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Product Excellence Using Six Sigma 1/24/2009
Introduction to Simulation for Variation Reduction 1
PEUSS 2008/2009©Warwick Manufacturing Group
Introduction to Simulation for Variation Reduction
Page 1
Introduction to Simulation for Variation Reduction
Product Excellence Using Six Sigma Module
PEUSS 2008/2009©Warwick Manufacturing Group
Introduction to Simulation for Variation Reduction
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Contents
Introduction
Tolerance Stacking
Tolerance Simulation Overview
Review & Close
Quality Maturation
Measurement Planning
Datums & LocatorsGeometric Dimensioning &Tolerancing
Break
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What is Simulation?
• Simulation is using mathematical tools to imitate real-life conditions and predict the likely results
• Why Simulate?– To confirm theories– To test assumptions– To reduce number of physical tests required– To reduce number of changes to production tools– To reduce development time
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Why Simulate Variation?
• Variation is a normal part of any manufacturing process
• Need to quantify if quality targets can be met• Need to design manufacturing processes as well
as nominal geometry• Need to quantify likely product conditions to
ensure that performance is maintained
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Simulation Types
• Product• Process• Effects
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Tolerance Stacking
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Tolerance Definitions
• Tolerance is the ‘limit of allowable variation’• Tolerance Zones are defined by the annotation
12.512.0
Limit Tolerance
12.25 ±0.25
Plus/MinusEqual Bilateral
12.00+ 0.5
0
Plus/MinusUnilateral
- 0.2+ 0.3
12.20
Plus/MinusUnequal Bilateral
• Tolerancing can be very confusing
• Ideally work to International Standards
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Tolerance Zones
• All tolerancing is based upon theoretical zones of acceptability• Within the zone any component form is acceptable, unless a
modifier has been specified• Tolerance Zones describe a theoretical feature parallel to the
toleranced feature which defines the limit of the tolerance• Tolerance Zones can be lines, planes, cylinders etc.
Virtual Boundary
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Influence of Tolerance
• Tolerance defines the limits of allowable variation
• Design must be capable of accepting the variation
• Product must function at limits of expected variation
• Test to limits, not Nominal design condition
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Tolerance Stacking
• Better described as Dimensional Variation Analysis (DVA)
• Prediction of potential scale of variation• Different Methods– Manual– Computer based– 1D– 3D
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Timing
Concept Design Prototype Production
ConceptApproval
ProjectApproval
Job 1
Product Requirements Defined
Design to Meet Product Requirements
Documentation
Measurement Plan
Achieve Capability
Ongoing ControlContinuous Feedback
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Variation Analysis Methods
• Straight Stack• Root Sum Square• Statistical Tolerancing• Simulation
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Straight Stack
• Worst Case
Variation = A + B + C …
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Root Sum Square
• Gives an approximation of SPC(Assumes Cp = Cpk = 1.0)
Variation = √ (A² + B² + C² …)
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Comparison of Results
Results• Straight Stack• RSS
± 1.00F
±0.75E
± 0.50D
± 1.50C
± 0.25B
±1.00A
ToleranceComponent
± 5.00± 2.26
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Statistical Tolerancing
• Specifies ‘Control Limits’ for the process• Assumes a normal distribution, centred on
nominal• Still analyse by stacking tolerance ranges• Not widely used or understood
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Limitations
• Manual tolerancing works best in 1D• Usually over simplifies analysis– Variation only considered in perpendicular planes– Difficult to calculate 2D & 3D variation– Misses sources of variation– Ignores effect of assembly sequence
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Variation Simulation
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• Wide variety of software tools available• Wide variety of sophistication and cost• There is no ideal simulation software• Use appropriate tool to situation
Variability Simulation Tools
Increasing Sophistication
3 D
1 DSimple
Basic
General
Specialised
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Variability Simulation Tools - Simple
Increasing Sophistication
Linear Tolerance Stack (Worst Case or RSS)
e.g. MS Excel, ‘fag packet’
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Variability Simulation Tools - Basic
Increasing Sophistication
Linear Tolerance Stack (Worst Case or RSS)
e.g. MS Excel Linear Tolerance Stack with statistical modelling (Monte Carlo)
e.g. 1DCS, Crystal Ball
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Variability Simulation Tools – 3D
Increasing Sophistication
Linear Tolerance Stack (Worst Case or RSS)
e.g. MS Excel Linear Tolerance Stack with statistical modelling (Monte Carlo)
e.g. 1DCS, Crystal Ball3D simulation of assembly variation (Monte Carlo)
e.g. VisVSA, 3DCS
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Variability Simulation Tools - Aesthetic
Increasing Sophistication
Linear Tolerance Stack (Worst Case or RSS)
e.g. MS Excel Linear Tolerance Stack with statistical modelling (Monte Carlo)
