High Flexibility Rotorcraft Driveshafts using Flexible Matrix Composites and Active Bearing Control

1
PS 2.2
High Flexibility Rotorcraft Driveshafts using
Flexible Matrix Composites and Active Bearing
Control Principal Investigators Kon-Well Wang,
Ph.D. Diefenderfer Chaired Professor in
Mechanical Engineering Charles Bakis,
Ph.D. Professor of Engineering Science and
Mechanics Edward Smith, Ph.D. Professor of
Aerospace Engineering Graduate Student supported
by RCOE Bryan Mayrides (M.S. student) Other Team
Members Hans DeSmidt (Ph.D. student) Ying Shan
(Ph.D. student)
2
Issues of Current Driveline Systems Problem
Statement and Technical Barriers

• Current Drivelines
• Segmented shafting with significant
• of flex couplings/bearings for
• misalignment compensation
• Passive dampers needed for supercritical speed
  shafts
• High Maintenance and Cost
• Component (bearings, couplings, dampers) wear
• Shaft balancing and alignment
• Strict shaft eccentricity tolerances

3
Program Goal and Ideas

• To address the issues with current systems and
  overcome the technical barriers for achieving a
  simple, high performance, low vibration, low
  cost, and low maintenance driveline of
  rotary-wing aircraft
• Reduce number of mechanical contact components
• Reduce maintenance need
• Suppress vibration and ensure stability

• Develop and utilize newly emerging materials and
  active control technologies -- a combination of
• Flexible matrix composite (FMC) materials and
• Active magnetic bearings (AMB)

IDEAS ?
4
Ideas

• Flexible matrix composite (FMC) materials with
  tailored ply orientations for shafting
• Soft in flexure and stiff in torsion to
  accommodate for large misalignment and
  effectively transmit power
• Without multi-segment shafting and large of
  bearings/couplings -- reduce cost and maintenance
  need

5
Ideas (cont.)

• Active magnetic bearings for low maintenance and
  vibration control
• While highly flexible composite driveshaft
  systems have many advantages, their vibration
  behavior could be issues that need to be
  addressed before realizing the idea
• Penn State researchers have explored the
  feasibility of active vibration control of
  tailrotor-drivetrain structure via active
  magnetic bearings (AMB) ? by proper controller
  design, the AMB actuator could be a good
  candidate for helicopter driveline control (size,
  weight, power) DeSmidt, Wang, and Smith, Proc of
  54th AHS Forum, 1998

• Non-contact -- no frictional wear
• Large frequency range -- ideal for active
  vibration control in rotorcraft setting
• Light backup roller bearings (only contact with
  active failure) for fail-safe purpose

6
2004 Review Comments and Actions

• Assess Potential Payoffs
• We have examined payoffs for supercritical
  driveline in previous studies this year we
  expanded the study to show potential payoffs
  (weight and component reductions) for subcritical
  drivelines via system design
• Assess Cost Benefit
• Qualitatively, reducing components/maintenance
  reducing cost
• To quantify cost benefit ? requires development
  on specific drive system with manufacturers and
  users (future RITA project)
• Examine Practicality of Magnetic Bearing
• Have achieved another successful demonstration of
  AMB controller for FMC shafting with
  uncertainties
• In the process of examining AMB design (weight,
  size, power) in rotorcraft setting via NASA Glenn
  design code (On-going effort)
• Have generated new ideas of hybrid active-passive
  failsafe devices as future basic research topics
• Address Failure Modes
• Thorough study beyond scope of current program
  Have generated ideas/plan to examine this issue
  as a future basic research topic

7
Research Issues and Task Objectives

• Materials and Composite Issues
• Structural Mechanics and Dynamics Issues
• Systems and Controls Issues

8
Research Issues and Task Objectives

• Materials and Composite Issues
• Rationale
• Traditional barrier to higher strain operation of
  fiber composites is matrix cracking
• Flexible, low-modulus matrix can potentially
  avoid cracking

• Technical Objectives
• Select a trial flexible matrix system
  (carbon/polyurethane)
• Develop filament winding process
• Characterize stiffness damping behavior and
  validate models over range of temperatures,
  frequencies, and strains
• Build lab-scale shafts for experimental
  validation of self-heating, structural dynamics,
  and to investigate fatigue behavior

