uncertainty quantification and dimension prediction in forging and cooling processes belur k....

Uncertainty Quantification and Dimension Prediction in

Forging and Cooling Processes

Belur K. Badrinarayan

Adviser: Dr. Ramana V. Grandhi

What are we trying to accomplish?

A

B

C

D

E

Image Processing

Computer simulations

(Database generation)

Comparator/Estimator (TIG)

Closed-die forging Roll forging

Introduction

Billet is cut and induction heated

Trimming

Cooling process

Inspection after

cooling Inspection

Project Overview

Thermo-mechanically Induced Geometric variation estimator Online software compatible with Predictive Process Control

System and Data Acquisition System Estimates the dimensional and geometrical relations between the

hot and cooled states of forgings Predicts dimensional error and suggests corrective measures

Cold part dimensions

DAS Info. (Hot part surface Temp. and

Dimensions)

TIG

Dimensional Specifications

Dimensional Error

PPCS

Cooling Process Information

Determine factors affecting final part dimensions

Quantify uncertainties in forging/cooling process

Predict hot part dimensions after forging

Incorporate into TIG

Reduce part rejection and production costs

Research Objectives

Finite Element Analysis

Part Geometry Cooling Process SimulationForging Process Simulation

Surrogate Models

Uncertainties Analysis

DOE Extract Responses

Hot Part Dimension Prediction

Research Approach

Research Approach





Forging Process Simulation

Inputs

Billet Temperature

Die Geometry

Friction Factor

Press Characteristics

Billet Shape

Computer Simulation of

Forging Process

Outputs

Under-fill

Strain Distribution

Loads

Strain-rates

Part Geometry

Material Properties

Research Approach

Cooling Process Simulation

Inputs

Heat Transfer Coefficient

Kinetic Models

Environment Temperature

Material Properties

Part Geometry

Computer Simulation of

Cooling Process

Outputs

Nodal Coordinates

Stress Distribution

Hardness Distribution

Volume Fraction of Phases

Part Geometry

Research Approach

Sensitivity Analysis



DEFORM HT ABAQUS/DANTE

Finite Element Package

Easy to model NO Phase

Transformation and Material property data

Easy to model Contains Phase






Surrogate Models


Research Approach

Research Approach


Criteria for Design Of Experiments

Process Variables Simulation Time

Accuracy Required

Conduct Simulations at DOE points

Design Scheme





Surrogate Models


Research Approach

Surrogate ModelsSurrogate models

(Response Surface Models/ Spline fit)

Response Surface Models Spline fit data

Regression curves

Linear, quadratic,…etc and denote design

variables is the number of

independent variables

j

k

jiiiji

k

iiii

k

iii xxbxxbxbbbxf

1,111

0),(ˆ

jxix

k

Surrogate Models

Interpolations, ensure that the curve fit passes exactly through each data point

Linear, quadratic,…etc

,)( 112

1 cxbxaxf 10 xxx ,)( 22

22 cxbxaxf 21 xxx

Research Approach





Surrogate Models


Research Approach

Research Approach

Upper and lower limit of the hot part

Acceptable cold part limits from industry

Measured part temperature after forging






Research Approach

Surrogate Models


Research Approach

Monte Carlo Simulations

Input variables(X)

x1

x2

xn

Responses (Y)

y1

y2

ym

Uncertainty Quantification AnalysisUncertainty Quantification Analysis

Trade-Off Studies Uncertainties Analysis

Billet Shape Initial temperature Position

Lubrication system Spray angle Spray time Spray speed

Operational and equipment uncertainties Stroke length Environment temperature Heat Transfer Control system time lag Human repeatability

Cooling Fan speed Conveyer speed

Material properties Non-Homogeneity

Scaling

Hot Forging Process Uncertainties

Stroke

Case Study-I

Metal wheel

Conduct forging and cooling simulations

Check effective stresses

Extract forging load after forging

Determine part dimensions after cooling

Conduct trade-off studies

Finite element model

Forging Process Cooling process

Forging load

Conduct Design of Experiments Initial temperature 1000 - 1300° C Stoke length 19 - 21 mm Friction 0.3 - 0.7 Heat transfer coefficient 0.01 - 0.09 KW/m2 K

Obtain responses Load Percentage change in hub dimensions

A

B

C

Material used: AISI 4140

Design process

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0 0.02 0.04 0.06 0.08 0.1

Outer Diameter

Hub Diameter

Hub Thickness

Percentage Change in Dimensions

Heat Transfer Coefficient (kW/m2 K)

