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Multi-Level Design Process For 3-D Preform Shape Optimization In Metal Forming Using The Reduced Basis Technique PowerPoint Presentation
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CDOC. Multi-Level Design Process For 3-D Preform Shape Optimization In Metal Forming Using The Reduced Basis Technique. Department of Mechanical and Materials Engineering Wright State University Dayton, OH 45435. CDOC. Presentation Outline. Research objectives

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slide1

CDOC

Multi-Level Design Process For 3-D Preform Shape Optimization In Metal Forming Using The Reduced Basis Technique

Department of Mechanical and Materials Engineering

Wright State University

Dayton, OH 45435

slide2

CDOC

Presentation Outline

  • Research objectives
  • Overview of forging process
  • Need for preform shape optimization
  • Research challenges
  • Reduced basis design approach
  • Case studies
  • Summary
slide3

CDOC

Research Objectives

  • Develop a methodology for 3-D preform shape optimization in forging
    • Identify 3-D preform shape parameters
    • Define optimization design parameters
    • Define finite element-based objectives and constraints
    • Establish explicit relationship between design parameters and objectives and constraints
  • Enable preform design for complex 3-D forging components
  • Develop a computationally feasible technique
  • Improve product quality
slide4

CDOC

Initial billet

Trimming

Preform

Blocker

Finisher

Tradeoff designs

Heat treatment process

Rejected

Machinable

Temperature distribution

Introduction to Metal Forming Process

Intermediate shapes

Forming process

Quality

check

Robust design

slide5

CDOC

Flash

Underfill

Reduced underfill

Need for Preform Shape Design

Initial shape

Preform shape

Blocker shape

Blocker shape

  • Minimize load
  • Minimize material waste
  • More uniform Material flow
  • Minimize geometric variation
  • Decrease production cost
  • Increase die life
slide6

CDOC

Conventional Preform Design Techniques

Preforms for steel finished forgings

  • Design guidelines
  • Empirical relations
  • Computer-aided design
    • Knowledge-based approach
  • Finite element approach
    • Forward simulations
    • Backward simulations

No preform

h=b

h = 2b

Finished forgings

Upset stock

Preforms

h = 3b

slide7

Design Issues

CDOC

  • 2D Assumptions for 3D parts
  • Plane-strain - No deformation in out-of-plane direction
  • Axisymmetric - Material flow is radial
  • Practical forgings are neither axisymmetric nor plane-strain
  • Require large number of parameters
  • Require large number of simulations
  • Long computational times

Shape parameters

Preform shapes

slide8

CDOC

Shape Optimization Methodology

Identify initial preform shape

Parameterize preform

shape

  • Reduced basis technique
    • Obtain basis shapes
    • Employ design variable linking

Determine critical

optimization parameters

  • Generate DOE points using Latin

Hypercube sampling techniques

  • Conduct forging simulations of the DOE

billets

  • Extract FEM output data

Construct surrogate

models

Optimize

slide9

CDOC

Axisymmetric 3-D metal hub

Finite element model of 2-D section

Reduced Basis Technique

  • Innovative technique for defining preform shapes
slide10

CDOC

Reduced Basis Technique

  • Innovative technique for defining preform shapes
  • Generate initial guess preform basis shapes
  • X and Y co-ordinates of boundary points define basis vectors

Metal hub

Basis 2[Y2]

Basis 3[Y3]

Basis 1[Y1]

(xi, yi)

Basis shape boundary points

slide11

CDOC

Desired boundary

False boundary

Basis 2[Y2]

Basis 3[Y3]

Basis 1[Y1]

Basis Vectors

  • Need large number of boundary points
      • Increases length of the basis vector
      • Require no extra computational cost
  • Define all of the basis shapes similarly
slide12

CDOC

Basis 2[Y2]

Basis 3[Y3]

Basis 1[Y1]

Basis Vectors

  • Need large number of boundary points
      • Increases length of the basis vector
      • Require no extra computational cost
  • Perform Gram-Schmidt orthogonalization
      • Produces independent basis shapes
slide13