Matrix Cracking
9
Materials and Composite Sub-Task

• Achievements 2001-2003/04
• Developed wet filament winding technique for
  trial flexible matrix composite shafts
  (carbon/polyurethane)
• Developed test apparatus method for
  characterizing frequency and temperature
  dependent damping stiffness of FMC laminas and
  laminates
• Developed validated models for frequency and
  temperature dependent damping stiffness of FMC
  laminas and laminates
• Developed model and test method to investigate
  self-heating behavior of rotating misaligned FMC
  shafts

• Summary of Accomplishments in 2004/05
• Refined and experimentally validated self-heating
  model of rotating misaligned FMC shafts

10
Internal Self-Heating Model and Experimental
Validation Method for Misaligned Rotating FMC
Shafts

• Input to the temperature model frequency and
  temperature dependent lamina
• properties of FMC material misalignment strain
  shaft speed
• The misalignment strain and rotation speed can
  be controlled. The stand can spin
• FMC shafts at up to 1.25 misalignment strain,
  and at speed up to 2500 RPM

11
Model Results and Experimental Validation
(45) deg. FMC
0.75, RMC
0.75, FMC

• Model capable of predicting self heating
  behavior of FMC
• materials and providing guidance for design and
  control of
• FMC shaft

• Self-heating of FMC shaft is insignificant
  compared to RMC

12
Effect of Temperature on Shaft Properties
Shaft Longitudinal Modulus
60/-60/25/-25s
45/-45/45/-45s

• Laminate design affects temperature sensitivity
  of shaft
• Tool developed can predict temperature effect on
  shaft properties ? provide design and control
  guidance

13
Research Issues and Task Objectives

• Materials and Composite Issues
• Structural Mechanics and Dynamics Issues
• Develop analysis tools for driveshaft dynamic
  loads/ deformation characterization (e.g., strain
  level, buckling, stability, damping effect on
  temperature property variation)
• FMC materials selection and structural
  tailoring/optimization to satisfy design desires
  (e.g., maximum allowable misalignment, minimum
  weight, and minimum internal damping)
• Systems and Controls Issues

14
Structural Mechanics and Dynamics Sub-Task

• Summary of Previous Work (2001-2003/04)
• FE model and analysis tools have been developed
  to analyze driveline static and dynamic
  characteristics (deformation,stress level,natural
  frequency, etc.)
• Utilizing the model and tools developed,
• Performed study to provide information regarding
  parameter effects on system (durability,
  stability, etc.)
• System parameters were tailored to achieve
  satisfactory system performance for supercritical
  driveline

15
Structural Mechanics and Dynamics Sub-Task

• Summary of Current Work (2004/05)
• Examined feasibility of designing FMC driveshafts
  for subcritical applications
• Maintain advantages of current supercritical
  driveline (light weight, fewer bearings) but
  without the shortcomings (high vibration, whirl
  instability, and external damper requirements)
• Performed optimization study where shaft
  parameters were tailored to find minimum weight
  and/or component driveline that meets performance
  requirements
• Examined applications for model/analysis tool
• Reducing weight in subcritical driveline
  (Blackhawk, Chinook)
• Design a driveline for a minimum number of
  components

16
Design Approach/Model Outline

• Inputs
• Helicopter properties (shaft geometry, speed,
  power)
• Applied loads (torque, misalignment, imbalance)
• Design variables (ply sequence, ply angles,
  bearings, outer diameter)
• Inputs used to iteratively calculate temperature
  dependent laminate properties and steady state
  temperature
• Accounts for self-heating (misaligned rotation)
  and considers atmospheric heating and rotor
  downwash cooling
• Laminate properties (at steady state temperature)
  to calculate performance indices
• Critical speed ratio (ensures subcritical)
• Tsai Wu strength factor (measure of strength)
• Torsional buckling safety factor
• Torsional yield safety factor
• Driveline with minimum weight/components is
  optimum design

17
Minimum Weight Design Study Results - Blackhawk

• Blackhawk current driveline specifications
• 5 segments
• 4 midspan flex couplings, 4 midspan bearings
• Driveline mass 31.3 kg (69 lbs)
• Blackhawk optimum FMC driveline specifications
• 1 segment with 60/-60/-25/25S layup
• 0 midspan couplings, 3 midspan bearings
• Driveline mass 21.6 kg (47.6 lbs)

