Sheet Metal Forming

2.810 Fall 2002Professor Tim Gutowski

Minoan gold pendant of bees encircling the Sun, showing the use of granulation, from a tomb at Mallia, 17th century BC. In the Archaeological Museum, Iráklion, Crete.

Historical Note;Sheet metal stamping was developed as a mass production technology for the production of bicycles around the 1890’s. This technology played an important role in making the system of interchangeable parts economical (perhaps for the first time).

Steps in making Hub Steps in Sprocket making

Stress Strain diagram – materials selection

Basic Sheet Forming Processes(from http://www.menet.umn.edu/~klamecki/Forming/mainforming.html)

Shearing

Bending

Drawing

Shear and corner press

Brake press

Finger press

Shearing Operation Force Requirement

Die

SheetPunch T

D

Part or slug

F = 0.7 T L (UTS)

T = Sheet ThicknessL = Total length ShearedUTS = Ultimate Tensile Strength of material

Yield Criteria

Y

Y/2

Tresca Mises

max = (2/3)1/2 Y max = (1/2) Y

Schematic of a Blanked Edge

Bending Force Requirement

PunchWorkpiece T

Die

L

Force

T = Sheet ThicknessW = Total Width Sheared

(into the page)

L =Span lengthUTS = Ultimate Tensile Strength of material

Engineering Strain during Bending: e = 1/((2R/T) + 1)R = Bend radius

Minimum Bend radius: R = T ((50/r) – 1) r = tensile area reduction

in percent

)(2

UTSL

WTF

Stress distribution through the thickness of the part

yY

Y

-Y

h

-Y

Y

Elastic Elastic-plastic Fully plastic

Springback

•Over-bend•Bottom•Stretch

tension

compression

Pure Bending

Bending & Stretching

Stretch Forming

Loading Pre-stretching

Wrapping Release

* source: http://www.cyrilbath.com/sheet_process.html

Stretch Forming

Stretch forming

Stretch Forming Force Requirement

F = (YS + UTS)/2 * A

F = stretch forming force (lbs)YS = material yield strength (psi)UTS = ultimate tensile strength of the material (psi)A = Cross-sectional area of the workpiece (in2)

• Example of Force Calculation

Calculate the force required to stretch form a wing span having a cross-sectional area of .50X120” made from 2219 aluminum alloy having a yield strength of 36,000 psi and a UTS of 52,000 psi:

F = 88000/2 * 60 = 2,640,000 lbs = 1320 tons

Calculate the force required to shear a 10” diameter, 1/8” thick blank from mild steel with a UTS of 45,000 psi:

F = 0.7 (.125)((10) 45,000 = 62 tons

Auto body panels

10 - 11 panels•3 to 5 dies each• ~$0.5M each• ~$20M investment

Tooling for Automotive Stamping

Machines

Material SelectionMaterial selection is critical in both product and process design.Formability is the central material property.This property must be balanced with other product and process considerations such as strength, weight, cost, and corrosion resistance.Auto vs. Aerospace Example

Auto Body Panel Airplane Body Panel

Progressive stamping stretch forming1010 Steel, cold-rolled 2024 Aluminum, T3 temper.04” sheet, custom order .08” sheet, oversizeDouble-sided Zinc clad mechanically polishedCost ~ $.35-.45/lb Cost ~ $4.0/lbUTS ~ 300 MPa UTS ~ 470 MPaYS ~ 185 MPa YS ~ 325 MPa Elongation ~ 42% Elongation ~ 20%n = .26 n = .16

Comparison of representative Parts: Aero and Auto

Auto AeroPart Description Body Panel Body Panel

54"X54" 54"X54"

Forming Process Progressive Stamping Stretch FormingMATERIAL

Material

1010 Steel, cold-rolled, .04" sheet, custom order double-sided Zinc clad

2024 Aluminum, T3 temper, .08" sheet,

oversize mechanically polished

Scrap 40% 20%Material Cost $0.45/lb $4.00/lbPer part $15.75 $105.00

LABORSet-up Time 1.5hr 1.0hrParts/Run 2,000 30Cycle Time 0.25 min 2.5 minTotal Labor 0.30 min 4.5 minLabor Rate** $20.00/hr $20.00/hrStretch-Form Labor Cost $0.10 $1.50

FIXEDEquipment $5,000,000 $1,000,000Tools/Dies $900,000 $45,000

(200 manhours labor)TOTAL TRANSFER COST $25 $265

Parts Received

Mylar Protection Applied

‘Burr’ Edges in tension

Stretch Forming Index

to Block‘Burr’

Edges and Inspect

Hand Trim

Chemical Milling

Aerospace Stretch Forming Body Panel Process

Clad and Prime Surfaces

Process Flow for Automobile Door Stamping Operation

Raw material

Blank material starting dimensions

Drawing

Pierce

FlangeRestrike

Design: Stretch Forming vs. Stamping

Stretch Forming Advantages over Stamping Tighter tolerances are possible: as tight as .0005

inches on large aircraft parts Little problem with either wrinkling or spring back Large, gently contoured parts from thin sheets

