Control of Manufacturing Process · 2019-09-12 · Control of Manufacturing Process Subject 2.830...

Control of Manufacturing Control of Manufacturing

ProcessProcess

Subject 2.830

Spring 2004Spring 2004

Lecture #3 Lecture #3

“Sources of Variation”“Sources of Variation”

February 10, 2004February 10, 2004

2/10/04 2.830 Lecture #3 © David E. Hardt all Rights Reserved 2

Topics for TodayTopics for Today

•• Causes of VariationCauses of Variation

–– Parameter UncertaintyParameter Uncertainty

•• Definition of Control Input to ProcessDefinition of Control Input to Process

–– Accessible, Deterministic ParametersAccessible, Deterministic Parameters

•• The Process Variation EquationThe Process Variation Equation

•• Process Control HierarchyProcess Control Hierarchy

–– Attacking the Variation EquationAttacking the Variation Equation

•• Control Loops in ManufacturingControl Loops in Manufacturing


Delineation of Process Delineation of Process

ParametersParameters

Y ( )

(ep ,es ,mp ,ms )

ep equipment properties

es equpment states

m p material properties

ms material states

Equipment MaterialE(t )“controls” Geometry &

Properties

ep, es mp, ms

Y


What Causes Variations?What Causes Variations?

If Y ( )

Any Change (or uncertainty) in

(ep ,es,m p ,ms)

•Which parameters are most certain and least variable?

(The good ones)

•Which parameters are least certain or most variable?

(The bad ones)


A Rough Scale of “Goodness”A Rough Scale of “Goodness”

ep Machine Structure, Stiffness

e

Constant / known

Variable / unknown

s Positions Forces, temperatures

ms Stresses, Surface Temp., Flowrate,

Concentration

mp Stress-strain, Tg, Viscosity, Reactivity,

Resistance

Based on What???


Now Consider a Typical Process:Now Consider a Typical Process:

e.g. Machininge.g. Machining

ep Structural Geometry

Structural stiffens, damping, and natural frequencies,

Tool Geometry

es Tool Velocity, Spindle Speed

Cutting Force

Tool Temperature and Heat Flux

ms Shear stress at tool interface

Bending Stresses in the workpiece

Temperature of chip area

mp Initial Geometry

Material hardness

Basic properties: Y, n, r, …


We Lost the Controls!We Lost the Controls!

Process Y Process Ouputs

Y ( )

Equipment MaterialE(t )“controls” Geometry &

Properties

•• Where are the control inputs?Where are the control inputs?

–– A specific A specific subsetsubset of the parametersof the parameters


Where are the Control Inputs to a Where are the Control Inputs to a

Process?Process?

E(t )

•• Example: the latheExample: the lathe

–– The tool positionThe tool position

–– The leadscrew positions?The leadscrew positions?

–– ??????

Equipment Material“controls” Geometry &

Properties


Control Inputs to a ProcessControl Inputs to a Process

•• What are the “best” inputs?What are the “best” inputs?

’s that are’s that are::

•• deterministicdeterministic

•• accessibleaccessible

•• “fast”“fast”

•• “effective”“effective”

–– significant effect on outputsignificant effect on output

E(t )Equipment Material

“controls” Geometry &

Properties


Back to the LatheBack to the Lathe

•• Tool PositionTool Position

–– Fast?Fast?

–– Accessible?Accessible?

–– Effective?Effective?

–– Deterministic?Deterministic?

•• What is accessible?What is accessible?


Back to the LatheBack to the Lathe

•• Tool PositionTool Position

–– FastFast yesyes

–– AccessibleAccessible nono

–– EffectiveEffective yesyes

–– DeterministicDeterministic ??

•• What is accessible?:What is accessible?:

–– Lead Screw RotationLead Screw Rotation

–– FastFast yesyes

–– AccessibleAccessible yesyes

–– EffectiveEffective yesyes

–– DeterministicDeterministic yesyes


BUT!BUT!

•• If the If the tool positiontool position is downstream of the is downstream of the leadscrewleadscrew

rotation it is no longer deterministic!rotation it is no longer deterministic!

WHY?

Uncertainties in:leadscrew pitch

bearing and nut backlash

machine deflectionsload

temperature

Other Examples?


DefinitionsDefinitions

•• AnAn InputInput is a Process Parameter that is:is a Process Parameter that is:

–– FastFast

–– AccessibleAccessible

–– EffectiveEffective

–– DeterministicDeterministic

•• AA DisturbanceDisturbance is a Variation in a Process Parameter Caused is a Variation in a Process Parameter Caused

By:By:

–– uncertainty or randomnessuncertainty or randomness

–– inaccessibilityinaccessibility

–– forced variationforced variation


Some QuestionsSome Questions

•• What parameters are the best candidates for Inputs?What parameters are the best candidates for Inputs?

•• What parameters have the greatest uncertainty?What parameters have the greatest uncertainty?

•• What process class has highest spatial resolution?What process class has highest spatial resolution?

