2.76 / 2.760 Lecture 12: Interfaces
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2.76 / 2.760 Lecture 12: Interfaces 2.76 Multi-scale System Design & Manufacturing Announcements Schedule TA Meetings Thursday design review (Oct. 21 not Nov. 21) FRs & DPs Concepts & approach Initial modeling (HTMs, systematic, random, actuation, flexures) Sensitivity and prioritization Scheduling & risk/mitigation 2.76 Multi-scale System Design & Manufacturing Homogeneous Transformation Matrices Rotations: 1 A H B (θ x ) = 0 y 0 0 0 cos(θ x ) − sin (θ x ) 0 0 sin (θ x ) 0 0 cos(θ x ) 0 0 1 A H B (θ y ) = x z cos(θ y ) 0 sin (θ y ) 0 0 1 0 0 0 0 0 1 − sin (θ y ) 0 cos(θ y ) 0 For small θ, cos(θ)~1 & sin(θ)~θ A H B (θ z ) = cos(θ z ) − sin (θ z ) 0 0 sin (θ z ) cos(θ z ) 0 0 0 0 1 0 0 0 0 1 Order of multiplication is important for large θ 2.76 Multi-scale System Design & Manufacturing Purpose of today Modeling of mechanical interfaces: “Rigid” Flexible Rigid-flexible Examples: “Rigid”: “Rigid”-Flexible: “Rigid”-Flexible: Kinematic couplings Flexure-couplings Quasi-kinematic coupling Thursday: Manufacturing & assembly Cross-scale interfaces Bolted joints 2.76 Multi-scale System Design & Manufacturing Constraint concept review 2.76 Multi-scale System Design & Manufacturing Exact constraint At some scale, everything is a mechanism Everything is compliant What we’ve done: Kinematics Arranging constraints in optimum topology Ideal constraints & small motions Constraints = lines (ideal) Now: Kinematics and mechanics Model & calculate stiffness/stress/motion Figure: Layton Hales PhD Thesis, MIT. 2.76 Multi-scale System Design & Manufacturing Constraint fundamentals Rigid bodies have 6 DOF DOC = # of linearly independent constraints DOF = 6 - DOC A linear displacement can be visualized as a rotation about a point which is “far” away Figure: Layton Hales PhD Thesis, MIT. 2.76 Multi-scale System Design & Manufacturing Statements Points on a constraint line move perpendicular to the constraint line Figure: Layton Hales PhD Thesis, MIT. Constraints along this line are equivalent Diagram removed for copyright reasons. Source: Blanding, D. L. Exact Constraint: Machine Design using Kinematic Principles. New York: ASME Press, 1999. 2.76 Multi-scale System Design & Manufacturing Statements Intersecting, same-plane constraints are equivalent to other same-plane intersecting constraints Instant centers are powerful tool for visualization, diagnosis, & synthesis 2.76 Multi-scale System Design & Manufacturing Abbe error Error due to magnified moment arm r 2.76 Multi-scale System Design & Manufacturing Statements Constraints remove rotational degree of freedom Length of moment arm determines the quality of the rotational constraint 2.76 Multi-scale System Design & Manufacturing Statements Parallel constraints may be visualized/treated as intersecting at infinity 2.76 Multi-scale System Design & Manufacturing Past / next We know how to lay out constraints to achieve a given behavior Need to understand how to model and optimize them Reality checks and useful numbers for decision making 2.76 Multi-scale System Design & Manufacturing “Rigid” Constraints 2.76 Multi-scale System Design & Manufacturing Generic mechanical interface Geometry & topology Relative form Surface finish Material Modulus, Poisson’s ratio, stress