Dimensional Variation With Cooling Rate

Percentage change

in dimensions Initial dimension – Final Dimension

Initial dimension 100*

Outer Diameter

Hub Diameter

Hub Thickness

Dimensional Variation with Initial Temperature

1.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

0 0.02 0.04 0.06 0.08 0.1

Outer Diameter at 1300º C

Hub Diameter at 1300º C

Hub Thickness at 1300º C

Outer Diameter at 1200º C

Hub Diameter at 1200º C

Hub Thickness at 1200º C



Initial temperature effects part dimensions

No significant dimensional variations due to change in cooling rate

-6

-4

-2

0

2

4

6

8

0 0.5 1 1.5 2 2.5 3

Outer diameter

Hub diameter

Hub thickness

Outer diameter

Hub diameter

Hub thickness

Outer diameter

Hub diameter

Hub thickness

+1mm

-1mm

no change

Dimensional Variation With Variation in Stroke Length

Stroke lengths variation ±1mm



Significant variation in hub thickness due to change in stroke length

Stroke length has no effect on other part dimensions

-6

-4

-2

0

2

4

6

8

0 0.02 0.04 0.06 0.08 0.1

Hub thickness at 1300º C






+1 mm

-1 mm

no change

Correlation effect on Dimensional Variation



Coupling effect is observed Effect of Stroke length is greater than part temperature

Stroke length has significant effect on load Load decreases with increase in temperature and decrease in

friction

0

10

20

30

40

50

60

70

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Initial temperature (1000 , 1300 °C) =(-1,1)

Stroke length (19 ,21 mm) = (-1,1)

Friction factor (0.7, 0.3) = ( -1 ,1)

Loa

d (1

06 N)

Design variables

Sensitivities on Load

Sensitivities on Dimensional change

Change in Stroke length has significant effect on dimensional change

Friction factor has no effect on dimensional change

-4

-2

0

2

4

6

8

-1 -0.5 0 0.5 1

Initial temperature(1000-1300 °C) =(-1,1)

Stroke length (19 - 21mm)=(-1,1)

Friction factor (0.7 - 0.3)=(-1,1)

Perc

enta

ge c

hang

e (%

)

Design variables

Uncertainty Quantification

Generate Response Surface model

Conduct Monte Carlo simulations

Input variables have normal distribution

Plot Probability Density Function (PDF)

Undersize parts are rejected

Oversize parts are machined

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

-3.3

9

-3.2

1

-3.0

2

-2.8

3

-2.6

5

-2.4

6

-2.2

8

-2.0

9

-1.9

0

-1.7

2

-1.5

3

-1.3

4

-1.1

6

-0.9

7

-0.7

9

-0.6

0

-0.4

1

-0.2

3

Mor

e

oversized parts

0

0.01

0.02

0.03

0.04

0.05

0.06

-1.7

9

-1.6

0

-1.4

0

-1.2

1

-1.0

1

-0.8

2

-0.6

2

-0.4

3

-0.2

3

-0.0

4

0.16

0.35

0.55

0.74

0.94

1.13

1.33

1.52

Mor

e

undersized parts

Effects of Stroke Length Variation

Mean initial temperature: 1200o C standard deviation: 10

Mean friction factor: 0.3 standard deviation: 0.02

Mean stroke length: 19.4-19.8 mm standard deviation: 0.1

0

0.01

0.02

0.03

0.04

0.05

0.06

-2.1

1

-1.9

4

-1.7

6

-1.5

9

-1.4

2

-1.2

5

-1.0

7

-0.9

0

-0.7

3

-0.5

5

-0.3

8

-0.2

1

-0.0

4

0.14

0.31

0.48

0.65

0.83

Mor

e

undersized partsoversized parts

Mean stroke length 19.4 mm



Negative value indicates increase in part thickness

Pro

ba

bili

ty

Percentage change in dimensions

Pro

ba

bili

ty


Pro

ba

bili

ty


Probability of Parts Out of Limits

Changing mean values affects the number of out-of-limit parts Cost of acceptance and rejection influences the mean values Costs are part dependent

Init

ial

Tem

per

atu

re (0 C

)

Sta

nd

ard

D

evia

tion

Fri

ctio

n F

acto

r

Sta

nd

ard

D

evia

tion

Str

oke

Len

gth

(m

m)

