1.
INTERACTIVE STACK UP INSTRUCTIONS
For: PLM default Stack Up Excel master with checklist, “Stack Up Form with Interactive list.xls”, “Stack Up Form
with Interactive list, Trig and IST.xls
WHEN AND WHY TO USE A INTERACTIVE STACKUP EXCEL SPREADSHEET
When you are going to do a lot of stack ups involving a lot of parts and the same dimensions.
When you are going to be working on a new design or major change and want to quickly investigate many
reiterations to establish new relationships.
When you are going to be making similar stack ups for different models involving different dimensions. Copying a
sheet and using it for a different model is easy.
When you want to avoid typos and transposed numbers to the same dimension, tolerance or description used in
many different stacks.
When you want to see the effect of one or more changes ripple through all the stacks and update the formula
driven results, standard, statistical, max and min automatically.
This is a tool to allow your stack to be created faster and accurately. The Stack results MAY be noted on a Stack
Up drawing in the following manners: 1) 2D text box manually typed on face of drawing (the most time
consuming). 2) Excel spreadsheet imported into cad drawing as text box (see below). 3) Results may be left
ONLY in the Excel spreadsheet (the least time consuming) and its location noted on the Stack Up drawing as
follows:
Attached to EWO in PDM. Copy of EXCEL spreadsheet at……………. TBD
4) Sometimes a Stack Up drawing is not required. Graphics may be added to a picture added to the Excel Sheet
to show the relationship
PLM Stack Up master and Checklist
PLM will launch the Excel Master and Checklist when Engineering Specification Stack Up creation method is
used. Select a network U: drive folder as the destination as it is backed up nightly. Your C: drive desktop is
not. See PLM online help for instruction procedure. Excel Stack Ups and any supporting graphic.doc’s shall
be attached to the ES Specification Design Document attached to the EWO. The requesting Engineer
should fill out the Checklist and add any additional stacks that may be required. See also Stack Up
Procedure.ppt located at: TBD
RENAME A COPY TO WORK ON
Pick “File” and “Save As” off the tool bar. Pick a folder in your directory, rename it and pick “Save”.
ENTERING YOUR DATA
The data shown on the variable list serves as an example of how the data should be entered. All the data is
entered in the variable list first before starting your stacks. The Excel form is set to display input and stack results
using four decimal places. Grouping data together by part number in the list makes it easier to find. Never pick
the entire list and use “Sort” to arrange the list in numerical order. The relationships in the stack ups will be
scrambled. Instead, insert row(s) in the list, pick the row(s) of cells out of order and move them in place. All
dimensions and tolerances are entered as positive values on the variable list. Minus signs are only added later in
the stacks where required.
Dimensions with title block tolerance or with stated equal bilateral tolerance on the drawing.
Enter the dimension in the Dim. column. Enter the tolerance in the Tol. column. It is not required to calculate Max
and Min limits for the Max and Min columns.
Created by Charles S. Roscoe Revised: 02/08/2010 1 of 21
Printed: 10/13/2013 22:46 A10/P10
2.
Converting unequal bilateral tolerances to an equal bilateral tolerance:
Enter dimensions with an equal bilateral tolerance, i.e. 63.465 ±0.165 not 63.5 +0.13 / 0.2, as in the case of a
Ring Gear mounting distance. Enter 25.4 MIN as 25.4 ± .0.0. Enter 25.4 MAX as 25.4 ± .0.0.
Limits dimensions:
Enter Max and Min limits in the Max and Min columns just as they appear on the drawing. Use this formula in the
Dim. Column cell =(Link to Max value+link to Min value)/2 to derive the mean . Use this formula in the Tol.
column cell =Link to Dim valueLink to Min value to derive the tolerance.
Use Excel to calculate the Dim and Tol. values instead of a hand calculator.
Max or Min only dimensions
14.7 Min Full Thread, Enter 14.7000±0.0000 not 7.5000±7.5000 because it can be more 14.7 but is not defined.
0.5 Max chamfer. Enter 0.2500±0.2500 or 0.5000±0.0000 because 0.0000 is the minimum.
Thread tables, Spline Summaries and USS Steel gage dimensions are usually limits dimensions and some are
Max or Min only dimensions. Check the standard or spec. and enter accordingly.
Reference dimensions
A reference dimension on a upper level drawing means the tolerance is controlled on a lower level drawing and
the sum shown may involve several dimensions. Do not enter the reference dimension with no tolerance or use
the title lock tolerance. A good example is the CL of Pinion to Cl of Diff dimension on a Axle Assy. The (12.7) and
±0.25 title block tolerance does not locate the Differential. The Ring Gear Mtg. distance and Diff Case flange to
Shaft hole Basic dimension and associated Postional tolerance does.
Bracketed Dimensions
Usually on an upper level drawing and are provided for customer or manufacturing knowledge only and are
controlled on a lower level drawings or indicate an alternate method of manufacture. An example is the second
referenced Axle Assy press up limits dimension samples uses when they can not press both tubes into a carrier
at the same time in the lab like the assembly plant does. Use the lower level dimensions and primary
manufacturing process unless otherwise specified.
BASIC dimensions
Basic dimensions have no tolerance. The tolerance is the GDT value with the feature the Basic dimension
locates. In the Input list identify the location description as Basic. Enter the dimension in the Dim. Column and
enter 0.0000 in the Tol. column. Such as: 95.5000±0.0000
GDT  Form Tolerances  Straightness, Flatness, Circularity, Cylindricity
Usually not used in axial stacks. Rules for Flatness when “Thru” or “To” features are quite detailed as to when
they do apply. Others sometime used in radial Stacks. Consult Stack Up manual Jason Stanley has in library for
examples.
GDT  Profile tolerances  Profile Of A Line, Profile Of A Surface
Enter the Basic dimension as described above. In the next row identify the feature and GDT tolerance such as:
COVER – FIN Inner bowl offset (1/2 1.5 Profile. Tol.). Next to it in the Dim column enter 0.0000. In the Tol.
Column enter 0.7500.
GDT  Orientation tolerances – Angularity, Perpendicularity, Parallelism
Usually not used in axial stacks when mating surfaces are of equal size. Tecease, Inc. sells an excellent self
instruction workbook that discusses the creation of Orientation Stack ups called GEOMETRIC TOLERANCING –
STACKS and ANALYSIS WORKBOOK for $46.00. Jason Stanley has purchased copy for the library. See this
for examples. Charlie Roscoe has a personal copy.
