2014 12 19 Stack Up Training

SIGMUND TRAINING

Understanding tolerance stacks the fundamental concept behind Sigmund.

Provide user the fundamental skills necessary to build and utilize Sigmund models for assembly design, optimization, and improvement.

Objective

Day 1Variations Definition and Sources Introduction to Tolerance Analysis Process Defining Assembly / Performance Requirements 1D Loop Diagram Conversion of Dimensions/Tolerances to Equally Bilateral Tolerances Worked Examples Exercises

Addressing Process Capability Tolerance Analysis Methods

Worst Case Model RSS and other Statistical Models

Comparison of Models Advantages & Disadvantages Worked Examples and explanation using Sigmund software Exercises

Syllabus

Day 2Geometric Dimensioning and Tolerancing OverviewDiametral & Radial Tolerance Stack-Ups Material Modifiers and their effect on Stack-Ups Worked Examples Exercises Worked Examples and explanation using Sigmund software

Estimating Assembly Quality Estimating Defect Rates Comparison of Allocated Tolerances by different Methods Multi-dimensional Tolerance Analysis Cost Implications of Tolerance Allocation Achieving Low Cost Worked Examples and explanation using Sigmund software Exercises

Syllabus

Major Industry Challenges - from a Quality magazine

From the respondents, 51% wants to reduce costs, 42% want to achieve tighter part quality standards,69% wants to invest to improve manufacturing efficiency, 59% wants to invest to reduce scrap and rework,83% believe assembly variation issues are responsible for quality issues

Loss of production time Cost of concessions Modifying tooling Increase in manufacturing cycle time Overall unnecessary added cost and time over-runs

Outcome of Quality Issues

DFQ Driven Design Process

Sources of Variation

Tolerances specified on the drawing Variation encountered in the inspection process Variation encountered in the assembly process

Of all the potential sources of variations, only the (1) specified tolerances, (2) datum feature shift and (3) assembly shift should be included in a tolerance stackup

Some Sources of Variation Manufacturing Process Limitations (Process Capability) Tool Wear Operator Error and Operator Bias Variations in Material Environmental Conditions Difference in Processing Equipment and Machines Difference in Processes adopted Maintenance of Machinery, Fixtures, Tools Inspection Process Variation and Shortcuts Assembly Process Variation Inspection Equipment Variations Human error lack of objectivity and judgment Repeatability in Inspection

Introduction to Tolerance Stacks

What is a Tolerance Stack ?

A method of mathematically predicting the resultant effect of piece part and sub-assembly tolerances along with assembly process and fixturing variation on a particular build objective of the assembly.

Why perform tolerance stack analysis?Analyze and optimize dimensional variability within an assembly system prior to building the system

Establish piece part tolerances required to build an acceptable quality product

Reduce the cost of the product by opening up tolerances Identify key tolerance contributors that affect a particular build objective

Reduce product cycle time and improve quality by making systematic improvements during the design phase of the assembly before it is released for tooling. Traditionally, prototypes were built and variation problems were solved by tweaking the tools using the trial and error method

Evaluate the impact of design geometry, tolerances, and locating scheme changes on build objectives

Determine whether an existing design and assembly tooling will meet the build objective requirements

A systematic method of approaching a tolerance stack, and selecting the contributing tolerances.A tolerance loop allows for the evaluation of not only the stack variation, but also the stack nominal value.

Tolerance Loops (Vector Loops)

1. Identify assembly build objecive.

2. Identify the contributing dimensions alongwith their tolerances that would influence the assembly build.

3. Convert the dimensions with their allocated tolerances to symmetric representation.

4. Derive the vector loop.

5. Select the method of tolerance analysis.

6. Perform tolerance stack up calculations.

7. Identify sensitivity.

Steps in stack up analysis

1. Part Drawings should be Correct and Complete in representation of functional dimensions and tolerance zones

2. Drawings could be based on a combination of Plus/ Minus Tolerancing and G D & T

3. Complete Understanding of Part and Assembly functionality

4. Understanding of Process Capability.

Pre-Requisites for Tolerance Analysis

There are 5 methods of analysis

1. Worst Case Analysis2. RSS AnalysisRSS (Root Sum Square)3. MRSS AnalysisMRSS (Modified Root Sum Square)4. PCRSS AnalysisProcess Centering RSS analysis 5. Monte Carlo Simulations

Types of Analysis

1-D tolerance stacks calculate assembly variation by stacking tolerances in a linear direction.

