Performing Tolerance Stack Ups Using Automated Excel Calculator By Arash Vakily

Performing Tolerance
Stack-ups Using
Automated Excel Form

Arash Vakily October 2009 1

Why do we Have to Perform Tolerance Stack-ups
You will know which dimensions to show on your drawings:
Only dimensions that are used in a tolerance stack-up are necessary to be shown on the drawing; plus a few extra dimensions
for clarification, total part size, etc. Also, if the dimensions necessary for tolerance stack-ups are not on the drawing, it will
create problems for you later.

Your time during an 8D / Root Cause Analysis will not be consumed to prove your design’s fit & function:
During DV and PV, no failures related to interference, clearance, or travel should occur if your stack-ups are correct. If there
are failures, it is easy to prove they are not related to design when the tolerance stack-up is ready.

No need for repetitive tool changes between DV and production (no trial and error):
When the product works first time all the time, no dimension related tool changes are necessary. Tool changes are expensive
and time consuming.

Your product will work without a glitch during the entire life of the program:
No need for very costly tool changes after production started, or calls from customer for expensive warranty claims.

Audits are not an issue:
To keep our company’s TS16949 certification, auditors come to check our design procedure on an annual basis. To be ready
for audits, we have to have our documents in order, including tolerance stack-ups.

It is easy to answer requests from suppliers regarding tolerances and dimensions of their tools:
When the suppliers ask if they can open a tolerance or change a nominal dimension, all you need to do is to put their
requested dimension or tolerance into your already prepared stack-up.


Introduction to Tolerance Stack-up
Concepts and Formulas


Dimension Chains

For any tolerance stack-up, a dimension chain
(sometimes called a loop) has to be established:
• Each dimension in a chain must belong to one part only.
• Dimensions in a chain must be adjacent.
• Dimension chain determines an assembly dimension
that is desired for calculation.
• Dimension chain starts from start point (S) of the
assembly dimension and ends at the finish point (F) of the
assembly dimension, forming a complete loop.

Example on this page shows assembly dimension G.
To calculate dimension G, a dimension chain is
established (L1 to L6).
Dimension G is calculated from the individual
dimensions. S F
S F


Tolerance Stack-up

G = L1+L2+… = Σ Li

Tolerance stack-up is to find the Max. and/or Min. of the assembly
dimension, using individual part dimensions in the dimension
chain.

G Max = L1 Max +L2 Min +… G Min = L1 Min +L2 Max +…
All dimensions in All dimensions in All dimensions in All dimensions in
positive direction negative direction positive direction negative direction

Li = Ni ± Ti G = L1+L2+… = (N1+T1) + (N2+T2) + … = (N1+N2+…) + (T1+T2+…)
Dimension
Tolerance Either add Max / Min dimensions Or add nominals and tolerances separately
Nominal


Different Approaches to Tolerance Stack-up

Li = Ni ± Ti

Dimension Nominal Tolerance

Calculation of Total Tolerance For the Assembly:
Mathematical Calculation
Worst Case Scenario (WCS)

General formula for
Statistical (N σ) statistical stack-ups

Special case for
Statistical (RSS) statistical stack-up
where Cpk=1


Definitions For Statistical Distribution
Probability

Min. Max.

Dim. value

Normal Distribution 6 σ Distribution
Cp = 1 Cp = 2

UL − LL C pk = C p (1 − k )
Cp =
6σ

Mean Shift


Statistical Tolerance Stack-up
Statistical Distribution For Each Dimension in the Chain

Statistical Distribution For Assembly

Assembly Processes That Statistical distribution of the assembly dimension calculated by statistical
Affect Fit and Function tolerance stack-up is a function of statistical distribution of each of the
(Using Fixtures, etc.) dimensions in the chain.
We can calculate the reject rate by statistical tolerance stack-up.


