Residual Stress Modeling in Machining Presented by by Jiann-Cherng - - PowerPoint PPT Presentation

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Residual Stress Modeling in Machining

Presented by by Jiann-Cherng Su And Dr. Steven Liang George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology

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Outline

Motivation Proposed Modeling Method – Force modeling – Temperature modeling – Residual stress modeling Questions?

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Motivation

Residual stress affects fatigue life Residual stress affects corrosion crack resistance Residual stress affects part distortion Machining induces residual stress

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Physics-Based Modeling Plan

Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces

1 1

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Predicting Cutting Forces

Sources of Cutting Forces

– Chip formation forces – Ploughing forces

Classical Models Based on Orthogonal/Oblique Machining Geometric Considerations for Non-Orthogonal Processes

– Side rake angle – Back rake angle – Tool edge radius – Tool nose radius

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Predicting Cutting Forces

Cutting Forces for Orthgonal Machining

Cutting Conditions

Rake angle, Cutting speed, Depth of cut, Width of Cut, Material Properties

Cutting Conditions

Rake angle, Cutting speed, Depth of cut, Width of Cut, Material Properties

Oxley’s Cutting Force Model

• Iterate to find TAB
• tan θ =1+2(π/4-φ)-Cn, λ=θ-φ+α
• R=Fs/cosθ, F=Rsinλ, N=Rcosλ, Fc=Rcos(λ−α)
• Iterate to find Tchip
• kAB, τint, kint

Oxley’s Cutting Force Model

• Iterate to find TAB
• tan θ =1+2(π/4-φ)-Cn, λ=θ-φ+α
• R=Fs/cosθ, F=Rsinλ, N=Rcosλ, Fc=Rcos(λ−α)
• Iterate to find Tchip
• kAB, τint, kint

Initial Value for Shear Angle (φ) Initial Value for Shear Angle (φ)

τint = kint ? τint = kint ?

φ, kAB, FC, FT φ, kAB, FC, FT

φ = φ + 0.1o φ = φ + 0.1o End End No Yes

Cutting Conditions

Rake angle, Cutting speed, Depth of cut, Width of Cut, Material Properties

Cutting Conditions

Rake angle, Cutting speed, Depth of cut, Width of Cut, Material Properties

Oxley’s Cutting Force Model

• Iterate to find TAB
• tan θ =1+2(π/4-φ)-Cn, λ=θ-φ+α
• R=Fs/cosθ, F=Rsinλ, N=Rcosλ, Fc=Rcos(λ−α)
• Iterate to find Tchip
• kAB, τint, kint

Oxley’s Cutting Force Model

• Iterate to find TAB
• tan θ =1+2(π/4-φ)-Cn, λ=θ-φ+α
• R=Fs/cosθ, F=Rsinλ, N=Rcosλ, Fc=Rcos(λ−α)
• Iterate to find Tchip
• kAB, τint, kint

Initial Value for Shear Angle (φ) Initial Value for Shear Angle (φ)

τint = kint ? τint = kint ?

φ, kAB, FC, FT φ, kAB, FC, FT

φ = φ + 0.1o φ = φ + 0.1o End End No Yes

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Predicting Cutting Forces

Geometric Transformation for Tool Nose Radius (Wang & Mathew)

Equivalent oblique transformation

( )

* * * * * * * * * * * * * *

cos tan sin sin tan cos tan sin cos sin sin cos sin cos i i F i i F F A K A K F A K A K F

c n c n ts c n cs R n c n n c f ts n c f n c n cs

+ − − = − = + = η α η α η α α α α α

Force components for non-zero

side cutting angle

S R S ts S R S ts cs

C F C F P C F C F P F P cos sin sin cos

3 2 1

− = + = =

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Ploughing Force Prediction

Ploughing Effects – Force contribution due to cutting edge roundness – Produces a size effect Slip-line field modeling (Waldorf 1999)

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) CA

w k P CA w k P

thrust cut

⎢ ⎣ ⎡ ⎥ ⎦ ⎤ + − + + + + + − − ⋅ ⋅ = ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ + − + + + + + − ⋅ ⋅ = η γ φ η γ θ η γ φ η η γ φ η γ θ η γ φ η cos 2 sin 2 2 1 sin 2 cos sin 2 sin 2 2 1 cos 2 cos ( )

