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adcats et byu edu conference Presentations Je

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  • pg 1
									                  Including GD&T Tolerance
                    Variation in a Commercial
                       Kinematics Application



Jeff Dabling
Surety Mechanisms & Integration
Sandia National Laboratories

   Research supported by:
 Summary
 Variation Propagation
 Obtaining Sensitivities
 Variation/Velocity Relationship
 Equivalent Variational Mechanisms in 2D
 EVMs in 3D
 Example in ADAMS
 3 Sources of Variation in Assemblies


DA      q                             q                R
                          R +DR                    R
 + A   q+           R             A
 A     Dq
            U                             U
            U +DU                         U + DU

        Dimensional and                    Geometric
           Kinematic
DLM Vector Assembly Model
    C
    L
                RL                                Gap

              Open Loop
                 RT
                                      e       i
                                  r
            Plunger                       
                          u                             Pad
                              q       Arm          g
        a                                                     Reel
b           Base      Closed Loop
    h        RL
How Geometric Variation Propagates
                      Y
  3D cylindrical                                    Rotational
  slider joint                                      Variation
                              X
                                                                  Flatness
                Z                                                 Tolerance
                                                                  Zone


                              Cylindricity   View normal to the cylinder axis
        Nominal
        Circle                Tolerance
                              Zone
                                             The effect of feature variations
Translational                  Flatness
                                             in 3D depends upon the joint
Variation                      Tolerance
                               Zone          type and which joint axis you
                                             are looking down.

       View looking down the cylinder axis
3D Propagation of Surface Variation
                     K Kinematic Motion
                     F Geometric Feature Variation
                 F                                   F

         K                                  K
                 y                                   y
                         x       K                       x       K

         z                   F              z                F

 K                                   K          F
             K
 Cylindrical Slider Joint                Planar Joint
Variations Associated with Geometric
Feature – Joint Combinations
                                                                                                             (Gao 1993)
       Geom
 Joints Tol
 Planar         R x Rz   Rx R z                         Rx R z   R x Rz    Rx Rz    Rx R z R xRzTy

 Revolute                R x Rz     R x Rz    Rx Rz     Rx R z   R x Rz    Rx Rz    Rx R z      Rx Rz    T x Tz   Tx T z

 Cylindrical             R x Rz     R x Rz    Rx Rz     Rx R z   R x Rz    Rx Rz    Rx R z      Rx Rz    T x Tz   Tx T z

 Prismatic     R xR yR z R xR yRz                      R xRy Rz R xR yR z Rx RyR z R xR yR z

 Spherical                          Tx TyTz            Tx TyTz                                 T x TyTz Tx T yTz Tx TyT z

 CrsCyl                    Ty         Ty        Ty        Ty                                      Ty               Ty

 ParCyl                  Ty R x     Ty Rx     T y R x Ty R x       Rx        Rx      Rx         Ty R x             Ty
                         T y Rx                         Ty R x   Ty R x    Ty R x   Ty R x                         Ty
 EdgSli E                                               Ty R x   Ty R x    Ty R x   Ty R x      Ty R x
        P Ty Rx          Ty R x
                         T y Rx     Ty R x    T y Rx    Ty R x   Ty R x    Ty R x   Ty R x      Ty R x             Ty
 CylSli C
        P Ty Rx          Ty R x                         Ty R x   Ty R x    Ty R x   Ty R x      Ty R x
        Pt                                                                                                         Ty
 PntSli    Ty              Ty                             Ty       Ty       Ty        Ty         Ty
        P
                                      Ty                  Ty                                     Ty                Ty
 SphSli S T                Ty                             Ty       Ty       Ty        Ty         Ty
        P    y
    Including Geometric Variation
   Variables used have nominal values of zero
   Variation corresponds to the specified tolerance value
         Rotational variation due to flatness              Rotational = ±Db
          variation between two planar surfaces:            Variation
                                                                        Flatness
                                                                        Tolerance = a
                                                                        Zone




         Translational   variation   due   to   flatness    Translational =±a/2
          variation:                                         Variation
                                                                   Flatness
                                                                   Tolerance =   a
                                                                   Zone
    Geometric Variation Example
   Translational: additional vector with                           f

    nominal value of zero. (a3, a4)                                                          .01
                                                         U2
   Rotational: angular variation in the joint                  q
    of origin and propagated throughout the                         R                    H

    remainder of the loop. (b1, b2)               A
                                                                             .02
                                                                                   .01