Created by Charles S. Roscoe Revised: 02/08/2010 2 of 21
Printed: 10/13/2013 22:46 A10/P10
3.
http://www.tecease.com/store/merchant.mv?
Screen=PROD&Store_Code=tecease&Product_Code=3500&Category_Code=STACK
GDT  Location tolerances  Position, Concentricity and Symmetry
Identify the feature and GDT tolerance such as: CASE – FIN Drive screw hole ID (1/2 0.18 Pos. Tol.). Next to it in
the Dim column enter 0.0000. In the Tol. Column enter 0.0900. Bonus tolerance may apply when MMC and LMC
modifiers are used. When RFS is used Bonus tolerance does not apply.
Build Dimension
A stated design goal typically achieved by selecting shim(s) to meet the requirement.
The design goal may be:
• A refined feature surface location WRT to another feature. A Mounting Distance.
• A clearance condition.
• A interference condition.
•
Examples include:
Pinion mounting distance. Achieved by measuring CL of Diff Bore to Carrier Brg. Bore and selecting shim to
meet the requirement. Once achieved this Pinion "Build Dimension" or Mounting Distance is used in all the
fore/aft Pinion axial stacks. The shims are not.
•
Ring Gear mounting distance. Achieved by measuring CL of Pinion to LH and RH Diff. Brg. Bore selecting
shim(s) to meet the preload requirement. Once achieved this Ring Gear "Build Dimension" or Mounting
Distance is used in all the cross car axial stacks. The shims are not.
•
HydraLok Diff Gear Axial Movement per ES289. See SU1127 and SU1135.
•
HydraLok Pressure Plate Total Pack Build Dimension. See SU1127 and SU1135.
When Dana does not have design control
Do not use the Dana title block tolerance for purchased part features, ie, Bearings, Seals, Screws etc.. The
supplier or appropriate industry standard controls the tolerance. Our Title Block tolerances do not apply and
should be omitted unless we are modifying the purchased part in some way. Such as a standard Hex Head Cap
screw XXXXXXX except with antirotation flat machined to dimension shown.
Special Characters
Use the Character Map under: Start/Programs/Accessories/System Tools, to copy symbols such as
±, π, α,÷, ≈, ≥ and ∅. The Font of the character must be changed to Symbol after you paste it into your Excel
sheet text string.
STARTING YOUR STACKUP
FINDING PRIOR ART (to use as a reference guide)
See Stack Ups  Cross Reference.xls Larry Sparks created at: TBD
When a new stack up is created please add it to keep this Cross reference up to date. Search it using key words
to find prior art relevant to your Stack Up.
PASTE SPECIAL FUNCTION
First copy a line from the variable list that contains the dimension that begins at the Zero line of the stack up.
Click on the left most cell in the row you wish to copy and drag across that row to the cell containing the tolerance
at the right. Click on the copy icon or type “Ctrl C”. Go to the same left most cell in the first line of the blank stack
format up that it corresponds to and click on it. You will always copy and paste starting in the same column. Go to
Edit, Paste Special and select “Retain links”. Do not hit enter. Click away from the cell or row you just pasted on
in any other cell. The pasted data now is linked to the variable list. Check by selecting a cell that you just pasted
special. It should list the cell you want it to reference along with a = sign in front of it. If it does not have the equal
sign it is not referencing the cell. Any change to that data in the variable list will update the stack ups where it is
used automatically. It is also possible to use a literal text expression that begins with a “ = “ sign that is not a
Created by Charles S. Roscoe Revised: 02/08/2010 3 of 21
Printed: 10/13/2013 22:46 A10/P10
4.
formula, such as “ = PITCH DIA “. Type “ ‘= ” in front of your text expression and the equal sign will appear in
front of your text. The “ ‘ “ symbol will not appear.
CHANGING THE SIGN OF A DIMENSION TO MINUS
Click on the dimension ONLY in the stack up, Not in the variable list. In the edit bar at the top of the window click
between the “=” sign and the dimension. Insert a ““ sign. The sum formula at the bottom of the stack will subtract
the value. Do not give tolerances in the variable list or in the stack ups a minus value.
CHANGING A DATA ENTRY  TEXT, DIMENSION or TOLERANCE
Make a change only on the variable list, NOT in a stack up. Every place else a line is used it is to be a linked
reference back the variable list. Descriptions are also a cell reference when you copy a line and paste special
and select retain links.
USING CHANGE FORMULAS TO MODIFY SEVERAL VALUES AT ONCE
I find it best to make a change to a value a formula in the variable list. If you want to see the affect of changing
one or more dimensions by a new factor without destroying the original value, do this. In the Excel Stack Up
document:, Stack Up Form with Trig and Interactive list.xls the original value in cell E15 is 13.95.
The change factor to apply is 0.7 and is entered in the column called CHANGE in cell J15. 13.95 is turned into a
formula by typing “=13.95+J15” in its place. Now it is a formula, (E15+(J15) or (13.950.7). The value returned
every where that cell is referenced is now 13.25. The same change value, 0.7, can be made a cell reference in
other rows in the variable list. In Row 21, cell J21,”=I3” was entered. The value returned is now a positive 0.7.
The value returned every where that change value is referenced would be changed by 0.7, + or , as desired by
the sign applied in the CHANGE column or in the formula.
TO INSERT A ROW IN THE VARIABLE LIST OR IN A STACK UP BOX
Click on the Row heading number where you want to insert a new row. Select “Insert” and “Row” off the tool bar.
Be sure to copy and paste any formulas required in the new stack up box row that are used to calculate the
results.
TO ADD CELL LOCATION IN REVISION BLOCK THAT WILL UPDATE – Mike Scharf found this.
Here is the example of how to use the Excel “address” function to record the location of a revised cell when
recording changes. The dollar sign “Absolute Cell Reference” $X$XX display in the CELL LOC. column means it
will automatically update even if you add more rows later. Use the formula bar to create the link in the revision
block to the cell as shown below in the example. See Excel Online help for more information about the Excel
“address” function.
Created by Charles S. Roscoe Revised: 02/08/2010 4 of 21
Printed: 10/13/2013 22:46 A10/P10
5.
TO DELETE A ROW IN THE VARIABLE LIST OR IN A STACK UP BOX
Click on the Row heading number of the row you want to delete. Select “Edit” and “Delete” off the tool bar. Use
Edit Find to find every instance of that row by key word or dimension.
