Mit2 72s09 lec08
1 like243 views
This document summarizes a lecture on flexures and compliant mechanisms. Some key points: - Flexures allow motion through member compliance and have advantages like smooth motion and miniaturization but disadvantages like limited range of motion and sensitivity to tolerances. - Important material properties for flexures include modulus, yield stress, and coefficients of thermal expansion. - Common flexure modules include hinges, levers, ellipses, and cantilevers. Constraint analysis is used to determine degrees of freedom. - Fabrication methods for flexures include EDM, waterjet cutting, milling, and etching which have tradeoffs in accuracy, speed, and materials used. Proper assembly is also important to minimize hysteresis.
![Elastomechanics (σ & ε) relationship
Elastic
σ = ε ⋅ E
Plastic
Material
Titanium V
Aluminum 7075
Stainless 316
Invar - Annealed
12L14 Steel True Stress-Strain Behavior
600
500
400
300
200
100
0
Failure 80
70
60
50
40
30
20
10
0
0.04 0.05
σ,kpsi
σ,MPa
0.00 0.01 0.02 0.03σy/E ε ,mm
/mm
1.00
0.70
0.09
0.19
Young’s modulus, E
190 GPa [27.4 Mpsi]
© Martin Culpepper, All rights reserved 14](https://image.slidesharecdn.com/mit272s09lec08-161228122114/85/Mit2-72s09-lec08-15-320.jpg)
Mit2 72s09 lec08
- 1. MIT OpenCourseWare http://ocw.mit.edu 2.72 Elements of Mechanical Design Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
- 2. 2.72 Elements of Mechanical Design Lecture 08: Flexures
- 3. Schedule and reading assignment Quiz ‰ Today: Bearing layouts (mid-class) ‰ Thursday: Hale 6.1 ‰ Soon: Bolted joint qualifying quiz Topics ‰ Flexure constraints and bearings… Degrees of Freedom Reading assignment ‰ Thursday: • Layton Hale’s thesis – Read 2.6, 2.7, 6.1, skim rest of Chapter 6 • Chapter 7 is cool to look at ‰ Tuesday: • Read: 8.1, 8.3 – 8.5, 8.7, 8.9 – 8.11 • Skim: 8.6, 8.8, 8.12 © Martin Culpepper, All rights reserved 2
- 4. Examples drawn from your lathe © Martin Culpepper, All rights reserved 3
- 5. Mechanisms: Compliant vs. rigid Rigid mechanisms Images removed due to copyright restrictions. Please see ‰ Sliding joints http://www.physikinstrumente.com/en/primages/pi_m850_tip_i4c_o_eps.jpg http://www.hexapods.net/images/M850Ani160-1-slow.gif ‰ 100s of nm resolution ‰ Large range ‰ kg load capacity Compliant mechanisms ‰ Motion from member compliance ‰ Angstrom resolution θy ‰ Limited range ‰ Limited load capacity z © Martin Culpepper, All rights reserved 4
- 6. Micro-scale precision machines © Martin Culpepper, All rights reserved 5
- 7. Static SEM: Drs. Andras Vladar & Jason Gorman (NIST) FIB: Dr. Konrad Jarush (Hitachi) © Martin Culpepper, All rights reserved Courtesy of Andras Vladar, Jason Gorman, and Konrad Jarausch. Used with permission. 6
- 8. system Lighting Forceps Lens Meso-scale devices: Biomedical Two -photon endomicroscope Scanning Two -photon endomicroscope Lighting Forceps Lens Scanning system © Martin Culpepper, All rights reserved 7
- 9. Nano-scale devices Stator CNT “Rigid” link “Compliant” joint Rotor xx yy F © Martin Culpepper, All rights reserved 8
- 10. Meso-scale precision machines © Martin Culpepper, All rights reserved 9
- 11. TMA ystem Lighting Forceps Lens Nano-scale devices TMA Two -photon endomicroscope Scanning s Two -photon endomicroscope Scanning system Lighting Forceps Lens Stator CNT “Rigid” link “Compliant” joint Rotor xx yy F © Martin Culpepper, All rights reserved 10
- 12. Dip pen nanolithography on DNA arrays What is fundamentally different? ‰ Size → Physics → Fabrication ‰ Raw materials Images removed due to copyright restrictions. Please see ‰ Surfaces vs. points or lines http://mcf.tamu.edu/images/DPN_process.png http://www.nanoink.net/d/Nano%20-%20Part%201_Sm_Lo-Res_240x180.wmv http://images.iop.org/objects/nano/news/4/12/10/diagnal.jpg ~20 mm ~1 mm Courtesy PI 250 mm © Martin Culpepper, All rights reserved 11
- 13. Nanomanufacturing © Martin Culpepper, All rights reserved 12