Oxide & contamination Surface energy Flows Mass (wear) Momentum (interface force) Energy (elastic, thermal, etc…) 2.76 Multi-scale System Design & Manufacturing A B Local geometry Surface roughness Waviness Shape / form Waviness can be due to: Roughness can be due to: Clamping forces Low frequency vibrations Equipment set up Bearing errors 2.76 Multi-scale System Design & Manufacturing High frequency vibrations Tool geometry and rubbing Variations in material Chip contact Exact constraint couplings Exact constraint: Constraint points = DOF to be constrained Deterministic saves $ Balls (inexpensive) Grooves (more difficult to make) Kinematic design the issues are: KNOW what is happening in the system MANAGE forces, deflections, stresses and friction Balls Tetrahedral groove V groove Figures: Layton Hales PhD Thesis, MIT. 2.76 Multi-scale System Design & Manufacturing Passive kinematic couplings Fabricate and forget: no active elements Goal: Repeatable location (1/4 micron is the norm) What is important? Contact point & contact force direction Contact stress Stiffness Friction & hysteresis No flexures Order of engagement Radial (x +y ) repeatability 2 0.5 0.2 1.5 1.0 0.1 0.0 0.5 0 Y error motion 0.3 2.0 10 20 Trial # 2.76 Multi-scale System Design & Manufacturing With flexures Y [µm] Wear in period Centroid Displacement [ µm ] 2 Figure: Layton Hales PhD Thesis, MIT. 30 -0.1 0 200 400 600 Cycle 800 1000 Common mechanical interfaces Elastic averaging Compliant kinematic Quasi-kinematic Accuracy Passive KC Active kinematic Repeatability Passive kinematic Accuracy & repeatability Active KC Quasi-KC Elastic C Elastic A Elastic B Error 2.76 Multi-scale System Design & Manufacturing Desired Position Error Minimize variation People Material properties Environment changes Stress Desired output Perceived Error System Measured output Actual output Forces Vibration Procedure 2.76 Multi-scale System Design & Manufacturing Friction Real error Stability & balanced stiffness Instant center can help you identify how to best constrain or free up a mechanism K || δ ⊥ ⋅ → CM k ⋅ CM δ << 1 K ⊥ δ || Diagram removed for copyright reasons. Source: Alex Slocum, Precision Machine Design. Poor Good Instant center if ball 1 is removed *Pictures from Precision Machine Design 2.76 Multi-scale System Design & Manufacturing Source of error motion Perspective on couplings Ideal: Couplings are static Reality: Deflections = motion How/why they move Friction and mating hysteresis Contact deflections A A B λ 2.76 Multi-scale System Design & Manufacturing B λ Point A Initial Position of Ball’s Far Field Point δl θc δr Contact Cone δz δn Final Position of Ball’s Far Field Point n l Distance of approach (δn) Initial Contact Point Initial Position of Groove’s Far Field Point z r Max τ Point B Final True Groove’s Far Field Point Final Contact Point Max shear stress occurs below surface, in the member with largest R 2.76 Multi-scale System Design & Manufacturing Solving for coupling errors Model ball-groove contacts as 6 balls on flats F F F Important relationships for ball-flat contact Contact pressure ⎛3 F ⋅R ⎞ a = ⎜⎜ ⋅ n e ⎟⎟ ⎝ 4 Ee ⎠ 1 3 3 F ⋅ < 1.5 ⋅ σ tensile for metals q= 2π a 2 2.76 Multi-scale System Design & Manufacturing Distance of approach ⎛9 F2 ⎞ δn = ⎜ ⋅ 2 ⎟ ⋅ 16 R E e ⎠ ⎝ 1 Stiffness [normal to