TO SEARCH FOR ORIGINS OR USES OF LINKED DATA
USING EDIT FIND
You can find where A dimension or tolerance is used elsewhere by using Edit Find in the tool bar at he top. Type
“XX.XX  (any value)” in the box at top. Select “by rows” in the “Search” box. Select “Values” not “Formulas” from
the “Look in” box. Pick “Find next” and the cursor will jump to the next cell where that “XX.XX” is used. Keep
picking it and it will cycle through the spreadsheet top to bottom and back again to the top where you started. If
different parts have the same value it will find those as well.
Created by Charles S. Roscoe Revised: 02/08/2010 5 of 21
Printed: 10/13/2013 22:46 A10/P10
6.
CHECKING EXCEL STACK UPS
The default page size is Letter, 81/2 x 11, and the Scaling is set to 65%. The Excel is in Page Break preview
mode so you see the dotted and solid blue Page Break lines. To print a larger copy for checking mark up
purposes, change the page size to 11 x 17 and the Scaling to 85%. You must change it back before checking
in the Design Document to PLM. PLM will not recognize the changes. If you do not, PLM will render the .pdf
version at the default setting and it will be all messed up. Changing column widths to accommodate a longer
part number may cause the page width to spill over and create extra sheets containing the last column(s) that
no longer fit. If you make one column wider make the description column narrower by the same amount.
Always do a print preview of the Excel sheet and the rendered .pdf version before competing the EWO to see
that Page Breaks are where you want them and they both display correctly. Delete the Graphic Aids tab on
the completed stack up also, otherwise it will appear on the rendered .pdf version.
USING THE AUDITING TOOL BAR
If it is not on your menu bar go to Tools, Customize and pick Auditing in the Toolbars box. Pick on the blue
bar at the top and drag it up to the menu bar at the top of the screen above the spreadsheet.
Click on any cell in a stack up containing linked data. To trace the links back to where it came from click the
first box called “Trace Precedents”. If the cell contains a formula all the cells that are involved in the result will
highlight in blue with a blue line and dot identifying each cell. Click again and the blue line will trace back to
the next level, and the next until a single beep (if your PC has speakers) signifies that you have reached the
origin of all the data.
Examples of use:
Stack 6MAX row correctly linked back to list…
Created by Charles S. Roscoe Revised: 02/08/2010 6 of 21
Printed: 10/13/2013 22:46 A10/P10
7.
Stack 1 Row not linked to Stack 3. No Audit arrows appeared. Stack 1 “± sign ” linked incorrectly to another
dimension in the list, not Stack 3.
In Stack 1  The range of cells included in the Statistical Tol. formula in cell G74 DOES NOT include the
0.4000 tolerance in cell G70.
Note that the blue Audit boundary box does not include the 0.4000 value. Results will update automatically
when it is corrected………….as shown at right.
USING CONTROL F
Select keys Ctrl and F and the following dialog box will open allowing you to search for specific text or a
value. Use the Replace button if you want to replace text in multiple places with something else. Four
corrections were done below in example this way. Change Look in: to Values using drop down arrow at
right if looking for a number.
Created by Charles S. Roscoe Revised: 02/08/2010 7 of 21
Printed: 10/13/2013 22:46 A10/P10
8.
EXCEL TO CAD  SDRC
It is now possible to import an Excel stack up into a SDRC drawing. Joe Hamilton and Mike Howard developed
this method. It may be possible to use a similar method on a Catia drawing. Procedure to follow at a later date.
1. Open Excel file.
2. Save As Type: Formatted text (space delimited). Creates name.prn file.
3. Open Command Prompt: (citrix, start, programs, command prompt)
At prompt type: ftpfw24sg##(workstation##)
enter user and password
put name.prn
4. In a file manager or unix, rename name.prn to name.txt
5. Import name.txt file into CAD drawing.
Once placed it is possible to use the editor add spaces between lines and change the text size. CAUTION: Any
change to a value here will not change the sums at the bottom of the stack up. The editor does not act the same
as a spreadsheet.
EXCEL TO CAD  Pro/E
Subject: prouser: Summary Excel importing to Pro/E
Author: rpeterson@Minntech.com at Internet
Date: 11/24/99 6:34 PM, Roger Peterson
Two methods worked:
Method (1) (This is what most replies referenced)
This is directly from the PTC knowledge base:
In the existing MS Excel spreadsheet, add the following columns:
1) Add a column to the left of the existing columns, and enter @[ preceded by a single quote.
2) Between each column of text, enter @]@[ preceded by a single quote.
3) Add an extra column to the right of the existing columns, and enter @] preceded by a single quote.
Save the file as a space delimited (*.prn) file, and then modify the file name to have a (*.txt) extension.
This text file can then be used in a drawing note, by selecting #detail; #create; #note; using the #file option.
Method (2) (This worked the best for me)
In the existing MS Excel spreadsheet, add the following columns:
1) Add a column to the left of the existing columns, and enter '@
2) Between each column of text, enter '@@
3) Add an extra column to the right of the existing columns, and enter '@ Save the file as a space delimited
(*.prn) file, and then modify the file name to have a (*.txt) extension. This text file can then be used in a
drawing note, by selecting #detail; #create; #note; using the #file option.
EXCEL TO CAD  Catia
See “CATIA IMPORT TEXT.doc” created by S. Campbell for method. Located at: TBD
EXCEL TO CAD  Unigraphics
See “IMPORTING STACKUP INTO UNIGRAPHICS.doc” created by E. Grosvenor for method. Located at:
TBD
Created by Charles S. Roscoe Revised: 02/08/2010 8 of 21
Printed: 10/13/2013 22:46 A10/P10
9.
Stack Up Drawings
Showing part numbers, revision levels, dimension locations, stack up loop path, ID numbers, special enlarged
drawing views and cross section(s) on a stack up drawing is extremely helpful to document the design status at
that moment in time.
The 2D and 3D will not exist later after extensive revisions have been made and will be hard to trace what
happened. The stack up drawing makes it easy for the Engineers to follow and serves as an instructional aid for
new Designers and Checkers.
However, the Supervisors now feel a CAD drawing is not required, only the Excel spreadsheet with simple point
A to B graphics is sufficient. This may suffice on a simple stack up but not for a full blown Axle Assembly or one
of high complexity. Expediency at the expense of clarity is not my choice.