(reduction of 5 components)
(reduction of 29.5)
Input Torque 734 Nm
Conventional Alloy
18
Minimum Weight Design Study Results - Chinook
Conclusion Designers go from subcritical to
supercritical to reduce weight, but weight
savings (even component reduction) can also be
realized by using FMC drivelines while
maintaining subcritical operation

• Chinook current driveline specifications
• 7 segments
• 6 midspan flex couplings, 6 midspan bearings
• Driveline mass 60.4 kg (133 lbs)
• Chinook optimum FMC driveline specifications
• 1 segment with 50/-50/-20/20S layup
• 0 midspan couplings, 5 midspan bearings
• Driveline mass 44.4 kg (97.9 lbs)

(reduction of 7 components)
(reduction of 25.5)
Input Torque 4067 Nm
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Minimum Component Design Study

• Observations
• Always eliminate all midspan couplings for FMC
  designs (both methods)
• The number of bearing components can be further
  reduced even with subcritical speed requirement
• Weight still saved for this case as compared to
  current design

• Model analysis tool applied to re-design
  driveline for minimum components (reduce
  maintenance needs) instead of minimum weight
• Can we still achieve weight savings when
  minimizing driveline components?
• One example Blackhawk with q1/-q1/-q2/q2s layup

Current Min Weight Min Comp
Lay-up - 60/-60/-25/25S 70/-70/-10/10S
OD (m) 0.0889 0.101 0.14
Midspan Couplings 4 0 0
Bearings 4 3 2
Weight (kg) 31.3 21.6 23.8
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Research Issues and Task Objectives

• Materials and Composite Issues
• Structural Mechanics and Dynamics Issues
• Systems and Controls Issues
• Effective vibration and stability control
  methodology
• Vibration suppression -- Shaft imbalance with
  uncertain magnitude and distribution
• Stability issues for supercritical shafting --
  whirl instability due to shaft internal damping
• Adaptive control to compensate for operating
  condition uncertainty and shaft property
  variations
• Actuator/system design in rotorcraft setting
  (size, weight, power)

21
Systems and Controls Sub-Task- Achievement Summary

• Achievements (2001- 2003/04)
• Preliminary study to identify issues and
  feasibility of AMB actuators/control in
  rotorcraft setting
• Developed state equation and uncertainty function
  formulation for the AMB-FMC driveshaft system
• Synthesized hybrid robust feedback/adaptive
  feed-forward control law for AMB driveline system
  and developed robust controller design
  methodology
• Analytically and experimentally evaluated and
  validated closed-loop controller performance on
  AMB-driveline testrig (on conventional segmented
  Alloy shaft)

22
Systems and Controls Sub-Task

• Summary of New Achievements (2004/05)
• Developed H?/Synchronous Adaptive Feed-Forward
  controller for AMB/FMC driveline system
• Suppress imbalance vibration
• Suppress whirl instability (if supercritical)
• Account for FMC shaft stiffness and damping
  uncertainties due to operating temperature
  variations
• Concurrent optimal design of control parameters
  and AMB locations to maximize closed-loop
  robustness
• Analytically and experimentally evaluated AMB/FMC
  driveline closed-loop performance on testrig
• Stability and vibration suppression performance
  and robustness
• Multiple operating conditions (various shaft
  speeds, load torques, and operating temperatures)

23
AMB-FMC Driveline System with Hybrid H? /Adaptive
Control
AMB-FMC Driveline System

• One-Piece FMC shaft with rigid couplings
  supported by Active Magnetic Bearings (AMB)
• Driveline subjected to shaft imbalance,
  misalignment, torque ambient temperature
  variations

24
AMB-FMC Driveline SystemClosed-Loop Robustness
Performance

• Due to FMC stiffness and damping temperature
  sensitivity, H?/AVC designed to be robust to
  variations about nominal temperature
• Closed-loop system has significant temp.
  robustness -20F lt T lt 190F

Test Results

• Limited sensor information required
• Only uses collocated AMB sensors
• No knowledge of shaft imbalance or operating
  temperature required

25
Plan for rest of 2005

• Materials and Composite Issues
• Evaluation of FMC fatigue behavior

• Structural Mechanics and Dynamics Issues
• Use structural dynamics model to select an
  optimum matrix material
• Incorporate a safety factor in the model to
  design against fatigue failure