                                                           U1                                      .01


                       b1 b2              b1 b2                         f
                                                      (a 3, a 4)
         b1 b2 a3      b1 b2 a4       b1 b2                                 R2
                                                          U2
               b1 b2          b1 b2                             q
                                                                    R3

                                                                                         H

                                                  A
                                                                    R1

                                                          U1                        (b 1, b 2)
Sensitivities from Traditional 3D
Kinematics
Sandor,Erdman 1984:
   3D Kinematics using 4x4 transformation matrices [Sij] in a
    loop equation

   Uses Derivative Operator Matrices ([Qlm], [Dlm]) to eliminate
    need to numerically evaluate partial derivatives


   Equivalent to a small perturbation method; intensive
    calculations required for each sensitivity
Sensitivities from
Global Coordinate Method
                                                                  (Gao 1993)

 Uses 2D, 3D vector equations
 Derives sensitivities by evaluating effects of
  small perturbations on loop closure equations
    Length Variation Rotational Variation




                                            (taken from Gao, et. al 1998)
Variation – Velocity Relationship
                                                           (Faerber 1999)
Tolerance sensitivity solution                                    24

                                                     r3

                                                     23


                                                             r4
                                                r2
                                                     22

                                                            21
                                                      r1

Velocity analysis of the equivalent mechanism




                                 When are the sensitivities the same?
2D Equivalent
Variational Mechanisms                                    (Faerber 1999)

    2D dimensional variations to a
    Add Kinematic Joints:
    kinematic model using kinematic
    elements
   Converts kinematic analysis to
    variation analysis
     Equivalent Variational Joint:
   Extract tolerance sensitivities from
    velocity analysis
                                                  Kinematic Assembly
           works for Cylinder Slider Parallel
    EvenSlider Planarstatic assemblies (no
      Edge                            Cylinders
    moving parts)




                                                    Static Assembly
            3D Equivalent
            Variational Mechanisms
                 3D Kinematic Joints:                                         Equivalent Variational Joints:




 Rigid (no motion)      Prismatic        Revolute        Parallel Cylinders




   Cylindrical          Spherical         Planar           Edge Slider




Cylindrical Slider     Point Slider   Spherical Slider   Crossed Cylinders
Geometric Equivalent
Variational Mechanisms
                                     f
            f                                                                         Y                      d                   f
                                 f
                                                          f       f                                     R1
                 f                                                                        f       X                  f
                                                                                 f
                                             f                f              f                                                   d
            f                                                               Z                                    R2
                                                                                      f

                Rigid                            Prismatic                       Revolute              Parallel Cylinders

                                                                                              f
                             Y                                                   f
                                         f            f                              f
                                             X                        f
        f            f
                                                  f
        Z                f                                                                                   f               f

       Cylindrical                               Spherical                           Planar              Edge Slider



                         R                                                                d                      d           R1
                 d
                                                      f                               f   R                              f


                                                                                                                                     R2
                             f
            f
    Cylindrical Slider                           Point Slider             Spherical Slider            Crossed Cylinders
  Example Model: Print Head



                                                            Geometric EVM
                                                                          A
                                                                              f3
Pro/E model                            h
                                  f2                                          a2
                Inset A                                                            a3
                                           q1
                f3   j
                          i                     g
                                                        Inset B
                k                                           f     B
                                                              e           f
                                                            d
                                                    c                              e
                                       Z                                                a1
                              b
                                       a                              c                 d
                                           X                                       f1
     Print Head Results
Results from Global Coordinate Method:
     A    B       D          E      G I J   K   L
C
f1
F
f3


Results from ADAMS velocity analysis:
     A    B       D          E      G I J   K   L
C
f1                                                  3D GEVM in ADAMS
F
f3
Research Benefits
   Comprehensive system for including geometric
    variation in a kinematic vector model
   More efficient than homogeneous transformation
    matrices
   Allows use of commercial kinematic software to
    perform tolerance analysis
   Allows static assemblies to be analyzed in addition to
    mechanisms
   Ability to perform variation analysis in more widely
    available kinematic solvers increases availability of
    tolerance analysis
Current Limitations
 Implementing EVMs is currently a manual
  system, very laborious
 Manual implementation of EVMs can be very
  complex when including both dimensional and
  geometric variation
 Difficulty with analysis of joints with
  simultaneous rotations
Questions?

								
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