Quick Review of Other Approaches to Statistical Tolerance Stack-ups

Bender Factor (RSS x 1.5) Arithmetic (worst case) stack of mean shifts
+ RSS stack of distributions with inflation
factors for each dimension’s distribution

Various Inflation Factors (c1,c2,…)

Since these alternative approaches are based on
assumptions in lieu of data, or need actual data to
be useful, we do not explore them further for our
theoretical tolerance stack-up.
Once we have enough data of actual parts, we
can perform a stack-up using the measured
dimensional data and general statistical tolerance
stack-up formulas for confirmation (if necessary).


Accounting for GD&T in Dimension Chains
Straight Dimensions GD&Ts Referenced to Datum(s)

Envelope

Envelope 0.2 0.2
Always half-half (unless specifically specified otherwise)
Direction does not matter for tolerance stack-ups
0.1 0.2 (Nominal value equivalent is zero for all GD&T)

GD&Ts With No Datum Reference – Present Special Case For Tolerance Stack-ups

Envelope

0.1 total

All of the GD&T tolerance falls on one side
Direction is important for tolerance stack-ups

Performing Tolerance Stack-ups
Using Automated Excel Form


What Does the Tolerance Stack-up Form Do and What it Doesn’t do For You

What Does the Form Do For you: What the Form Doesn’t Do:
1. It automates the mathematical calculation of the stack-up so you only 1. It doesn’t replace your
need to do the engineering work and evaluation. engineering evaluation.
2. It calculates 3 types of tolerance stack-ups: Worst case scenario 2. It doesn’t make a dimension
(mathematical), Statistical (N σ), and RSS (Root sum square) tolerance chain (loop) for you.
stack-ups.
3. It doesn’t replace the need for
3. It makes the above 3 calculations in 3 temperatures: Ambient, -40°C and your understanding of tolerance
+85°C stack-up and the design of the
parts in order to correctly
4. It makes changes very easy, you can change dimensions or tolerances and
establish your tolerance stack-up
immediately see the effect of it on all of your tolerance stack-ups.
chain.
5. It makes responding to supplier’s requests regarding opening the
tolerances very easy, you can immediately check the effect of their
requested change on all of your tolerance stack-ups.
6. It keeps a verifiable, understandable record of your work that becomes
very useful when an audit is done on your project.
7. It helps with 8Ds and root cause analysis of the test failures as you can
easily prove whether dimensions are creating an issue by substituting
measured dimensions with theoretical ones.
8. It can save you time because you can re-use your previous tolerance
stack-ups already made with this form for a new similar project.
9. It helps you determine what dimensions and tolerances you need on your
drawing and their values by its ease of modifiability and instant results.


Choosing the Tolerance Stack-ups that Need to be Performed

Use DFMEA to determine the tolerance stack-ups that are necessary. Prepare a list of tolerance stack-ups needed
for your product.

The proper time to prepare a DFMEA is at the design concept stage, and before completing the modeling.


Preparing the Drawings for Use in Tolerance Stack-up Form

1. Number your dimensions in all drawings 2. Assign a letter (A,B,C…) to each part
Balloon numbers should be in a different layer You will use this letter later to extract the
so they can be turned off when desired. dimensions into the stack-up form. A

Ballooning the dimensions helps you communicate with your supplier better and without error by referring to the
dimension number.
When you receive a dimensional layout report from your supplier that is done to your balloon numbers, you can
easily find your dimensions and compare them with drawing dimensions.

The proper time to calculate tolerance stack-ups is before completing prototype drawings.

Copying Tolerance Stack-up Files into Your Directory

1. Tolerance stack-up files are in the following location: F:SWITCHEngineersTolerance Stack-up Forms
2. Copy all 3 files in the mentioned directory and paste them into your own directory.
3. Please ensure Not to save over these files. They are for public use and therefore can not be locked.

Very Important Note: After you start using your tolerance stack-up files, moving the files can create issues
with file dependencies and give you incorrect results. Try not to move them at all.
The only way to move the files is to have ALL of your stack-up files open and use “Save As” while all of them
are open. CAD users (UG and CATIA) will appreciate that the same issue exists with moving CAD files.

