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gd&T
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Welcome to a Course On
Geometric Dimensioning and Tolerancing (GD&T) Based on
ASME Y14.5M-1994 with Introduction to Dimension
Management / Engineering
For
General Motors Technical Center, Bangalore, INDIA
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Focus Areas …
� CAD Data InterOperability : Consistent representation of 3D
CAD data in variety of CAD/CAM/CAE applications and platforms.
� InterChangeability: Predicting Dimensional Variations, its impact
and causes at the product and assembly level at early design
stage.
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Relationships …
� InterOperability:
– With International TechneGroup Incorporated, USA having more than
20 years of Experience in CAD Data InterOperability technology,
solutions and services.
iiii22225
Relationships …
• InterChangeability:
• With Dimensional Control Systems Inc., USA having more than 15
years of experience in Dimensional Control Techniques, Solutions
and Services.
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Our Offerings …
•CAD Data InterOperability:
•Focused & Customized Training Programs on:
•CAD/CAM/CAE Data Exchange : Problems and Solutions from CAD, CAE, CAM Perspective.
•CAD Model Quality Assessment : CAD Model Quality evaluation from downstream application
perspective
•Software Solutions For:
•Effective Data exchange between heterogeneous CAD/CAM systems: Regardless of source,
target application, standard and formats !! Solutions Include CADfix, IGES/Works,CAD/IQ.
•Model Quality Assessment from Downstream application perspective
•Quality Services for:
•Data Exchange, Data Migration, Lower version to higher or vice-a-versa
•‘Vendor – Supplier’ data integration : ensuring effective data exchange with minimal / NO
rework at either ends.
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Our Offerings …
•InterChangeability:
•Focused & Customized Training Programs on:
•Dimensional Management : Understanding and appreciation of computer aided tools for.
Takes participants thru evolution, various approaches and real life problems from their
application areas.
•Software Solutions For:
•Dimensional Management / Stack Analysis: Solutions embedded in CATIA V5 as Gold
Partner and also Stand Alone solutions for data coming from other CAD platforms !! Solutions Include 1-DCS, DCS-DFC, 3DCS-SA, 3DCS-CAA V5 Designer, 3DCS-CAA V5 Analyst,
GDM3D
•Quality Services for:
•Dimensional Engineering / Management : Base Line tolerance model creation, reporting with
suggestions and recommendations. Follow-on consulting
•Per requirement, includes 1D, 1D with GD&T, Full 3D simulations, Piece – part variations,
assembly variation prediction against desired objectives.
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Training Programs in Dimensional Management / Engineering
Basic knowledge of GD&T
24hrs(3 days)
Introduction to Digital Product Definition Data Practices (SolidModel Tolerancing) per ASME Y14.41:2003
8
None8hrs
(1 day)Engineering Limits & Fits with introduction to ANSI B4.2-1978
and ISO-286 Standards7
Basic knowledge of GD&T
24hrs(3 days)
Introduction to Dimensioning and Tolerancing Principles for Gages and Fixtures Based on ASME Y14.43:2003
6
Basic knowledge of GD&T
32hrs(4 days)
GD&T and Tolerance Stack-up Analysis for an Automobile: A Practical Approach to Control and Calculate Dimensional
Variations5
Basic knowledge of GD&T preferred
32hrs(4 days)
CATIA V5 Based GD&T/Tolerance Stack-up Analysis using DCS (Dimensional Control Systems Inc., USA) Software Solutions.
(Covers exposure to 1DCS,DCS-DFC and 3DCS-CAAV5 Analyst)
4
Basic knowledge of GD&T
24hrs(3 days)
Tolerance Stack-up Analysis using Co-ordinate System of Dimensioning and GD&T : A practical Approach to Solve
Assembly Build Problems3
Basic knowledge of GD&T
24hrs(3 days)
Advanced Geometric Dimensioning & Tolerancing (GD&T): Concepts & Applications as per ASME Y14.5M:1994
2
None24hrs
(3 days)Fundamentals and Interpretation of Geometric Dimensioning
and Tolerancing (GD&T) as per ASME Y14.5M:19941
Pre-requisiteDuration Course TitleSr#
Courses from iSquare, Pune in the domain of Dimensional Variation Management
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How is this course organized?
� Total 10 Sessions; 3days
� Pre-defined objectives at the beginning of each session
� Classroom exercises at the end of each session
� Homework
� Extended hours as necessary
� Assumption : Understanding of GD&T controls
� Feel free to interrupt and ask Questions
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History
� In practice, the parts are produced with some variation to
accommodate process capabilities and interchangeability – called
tolerances
� Generally, tolerances are specified in plus/minus
� Plus/minus system worked quite well and even today used in
many applications.
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� Later, the idea of locating round features such as pins/holes etc, with
round tolerance zone rather than traditional square tolerance zone
introduced which later caught up and adopted by military standards and
late became unified ANSI standard
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Introduction to GD&T
� Simple part for own use… No need for drawings when designer, inspector and
manufacturer are same!
� Designer often creates an assembly, parts fit together with optimal clearances, He conveys ideal size (nominal dimensions) and shapes to each manufacturer.
� Volume production?:
– Impossible to make every part identical
– Every manufacturing process has unavoidable variations that cause variations in manufactured parts.
– Designer,with due consideration must analyze how much variation may be allowed in size, form, orientation and location.
– Then along with nominal dimensions, he must communicate magnitude of such variations or TOLERANCE each characteristics can have and still contribute to functional assembly.
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How to Communicate such Variation?
� Often words are inadequate; eg. A note “Make this surface a real flat”
only has meaning where all concerned parties can do following:
– Understand English
– Understand to which surface the note applies and extent of the surface
– Agree on what “Flat” means
– Agree on exactly how flat is “Real Flat”!!
� To overcome miscommunication, throughout 20th century a specialized
language based on graphical representations and math has evolved to
improve communication. Such language is currently recognized as
“Geometric Dimensioning and Tolerancing (GD&T)”
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So, what is GD&T?
� It’s a language for communicating Engineering Design Specifications; approved by ANSI, ASME and United States Department of Defense (DoD)
� GD&T Includes all symbols, definitions, mathematical formulae and application rules critical to embody a viable engineering language.
� It conveys both: ie. Nominal (or ideal) dimensions and variations (or tolerances allowed for that dimension.
� It enhances co-ordinate system dimensioning and describes designers intent
� Designer’s requirements can be completely specified using GD&T symbols thus eliminating/reducing foot notes on drawings.
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What GD&T is NOT …
� Its not a creative design tool; it can’t suggest how certain part surfaces should be controlled (methods …)
� It does not convey parts’ intended function. Eg. Designer created a bore to function as hydraulic cylinder to withstand 15kg/cm2 pressure; however GD&T can’t convey the purpose (intended function) of part.
� GD&T specifications can address size, form, orientation, location and/or smoothness of bore based upon stress/fit considerations of design by designers’
experience.
� Its incapable of specifying manufacturing processes to achieve desired tolerances/variations
� Its not a replacement to co-ordinate dimensioning system.
� To summarize, GD&T is a language that designers use to translate design requirements into measurable specifications.
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Where does GD&T come from? (references…)
� GD&T vocabulary and grammatical rules are provided in:
– ASME Y14.5M-1994 Geometric Dimensioning and Tolerancing
– ASME Y14.5.1M-1994 Mathematical Definition of Dimensioning and Tolerancing Principals
� To avoid confusion, hereafter we will call first standard as “Y14.5” and the later as “Math Standard”
� Later, we will see differences between other International Standard (more followed in Europe) “ISO GD&T” and the US dialect.
