2.830j / 6.780j / esd.63j control of manufacturing ... · control of manufacturing processescontrol...
TRANSCRIPT
![Page 1: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/1.jpg)
MIT OpenCourseWare ____________http://ocw.mit.edu
2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303)Spring 2008
For information about citing these materials or our Terms of Use, visit: ________________http://ocw.mit.edu/terms.
![Page 2: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/2.jpg)
Control of Manufacturing ProcessesControl of Manufacturing Processes
Subject 2.830/6.780Spring 2008Lecture #3
“Process Variation – Physical Causes and Interpreting Data”
February 12, 2008
Subject 2.830/6.780Spring 2008Lecture #3
“Process Variation – Physical Causes and Interpreting Data”
February 12, 2008
![Page 3: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/3.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 2Manufacturing
Agenda
• Process Definitions– Geometry Change Causality
• Taxonomy for Control– Classification of Change Methods
• “Mechanical” Examples– Turning– Bending– Molding
• Origins of Variation– States and Properties
![Page 4: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/4.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 3Manufacturing
Process Model for Control
Equipment MaterialE(t )“controls” Geometry
&Properties
Y = Φ(α )α ≡ process parameters
What are the α’s?
Process Y ≡ Process Outputs
![Page 5: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/5.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 4Manufacturing
Back to the Process: What Causes the Output Change?
• A Directed Energy Exchange with the Equipment
Equipment MaterialE(t ) Geometry
&Properties
E(t ) →
mechanicalelectricalthermalchemical
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
⎫
⎬ ⎪ ⎪
⎭ ⎪ ⎪
![Page 6: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/6.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 5Manufacturing
Modes of Geometry Change?• Removal of Material• Plastic Deformation of Material• Addition of Material• Formation of Material from a Gas or Liquid
• Any others???
![Page 7: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/7.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 6Manufacturing
–– location of max. shear stress in turninglocation of max. shear stress in turning
What Controls the Geometry Change?
Location and Intensity of Energy ExchangeLocation and Intensity of Energy Exchange•• ExamplesExamples:
![Page 8: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/8.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 7Manufacturing
What Controls the Geometry Change?
Location and Intensity of Energy ExchangeLocation and Intensity of Energy Exchange•• ExamplesExamples:
–– heat transfer at the mold surface in injection moldingheat transfer at the mold surface in injection molding
![Page 9: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/9.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 8Manufacturing
– location of laser beam in laser cutting
Location and Intensity of Energy ExchangeLocation and Intensity of Energy Exchange•• ExamplesExamples:
Control of Geometry Change?
![Page 10: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/10.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 9Manufacturing
–– reaction rate reaction rate -- time product on substrate surface in LPCVDtime product on substrate surface in LPCVD
Location and Intensity of Energy ExchangeLocation and Intensity of Energy Exchange
Control of Geometry Change?
![Page 11: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/11.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 10Manufacturing
Control of Geometry Change?
Location and Intensity of Energy ExchangeLocation and Intensity of Energy Exchange•• displacement field in sheet forming :
![Page 12: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/12.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 11Manufacturing
Two Extremes of Interactions
Area of E(t) << Total Area: Serial Process
Area of E(t) ~ Total Area: Parallel Process
v(t)
y(t)K(s)
![Page 13: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/13.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 12Manufacturing
Two Extremes of Interactions
• Concentrated, “Lumped” Energy Port– Small Area Wrt Total Part Geometry
• Distributed Energy Port– Area ~ Total Part Geometry
![Page 14: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/14.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 13Manufacturing
What Determines Part Geometry Change?