e.g. 1DCS, Crystal Ball3D simulation of assembly variation (Monte Carlo)
e.g. VisVSA, 3DCSVisualise effects of assembly variation
e.g. Aesthetica
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Variability Simulation Tools – FE Based
Increasing Sophistication
Linear Tolerance Stack (Worst Case or RSS)
e.g. MS Excel Linear Tolerance Stack with statistical modelling (Monte Carlo)
e.g. 1DCS, Crystal Ball3D simulation of assembly variation (Monte Carlo)
e.g. VisVSA, 3DCSVisualise effects of assembly variation
e.g. Aesthetica
FE element modelling of component distortion during assembly
e.g. TAA
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How Simulation Software Works
• Creates ‘bin’ of parts for each tolerance specified– Uses Monte Carlo Random Number generation– Creates a normal distribution for parts– Mean centred upon nominal and ±3ó coincident with
specification limits
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How Simulation Software Works
• Randomly takes one part from each ‘bin’ and performs straight stack analysis
+ ++ +
+ =
Source E
Result
Source A
NominalLSL USL
Source B
NominalLSL USL
Source C
NominalLSL USL
Source D
NominalLSL USL
NominalLSL USL
Source F
NominalLSL USL
• Stores result for each run and repeats
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How Simulation Software Works
• Sums up all runs to give overall result– Mean– Range– Distribution– Cp & Cpk
– Numbers and percentage out of tolerance
• Can also evaluate influence of features– Re-runs analysis with only one variable– Compares predicted variability with global prediction
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Simulation Examples
Assembly Sequence
Define Measurements
Run Simulations
Review Results
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Assembly Sequence
VisVSA
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Define Measurements
VisVSA
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Run Simulations
VisVSA
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Review Results
VisVSA
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Tapers and Misalignments
Aesthetic Results Review
Icona aesthetica
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Aesthetic Results Review
Flushness and See-through
Icona aesthetica
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Simulation Results
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Simulation Requirements
• Quality Targets• CAD Data• Datums & Locators• Part Tolerances• Material Specification• Assembly Sequence• Joining Positions and Sequence• Fixture Designs and Tolerances• Measurement Points
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Simulation Limitations
• Garbage in, Garbage Out!• Usually ignore flexibility, stresses, clamping
forces, thermal effects etc.– Firstly assume all parts are rigid
• Point representations of surfaces• Simulations assume part variation Cp = Cpk = 1.0– Variation is actually a combination of offset mean and
range
• Requires Skilled Analysts and TIME!
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Datums & Locators
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Datums
• All measurements must have a ‘start point’• Choice of datums can be hugely influential• Physical datums are also how parts are held
during assembly• Datums need to be clearly identified• Datums can be ‘global’ or ‘local’
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Global and Local Datums
• Global Datums– Refer all features to a Master Set of References– Determine absolute position or variation– Features considered in isolation
• Local Datums– Refer limited number of features to a singe reference– Determine relative position or variation– Used to control a group of features
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Six Degrees of Freedom
• A Datum scheme must constrain all 6 Degrees of Freedom unless the part is required to move
Movement is made up ofTx – Translation in X Plane
Lateral Translationalong X Axis
Lateral Translationalong Y AxisTy – Translation in Y Plane
Lateral Translation along Z Axis
Tz – Translation in Z Plane
Rotation aboutX Axis (Roll)
Rx – Rotation about X Axis
Rotation about Y Axis (Pitch)
Ry – Rotation about Y Axis
Rotation about Z Axis (Yaw)
Rz – Rotation about Z Axis
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Datum Definition
• Datums are theoretically exact features or surfaces• Create framework of three mutually perpendicular planes• Primary Datum constrains three degrees of freedom• Secondary Datum constrains two degrees of freedom• Tertiary Datum constrains the final degree of freedom• Known as ‘3-2-1’• Generally labelled ‘ABC…’
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3-2-1 Datum Locator Scheme
Primary DatumIdeally 3 Points of ContactStops Z Translation, Roll & Pitch Rotation
Secondary DatumIdeally 2 Points of ContactStops Y Translation &Yaw Rotation
Tertiary DatumIdeally 1 Point of ContactStops X Translation
Z
Y
X
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Hole & Slot Datums
• Alternative to surface datums• Use pins through holes to locate parts• Tertiary datum slots more effective than
diamond pins
Variation
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Datum Definition
A A125 x 25
This Symbol is used to identify the continuous
Datum Plane
This Symbol is used to identify the size and
Position of the Datum Targets that make up the
Datum Plane
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Datum Documentation
• Datums should ideally be identified on the CAD Model
• Datums should be used irrespective of process undertaken
• Datum definition is an instruction to toolmakers, fixture designers, etc.