� ASME offers no .800. number for help on technical issues and interpretations. At times interpretation could be dispute, so users are advised to refer to text / reference books and your organization’s internal staff.
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Why do we use GD&T?
•Designer specifies distance to holes’ ideal location
•Manufacturer measures this distance and marks a “x” spot and drills a hole.
•The Inspector then measures the actual distance to that hole.
•ALL THREE PARTIES MUST BE IN PERFECT AGREEMENT ABOUT THREE THINGS:
•From where to start the measurement?
•What direction to go?
•And where measurement ends?
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So,
� When measurements are precise to two digits, the slightest difference in
interpretation (origin / direction /end )can lead to a usable part or
expensive paperweight!!
� Even if everyone agrees to measure to holes’ center, a egg shaped hole
presents a variety of “centers” and each center is defensible based on
different design considerations
You may find claims that GD&T affords more tolerance for manufacturing, but by
itself, it doesn't. GD&T affords however much or little tolerance the designer
specifies. Just as a common claim that using GD&T saves money, but hardly
such claims are accompanied with cost or ROI analyses.
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Yet another example …
• Drawing of an Automobile Wheel Rotor
• Has neat and uniform appearance
•…. But leaves many features totally out of control!!
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From Rotor Drawing;
� What if it were important that the n 139.7 bore to be perpendicular to
mounting face?
� What if it was critical that n 139.7 bore and OD n279.4 be on the same
axis?
Nothing on the drawing addresses it!
Next slide shows the part that can be built and still meet specifications…
however the part may not function in an assembly and therefore lead to
assembly rejection…
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The “no-sense” Wheel Rotor … dimensionally in spec!
Manufactured part that conforms to the drawing without GD&T
178.08
68.94
20.60
152.55279.24 139.59 78.79
68.78
20.80
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Shortcomings of Co-ordinate System of Dimensioning …
Defining the Form of
part feature
Controlling angular
relationships
Locating Part Features
Chamfers and Radii
Overall Size of
component
Correct / Incorrect UseApplication
Coordinate Dimension Usage
Co-ordinate tolerancing is a dimensioning system where a part features are defined by means of rectangular dimensions with given tolerances. Such system has three shortcomings:
× Square or Rectangular Tolerance Zones
× Fixed Size Tolerance Zones
× Ambiguous instructions for Inspection
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Wheel Rotor in ‘Control’ with GD&T
• Mounting face being important for the function of the rotor; has been made flat within 0.1.
• Later Mounting face assigned as Datum A (foundation for drawing..)
• Another critical face of Rotor has been made parallel to Datum A within 0.16
• The Dia 139 bore has been made Perpendicular to mounting face; therefore directly controlled to our foundation (ie. Datum A) and labeled as Datum B
• Together Datum A and B form a sturdy reference from which dia. 10 bolt holes and other round features can be derived/ located
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� Datum features A and B provide a very uniform and well aligned
framework from which a variety of relationships and fits can be precisely
controlled.
� Thus, GD&T provides unique, unambiguous meaning for each control.
GD&T then, is simply means of controlling surfaces more precisely and
unambiguously.
� This is fundamental reason for using GD&T. Clear communication
assures that manufactured parts will function and that those functional
parts will not be rejected later due to misunderstanding /
miscommunication.
� So, fewer arguments … Less Scrap.
Contd …
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Hence, GD&T …
� Adds clarity over co-ordinate system of dimensioning
� Eliminates notes on the drawings
� Depicts designers intent and inspection criteria
� Most significant difference between GD&T and co-ordinate dimensioning
is location of round features. The co-ordinate system had square
tolerance zone that rejected some good parts!!
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Hidden costs that GD&T reduces (Quick ROI)
� Designers / Manufacturers / Inspectors wasting time to interpret drawings and questioning the designers
� Rework of manufactured parts due to misunderstanding
� Inspection deriving meaningless data from parts while failing to check critical relationships.
� Handling and documentation of functional parts that are rejected!
� Sorting, reworking, filing, shimming of parts … often additional operation.
� Assemblies failing to operate, failure analysis, Quality problems, Customer complaints, loss of market share, product recall, loss of customer loyalty.
� Meetings, corrective actions, debates, drawing changes and interdepartmental vendettas resulted from failure!
ALL THE ADD UP TO AN ENORMOUS, YET UNACCOUNTED COST. BOTTOM LINE? USE GD&T BECAUSE ITS RIGHT THING TO DO. IT’S ALL PEOPLE ALL OVER THE WORLD UNDERSTAND AND IT SAVES MONEY
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So, When do we use GD&T?
In absence of GD&T specifications, a parts’ ability to satisfy design requirements depends largely upon four “laws”
� Workmanship Skills / Pride. Every industry has unwritten customary standards of product quality and most workers strive to achieve them. But these standards are minimal requirements. Further workmanship customs of precision aerospace machinists are rarely shared by ironworkers.
� Common Sense. Experienced manufactures develop fairly reliable sense as what the part is suppose to do. Even without inadequate specifications, he will try to make bore straight and smooth if he suspects it’s a hydraulic cylinder.
� Probability. Today’s modern precision machine tools have accuracy / repeatability say upto0.0002mm, therefore, it is assumed that part dimensions should never vary more than that. Further there is no way to predict what process may be used, how many and in what sequence to produce a part.
� Title Block, or contractual standards. Sometimes, these provide clarification. But often they are very old and inadequate for modern high-precision tools. An example of a title block note is “All surfaces to be flat within 0.005”
All above “laws” carries obvious risk. Where designer deems the high risk, GD&T Specifications should be spelled out rigorously .
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How Does GD&T Work? - Overview
In previous slides, we alluded to goal of GD&T: To guide all parties towards reckoning
part dimensions the same, including the origin, direction and destination for each measurement. GD&T achieves this goal through four simple steps:
1. Identify part surfaces to serve as origins and provide specific rules explaining how these surfaces establish the starting point and direction for measurement.
2. Convey the nominal (ideal) distances and orientations from origin to other surfaces
3. Establish boundaries and / or tolerance zone for specific attributes of each surface along with specific rules for conformance.
4. Allow dynamic interaction between tolerances (simulating actual assembly possibilities) where appropriate to maximize tolerances.
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Size Limits (Level 1 Control)
For every feature of size, the designer shall specify the largest and the smallest the feature can be.
Previously we discussed the exact requirements these size limits impose on the feature. The standards provide three options for specifying size limits on the drawings.
– Symbols for Limits and fits
For example, n12.45LC5 or 30f7 (ANSI B4.1 (inch) or ANSI B4.2 (metric))
– Limit dimensioning
– Plus and Minus Tolerancing
12.34
12.30
φ
φ12.45 12.49φ −
or0.35
0.2524.54φ +
−11.65 0.45±
or
iiii222285
Millimeter values
• When a dimension is less than one mm, zero must precede the decimal point
ex. 0.4 NOT .4
• When a dimension is a whole number, neither a decimal point nor zero is used
ex. 45 NOT 45.00
• When a dimension is a whole number and decimal, zero does not follow decimal number
ex. 47.5
• A dimension does not use a comma or space
ex 3450 NOT 3,450 or 3 450
• A tolerance for dimension can have more numbers of decimal places than dimension itself.
ex. 47`̀̀̀0.34
• When unilateral dimension is used, no sign be used with zero; ex.
• When a bilateral tolerance is used, both; the plus and minus tolerance must have identical number of decimal places
ex.
0.76
045φ + 0
0.4534φ −or
0.76
0.4545φ +
−
0.55
0.434φ +
−NOT
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Millimeter values
• When a limit dimension is used, the decimal places must match. ex:
• Basic dimension can have any number of decimal places in Feature Control Frame.
