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Variation Modeling and Design for Compliant Assemblies Prof. S. Jack Hu and Dr. K. Iyer Department of Mechanical Engineering and Applied Mechanics The University of Michigan. Compliant Sheet Metal Assembly. Variation Simulation Methods. Worst Case: (Conway, 1948; Chase and Parkinson, 1991)

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slide1

Variation Modelingand Design for Compliant AssembliesProf. S. Jack Hu and Dr. K. IyerDepartment of Mechanical Engineering and Applied MechanicsThe University of Michigan

variation simulation methods
Variation Simulation Methods

Worst Case:

(Conway, 1948; Chase and Parkinson, 1991)

Root Sum Squares (RSS):

(Spotts, 1978, Lee and Woo, 1990)

Monte Carlo Simulation:

(Craig, 1989)

slide5

Example of

Variation Stackup

slide6

Introduction

Type

Rigid Body Assembly

Compliant Assembly

Properties

B) Unique Properties of Compliant Assembly

Assembly Examples

PC Based Compliant Assembly Variation Analysis

Assembly

Mechanism

Locating

Principle

Variation

Propagation

Geometry Closure

Force & Geometry Closure

“N-2-1”

“3-2-1”

Deformation and Spring-back

Rigid-body Motion

Assembly Characteristics

slide7

Understanding Variation “Stack-up” in Compliant Sheet Metal Assembly(Simple 1D model)

Clamping forces

Springback:

slide8

Part 1

10

1

100

Part 2

10

2

100

W

h

L

(mm)

same material

Example

When 1 and 2 are independent,

Characteristics:

(1) The assembly variation can be less than that of individual

components,

(2) The assembly variation is dominated by the variation of the

more rigid component.

compliant assembly variation analysis cava overview
Compliant Assembly Variation Analysis (CAVA): Overview

(Liu and Hu, 1997;

Long and Hu, 1998)

slide14

Create model

  • Calculate
  • Evaluate
  • Modify the model

CAVA Operating Procedures

slide16

Process for Sheet Metal Assembly

The “3-2-1”

fixture

elements

are closed

The additional

“N-3” clamps

and weld guns

are closed

Welding. Then fixtures &

clamps released,

and sheet metal

spring-back

variation characteristics in sheet metal assembly
Variation Characteristics in Sheet Metal Assembly

(a) Rigid body motion by “3-2-1” fixture

(b) Deformed part held by additional clamps and weld guns

Va = [S1] Vp + [S2] Vt = [S] Vs

(c) Spring-back after tooling release

robustness evaluation

R2

C

RobustnessEvaluation

Variation Transmission Ratio

Sensitivity Index

(Lee, Long and Hu; 2000)

Robustness Index

K = lN

cava applications joint design

Measure

Variation Sources

Node

Dir.

41

37

63

233

247

255

313

309

335

505

519

527

274

2

0.5810

0.0245

0.0549

-0.1230

0.0088

0.1860

4.2300

-0.0473

0.4400

-0.8390

0.0130

1.2800

276

2

0.8090

-0.0859

0.0432

-0.0608

-0.0096

-0.0026

5.9000

-0.4340

0.3650

-0.5840

-0.0207

0.1420

309

2

0.2780

0.2130

0.2540

-0.0091

-0.0002

0.0090

2.1800

0.5550

2.0000

-0.0717

-0.0027

0.0717

498

2

-0.0026

-0.0096

-0.0608

0.0432

-0.0858

0.8090

0.1420

-0.0207

-0.5840

0.3650

-0.4340

5.9000

500

2

0.1860

0.0088

-0.1230

0.0549

0.0245

0.5810

1.2800

0.0130

-0.8390

0.4400

-0.0473

4.2300

519

2

0.0090

-0.0002

-0.0091

0.2540

0.2130

0.2780

0.0717

-0.0027

-0.0717

2.0000

0.5550

2.1800

CAVAApplications: Joint Design
slide20

Lap Joint

Butt Joint

Lap-Butt Joint

K

8.56

27.61

11.98

Average Deviation

(mm)