groove surface] 3 kn = 2 ⋅ δ 1 2 1 ⋅ R 2 ⋅ Ee System of six contact points Ideal in-plane constraints 2.76 Multi-scale System Design & Manufacturing Real in-plane constraints Modeling round interfaces Equivalent radius 1 R1major + 1 1 R1min or + 1 R2 major + 1 R2 min or Equivalent modulus Ee = 1 1 − η1 1 − η 2 + E1 E2 2 Poisson’s ratio 2 Contact stiffness 30 Young’s modulus k [N/micron] Re = 20 10 05 0 0 2 ⎛9 Fn ⎞ ⎟ δ n = ⎜⎜ ⋅ 2 ⎟ ⎝ 16 Re ⋅ Ee ⎠ 1 ( 0 .5 500 750 Fn [N] 3 Important scaling law k n (δ n ) = 2 ⋅ Re 250 ) ⋅ Ee ⋅ δ n 0 .5 2.76 Multi-scale System Design & Manufacturing ( k n (Fn ) = Constant ⋅ Re 3 ⋅ Ee 1 2 3 )⋅ F n 1 3 1000 Importance of preload Preload keeps the fixture parts together increase ball-groove in contact increase contact stiffness ⎛9 Fn ⎞ ⎜ ⎟ δn = ⎜ ⋅ 2 ⎟ ⎝ 16 Re ⋅ Ee ⎠ 1 ⎛3 F ⋅R ⎞ a = ⎜⎜ ⋅ n e ⎟⎟ ⎝ 4 Ee ⎠ 3 1 3 k [N/micron] Increase preload: 2 In-plane stiffness 80 60 40 20 0 0 250 Stiffness scales as: k n (δ n ) = dF dδ n 500 Preload [N] Important scaling law ( ⋅ E )⋅ δ k (F ) = Constant ⋅ (R ⋅ E )⋅ F Preload should have high repeatability k n (δ n ) = 2 ⋅ Re 0. 5 1 0. 5 e n 2.76 Multi-scale System Design & Manufacturing n n e 6 1 2 e n 3 750 1000 Load balance: Ford and moment Force balance (3 equations) K K K K K K K K K ΣFrelative = 0 = (Fpreload + FError ) + (FBall _ 1 + FBall _ 2 + FBall _ 3 + FBall _ 4 + FBall _ 5 + FBall _ 6 ) Moment balance (3 equations) G G G G )+ (M )+ (M ) = (rK × FK + rK = Σ (M M 6 relative i =1 Ball _ i preload error preload preload K K K ) × + Σ × F r F error Error Ball _ i Ball _ i G K K K K K K K K K K K K K K K K ΣM relative = (rpreload × Fpreload + rerror × FError ) + (rBall _ 1 × FBall _ 1 + rBall _ 2 × FBall _ 2 + rBall _ 3 × FBall _ 3 + rBall _ 4 × FBall _ 4 + rBall _ 5 × FBall _ 5 + rBall _ 6 × FBall _ 6 ) Ball far-field point Constraint B Given geometry, materials, A preload force, error force, Groove far-field points solve for local distance of approach 2.76 Multi-scale System Design & Manufacturing Ball motions: Displacements ⎛ Fn ⎞⎟ 9 ⎜ = −⎜ ⋅ 2 ⎜ 16 Re ⋅ Ee ⎟⎟ ⎠ ⎝ 2 K Σδ n _ Ball _ iA 1 3 K ⋅ nˆ Ball _ iA Σδ n _ Ball _ iB Ball _ iA K K ⎛ Fn ⎞⎟ 9 ⎜ = −⎜ ⋅ 2 ⎜ 16 Re ⋅ Ee ⎟⎟ ⎠ ⎝ 2 1 3 ⋅ nˆ Ball _ iB Ball _ iB K Σδ Ball _ i = δ Ball _ iA + δ Ball _ iB Ball far-field point Constraint A B1 B2 B Groove far-field points 2.76 Multi-scale System Design & Manufacturing B3 Coupling motions Given 3 points (e.g. ball centers) (1) Define centroid of the points & attach CS (2) Define plane equation & normal vector at CS Compliance errors cause plane/normal to shift Differences in coefficients give: Centroid (δx, δy, θz) Normal vector (θx, θy, δz) For small θi εz ~ θi sin(θi)~θi cos (θi) ~1 2.76 Multi-scale System Design & Manufacturing Solving for coupling errors Step 1: Analyze ball center displacements Step 2: Obtain centroid displacements Translations: δx, δy, δz Rotations: εx, εy , εz Step 3: Calculating error at any point Fixture Loading Errors Deflection F B1 B2 B3 2.76 Multi-scale System Design & Manufacturing ⎛∆ x⎞ ⎜ i ⎜∆ y ⎟ ⎜ ∆ z i⎟ ⎜ i ⎝ 1 ⎠ Error at i ⎛ 1 ⎜ ⎜ εz ⎜ −ε y ⎜ ⎝ 0 −ε z ε y δ x ⎞ ⎛ X − x c ⎞ ⎛ X − x c ⎞ ⎜ i ⎜ i 1 −ε x δ y ⎟ ⎜ Y − y c ⎟ ⎜ Y − y c ⎟ ⋅ i − i ⎟ ⎟ ⎜ ⎜ Z − zc ⎟ Z − zc εx 1 δz ⎜ i ⎜ i 0 0 1 ⎠⎝ 1 ⎠ ⎝ 1 ⎠ Centroid errors Abbe arm Solving for coupling errors Error ⎛∆ x⎞ ⎜ ⎜∆ y ⎟ ⎜∆ z ⎟ ⎜ ⎝ 1 ⎠ i i i Amplification Distance from Arm centroid HTM ⎛ 1 ⎜ ⎜ εz ⎜ −ε y ⎜ ⎝ 0 −ε z ε y δ x ⎞ ⎛ X − x c ⎞ i ⎛ X − xc ⎞ ⎜ ⎜ 1 −ε x δ y ⎟ ⎜ Y − y c ⎟ ⎜ Y − y c ⎟ ⋅ − ε x 1 δz ⎟ ⎜ Z − zc ⎟ ⎜ Z − zc ⎟ ⎜ ⎜ 0 1 ⎠⎝ 1 ⎠ ⎝ 1 ⎠ 0 i i i i B1 B2 B3 2.76 Multi-scale System Design & Manufacturing i Environmental: Temperature Thermal expansion ∆x = α ⋅ ∆T ⋅ x α µ m/ o C/m Cast iron 13 Carbon steel [AISI 1005] 13 Stainless steel [AISI 303] 18 Aluminum 6061 T6 24 Yellow brass 20 Delrin (polymer) 85 µ inch/ oF/inch 7 7 10 13 11 47 Which is better with respect to in-plane errors if: ∆Ttop > ∆Tbottom ∆Ttop = ∆Tbottom ∆Ttop < ∆Tbottom Balls Tetrahedral groove V groove Figure: Layton Hales PhD Thesis, MIT. 2.76 Multi-scale System Design & Manufacturing Example: Surface finish trace & metric 1 L Ra = ⋅ ∫ y dx L 0 Mean y 2.76 Multi-scale System Design & Manufacturing x Surface finish Producing fine surface is expensive/time consuming Reference chart: Common surface roughness (Ra in micro-inches) Process 2000 1000 500 Sawing Drilling Milling Turning Grinding Polishing 2.76 Multi-scale System Design & Manufacturing 250 125 63 32 16 8 4 2 1 ½ Contact problems Surface topology (finish): Wear and Fretting: A B λ B λ Mate n A Mate n + 1 Wear on Groove 50 cycle repeatability ~ 1/3 µm Ra Friction depends on surface finish! Finish should be a design spec Surface may be brinelled if possible High stress + sliding = wear Metallic surfaces = fretting Use ceramics if possible (low µ and high strength) Dissimilar metals avoids “snowballing” Friction: Friction = Stored energy, over constraint Flexures can help (see right) Lubrication (high pressure grease) helps Beware of settling time 2.76 Multi-scale System Design & Manufacturing Image removed for copyright reasons. See Figure 4, “Ball in a V Groove…” in Schouten, et. al., “Design of a kinematic coupling for precision applications.” Precision Engineering, vol. 20, 1997. Repeatability with & w/o lubrication Displacement, µm Magnitude depends on coupling design and test conditions Radial Repeatability (Unlubricated) 2 Graph removed for copyright reasons. See Slocum, A. H. “Kinematic couplings for precision fixturing: Experimental determination of repeatability and stiffness.” Precision Engineering, 1988. 0 Number of Trials Displacement, µm The trend of the data is important Slocum, A. H., Precision Engineering, 1988: Kinematic couplings for precision fixturing– Experimental determination of repeatability and stiffness 2 60 0 Radial Repeatability (Lubricated) Graph removed for copyright reasons. See Slocum, A. H. “Kinematic couplings for precision fixturing: Experimental determination of repeatability and stiffness.” Precision Engineering, 1988. 0 2.76 Multi-scale System Design & Manufacturing Number of Trials 60 0 Effect of Hard Coatings What should be the affect of adding TiN coating? TiN = low friction TiN = high surface energy Results of non-lubricated, TiN coated tests Centroid δ y error motion [ Stability test ] 80.00 [ Stability test ] 500 400 60.00 Displacement [µ radian] Displacement [microns] Centroid ε y error motion 40.00 20.00 0.00 -20.00 -40.00 300 200 100 0 -100 -200 -300 -60.00 -400 -80.00 -500 0 100 200 300 400 Cycle 500 2.76 Multi-scale System Design & Manufacturing 600 700 0 Cycle 500 Flexible constraints 2.76 Multi-scale System Design & Manufacturing