54.15
54.00
53.15
53NOT
50 50.35 50.00or NOTex.
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Few Examples
All dimensional limits are absolute. A dimension is considered to be followed by zeros after the last significant digit.
20.2 means 20.2000…
160 means 160.0000…
Interpreting 80.5 - 80.2 :
-If part measures 80.199… part is rejected
- If part measures 80.499… part is accepted
iiii222290
Part Features
Up till now, we used term Surfaces and Features loosely and almost
interchangeably. To speak GD&T, we should begin to use terms as
defined in Y14.5
Feature is the general term applied to physical portion of a part such as
surfaces, pin, tab, hole or a slot.
Usually, part feature is a single surface (or a pair of opposed parallel plane
surfaces) having uniform shape. You can establish datums from, and
apply GD&T controls to features only.
There are two general types of features. Those that have built-in dimension
of “size” and those that don’t.
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Non Size Features
A nonsize feature is a surface having no unique intrinsic size (diameter or
width) dimension to measure. It includes following:
� A nominally flat planer surface
� An irregular or ‘warped’ planer surface, such as face of windshield or
airfoil.
� A radius – a portion of cylindrical surface encompassing less than 180deg
of arc length.
� A spherical radius – a portion of a spherical surface encompassing less
than 180deg of arc length.
� A revolute – a surface such as cone, generated by revolving a line about
an axis.
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Features of Size
A feature of size is one cylindrical or spherical surface or a set of two
opposed elements or opposed parallel surfaces, associated with size
dimension.
Holes are ‘internal’ features of size. Pins are ‘external’ features of size.
Features of size are subject to principals of material condition modifiers (to be discussed later…)
‘Opposed parallel surfaces’ means the surfaces are designed to be parallel
to each other. To qualify as ‘opposed’, it must be possible to construct a
perpendicular line intersecting both surfaces. Only then, we can make a
meaningful measurements of size between them. From now on, we will
call this type of feature a width-type feature
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Bounded Features (Partial Size Features)
This type of feature is neither a sphere, cylinder, nor
width type feature, yet has two opposed elements.
The “D” hole for example is called “irregular feature of
size” by some text books. Y14.5’s own coverage
for this type of feature is limited. Although feature
has obvious MMC and LMC boundaries, its
arguable whether feature is “associated with size dimension”
For now, we’ll consider this type feature as bounded
feature of non size
=??
12`̀̀̀0.2
5`̀̀̀0.15
12`̀̀̀0.2
11`̀̀̀0.15
20`̀̀̀0.2
5`̀̀̀0.1 5`̀̀̀0.1
5`̀̀̀0.1
5`̀̀̀0.120.2
4.9 4.95
5.05
5.1
iiii222296
Material Condition
Material condition is yet another way of thinking about the size of an object considering object’s nature.
For example, nature of a pizza is base with topping. If you have exxxtraa topping, its’
material condition increases and pizza gets bigger and thicker.
The Nature of a cannon is that its void, as erosion decreases its material condition, cannon gets bigger.
If a mating feature of size is as small as it can be, will it fit tighter or sloppier? We can’t answer until we know whether we’re talking of internal or external feature (hole / pin), but when you know feature of size has less material, it will fit loosely regardless of its type.
In layman’s term, Material Condition is features size in the context of its intended function.
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MMC & LMC
� Maximum Material Condition (MMC mmmm) is the condition in which a feature of size
contains maximum amount of material within the stated limits of size.
One can think of MMC as the condition where the most part material is present at the surface of
feature, or where part weighs the most (everything else being same). This translates to smallest
allowable hole or the largest allowable pin, relative to specified size limits.
� Least Material Condition (LMC llll) is the condition in which feature of size contains
minimum amount of material within stated limits of size.
One can think of LMC as the condition where the least part material is present at the surface of
feature, or where part weighs the least (everything else being same). This translates to largest
allowable hole or the smallest allowable pin, relative to specified size limits.
iiii222299
Basic Dimensions
Basic Dimension is a numerical value used to describe (1) the theoretically
exact size, true profile, orientation or (2) a location of feature or a gage
information (datum targets).
When a basic dimension is used to define part features, it provides nominal
location from which permissible variations are established by Geometric
Tolerances.
Basic dimensions are usually denoted by numerical value enclosed in a
rectangle or by addition a general note such as “un-toleranced dimensions
are basic”
Basic dimensions must be accompanied by geometric tolerance to specify
how much tolerance the part feature may have
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Basic Dimension Example
Basic dimensions …
•Can be used to define theoretically exact location, orientation or true profile of part features or gage information.
•That define part features must be accompanied by a geometric tolerance.
•That define gage information do not have a tolerance shown on the drawing.
•Are theoretically exact (but gage makers’ tolerance do apply)
iiii2222104
GD&T Symbols(An attempt to explain Wheel Rotor Drawing w/o GD&T Symbols)
Tedious to Explain requirements,
instead use symbols. They are better.
•Any one can read write symbols
•Symbols mean exactly same thing to
everyone.
•Symbols are compact and reduce clutter
•Quicker to draw and CAD softwares
can draw them automatically.
•They can be easily spotted visually. Compare this with GD&T’ed Drawing
and find all positional callouts… !!
iiii2222107
Feature Control Frame (FCF)
Each geometric control for a feature is conveyed on a drawing by a rectangular box called feature
control frame. A typical FCF is divided in compartments expressing following sequentially left to right.
•1st Compartment contains geometric characteristic symbol from 14 available symbols.
Geometric Characteristic
Symbol
Tolerance Modifying Symbol
Geometric Tolerance
Value
Primary Datum
Secondary Datum
Tertiary Datum
Datum Material Condition Modifiers
1st 2nd 3rd 4th 5th
Compartments
iiii2222110
General Characteristics (Type wise) and corresponding ASME sections
6.7.1.2.2ttttTotal Runout
6.7.1.2.1hhhhCircular Runout
Runout
5.13iiiiSymmetry
5.11.3rrrrConcentricity
5.2jjjjPosition
Location
6.6.3ffffParallelism
6.6.4bbbbPerpendicularity
6.6.2aaaaAngularity
Orientation
For Related
Features
6.5.2(a)ddddSurface Profile
6.5.2(b)kkkkLine Profile
Profile
For Individual
or Related
Features
6.4.4ggggCylindricity
6.4.3eeeeCircularity
6.4.2ccccFlatness
6.4.1uuuuStraightness
FormFor Individual Features
ASME SectionSymbolDescriptionTolerance Type
Geometric Category
iiii2222113
Feature Control Frame Placement
Place the frame below or attached to a leader-directed callout or dimension pertaining to the
feature.
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Feature Control Frame Placement
Attach either side or either end of frame to an extension line from the feature, provided it is a plane
surface.
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Feature Control Frame Placement
Attach either side or either end of the frame to an extension of the dimension line pertaining to a
feature of size.
iiii2222117
Reading Feature Control Frame …
It is easy to translate FCF into English and read a loud from left to right. Previous tables (slide#
110,111) show equivalent English words to the left of each symbol. Then we just add the following English language preface for each compartment:
1st Compartment: “The …”
2nd Compartment: “… of this feature shall be within …”
3rd Compartment: “… to primary datum …”
4th Compartment: “… and to secondary datum …”
5th Compartment: “… and to tertiary datum …”
With this, feature control frame shown above is reads as: “The Position of this feature shall be within
cylindrical tolerance zone of diameter 1 at maximum material condition to primary datum A and to
secondary datum B at maximum material condition and to tertiary datum C at maximum material
condition”
Isn’t it Easy?
iiii2222118
Summarizing FCFs …
� FCF is specified to each feature or group of features
� FCF provides instructions form, orientation and position of features; thus
providing setup for mfg and inspection.