Sta

nd

ard

D

evia

tion

No.

of

Iter

atio

ns

Low

er L

imit

(%

)

Up

per

Lim

it (

%)

1200 10 0.3 0.02 19.4 0.1 100000 26831(26.83) 18(0.018)

1200 10 0.3 0.02 19.6 0.1 100000 443(0.443) 5154(5.1540)

1200 10 0.3 0.02 19.8 0.1 100000 0(0) 64534(64.53)

1250 10 0.3 0.02 19.4 0.1 100000 19591(19.59) 32(0.032)

1250 10 0.3 0.02 19.6 0.1 100000 228(0.22) 8075(8.07)

1250 10 0.3 0.02 19.8 0.1 100000 0(0) 72619(72.61)

Case II

Model Metaldyne hub front axle (part no. 4638)

Conduct sensitivity of cold part dimensions in the cooling process

Initial temperature

Dimensional variation during forging

Develop a mathematical model representing the cooling process

Determine acceptable hot part dimensions before cooling for TIG

Aids in better quality control

Quality Control Parameters

Hub Front Axle

Parallel between planes

1

I.D to O.D run out

Perpendicularity between planes

4

5

6

7

10

11

12

13

14

9

2

3

14 dimensions checked for quality control

Part Modeling

Section I (upper limit) Section II (lower limit)

Dimension Initial Lower Upper Outer section Inner section4 77.48 75.85 78.35 76.27 77.005 31.12 29.92 31.90 30.66 30.636 14.92 14.14 15.65 14.70 14.677 15.92 15.14 16.64 15.69 15.7110 28.20 27.00 28.50 27.68 27.7711 56.87 55.50 57.00 55.90 55.9912 70.97 69.39 70.15 69.85 69.9613 75.54 73.50 75.00 74.31 74.3114 32.20 30.50 32.00 31.61 31.66

Section II

Section I

Dimensions of both sections do not change significantly after cooling; section I is considered for further analysis

All dimensions in mm

Material used : AISI 5140

Validate section assumption for further analysis

Location - 2

Location -3

Location - 1

Parameters checked at three critical locations Temperature drop Volume fraction Principal stresses

Cooling Process Validation

Maximum Principal Stress (Mpa)

Point 1

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000 1200 1400

AC-AustiniteAC-Ferrite & PearliteAC-BainiteAC-Quenched MartensiteAC-Pearlite

Vol

ume

Fra

ctio

n

Volume Fraction (Location-1)

Location -1

Martensite formation is insignificant

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200 1400

Cooling P1

Time (sec)

Tem

pera

ture

(º

C)

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000 1200 1400

AC-Austinite

AC-Ferrite & Pearlite

AC-Bainite

AC-Quenched Martensite

AC-Pearlite

Vol

ume

Fra

ctio

n

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200 1400 1600 1800

Cooling P2

Time (sec)

Tem

pera

ture

(°

C)


Location -2

Point 3

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000 1200 1400

AC-Austinite

AC-Ferrite & Pearlite

AC-BainiteAC-Quenched Martensite

AC-Pearlite

Vol

ume

Fra

ctio

n

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200 1400

Cooling P3

Time (sec)

Tem

pera

ture

(°

C)


Location -3

Volume of the part increases at this location

-40

-20

0

20

40

60

80

100

120

140

0 200 400 600 800 1000 1200 1400

AC-1000-P1

AC-1000-P2

AC-1000-P3

Principal Stresses

Time (sec)

Max

Prin

cipa

l Str

ess

(Mpa

)

Martensite formation is less

Principal stresses follow acceptable industrial trend

Development of Dimension Estimator

Conduct Design Of Experiments

Compute percentage change in final cold part dimensions as

responses

Determine correlation effect of process variables to obtain

number of parameters for the surrogate model

Spline fit DOE data to obtain surrogate model

Surrogate model predicts acceptable hot part dimensional limits

Validate predicted dimensions

D10 Plotted Dimension0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 3 5 7 9 11 13

1200º C 1000º C 800º C

Design Of Experiments

Per

cen

tag

e C

han

ge in

Dim

ensi

ons

(D10

)

Correlation effect on Final Dimension

No correlation effect Final dimensions depend on the individual initial part

dimensions and temperature

Initial part dimensions varied individually to determine correlation effects

Final Dimensional Variation

Spline fit variations to predict the limits on hot part dimensions

as a function of initial part temperature

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

D4 D5 D6 D7 D10 D11 D13 D14

Dimensions

Per

cent

age

chan

ge in

dim

ensi

on

Temperature - 1000º C

Responses are different and independent for all part dimensions

Mathematical Model Validation Compare predicted and computed dimensions (upper

and lower limit)