η δ sin = CA

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Research Plan

Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces

1 1 2 2

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Thermal Modeling

Thermal Effects

– Thermal strain – Material properties – Potential phase change

Sources of Heat

– Shear zone – Tool edge rubbing

Previous Research

– Jaeger’s moving heat source – Komanduri metal cutting modeling

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Thermal Modeling

Equation Description Equation

Temperature Rise Due to Shear

( )

( )

( ) ( ) ( ) ( )

dli li Z t X li VB a V K li Z X li VB a V K e k q Z X

workpiece cut workpiece cut L a V VB li X workpiece shear shear workpiece

workpiece cut

⎪ ⎭ ⎪ ⎬ ⎫ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − + + − + + ⎪ ⎩ ⎪ ⎨ ⎧ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + − + =

∫

− − − − 2 2 2 2 2 ) sin ' ' '

sin ' ' ' 2 ' ' ' cos 2 sin ' ' ' ' ' ' cos 2 2 ' ' ' , ' ' ' φ φ φ φ π θ

θ

Temperature Rise from Rubbing

( ) ( ) ( )

( )

( ) ( )

' ' ' ' ' ' ' ' ' ' ' ' 2 ' ' ' ' ' ' 1 ' ' ' , ' ' '

2 2 2 ' ' ' ' ' ' \ 2

dx Z x X a V K e x q x B k Z X

workpiece cut a V x X VB rubbing workpiece rubbing workpiece

workpiece cut

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + − =

− − −

∫

π θ

Temperature Rise in Workpiece

rubbing shear total

θ θ θ + =

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Thermal Modeling

Cutting Speed = 230 ft/min Shear Angle = 30 deg Shear Heat Intensity = 11830 J/cm2-s

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Research Plan

Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces Process Conditions

• Speed, Feed, Depth of Cut
• Cutting Tool Geometry
• Workpiece Material Properties

Residual Stress Modeling

• Rolling/Sliding Contact
• Stress Fields
• Incremental Plasticity Equations
• Coordinate Transformations
• X-Ray Measurements
• Experiment/Validation

Workpiece Temperature Temperature Modeling

• Moving Heat Source
• Stationary Heat Source
• Experiment/Validation

Cutting Force Modeling

• Chip Formation Force (Oxley)
• Ploughing Force (Waldorf, Smithey)
• Tool Geometry (Huang)

Experiments/Validation Cutting Forces

1 1 2 2 3 3

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Sources of Stress in Workpiece

Primary Deformation Zone

– Inclined shear stress – Inclined normal stress

Tool Edge Stress

– Shear stress (rubbing) – Normal stress (indentation)

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Stress Modeling

Stress Field Due to Normal and Tangential Load

( )( ) ( )

[ ]

( )( ) ( )

[ ]

( ) ( )

[ ]

( )( ) ( )

[ ]

( )( ) ( )

[ ]

( )( ) ( )

[ ]

ds z s x s x s q z ds z s x s x s p z ds z s x s x s q z ds z s x s p z ds z s x s x s q ds z s x s x s p z

a b a b xz a b a b z a b a b x

∫ ∫ ∫ ∫ ∫ ∫

− − − − − −

+ − − − + − − − = + − − − + − − = + − − − + − − − =

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 3 2 2 2 2

2 2 2 2 2 2 π π τ π π σ π π σ

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Stress Modeling

Rolling Contact Model (Merwin & Johnson, 1963)

– Stress history experienced by workpiece – Total strain assumed equal to elastic strain – Elastic-perfectly plastic material behavior – Incremental plasticity

• 0.04
• 0.03
• 0.02
• 0.01

0.01 0.02 0.03 0.04

• 250
• 200
• 150
• 100
• 50

50 100 Distance from Tool Tip (mm) Stress Magnitude (MPa)