1-D Tolerance (Linear) Stack Analysis

Example

Worst case stacks simply sum all the tolerances in the assembly in a linear direction and predicts the maximum variation expected for a particular build objective.Build Objective Variation Range = Range D1 + Range D2 + Range D3

Sl. No. Nominal +/- Range1 10 0.02 0.042 -4 0.02 0.033 -3 0.01 0.02

3 0.09

3 +/- 0.0453.045 max2.955 min

Worst Case method - calculation

Exercise 1

Exercise 1 - Sigmund

Exercise 2

Centering of Manufacturing Process

Exercise 2 - Sigmund

Exercise 3

Exercise 3 - Sigmund

Exercise 4

Exercise 4 Sigmund - X

Exercise 4 Sigmund - Y

Exercise 5

Exercise 5 Sigmund

Ignores tolerance distribution types Assumes all tolerances at their extreme limits Guarantees 100% assembleability Drives tight piece part tolerances / higher costs Restrict to critical mechanical interfaces It is more conservative

Worst Case method - assumptions

Definition:In this type of analysis, the square root of the sum of squares of individual tolerances is calculated to predict the build objectiveVariation.

RSS Formula:Build Objective Variation

RSS method (Root Sum Squares) - calculation

Sl. No. Nominal +/- Range Range^2

1 10 0.02 0.04 0.00162 -4 0.015 0.03 0.00093 -3 0.01 0.02 0.0004

3 0.00290.054

3 +/- 0.027

3.027 max2.973 min

RSS method (Root Sum Squares) - calculation

Worst Case will drive tighter tolerance, increase cost.RSS will open up tolerance, reduce cost.

RSS Variation Worst Case Variation

3 0.027 3 0.045

Worst Case vs RSS Results - Comparison

Exercise 6

Exercise 6 Loop

Exercise 6 Sigmund

Exercise 7

Exercise 7 Loop

Exercise 7 Sigmund

Exercise 8

Exercise 8 Solution - X

Exercise 8 Solution - Y

COST You make a million parts, and it costs you Rs.1.00 per part.

Now decide to go with cheaper, less accurate parts. Now your cost is Rs.0.99 per part, but 1,000 parts won't fit.

In the first, scenario, your cost is: Rs1.00/part * 1,000,000 parts = Rs.1,000,000

In the second scenario, your cost is: Rs.0.99/part * 1,000,000 parts = Rs.990,000,

but you have to throw away the 1,000 rejects which cost Rs.0.99/part. So your total cost in second scenario is:

Rs.990,000 + 1,000*Rs.0.99= Rs.990,990. Which means you save Rs.9,010.

All processes are under statistical control All tolerances follow normal distribution All tolerances are independent Parts used in assembly have been thoroughly mixed and

selected at random The probability of individual tolerances coming in at their

extreme limits simultaneously is almost zero

RSS method (Root Sum Squares) - assumptions

Definition:It is very similar to standard RSS analysis. The exception is that a constant, typically referred to as k, is added to the RSS equation to give a more accurate picture of what is actually happening in the assembly process.

Application of a linear correction factor to the RSS method may provide more realistic results under non-normal distributions or mean shifts.

Modified RSS Analysis (MRSS)

041.0000725.05.1

01.0015.002.05.1 222

RSSMRSS KTT

23

22

21

2.. DDDOB RangeRangeRangeRange

041.0081.00029.05.1

02.003.004.0

)()(222

....

K

RangeRange RSSOBMRSSOB

3 0.041

Modified RSS Analysis (MRSS) - calculation

Process Capability

A process capability study involves taking periodic samples from the process, under controlled conditions, and determining the sample Mean and Standard Deviation.

Measure the variability of the output of a process Compare the variability with the product specifications or product tolerance

Identification, Understanding and Addressing Assignable Causes is an important Pre-requisite to ensure accuracy and repeatability of estimates.

Where does this 1.5 sigma difference come from?

Manufacturing Industry has determined, through years of process and data collection, that processes vary and drift over time what they call the Long-Term Dynamic Mean Variation.

It is also a way to allow for unexpected errors or movement over time.

This variation typically falls between 1.4 and 1.7.

Real processes dont maintain 3s Mean values drift from nominal Compensate for mean shift in stacks to ensure

correlation with real world

Process Centering (PCRSS)

+ TNominal- T

MS

Worst Case Variation RSS Variation PCRSS Variation MRSS Variation

3 0.045 3 0.027 3 0.031 3 0.041

Results - Comparison

Each tolerance is assigned a random value, based on its distribution.