Actual start Upper final Predicted Final Error (mm) Percentage error4 77.5 78.35 79.19 78.363 0.0129 0.01655 31.1 31.9 32.25 31.896 -0.0039 -0.01216 14.9 15.65 15.82 15.645 -0.0048 -0.03077 15.9 16.64 16.83 16.632 -0.0084 -0.0504

10 28.2 28.5 28.82 28.499 -0.0008 -0.002911 56.8 57 57.61 56.992 -0.0078 -0.013613 75.4 75 75.84 75.002 0.0024 0.003214 32.2 32 32.36 32.003 0.0034 0.0105

RequiredDimension

Hot 900 (Upper Limit)

Actual start Lower final Predicted Final Error (mm) Percentage error4 77.5 75.85 76.66 75.850 0.0003 0.00045 31.1 29.92 30.25 29.927 -0.0067 -0.02266 14.9 14.16 14.32 14.171 -0.0111 -0.07827 15.9 15.14 15.31 15.139 0.0014 0.009410 28.2 27 27.3 26.996 0.0035 0.013011 56.8 55.5 56.1 55.497 0.0032 0.005713 75.4 73.5 74.32 73.503 -0.0033 -0.004414 32.2 30.5 30.84 30.498 0.0017 0.0055

Hot 900 (Lower limit) RequiredDimension

All dimensions in mm

Upper dimensional limit

Lower dimensional limit

Error is found to be within permissible limits

Summary

Quantified forging/cooling process uncertainties

Investigated trade-off studies to improve process design

Developed surrogate model to predict hot part dimensional

limit for various input temperature

Incorporated hot part dimension predictor into TIG

Reduced part rejection rate during forging

Any questions ???

Thank you

ferrite_4120

500

550

600

650

700

750

1 10 100 1000

1%

10%

50%

70%

ferrite_4140

500

550

600

650

700

750

1 10 100 1000

1%

10%

30%

ferrite_4150

500

550

600

650

700

750

1 10 100 1000

1%

10%

30%

ferrite_4130

500

550

600

650

700

750

1 10 100 1000

1%

10%

50%

pearlite_4120

500

550

600

650

700

750

1 10 100 1000

1%

10%

30%

pearlite_4140

500

550

600

650

700

750

1 10 100 1000

1%

10%

50%

70%

pearlite_4150

500

550

600

650

700

750

1 10 100 1000

1%

10%

50%

70%

90%

pearlite_4130

500

550

600

650

700

750

1 10 100 1000

1%

10%

50%

30%

bainite_4140

300

350

400

450

500

550

1 10 100 1000

1%

10%

50%

90%

bainite_4150

300

350

400

450

500

550

1 10 100 1000

1%

10%

50%

90%

bainite_4130

300

350

400

450

500

550

1 10 100 1000

1%

10%

50%

90%

bainite_4120

300

350

400

450

500

550

1 10 100 1000

1%

10%

50%

90%

Kinetic Models

• Kinetic Models (DEFORM)

) + T( exp -1 21

where

ξp = Volume fraction

fT (T) = Temperature dependent

transformation

))(exp(1 nTp tTf

= ConstantsT = Temperature in

Kelvint = Time n = Integer from 1- 4

7 1

74

6

5

3

2 1)(

TTTfT

ξ = volume fraction

, 21 = constants

T = Temperature in Kelvin

Diffusion phase transformation Diffusionless phase transformation

Kinetic Model

BPFA 1

0,1 )0(),)(()1()( FFFequilFAFFF

F TTdt

dFF

01 )0(,)1()( PPAPPP

P PPTdt

d

0,1 )0(),)(()1())(( BBBstasisBABeBBB

BTT

dt

dBB

sBPFM

CM

CeMMM

s

M

MTC

MT

dT

d

MM ),1()1())((

,0

1)()( Volume fractions of the phases are denoted by , with subscripts of A,F,P,B, and M referring to austenite, ferrite, pearlite, bainite, and martensite. Time is represented as t, temperature as T, Carbon wt. % by C. The mechanical properties of each phase are input from the DANTE material datafiles, and the mechanical response of the composite structure as it changes during heat treatment is calculated.