- 14. Advantages of flexures y x y θz x y Z y x z θy y x z Advantages ‰ Smooth, fine motion ‰ Linear/elastic operation in absence ‰ Failure modes are well understood ‰ Monolithic or assembled ‰ 2D nature lends to 2½D mfg. ‰ Miniaturization Disadvantages ‰ Accuracy and repeatability sensitive to several variables ‰ Limited motion/stroke (usually a few to 10s % of device size) ‰ Instabilities such as axial or transverse buckling ‰ Dynamics ‰ Sensitivity to tolerance © Martin Culpepper, All rights reserved 13
- 15. Elastomechanics (σ & ε) relationship Elastic σ = ε ⋅ E Plastic Material Titanium V Aluminum 7075 Stainless 316 Invar - Annealed 12L14 Steel True Stress-Strain Behavior 600 500 400 300 200 100 0 Failure 80 70 60 50 40 30 20 10 0 0.04 0.05 σ,kpsi σ,MPa 0.00 0.01 0.02 0.03σy/E ε ,mm /mm 1.00 0.70 0.09 0.19 Young’s modulus, E 190 GPa [27.4 Mpsi] © Martin Culpepper, All rights reserved 14
- 16. Important material properties Nominal values ‰ Modulus ‰ Yield stress ‰ Coefficient of thermal expansion ‰ Thermal diffusivity ‰ Density Material property ratios Normalized Values Material σy/E αdiff/αCTE E/ρ Cost Titanium V 1.00 0.14 0.92 3.77 Aluminum 7075 0.70 1.00 1.00 1.00 Stainless 316 Invar - Annealed 0.09 0.19 0.13 0.87 0.94 0.70 3.50 5.21 © Martin Culpepper, All rights reserved 15
- 17. Modules Lever Chevron © Martin Culpepper, All rights reserved 16
- 18. Modules cont. Ellipse Cantilever/flexure blade © Martin Culpepper, All rights reserved 17
- 19. Modules cont. Flexure hinge Torsion Parallel four bar Double parallel four bar © Martin Culpepper, All rights reserved 18
- 20. Module cont.: Cross flexure pivot Deformation scale 1 : 1 75 mm 25 N 25 N 25 N || ┴ ┴op© Martin Culpepper, All rights reserved 19
- 21. Review of constraint fundamentals Rigid bodies have 6 DOF ‰ Constraints have lines of action ‰ C = # of linearly independent constraints ‰ DOF = 6 – C → F = 6 – C z y x Stage Ground © Martin Culpepper, All rights reserved 20
- 22. DOF in constraint-based design A linear displacement may be visualized as a rotation about a point which is “far” away R to infinityR © Martin Culpepper, All rights reserved 21
- 23. Two principles of projective geometry Projective geometry comes in useful here ‰ Parallel lines intersect at infinity ‰ Translation represented by a rotation line at a hope of “infinite radius” Image courtesy of John Hopkins MIT MS Thesis R © Martin Culpepper, All rights reserved 22
- 24. Constraint fundamentals Blanding’s RULE OF COMPLIMENTARY PATTERNS ‰ Each permissible Freedom (F) is a rotation about a line and each permissible freedom rotation line must intersect each Constraint (C) Remember these principles of projective geometry ‰ Parallel lines intersect at infinity ‰ Translation represented by a rotation line at a hope of “infinite radius R = 6 – C = 6 – 5 = 1... so where is it? C5 C4 C5 C4 C1 C1 R1C2 C2 C3 C3 © Martin Culpepper, All rights reserved 23
- 25. 24© Martin Culpepper, All rights reserved Examples There will be a quiz on this NC 2 y z x R2 R1 1 R1
- 26. Flexure bearing systems y Spherical ball joint z x R1 R2 6 – C = F R3 © Martin Culpepper, All rights reserved 25
- 27. Flexure bearing systems y Blade flexure x 6 – C = F z © Martin Culpepper, All rights reserved 26
- 28. Flexure bearing systems Parallel guiding mechanism y x z6 – C = F © Martin Culpepper, All rights reserved 27
- 29. Flexure bearing systems y Doodle hopper… z R1 R2 x 6 – C = F © Martin Culpepper, All rights reserved 28
- 30. Parallel addition rules z What is parallel ? Elements are not in the same load path. Loads are split between the elements Add constraints so where there is a common DOF, then have mechanism DOF Example: For instance, there are no conflicts in displacement to θz Adapted from Layton Hale’s Ph.D. Thesis (MIT) © Martin Culpepper, All rights reserved 29
- 31. Series addition rules What is series? -Differentiate series by load path -Shared load path = series Series: Add DOF Find common constraints Follow the serial chain Adapted from: Layton Hale’s Ph.D. Thesis (MIT) © Martin Culpepper, All rights reserved 30