TO COPY A STACK UP INTO A Email (as a picture that can not be changed)
1. With left mouse button drag across stack(s) from upper left to bottom right in Excel spreadsheet.
2. At the Excel tool bar at top pick “Edit”, “Copy”. A dark shimmering border will appear around it.
3. Click any where in field of Email text to select insertion point.
4. At the Lotus Notes tool bar at top pick “Edit”, “Paste Special” and “Picture” from the dialog box that
appears. After it appears it will be wider than the page and it will not all print.
To change the scale of the picture on the page
5. First pick the picture.
6. A dark border will appear around it. At the Lotus Notes toolbar bar at the top notice that the word “Text”
has changed to “Picture”.
7. At the Lotus Notes tool bar at top pick “Picture”, “Picture Properties”. A dialog box will appear.
8. To modify, adjust BOTH the scaling percentages downward from 100%. Usually 50/50 to 70/70 will be
the scaling range that fits the picture to the page the best.
To see a print preview of the adjustments before sending Email
9. At the Lotus Notes tool bar at top pick “File”, “Print” and the “Preview” button at the bottom of the dialog
box that appears.
10. To adjust scaling, select “Cancel”, and go back to step 5. Or
11. Select “Done” and “OK” from the first dialog box to print.
12. Send Email in usual manner.
Created by Charles S. Roscoe Revised: 02/08/2010 9 of 21
Printed: 10/13/2013 22:46 A10/P10
10.
Using Trigonometry in Excel
In Excel the default result returned is in Radians. (See formula1 in chart) There are two ways to modify the base
formula to have the result display in Degrees. (See formulas 2 and 3 below in the chart)
COLUMN E
ANGLE D
B
33.7800
A
E
=
COLUMN G
ArcTan A / B BASIC FORMULA
A
TRIG ID
13.5000 ROW 95
FORMULA 1
ANGLE D
D
=ATAN(G95/E95)
0.3802001 RESULT IN RADIANS
=
=ATAN(G95/E95)*180/PI()
21.783861 RESULT IN DEGREES
FORMULA 3
ANGLE D
C
=
FORMULA 2
ANGLE D
B
=
=DEGREES(ATAN(G95/E95))
21.783861 RESULT IN DEGREES
The best way to display the result of an Trig. Calculation is to first construct a matrix and input the (max/max,
nom/nom, min/min) limits from the two variables and calculate the needed results to fill in as much of the matrix
as needed. The max and min limits from the matrix are added together and divided by two to get the adjusted
mean and an equal bilateral tolerance for ease in calculation purposes in later stack ups. See the example below
from Stack Up Form with Interactive list, Trig and IST.xls.
ANGLE D
P/N
1234567
1234567
1234567
1234567
DESCRIPTION OF TRIG CALCULATION  EXAMPLE SHOWN
REV DESCRIPTION
A LENGTH 1
A LENGTH 2
A
A
TRIG ID
A
B
LENGTH 1
LENGTH 2
A
E
B
C
D
Created by Charles S. Roscoe Revised: 02/08/2010 10 of 21
DIM.
13.25
33.74
SUM SQS
SQ RT
0.062500
0.001600
0.2532
0.064100
A
13.25
±
0.2183 = STAT TOTAL/(SUM/TOL)
B
33.74
±
0.0349 = STAT TOTAL/(SUM/TOL)
0.2532 = SUM AGREES W/ SQ RT
ANGLE D = ArcTan A / B
A MAX
A NOM
A MIN
STANDARD TOLERANCE
13.5000
13.2500
13.0000
B MAX
33.7800
21.78386
21.0489
B NOM
33.7400
21.4404
B MIN
33.7000
21.8307
21.09445
MAX
NOM
MIN
ANGLE D
+
0.3903 ACTUAL
STANDARD
21.4404 0.3915 BILATERAL TOL.
TOLERANCE
21.4398 ±
0.3453 ADJ MEAN & TOL.
A MAX
A NOM
A MIN
STATISTICAL TOLERANCE
13.4683
13.2500
13.0317
B MAX
33.7749
21.74039
21.0986
B NOM
33.7400
21.4404
B MIN
33.7051
21.7812
21.13851
MAX
NOM
MIN
ANGLE D
+
0.3408 ACTUAL
STATISTICAL
21.4404 0.3417 BILATERAL TOL.
TOLERANCE
21.4399 ±
0.3413 ADJ MEAN & TOL.
±
±
TOL.
0.2500
0.0400
Printed: 10/13/2013 22:46 A10/P10
11.
Individual Statistical Tolerance (IST) Formula
Assume that a standard stack up with at least two dimensions, ALL with the same tolerance, shows interference
in the worst case. Assume now that you want to use two individual statistical tolerance's in a statistical worst case
relationship, How do you calculate it? How do you calculate the statistical tolerance for the individual dimensions
that will have to be controlled using SPC? The dimensions must be flagged with the ASME Y14.5M  1994
symbol on the drawing.
ST
To calculate the individual statistical tolerance's in a stack up, with at least two individual dimensions, with the
same tolerance is easy. Divide the SQ. RT. of the SUM OF THE SQUARES by the number of identical entries
used.
DIMTOL
CALC.
SUM OF THE SQS
15 ± 0.75
0.75 X 0.75
= 0.5625
10 ± 0.75
0.75 X 0.75
= 0.5625
STANDARD

1.125
each dimension to be controlled using SPC.
SQ. RT = 1.060660 /2 = 0.530330 Is the statistical tolerance for
DIMTOL
15 ± 0.53
ST
to be controlled by SPC
10 ± 0.53
ST
to be controlled by SPC
STATISTICAL
To calculate the individual statistical tolerance's in a stack up with at least two individual dimensions with different
tolerance's requires a different formula.
DIMTOL
CALC.
SUM OF THE SQS
15 ± 1.5
1.5 X 1.5
= 2.25
10 ± 0.75
0.75 X 0.75
= 0.5625
STANDARD
2.8125
SQ. RT = 1.677051 This can not be divided by two as it was
above.