Diffusive mobility functions are a function of temperature, while the martensite mobility is a function of carbon.

BPF ,,

mobility equations

FE-C Diagram

Temperature distribution Effective stress

Heat transfer coefficient 0.05 KW/m2 K

Point locations

Output Parameters

0

100

200

300

400

500

600

700

800

900

0 500 1000 1500 2000

Point 1

Point 2

Point 3

Point 4

Time (sec)

Temperature ( o C)

0

50

100

150

200

250

0 500 1000 1500 2000 2500

Point 1Point 2

Point 3Point 4

Time (sec)

Effective Stress ( MPa )

Section A

Section B

Section C

Initial Area of the component = 1066.4 mm2

Stroke variation (0 mm)

Heat Transefer

(KW/ m2 K)0.05 0.1 2

Section A 9.9226 9.9818 14.1075Section B 3.9106 4.0628 1.3858Section C 5.7314 5.7647 5.7273

Shrinkage Area ( mm2 )

0

2

4

6

8

10

12

14

16

0.05 0.1 2

Heat Transfer Coefficent

Sh

rin

kag

e A

rea

Section A

Section B

Section C

(KW/m2 K)

Distortion Variation With Cooling Rate

Representation of distortion as area

No significant change in distortion for air cooling

Section A

Section B

Section C

Thickness -1

Heat Transefer

(KW/ m2 K)0.05 0.1 2


Shrinkage Area (mm2)

0

2

4

6

8

10

12

14

16

0.05 0.1 2


Sh

rin

kag

e A

rea

Section A

Section B

Section C

Initial Area of the component = 974.21 mm2

At stroke Length +1 mm

(KW/m2 K)

Distortion Variation With Cooling Rate

Section A

Section B

Section C

Initial Area of the component = 1106.7mm2

Thickness +1

Heat Transefer

(KW/ m2 K)0.05 0.1 2


Shrinkage Area (mm2)

0

2

4

6

8

10

12

14

16

0.05 0.1 2


Sh

rin

kag

e A

rea

Section A

Section B

Section C

Distortion Variation With Cooling RateAt stroke Length -1 mm

(KW/m2 K)

Phase Transformation model

Axisymmetric disk

AT1= .57002

AT2=166.062

AT3=200

AT4=6

AT5=620.634

AT6=200

AT7=6

n= 1

AT1= 8E-8

AT2=300

AT3=300

AT4=6

AT5=300

AT6=900

AT7=6

n= 2.5

Ferrite Pearlite

Martensite

= 0.016906

= - 5.84948

Constants for the equation

AT1= .305e-4

AT2=150

AT3=200

AT4=6

AT5=550

AT6=200

AT7=6

n= 4

Bainite

Time Vs Temperature

Volume Fraction of Ferrite

Volume Fraction of Pearlite

Volume Fraction Of Bainite

Approach

DEFORM HT ABAQUS/DANTE

Finite Element Package

Easy to model Less convergence

problems NO Phase

Transformation Models Material data needed

Easy to model Some convergence

problems Contains Phase




Surrogate Models




Approach

Enhanced Design

Uncertainties

Initial billet temperature

Ambient temperatures

Material properties

Scaling

Press accuracyOperators

repeatability

Control system time lag

Defects in bulk formed materials

+ Lubrication system

Cooling rates

Forging / Cooling Process Design

Material waste

Final product dimensions

Product quality and reliability

Process design

Design Variables

Material properties

Press specifications


Friction

Die temperature

Ambient temperature

Heat transfer coefficient



Surrogate Models


Enhanced Design

Uncertainties


Ambient temperatures

Material properties

Scaling

Press accuracyOperators

repeatability

Control system time lag

Defects in bulk formed materials

+ Lubrication system

Cooling rates

Forging / Cooling Process Design

Material waste

Final product dimensions

Product quality and reliability

Process design

Design Variables

Material properties

Press specifications


Friction

Die temperature

Ambient temperature

Heat transfer coefficient

Identify critical process parameters

Computationally evaluate variations in the parameters

Develop surrogate models for forging and cooling processes

Conduct Monte Carlo simulations

Predict the probability of part failure

Determine effect on production cost

Generate acceptable hot part dimensions before cooling

Approach

uncertainty quantification and dimension prediction in forging and cooling processes belur k....

Documents

forgingcooling process

cooling inspection slide

grandhi slide

uncertainties analysis

material property data

cooling processes belur

geometry friction factor

doe extract responses