Control of Manufacturing Process

Control of Manufacturing Process Subject 2.830 Spring 2004 Lecture #2 Process Modeling for Control February 5, 2004

Key Topics Process Taxonomy for Control Classifying the Universe of Processes Control versus Variation The Good, Bad and Ugly Process Model for Control Equipment & Material Distinctions Process Parameters: States & Properties 2/5/04 2.830 Lecture #2 2

Recall the Model Equipment E(t ) Material Geometry & Properties What Controls the Geometry Change? 2/5/04 2.830 Lecture #2 3

What Controls the Geometry Change? Location and Intensity of Energy Exchange Examples: Location of Max. Shear Stress in Turning Heat Transfer at the Mold Surface in Injection Molding Displacement Field in Sheet Stamping Reaction Rate - Time Product on Substrate Surface in LPCVD Location of Laser Bean in Laser Trimming 2/5/04 2.830 Lecture #2 4

Two Extremes of Interactions Area of E(t) << Total Area: Serial Process v(t) Area of E(t) ~ Total Area: Parallel Process K(s) y(t) 2/5/04 2.830 Lecture #2 5

For Lumped case: What Determines Part Geometry Change? time - trajectory of the port location e.g. tool paths For Distributed Case: Shape of the energy distribution patterns molds masks 2/5/04 2.830 Lecture #2 6

Examples Serial (Lumped) Processes Machining - Tool Path Laser Cutting - Beam path Bending - Tool Depth Stereolithography - Beam Path Three D Printing - Binder Path 2/5/04 2.830 Lecture #2 7

Examples Parallel (Distributed) Processes Draw Forming - Die Shapes Injection Molding - Mold Shape Chemical Etching - Mask Shape CMP - Tool Shape Plating - Substrate Shape 2/5/04 2.830 Lecture #2 8

Toward a Process Taxonomy Classify by Change Mode Why? Classify by Interaction area (serial/parallel) So what? Sensitivity, resolution Flexibility, controllability, rate Classify by Energy Domain Who cares?? Rate, resolution 2/5/04 2.830 Lecture #2 9

Toward a Process Taxonomy Transformation Methods Serial Interaction Parallel Interaction Dominant Energy Domain Mechanical Thermal Chemical Electrical Dominant Energy Domain Mechanical Thermal Chemical Electrical 2/5/04 2.830 Lecture #2 10

Process Taxonomy Eye Chart for Control Transformation REMOVAL Mode SERIAL PARALLEL Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical Electrical Cutting Laser Cutting EDM Die Stamping ECM EDM Grinding "Flame" Cutting Photolithography Broaching Plasma Cutting Polishing Water Jet Transformation ADDITION/JOINING Mode SERIAL PARALLEL Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical Electrical 3D Printing Laser E-Beam Welding HIP Sintering LPCVD Ultrasonic Sintering Arc Welding Plating Welding Resistance Welding Transformation FORMATION Mode SERIAL PARALLEL Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical Electrical Plasma Spray Stereolithography Inertia Bonding Casting Diffusion DBM Molding Bonding Transformation DEFORMATION Mode SERIAL PARALLEL Energy Source Mechanical Thermal Chemical Electrical Mechanical Thermal Chemical Electrical Bending Line Heating Drawing Forging(open) Forging(die) Rolling 2/5/04 2.830 Lecture #2 14

Transformation REMOVAL Mode SERIAL Process Taxonomy: Removal Energy Source Mechanical Thermal Chemical Electrical Cutting Laser Cutting EDM Grinding "Flame" Cutting Broaching Plasma Cutting Polishing Water Jet PARALLEL Mechanical Thermal Chemical Electrical Die Stamping ECM EDM Photolithography 2/5/04 2.830 Lecture #2 15

