𝟐𝝃𝝃𝒇𝒇𝜴𝜴 𝜷𝜷�𝟐𝟐 �𝜴𝜴𝟒𝟒 𝜷𝜷𝟐𝟐−�𝟒𝟒𝝃𝝃𝒇𝒇𝝃𝝃𝒊𝒊 𝜷𝜷+𝟏𝟏 𝜷𝜷𝟐𝟐+(𝒏𝒏𝟐𝟐𝝁𝝁+𝟏𝟏)�𝜴𝜴𝟐𝟐+𝟏𝟏�𝟐𝟐 +𝟒𝟒�𝜴𝜴�𝝃𝝃𝒇𝒇 𝜷𝜷+𝝃𝝃𝒊𝒊�−𝜴𝜴𝟑𝟑 𝜷𝜷�𝝃𝝃𝒇𝒇(𝒏𝒏𝟐𝟐𝝁𝝁+𝟏𝟏)+𝝃𝝃𝒊𝒊 𝜷𝜷��𝟐𝟐 where  n i s the multiplication ratio of the linear magnetic gearbox in the Z -TVA,  𝜴𝜴 is the frequency ratio between excitation and natural frequencies 𝜴𝜴=𝒘𝒘 𝒘𝒘𝒏𝒏,  𝜷𝜷 is the ratio between the natural frequencies of the Z -Damper and the main mass 𝜷𝜷 =𝒘𝒘𝒇𝒇 𝒘𝒘𝒊𝒊,  NASA/CP—2018-219887 180
The internal natural frequencies of the Z -Damper  and main system natural frequencies can be defined as   𝝎𝝎𝒇𝒇=�𝒌𝒌𝒇𝒇 𝒎𝒎𝒇𝒇 𝒇𝒇𝒏𝒏𝒂𝒂      𝝎𝝎𝒊𝒊=�𝒌𝒌 𝒎𝒎 respectively.   𝝃𝝃𝒇𝒇 and 𝝃𝝃𝒊𝒊 are the TVA and the structural damping ratios 𝝃𝝃𝒇𝒇=𝒄𝒄𝒇𝒇 𝟐𝟐�𝒌𝒌𝒇𝒇·𝒎𝒎𝒇𝒇 𝒇𝒇𝒏𝒏𝒂𝒂 𝝃𝝃𝒊𝒊=𝒄𝒄 𝟐𝟐√𝒌𝒌·𝒎𝒎 The p revious equation properly describes the dynamic behavior of  both the Z -Damper and the Z -TVA.  Dev ices Description   Two  passive prototypes are designed, manufactured and tested in a relevant environment  to demonstrate  the impedance matching principle. First, a prototype of a high- temperature enhanced eddy current damper  (Z-Damper) able to operate at nominal temperatures up to 200ºC and second, a mass reduced tuned  vibration absorber (Z -TVA). Fig. 3 shows  both prototypes installed in the test bench and ready to be tested.  Figure 3. Z-Damper prototype (left) and Z -TVA prototype (right)   The phil osophy of the Z -Damper prototype is to maximize damping at a desired frequency determined by  design specifications. Operation at 200ºC was required. The philosophy of the Z -TVA was to demonstrate  a single degree of freedom tuned vibration absorber with a highly reduced internal mass  (𝒎𝒎𝒇𝒇) but similar  performance to a classic tuned vibration absorber. A design resonant frequency of 18 Hz  was fixed by  design for the TVA. A summary of performance and figures of both prototypes is given in Table 1.   NASA/CP—2018-219887 181
Table  1. Z-Damper and Z -TVA prototypes main characteristics   Z-TVA Z-Damper Gear Ratio  7:1 7:1 -  Diameter  82 105 mm  Length  493 491 mm  Total Weight  9.6 19.6 kg  TVA weight  3.6 NA kg  Maximum input displacement >±5 >±5 mm  Max. Input  Force (25ºC) 4670  6500  N  Temperature sensitivity -2.9 -1.8 N/ºC   Operational Temperature Range   (validated by tests)  [RT,95] [-50 to 200]  ºC  Survival  Temperature  Range   (validated by tests)  [-70,95]  [-70,270]  ºC  Internal Resonant Frequency  18 12 Hz  Internal mass ( ma) 3.6 8.5 kg  Input maximum stiffness  (k) 2081  2548  N/mm  Fast-stage stiffness  (ka) 42 52 N/mm  Max. Equivalent viscous damping  coefficient at 12 Hz (200ºC)  NA 35 Ns/mm   Z-Damper description The Z -Damper prototype has been designed with a gear ratio of 7:1. Fast-moving stage and stator are  mainly composed of ring shaped permanent magnets made of SmCo 32H with a high temperature  resistance to demagnetization. The input stage is mainly composed of FeCo alloy laminated rings. FeCo  rings  were heat treated for an optimum  magnetic and mechanical performance.  Ti grade- 5 ring spacers are  used to control the gap between the different elements in the gearbox. Most structural elements of the device (shafts, flanges, rods…) are made also of Ti grade 5 due to its excellent  mechanical strength and  relative ly low density. Self -lubricated PFTE bearings  are used in order to allow relative motion between the  different stages  of the device. The materials used in the Z -Damper allow operation of the device  at very  high temperatures, theoretically up to 300 ºC.   Fi nally, the outermost layer of the Z -Damper is composed of an electrolytic copper finned shell. Eddy  currents are generated in the shell by motion of the fast stage permanent magnets (PMs), and then the  generated heat is dissipated to the environment  by force d convection. Fig.4 shows a real picture of the Z - Damper and a schematic representation:   NASA/CP—2018-219887 182
Figur e 4. Z -Damper prototype (top) and diagram of the internal elements of the Z -Damper (bottom)   Z-TVA description The Z -TVA prototype has been designed with a gear ratio of 7:1. The stator and the fast -moving stage are  mainly composed of NdFe N48H ring permanent magnets , axially magnetized. Permanent magnets are  placed with facing opposing polarities  and kept in position using e poxy adhesives and mechanical fixtures.  The input stage is mainly composed of low carbon steel AISI 1010 laminated soft magnetic teeth that  are  assembled inside a Ti gr ade 5 seamless tube. Non- magnetic titanium spacers are used  for a proper  disposition of the soft magnetic teeth in the magnetic gearbox.   Lin ear ball bearings, grease lubricated, are used to allow relative motion between the fast -moving stage  and the input , and grease- lubricated bushings are used between the stator and the input stage. Most of the  structural components of the device are manufactured using Ti grade 5 due to its high yield strength and  low density. Fig. 5 s hows  a real picture and  a partial cross section of the device.   NASA/CP—2018-219887 183