The tolerances are summed relative to the tolerance loop.

Process is repeated for N number of simulations.

Results are statistically evaluated and displayed graphically.

Monte Carlo Simulation

Thermal VariationsFor dimension D D at room temperature Tr, the dimension at high temperature T will become

[1 + (T-Tr)] (D D)

where is the thermal coefficient. Therefore, [1 + (T-Tr)] will be entered as a trig-factor in the variable node D1.

For example if, for SS 316 L at 100 deg C is 1.65E-005 / deg K and for SS 316 L at 30 deg C is 1.60E-005 / deg K

Trignometric factor for expansion is [1 + 1.65E-5(100-30)] = 1.001155

Trignometric factor for contraction is [1 - 1.65E-5(100-30)] = 0.998845

Exercises with GD&T

Exercise 9

Exercise 9 Solution

Exercise 10

Exercise 10 Solution

Exercise 11

Exercise 11 Solution

Exercise 12

Exercise 12 Solution

FIXED FASTENER

Exercise 13

Exercise 13

Exercise 13

Exercise 13 - objective

Exercise 13 Loop

Exercise 13 Sigmund left bottom gap

Exercise 13 Sigmund right top gap

Exercise 13 Sigmund overall length

Exercise 14

Exercise 14

Exercise 14

Exercise 14 - calculation

Exercise 14 Sigmund

Exercise 15

Exercise 15

Exercise 15 - Loop

Exercise 15 Sigmund

Exercise 16

Exercise 16

Exercise 16

Exercise 16

Exercise 16

Exercise 16

Exercise 16

Exercise 16 Sigmund maximum gap

Contributing tolerances dont act in the direction of the build objective (at an angle) Necessary to trig it outMany real world examples

2D Tolerance Stacks

3 0.01D1

5.83 ??B.O.

4 0.02D2

45o

2D Tolerance Stacks

)245sin(21.. DDOB

828.5)45sin(43.).( nomOB

950.5)47sin(02.401.3.).( max OB

704.5)43sin(98.399.2.).( min OB

122.0124.0828.5

2D Tolerance Stacks

)45sin(21.. DDOB Mean:

707.021.. DDOB 828.5828.23.. OB

Range:

)45sin(21.. DDOB RangeRangeRange

024.0048.0707.004.002.0.. OBRange

2D Tolerance Stacks

Tolerance Analysis, Synthesis & Optimisation using Vector Loop Method of Stack Up

1. Sigmund Stacks - Standalone - without any CAD requirement 2. SigmundWorks - SolidWorks Integrated

3. SigmundPro - ProE / Creo Integrated

4. SigmundEdge - SolidEdge Integrated

Using 3D Virtual Manufacturing Method5. Sigmund ABA - 3D CAD Tolerance Analysis - with animation

6. Sigmund ABA Kinematics - 3D CAD Tolerance Analysis + Tolerance Variation in Kinematic Mechanisms -

with animation

Sigmund Solution Suite

Current Practices Vs Sigmund Best-in-Class Practices

CAD Part Geometry

Tooling Geometry

Assembly Sequence & Index Plan

Process Capability

Product Specification

Measurement Plan

Dataset Tolerances, Datum and GD & T

PPM Estimation

Inspection Dimensions

PPM Estimation

Cost Optimized Tolerances

Key Characteristics

Tolerance Cost Drivers

Performance

Answers to Quality Challenges

Assured Quality on adherence to DM Plan

Eliminates Cost due to Poor Quality

Ensures Quality in First Prototype !

Dimensional Management Plan e-Method

Slide 1ObjectiveSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Tolerance Loops (Vector Loops)Slide 14Slide 15Slide 161-D Tolerance Stack Analysis (Linear Stack Analysis)Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Worst Case vs RSS Results ComparisonSlide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Slide 61Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Slide 69Slide 70Slide 71Slide 72Slide 73Slide 74Slide 75Slide 76Slide 77Slide 78Slide 79Slide 80Slide 81Slide 82Slide 83Slide 84Slide 85Slide 86Slide 87Slide 88Slide 89Slide 90Slide 91Slide 92Slide 93Slide 94Slide 95Slide 96Slide 97Slide 98Slide 99Slide 1002-D Tolerance StacksSlide 102Slide 103Slide 104Slide 105Slide 106Slide 107Slide 108