• For Lumped case:– time - trajectory of the port location
• e.g. tool paths
• For Distributed Case: – Shape of the energy distribution
• patterns• molds• masks
![Page 15: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/15.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 14Manufacturing
Examples• Serial (Lumped) Processes
– Machining - Tool Path– Laser Cutting - Beam path– Bending - Tool Depth– Stereolithography - Beam Path– Three D Printing - Binder Path
![Page 16: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/16.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 15Manufacturing
Examples• Parallel (Distributed) Processes
– Draw Forming - Die Shapes– Injection Molding - Mold Shape– Chemical Etching - Mask Shape– CMP - Tool Shape– Plating - Substrate Shape
![Page 17: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/17.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 16Manufacturing
Toward a Process Taxonomy• Classify by Change Mode
– Why?• Classify by Interaction area (serial/parallel)
– So what?• Classify by Energy Domain
– Who cares??
Sensitivity, resolution
Flexibility, controllability, rate
Rate, resolution
![Page 18: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/18.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 17Manufacturing
Process Taxonomy for ControlTransformation REMOVAL
Mode SERIAL PARALLELEnergy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical Electrical
Cutting Laser Cutting WIRE EDM Die Stamping ECM EDMGrinding "Flame" Cutting CMP PhotolithographyBroaching Plasma Cutting Chem MillingPolishingWater Jet
Transformation ADDITION/JOININGMode SERIAL PARALLEL
Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical ElectricalUltrasonic Laser E-Beam Welding HIP Sintering LPCVDWelding Sintering Arc Welding Inertia Bonding Plating3D Printing Resist. Welding Phys. Depos.
Transformation FORMATION Mode SERIAL PARALLEL
Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical ElectricalPlasma Spray Stereolithography Casting DiffusionDBM Molding Bonding
Transformation DEFORMATION Mode SERIAL PARALLEL
Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical ElectricalBending Line Heating DrawingForging(open) Forging(die)Rolling
![Page 19: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/19.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 18Manufacturing
Process Model for Control
Equipment MaterialE(t )“controls” Geometry
&Properties
Y = Φ(α )α ≡ process parameters
What are the α’s?
Process Y ≡ Process Ouputs
![Page 20: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/20.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 19Manufacturing
Process Parameters
• Equipment Energy “States”• Equipment Constitutive “Properties”
• Material Energy “States”• Material Constitutive ”Properties”
Equipment MaterialE(t )
![Page 21: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/21.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 20Manufacturing
Energy States
Energy Domain Energy or Power Variables
Mechanical F, v ; P, Q or F, d ; σ, ε
Electrical V,I
Thermal T, ds/dt (or dq/dt)
Chemical chemical potential, rate
Equipment MaterialE(t )
![Page 22: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/22.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 21Manufacturing
Properties• Extensive: GEOMETRY• Intensive: Constitutive Properties
– Modulus of Elasticity, damping, mass– Plastic Flow Properties– Viscosity– Resistance, Inductance, Capacitance– Chemical Reactivity– Heat Transfer Coefficient
![Page 23: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/23.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 22Manufacturing
A Model for Process Variations
• Recall:
• One or more α’s “qualify” as inputs : u
• The first order Variation ΔY gives the “Variation Equation”
Y = Φ(α )
Y = Φ(α ,u); u = vector of inputs
Equipment MaterialE(t )“controls” Geometry
&Properties
![Page 24: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/24.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 23Manufacturing
Parallels From Lecture 2
Image removed due to copyright restrictions. Please see Fig. 26 in Boning, D. S., et al. “A General Semiconductor Process Modeling Framework.” IEEE Transactions on Semiconductor Manufacturing 5 (November 1992): 266-280.
![Page 25: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/25.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 24Manufacturing
The Variation Equation
Δ Y = ∂Y∂α
Δα +∂Y∂u
Δ u
DisturbanceSensitivity
Disturbances
Control Sensitivity or “Gain”
Control Inputs
ProcessInput “u” Output “u”
Parameters “α”
![Page 26: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/26.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 25Manufacturing
Simple Machining
• Process Type?
• Equipment States and Properties?
• Material States and Properties?