Figure 5. Z-TVA prototype (top) and diagram of the internal elements of the Z -TVA (bottom)   Test B ench and Set Up  Bot h the Z -Damper and the Z -TVA were tested at a component level.  A dedicated test bench  (Fig. 6)  has  been designed, manufactured and set up to demonstrate the Z -Damper concept. The test bench is mainly  composed of a bench structure (1)  and a supporting structure (2), a 15.7 -kN hydraulic actuator with  hydrodynamic seals for high- frequency actuation from Moog ( 3). The actuator is feed with ISO grade 32 oil  pumped by the hydraulic group equipped with a 15  CV electric motor (4). A climatic chamber is used to  control the prototype temperature (5), a 3- kW high- temperature- resistant centrifugal fan (6) and a PID - controlled 12-kW heat resistor (7) are used to control the ventilation flow and the climatic chamber  temperature. The test bench is controlled from a fixed PC station (8). Finally, flexible high temperature  resistant ducts  are used for recirculation of the ventilation air (9) .   Input  position is measured by a LVDT sensor with 0.01- mm accuracy. Input force is measured by a HBM  U10M traction- compression load cell with a measurement ra nge up to 25 kN and 0.02 precision class. The  position of the fast -moving stage is measured by a Micro- Epsilon optoNCDT ILD -1402 laser triangulator  with 5-μm resolution. Several PT-100 temperature sensors in a 4- wire configuration are used to  characterize the temperature of the flowing air and the prototype temperature. The data acquisition system  is composed of NI9217, NI9203 and NI9263 acquisition cards from National Instruments  installed in a NI  9188 rack.   NASA/CP—2018-219887 184
Figur e 6. Test bench   Test  Results   Z-Damper tests results Fig.7 shows the input and fast stage displacement of the Z -Damper at room temperature when no copper  dissipater is installed. A n input sinusoidal excitation of about 1-mm amplitude is forced at different excitation  frequencies from 1 to 60 Hz.  Displacement multiplication (n=7) induced by the magnetic gear is observed  even at low frequencies.   Fi gure 7. Input and fast stage position vs. time for different sinusoidal harmonic excitation frequencies   NASA/CP—2018-219887 185
Fig.  8 shows the theoretical prediction and the experimental results of the internal normalized displacement,  as described in Eq. 7, of the Z -Damper fast stage as a function of the excitation frequency. Results including  the outermost copper dissipater (blue data) and not including it (black data) are provided. The increase in  damping is evident when the copper dissipater is installed.   Fi gure 8. Normalized displacement of the Z -Damper with copper dissipater (blue) and without copper  dissipater (black) for different excitation frequencies.   Fig . 9 shows the experimental input force of the Z -Damper when subjected to sinusoidal harmonic  excitations  of 2-mm amplitude  and at  a temperature of  200ºC. Good agreement with theoretical predictions  of Eq. 10 is  observed. It can also be observed how the damping input force is maximized at the desired  resonant frequency.   Fi gure 9. Theoretical prediction (blue) and experimental data (black) of the Z -Damper input force for  different excitation frequencies.  0,010,1110 0,1 1 10 100Normalized Displacement [xfast/Xinput] Frequency [Hz]Harmonic Oscillator ξ=0.25, ω n=12.5 Hz  Harmonic Oscillator ξ=1.5, ω n=12.5 Hz  Z-Damper_without copper Z-Damper_with copper at RT70 7 0,7 0,07 NASA/CP—2018-219887 186
Fina lly, Fig. 10 shows the hysteresis loops of the Z -Damper at various temperatures. Maximization of the  dissipated energy is obtained at the operational temperature of 200ºC.  From damping curves at 200ºC , a  maximum viscous damping coefficient of 35 Ns/mm has been calculated.   Fi gure 10. Input  forces vs. input position for a 2-mm input sinusoidal vibration of 12 Hz at different  temperatures from room temperature to 200ºC.   Z-TVA Test Results Fig.11 shows the normalized displacement of the inertial mass of the Z -TVA. Very good agreement is  reached with theoretical predictions from Eq. 7.   Fi gure 4. Normalized displacement of the Z -TVA fast moving stage for various sinusoidal harmonic  excitation frequencies.   770 0,7Normalizedisplacement [Xfast/Xinput] NASA/CP—2018-219887 187