• Systems and Controls Issues
• Evaluate design issues (size, weight, power) of
  AMB actuator in rotorcraft setting via NASA Glenn
  AMB code
• Compare weight/size with conventional bearing
  system

26
Overall Project Accomplishments Conclusions

• We have shown, while maintaining torque
  transmitting capability
• FMC shafting
• Eliminates segments and flexible
  couplings/bearings reduces components and
  maintenance needs
• Reduces strict requirements for alignment
• Reduces weight
• AMBs
• Eliminate contact bearings reduce maintenance
• Reduce vibration level with robust performance
  w.r.t. uncertainties (temperature, operating
  conditions, etc.)
• Reduce strict requirements for balancing,
  alignment, and tolerance

• The feasibility and advantages of utilizing FMC
  and AMB technologies to improve current
  rotorcraft driveline systems have been
  demonstrated for both super- and sub-critical
  drivelines
• Tools have been developed which can be utilized
  for specific driveline system development
  applications
• Manufacturing and characterization processes
• Analytical and experimental methods
• Design and control algorithms

27
Overall Project Future Directions

• Application and development work (RITA type
  projects)
• The analytical and experimental tools developed
  can be utilized for the development and
  evaluation of specific future drivelines with FMC
  shafting and/or AMB technology
• Basic research possibilities
• FMCs with materials enhancement (environment,
  fatigue, failure modes, etc.) for advanced
  rotorcraft applications
• Active-passive hybrid non-contact bearings
  Enhance driveline fail-safety and stability while
  retaining merits of AMBs
• Distributed auto-balancing techniques Enhance
  vibration reduction of driveline without active
  action

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Publications

• Shan, Y., and Bakis, C.E., Static and Dynamic
  Characterization of a Flexible Matrix Composite
  Material, Proc. 58th American Helicopter Society
  Annual Forum, Montreal, Quebec, June 2002.
• Shan, Y., and Bakis, C.E., Frequency and
  Temperature Dependent Damping Behavior of
  Flexible Matrix Composite Tubes, 35th
  International SAMPE Technical Conference, Dayton,
  OH, Sept. 28 Oct. 2, 2003.
• Shin, E., Wang, K.W., and Smith, E.C.,
  Characterization of Flexible Matrix Composite
  Rotorcraft Driveshafts, Proc. 59th American
  Helicopter Society Annual Forum, Phoenix, AZ, May
  2003.
• DeSmidt, H.A., Wang, K.W., Smith, E.C., and
  Provenza, A.J., Stability Control of Driveline
  System with Internal Damping and Non-Constant
  Velocity Couplings, Proc. ISCORMA-2 Conference,
  Gdansk, Poland, Aug. 2003.

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Publications (Cont.)

• DeSmidt, H.A., Wang, K.W., and Smith, E.C.,
  Multi-Harmonic Adaptive Vibration Control of
  AMB-Driveline Systems with Non-Constant Velocity
  Couplings, Proc. ASME Design Technical
  Conference-19th Biennial Conference on Mechanical
  Vibration and Noise, Chicago, IL, Sept. 2003.
• DeSmidt, H.A., Wang, K.W., and Smith, E.C.,
  Multi-Harmonic Adaptive Vibration Control of
  Magnetic Bearing-Driveshaft with Auxiliary
  Feedback Theory and Experiment, Proc. 45th AIAA
  Structures, Structural Dynamics and Materials
  Conference, Palm Springs, CA, April 2004.
• DeSmidt, H.A., Wang, K.W., and Smith, E.C.,
  Stability of a Segmented Supercritical Driveline
  with Non-Constant Velocity Couplings Subjected to
  Misalignment and Torque, Journal of Sound and
  Vibration Vol. 277, No. 4-5, pp. 895-918, 2004.
• DeSmidt, H.A., Wang, K.W., and Smith, E.C.,
  Adaptive Control of Flexible Matrix Composite
  Rotorcraft Drivelines, Proc. 60th American
  Helicopter Society Annual Forum, Baltimore, MD,
  June 2004.