![Page 27: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/27.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 26Manufacturing
Cutting Force ModelOrthogonal Cutting
Uncut ChipThicknesst o
ChipWidthb
RakeAngle α
CuttingSpeed v
Fc=“Strength” x AreaStrength = Ultimate Tensile Strength (UTS)
Area ~ b to
![Page 28: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/28.jpg)
Tool Offset
Tool Position
Sources of Variation?
vTool Reference Frame
Machine Reference Frame
Workpiece Reference Frame
Initial Geometry
Final Geometry
![Page 29: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/29.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 28Manufacturing
Simple Machining (Orthogonal Turning
![Page 30: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/30.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 29Manufacturing
![Page 31: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/31.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 30Manufacturing
CNC Data
0.6235
0.6237
0.6239
0.6241
0.6243
0.6245
0.6247
0.6249
0.6251
0.6253
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
OuterMiddleInner
Operating Points:High Feed=1Low Feed = 2
![Page 32: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/32.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 31Manufacturing
Average Values
y = 1E-04x2 - 9E-05x + 0.624
0.6234
0.6236
0.6238
0.624
0.6242
0.6244
0.6246
0.6248
0.625
0.6252
0.6254
0.5 1 1.5 2 2.5 3 3.5
High Feed
![Page 33: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/33.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 32Manufacturing
y = -2E-05x2 + 0.0001x + 0.624
0.6236
0.6237
0.6238
0.6239
0.624
0.6241
0.6242
0.6243
0.6244
0.6245
0.6246
0.6247
0.5 1 1.5 2 2.5 3 3.5
Average Values
Low Feed
![Page 34: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/34.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 33Manufacturing
Machining: Conclusions
• Geometry Transformation is (In General) well behaved– Not highly sensitive to material property
variations– New Surface Where Tool is Located
• Dominant Sources of Variation:– Tool Positioning errors - Equipment
Properties and States• Feedback control of Positions is a good idea
-> CNC control!
![Page 35: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/35.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 34Manufacturing
Brake Bending
M M
ε
σ
Images removed due to copyright restrictions. Please see:
http://www.falconfab.com/MVC-016F.JPG
http://www.falconfab.com/MVC-007F.JPG
http://edevice.fujitsu.com/fj/DATASHEET/epk/fpt-100p-m20.pdf
![Page 36: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/36.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 35Manufacturing
Bending• Process Type?
• Equipment States and Properties?
• Material States and Properties?
![Page 37: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/37.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 36Manufacturing
Simple Model : Pure Moment Bending
Constant Radius Tool
Springback
![Page 38: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/38.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 37Manufacturing
Simple Bending Mechanics: Parameter Effects
• Tool Shape (Rtool) determines the shape under load
• Elastic Springback determines the final shape
• What determines the springback?
![Page 39: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/39.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 38Manufacturing
h
b
M
r = 1/K
y
ε=K y
M
K = curvature of the toolingK = curvature of the toolingh = thickness of the sheeth = thickness of the sheetεε(y) = through thickness strain(y) = through thickness strain
What is M(K) (or K(M)) ?
Simple Bending Model
![Page 40: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/40.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 39Manufacturing
h
b
M
r = 1/K
y
ε=K y
M
ε(y) = Ky
M = σ(y)ybdy−h/ 2
h / 2
∫dAmoment arm σ(y) = ?