•• What process class has What process class has highesthighest temporal resolution?temporal resolution?

•• What process class has the What process class has the lowestlowest spatial and temporal spatial and temporal

resolution?resolution?

•• Which has the highest precision?Which has the highest precision?


Some Answers?Some Answers?

•• What parameters are the best candidates for Inputs?What parameters are the best candidates for Inputs?

–– Machine StatesMachine States

•• What parameters have the greatest uncertainty?What parameters have the greatest uncertainty?

–– Material PropertiesMaterial Properties

•• What process class has highest spatial resolution?What process class has highest spatial resolution?

–– Serial ProcessesSerial Processes

•• What process class has What process class has highesthighest temporal resolution?temporal resolution?

–– Mechanical ProcessesMechanical Processes

•• What process class has the What process class has the lowestlowest spatial and temporal spatial and temporal

resolution?resolution?

–– Thermal, Chemical and Electrical all are highly diffusiveThermal, Chemical and Electrical all are highly diffusive

•• Which has the highest precision?Which has the highest precision?

Equipment Material“controls” Geometry &

Properties


A Model for Process VariationsA Model for Process Variations

Equipment Material

“controls”

Geometry &

Properties

•• Recall:Recall:

•• One or more One or more ’s’s “qualify” as inputs : “qualify” as inputs : uu

•• The first order Variation The first order Variation Y gives the “Variation Equation”Y gives the “Variation Equation”

Y ( )

Y ( ,u); u vector of inputs


The Variation Equation

YY Y

uu

Disturbance

Sensitivity

Disturbances

Control

Sensitivity or

“Gain”

Control Inputs


Primary Process Control Goal: Primary Process Control Goal:

MinimizeMinimize YYY 0How do we make ?

YY Y

uu

•• holdhold uu fixed (fixed ( uu = 0)= 0)

–– operator training (SOP’s)operator training (SOP’s)

–– good steadygood steady--state machine physicsstate machine physics

•• minimize disturbancesminimize disturbances

-->> minmin

This is the goal of Statistical Process Control (SPC) This is the goal of Statistical Process Control (SPC)


OROR

YY Y

uu Y 0

•• hold u fixed (hold u fixed ( uu = 0)= 0)

•• minimize the term:minimize the term: the disturbance sensitivitythe disturbance sensitivity

This is the goal of Process Optimization This is the goal of Process Optimization

Y

••AssumingAssumingY

( ) = operating point= operating point


OROR

YY Y

uu Y 0

•• manipulatemanipulate uu by measuring by measuring Y such thatY such that

uY

u

Y

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


Statistical Process Control

YY Y

uu

Detect

and

Minimize


Process Optimization

YY Y

uu

Empirically

Minimize


Output Feedback Control

YY Y

uu

Manipulate

Actively

Such that

Y

uu

Y

Compensate for Disturbances


Process Control HierarchyProcess Control Hierarchy

•• Reduce DisturbancesReduce Disturbances–– Good HousekeepingGood Housekeeping

–– Standard Operations (SOP’s)Standard Operations (SOP’s)

–– Statistical Analysis and Identification of Sources (SPC)Statistical Analysis and Identification of Sources (SPC)

–– Feedback Control of MachinesFeedback Control of Machines

•• Reduce Sensitivity (Reduce Sensitivity (increase “Robustnessincrease “Robustness”)”)–– Measure Sensitivities via Designed ExperimentsMeasure Sensitivities via Designed Experiments

–– Adjust “free” parameters to minimizeAdjust “free” parameters to minimize

•• Measure output and manipulate inputsMeasure output and manipulate inputs–– Feedback control of Output(s)Feedback control of Output(s)


Limitations?Limitations?

•• SPC?SPC?

•• DOE/PO?DOE/PO?

•• FBC?FBC?


SummarySummary

•• Process CausalityProcess Causality

–– Tracing Inputs to OutputsTracing Inputs to Outputs

•• Control Loops in the Process Control Control Loops in the Process Control

HierarchyHierarchy

–– Machine State Control to minimize Machine State Control to minimize

–– Material State Control to minimize Material State Control to minimize

–– Direct Output Feedback ControlDirect Output Feedback Control


Process Causality PremisesProcess Causality Premises

Equipment MaterialE(t )controls Geometry &

Properties

•Process outputs are material geometryg yg y and propertiesp pp p•Changes in Geometry and Properties are caused by

changes in material state

•Changes in material state are caused by energy input aareep pp pppp pp pppfrom the equipment

•The energy distribution transferred from the equipmentyis

determined by the state and propertiesp p of the equipment

•The means to controluts arets areuts arets areuts arets areuts arets are the output is to manipulate the

distribution of energyp atatppmamamama ririrrtereereererefrom machine to material

eteteproperties of the e


Process Causality PremisesProcess Causality Premises

•• Process outputs are material Process outputs are material geometrygeometry andand propertiesproperties