Input  force of the Z -TVA has been also measured at different excitation frequencies. Despite that good  agreement has been found between the experimental data and the theoretical predictions from Eq.10 at  the resonance region, minor discrepancies have been found at lower frequencies. The reasons for that are  not very well understood and fur ther investigation is still required.   Fi gure 5. Input force vs. excitation frequency of the Z -TVA.   Theoretical Performance Evaluation   Si nce the conducted tests did not include a vibrating mass system as the one described in Fig. 2, an  evaluation was conducted of the performance as a tuned vibration absorber of the Z -TVA based on the  experimentally validated model described in Eq.12. Fig. 12 shows the expected normalized displacem ent  of three different systems:   •A  5000- kg vibrating mass and a typical system stiffness of 4.8·107 N/m with a natural frequency of 18 Hz,  with no tuned vibration isolation device but typical structural damping ( ξ=0.01) •Sys tem with structural damping ( ξ=0.01) and a 150- kg optimal TVA. (𝝁𝝁=𝟎𝟎.𝟎𝟎𝟑𝟑,𝛏𝛏𝒇𝒇=𝟎𝟎.𝟏𝟏𝟎𝟎𝟏𝟏,𝜷𝜷=𝟎𝟎.𝟗𝟗𝟗𝟗) •Sys tem with structural damping ( ξ=0.01) and a 9.6 kg Z -TVA device. (𝝁𝝁=𝟎𝟎.𝟎𝟎𝟎𝟎𝟎𝟎𝟗𝟗𝟑𝟑,𝛏𝛏𝒇𝒇=𝟎𝟎.𝟏𝟏𝟏𝟏𝟑𝟑,𝜷𝜷=𝟎𝟎.𝟗𝟗𝟗𝟗 ) Fig. 13  shows  the vibration isolation performance obtained with the three different isolation methods.  Perfect overlapping of the curve of the t ransmissibility of the Z -TVA and a classic TVA is observed.   However, it is very remarkable that the weight of the TVA system is more than one order of magnitude  larger than the proposed Z -TVA solution.   NASA/CP—2018-219887 188
Figur e 6. Normalized displacement of the vibrating mass vs. excitation frequency when no damping  system (red dashed line), a classic optimized TVA with  150 kg (black line) and a Z -TVA of 9.6 kg attached  to the vibrating structure.   Con clusions and Lessons Learned   Z-D amper is a new technology for vibration isolation in aerospace structures and equipment . It takes advantage of  impedance matching in a magnetic  linear gear to optimize vibration isolation performance. At the same time, it reduces the weight and space requirements of the solution.  Since there  is no  contact between moving parts  except from the supporting linear bearings, it is suitable for long- life operation in space environmental conditions  without wear or debris generation. In t his paper the theoretical dynamics of Z -Damper is presented and experimentally validated. Two  prototypes of the technology were designed, manufactured and tested: a prototype of an enhanced eddy  current damper (Z -Damper) able to operate at temperatures up to 200ºC and a prototype of an extra- light  tuned vibration absorber (Z -TVA). The Z- TVA was designed with a resonant frequency of 18 Hz. With only  9.6-kg mass, it showed a similar performance to a classic tuned vibration absorber of 150 kg, demonstrating  the potential of the technology for significant weight -saving and tight space requirements.   Some lessons learned during the project are:   •A Z-Damper high temperature eddy current damper can achieve high damping ratios (up to 35 Ns/mm) at operational temperatures up to 200ºC  even for low input displacement amplitudes . •The use of a magnetic linear gear allows a high reduction of the inertial mass of a tuned vibration absorber. The Z -TVA demonstrated a similar performance to a classic TVA more than 10 times heavier . Ac knowledgements  and Previous Publication Record   Thi s work has been partially funded by the Seventh Framework Clean Sky Program of the EU Commission,  under grant  JTI-CS-2013- 02-SFWA -03-013.  NASA/CP—2018-219887 189
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What causes microvibration in mechanisms?  Physical causes of microvibration can be anything generating forces in the mechanism. A non-exhaustive  list of causes is rotor imbalance, mechanical bearing irregularity, bearing friction and imperfections, motor  cogging, stepper motors, and gear meshing and contact. Knowledge and understanding of these causes  is key to optimize a mechanism for low microvibration.  