30
Publications (Cont.)

• DeSmidt, H.A., Wang, K.W., Smith, E.C., and
  Provenza, A.J., On the Robust Stability of
  Segmented Driveshafts with Active Magnetic
  Bearing Control, Journal of Vibration and
  Control, Vol. 11 pp.317-329, 2005.
• Shan, Y., and Bakis, C.E., Internal Heating
  Behavior of Flexible Matrix Composite
  Driveshafts, Proc. 61st American Helicopter
  Society Annual Forum, Grapevine, Texas, 1-3 June
  2005.
• Mayrides, B., Wang, K.W., and Smith, E.C.,
  Analysis and Synthesis of Highly Flexible
  Helicopter Drivelines with Flexible Matrix
  Composite Shafting, Proc. 61st American
  Helicopter Society Annual Forum, Grapevine,
  Texas, 1-3 June 2005.
• DeSmidt, H.A., Wang, K.W., and Smith, E.C.,
  Multi-Harmonic Adaptive Vibration Control of
  Misaligned Driveshaft Systems An Experimental
  Study, Proc. of the 12th International Congress
  on Sound and Vibration, Lisbon, Portugal, July
  2005.

31
External Interactions, Leveraging and Technology
Transfer

• Have had discussions with Army NASA Glenn (Bill,
  Provenza), Bell (Brunken, Riley), Boeing
  Philadelphia (Robuck, Gabrys), Boeing Mesa
  (Hansen), Lord Corporation (Potter), and UTRC
  (Davis) on various aspects of this project
• Have worked with Army NASA Glenn on designing and
  fabricating test fixtures as well as Magnetic
  Bearing setup and calibration
• Have visited Bell and discussed with Brunken and
  Riley addressing temperature effect based on
  their suggestions have continued discussion
  since then
• Mark Robuck (Boeing Philadelphia) has visited
  Penn State in 2003 and discussed future
  collaboration possibilities in joining efforts
  for government contracts in this area have
  continued to follow up
• Leveraged upon Army/NASA Glenn GSRP Fellowship,
  Army DURIP, Weiss Fellowship, and internal funds
  from the Structural Dynamics and Controls Lab

32
Questions?
The End
33
Schedule and Milestones
2001
2002
2005
2004
2003
Tasks

• Refinement of driveline model
• Perform analysis on driveline model to provide
  info for FMC
• FMC selection/ synthesis
• FMC material characterization
• Structure tailoring/optimization
• AMB control law synthesis and overall system
  analysis
• Sub-scale shaft/test stand development
• Initial testing for validation of model and
  approach
• Refinement of material systems and processing
  methods
• Evaluation of FMC fatigue behavior
• Adaptive control design and closed-loop stability
  and performance analysis for FMC/AMB driveline
  system
• Concurrent system integration and analysis AMB
  sizing and design for rotorcraft setting
• Integrated system testing and evaluation

34
Materials and Composite Sub-Task Key
Accomplishments and Conclusions

• Key Accomplishments
• Developed manufacturing process for building FMC
  driveshafts
• Characterized both static and dynamic properties
  of FMC driveshaft material
• Developed models to predict self-heating behavior
  of misaligned FMC shafts from the basic lamina
  properties
• Experimentally validated shaft self-heating model
• Investigating FMC shaft fatigue behavior
• Conclusion
• FMC shaft material shows significant improvement
  on strain to failure, fatigue resistance, and
  self-heating behavior over the conventional
  composite materials
• Despite the large damping capacity of FMC shaft
  materials, internal self-heating behavior of FMC
  shaft under misaligned rotating conditions is
  much less significant than that of RMC

35
Structural Mechanics Dynamics Sub-Task- Key
Accomplishments Conclusions

• Key Accomplishments
• Developed versatile model and analysis tool to
  tailor FMC designs to meet certain performance
  standards
• Applied model to supercritical drivelines to
  prove that FMC shafts can meet performance
  requirements
• Showed possible weight saving advantage of FMC
  shafting by optimizing designs for specific
  subcritical drivelines (Blackhawk, Chinook)
• Conclusion Through selective tailoring of FMC
  driveshafts, the number of components and system
  weight can be reduced on helicopter drivelines
• The single piece subcritical FMC driveline
  effectively addresses potential short comings of
  current drivelines
• Eliminates mid-span flex couplings decreases
  maintenance and replacement costs
• Reduces overall system weight