•• Changes in Geometry and Properties are caused by Changes in Geometry and Properties are caused by

changes in changes in material statematerial state

•• Changes in material state are caused by Changes in material state are caused by energy input energy input

from the equipmentfrom the equipment

•• The energy The energy distributiondistribution transferred from the transferred from the equipmentequipment isis

determined by the determined by the statestate andand propertiesproperties of the equipmentof the equipment

•• The means to The means to controlcontrol the output is to manipulate the the output is to manipulate the

distribution of distribution of energyenergy fromfrom machine to material machine to material


Review of Theme/Lab Review of Theme/Lab

ProcessesProcesses

•• Lab: Produce parts using the followingLab: Produce parts using the following

–– CNC TurningCNC Turning Serial, Removal, MESerial, Removal, ME

–– Brake BendingBrake Bending Serial, Deformation, MESerial, Deformation, ME

–– Sheet ShearingSheet Shearing Parallel Removal, MEParallel Removal, ME

–– Injection MoldingInjection Molding Parallel, Formation, ThermalParallel, Formation, Thermal

–– ThermoThermo--formingforming Parallel, Deformation, ThermalParallel, Deformation, Thermal


CNC TurningCNC Turning

D(x)




Sources of Variation?Sources of Variation?

Initial

Geometry

Workpiece

Reference

Frame

Final Geometry

Machine

Reference

Frame

Tool Offset

Tool Position

vTool Reference

Frame

•• Geometry ErrorsGeometry Errors

–– Calibration, “Slop”Calibration, “Slop”

•• Machine DeflectionMachine Deflection

•• Material DeflectionMaterial Deflection

•• Tool Shape ChangesTool Shape Changes

–– WearWear

–– Built Up EdgeBuilt Up Edge

Key Process Variable is therefore the Cutting Force


Uncut Chip

Thickness

t o

Chip

Width

b

Rake

Angle

Cutting

Speed v

Cutting Force ModelCutting Force Model

Orthogonal CuttingOrthogonal Cutting

Thus:

Fc = UTS d f u

UTS = material

property

f = equipment state

d = equipment state

What happened to v?




Sheet Shearing ModelingSheet Shearing Modeling

•• Parallel Case:Parallel Case:

BACKGAUGE


Serial ShearingSerial Shearing

b

Fc ~ UTS * h * b

UTS ~ 30,000 psi

b=20 in.

h = 0.06

Fc = 36,000 lb.!

Why:




Injection Molding CycleInjection Molding Cycle

Reciprocating Screw

Hydraulic Unit




Heat Transfer in the MoldHeat Transfer in the Mold

•• q = k A T/ xq = k A T/ x

–– Rate decreases as T/ x decreasesRate decreases as T/ x decreases

•• Mold heat & polymer coolsMold heat & polymer cools

•• dT/dtdT/dt == TT22/ x/ x22

–– = k / = k / CCpp

•• Polymers have low k and high Cp

q

q

Polymers have low k and high Cp


Hydraulic Pressure ControlHydraulic Pressure Control



ThermoformingThermoforming

Po

T1>Tg

T2

• Parallel

deformation

process

• Material

formed at

elevated

temperature

T2



Key Material Properties:Key Material Properties:

E

Tm

Working

Region

TTg


Brake Bending of SheetBrake Bending of Sheet

M M



Simple Model : Pure Moment Simple Model : Pure Moment

BendingBending

Springback

Constant Radius Tool


Simple Bending Mechanics: Simple Bending Mechanics:

Parameter EffectsParameter Effects

•• Tool Shape (Tool Shape (RRtooltool) determines the shape ) determines the shape under loadunder load

•• Elastic Springback determines the final Elastic Springback determines the final shapeshape

•• What determines the springback?What determines the springback?


Simple Bending ModelSimple Bending Model

M

r = 1/K

y

=K y

M h

b

K = curvature of the toolingK = curvature of the tooling

h = thickness of the sheeth = thickness of the sheet

(y) = through thickness strain(y) = through thickness strain

What is M(K)

(or K(M)) ?


Simple Beam TheorySimple Beam Theory

h

b

M

r = 1/K

y

=K y

M

(y) Ky

M (y)ybdyh/ 2

h / 2

dAmoment arm

d

y

dAb

h

dy

(y) = ?


Material Model: Material Model:

Elastic Perfectly PlasticElastic Perfectly Plastic

E

Y

Y


The MThe M--K CurveK Curve

M

MY

EI

KKY

3/2 MY

Loading

EIUnloading

Ktool

K

Kpart


Final Shape: SpringbackFinal Shape: Springback

KMmax

EIKpart Ktool K

K = shape of tool

E= material property

I1

12bh

3cubic dependence on thickness

Mmax ?

Mmax = (KY, EI)

Strong Dependence on

yield properties


Effect of Material Variations: Effect of Material Variations:

Increase in Yield StressIncrease in Yield Stress

M

K

EI

KY

MY

Ktool

K

Kpart

MY’

K


See You in LabSee You in Lab

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