� FCF contain information for proper part orientation in relation to specified
Datums
iiii2222129
Features of Size : Four fundamental Levels of Control
� Four different levels of GD&T control can apply to a feature of size.
� Each higher level control adds a degree of constraint demanded by
features functional requirement; however as we move up the level ladder,
the lower level control remain in effect.
� Thus a single feature may subject to many tolerance simultaneously!
� Level 1: Controls size and (for cylinders and spheres) circularity at each
cross section only
� Level 2: Adds overall Form Control
� Level 3: Adds Orientation Control
� Level 4: Adds Location Control
iiii2222132
Math Standard : establishing size limit boundaries
•Start with geometric element: Spine
•The Spine for a cylindrical feature (such as pin / hole) is a simple non-self-intersecting curve in space.
•Spine could be straight or wavy
•Take a imaginary steel ball whose diameter = small size limit of the cylindrical feature.
•Sweep balls’ center along the spine.
•This generates a “wormlike” 3D boundary for the features’ smallest size
•Similarly, we take another spine and sweep another ball whose diameter = large size limit of the cylindrical feature
•This generates second 3D boundary, this time for the features’ largest size.
Generating a Size Limit Boundary
iiii2222133
Math Standard : establishing size limit boundaries
�This shows a cylindrical feature of size
conforms to its size limits when its surface can contain the small boundary and be
contained within larger boundary.
�Under Level 1 Control, the curvatures and relative locations of each spine may
be adjusted as necessary to achieve the
hierarchy of containments as above;
except that the small size boundary shall
be entirely contained within large size limit boundaryConformance to limits of size for a cylindrical
feature
iiii2222141
Level 2 Control: Overall Feature Form
�As shown in figure left, features of
size should achieve clearance fit in an assembly
�Designer calculates the size
tolerances based on assumption that each feature, internal and external is Straight. In this example, the designer knows that n20.5 max pin will fit in a n20.6 min hole if both are straight.
iiii2222142
�If pin is banana shaped and hole is
lazy “S” shaped, they usually won’t go together, because Level 1’s size
limit boundaries can be curved, they
can’t assure assemblability.
�Level 2 adds control of overall
geometric shape or “form” of a feature of size by establishing a
perfectly formed boundary beyond
which feature’s surface(s) shall not
encroach.
Level 2 Control: Overall Feature Form (contd …)
20.5
20.6
iiii2222145
Perfect Form at MMC Only (Rule #1)
� Y14.5 established a default rule for perfect form based upon assumption
that most features of size must achieve a clearance fit.
� Y14.5’s Rule #1 decrees that, unless otherwise specified or overridden by
another rule, a features MMC size limit spine shall be perfectly formed
(straight or flat depending upon type). This invokes a boundary of perfect
form at MMC (also called an envelope)
� Rule #1 does not require the LMC boundary to have a perfect form.
� This Rule #1 is also referred as ‘Taylor’s Envelope Principle’
iiii2222146
Perfect Form at MMC Only (Rule #1)
�The figure left shows how Rule #1 establishes a n. .501
boundary of perfect form at
MMC (envelope) for pin.
Similarly, Rule #1 mandates a n. .502 boundary of perfect
form at MMC (envelope) for the hole.
�The figure also shows how
matability is assured for any pin that can fit inside its n.
.501 envelope and any hole that can contain its n..502
envelope.
�This simple hierarchy of fits is called as the envelope
principle.
20.5
20.6
19.5
21.4
20.5
20.6
iiii2222147
Rule #1 Example (External FOS)
Every Cross-sectional measurement must be
within limits of Size
Part shall be always contained within MMC
Envelope
iiii2222148
Boundary of Perfect formMMC Envelope
Every cross-sectional measurement must be within limits of size
Rule #1 Example (Internal FOS)
Hole shall be always outside the MMC perfect form
Envelope
iiii2222152
Perfect Form at neither MMC nor LMC
Figure above is a drawing for electrical bus bar. Note that cross sectional dimensions have
relatively close tolerances, not because bar fits closely inside anything, but rather needed to assure a minimum current carrying capacity without wasting expensive copper. Neither the MMC
nor the LMC boundary needed perfectly straight.
However, if bus bar is custom rolled, or machined from a plate, it won’t automatically be exempted from Rule #1. In such a case, Rule #1 shall be explicitly nullified by adding a note as
shown.
iiii2222153
Rule #1 Arguments …
Many experts argue that Rule #1 is actually the “exception” that fewer than half of all
features of size need any boundary of perfect form.
Which means, for majority of features of size, Rule #1’s perfect form at MMC requirement accomplishes nothing except to drive up costs!!
The Solution is that Y14.5 prescribes the “perfect form not required” note and engineers simply fail to add it more often. Interestingly, ISO defaults to “perfect
form not required” (sometimes called as independency principal) and requires special symbol to invoke the “envelope” of perfect form at MMC. This is one of the major differences between ISO and Y14.5
Every engineer should consider for every feature of size whether a boundary
of perfect form is a necessity or a waste?
iiii2222154
Why Rule #1?
� Ensures assembleability through InterChangeability
� Automatically separates bad parts that encroach envelope of
perfect form at MMC
� For welded parts, rule #1 applies after welding operation is
performed (since one or more parts when welded become single
part)
iiii2222155
Rule #2
� Rule #2 states that in absence of modifier (such as m or l) in
tolerance or datum compartment, the tolerance applies on RFS (Regardless of Feature Size) basis. In short, modifier s is no
longer used.
0.25 0.25
15 0.15φ ± 15 0.15φ ±
iiii2222156
Boundaries:
Virtual Condition (Fixed Size)Inner & Outer (Variable Size)
Worst Case IB/OB (Fixed Size)
iiii2222157
Virtual Condition Boundary for Overall Form
There are cases, where perfect
form boundary is needed, but at different size than MMC or LMC.
Figure on left shows a slender pin
that will mate with very flexible
socket in a mating connector. Pin
being slender, its difficult to manufacture pins satisfying Rule
#1’s boundary of perfect form at
MMC and LMC.
Moreover, since mating connector has
flared lead in, such near perfect straightness isn’t functionally
necessary.MMC virtual condition of a cylindrical
feature
iiii2222158
Another example shows a flat
washer to be stamped out of a sheet.
Note that thickness has close
tolerance because excessive
variation may cause motor shaft
misalignment.
Here again, for the tolerance and
aspect ratio, Rule #1 would be
unnecessarily restrictive,
nevertheless, envelope is needed to prevent badly warped washers
jamming in an automated assembly
equipment
Virtual Condition Boundary for Overall Form (Contd …)
MMC virtual condition of a width-type feature
iiii2222161
So, Virtual Condition Boundary is…
� Virtual Condition is NOT a Control
� It’s a condition of a feature established by collective efforts of Size,
Geometric Tolerances and Modifiers
Virtual Condition Boundaries can be established for Internal and External
Features of size.
iiii2222164
VCB = Hole Size – Total Tolerance
OR
VCB = MMC Size limit – Geo Tol29.750.350.250.130.1
29.750.40.30.130.15
29.750.50.40.130.25 (LMC)
29.750.250.150.130
29.750.20.10.129.95
29.750.100.129.85 (MMC)
VCBTotal TolBonus TolPosition TolHole Size
VCB of Location for Internal FOS controlled at MMC
iiii2222166
VCB of Location for External FOS controlled at MMC
29.650.30.20.129.35
29.650.350.250.129.3 (LMC)
29.650.250.150.129.4
29.650.150..050.129.5
29.650.100.129.55 (MMC)
VCBTotal TolBonus TolPosition TolPin Size VCB = Pin Size + Total Tolerance
OR
VCB = MMC Size limit + Geo Tol
iiii2222168
VCB of Orientation (controlled at MMC)
Tolerance Zone = nnnn0.3 at MMC
VCB = MMC + GTol
VCB = 12.6 + 0.3 = nnnn12.9
In this case VCB is same as Outer Boundary (worst case)
Tolerance Zone = nnnn0.3 at MMC
VCB = MMC - GTol
VCB = 13.2 - 0.3 = nnnn12.9
In this case VCB is same as Inner Boundary (worst case)
In either case, controlled feature never encroaches respective VCBs. VCBs lie in air space.
iiii2222170
Figure at left shows a part where straightness of
datum feature A is necessary to protect wall thickness.