36
Systems and Controls Sub-Task- Key
Accomplishments Conclusions

• Key Accomplishments
• Developed comprehensive AMB/FMC driveline
  dynamics analytical model
• Developed feedback/adaptive feed-forward
  vibration and stability control strategy for
  AMB/FMC driveline which adaptively suppresses
  imbalance vibrations and is robust w.r.t. shaft
  temperature variations
• Developed frequency scaled AMB/FMC
  driveline-foundation testrig
• Experimentally implemented robust
  feedback/adaptive feed-forward control and
  validated AMB/FMC closed-loop performance at
  multiple operating conditions
• Conclusion - Use of AMB with supercritical FMC
  driveline feasible beneficial
• The non-contact and active control aspects of AMB
  complement the low maintenance aspects of
  one-piece rigidly coupled FMC driveline
• AMB with H?/AVC control effectively addresses
  potential short comings of supercritical FMC
  drivelines
• Suppress supercritical whirl instability due to
  large FMC damping
• Suppress relatively large imbalance vibration due
  to FMC shafting manufacturing tolerances
• Accounts for stiffness and damping variation due
  to temperature sensitivity

37
Blackhawk Fixed OD Design Study Results
Current q1/-q1/-q2/q2 q1/-q1/-q2/q2 q1/-q1/-q2/q2 q1/-q1/-q2/q2s q1/-q1/-q2/q2/q3/-q3 q1/-q1/-q2/q2/q3/-q3
Design Metal DC1 DC2 DC3 DC1-3 DC1-2 DC3
Classification Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical
Material Aluminum FMC FMC FMC FMC FMC FMC
Lay-up - 50/-50/-15/15 60/-60/-30/30 65/-65/-30/30 45/-45/-15/15s 15/-15/-55/55/30/-30 55/-55/-15/ 15/30/-30

of segments 5 1 1 1 1 1 1
of couplings 6 2 2 2 2 2 2
of bearings 4 3 4 4 3 3 3

Outer diameter 0.0889 m 0.0889 m 0.0889 m 0.0889 m 0.0889 m 0.0889 m 0.0889 m
Wall thickness 2.413 mm 3.881 mm 3.079 mm 3.5 mm 3.775 mm 3.757 mm 3.757 mm
Eqv. Axial Stiff 75 Gpa 45.1 Gpa 23.5 Gpa 25.9 Gpa 43.2 Gpa 43.2 Gpa 43.2 Gpa
Eqv. Tors. Stiff 27 Gpa 17.7 Gpa 21.6 Gpa 19.3 Gpa 18.1 Gpa 18.2 Gpa 18.2 Gpa

Tsai-Wu S.F. - 3.27 3.82 3.87 3.08 3.28 3.23
Buckling torque S.F. 10.49 2.16 4.49 6.45 10.57 5.42 9.15
Yield torque S.F. 8.65 8.97 9.84 9.87 8.49 9.33 9.47
Critical speed 103.9 Hz 87.7 Hz 95.0 Hz 99.2 Hz 86.0 Hz 86.0 Hz 86.0 Hz
Critical speed ratio 0.66 0.78 0.72 0.69 0.80 0.80 0.80

Operating strain, exx - 1189 me 1199 me 1132 me 1241 me 1193 me 1211 me
Operating strain, eyy - 1021 me 711 me 508 me 1487 me 1066 me 1082 me
Operating strain, exy - 942 me 949 me 946 me 948 me 913 me 926 me

Shaft mass 13.85 kg 10.95 kg 8.77 kg 9.92 kg 10.66 kg 10.61 kg 11.61 kg
Total system mass 31.25 kg 23.15 kg 24.81 kg 25.96 kg 22.87 kg 22.82 kg 23.82 kg
Mass reduction - 25.92 20.61 16.93 26.83 26.99 23.79
38
Blackhawk Varied OD Design Study Results
Redesigned Redesigned Redesigned q1/-q1/-q2/q2 q1/-q1/-q2/q2 q1/-q1/-q2/q2 q1/-q1/-q2/q2s q1/-q1/-q2/q2s
Design DC1 DC2 DC3 DC1 DC2 DC3 DC1 DC2 -3
Classification Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical
Material Aluminum Aluminum Aluminum FMC FMC FMC FMC FMC
Lay-up - - - 55/-55/-20/20 70/-70 -25/25 60/-60/-30/30 60/-60/-25/25s 55/-55/-20/20s
   
of segments 5 5 5 1 1 1 1 1
of couplings 6 6 6 2 2 2 2 2
of bearings 4 4 4 3 3 4 3 3
   