Simple Beam Theory
dσy
dAb
hdy
![Page 41: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/41.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 40Manufacturing
σ
ε
E
εY
σY
M =32
Elastic Perfectly Plastic Model
My 1− 13
Ky
K⎛ ⎝ ⎜
⎞ ⎠ ⎟
2⎛
⎝ ⎜ ⎞
⎠ ⎟
KY = εY / (h / 2)
MY = EI KY
![Page 42: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/42.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 41Manufacturing
The M-K Curve
M
K
EI
KY
MY
3/2 MY
Loading
EIUnloading
KtoolKpart
ΔK
![Page 43: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/43.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 42Manufacturing
Final Shape: Springback
ΔK =Mmax
EI∴ Kpart = Ktool − ΔK
K = shape of tool
E= material propertyI =
112
bh 3 cubic dependence on thickness
Mmax = ?Mmax = Φ (KY, EI)
Strong Dependence on yield properties
![Page 44: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/44.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 43Manufacturing
Effect of Material Variations: Increase in Yield Stress
M
K
EI
KY
MY
Ktool
ΔK
Kpart
MY’
ΔK
![Page 45: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/45.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 44Manufacturing
Bending Experiments
• Bend to 2 different depths• Two different materials
– 0.028” Steel– 0.032” Aluminum
![Page 46: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/46.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 45Manufacturing
Steel vs. Aluminum
M
K
EIsteel
KtoolKpart
EIAl
E t EI
3.00E+07 0.028 54.88
1.00E+07 0.036 38.88
![Page 47: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/47.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 46Manufacturing
Bending by Operating Point
90.00
100.00
110.00
120.00
130.00
140.00
150.00
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70
Operating Points:Steel - Low Depth = 1Steel - High Depth = 2Alum - Low Depth = 3Alum - High Depth = 4
144
109.5
137.3
99.6
~5%
~10%
![Page 48: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/48.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 47Manufacturing
Other Possible Variations
• Yield Stress (+ 10%reported)– Chemistry, working history
• Thickness– Rolling mill quality– Design vs. manufacturing specs
• Tooling Errors
![Page 49: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/49.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 48Manufacturing
Conclusions• Some Variations Easily Explained
– Deterministic parameter changes • Thickness and Material Selection Δmp (Material Parameter)
– Intentional Input changes• Depth changes Δes (Equipment state)
• Other Variations ???– Property Variations within Material Δmp
– Machine Errors Δep and Δes (e.g. deflection and position error)
Δ Y = ∂Y∂α
Δα +∂Y∂u
Δ u
![Page 50: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/50.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 49Manufacturing
Conclusions for Brake Bending
• Equipment Errors have Strong Effect on Final Shape
– Punch Penetration -> Δes (Equipment state)
– Die Width -> Δep (Equipment Parameter)
SO WHAT? Large ∂Y/∂αLarge Δα
![Page 51: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/51.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 50Manufacturing
Injection Molding
Reciprocating Screw
Hydraulic Unit
![Page 52: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/52.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 51Manufacturing
Injection Molding Process
Process Type?
Equipment States and Properties?
Material States and Properties?
Image courtesy Wikimedia Commons, http://commons.wikimedia.org
![Page 53: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/53.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 52Manufacturing
Geometry Determinants• Mold Shape• Material Shape Change upon
Cooling– Residual Stress Effect– Thermal Expansion or contraction
• Extent of Mold Filling
![Page 54: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/54.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 53Manufacturing
Key Material Properties:Flow into Mold
E
TTg Tm
Viscosityν(T)
P = R(ν) Q
![Page 55: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/55.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 54Manufacturing
Effect of Temperature on FlowQ = P/R R = resistance to flow α ν
ν(T) = AeER(To-T)
where: T = temperatureR = gas constantE = activation energy for viscosity
![Page 56: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/56.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 55Manufacturing
Key Material Properties:Cooling
E
TTgTm
![Page 57: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/57.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 56Manufacturing
Packing Phase
Solidification of Part
Hydraulic
Cavity
Hold Pressure
Time
Pre
ssur
e
![Page 58: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/58.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 57Manufacturing
Heat Transfer: Filling