Here, the straightness tolerance modified to LMC
supplants the boundary of perfect form at LMC.
The tolerance establishes a virtual condition
boundary embedded in a part material beyond which feature surface shall not encroach.
For datum feature (external) A, the diameter of
such virtual boundary equals to LMC size limit minus the straightness tolerance value: n19.7-
n0.3=n19.4
Note the difficulty of verifying conformance where
the virtual condition boundary is embedded in part
material and can’t be simulated with hard gages.
LMC Virtual Condition Example
LMC virtual condition of a cylindrical feature
For OD
iiii2222171
Tolerance Zone = nnnn0.3 at LMC
VCB = LMC - GTol
VCB = 12.3 - 0.3 = nnnn12.0
In this case VCB is same as Inner Boundary (worst case)
Tolerance Zone = nnnn0.3 at LMC
VCB = LMC + GTol
VCB = 13.6 + 0.3 = nnnn13.9
In this case VCB is same as Outer Boundary (worst case)
In either case, controlled feature never encroaches respective VCBs. VCBs are embedded in material.
VCB of Orientation (controlled at LMC)
iiii2222172
Inner & Outer Boundaries
As per Y14.5,
� Inner Boundary is defined as:– A Worst case Boundary (ie locus) generated by the smallest feature (MMC for Internal
Feature and LMC for External feature) minus the stated Geometric Tolerance Value and any additional Geometric Tolerance (if applicable) from the features’ departure from its specified material condition.
� Outer Boundary is defined as:– A Worst case Boundary (ie locus) generated by the largest feature (LMC for Internal
Feature and MMC for External feature) plus the stated Geometric Tolerance Value and any additional Geometric Tolerance (if applicable) from the features’ departure from its specified material condition.
� Worst Case Boundary is defined as:– It is a general term to refer to the extreme boundary of a FOS that is the worst case for
assembly. Depending upon dimensioning method, the WCB can be Inner or Outer or Virtual Condition Boundary.
iiii2222173
Inner & Outer Boundaries Example
OB = nnnn20.15
IB = (20 - 0.14)=19.86
OB = nnnn20.15OB = (nnnn20.15+0.3) = nnnn20.45
iiii2222174
RFS Case : Inner and Outer Boundaries
•When Geometric tolerances are applied on RFS Basis, i.e. there is no modifier such as mmmm or llll in tolerance portion of FCF, the OBs and IBs are calculated as:
OB = nnnn12.6 + 0.3 = nnnn12.9
WCOB = MMC + GTol = nnnn12.9
IB = nnnn13.2 - 0.3 = nnnn12.9
WCIB = MMC - GTol = nnnn12.9
For External FOS:WCOB = MMC + Geometric Tolerance
WCIB = LMC – Geometric ToleranceFor Internal FOS:
WCIB = MMC – Geometric ToleranceWCOB = LMC + Geometric Tolerance
iiii2222175
Summarizing Boundary Calculations …
OB = MMC + GTol + Bonus
IB = VCB = LMC - GTol
External
IB = MMC – GTol – Bonus
OB = VCB = LMC + GTol
Internal
FOS with GD&T at LMC
OB = VCB = MMC + GTol
IB = LMC – GTol - Bonus
External
IB = VCB = MMC – GTol
OB = LMC + GTol + Bonus
Internal
FOS with GD&T at MMC
OB = MMC + GTolExternal
IB = MMC - GTolInternal
FOS with GD&T at RFS
OB = MMCExternal
IB = MMCInternal
FOS with no GD&T
Formula to calculate WCBFOS TypeType of Control
GTol = Geometric Tolerance
iiii2222177
Actual Mating Envelope
The Actual Mating envelope is a surface, or a pair of parallel plane surfaces, of perfect form which
correspond to a part feature of size as follows:
� For External Feature: A similar perfect feature counterpart of smallest size, which can be
circumscribed about the feature so that it just contacts the feature surface(s). For examples a
smallest cylinder of perfect form or two parallel planes of perfect form at minimum separation
that just contacts the surface(s).
� For Internal Feature: A Similar perfect feature counterpart of largest size, which can be
inscribed within the feature so that it just contacts the feature surface(s). For example a largest
cylinder of perfect form or two parallel planes of perfect form at maximum separation that just
contact(s) the surface(s).
� In certain cases, the orientation, or the orientation and location of an actual mating envelope shall be restrained to one or two datums (see next figure)
iiii2222181
Bonus Tolerance
Bonus Tolerance is an additional tolerance for geometric control.
Whenever a geometric tolerance is applied to FOS and it containsan MMC (m) or LMC (l) modifier in the tolerance portion of
FCF, a bonus tolerance is permissible
When MMC modifier is used in tolerance portion of FCF, it means the
stated tolerance is applies when toleranced FOS is at its
maximum material condition. When the actual mating size of
feature departs from MMC (towards LMC), an increase in the
stated tolerance = amount of departure is permitted. Thus this
increase or extra tolerance is called as ‘Bonus Tolerance’
iiii2222182
Bonus Tolerance Examples
• Bonus tolerance is an additional tolerance for a geometric control.
• Bonus tolerance is only permissible when an MMC (or LMC) modifier is shown in the tolerance portion of a feature control frame.
• Bonus tolerance comes from the FOS tolerance
•Bonus tolerance is the amount the actual mating size departs from MMC (or LMC)
0.70.30.43.5 (lmc)
0.60.20.43.6
0.50.10.43.7
0.400.43.8(mmc)
Total Tol
Bonus Tol
Specified Straightness Tol
Plate Thickness
Wide gage (2 plates)
iiii2222183
Bonus Tolerance Examples
m m m m denotes Bonus tolerance is permissible
m m m m denotes Bonus tolerance is permissible
Bonus tolerance comes from Size (FOS) Tolerance. In this
case, Max bonus=0.4
Bonus tolerance comes from Size (FOS) Tolerance. In this
case, Max bonus=0.2
No Bonus applicable. Tolerance applied to non FOS
iiii2222192
Level 3 Control: Virtual Condition Boundary for Orientation
� For two mating features of size, Level 2 control “overall perfect form boundary” can only
assure assemblability in absence of any orientation or location restraint between two features. Ie. Features are “free floating” to each other.
In the example at left, pin fitting into a hole. We
added a large flange for each part. The requirement is the both flanges shall bolt together and make full
contact.
This introduces an orientation restraint between two
mating features. When flange faces are bolter
together tightly, the pin and the hole must be square to their respective flange faces. Though the
pin and the hole might each respect their MMC
boundaries of perfect form; nothing prevents from
boundaries being badly skewed to each other. (see
fig on next page)
iiii2222193
We can address the requirement by
taking the envelope principle one step further to Level 3 Control.
An orientation tolerance applied to a
feature of size, modified to MMC ot
LMC, establishes a virtual boundary
beyond which surface(s) of features shall
not encroach
In addition to Level 2 control of perfect form, this new boundary has perfect orientation in all
applicable degrees of freedom (360deg) relative to any datum features we select.