Copy and paste all 3 files into your directory


Opening and Saving the Tolerance Stack-up Forms
1. Open file Master dimension input sheet - Tolerance stack-ups Marked as (1) in the picture below.
Note: This file name can NOT be changed because other files refer to this name to link to this file.
2. Open file Tolerance Stack Study Form Vx-x AV xxxx xx xx Marked as (2) in the picture below.
This file can be saved as any name that you want (e.g. Your stack-up name or number.)
3. The third file is not needed at this point and will not be discussed in this presentation.

Your Directory

1

2 Always choose “Enable Macros”.

Always Choose “Update”.


General Tips for Using Tolerance Stack-up Forms

Bright yellow cells are important cells that have to Light blue (Cyan) cells contain formulas.
be filled by the user for each tolerance stack-up. Values can not be entered in these cells.

White cells are optional to fill by the user.

Hold your mouse over cells with a small red triangle to see the tips and instructions.

Each Tolerance Stack-up has multiple tabs, used for different purposes.

1. Establishing A Dimension Chain (Loop) For the Tolerance Stack-up

This is an example of a dimension chain. In the next pages, you will see how this chain is established.

SF: Assembly dimension of Interest
Other vectors: Comprise the dimension chain

Important Note: If there is a clearance in your assembly at nominal, ensure to place the components of the
assembly in a way to create the worst possible case for your tolerance stack-up. i.e. ‘move’ the parts to the
extreme to create the absolute worst case, such that if you are calculating Min., it becomes the smallest possible
value and visa-versa. You may need separate tolerance stack-ups for Min. and Max. values in this situation.
See example 2 in this presentation.

2. Entering Part Information in Master Dimension Input Sheet

In the Master Dimension Input Sheet, tab “Part descriptions”, enter project data and part data as shown in the
example below.

Master dimension input sheet - Tolerance stack-ups.xls

Fill the information for the
parts needed for your first
stack-up. More information
can be added later.


3. Entering Dimensions From the Drawings

In the Master Dimension Input Sheet, tab “Input”, enter dimensions as shown in the example below.

Part names that you entered
will show on top of each table

Examples below show how to enter
various dimensions and GD&T.

1 You can enter only the
dimensions that are used
in your current tolerance
3 stack-up regardless of
their order or dimension
number. More data can
6 be added later.

9 All the tolerances in
column –tol are considered
negative (multiplied by -1).
12 Therefore, in most cases
GD&T not
there is no need to input a
referenced to a
minus sign.
datum

19
All other GD&T


4. Entering Tolerance Stack-up Information and Part Letters

Enter part letters which are involved in the
Enter information about the tolerance stack-up including tolerance stack-up (for calculation in hot
DFMEA failure mode and effect (To see immediate and cold temperatures).
effect of changing dimensions).


5. Entering All of the Dimension IDs and Their Directions From the Chain

Start from item 1 in your chain and enter
the dimension ID (e.g. B1) and its
direction (Pull down + or – from the list).
Repeat this for all dimensions in the chain.

Dimension ID

Item 1 Negative Y direction


6. Entering Critical Inputs for Engineering Evaluation

5. Choose one of the three methods
that you want to use for this stack-up.
1. Only if you find out that the direction of your assembly
It will show in the summary sheets.
dimension SF (and as a result your dimension chain) is
Other two methods will be grayed out. backwards, change this sign from + to -

2. Enter Minimum and Maximum values
acceptable for the assembly dimension that you 4. For statistical stack-up (N σ),
are calculating. Determination of these values you can choose the value of N
are based on your engineering evaluation. between 3 and 6. See
corresponding reject rates in tab
3. The form will determine pass or fail criteria “In a Glance”.
for three types of tolerance stack-ups
Important Note: Always try to pass WCS criteria. Only if all other efforts fail (changing dimensions and modifying
design), statistical tolerance stack-up should be used to determine the degree of risk / failure rate.