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Stress Modeling

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McDowell-Hybrid Algorithm

Solve for and simultaneously for stress increments “Blends” Elements of Other Rolling Contact Algorithms – Sehitoglu & Jiang (elastic stress field for all in-plane components) – Earlier McDowell & Moyer (no strain in cutting direction) – Implements linear kinematic hardening behavior

xx

σ &

yy

σ &

( ) [ ] ( ) ( ) [ ] ( )

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + + + ∆ + + − Ψ = + + + + ∆ + + − =

xx xz zz zz zz yy yy xx xx zz yy xx xx xz zz zz zz yy yy xx xx zz yy xx xx

n n n n n h T E n n n n n h T E

* * * * * * * *

2 1 1 2 1 1 τ σ σ σ α σ σ ν σ τ σ σ σ α σ σ ν σ ε & & & & & & & & & & & & & & &

( ) [ ] ( )

2 1 1

* * *

= + + + + ∆ + + − =

yy xz zz zz zz yy yy xx xx zz xx yy yy

n n n n n h T E τ σ σ σ α σ σ ν σ ε & & & & & & & &

Increments of and are from the elastic solution

zz

σ &

xz

τ &

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Supporting Equations

Equation Description Equation

Plastic strain rate (normality flow rule)

ij kl kl p ij

n n S h & & 1 = ε

Deviatoric stress

kk ij ij ij

S σ δ σ & & & 3 1 − =

Components of unit normal in plastic strain rate direction (on the yield surface)

k S n

ij ij ij

2 α − =

Von Mises yield surface

( )( )

2 1

2 =

− − − = k S S f

ij ij ij ij

α α

Linear kinematic hardening rule

ij kl kl ij

n n S & & = α

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Sample Results

Thiele & Melkote (1999) Turning Parameter Value

Material AISI 52100 HRC 57 Tool TNGA-432 KD050 (Low content CBN) Tool Holder DTGNL-164D Tool Nose Radius 0.813 mm Tool Edge Hone Radius 0.0229mm, 0.1219mm Cutting Speed 121.9 m/min Feed 0.11 mm/rev Depth of Cut 0.254 mm

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Sample Force Prediction Results

Force Prediction and Measurement Comparison Hone = 0.0229mm, Feed = 0.10mm/rev

10 20 30 40 50 60 70 80 90

Axial Force Radial Force Cutting Force

Force (N) Measured Predicted

Force Prediction and Measurement Comparison Hone = 0.1219mm, Feed = 0.10mm/rev

50 100 150 200 250 300 350

Axial Force Radial Force Cutting Force

Force (N) Measured Predicted

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Sample Results

Thiele & Melkote (1999)

Residual Stress (Hone Radius = 0.0229 mm)

• 1400
• 1200
• 1000
• 800
• 600
• 400
• 200

200 0.05 0.1 0.15

Depth (mm) Hoop Residual Stress (MPa) Experimental Hoop Residual Stress Predicted Hoop Residual Stress

Residual Stress (Hone Radius = 0.0229 mm)

• 1500
• 1000
• 500

500 1000 0.05 0.1 0.15

Depth (mm) Axial Residual Stress (MPa) Experimental Axial Residual Stress Predicted Axial Residual Stress

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Sample Results

Thiele & Melkote (1999)

Residual Stress (Hone Radius = 0.1219 mm)

• 2000
• 1800
• 1600
• 1400
• 1200
• 1000
• 800
• 600
• 400
• 200

200 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Depth (mm) Hoop Stress (MPa) Hoop Residual Stress Predicted Hoop Residual Stress

Residual Stress (Hone Radius = 0.1219 mm)

• 2000
• 1500
• 1000
• 500

500 1000 1500 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Depth (mm) Axial Stress (MPa) Axial Residual Stress Predicted Axial Residual Stress

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Summary

Model predicts cutting forces closely Model predicts magnitude of residual stresses well Model predicts depth of penetration of residual stresses well

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Questions?

• 0.45
• 0.4
• 0.35
• 0.3
• 0.25
• 0.2
• 0.15
• 0.1
• 0.05
• 4
• 2

2 4

• 4
• 3.5
• 3
• 2.5
• 2
• 1.5
• 1
• 0.5

Tool Workpiece