Basis shapes

Forged parts

Design Parameters Definition

  • Weighted combination of orthogonal basis shapes
slide14

Y1

a1 ×

Y2

a2 ×

Y3

a1

a2

a3

a3 ×

Forged part

0 ≤ ai ≤ 1

Design Parameters Definition

  • Weighted combination of orthogonal basis shapes

Basis shapes

slide15

Y1

a1 ×

Y2

a2 ×

Y3

a1

a2

a3

a3 ×

Forged part

0 ≤ ai ≤ 1

Design Parameters Definition

  • Weighted combination of orthogonal basis shapes

Basis shapes

slide16

Y1

a1 ×

Y2

a2 ×

Y3

a1

a2

a3

a3 ×

0 ≤ ai ≤ 1

Forged part

Design Parameters Definition

  • Weighted combination of orthogonal basis shapes

Basis shapes

slide17

Y1

a1 ×

Y2

DOE

points

a2 ×

Resultant preform shapes

Y3

  • Scaling maintains constant volume for resultant preforms
  • Weights (ai) are the design parameters

a3 ×

0 ≤ ai ≤ 1

Design Parameters Definition

  • Weighted combination of orthogonal basis shapes

Basis shapes

slide18

CDOC

Underfill

Max

Underfill

Med

Min

Strain variance

Construction of Surrogate Model

  • Generate Latin Hypercube sampling points
  • Perform finite element simulations
  • Obtain objectives and constraints

Variable 2

Variable 1

  • Construct response surface model
slide19

CDOC

Optimization Statement

  • Design variables
    • Weighting factors of reduced basis technique (ai)
  • Cost function
    • Minimize strain variance f(ai)
  • Subject to
    • Underfill g(ai) ≤ 0
  • Side bounds on weights
    • 0 ≤ ai ≤ 1
slide20

CDOC

Basis 3 [Y3]

Basis 2 [Y2]

Basis 4 [Y4]

Basis 1 [Y1]

Design Optimization

h1

h1 = 1.25 x b1

h2 = 1.50 x b2

b1

b2

h2

Symmetry

axis

Cross-sectional view

Rail section

  • Four basis shapes generated

Basis shapes

Finite element simulations

Final forged parts

slide21

CDOC

Response

Iteration number

Results

Optimized billet

Iteration history of objective and constraint functions

Final forged part

Strain variance : 0.0647

Flash : 3 %

slide22

CDOC

Basis 3 [Y3]

Basis 2 [Y2]

Basis 4 [Y4]

Basis 1 [Y1]

Simple basis shape

Inappropriate basis shape

Viable basis shapes

Need For Multi-Level Design Process

  • Single level design requires appropriate starting basis shapes
  • No information available for a new product
  • Enable design with geometrically simple basis shapes
slide23

CDOC

Multi-Level Optimization Routine

Generate starting guess shapes

Define design parameters

(Level L)

Reduced basis method

DOE techniques

Obtain design points

Build new basis shapes (L=L+1)

Conduct FEM analysis using DEFORM-3D

Obtain objective and constraints

Generate surrogate model using response surface method

Redesign using optimization algorithm

No

Yes

Optimum preform

Constraint satisfied?

slide24

CDOC

Basis 2 [Y2]

Basis 3 [Y3]

Basis 1 [Y1]

Basis shapes

Final forged part

Best shape

Best weights

Final forged part

Case Study – 1

(Level 2)

(Level 1)

  • Multi-Level design optimization

Rail section

slide25

CDOC

Basis 2 [Y2]

Basis 3 [Y3]

Basis 1 [Y1]

Basis shapes

Final forged part

Best shape

Best weights

Final forged part

Case Study – 1

(Level 3)

(Level 2)

Rail section

slide26

CDOC

Basis 3 [Y3]

Basis 2 [Y2]

Basis 1 [Y1]

Optimum shape

Optimum weights

  • Complete die fill
  • Flash: 3 %

Final forged part

Case Study – 1(Level 3)

Rail section

Basis shapes

Final forged part

slide27

CDOC

Multi-level design scheme

Single-level design scheme

Basis 1 [Y1]

Basis 2 [Y2]

Basis 3 [Y3]

Basis 3 [Y3]

Basis 2 [Y2]

Basis 4 [Y4]

Basis 1 [Y1]

Optimum billet

Optimum billet

Result Comparison

Single-level

  • Multi-level design scheme leads to optimum billet
  • Computational time increases
  • Expert knowledge can be used for single-level design scheme

Multi-level

slide28

CDOC

Zone B

Zone A

h

b

h = b

Case Study - 2

  • h/b ratio is one
  • Three simple billet shapes as basis shapes
  • All basis shapes give underfill
  • Flash: 3 %
  • Quarter model for forging simulation

3-D Metal hub

3xh

2.2xh

1.5xh

Basis 1 [Y1]

Basis 2 [Y2]

Basis 3 [Y3]