DIMTOL
STAT TOTAL/(SUM/TOL)
=
INDIVIDUAL STATISTICAL TOLERANCE
15 ± 1.5
1.677051/((1.5+0.75)/1.5)
=
1.118034
10 ± 0.75
1.677051/((1.5+0.75)/0.75)
=
0.559017
STANDARD
1.677051 NOTE: SUM equals SQ. RT. above.
15 ± 1.12
ST
to be controlled by SPC
10 ± 0.56
ST
to be controlled by SPC
STATISTICAL
Created by Charles S. Roscoe Revised: 02/08/2010 11 of 21
Printed: 10/13/2013 22:46 A10/P10
12.
My Conclusion from the above examples:
Statistical Tolerances and SPC may be used to control greater individual arithmetic tolerances in an
assembly that cause interference to the lesser individual statistical tolerance values to permit assembly. The
lesser individual statistical tolerance must be identified with the
ST
symbol.
The definition and examples in ANSI Y14.5M1994 argue the reverse application. The 2.16.1 definition
assumes that assembly tolerances fit correctly but are found to be to restrictive. Then Statistical Tolerances
and SPC may also be used to permit increased individual feature tolerance. The Greater individual statistical
tolerance must be identified with the
ST
symbol. See excerpt from ANSI Y14.5M1994, 2.16 below.
Created by Charles S. Roscoe Revised: 02/08/2010 12 of 21
Printed: 10/13/2013 22:46 A10/P10
13.
Validity of Statistical and Realistic results
See SAE Article 680490.pdf at: TBD
My question to Don Day, President of Tec Ease.
Applying 1.5 x Statistical to get the Realistic tolerance I sometimes get limits that are greater than the
Standard limits or WOW. I have a rough time believing, let alone trying to explain that MAX MRSS and MIN
MRSS limits can do that. This usually happens when a few dimensions are in the stack and there is a great
difference between the tolerance values. 1.5 appears to be just a ARBITRARY fudge factor really.
I have purchased and read your book GEOMETRIC TOLERANCING STACKS and ANALYSIS
WORKBOOK. On page 86 you say that the MRSS correction factor is between 1.4 and 1.6.
Reply from Don Day of TecEase.
Hi Charles,
Correct!! With only a few vectors most companies should stay away from statistical tolerancing. My
recommendation is that you want to have 5 or more tolerances involved.
Worst on Worst RSS
MRSS
# of vectors (% of WOW)
(% of WOW)
2
70.71%
X 1.5 = 106.065%
3
57.74%
X 1.5 = 86.61%
4
50%
X 1.5 = 75.00%
5
44.72%
X 1.5 = 67.08%
With 4 vectors, for example 1.5 times RSS = 75% of WOW.
For most companies, when several vectors are involved WOW is extremely pessimistic while pure RSS is very
optimistic. The 1.4 to 1.6 values are derived from empirical data and are not exact. In fact, none of statistical and
probability tolerancing is exact.
We should always remember that statistics was first developed for the kings of Europe to gain an edge on the other
kings when they gambled. So, I always like to point out that when using statistical tolerancing it is a gamble. It is
avoided by companies in the nuclear industry because they are not willing to take a gamble.
Thanks for the email. I hope this clears this up a bit.
Best regards,
Don Day
My reply
Hi Don,
It finally happened. I needed to explain RSS/WOW tolerance relationships to someone else. I had to
understand how you came up with the calculations you sent earlier. I agree completely. I discovered a
couple other relationships in the process.
The PROOF results below in stacks 1 thru 4 agree with your calculations when stack up tolerances are all
the same value.
Created by Charles S. Roscoe Revised: 02/08/2010 13 of 21
Printed: 10/13/2013 22:46 A10/P10
14.
1
P/N
111111
222222
TWO IDENTICAL TOLERANCES
REV DESCRIPTION
 TEST 1
 TEST 2
PROOF:
1.06066
÷
1.00000
106.06602
%
STANDARD
STATISTICAL
REALISTIC
2
P/N
111111
222222
333333
STATISTICAL
REALISTIC
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
0.80000
34.00000
9.00000
MEAN
69.80000
2.74803
69.80000
2.74803
69.80000
2.74803
±
±
±
TOL.
0.50000
0.50000
TOL
1.00000
0.03937
0.70711
0.02784
1.06066
0.04176
MAX
27.00000
1.06299
26.70711
1.05146
27.06066
1.06538
MIN
25.00000
0.98425
25.29289
0.99578
24.93934
0.98186
% Tol
50.00000
50.00000
% SUM
100.00000
±
±
±
±
±
±
TOL.
0.50000
0.50000
0.50000
TOL
1.50000
0.05906
0.86603
0.03410
1.29904
0.05114
MAX
28.30000
1.11417
27.66603
1.08921
28.09904
1.10626
MIN
25.30000
0.99606
25.93397
1.02102
25.50096
1.00397
% Tol
33.33333
33.33333
33.33333
% SUM
100.00000
FOUR IDENTICAL TOLERANCES
REV

DESCRIPTION
TEST 1
TEST 2
TEST 3
TEST 4
PROOF:
1.50000
÷
2.00000
75.00000
%
STANDARD
STATISTICAL
REALISTIC
4
PROOF:
1.67705
÷
2.50000
67.08204
%
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
0.80000
34.00000
MEAN
60.80000
2.39370
60.80000
2.39370
60.80000
2.39370
DESCRIPTION
TEST 1
TEST 2
TEST 3
STANDARD
3
P/N
111111
222222
333333
444444
555555
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
0.80000
MEAN
26.80000
1.05512
26.80000
1.05512
26.80000
1.05512
±
±
THREE IDENTICAL TOLERANCES
REV

PROOF:
1.29904
÷
1.50000
86.60254
%
P/N
111111
222222
333333
444444
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
MEAN
26.00000
1.02362
26.00000
1.02362
26.00000
1.02362
±
±
±
±
±
±
±
TOL.
0.50000
0.50000
0.50000
0.50000
TOL
2.00000
0.07874
1.00000
0.03937
1.50000
0.05906
MAX
62.80000
2.47244
61.80000
2.43307
62.30000
2.45276
MIN
58.80000
2.31496
59.80000
2.35433
59.30000
2.33465
% Tol
25.00000
25.00000
25.00000
25.00000
% SUM
100.00000
FIVE IDENTICAL TOLERANCES
REV

DESCRIPTION
TEST 1
TEST 2
TEST 3
TEST 4
TEST 5
STANDARD
STATISTICAL
REALISTIC
Created by Charles S. Roscoe Revised: 02/08/2010 14 of 21
±
±
±
±
±
±
±
±
TOL.