Outer diameter 0.097 m 0.097 m 0.095 m 0.094 m 0.102 m 0.085 m 0.101 m 0.098 m
Wall thickness 1.811 mm 1.811 mm 1.938 mm 2.982 mm 2.993 mm 3.607 mm 2.268 mm 2.590 mm
Eqv. Axial Stiff 75 Gpa 75 Gpa 75 Gpa 38.5 Gpa 35.4 Gpa 23.5 Gpa 32.0 Gpa 38.5 Gpa
Eqv. Tors. Stiff 27 Gpa 27 Gpa 27 Gpa 18.7 Gpa 14.5 Gpa 21.6 Gpa 19.3 Gpa 18.7 Gpa
   
Tsai-Wu S.F. - - - 3.09 3.03 3.87 2.90 3.08
Buckling torque S.F. 5.37 5.37 6.3 2.10 4.12 6.22 5.24 6.35
Yield torque S.F. 8.01 8.01 8.18 8.88 9.44 10.13 8.46 8.07
Critical speed 113 Hz 113 Hz 110.5 Hz 86.8 Hz 90.5 Hz 90.1 Hz 85.8 Hz 90.9 Hz
Critical speed ratio 0.61 0.61 0.62 0.79 0.76 0.76 0.80 0.75

Operating strain, exx - - -  1317 me 1367 me 1217 me 1495 me 1296 me
Operating strain, eyy - - - 907 me 418 me 722 me 831 me 893 me
Operating strain, exy - - - 1006 me 1093 me 902 me 1091 me 1056 me

Shaft Mass 11.44 kg 11.44 kg 11.97 kg 9.01 kg 9.83 kg 9.74 kg 7.43 kg 8.20 kg
Total system mass 30.58 kg 30.58 kg 30.68 kg 22.03 kg 24.14 kg 24.95 kg 21.57 kg 21.86 kg
Mass reduction - - - 27.95 21.05 18.67 29.45 28.73
39
Chinook Fixed OD Design Study Results
Current q1/-q1/-q2/q2 q1/-q1/-q2/q2 q1/-q1/-q2/q2 q1/-q1/-q2/q2s q1/-q1/-q2/q2s q1/-q1/-q2/q2/q3/-q3 q1/-q1/-q2/q2/q3/-q3
Design Metal DC1 DC2 DC3 DC1-2 DC3 DC1-2 DC3
Classification Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical
Material Aluminum FMC FMC FMC FMC FMC FMC FMC
Lay-up - 65/-65/-35/35 70/-70/-35/35 5/-5/-55/55 50/-50/-20/20s 55/-55/-5/5s 55/-55/-15/ 15/45/-45 45/-45/-5/ 5/45/-45
 
of segments 7 1 1 1 1 1 1 1
of couplings 8 2 2 2 2 2 2 2
of bearings 6 6 6 5 5 5 5 6
 
Outer diameter 0.1143 m 0.1143 m 0.1143 m 0.1143m 0.1143 m 0.1143 m 0.1143 m 0.1143 m
Wall thickness 3.048 mm 3.976 mm 4.574 mm 6.866 mm 4.254 mm 6.866 mm 4.125 mm 4.358 mm
Eqv. Axial Stiff 75 GPa 18.2 Gpa 20.2 Gpa 56.5 Gpa 36.1 Gpa 56.5 Gpa 32.2 Gpa 37.8 Gpa
Eqv. Tors. Stiff 27 Gpa 21.2 Gpa 18.7 Gpa 13.3 Gpa 20.0 Gpa 13.3 Gpa 20.5 Gpa 19.6 Gpa
 
Tsai-Wu S.F. - 2.09 2.12 3.13 2.07 3.01 2.03 3.05
Buckling torque S.F. 4.03 2.27 3.37 2.31 3.44 14.43 3.84 3.36
Yield torque S.F. 3.26 3.37 3.38 3.44 3.18 3.36 3.11 3.11
Critical speed 198.2 Hz 152.2 Hz 158.9 Hz 187.0 Hz 158.1 Hz 187.0 Hz 150.0 Hz 214.6 Hz
Critical speed ratio 0.58 0.76 0.73 0.62 0.73 0.62 0.77 0.54
 