7. Reading the Summary and Detailed Results of the Tolerance Stack-up
Worst Case Scenario Results (Left Page)

Temperatures Nominals at each
temperature Tolerances at each
temperature Summary of results for Worst
Case Scenario (includes ALL
Max. & Min. value of the assembly dimension being calculated at each temperature temperatures)

Statistical Including RSS Results (Right Page)

Nominals at each Tolerances at each temperature
Temperatures temperature Summary of results for
Statistical Stack-ups
(includes ALL
Max. & Min. value of the assembly dimension being calculated at each temperature temperatures)

8. Reviewing & Updating All Your Tolerance Stack-ups in a Glance

All of the Tolerance Stack-up final results are shown in the tab “In a glance”

You can review the impact of changing a dimension or tolerance
immediately by having your stack-up and “Master dimension input
sheet” open. If you change a dimension or tolerance in the Master
dimension input sheet, the result of all stack-ups will automatically
update in real time. Therefore, you can immediately determine which
stack-up result changes to “fail” and find out its related failure mode.


9. Printing A Summary of All of the Tolerance Stack-ups

Go to tab “Results Summary”. You can print all of the important values of the tolerance stack-ups
(up to 20 tolerance stack-ups in one file) including detailed results in one page


10. Adding More Tolerance Stack-ups to a File

First tab for stack-up is called “1”
The first stack-up is done in sheet 1

To add a new tolerance stack-up sheet, right click on tab “Template”
NOTE: Always leave the
Choose “Move or Copy” tab “Template” empty and
Check the box “Create a copy” ready for making a copy
Choose a location for your new tab (you can drag it to any location later
Press “OK”

11. Advanced Features of the Tolerance Stack-up Form in a Glance
Hold your mouse on the red triangles to see full instructions for each column

If the dimension in your drawing has a critical characteristic, you can enter
C in this column. This will ONLY affect statistical stack-up (N σ).

To project a dimension that is on an angle to the axis of tolerance stack-up,
use Sin, Cos, Tan, Cot and related angle in degrees in these columns

To multiply (or divide) a dimension, use this column. Best example of using this column is
when the dimension is a diameter and you need the radius. Use a multiplier of 0.5 and the
dimension and tolerances are multiplied by 0.5 (same as dividing by 2).

To use a formula of your own, or to use the results of another tolerance stack-up, or even to use Min and Max
results from two different stack-ups, enter F in the left column. Enter appropriate command in the right column
(“Notes”).
Note: In order to calculate the stack-up in Max./Min. temperatures, the form needs to know which part is used for
the formula. Enter the part letter plus a zero (H0 in example above) to enable the form to calculate the temperature
stack-ups.

Hold your mouse over this cell to see full instructions and examples for using various types of formulas


12. More Advanced Features of the Tolerance Stack-up Form in a Glance
Hold your mouse on the red triangles to see full instructions for each column

ONLY if you are certain that the distribution type for your
dimension is not a Normal distribution, you can choose Uniform
distribution. Exercise caution when using this feature. Also, it has
to be used as a per-dimension basis only, not for all dimensions.
If necessary, you can define specific values for Process capability (Cp) and Mean shift (k) which calculate a
specific Cpk. Exercise extreme caution when using these columns and ensure Supplier Quality and Supplier are
in agreement with you. ( Cpk = Cp . k )
It should not become necessary to use these columns, as Omron Supplier Quality has specific rules which are
embedded in the critical characteristic explained previously.
Note: If a dimension is marked as a critical characteristic (See last page), the value for Cpk will be determined
automatically. Therefore any values that you enter for Cp and k will not be considered. ( Cpk = Cp . k )


13. Turning Supplier Data On and Off
ON OFF

Unless that you are entering supplier measured data, in order to avoid clutter, click
on the button shown and choose “OFF” to hide all supplier data.


14. Using Multiple Files for Larger Projects

Excel program and your computer have limitation on the amount of data that can be stored in a file. Also, the form is
designed for up to 20 tolerance stack-ups. If you exceed the memory or 20 tolerance stack-ups, use another Tolerance
Stack-up Study Form in the same directory for your tolerance stack-ups. Do not use another Master dimension input sheet.
ALL Tolerance Stack-up Study Forms (you can change their name) in one directory read their values from the same Master
input dimension sheet.