The shape and size of the virtual condition for orientation are governed by the same rules as for
form at Level 2. Again, a single feature of size can subject to multiple levels of control, thus
multiple virtual condition boundaries.
In figure above, we’ve restrained virtual condition boundary perpendicular to flange face and shows how matability is assured for any part having a pin that can fit inside its n21 MMC virtual
condition boundary and any part having a hole that can contain its n21 MMC virtual condition
boundary.
Level 3 Control: Virtual Condition Boundary for Orientation
VCB=(n21.5-0.5)=n21
VCB=(n20.5+0.5)=n21
nnnn21
iiii2222195
Level 4 Control: Virtual Condition Boundary for Location
For two mating features of size, Level 3’s virtual condition
boundary for orientation can only assure assemblability in
absence of any location restraint between two features, for
example where no other mating features impede optimum
location alignment between or pin and hole.
In the figure left, we moved the pin and hole close to the
edges of flange and added a large boss and bore mating interfaces at the center of the flanges.
When flange faces are tightened together with bots
and the boss and bore are fitted together, the pin
and the hole must each still be very square to their
respective flange faces.
However the parts can no longer slide freely to
optimize the location alignment between the pins
and the hole.
This necessitates the additional restraint that the
pins and holes must be accurately located relative to its respective boss or bore.
iiii2222196
Level 4 Control: Virtual Condition Boundary for Location (contd …)
A Positional tolerance applied to a feature of
size, modified to MMC or LMC, takes the virtual condition one step ahead: Level 4.
In addition to perfect form and perfect
orientation, the new boundary shall have
perfect location in all applicable degrees of
freedom relative to any datum features we select.
The shape and size of virtual boundary for
location is governed by the same rules as for
form at Level 2 and for orientation at Level 3 with one addition.
For spherical feature, the tolerance is preceded by the ‘Sn’ symbol and specifies a virtual
condition boundary that is sphere.
A single feature of size may be subjected to multiple levels of control thus multiple virtual
condition boundaries … one for each form, orientation, location tolerance applied
nnnn20.7 VCB
nnnn35 VCB
50
iiii2222197
In the example above, we identified two datums for each part and added dimensions and
tolerances for our understanding of assembly.
The center boss has MMC size limit of n34.5 and perpendicularity tolerance of n0.5 at MMC.
Since its external feature of size, its virtual condition is
n34.5+n0.5=n35.
The bore has an MMC limit of n35.5 and perpendicularity tolerance of n0.5 at MMC.
Since its internal feature of size, its virtual condition is
n35.5-n0.5=n35
Note that for each perpendicularity tolerance, the datum feature is the flange face
Each virtual condition boundary for orientation is restrained perfectly perpendicular to its
referenced datum, derived from flange face.
Level 4 Control: Virtual Condition Boundary for Location (contd …)
iiii2222198
Next, The pin and hole combination requires MMC virtual condition boundaries with location restraint added. Note that each location tolerance, the primary datum feature is the respective flange face and secondary datum feature is center boss or bore.
Each virtual condition boundary for location is restrained perfectly perpendicular to its referenced primary datum, derived from flange face. Each boundary is additionally restrained perfectly located relative to its referenced secondary datum, derived from boss or bore.
This restraint of both orientation and location on each part is crucial for perfect alignment between boundaries on both parts, thus assemblability.
The pin has MMC size limit of n20.4 and a positional tolerance of n0.3 at MMC. Since its external feature of size, its virtual condition is n20.4+n0.3=n20.7
The hole has an MMC size limit of n21 and a positional tolerance of n0.3 at MMC. Since its internal feature of size, its virtual condition is n21-n0.3=n20.7
Any pin contained within its n20.7 boundary can assemble with any hole containing its n20.7 boundary.
Try this without GD&T!!
Level 4 Control: Virtual Condition Boundary for Location (contd …)
iiii2222211
Derived Elements
Many Geometric Elements can be derived from any feature. A Geometric tolerance RFS applied to
a feature of size controls’ one of the following:
1. Derived median line(from a cylindrical feature)
2. Derived median plane (from a width type of feature)
3. Feature center Point (from a spherical feature)
4. Feature Axis (from a cylindrical feature)
5. Feature center plane (from a width type feature)
A Level2 (straightness or Flatness) tolerance nullifies Rule #1’s boundary of perfect form at MMC. Instead, a separate tolerance controls overall feature form by constraining a derived median
line or derived median plane (according to type of feature)
iiii2222213
Derived Elements (Contd…)
As shown in figure left, in absence of
material condition modifier means that
straightness tolerance applies RFS by
default. This specifies a tolerance zone
bounded by a cylinder having a diameter equal to the tolerance value, within which
the derived median line shall be
contained.
Tolerance zone for straightness control at RFS
iiii2222214
Derived Elements (Contd…)
In above figure, the Straightness tolerance applies RFS by default.This specifies a tolerance
zone bounded by two parallel planes, separated by a distance equal to tolerance value, within which the entire derived median plane shall be contained.
Both size limits are still in force, but neither the spine for the MMC size boundary nor the spine
for LMC size boundary need to be perfectly formed.
As you will note, it’s a difficult deriving a median plane, But where its’ necessary to control overall form within a tolerance that remains constant, regardless of feature size, there is no
simpler options.
Tolerance zone for Straightness control at RFS
iiii2222217
Use MMC for clearance fits…
� Use MMC for any feature of size that assembles with another feature of size on a mating part and foremost concern is that the two mating features clear (not interfere with) each other.
� Use MMC on any datum reference were the datum feature of size itself makes a clearance fit, and the features controlled to it likewise make clearance fits.
� Because clearance fits are so common and permits functional gaging, many designers have wisely adopted MMC as a default (previously Y14.5 made it the default, now its RFS).
� Where a screw thread must be controlled with GD&T or referred asdatum, try to use MMC
iiii2222218
Use LMC for Minimum stock protection
� Use LMC where you must guarantee a minimum ‘shell” of material all over a surface of any
feature of size, for example:
– For a cast, forged or rough machined feature to assure stock for cleanup in a subsequent
cleanup operation.
– For a non mating bore, fluid passes etc to protect minimum wall thickness for strength.
– For a non mating boss around a hole, to protect minimum wall thickness for strength
– For a gaging features of a functional gage to assure the gage won’t clear a non
conforming part
– …..
We don’t often see LMC applied to datum features, but consider an assembly where datum
features of size pilot two mating parts that must be well centered to each other. LMC applied to
both datum features guarantee a minimal offset between the two parts regardless of how the loose the fit. This is a valuable technique for protecting other mating interfaces in the assembly.
LMC is an excellent choice for datum references on functional gages.
iiii2222219
Use RFS for Centering
� RFS is obsessed with a feature’s center to the point of ignorance of features’ actual size. In fact, RFS does not allow dynamic interaction between size and location or between size and orientation of feature.
� However, this apparent limitation of RFS actually makes it an excellent choice for self centering mating interfaces where the mating features always fit together snugly and center on each other regardless of their actual mating size. For example:
– Press fits
– Tapers such as Morse Tapers and countersinks for flat headed screws.
– Elastic parts, or elastic intermediate parts such as “O” rings
– An adjustable interface where an adjusting screw, shim, sleeve etc will be used on assembly to center a mating part.
Certain geometric characteristics, such as run out and concentricity where MMC or LMC are so inappropriate that the rule prohibit material condition modifiers. For these type of tolerances, RFS always applies.
RFS principal now apply by default in absence of any material condition modifier.