• Tpart > Tmold therefore always cooling• Interior hotter than surface• If Tpart on surface < Tg flow stops
– Short Shot• Viscosity is strong function of Temperature
![Page 59: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/59.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 58Manufacturing
Heat Transfer in the Mold
• q = k A ∂T/∂x– Rate decreases as ∂T/∂x decreases
• Mold heat & polymer cools
• dT/dt = α ∂T2/∂x2
– α = k / ρ Cp• Polymers have low k and high Cp
q
q
![Page 60: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/60.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 59Manufacturing
Process Control Issues
• Control Change in Shape upon Cooling– Consistent Mold Filling– Consistent Mold Pressure
• Consistent Residual Stresses– Consistent Thermal environment
• Consistent Thermal Distortion
![Page 61: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/61.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 60Manufacturing
Typical Equipment Control Systems
• Injection Velocity or Injection Pressure• Nozzle Temperature• Mold Temperature• Barrel Heater Temperature
Equipment States
![Page 62: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/62.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 61Manufacturing
Sources of Variation• Material Properties
– Flow Propertiesν(T) relationship (especially if moist)
– Thermal properties (ditto)– Also effects of “regrind”
![Page 63: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/63.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 62Manufacturing
Example: Effect of Blending
3.1300
3.1250
3.1200
3.1150
3.1100
3.1050
3.100067 87 101 113 134 149 167 185 200 215 239 257 284 302 317
Shot Number
Virgin 50% Regrind Virgin 100% Regrind V i
Average Part Weight
Wei
ght (
g)
Figure by MIT OpenCourseWare.
![Page 64: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/64.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 63Manufacturing
Lab Data
• Variable Hold Time
• Variable Injection Velocity
![Page 65: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/65.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 64Manufacturing
![Page 66: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/66.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 65Manufacturing
![Page 67: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/67.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 66Manufacturing
Injection Molding Data
2.025
2.030
2.035
2.040
2.045
2.050
2.055
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69
Operating Points:Low Hold - Low Velocity=1Low Hold - High Velocity=2High Hold - Low Velocity=3High Hold - High Velocity=4
![Page 68: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/68.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 67Manufacturing
Injection Molding NTU
40
40.1
40.2
40.3
40.4
40.5
40.6
40.7
40.8
1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121 127 133 139
Shift Changes
![Page 69: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/69.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 68Manufacturing
I.M. NTU (no Group 1)
40.45
40.5
40.55
40.6
40.65
40.7
40.75
40.8
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94
Operating Points:Low Hold (5 s) - Low Velocity (50 %) = 1Low Hold (5 s) - High Velocity (75 %) = 2High Hold (10 s) - Low Velocity (50 %) = 3High Hold (10 s) - High Velocity (75 %) = 4
![Page 70: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/70.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 69Manufacturing
Sources of Variation• Equipment Properties
– Heat Transfer Properties– Mold Flow Passages
• Equipment States– Barrel and Nozzle Temperatures– Mold Temperatures– Flow Rates– Packing Pressure
![Page 71: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/71.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 70Manufacturing
Conclusions
• I.M. is a Complex, Parallel Formation Process• Strong Dependence on Material Properties
– Viscosity sensitivity – Heat Transfer Sensitivity
• Thermal State Must be Well Controlled– Many opportunities on the equipment– Material State very hard to do
• Distributed• Interference with Process
![Page 72: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/72.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 71Manufacturing
ΔY = ∂Y∂α
Δα +∂Y∂u
Δu
DisturbancesEquipment Property ChangesMaterial Property ChangesMaterial State UncertaintyEquipment State Uncertainty
Control Inputs:Equipment States
Conclusions: Variation
![Page 73: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/73.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 72Manufacturing
Process Model for Control
Equipment MaterialE(t )“controls” Geometry
&Properties
Y = Φ(α )α ≡ process parameters
What are the α’s?
Process Y ≡ Process Ouputs
![Page 74: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/74.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 73Manufacturing
What are the Process Parameters?