Forged part

  • [Y1] and [Y2] give underfill at Zone Aand [Y3] at Zone B
slide29

CDOC

Results

  • Three design variables
  • 15 DOE points generated
  • None give complete die fill

Optimum weights

Forged part with complete die fill

Preform shape

  • Achieved optimum shape in single level
  • Requires multi-level design process for higher h/b ratios
slide30

CDOC

h

b

3-D Metal hub

Quarter models with

section view (h/b = 2)

Case Study - 3

  • 3-D Metal hub with h/b = 2
  • Allowable flash percentage: 2%
  • Quarter model assumed for forging simulations
slide31

CDOC

Basis 3 [Y3]

Basis 1 [Y1]

Basis 2 [Y2]

Basis shapes (quarter models)

Level 1

  • Three basis shapes selected in Level 1
  • Fifteen DOE points for building the RSM
slide32

CDOC

Level 1 Results

Top die profile

  • Level 1 best shape : Basis 3

Underfill

Forged part

  • No other basis shape combinations give less underfill
  • Need to satisfy the underfill constraint
  • Tapering profile of the Basis 3 is crucial
slide33

CDOC

Level 2

  • Basis 1 is the Level 1 best shape
  • Variation of Basis 1 form Basis 2 and Basis 3

Basis 1 [Y1]

Basis 2 [Y2]

Basis 3 [Y3]

Basis shapes (quarter models)

  • Basis 2 and Basis 3 have opposing profiles
slide34

CDOC

Level 2 Results

  • No underfill
  • Flash volume: 2%
  • Basis 2 has the maximum contribution

Optimum weights

Preform shape

Forged part with complete die fill

Performance characteristics

slide35

CDOC

Rear end

Steering link

Top view

Front end

Isometric view

Side view

Case Study - 4 (Steering Link)

  • High volume forged component
  • Huge material waste (30%) occurs
  • Cross-sections vary along all three axes
slide36

CDOC

Level 1 Basis Shapes

Basis 1

  • Allowable flash percentage: 5%
  • Three simple basis shapes
  • All basis shapes give more underfill at the front end
  • Each basis vector contains 648 shape co-ordinates (216 points)

Basis 2

Basis 3

slide37

CDOC

Resultant Shapes

  • Reduced basis technique decreases the number of design variables to three

Basis 1

Basis 2

Possible preform

shapes

Basis 3

slide38

CDOC

Level 1 Results

Level 1 best weights

Level 1 best shape

Forged part with underfill

  • Rectangular nature of Basis 3 is most crucial
  • Contribution of Basis 2 provides the tapering profile
  • Level 1 best shape becomes the Basis 1 in Level 2
slide39

CDOC

Level 1 Results

Level 1 best shape

Forged part showing underfill

Performance characteristics

Level 1 best shape

Level 1 best shape

Basis 1

Basis 2

Basis 2

Basis 3

Flash %

Strain Variance

Required flash percentage

Basis 3

Basis 1

Basis shape

Basis shape

Flash percentage

Strain variance

slide40

CDOC

Level 2

Basis 1

  • Four basis shapes in Level 2
  • Each basis shape has different cross-section
  • Number of shape co-ordinates are 1125 (375 points)

Basis 2

Basis 3

Basis 4

Basis shapes

slide41

CDOC

Resultant Shapes

Basis 1

  • Four deign variables

Basis 2

Possible preform

shapes

Basis 3

  • Increasing the number of basis shapes also increases the DOE points to 25 from 15

Basis 4

slide42

CDOC

Level 2 Results

Optimum Weights

Optimum Preform

Final Forged Part

  • Complete die fill achieved, Flash volume: 5%
  • Contribution of Basis 1 reduces the curvature of Basis 2
  • Basis 3 Cross-sectional radii reduced
  • Any contribution of Basis 4 increases the strain variance
slide43

CDOC

Level 2 Results

Optimum Preform

Final Forged Part

Performance characteristics

Basis 2

Preform

Basis 1

Basis 4

Basis 2

Basis 4

Strain Variance

Flash %

Preform

Basis 3

Basis 1

Basis 3

Basis shape

Basis shape

Flash percentage

Strain Variance

slide44

CDOC

Summary

  • Introduced a novel concept for 3-D preform design
    • Reduced basis technique
  • Enables design variable definition for complex 3-D components
  • Utilized simple basis shapes in multi-level optimization
  • Knowledge based basis shapes aids faster optimization
  • Optimum preform shapes can be easily manufactured
  • Applicable for both 2-D and 3-D forging processes