Stretch forming Disadvantages over Stamping Complex or sharply cornered shapes are difficult

or impossible to form Material removal – blanking, punching, or

trimming – requires secondary operations Requires special preparation of the free edges

prior to forming

Springback

Elastic Springback Analysis

L

x

y

h

b

1. Assume plane sections remain plane:y = - y/

2. Assume elastic-plastic behavior for material

M

= 1/K

My

E

y

Y = E

Y

M

1/

EI

1/Y

MY

Loading

EI Unloading

R0R1

3. We want to construct the following Bending Moment “M” vs. curvature “1/” curve

Springback is measured as 1/R0 – 1/R1 (2)Permanent set is 1/R1

4. Stress distribution through the thickness of the beam

yY

Y

-Y

h

-Y

Y

Elastic Elastic-plastic Fully plastic

5. M = A y dA

Elastic region

At the onset of plastic behavior = - y/ E = - h/2 E = -Y (4)

Y

This occurs at 1/ = 2Y / hE = 1/Y (5)

d

y

dAb

hdy

Substitution into eqn (3) gives us the moment at on-set of yield, MY

MY = - EI/Y = EI 2Y / hE = 2IY/h (6)

After this point, the M vs 1/r curve starts to “bend over.” Note from M=0 to M=MY the curve is linear.

EI

dAy

EydAM 2

(3)

In the elastic – plastic region yY

Y

Ybyyh

Yb

yb

y

YyYb

Ybydyy

yYbydyybdyM

YY

y

Y

h

y

h

y

y

Y

Y

Y

Y

Y

222

0

32/2

2/

0

3

2)

4(

32

22

22

22

2/3

11

4 h

yY

bhM Y

Note at yY=h/2, you get on-set at yield, M = MY

And at yY=0, you get fully plastic moment, M = 3/2 MY

(7)

To write this in terms of M vs 1/ rather than M vs yY, note that the yield curvature (1/Y can be written as (see eqn (1))

2/

1

hY

Y

(8)

Where Y is the strain at yield. Also since the strain at yY is -Y, we can write

Y

Y

y

1

(9)

Combining (8) and (9) gives

1

)1(

2/YY

h

y (10)

Substitution into (7) gives the result we seek:

2

1

)1(

3

11

2

3

Y

YMM (11)

M

1/

EI

1/Y

MY

Loading

EI Unloading

R0R1

Eqn(11)

Elastic unloading curve

1

11

)1( R

MM

Y

Y

(12)

Now, eqn’s (12) and (13) intersect at 1/ = 1/R0

Hence,

2

010 1

)1(

3

11

2

311

)1( RM

RR

M YY

Y

Y

Rewriting and using 1/ = 2Y / hE, we get

320

10

4311

hE

YR

hE

Y

RR(13)

New developments

Tailored blanksBinder force controlSegmented diesQuick exchange of diesAlternative materials; cost issues

-

SHAPEMEASUREMENT

SHAPECONTROLLER

WORKPIECE

desiredshape +

shapeerror

finishedpartDISCRETE DIE

SURFACE

DISCRETE DIEFORMING PRESS

CONTROLLER

TRACING CMM

Part Error

Die ShapeChange

NewPartShape

The Shape Control Concept

Conventional Tooling

Tool

Pallet

Parking Lot

60 Ton Matched Discrete Die Press(Robinson et al, 1987)

Tool SetupActuators

Programmable Tool

Passive Tool

Press Motion

Cylindrical Part Error Reduction

0

10

20

30

40

50

60

P1 P2 P3 P4

PART CYCLE

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

RM

S E

rro

r [x

0.00

1 in

.]

MAX

RMS

SSYYSSTTEEMM EERRRROORR TTHHRREESSHHOOLLDD

MA

XIM

AL

SH

AP

E E

RR

OR

[x0

.00

1 i

n.]

Large Scale Tool

6 feet

Stretch Forming with Reconfigurable Tool @ Northrop Grumman

Stamping and TPS: Quick Exchange of Dies

Ref. Shigeo Shingo, “A Revolution in Manufacturing: The SMED System” Productivity Press. 1985

 

•Simplify, Organize, Standardize,

•Eliminate Adjustments,

•Convert Internal to External Set-Ups

Standard fixtures

Alternative materials for auto body panels

Comparison Steel Vs SMC

$0.35/lb0.03 thick7.6 lb40% scrap$4.25 mat’l cost400/hr5 workers$18.90/hr (Union)$0.24 labor cost$5,000,000 equipment$900,000 tools$7.71 unit cost at 100,000 units

$0.65/lb.0.12 thick7.0 lb6% scrap$4.84 mat’l cost40/hr$12.50/hr (non-Union)$0.63 labor cost$1,200,000 eqipment$250,000 tools$7.75 unit cost at 100,000 units

Ref John Busch

Cost comparison between sheet steel and plastics and composites for automotive panels ref John Busch

Environment

punching Vs machining

hydraulic fluids and lubricants

scrap

energy

painting, cleaning

Steel can production at Toyo Seikan

See Appendix D; http://itri.loyola.edu/ebm/

Summary

Note on Historical Development

Materials and Basic Mechanics

Aerospace and Automotive Forming

New Developments

Environmental Issues

Solidworks and Metal Forming your

Chassis

Readings

1. “Sheet Metal Forming” Ch. 16 Kalpakjian (3rd ed.)2. “Economic Criteria for Sensible Selection of Body

Panel Materials” John Busch and Jeff Dieffenbach3. Handout from Shigeo Shingo, The SMED System4. “Steps to Building a Sheet Metal Chassis for your

2.810 Car Using Solidworks”, by Eddy Reif5. “Design for Sheetmetal Working”, Ch. 9

Boothroyd, Dewhurst and Knight