0.50000
0.50000
0.50000
0.50000
0.50000
TOL
2.50000
0.09843
1.11803
0.04402
1.67705
0.06603
MAX
72.30000
2.84646
70.91803
2.79205
71.47705
2.81406
MIN
67.30000
2.64961
68.68197
2.70401
68.12295
2.68201
% Tol
20.00000
20.00000
20.00000
20.00000
20.00000
% SUM
100.00000
Printed: 10/13/2013 22:46 A10/P10
15.
5
P/N
111111
222222
333333
444444
555555
666666
SIX IDENTICAL TOLERANCES
REV

DESCRIPTION
TEST 1
TEST 2
TEST 3
TEST 4
TEST 5
TEST 6
PROOF:
1.83712
÷
3.00000
61.23724
%
STANDARD
STATISTICAL
REALISTIC
6
P/N
111111
222222
333333
444444
555555
666666
777777
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
0.80000
34.00000
9.00000
100.00000
MEAN
169.80000
6.68504
169.80000
6.68504
169.80000
6.68504
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
0.80000
34.00000
9.00000
100.00000
15.00000
MEAN
184.80000
7.27559
184.80000
7.27559
184.80000
7.27559
±
±
±
±
±
±
±
±
±
TOL.
0.50000
0.50000
0.50000
0.50000
0.50000
0.50000
TOL
3.00000
0.11811
1.22474
0.04822
1.83712
0.07233
MAX
172.80000
6.80315
171.02474
6.73326
171.63712
6.75737
MIN
166.80000
6.56693
168.57526
6.63682
167.96288
6.61271
% Tol
16.66667
16.66667
16.66667
16.66667
16.66667
16.66667
% SUM
100.00000
SEVEN IDENTICAL TOLERANCES
REV

DESCRIPTION
TEST 1
TEST 2
TEST 3
TEST 4
TEST 5
TEST 6
TEST7
PROOF:
1.98431
÷
3.50000
56.69467
%
STANDARD
STATISTICAL
REALISTIC
±
±
±
±
±
±
±
±
±
±
TOL.
0.50000
0.50000
0.50000
0.50000
0.50000
0.50000
0.50000
TOL
3.50000
0.13780
1.32288
0.05208
1.98431
0.07812
MAX
188.30000
7.41339
186.12288
7.32767
186.78431
7.35371
MIN
181.30000
7.13780
183.47712
7.22351
182.81569
7.19747
% Tol
14.28571
14.28571
14.28571
14.28571
14.28571
14.28571
14.28571
% SUM
100.00000
If stack up tolerance values vary greatly, as in stacks 7 thru 12, the RSS/WOW percentage changes. Even with more
than 5 tolerances, the RSS Realistic tolerance may exceed WOW Standard tolerance. Note in stacks 8 thru 12, those
with more than 3 different tolerances. If any one tolerance is more than 60% of the total, the RSS tolerance may
begin to exceed the WOW tolerance.
7
P/N
AAAAAA
BBBBBB
TWO DIFFERENT TOLERANCES
REV DESCRIPTION
 TEST A
 TEST B
PROOF:
0.08112
÷
0.07500
108.16654
%
STANDARD
STATISTICAL
REALISTIC
8
AAAAAA
BBBBBB
CCCCCC
PROOF:
0.19062
÷
0.19000
100.32841
%
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
MEAN
26.00000
1.02362
26.00000
1.02362
26.00000
1.02362
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
0.80000
MEAN
26.80000
1.05512
26.80000
1.05512
26.80000
1.05512
±
±
±
±
±
TOL.
0.03000
0.04500
TOL
0.07500
0.00295
0.05408
0.00213
0.08112
0.00319
MAX
26.07500
1.02657
26.05408
1.02575
26.08112
1.02682
MIN
25.92500
1.02067
25.94592
1.02149
25.91888
1.02043
% Tol
40.00000
60.00000
% SUM
100.00000
THREE DIFFERENT TOLERANCES
REV

DESCRIPTION
TEST A
TEST B
TEST C
STANDARD
STATISTICAL
REALISTIC
Created by Charles S. Roscoe Revised: 02/08/2010 15 of 21
±
±
±
±
±
±
TOL.
0.03000
0.04500
0.11500
TOL
0.19000
0.00748
0.12708
0.00500
0.19062
0.00750
MAX
26.99000
1.06260
26.92708
1.06012
26.99062
1.06262
MIN
26.61000
1.04764
26.67292
1.05011
26.60938
1.04761
% Tol
15.78947
23.68421
60.52632
% SUM
100.00000
Printed: 10/13/2013 22:46 A10/P10
16.
9
P/N
AAAAAA
BBBBBB
CCCCCC
DDDDDD
FOUR DIFFERENT TOLERANCES
REV

DESCRIPTION
TEST A
TEST B
TEST C
TEST D
PROOF:
0.4956
÷
0.4950
100.1262
%
STANDARD
STATISTICAL
REALISTIC
10
P/N
AAAAAA
BBBBBB
CCCCCC
DDDDDD
EEEEEE
STATISTICAL
REALISTIC
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
0.80000
34.00000
9.00000
100.00000
15.00000
MEAN
184.80000
7.27559
184.80000
7.27559
184.80000
7.27559
±
±
±
TOL.
0.03000
0.04500
0.11500
0.30500
TOL
0.49500
0.01949
0.33042
0.01301
0.49562
0.01951
MAX
61.29500
2.41319
61.13042
2.40671
61.29562
2.41321
MIN
60.30500
2.37421
60.46958
2.38069
60.30438
2.37419
% Tol
6.06061
9.09091
23.23232
61.61616
% SUM
100.00000
±
±
±
±
±
±
±
±
TOL.