1.45

9.64

3.70

Joint Design: Robustness vs. Architecture

1) Parts variations are absorbed in lap joints

2) Parts variations are magnified in butt joints

slide21

Case #

1

2

3

4

Locations of clamps

C1, C2, C3

C1, C2,

C3, C4

C1, C2,

C3, C5

C1, C2, C3, C4, C5

K

0.8465

0.8429

0.7536

0.7110

CAVAApplications: Fixture Configuration Design

slide23

Serial Line Configuration

Parallel Line Configuration

CAVAApplications: Assembly Line Configuration

slide25

Line Configuration Variation

Single Assembly Station

Serial Line Assembly

slide26

Robustness

Kp

Kt

Station 1

0.9480

14.8973

Station 2

0.7007

0.2774

System

0.66

10.70

Line Configuration Robustness

  • Contributions of tooling and part variations can be different in
  • different stations and joint designs.
  • 2) A parallel configuration should be avoided with a station for which Kt > 1
slide27

Work Impact

  • A new methodology and variation simulation software, CAVA, has been developed which can be used to
    • Evaluate the dimensional capability of product architectures
      • Joint structure
      • The number and location of welds
    • Evaluate the dimensional capability of processes
      • Fixture schemes
      • Assembly sequence
assembly of parts with non flat surfaces
Relevance

Fatigue crack initiation

Fretting

Wear

Leakage

Electrical contact resistance

…any situation where the integrity of a contact interface is important

Assembly of Parts with Non-Flat Surfaces
slide29

2

1

Bolted Joint Model

1

3

slide30

32mm

16mm

24mm

16mm

2-D FEA of Surface Waviness

  • Abaqus software
  • Axisymmetric model plates (CAX4 elements)
  • Bolt in plane stress (CPS4 elements)
  • Bolt thickness (3-direction) varies to simulate circular cross section
  • Hole properties “smeared”
  • Sliding between plates possible
  • Stick conditions assumed at all bolt-plate interfaces
slide33

Preliminary Indications

  • Joint compliance:
    • 176 mm/GN (II) > 30 mm/GN (IV) > 26 mm/GN (III) > 8.5 mm/GN (I)
  • Peak contact pressure, total gap and compliance are all related to each other.
  • Contact pressure distribution is non-“elliptical”.
    • Local bending at the contact surfaces is significant and affects the contact pressure and slip distributions.
  • Gap closure has may have a complex relationship to waviness
    • more wavy can mean more closure (compare III and IV)
  • Friction coefficient appears to have no effect on the contact pressure and slip distributions.
slide35

Preliminary Parametric Study

  • Models I and IV considered
  • Material property change: steel vs. Al
    • T= 20 C,m= 0.4
  • Temperature rise: 20 C  150 C
    • Al (material properties),m= 0.4
  • Friction coefficient change:m=0 and 0.4
    • Steel (material properties), T = 20 C
results
Effect of material property:

For perfectly flat contact, the effects on contact pressure and gap distribution are negligible

For wavy contact, the total gap and maximum gap increase dramatically with decreasing material stiffness (Al)

The machining tolerances applied to steel are not directly transferable to Aluminum

Effect of temperature rise:

Possibly complex alteration of the contact area, pressure and gap distributions in flat and wavy contacts

Effect of friction coefficient:

Does not alter contact pressure distribution

Can affect the gap distribution if waviness is significant

Inverse relationship with initial contact area indicated

highermpromotes gap closure.

Results
additional results
Increase in compliance with Al is ~ 3X:

8.5 mm/GN to 25 mm/GN in model I

30 mm/GN to 82.2 mm/GN in model IV

Thermal springback:

539 mm/GN in model I (64.7 mm)

480 mm/GN in model IV (57.6 mm)

Effect ofmon compliance is negligible

Additional Results
work in progress
A) Inclusion of gasket

Solution for perfectly flat contact (model I) has been obtained.

Modeling the highly localized, non-linear deformation of gasket material in the presence of surface waviness is currently receiving attention.

Work in Progress

Gasket

slide42
B) Multi-rivet joints

effects of clamping sequence

C) Closed-form solution for wavy contact

P

E2, n2

E1, n1