RFS is a poor choice for in clearance fit mating interfaces because it does not allow dynamic tolerance interaction. That means smaller tolerance, usable parts are rejected and higher scarp and costs
iiii2222223
Straightness Tolerance for Line (Surface) Elements
When straightness tolerance FCF is specified as shown in figure above, the tolerance controls only line elements of
that feature. The FCF may only appear in a view where the controlled surfaces is represented by a straight line.
Tolerance specifies a tolerance zone plane containing a tolerance zone bounded by two parallel lines separated by
distance equal to tolerance value. As the tolerance zone plane sweeps the entire feature surface, the surface’s
intersection with plane shall anywhere be contained within the tolerance zone (between two lines). Within the plane,
the location and orientation of tolerance zone may adjust continuously to part surface while sweeping.
iiii2222224
Straightness Control Applied to Line (Surface) Element
When straightness control is applied to surface elements,
– The tolerance zone applies to surface element
– The tolerance zone is two parallel lines
– Rule#1 applies
– The Outer/Inner Boundary is not affected
– No tolerance modifiers may be specified
– The straightness tolerance value specified must be less than the size tolerance.
– No Datum reference required in FCF
– The control must be directed to surface elements
– The straightness control must be applied in the view where the controlled elements are shown as a line
iiii2222225
A straightness tolerance control frame placed according to option a or d specified in slide #108 replaces Rule #1’s requirement of perfect form at MMC with a separate
tolerance controlling the overall straightness of the cylindrical feature. Where the tolerance is modified to MMC or LMC, it establishes a Level 2 virtual condition boundary as described earlier.
Unmodified, the tolerance applies RFS and establishes a central tolerance zone as described earlier within which the features’ derived median line shall be contained.
Straightness Tolerance Applied to a Cylindrical FOS
Straightness Applied on MMC Basis
iiii2222226
Straightness Control Applied to a Cylindrical FOS
When straightness control is applied to a FOS, – The tolerance zone applies to the axis or centerplane of
the FOS
– Rule#1 is overridden
– The Virtual condition or Outer/Inner Boundary of the FOS is affected
– The MMC Modifiers may be specified in the tolerance portion of the control
– If tolerance modifiers are specified (MMC), the bonus tolerance applies
– The straightness tolerance value specified may be greater than the size tolerance.
– A fixed gage may be used to inspect straightness.
– No Datum references can be specified in the FCF
– The control must be associated with a FOS dimension
– If applied to cylindrical FOS, a diameter symbol n should be specified in the tolerance portion of FCF
iiii2222227
Flatness Tolerance Applied to a Planer Surface
When a Flatness FCF is placed according to options b or c as
in slide #78, the tolerance applies to single nominal flat
feature. The flatness FCF may be applied only in a view
where the element to be controlled is represented by a
straight line.
This specifies a tolerance zone bounded by two parallel
planes separated by distance equal to the tolerance value,
within which the entire feature surface shall be contained. The
orientation and location of tolerance zone may adjust to the
part surface.
A flatness tolerance cannot control whether the surface is
fundamentally concave, convex or stepped, just the maximum
range between its highest and lowest undulations.
For a width type of feature of size, Rule #1 automatically limits the flatness deviation of each surface.
Thus to have any meaning, a separate flatness tolerance applied to either single surface must be less
than the total size tolerance.
The specified tolerance in the FCF is implied as RFS. MMC/LMC does not apply to flatness control
because only surface area is controlled and area have no size
iiii2222228
� When Flatness control is applied to Planar Surface:
– No Datum references can be specified in the FCF
– The control must be applied to a planar surface
– No tolerance Modifiers can be specified in the FCF
– The tolerance value specified must be less than any other geometric controls that limit the
flatness of the surface.
– The tolerance value specified must be less than the size tolerance.
� Typical Flatness Control Application:
– For a Gasket or a Seal
– To attach a mating part
– For better contact of datum feature with datum plane.
Flatness Control Applied to a Planar Surface
iiii2222230
Circularity Tolerance
A circularity tolerance controls a
features’ circularity (roundness) at individual cross section. So, a circularity
tolerance may be applied to any type of
feature having uniformly circular cross
sections, including sphere, cylinders,
revolute (cones), tubular shapes, rods, torus shapes.
When applied to non-spherical feature,
the tolerance specifies a tolerance zone
plane containing an annular tolerance
zone (ring shaped) bounded by two concentric circles whose radii differ by
an amount equal to tolerance value.
iiii2222231
The tolerance zone plane shall be swept along a simple non-self-intersecting tangent continuous
curve (spine). At each point on the spine, the tolerance zone plane shall be perpendicular to the spine and tolerance zone centered on the spine.
As the tolerance zone sweeps the entire feature surface, the surfaces’ intersection with the plane
shall anywhere be contained within an annular tolerance zone (ie. Between two circles). While
sweeping, the tolerance zone may continually adjust in overall size, but shall maintain the
specified radial width.
This effectively removes diametrical taper from circularity control. Additionally, the spines
orientation and curvature may be adjusted within aforesaid constraints. So, in addition this
effectively removes straightness from circularity control
A circularity tolerance greater than the total size tolerance has no effect. It is preferred that circularity tolerance be less than half the size tolerance to limit multi-lobbed deviations (egg
shaped or tri-lobed).
Circularity Tolerance (contd…)
iiii2222232
Circularity Application
When Circularity is applied to circular elements:
– The diameter must be within its size tolerance
– The circularity control does not override Rule #1
– The circularity tolerance must be less than size tolerance
– The circularity control does not affect the Boundaries of the FOS
– No Datum references can be specified in the FCF
– No Tolerance modifiers can be specified in the FCF
– The control must be applied to diametrical feature
iiii2222233
Cylindricity Tolerance
A Cylindricity tolerance is a composite control of
form that includes circularity, straightness, and taper of a cylindrical feature.
A cylindricity tolerance specifies a tolerance
zone bounded by two concentric cylinders
whose radii differ by an amount equal to the
tolerance value. The entire feature surfaces shall be contained within the tolerance zone
(between two cylinders). The tolerance zone
cylinders may adjust to any diameter, provided
their radial separation remains equal to the
tolerance value . This effectively removes feature size from cylindricity control.
As with the circularity tolerance, a cylindricity tolerance must be less than half the size tolerance
to limit multi-lobbed from deviations
Since neither circularity nor a cylindricity tolerance can nullify size limits for a feature, there is
nothing to be gained by modifying either tolerances to MMC or LMC
iiii2222234
Cylindricity Tolerance over a Limited Length or Area
Some designs require form control over a limited length or area of the surface, rather
than the entire surface.
In such cases, as shown above, draw a thick chain line adjacent to the surface,
dimensioned for length and location as necessary. Form tolerance applies only within
the limits as indicated by chain line.
iiii2222235
Cylindricity Application
When Cylindricity is applied to cylindrical surfaces:
– The diameter must be within its size tolerance
– The cylindricity control does not override Rule #1
– The Cylindricity tolerance must be less than size tolerance
– The Cylindricity control does not affect the OB of the FOS
– No Datum references can be specified in the FCF
– No Tolerance modifiers can be specified in the FCF
– The control must be applied to cylindrical feature
iiii2222238
Radius Tolerance
A radius is a portion of a cylindrical
surface encompassing less than 180o
arc length. A radius tolerance denoted
by R, establishes a zone bounded by a
minimum radius arc and maximum
radius arc, within which the entire
surface feature shall be contained. By default, each arc shall be tangent to the
adjacent part surfaces.
iiii2222240
Controlled Radius Tolerance
Where a symbol CR is applied to a radius, the
tolerance zone will be as described in previous slide #176. But there are additional
requirements for the surface. The surface
contour shall be fair curve without any
reversals.