Several aspects complicate dealing with mechanisms as noise sources:  •Noise is generated in six degrees of freedom (DOF). Measurement or analysis of the mechanism needs to assess all six DOF, and not remain limited to the DOF most directly related to the mechanism motion, e.g. the rotation axis for a SADM. •The phase of the six DOF of noise may be important but is often lost when multiple noise source data is combined for analysis. This is particularly relevant at spacecraft level, but could be of note to a mechanism designer in charge of delivering multiple mechanisms. •The dynamic coupling of the noise source to the spacecraft affects the noise injected into the spacecraft. This aspect is typically handled at system level. •Noise generation depends on operational parameters (for example APM noise is dependent on axis position as well as rotational speed). For mechanisms with multiple degrees of freedom, this could lead to a cumbersome verification campaign. From a design point of view, the modal design of mechanisms is typically aimed at surviving the launch. Structural modes of the mechanism will amplify noise generated internally to the mechanism. These modes can differ significantly for different configurations of the mechanism and may lead to additional design constraints. •Some noise sources have varying noise performance over time. Mechanical wear of certain components can worsen the performance. In addition, some mechanisms may show intermittent periods of generating higher noise, for example if bearing cage instability occurs. •There is unavoidable inherent variability between individual seemingly identical noise sources. Figure 1 shows how 8 identical RWs may vary in noise up to one order of magnitude in Power Spectral Density (PSD). •The noise performance may be affected by vacuum, temperature, gravity effects, exposure to vibration and shock, and changes over life. Figure 1 shows how the noise of these RWs increases after vibration test. Figure 2 shows how different levels of pressure impact the modal behavior of another RW. This RW is evacuated. Removing the ambient pressure changes the shape of the thin walled pressure vessel, which in turn stiffens the main lateral mode. These aspects have an impact on how the microvibration requirements are derived and need to be  verified.  Figure 1. RW noise for several identical units and impact of vibration tests. Image courtesy of SSTL.  NASA/CP—2018-219887 192
Figure 2. Reaction wheel noise at different pressure. Images courtesy of Bradford Engineering [2]. The  structural modes are excited by the internally generated noise and strong amplification can be seen  across the speed range. One of these modes is sensitive to the surrounding pressure and changes.  Case study: On ground versus on orbit noise behavior for a dry RW  For a European Space Agency (ESA) R&D study, Surrey Satellite Technology Ltd (SSTL) performed inorbit microvibration measurements using an in-situ microvibration monitoring system [1]. Several different  noise sources were measured, but the most surprising results appear on two reaction wheels that are  identical except for the lubricant used. One wheel uses a synthetic oil, whereas the other uses dry  lubricant in the form of a sacrificial bearing cage.  Figure 3 shows how the dry-lubricated RW becomes significantly noisier on orbit. In comparison, its oillubricated counterpart behaves the same in orbit as it did during on ground tests, as shown in Figure 4.  The explanation put forward by SSTL theorizes particles generated by the sacrificial bearing cage are  kept out of the bearing raceway on ground due to gravity effects but may impact the noise signature of  the RW in absence of gravity. This example demonstrates how assessing microvibration generated by a  mechanism can be significantly impacted by the conditions on ground.  Measurements for these reaction wheels and other noise sources were taken over a time period of 18  months. In that time, no clear degradation of the microvibration performance was recorded. However, in  case there is a real concern regarding microvibration degradation performance for a specific mechanism,  a monitor such as the one flown by SSTL can be used for in situ health monitoring. Early warning of  changing performance gives the spacecraft operator the opportunity to take the necessary corrective  action where possible.  NASA/CP—2018-219887 193
Figure 3. Noise signature for the dry lubricated RW: in-orbit data (red), on-ground spacecraft data (green)  and Kistler data (blue). Image courtesy of SSTL [1].  Figure 4. Noise signature for the oil lubricated RW: in-orbit data (red), on-ground spacecraft data (green)  and Kistler data (blue). Image courtesy of SSTL [1].  NASA/CP—2018-219887 194