0.03000
0.04500
0.11500
0.30500
0.79500
TOL
1.29000
0.05079
0.86093
0.03389
1.29139
0.05084
MAX
71.09000
2.79882
70.66093
2.78193
71.09139
2.79887
MIN
68.51000
2.69724
68.93907
2.71414
68.50861
2.69719
% Tol
2.32558
3.48837
8.91473
23.64341
61.62791
% SUM
100.00000
SIX DIFFERENT TOLERANCES
REV

DESCRIPTION
TEST A
TEST B
TEST C
TEST D
TEST E
TEST F
PROOF:
3.36284
÷
3.36000
100.08467
%
STANDARD
STATISTICAL
REALISTIC
12
PROOF:
8.77033
÷
8.76000
100.11795
%
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
0.80000
34.00000
9.00000
100.00000
MEAN
169.80000
6.68504
169.80000
6.68504
169.80000
6.68504
DESCRIPTION
TEST A
TEST B
TEST C
TEST D
TEST E
STANDARD
11
P/N
AAAAAA
BBBBBB
CCCCCC
DDDDDD
EEEEEE
FFFFFF
GGGGGG
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
0.80000
34.00000
9.00000
MEAN
69.80000
2.74803
69.80000
2.74803
69.80000
2.74803
±
±
±
±
FIVE DIFFERENT TOLERANCES
REV

PROOF:
1.29139
÷
1.29000
100.10811
%
P/N
AAAAAA
BBBBBB
CCCCCC
DDDDDD
EEEEEE
FFFFFF
MM
INCH
MM
INCH
MM
INCH
DIM.
20.00000
6.00000
0.80000
34.00000
MEAN
60.80000
2.39370
60.80000
2.39370
60.80000
2.39370
±
±
±
±
±
±
±
±
±
TOL.
0.03000
0.04500
0.11500
0.30500
0.79500
2.07000
TOL
3.36000
0.13228
2.24190
0.08826
3.36284
0.13240
MAX
173.16000
6.81732
172.04190
6.77330
173.16284
6.81743
MIN
166.44000
6.55276
167.55810
6.59678
166.43716
6.55264
% Tol
0.89286
1.33929
3.42262
9.07738
23.66071
61.60714
% SUM
100.00000
SEVEN DIFFERENT TOLERANCES
REV

DESCRIPTION
TEST A
TEST B
TEST C
TEST D
TEST E
TEST F
TEST G
STANDARD
STATISTICAL
REALISTIC
±
±
±
±
±
±
±
±
±
±
TOL.
0.03000
0.04500
0.11500
0.30500
0.79500
2.07000
5.40000
TOL
8.76000
0.34488
5.84689
0.23019
8.77033
0.34529
MAX
193.56000
7.62047
190.64689
7.50578
193.57033
7.62088
MIN
176.04000
6.93071
178.95311
7.04540
176.02967
6.93030
% Tol
0.34247
0.51370
1.31279
3.48174
9.07534
23.63014
61.64384
% SUM
100.00000
The difference of one tolerance value compared to the others used in the stack up, has as great an influence on the
RSS/WOW percentage as the number of tolerances.
Thx for you earlier explanation and historical context.
Charlie
Created by Charles S. Roscoe Revised: 02/08/2010 16 of 21
Printed: 10/13/2013 22:46 A10/P10
17.
As a result of the above discussion on Statistical validity
In stack ups with less than five tolerances, enter the following text as a warning. See example below.
STATISTICAL STACK RESULTS USING LESS THAN FIVE TOLERANCES ARE NOT VALID
REALISTIC STACK RESULTS USING LESS THAN FIVE TOLERANCES ARE NOT VALID
73
P/N
2011108
73A1
73B3
2009960
AXIAL DISTANCE  CIRCLIP TO DIFF GEAR VERTICAL GROOVE WALL.
WITH RING EXPANDED AND CONTACTING DIFF GEAR GROOVE ID AND 34.5 DEGREE ANGLE IS THERE SIDE CLEARANCE? NO!
INTERFERENCE TRANSITION FIT. CIRCLIP CAN NOT EXPAND FULLY INTO DIFF GEAR GROOVE AS GRAPHIC SHOWS. CIRCLIP
WILL STOP SHORT AGAINST 34.5 DEGREE DIFF GEAR ANGLE. SEE STACK 74 GRAPHIC.
REV DESCRIPTION
A CIRCLIP (OD RADIUS)
AXIAL DISTANCE  CL OF CIRCLIP TO CONTACT POINT ON DIFF
GEAR GROOVE
AXIAL DISTANCE  CIRCLIP CONTACT POINT ON DIFF GEAR
GROOVE TO GROOVE OD CORNER
C GEAR  NET FORMED DIFF FIN (CIRCLIP GROOVE AXIAL DISTANCE)
STANDARD
INTERFERENCE
STATISTICAL STACK RESULTS USING LESS THAN FIVE TOLERANCES ARE NOT VALID
REALISTIC STACK RESULTS USING LESS THAN FIVE TOLERANCES ARE NOT VALID
DIM.
1.0000 ±
% Tol
10.0458
0.8217 ±
MM
INCH
MM
INCH
MM
INCH
TOL.
0.0175
0.0218
12.5364
0.0349
0.1000
TOL
0.1742
0.0069
0.1095
0.0043
0.1643
0.0065
20.0131
57.4047
% SUM
100.0000
0.2990
1.4000
MEAN
0.1227
0.0048
0.1227
0.0048
0.1227
0.0048
±
±
±
±
±
MAX
0.0515
0.0020
0.0131
0.0005
0.0416
0.0016
MIN
0.2969
0.0117
0.2322
0.0091
0.2870
0.0113 OK CSR
Realistic tolerances used to make Worst Case Layouts
When many feature standard Worst of Worst (WOW) tolerances are used in a layout to construct worst case
conditions of several parts and features, the opinion may a rise that the WOW and Statistical results are to
extreme. The IST / IRT formula may be use to find the smaller IRT for all the parts feature tolerances. The parts
are modified these IRT conditions in the layout. A less extreme worst case condition result will be found using this
method.
Caution: Use this only when the utmost faith is placed in the ability of the process or supplier to control the stated
tolerances. Otherwise this method will give a false sense of security about the relationship in question.
Created by Charles S. Roscoe Revised: 02/08/2010 17 of 21
Printed: 10/13/2013 22:46 A10/P10
18.
Radial Stack Ups
Two separate stacks with features representing worst case conditions must be performed when parts can move
around WRT each other. An ABS Sensor Air Gap stack up is an example, see below. A Worst Case layout can
be created as well to verify it as well. In Excel, either Max Min dimensions can be used (see examples below) or
Mean +/ Tol. dimensions, you will get the same result. With Mean +/ Tol. Dimensions, the Minimum TIGHT fit
gives the MIN result and the Maximum LOOSE fit gives the MAX result. Add together and divide by two for the
mean value and tolerance.Mean +/ Tol. Dimensions in Excel will give you Statistical and Realistic results. Max
Min dimensions will not.