- 32. Parallel and series systems Take care of series first, define them as single element then go through parallel Series Parallel Redundancy does not add Degrees of freedom Adapted from Layton Hale’s Ph.D. Thesis (MIT) © Martin Culpepper, All rights reserved 31
- 33. Accuracy The accuracy of most flexures is sensitive to: ‰ 1. Small variations in dimensions, e.g. δthickness ‰ 2. Young’s Modulus (E) ‰ 3. Time variable errors • Creep • Stress relaxation • Thermal • Dynamic/vibration © Martin Culpepper, All rights reserved 32
- 34. Repeatability Flexures can exhibit Angstrom-level repeatability if: ‰ Low material hysteresis • Single crystal materials useful ‰ No dislocation motion • σ << σyield ‰ Load is repeatable • Magnitude • Direction ‰ Assembly is correct • No micro-slip • No friction in assembly • No yield during assembly © Martin Culpepper, All rights reserved 33
- 35. Accuracy and repeatability Difficult to obtain without calibration or adjustment ‰ Geometry ‰ Materials ‰ Loading ‰ Assembly/integration ‰ Environmental © Martin Culpepper, All rights reserved 34
- 36. Links between kinematics and elasticity Cantilever L F F ⋅ L3 δ = 3⋅ E ⋅ I h b δ L 1 n h 1 3 I = ⋅b⋅h 12 ⎛ E ⋅b ⎡ h ⎤ 3 ⎞ dF d ⎧⎪E ⋅b ⎡ h ⎤ 3 ⎫⎪ E ⋅b ⎡ h ⎤ 3 F = ⎜ ⎜ 4 ⋅⎢ ⎣L⎥ ⎦ ⎟ ⎟⋅δ k = dδ = dδ ⎨ 4 ⋅⎢ ⎣L⎥ ⎦ ⋅δ ⎬ → 4 ⋅⎢ ⎣L⎥ ⎦⎝ ⎠ ⎩⎪ ⎭⎪ © Martin Culpepper, All rights reserved 35
- 37. Links between kinematics and elasticity Cantilever L F ΔL = 0.05⋅ L b δ h Δh = 0.05⋅h Δb = 0.05⋅b k + Δk = E ⋅(b + Δb)⋅ ⎡ ⎢⎣ h + Δh ⎤ ⎥⎦ 3 → E ⋅b ⋅ ⎡ ⎢⎣ h ⎤ ⎥⎦ 3 ⋅ ⎛ ⎜ ⎜ 1.05⋅ ⎡ ⎢⎣ 1.05⎤ ⎥⎦ 3 −1 ⎞ ⎟ ⎟ = k ⋅(1+ 0.42) 4 L − ΔL 4 L ⎝ 0.95 ⎠ Δk = 0.42⋅k © Martin Culpepper, All rights reserved 36
- 38. Fabrication processes: EDM EDM positives ‰ Accuracy (micrometers) ‰ 3D ‰ Surface finish (sub-micrometers) Image removed due to copyright restrictions. Please see http://www.physikinstrumente.com/en/about/images/pi_WIREEDMC_i4c_K50_eps.jpg EDM drawbacks ‰ Time (mm/minute) ‰ Cost © Martin Culpepper, All rights reserved 37
- 39. Fabrication processes: Waterjet Waterjet positives ‰ Low force ‰ Many materials including brittle materials and heat sensitive materials ‰ Rapid (inches/min) Images courtesy of xiaming on Flickr. Waterjet drawbacks ‰ Thickness limitations ‰ Kerf limitations ‰ Draft limitations ‰ Accuracy ~ 125 micrometers © Martin Culpepper, All rights reserved Images courtesy of Iansoper on Flickr. 38
- 40. Fabrication processes: Milling/cutting Milling/cutting positives ‰ Flexibility ‰ Any material ‰ Nearly any shape Milling/cutting drawbacks ‰ Fixturing ‰ Compliance of parts ‰ Work hardening ‰ Surface damage Image courtesy of jiskar on Flickr. Please see any other image of milling, such as http://students.washington.edu/dennyt/fsae/cnc/wc_fixtplate.jpg © Martin Culpepper, All rights reserved 39
- 41. Fabrication processes: Etching Etching positives ‰ 2½ D topologies/shapes ‰ Monolithic ‰ Micron-level features Etching drawbacks ‰ Dimensional control ‰ Scallops Images removed due to copyright restrictions. Please see: http://www.ee.ucla.edu/~dejan/ee115c/ucla-graphics/IBM_metal_stack.jpg http://www.stsystems.com/uploaded_files/1101/images/scallops.jpg Milanovic, Veljko, et al. "Deep Reactive Ion Etching for Lateral Field Emission Devices." IEEE Electronic Device Letters 21 (June 2000): 271-273. Milanovic, Veljko, et al. "Micromachining Technology for Lateral Field Emission Devices." IEEE Transactions on Electron Devices 48 (January 2001): 166-173. Please see 371762. "How Microprocessor Work." February 14, 2009. YouTube. Accessed October 28, 2009. http://www.youtube.com/watch?v=loMz_l_Fpx4 © Martin Culpepper, All rights reserved 40
- 42. Assembly Stress and energy ‰ Proper thickness of clamps and clamping load distribution ‰ Spring washer provide force source Fusing ‰ Clamps members should “yield” before flexure ‰ Spring washer provide force source Surface conformity ‰ Micro-slip is a major cause of hysteresis ‰ Deburring and potting/bonding Misalignment = systematic errors © Martin Culpepper, All rights reserved 41 Images removed due to copyright restrictions. Please see Fig. 8.5 and 8.6 in Smith, Stuart. Flexures: Elements of Elastic Mechanisms. Amsterdam, Holland: Gordon & Breach, 2000.