Kin Coupling Wayman

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Transcript of Kin Coupling Wayman

Kinematic CouplingsGus Hansen Phil Wayman Sunny Ng

AgendaCoupling Definition Methods of Coupling Kinematic Coupling Design Critical Design Issues Compliant Kinematic Couplings Conclusion

What is a CouplingFor the purposes of this discussion, a coupling is a device with the following characteristics:

A coupling connects two parts or assemblies It can be separated and rejoined at will The resulting connection will have some level of stiffness. The specific locating features of the connection will result in some level of accuracy and repeatability.

Methods of CouplingPin/Hole Method Elastic Averaging Method QuasiQuasi-Kinematic Method PlanarPlanar-Kinematic Method Kinematic Method

Pinned JointsAdvantages

A seal between the coupling components Jamming & Wedging = high assembly/mfg cost Slop = component relative location not uniquely defined. Repeatability Tolerance

Disadvantages

Elastic AveragingAdvantage:

Capability of withstanding high loads Large amount of contact area allow for a stiff joint design. Better repeatability than pin joint Grossly over constrained Susceptible to surface finish & contaminants Repeatability requires an extended period of wear-in wear-

Disadvantage:

QuasiQuasi-Kinematic CouplingAdvantage = Disadvantage

Near kinematic Improve load capacity over K.C. Not as over constraint as Elastic Averaging Less sensitive in placements of their locating features = mfg. cost lower

Planar Kinematic CouplingExtension to QKC

Mixed nature of coupling

Large contact surface with line or point to constraint degrees of freedom

High stiffness and load capacity Good repeatability

Kinematic CouplingAdvantage

Low cost Sub-micron Subrepeatability Less sensitive to contamination High stress concentration Does not allow for sealing joints

Disadvantages

Methods of CouplingCoupling Type Basic Pin Joint Elastic Averaging Planar Kinematic QuasiQuasiKinematic Kinematic Contact TypeSurface Surface Mixed Line Point

Repeatability Stiffness/Load Industrially Capacity IdealPoor (~5 Qm) Fair (~1 Qm) Good Good (~0.5 Qm) Excellent (~0.01 Qm) High High High Medium to High Varies (Usually Low) Fair Good Good Good Poor

Found at http://pergatory.mit.edu/kinematiccouplings/html/design_process/define.html

Kinematic CouplingHistory: (from Optimal Design Techniques for Kinematic Couplings, L.C. Hale, A.H. Slocum)

James Clerk Maxwell (1876, 3-vee) 3Lord Kelvin (Kelvin Clamp) Professor Robert Willis (~1849) Economical No wear in period Contaminates

Other Advantages:

Kinematic Coupling Design ProcessRequirements InputsDisplacement

Disturbance

Force

Kinematics Material Geometry

Coupling SystemOthers

Desire OutputsDesired Location

Actual OutputsActual Location

Improvement

Kinematic Coupling Design ProcessRequirements InputsDisplacement

Force

Displacement Disturbance

Kinematics Material Geometry

Coupling SystemOthers

Desire OutputsDesired Location

Actual OutputsActual Location

Improvement

RequirementsIdentify the various parameter for the coupling system

Accuracy Repeatability Interchangeability

Understanding constrain & bounds of these parameter Place priority on requirements helps identify critical path to a successful solution

InputsCoupling Force Displacement Thermal Disturbances

Vibration Temperature fluctuation

Kinematic Coupling Design ProcessForce Disturbance InputsDisplacement

Force

Displacement Disturbance

Kinematics Material Geometry

Coupling SystemOthers

Desire OutputsDesired Location

Actual OutputsActual Location

Improvement

Error/Source AnalysisKinematic/Geometry/Materials

Example: Three-Groove K.C. ThreeBalls diameters, groove radii Coordinate location of balls Contact force direction Preload force magnitude and direction External load magnitude and direction Youngs modulus & Poissons Ratio of materials

Error/Source AnalysisStress and deflection at contact pts. Force and momentum equilibrium Six error motion terms

Kinematic Coupling Design ProcessForce Disturbance InputsDisplacement

Force

Displacement Disturbance

Kinematics Material Geometry

Coupling SystemOthers

Desire OutputsDesired Location

Actual OutputsActual Location

Improvement

Improvements

Desire Output

Spreadsheet instantaneous results Assembly techniques & calibrationRefine procedures w/ minor alignment adjust Symmetric torque pattern Apply stepped preload (25%50%75%100%) (25%50%75%

Lubricate the fasteners and the contact surfaces Solid Lubricant

Sprayable

MoS2, PTFE Polyamide, Polyethylene Graphite

Water Dilute-able DiluteNonNon-combustible Low in Solvents

Kinematic Coupling Design ProcessForce Disturbance InputsDisplacement

Force

Displacement Disturbance

Kinematics Material Geometry

Coupling SystemOthers

Desire OutputsDesired Location

Actual OutputsActual Location

Improvement

Actual OutputAlignment error with galaxy NGC383 must be less than 2 micron!!!!Ooo.. Challenging . NOT!!!!