GDT in the Radial Stacks
To find the worst case TIGHT fit all the GDT is MINUS, subtracted out. See 3B Min below. To find the worst case
LOOSE fit all the GDT is PLUS, added in. See 3B Max below.
Created by Charles S. Roscoe Revised: 02/08/2010 18 of 21
Printed: 10/13/2013 22:46 A10/P10
19.
Orientation in Radial Stacks
When the cumulative effect of stacked parts can cause the tilting of the total assembly use the Ratio or
Proportional formula to calculate the effect.
Ratio: The relative size of two quantities expressed as the quotient of one divided by the other; the
ratio of a to b is written as a:b or a/b.
Proportion: An equality between two ratios. This equality means the shared included angle is equal
and this allows you to solve for any unknown of the four integers.
12 / 6 = 8 / 4,
A / B = C / D ...are geometrical proportions.
The latter is read, 'the ratio of A to B equals the ratio of C to D', or more concisely, 'A is to B, as C to
D'. If "A" is the unknown then to solve for it you cross multiple and divide.
(B x C)/D = A or (6 x 8)/4 = 12. The formula is reordered to solve for B, C, or D.
Note in above graphic example above that the Sensor Adapter is screwed flush to an AS FORGED Knuckle
surface. The Knuckle "as forged" Adapter mounting surface deviation tolerance is +1.50 WRT Datum A.
This surface is NOT machined and flat. There is not a finished spot face or Perpendicularity to the Knuckle
bearing bore. The Adapter Sensor MTG surface has no parallelism to the other side. The Adapter sensor
mounting surface deviation is ±0.25. The feature tolerance is all that control parallelism to the mounting face.
These surfaces can tilt to the limit of the feature tolerances. The effect is very great and will increase the
interference.
Use toleranced values for the two worst case tilt results in the Excel stack up so Statistical and
Realistic results will be correct. Include at the bottom after the detail dimensions.
Created by Charles S. Roscoe Revised: 02/08/2010 19 of 21
Printed: 10/13/2013 22:46 A10/P10
20.
Parameters for Knuckle MTG surface tilt Proportional Formula calculation given as example.
A = UNKNOWN TILT OF SENSOR TIP
B = 38.0+/0.3 SENSOR LENGTH
C = 0.75+/0.75 KNUCKLE SURFACE DEVIATION
D = 25 +1.5/0 ADAPTER BODY WIDTH
A/B=C/D
A/B=C/D
A/B=C/D
A = (Bmean X Cmean)/Dmean A = (38 X 0.75)/25.75
A = (Bmax X Cmax)/Dmin
A = (38.3 X 1.5)/25
A = (Bmin X Cmin)/Dmax
A = (37.7 X 0.00)/26.5
A = 1.11 Mean Sensor Tilt
A = 2.30 Max Sensor Tilt
A = 0.00 Min Sensor Tilt
Excel format for Proportional Formula at:
TBD
There are four tabs. Each solves for one of four possible unknowns A, B, C, and D that finds the mean value
with a tolerance. Copy, paste the desired calculation format box into your stack up to solve for Orientation tilt
calculations.
WORD Graphics
Use Word and the Drawing tool bar to graphically represent your sketches and show the effects of GDT,
diametral clearances and see the results. Inch is the default system used in the Drawing tool bar. An example is
shown below, 25.4 X Size, that may be measured exactly using a inch scale to verify Metric dimensions.
Word distorts very little when printed. Excel Graphics distort much more in one direction than in the other.
For greatest accuracy make sketch on Word.doc then Copy and Paste in to Excel stack Up.
Created by Charles S. Roscoe Revised: 02/08/2010 20 of 21
Printed: 10/13/2013 22:46 A10/P10
21.
+0.04 RADIAL
CLEARANCE @ MMC
.25020 CASE AND PIN
THREADS ARE CONCENTRIC
+0.143
RADIAL
CLEARANCE @ MMC
0.065
X2
0.130 DIAMETER
POSITIONAL
TOLERANCE ZONE
0.038
X2
0.076 DIAMETER
POSITIONAL
TOLERANCE ZONE
0.063 RADIAL
INTERFERENCE @ MMC
+0.04
RADIAL
CLEARANCE @ MMC
DOUBLE CHECK
4.825±0.075
(4.75 Min shown)
Case Pin Hole ID and
∅0.13 Pos. Tol.
4.620±0.050
(4.67 Max shown)
Lock Pin OD and
∅0.076 Pos. Tol.
25.4 X SIZE
REF: CASE ASSY – DIFF T/L
X80579
X53090 DIFF  SHAFT
X50391 CASE – FIN T/L
48148 LOCK – DIFF SHAFT
+2.375
0.065
0.038
2.335
0.063
–
CASE HOLE ID RADIUS
½ CASE POS. TOL.
½ LOCK PIN POS. TOL.
LOCK PIN OD RADIUS
MIN RADIAL INTERFERENCE
+2.375
+0.065
+0.038
2.335
+0.143
–
CASE HOLE ID RADIUS
½ CASE POS. TOL.
½ LOCK PIN POS. TOL.
LOCK PIN OD RADIUS
MAX RADIAL CLEARANCE
GDT STACK UP AT MMC – BEST CASE FIT
GDT STACK UP AT MMC – WORST CASE FIT
+4.825 +/ 0.075 – CASE PIN HOLE ID
4.620 +/ 0.050 – LOCK PIN OD
+0.205 +/ 0.125 – DIAMETRAL CLEARANCE
+4.825 +/ 0.075 – CASE PIN HOLE ID
4.620 +/ 0.050 – LOCK PIN OD
+0.205 +/ 0.125 – DIAMETRAL CLEARANCE
+0.330  MAX @ LMC
+0.330  MAX @ LMC
+0.080
+0.130
+0.076
+0.286
/2
+0.143
+0.080
0.130
0.076
0.126
/2
0.063
–
–
MAX @ MMC
CASE ID POS. TOL. TO ¼20 UNC2B
PIN OD POS. TOL. TO ¼20 UNC2A
SUM
– RADIAL CLEARANCE
Created by Charles S. Roscoe Revised: 02/08/2010 21 of 21
–
–
MAX @ MMC
CASE ID POS. TOL. TO ¼20 UNC2B
PIN OD POS. TOL. TO ¼20 UNC2A
SUM
– RADIAL INTERFERENCE
Printed: 10/13/2013 22:46 A10/P10
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