Center for Continuing Engineering Education

Tolerance Stack-up Analysis

About This Course

Through This Course, Participants Will Be Able To:

o Calculate minimum and maximum wall thicknesses, air spaces and

interferences for assemblies.
o Create loop analysis/circuit diagrams for tolerance stack-up analysis for
both plus and minus toleranced dimensions and geometric tolerances.
o Create both simple and complex number charts for stack-up analysis using
a variety of geometric tolerances, basic dimensions, resultant conditions,
virtual conditions and plus and minus toleranced dimensions.
o Do tolerance stack-up analysis for floating fastener situations for clearance
holes, screws and shafts.
o Do tolerance stack-up analysis for fixed fastener situations using, screws,
clearance holes, slots, tabs, overall dimensions and projected tolerance
zones for threaded holes.
o Calculate minimum and maximum gaps for assemblies that use a variety
of datum structures.
o Learn a system of logic and mathematics to analyze tolerances.

Topics
Course participants will be trained to apply tolerance stack-up analysis techniques
to a wide variety of assemblies, from the very simple to the more complex
situations commonly faced in industry today. Both plus and minus and
geometrically toleranced assemblies will be examined and stack-up analysis
taught and practiced on each. Many different datum structures will be discussed
and analyzed. The concepts taught in this course are: loop analysis (also known as
circuit diagrams), number charting, virtual condition, resultant condition, inner
and outer boundaries, minimum airspace, maximum wall thickness, maximum
interference, minimum and maximum overall dimensions, fixed and floating
fastener assembly conditions, projected tolerance zones, the logic of stackup
analysis, and much more.

Who Should Attend

This course is directed to anyone with the professional responsibility of analyzing
or applying tolerances to assemblies, or anyone seeking a more thorough
understanding of tolerance analysis. Attendees should have a basic working
knowledge of ASME Y 14.5M1994 (the current American standard on
dimensioning and tolerancing). However, the basics of all principles used in this
course are either thoroughly covered or (in the case of the refresher section)
explained to a level that will allow all participants to be successful in learning the
techniques of tolerance stack-up analysis.
Course Instructor
James D. Meadows is president of James D. Meadows and Associates, Inc., a
seminar and consulting corporation specializing in geometric dimensioning and
tolerancing (GD&T). He has been a full time consultant, lecturer and author of the
application, usage and measurement of GD&T since 1983. Mr. Meadows is a
member of eight American National Standards Institute (ANSI) and International
Organization for Standardization (ISO) committees. He serves as chairman for
ASME Y14.43, the committee on Dimensioning and Tolerancing of Functional
Gages. He is the author of four books currently available on Geometric
Dimensioning and Tolerancing, Measurement of Geometric Tolerances in
Manufacturing, and Tolerance Stack-Up Analysis.

Program Schedule

Day 1
7:30 am Registration/Cheek-In
See facility lobby
8:00 am Lecture/Discussion
4:30 pm Adjourn
Day 2
8:00 am Lecture/Discussion
4:30 pm Adjourn
Day 3
8:00 am Lecture/Discussion
1:00 pm Adjourn (without lunch)

Frequent breaks with coffee and soft drinks are planned.

Group luncheons are included except for Day 3
Note adjournment at 1:00 pm on Day 3.

Course Outline

Class exercises with answers follow each section to augment and illustrate the
key concepts of each section.