• Care should be taken not to over-constrain parts
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Datum Selection
• Datums need to be logical• Datums should apply to multiple processes– Component manufacturing– Inspection– Assembly
• Need to be on most stable part of product
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Coincident & Transferred Datums
• Datums should be reused as much as possible between processes
• Not reusing datums introduces another source of variation
• Pick ‘Master’ Datums for an assembly and carry through
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Example of a ‘321’ Datum Scheme
Main Floor Panel
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Datum Transfer
Datums retained from PanelDatums retained from Panel Datums transferred from Datums transferred from
symmetrically opposite symmetrically opposite
PanelPanel
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Basic GD&TInterpretation & Specification
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GD&T Standards
• GD&T Standards used to ensure– Common Language– Common Interpretation– No Ambiguity
• ISO – BS8888 consolidation ‘kit’• ANSI – Y14.5M 1994
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Features of Size
• Full extent of element identified• Tolerance applies to whole of feature• Tolerance Zones projected from feature• Default action unless a modifier is specified
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Feature Control Frame
• Box divided into compartments used to define:– Geometric
Characteristic– Tolerance Value– Modifiers– Datum References
• Order of Datums is important
First Compartment always contains the geometric characteristic symbol
0.2
0.2
0.2 M
Second Compartment always contains the tolerance value & any modifiers
A
A B C
Third, Fourth & Fifth Compartment always contain the datum information
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Tolerance Zones
Variation lost if design cannot accept extremes of tolerance in both directions.
Additional variation allowed, without changing specification, if design allows extremes of variation in both directions. (57% Greater Tolerance Zone)
Positional Tolerance specified as ±1.5mmNominal
1.5
1.5
1.5
1.5
2.12 1.5
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GD&T Characteristic Symbols
CHARACTERISTIC
Angularity
SYMBOLStraightness
Flatness
Circularity (Roundness)
Concentricity
Profile of a Line
Profile of a surface
Perpendicularity
Parallelism
Position
Cylindricity
Circular Runout
Symmetry
DATUM REF. USECATEGORY
Form
Profile
Orientation
Total Runout
Location
Runout
Never
Sometimes
Always
Indi
vidu
al F
eatu
res
Rel
ated
Fea
ture
s
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Denotes for Information Only( )Reference
As above, with no flats or reversals in ZoneCRControlled Radius
Creates a Tolerance Zone defined by 2 arcsRRadius
Modifies shape of Tolerance ZoneDiameter
Only Tangent Plane needs to be in Tolerance Zone
Tangent Plane
Tolerance Zone Projected above part surfaceProjected Tolerance Zone
e.g. Smallest Shaft or Largest HoleLeast Material Condition (LMC)
e.g. Largest Shaft or Smallest HoleMaximum Material Condition (MMC)
UsageSymbolTerm
Modifiers
M
L
P
T
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Measurement Planning
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Measurement of Variation
• Need to quantify variation• Not practical to measure entire feature• Assume measured variation is consistent across
whole feature• Need to specify how variation is to be quantified
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Measurement Points
• Measure Feature at Point of Control• X,Y,Z of point specified• I,J,K of measurement direction specified• Structure of points gives opportunity to reduce
measurements as maturation progresses• Correlation across product• Points defined on CAD Model• Part & Process Capability maintained
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Measurement Direction Requirement
Part Surface
CAD Surface
Target
Point
Probe DirectionSame result on
Nominal Geometry gives different result
on physical part
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Measurement Point Structure
4 4
Level 4 Process Development Part Level
3 3
Level 3 Process Proving Sub-Assemblies
2 2
Level 2 Process Capability Major Assemblies
ProductComponent
Frequency Volume
1 1
Level 1 Process Monitoring Craftsmanship
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Measurement point / Edge point
Edge point
Hole / Slot / Nut hole
Locating pins
Locating datum
Measurement Planning Example
4 4
Process Development
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4 4
3 3
Process Proving
Measurement point / Edge point
Edge point
Hole / Slot / Nut hole
Locating pins
Locating datum
Measurement Planning Example
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Measurement point / Edge point
Edge point
Hole / Slot / Nut hole
Locating pins
Locating datum
4 4
3 3
2 2
Process Capability
Measurement Planning Example
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Measurement point / Edge point
Edge point
Hole / Slot / Nut hole
Locating pins
Locating datum
Measurement Planning Example
4 4
3 3
2 2
1 1
Process Monitoring
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Link to Simulation
• Target Points in Simulation Become Measurement Points
• Utilise Level 1 and Level 2 Points in Simulation• Must use common labelling system– Corporate system to give each point an unique ID
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Documentation & Reporting
• Must use measurement results to drive;– Product Quality improvement– Simulation Improvements
• Management must understand SPC• Use IT networks to eliminate ‘decoration’ of
CMM rooms
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Quality Maturation
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DVA Calibration
• DVA studies are not 100% accurate• Combine Quality Maturation activities with DVA
Study Calibration• Look at General Results and focus on– Areas of excessive variation– Areas of significant discrepancies between simulation
and measurement results
• Use ‘Slow Build’ technique for next build phase
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Slow Build
• Know what goes into the process• Understand what happens within the process– Know condition of tooling– Take intermediate stage measurements
• Re-run DVA simulation with part offset means and variation range
• Useful problem investigation technique• Time consuming & takes preparation
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Review & Close
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References
• Achieving Dimensional Quality by Applying the Technology of Dimensional Management, by Curt Larson, Right Tech Inc. 1994
• Fundamentals of Geometric Dimensioning & Tolerancing, 2nd Edition – Metric, by Alex Krulikowski, Effective Training Inc. 1997