• Equipment Energy “States”• Equipment Constitutive “Properties”
• Material Energy “States”• Material Constitutive ”Properties”
![Page 75: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/75.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 74Manufacturing
Energy States
Energy Domain Energy or Power Variables
Mechanical F, v ; P, Q or F, d ; σ, ε
Electrical V,I
Thermal T, ds/dt (or dq/dt)
Chemical chemical potential, rate
![Page 76: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/76.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 75Manufacturing
Properties• Extensive: GEOMETRY• Intensive: Constitutive Properties
– Modulus of Elasticity, damping, mass– Plastic Flow Properties– Viscosity– Resistance, Inductance, Capacitance– Chemical Reactivity– Heat Transfer Coefficient
• Which has the highest precision?
![Page 77: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/77.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 76Manufacturing
A Model for Process Variations
• Recall:
• One or more α’s “qualify” as inputs : u
• The first order Variation ΔY gives the “Variation Equation”
Y = Φ(α )
Y = Φ(α ,u); u = vector of inputs
Equipment Material
“controls”
Geometry &Properties
![Page 78: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/78.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 77Manufacturing
The Variation Equation
ΔY = ∂Y∂α
Δα +∂Y∂u
Δu
DisturbanceSensitivity
Disturbances
Control Sensitivity or “Gain”
Control Inputs
![Page 79: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/79.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 78Manufacturing
Primary Process Control Goal: Minimize ΔY
ΔY → 0How do we make ?
• hold u fixed (Δu = 0)– operator training (SOP’s)– good steady-state machine physics
• minimize disturbancesΔα ->Δαmin
ΔY = ∂Y∂α
Δα +∂Y∂u
Δu
This is the goal of Statistical Process Control (SPC) This is the goal of Statistical Process Control (SPC)
![Page 80: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/80.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 79Manufacturing
OR
ΔY → 0
• hold u fixed (Δu = 0)
• minimize the term: the disturbance sensitivity
ΔY = ∂Y∂α
Δα +∂Y∂ u
Δu
This is the goal of Process Optimization This is the goal of Process Optimization
∂Y∂α
••AssumingAssuming ∂Y∂α
= Φ(α ) αα = operating point= operating point
![Page 81: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/81.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 80Manufacturing
OR
ΔY → 0
• manipulate Δu by measuring ΔY such that
ΔY = ∂Y∂α
Δα +∂Y∂u
Δu
This is the goal of Process Feedback Control This is the goal of Process Feedback Control
••Compensating for (not eliminating) disturbancesCompensating for (not eliminating) disturbances
Δu∂Y∂u
= −∂Y∂α
Δα
![Page 82: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/82.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 81Manufacturing
Statistical Process Control
ΔY = ∂Y∂α
Δα +∂Y∂u
Δu
Detect and Minimize
![Page 83: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/83.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 82Manufacturing
Process Optimization
ΔY = ∂Y∂α
Δα +∂Y∂u
Δu
Empirically Minimize
![Page 84: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/84.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 83Manufacturing
Output Feedback Control
ΔY = ∂Y∂α
Δα +∂Y∂u
Δu
Manipulate Actively Such that
∂Y∂u
Δu = −∂Y∂α
Δα
Compensate for Disturbances
![Page 85: 2.830J / 6.780J / ESD.63J Control of Manufacturing ... · Control of Manufacturing ProcessesControl of Manufacturing Processes Subject 2.830/6.780 Spring 2008 Lecture #3 “Process](https://reader034.vdocument.in/reader034/viewer/2022042309/5ed6b5decaf45b18673a5abe/html5/thumbnails/85.jpg)
2.830J/6.780J Lecture #3 © David E. Hardt 84Manufacturing
Process Control Hierarchy
• Reduce Disturbances– Good Housekeeping– Standard Operations (SOP’s)– Statistical Analysis and Identification of Sources (SPC)– Feedback Control of Machines
• Reduce Sensitivity (increase “Robustness”)– Measure Sensitivities via Designed Experiments– Adjust “free” parameters to minimize
• Measure output and manipulate inputs– Feedback control of Output(s)