1.The Basics of Tolerance Stack Up Analysis

 Where to begin a stack
 Designating positive and negative routes
 What are you calculating, what dimensions are factors
 How to push the parts to create the worst case
 Which geometric tolerances are factors?
 Finding the mean
  Calculating boundaries for GD&T, MMC, LMC and RFS material
condition modifiers
 Mean boundaries with equal bilateral tolerances
2.Analysis of an eleven part assembly using plus and minus tolerancing
 The calculations
 The loop analysis chart
 The numbers analysis chart
 Finding MIN and MAX gaps
3.Vertical vs. horizontal analyses for features of size
 Where to start and end
 Graphing the loop
 Minimum and maximum gap analysis
4.Assemblies with plus and minus tolerances
 Multiple dimension loops
 Positive and negative values
 Airspace vs. interferences
5.Floating fastener five part assembly analysis
 Resultant and virtual conditions
 Inner, outer, and mean boundaries
 Converting to radii
 Mixing widths and diameters
 Complex loop analyses with geometric dimensioning and
tolerancing
6.Fixed fastener assemblies
 Calculating overall minimum and maximum assembly dimensions
 Mixing holes, slots, tabs and shafts
 Calculating minimum and maximum gaps within the assembly
 Projected tolerance zones for total runout as a factor
 Determining if geometric tolerances are a factor
 Ruling out features and patterns as factors
7.A rail assembly
 Threaded features
 Multiple geometric controls
 Projected tolerance zones
 Gaps with and without perpendicularity as a factor
 Calculating interference
 Theoretically vs. physically worst case possibilities
 When logic becomes an integral step
 Factoring in assembly conditions
 Maximum wall thickness vs. minimum airspace for assemblies
8.Single part analysis
 Two-single segment positional controls
 Switching datum reference frames and accumulating geometric
tolerances
 Datum features a MMC (pattern shift)
 Profile tolerances, flatness
  Envelopes of perfect form at MMC
 Creating envelopes of perfect orientation at MMC
 MIN and MAX axial separation
 Datum planes vs. datum features
 Separate requirements and accumulating tolerance
 Tolerances in degrees; trig functions introduction
 Composite positional tolerancing
9.Five part rotating assembly analysis
 Position, perpendicularity, parallelism, profile, flatness
 Threaded holes with projected tolerance zones
 Mounted screws
 Part to part analysis (from two parts to an infinite number)
 Runout, total runout, concentricity, positional coaxiality
 Simplifying a complex assembly
 Determining assembly housing requirements
 Radial clearance MIN and MAX calculations
 Interference calculations
10.Trigonometry and Proportions in Tolerance Stack-Up Analysis
 Rocking datum features
 Constructing a valid datum
 Consideration of differing orientations from measurement to
assembly
 An in-depth assembly analysis using trigonometric functions
 Computer programs versus personal analysis
 Vertical stacking as it effects horizontal housing requirements
 When stacked parts are not flat or parallel
 Formulae to calculate worst case fit conditions when trig is a factor
 Using proportions and trigonometry to calculate fit conditions
beyond the GD&T formulae
11.The Theory of Statistical Probability
 Review of statistical concepts
 Gaussian frequency curve, standard deviations, plus or
minus 3 sigma, root sum square formula
 Steps to calculate and apply statistical tolerances
 Statistical tolerancing applied
 to plus and minus toleranced assemblies
 to geometric toleranced assemblies
 When best to allow statistical tolerances and when it should not be
 The logic of statistical tolerancing
 Modifying the root sum square formula with a safety/correction
factor
 Reintegrating the statistical tolerance into the assembly
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Tolerance Stack-Up Analysis Show Entire ThreadBeta

Posted by: Gabriel Search The Forum

Posted on: Monday, 9th December 2002, 11:41 AM. By Individual Post
By Thread
Past 1 Day of Posts
Assumptions: Both components have the same symetrical Past 2 Days of Posts
tolerance arround their nominal value, and both nominal values Past Week of Posts
sum 40. The manufacturing process of both components have the By Keyword or
Phrase
same variation and meet the capability requirement of Cpk not
lower than 1.33. The assembly process adds no extra variation on
the toal length (i.e L=L1+L2)

Because Cp=2 and tolerance range=2mm, then S=1/6mm for the assembly. Also, because
Cpk>1.5 the average must be at least 4.5 S = 0.75mm away from the closest limit, so the
maximum shif of the average from the target value (40) is 0.25mm.

To assure that the assembly average will not be more than 0.25mm away from the target, the
average of the components must not be more than 0.125mm away from the target.

S^2 = S1^2 + S2^2= 2 x S1^2 ==> S1 = S/sqrt(2) = 0.11785mm (this is the standard deviation of
the manufacturing process of the components). The average of the manufacturing process of the
components shall be at least 4 x S1 = 0.47140mm away from the specification limit to assure a
Cpk>1.33.

If we take "Distance form the specification limit to the average" = 0.47140mm and "Distance form
the average to the target" = 0.125mm; then "Distance from the specification limit to the target" =
0.125mm + 0.47140mm = 0.59640mm (let's say 0.6mm?)

So a tolerance of +/-0.6 for the components will assure a Cp=2 and Cpk>1.5 for the assembly, if
the components are manufctured with a Cpk>1.33.

Note however that you said Cp=2, and not Cp>2, that means that S1=0.11785mm and not
smaller. If S1 was improved (reduced), you could offset more and more the average of the
components mantaining a Cpk>1.33, In the limit, with a very low variation in the components (S1)
you could keep a Cpk>1.33 withh all the distribution very close to the specification limit (let's say
+0.6mm) and the sum of components will be arround 40 +1.2mm (i.e. out of tolerance)