Operating strain, exx - 1654 me 1534 me 1166 me 1502 me 1214 me 1622 me 1121 me
Operating strain, eyy - 769 me 556 me 585 me 1424 me 608 me 1210 me 1116 me
Operating strain, exy - 2575 me 2565 me 2446 me 2583 me 2545 me 2533 me 2527 me

Shaft Mass 25.65 kg 16.59 kg 18.98 kg 27.89 kg 17.70 kg 27.89 kg 17.19 kg 18.12 kg
Total system mass 60.44 kg 48.7 kg 51.09 kg 54.80 kg 44.61 kg 54.80 kg 44.10 kg 50.23 kg
Mass reduction - 19.42 15.47 9.33 26.19 9.33 27.04 16.89
40
Chinook Varied OD Design Study Results
Redesigned Redesigned Redesigned q1/-q1/-q2/q2 q1/-q1/-q2/q2 q1/-q1/-q2/q2 q1/-q1/-q2/q2s q1/-q1/-q2/q2s q1/-q1/-q2/q2s
Design DC1 DC2 DC3 DC1 DC2 DC3 DC1 DC2 DC3
Classification Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical Subcritical
Material Aluminum Aluminum Aluminum FMC FMC FMC FMC FMC FMC
Lay-up - - - 55/-55/-30/30 65/-65/-35/35 5/-5/-50/50 50/-50/-20/20s 50/-50/-20/20s 50/-50/-5/5s
     
of segments 7 7 7 1 1 1 1 1 1
of couplings 8 8 8 2 2 2 2 2 2
of bearings 6 6 6 6 6 5 5 5 5
     
Outer diameter 0.122 m 0.117 m 0.122 m 0.106 m 0.11 m 0.11 m 0.118 m 0.116 m 0.11 m
Wall thickness 2.458 mm 2.820 mm 2.458 mm 4.613 mm 4.551 mm 7.152 mm 3.809 mm 4.040 mm 7.152 mm
Eqv. Axial Stiff 75 Gpa 75 Gpa 75 Gpa 20.5 Gpa 18.2 Gpa 56.4 Gpa 36.1 Gpa 36.1 Gpa 56.4 Gpa
Eqv. Tors. Stiff 27 Gpa 27 Gpa 27 Gpa 23.5 Gpa 21.2 Gpa 14.5 Gpa 20.0 Gpa 20.0 Gpa 14.5 Gpa
     
Tsai-Wu S.F. - - - 2.22 2.12 3.14 2.04 2.06 3.01
Buckling torque S.F. 2.28 3.15 2.28 2.08 3.01 2.08 2.64 3.04 13.25
Yield torque S.F. 3.02 3.15 3.02 3.83 3.44 3.32 3.05 3.10 3.29
Critical speed 174.1 Hz 166.3 Hz 174.1 Hz 148.4 Hz 145.5 Hz 179.9 Hz 164.0 Hz 160.8 Hz 179.9 Hz
Critical speed ratio 0.66 0.69 0.66 0.78 0.79 0.64 0.70 0.72 0.64
     
Operating strain, exx - - - 1542 me 1704 me 1144 me 1490 me 1495 me 1195 me
Operating strain, eyy - - - 1210 me 792 me 817 me 1413 me 1417 me 854 me
Operating strain, exy - - - 2372 me 2466 me 2338 me 2675 me 2625 me 2442 me

Shaft Mass 22.22 kg 24.35 kg 22.22 kg 17.68 kg 18.15 kg 27.81 kg 16.45 kg 17.11 kg 27.81 kg
Total system mass 59.53 kg 60.06 kg 59.53 kg 47.13 kg 48.88 kg 53.57 kg 44.35 kg 44.47 kg 53.57 kg
Mass reduction - - - 20.83 18.61 10.01 25.50 25.30 10.01
41
AMB Design
AMB Mass vs Bias Current
L
OD
Fmax 110 Lbf

• Comprehensive Radial AMB Design Code
• Max force (Fmax) and current determined by
  material magnetic flux saturation and current
  density/RMS heating limitations
• Based on required Fmax for given shaft OD and
  airgap, code optimizes AMB rotor, stator and pole
  geometries and coil winding parameters for
  minimum weight.
• AMB mass similar to existing AH-64 contact hanger
  bearing

Mass, kg
Fmax 90 Lbf
Fmax 70 Lbf
Bias Current Design Level, Amps