You can also open multiple files including Master
dimension input sheet, change a dimension or
You can open multiple files including Master tolerance value while monitoring all the tolerance
dimension input sheet at the same time and work on stack-up results to see if changing a dimension or
them simultaneously to save time. tolerance has an adverse affect on any of the stack-ups.


Examples of Tolerance Stack-ups
Preformed Using Excel Form


Example 1: Interference Between Housing and Base For Rattle Prevention

In this example, we examine the interference (or clearance,
if exists) between housing and base of a switch. The PCB is
‘sandwiched’ between the housing and the base. The base
Housing has flexible features that interfere with PCB (shown in red
in the picture across).

It is necessary to have an interference at all times to
prevent rattle between housing and base. This is the
DFMEA failure effect.

PCB

Interference

Base
This tolerance stack-up is simple and straight-forward.
Its principle can be used for e-pads between housing and
base as well.


Established Dimension Chain (Loop) For Example 1

A

I B

Y
5 A8
S 6 I4
B1 1 F 4 A7

B3 2 3 A6

X

Example 1 Completed - Overview

Example 1 is explained and completed live during the presentation.


Example 1 Completed - Inputs


Example 1 Completed - Outputs

Summary Results:

Detailed Results:

Results Shown in the tab “In a glance”:


Example 2: Switch Cell Activation
Button is always pushed fully Actual direction of the
up by spring and follower. gap/interference Button
Housing Pins
Rotation

Y

Hole Slot
There is a clearance in X direction between PCB assembly hole and housing pin

In this example, we need to ensure that the micro-switch is activated at a
certain angle (in this case 14°).
For this purpose, we position the button at 14° and position the micro-switch
at its worst case (lowest point) of activation. Then we calculate the
Micro switches shown in 3 positions gap/interference between button actuator and micro-switch lever in Y
direction. This value must be zero or less (interference). If this value is
positive (gap), it means that the button actuator will not reach the micro-
switch lever.
Although the gap/interference is at an angle to Y axis, since we only need a
Micro switches are self-centering in the PCB holes zero clearance or less (we are not interested in the value itself), we can project
the vector on Y axis to make the calculations less complicated.

Example 2 Completed – Overview (Main Page)

Example 2 is explained and completed live during the presentation.


Example 2 Completed – Overview (Supplementary Stack-up 1)

Supplementary Stack-up 1 calculates Min. value of dimension #2 of the main stack-up dimension chain in X direction .


Example 2 Completed – Overview (Supplementary Stack-up 2)

Supplementary Stack-up 2 calculates Max. value of dimension #2 of the main stack-up dimension chain in X direction .


Example 2 Completed – Inputs (Page 1 of 6)

Main Tolerance Stack-up Page:

α

Only 1 digit after decimal point is shown on the form



Main Tolerance Stack-up Page Continued:

Dim #2

Dimension #2 of the main stack-up dimension chain is dependant on button rotation and has to be separately calculated .



Supplementary Stack-up 1:



Supplementary Stack-up 1 Continued:

No input is necessary in these areas because the only use of this supplementary stack-up is the detailed stack-up
results which are used in the main stack-up. No pass or fail decision is made based on this supplementary stack-up.

Values used from this page: Nominal WCS in ambient: Min. WCS in ambient:

2x Min 2x Max

Calculations for the Min. and Max. of dimension #2 of the main tolerance stack-up are slightly different as shown above.



Supplementary Stack-up 2:



Supplementary Stack-up 2 Continued:

No input is necessary in these areas because the only use of this supplementary stack-up is the detailed stack-up
results which are used in the main stack-up. No pass or fail decision is made based on this supplementary stack-up.

Values used from this page: Nominal WCS in ambient: Min. WCS in ambient:

2x Min 2x Max

Calculations for the Min. and Max. of dimension #2 of the main tolerance stack-up are slightly different as shown above.


Example 2 Completed - Outputs

Summary Results:

Detailed Results:

Detailed Values Used From Supplementary (Intermediate) Stack-ups Using Formula Function In the Main Stack-up (Dim 2):

Results Shown in the tab “In a glance”:


Thank You For Your
Participation


Performing Tolerance Stack Ups Using Automated Excel Calculator By Arash Vakily

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