Process Taxonomy: Transformation DEFORMATION Mode SERIAL Deformation Energy Source Mechanical Thermal Chemical Electrical Bending Line Heating Forging(open) Rolling PARALLEL Mechanical Thermal Chemical Electrical Drawing Forging(die) 2/5/04 2.830 Lecture #2 16

Transformation ADDITION Mode SERIAL Process Taxonomy: Addition Energy Source Mechanical Thermal Chemical Electrical 3D Printing Laser E-Beam Welding Ultrasonic Sintering Arc Welding Welding Resistance Weldin RAPID PROTOTYPING METHODS PARALLEL Mechanical Thermal Chemical Electrical HIP Sintering LPCVD Plating 2/5/04 2.830 Lecture #2 17

Transformation FORMATION Mode SERIAL Process Taxonomy: Formation Energy Source Mechanical Thermal Chemical Electrical Plasma Spray Stereolithography DBM PARALLEL RAPID PROTOTYPING METHOD Mechanical Thermal Chemical Electrical Inertia Bonding Casting RIM Molding Diffusion Bonding 2/5/04 2.830 Lecture #2 18

Control vs. Variation Control Is Intentional and Deterministic Variation Is Unintentional And/or Random 2/5/04 2.830 Lecture #2 19

Material Variations What Causes Variation in the Process Output? Properties, Initial Geometry Equipment Variations Non-repeatable, long term wear, deflections Operator Variations Inconsistent control, excessive tweaking Environment Variations Temperature and Handling inconsistencies 2/5/04 2.830 Lecture #2 20

Process Model for Control controls Equipment E(t ) Material Geometry & Properties Process Y Process Ouputs Y = Φ(α) α process parameters What are the α s? 2/5/04 2.830 Lecture #2 21

What are the Process Parameters? Equipment Energy States Equipment Constitutive Properties Material Energy States Material Constitutive Properties 2/5/04 2.830 Lecture #2 22

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 2/5/04 2.830 Lecture #2 23

Properties Extensive: GEOMETRY Intensive: : Constitutive Properties Modulus of Elasticity, damping, mass Plastic Flow Properties Viscosity Resistance, Inductance, Capacitance Chemical Reactivity Heat Transfer Coefficient 2/5/04 2.830 Lecture #2 24

Topics for Today Causes of Variation Parameter Uncertainty Definition of Control Input to Process Accessible, Deterministic Parameters The Process Variation Equation Process Control Hierarchy Attacking the Variation Equation Control Loops in Manufacturing 2/5/04 2.830 Lecture #2 25

Delineation of Process Parameters Y =Φ(α) α = (e p,e s,m p,m s ) e p = equipment properties controls Equipment e p, e s E(t ) α Material m p, m s Y Geometry & Properties e s = equpment states m p = material properties m s = material states 2/5/04 2.830 Lecture #2 26

What Causes Variations? If Y = Φ(α) Any Change (or uncertainty) in α α = (e p,e s,m p,m s ) Which parameters are most certain and least variable? (The good ones) Which parameters are least certain or most variable? (The bad ones) 2/5/04 2.830 Lecture #2 27

A Rough Scale of Goodness Constant / known e p Machine Structure, Stiffness Variable / unknown e s m s m p Positions Forces, temperatures Stresses, Surface Temp., Flowrate, Concentration Stress-strain, T g, Viscosity, Reactivity, Resistance Based on What??? 2/5/04 2.830 Lecture #2 28

Now Consider a Typical Process: e.g. Machining e p Structural Geometry Structural stiffens, damping, and natural frequencies, Tool Geometry e s Tool Velocity, Spindle Speed Cutting Force Tool Temperature and Heat Flux m s Shear stress at tool interface Bending Stresses in the workpiece Temperature of chip area m p Initial Geometry Material hardness Basic properties: σ Y, n, r, 2/5/04 2.830 Lecture #2 29

We Lost the Controls! Process Y Process Ouputs Y = Φ(α) controls Equipment E(t ) Material Geometry & Properties Where are the control inputs? A specific subset of the parameters 2/5/04 2.830 Lecture #2 30