Made by Lockheed Martin SSC

Critical Design IssuesMaterial Selection Geometry Specification

Critical Design IssuesMaterial SelectionSteel vs. CeramicsCycle count considerations Fracture toughness considerations Repeatability considerationsSili Nitri e Repeatability I itial . Qm Ball Ball & Groove 50 nm < 0.1 Qm W r I 10 Qm 0.1 Qm < 0.1 Qm

Steel all roove

Groove

Adapted from Design of three-groove kinematic couplings, Slocum, Alexander

Critical Design IssuesMaterial SelectionSteel vs. Silicon Carbide

From Kinematic Couplings for Precision Fixturing-Part 1:Formulation of design parameters, Slocum, Alexander

Critical Design IssuesGeometry Specification

BallBall-Mounting MethodsGrind flat Annular grooves Grind/machine a shaped seat

Hemisphere Cone Tetrahedron

SymmetryReduces manufacturing costs Simplifies design Allows coupling for rotary joints

Combining Kinematic & ElasticCompliant Kinematic Couplings (CKCs) combine features of Elastic Averaging Couplings and Pure Kinematic Couplings The merger of concepts combines strengths from both, with some compromises

Types of CKCsFlexural Ball & Cone Tangential flexures allow spheres to seat in three cones. This has the following advantages: Over-constrained condition which would occur if solid arms were used does not occur. Load between ball and cones is thru line contact, instead of point contactload capability is increased. Load limit defined by lesser of flexure load limit and Hertzian contact at balls. Requirement for precision location of cones and balls is relaxed. Tangential Flexure, 3 Pl

(Hale 1999)

Sphere in Cone ContactCan we approximate the line contact of a sphere in a cone as contact between 2 parallel cylinders?

D2

If so, can we use the following contact stress from Rourke? Max W= 0.798*[p/(KDCE)]1/2 Where CE = (1-R2)/E1 (1-R2)/E2 D2 = ball diameter KD = D2 for D1 = = cross section of cone p = load per unit length of contact = PN/L. Hale (1999) has posed this as a possible method, without above stress formula

P

P

D1 Line of contact (L) Conical Seat

eeds further validation, but contact area is larger than ball in V or on Flat

Types of CKCsV-Groove Beam Flexures (Kineflex )TM

Balls mating with V-grooves through beam flexures locate and clock coupling. This has the following advantages: Location and clocking geometry same as kinematic 3 ball & V groove (6 contact points) Flexures allow plates to be adjusted, or clamped together after location is set. The distance between the two plates is no longer determined by the tolerances of the balls and V groovesthis removes an overconstraint if spacing between the plates or clamping are desired attributes.

(Culpepper, Slocum)

Types of CKCsV-Groove Beam Flexures

(Culpepper, Slocum)

Types of CKCsAxial Spring Ball Plunger Balls mating with V-grooves through spring force locate and clock coupling. This has the following advantages: Location and clocking geometry same as kinematic 3 ball & V groove (6 contact points) Springs allow spacing between the coupling plates to be adjusted, or clamped together. The distance between the two plates is no longer determined by the tolerances of the balls and V groovesthis removes an overconstraint if spacing between the plates or clamping are desired attributes.

(Culpepper, Slocum)

Types of CKCsAxial Spring Ball Plunger

High accuracy, at reasonable cost?

(Culpepper, Slocum)

Cheaper version, with less accuracy?

Types of CKCsActively Controlled CKCs Balls mate in V-grooves whose spacing can be actively controlled. This has the following advantages: Location and clocking geometry same as kinematic 3 ball & V groove (6 contact points) Translation and rotation (6 DOF) of the pallet can be adjusted by changing groove plate spacing. Electronic feedback can provide closed loop control of pallet location. Tested accuracy of 60 nm/2 microradians under closed loop control. $$$ ???(Culpepper, Varadaranjan)

CKC Repeatability ComparisonDifferent sources show CKC repeatabilities between 5 and .25 Qm

(Culpepper, Slocum)

CKC repeatability falls between pinned joints and elastic averaging.

CKC SummaryCKCs are a compromise between elastic averaged and kinem