Adding and taking away constraints Why? Want less than 6 DOF constraint E.g.: Planar alignment ∆z for sealing/stiffness Add compliance to permit z motion This is equivalent to adding a DOF Care must be taken to make sure Compliant direction is not in a sensitive direction Parasitic errors in sensitive directions are acceptable Compliant Stiff ↕ ↔ 2.76 Multi-scale System Design & Manufacturing Compliant ↕ Stiff ↔ Compliant ↕ Stiff ↔ Out-of-plane use of flexures Compliant Stiff Rigid ↕ ↔ Compliant Stiff ↕ ↔ Compliant Stiff ↕ ↔ Passive Compliance Fnest Fnest Ferror Ferror L Compliant ↕ Stiff ↔ S Compliant ↕ Stiff ↔ z 2.76 Multi-scale System Design & Manufacturing L-S z System of six contact points Ideal in-plane constraints 2.76 Multi-scale System Design & Manufacturing Real in-plane constraints Example: Cantilevered balls Characteristics Stroke ≤ 0.25 inches Repeatability 5 -10 microns Ball movement in non-sens. direction Applications/Processes 1. Assembly 2. Casting Design Issues (flexure) Courtesy of Prof. Alex Slocum. Used with permission. L 2 1. Kr ~ w2 t 2. Tolerances affect Kr F w t 2.76 Multi-scale System Design & Manufacturing δ Cost $ 10 - 200 U.S. Patent 5, 678, 944, Slocum, Muller, Braunstein Axial bushings with spring preload Characteristics 1. Repeatability (2.5 micron) 2. Stroke ~ 0.5 inches Applications/Processes 1. Assembly 2. Casting U.S. Patent 5, 678, 944, Slocum, Muller, Braunstein 3. Fixtures 2.76 Multi-scale System Design & Manufacturing Courtesy of Prof. Alex Slocum. Used with permission. Design Issues (flexures) 1. Kr = Kguide Kspring 2. Press fit tolerances Cost $ 2000 System of six contact points Flexure arms Ideal in-plane constraints 2.76 Multi-scale System Design & Manufacturing Real in-plane constraints Flexure grooves reduce friction effect + = z y x Y displacements 50 Measured [microns] 1 25 0 -25 -50 -50 -25 0 25 Command [microns] 50 Y error motion 0.3 3 Y [µm] 0.2 2 Flexure arms 0.1 0.0 -0.1 0 2.76 Multi-scale System Design & Manufacturing 200 400 600 Cycle 800 1000 “Rigid”-flexible constraints 2.76 Multi-scale System Design & Manufacturing Exact & near kinematic constraint [US Pat. 6 193 430] Ball Ball V grooves Axi symmetric groove Groove Seat Side Reliefs Quasi-kinematic Kinematic Contact: Repeatability: Cost: Sealing: Time: Point / small area 80 nm $10s to $1000s With flexures > 60 minutes 2.76 Multi-scale System Design & Manufacturing Arc 250 nm $ 0.75 Integrated < 20 s QKC methods vs kinematic method Components and Definitions y x Relief Relief Cone Seat Ball Groove Surface Peg Surface Force Diagrams 2.76 Multi-scale System Design & Manufacturing Contact Point Constraint in QKCs Contact angle and degree of over constraint y x θcontact θcontact QKC constraint compared to “ideal” coupling QKC Ideal KC k Stiffness parallel to bisecting planes || Bisector CM k = = Stiffness perpendicular to bisecting planes k ⊥ Bisector 2.76 Multi-scale System Design & Manufacturing Solving for coupling errors Step 1: Analyze ball center displacements Step 2: Obtain centroid displacements Translations: δx, δy, δz Rotations: εx, εy , εz Step 3: Calculating error at any point Fixture Loading Errors Deflection F B1 B2 B3 2.76 Multi-scale System Design & Manufacturing ⎛∆ x⎞ ⎜ i ⎜∆ y ⎟ ⎜ ∆ z i⎟ ⎜ i ⎝ 1 ⎠ Error at i ⎛ 1 ⎜ ⎜ εz ⎜ −ε y ⎜ ⎝ 0 −ε z ε y δ x ⎞ ⎛ X − x c ⎞ ⎛ X − x c ⎞ ⎜ i ⎜ i 1 −ε x δ y ⎟ ⎜ Y − y c ⎟ ⎜ Y − y c ⎟ ⋅ i − i ⎟ ⎟ ⎜ ⎜ Z − zc ⎟ Z − zc εx 1 δz ⎜ i ⎜ i 0 0 1 ⎠⎝ 1 ⎠ ⎝ 1 ⎠ Centroid errors Abbe arm New model for QKC stiffness Geometry Material Applied Loads [Fp & Mp] Resultant Forces [ni & Fi] Deflections δ -> ∆r Material Contact Stiffness fn(δn) QKC Model Force/Torque Geometry Displacements Stiffness 2.76 Multi-scale System Design & Manufacturing Relative Error Contact mechanics f n (θ r ) = K [δ n (θ r )] ^ k ^ n b ^l Rotating CS ^ n ^l ^ s Rc ^ i 100 50 0 -0.02 -0.01 0 0.01 Distance in L, in 2.76 Multi-scale System Design & Manufacturing 0.02 400 000 Init 300 000 ding a o ia l L Re-l oad 150 200 000 d Hertz Profile 500 000 Unlo a FEA Profile Contact Unit Force [N/m] Contact Pressure, kpsi 200 Force per unit of line contact Surface Contact Pressure - Elastic Hertz 100 000 0 0 50 100 150 Distance of Approach [microns] 200 QKC Performance y Centroid Displacement Centroid Rotation 2.0 8 6 1.5 4 2 1.0 0 -2 -4 0.5 -6 -8 0.0 0 5 10 15 20 Trial 1st Component 2nd Component 2.76 Multi-scale System Design & Manufacturing 25 30 x Centroid Rotation (θz) [ µ radians] Radial Centroid Displacement [ µm ] QKC In-plane Repeatability Probe 1 Probe 3 Probe 2 Practical use: DuratecTM assembly Characteristics: Ford V6 300,000 / year Cycle time: < 30 s Sensitive to misalignment Rotation Oil Repeatability 10 µm Coupling + others Process 5 µm 0 µm 0.01 µm 0.10 µm 1.0 µm Elastic averaging Compliant kinematic Quasi-kinematic Active kinematic Passive kinematic 2.76 Multi-scale System Design & Manufacturing Photos by Prof. Martin Culpepper, courtesy of Ford Motor Company. Used with permission. 10 µm Goal: 5 micron assembly Components Coupling + others Process Block Bedplate Pinned joint engine Assembly Bolts QKC equipped engine Bedplate Block 2.76 Multi-scale System Design & Manufacturing Photos by Prof. Martin Culpepper, courtesy of Ford Motor Company. Used with permission. 10 µm 5 µm DuratecTM QKC in detail 2.76 Multi-scale System Design & Manufacturing Photos by Prof. Martin Culpepper, courtesy of Ford Motor Company. Used with permission. Low-cost couplings Kinematic elements Manufacturing + Diagrams removed for copyright reasons. “Cast + Form Tool = Finished” OR + Constraint diagrams Metrics Example QKC Joint Metrics 1.0 0.8 CM 250 Kr max 200 0.6 150 0.4 100 0.2 50 0 30 60 90 120 θ contact 2.76 Multi-scale System Design & Manufacturing 150 180 Kr max [ N/µ m ] CM Solving for coupling errors Error ⎛∆ x⎞ ⎜ ⎜∆ y ⎟ ⎜∆ z ⎟ ⎜ ⎝ 1 ⎠ i i i Amplification Centroid Arm displacement HTM ⎛ 1 ⎜ ⎜ εz ⎜ −ε y ⎜ ⎝ 0 −ε z ε y δ x ⎞ ⎛ X − x c ⎞ i ⎛ X − xc ⎞ ⎜ ⎜ 1 −ε x δ y ⎟ ⎜ Y − y c ⎟ ⎜ Y − y c ⎟ ⋅ − ε x 1 δz ⎟ ⎜ Z − zc ⎟ ⎜ Z − zc ⎟ ⎜ ⎜ 0 1 ⎠⎝ 1 ⎠ ⎝ 1 ⎠ 0 i i i i i B1 B2 B3 2.76 Multi-scale System Design & Manufacturing Error at i Centroid errors Abbe arm Load sources: Alignment Forces/loads can vary Journal 4 Result is variation in position y x T f2 T f1 T f3 δy at Journal 4 Frequency 2000 1000 0 -0.515 -0.455 -0.395 -0.335 microns 2.76 Multi-scale System Design & Manufacturing Photos by Prof. Martin Culpepper, courtesy of Ford Motor Company. Used with permission. -0.275 Form-in-place process Assemble Mate Pre-load Recovery Groove surface after burnishing process microns Elastic recovery restores gap 2.76 Multi-scale System Design & Manufacturing microns