Where are the Control Inputs to a Process? controls Equipment E(t ) Material Geometry & Properties Example: the lathe The tool position The leadscrew positions???? 2/5/04 2.830 Lecture #2 31

Control Inputs to a Process controls Equipment E(t ) Material Geometry & Properties What are the best inputs? α s that are: deterministic accessible fast effective significant effect on output 2/5/04 2.830 Lecture #2 32

Tool Position Fast? Accessible? Effective? Deterministic? Back to the Lathe What is accessible? 2/5/04 2.830 Lecture #2 33

Back to the Lathe Tool Position Fast Accessible Effective Deterministic? What is accessible?: Lead Screw Rotation Fast Accessible Effective Deterministic yes no yes yes yes yes yes 2/5/04 2.830 Lecture #2 34

BUT! If the tool position is downstream of the leadscrew rotation it is no longer deterministic! Uncertainties in: leadscrew pitch bearing and nut backlash machine deflections load temperature WHY? Other Examples? 2/5/04 2.830 Lecture #2 35

Definitions An Input is a Process Parameter that is: Fast Accessible Effective Deterministic A Disturbance is a Variation in a Process Parameter Caused By: uncertainty or randomness inaccessibility forced variation 2/5/04 2.830 Lecture #2 36

Some Questions What parameters are the best candidates for Inputs? What parameters have the greatest uncertainty? What process class has highest spatial resolution? What process class has highest temporal resolution? What process class has the lowest spatial and temporal resolution? Which has the highest precision? 2/5/04 2.830 Lecture #2 37

Some Answers? What parameters are the best candidates for Inputs? Machine States controls Equipment Material What parameters have the greatest uncertainty? Material Properties What process class has highest spatial resolution? Serial Processes What process class has highest temporal resolution? Mechanical Processes What process class has the lowest spatial and temporal resolution? Thermal, Chemical and Electrical all are highly diffusive Which has the highest precision? Geometry & Properties 2/5/04 2.830 Lecture #2 38

A Model for Process Variations controls Equipment Material Geometry & Properties Recall: Y = Φ(α) One or more α s qualify as inputs : u Y =Φ(α,u); u = vector of inputs The first order Variation Y Y gives the Variation Equation 2/5/04 2.830 Lecture #2 39

The Variation Equation Y = Y Disturbance Sensitivity α α Disturbances + Y u u Control Sensitivity or Gain Control Inputs 2/5/04 2.830 Lecture #2 40

Primary Process Control Goal: Minimize Y How do we make Y 0? Y = Y α α hold u fixed ( u( = 0) + Y u u operator training (SOP s) good steady-state state machine physics minimize disturbances α -> α α min This is the goal of Statistical Process Control (SPC) 2/5/04 2.830 Lecture #2 41

OR Y = Y α α + Y u u Y 0 hold u fixed ( u( = 0) Y minimize the term: α the disturbance sensitivity This is the goal of Process Optimization Assuming Y α =Φ(α) α = operating point 2/5/04 2.830 Lecture #2 42

OR Y = Y α α + Y u u Y 0 manipulate u by measuring Y Y such that u Y u = Y α α This is the goal of Process Feedback Control Compensating for (not eliminating) disturbances 2/5/04 2.830 Lecture #2 43

Statistical Process Control Y = Y α α + Y u u Detect and Minimize 2/5/04 2.830 Lecture #2 44

Process Optimization Y = Y α α + Y u u Empirically Minimize 2/5/04 2.830 Lecture #2 45

Output Feedback Control Y = Y α α + Y u u Manipulate Y u u = Y α α Actively Such that Compensate for Disturbances 2/5/04 2.830 Lecture #2 46

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) 2/5/04 2.830 Lecture #2 47

Limitations? SPC? DOE/PO? FBC? 2/5/04 2.830 Lecture #2 48