This means a tangent continuous curve that is everywhere convex or concave.
iiii2222241
When Do We use a Form Tolerance?
As a general rule, apply a form (only) tolerance to a non datum feature only where
there is some risk that the surface will be manufactured with form deviations severe enough to cause problems in subsequent manufacturing operations, inspection, assembly or function of the part.
For example,
� A flatness tolerance might be appropriate for a surface that seals with a gasket.
� A roller bearing might be controlled with a cylindricity tolerance
� A conical bearing race might have both a straightness of surface element tolerance and a circularity tolerance
iiii2222244
Summarizing Form Tolerances
No
No
May*
No
Overrides Rule#1?
NoNoNoNoYesggggNoNoNoNoYeseeeeNoMay*May*YesYes
NoNoNoNoYescccc
FOS?Surface?
Datums referencing?
Are boundaries affected?
Use of mmmmor llll?
Correct to apply to ...Geometric Control
* When applied to FOS
iiii2222248
What is Datum?
A Datum is a theoretically exact point, axis or plane derived
from the true geometric counterpart of a specified datum feature.
A datum is an origin from which the location or geometric
characteristics of features of a part are established.
A datum feature is an actual feature of a part that is used to establish a datum.
A datum reference is an alphabetic letter specified in a
compartment following a Geometric tolerance in a
feature control frame. It specifies a datum to which the
tolerance zone or acceptance boundary is basically related.
A feature control frame may have zero, one,two or three
datum references.
iiii2222249
“Datum feature” begets “True
geometric counterpart” which begets a “datum” which is building block for “Datum Reference Frame”, which is the
basis of establishing tolerance zone for other features.
We shall refer to this figure often
Establishing Datum
Reference Frames from
Part Features
iiii2222250
Datum Feature
Recall our session #1, where we said:
The first step in GD&T is to “identify part surfaces to serve as origins and provide
specific rules explaining how these surfaces establish the starting point and direction for measurements”
Such a part surface is called as “datum feature”
Builders understood the need for a consistent and uniform origin from which to base their measurements. It was a patch of leveled ground once. For precision manufacturing, it’s a flat surface or a straight and round diameter on a machine
part. Although any type of part feature can be a datum feature, selecting one is bit like hiring a CEO who will provide strong moral center and direction for the entire organization.
So, what qualifications of CEO should we look for…?
iiii2222251
Datum Feature Selection
� The most important quality you want in CEO (datum
feature) is leadership. A good datum feature is a surface that most strongly influences the origin
and/or location of parts in its assembly. We shall call
it a functional datum feature.
� Rather than a being a slender and small, a good
datum feature such as shown below, should have “broad shoulders” able to take on the weight of the
part and provide overall stability. Avoid shaky and
unfinished surfaces with high and low spots.
� Just as you want your CEO highly visible, choose a datum feature that is always accessible for fixturing
manufacturing, or at various stages of inspection
during stages of manufacturing
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Functional Hierarchy
�Its tough to judge leadership from void
�Spot it intuitively when you see how a prospect (parts and features) relates to each other
�In the assembly figure left for a car engine, consisting of three parts : Engine block, Cylinder Head and Rocker Arm cover, we intuitively rank the dependencies as:
Engine block makes a foundation, to
which we bolt on the cylinder head to
which in turn we bolt rocker arm
cover.
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Identifying Datum Features
Once the CEO (datum feature) has sworn in, he needs to
put a ‘badge’ to denote its’ authority. So, instead of a star, we use the ‘datum feature’ symbol as shown
below.
The symbol consists of a capital letter enclosed in a square
compartment, a leader line extending from the frame to datum feature and a terminating triangle. The triangle may
be solid filled, making it easier to spot on a drawing.
Each datum feature shall be identified with a different latter of alphabet (except I, O, Q). When alphabets are exhausted,
double letters (AA through AZ, BA through BZ etc) are used
and compartment is stretched to fit.
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Datum Feature Symbol Application
A Datum feature symbol is
applied to concerned feature surface outline, extension line,
dimension line, or feature control
frame (FCF) as follows:
(a) Placed on the outline of a
feature surface, or on an extension line of feature outline, clearly
separated from dimension line,
when the datum feature is surface
itself.
iiii2222260
Datum Feature Symbol Application (contd…)
(b) Placed on an extension of a dimension line of a feature of size when datum is an axis or
center plane. If there is insufficient space for two arrows, one of the arrow may be replaced with datum feature triangle
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Datum Feature Symbol Application (contd…)
( c ) Placed on the outline of a cylindrical feature surface, or the extension of the the feature
outline, separated from the size dimension, when the datum is the axis. The triangle may be drawing tangent to the feature
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Datum Feature Symbol Application (contd…)
(d) Placed on a dimension leader line
to the feature size dimension, where no geometric tolerance and feature
control frames are used.
(e) Placed above or below and attached to
the feature control frame when the feature (or a group of features controlled is the
datum axis or datum center plane
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Summarizing Datum Feature Symbol Application ( for FOS datum features)
(a) Datum is axis (b) Datum is axis (c) Datum is common axis
(d) Datum is center plane
(e) Datum is centerplane
iiii2222273
� Usually, it takes two or three
datums to build this complete DRF.
� Since each type if datum has
different abilities, it is not vary
obvious which one can be
combined, nor it is obvious how to build DRF needed for a
particular application.
Datum Reference Frame (DRF) (contd…)
Datum Reference Frame as Per ASME Y14.5
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DRF Development Example 1
With reference to this drawing, answer following
questions …
• How many datum features are there for this part?• What are types of datum features and Datums?
• What are tolerance zone shapes and sizes for various
FCFs?
• How are tolerance zones orientated and/or located to
DRF?• Are the tolerance zones fixed or flexible ? If flexible , how
much is maximum permissible bonus tolerance ?
• Write down your observation on selection of datum
features
• Does the DRF imply any sequence of mfg. operation?• How many DOF each datum feature removes from part?
How many DOF available at the end?
)
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DRF Development Example 2
With reference to this drawing, answer
following questions …
• How many datum features are there for this
part?
• What are types of datum features and
Datums?• What are tolerance zone shapes and sizes
for various FCFs?
• How are tolerance zones orientated and/or
located to DRF?
• Are the tolerance zones fixed or flexible ? If flexible , how much is maximum permissible
bonus tolerance ?
• Write down your observation on selection of
datum features
• Does the DRF imply any sequence of mfg. operation?
• How many DOF each datum feature
removes from part? How many DOF available
at the end?
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DRF Development Example 3
With reference to this drawing, answer
following questions …
• How many datum features are there for this
part?
• What are types of datum features and Datums?
• What are tolerance zone shapes and sizes for various FCFs?
• How are tolerance zones orientated and/or
located to DRF?
• Are the tolerance zones fixed or flexible ? If
flexible , how much is maximum permissible bonus tolerance ?
• Write down your observation on selection of
datum features
• Does the DRF imply any sequence of mfg.
operation?• How many DOF each datum feature removes
from part? How many DOF available at the end?
iiii2222300
Comparison of Datum Precedence – Case B
Case b
• To simulate datum feature A, an adjustable gage/fixture is required.
•Once datum feature A is simulated, it decides orientation of part.
•The axis of two small holes shall be parallel to datum A, and perpendicular to datum feature simulator for B
•Note that small holes’ axis is not perpendicular to datum feature B
•No relative movement allowed between datum feature A and its simulator.
Ref Slide 268
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Comparison of Datum Precedence – Case C
Case c
•Once datum feature B is simulated, it decides orientation of part.
•The axis of two small holes shall be perpendicular to datum feature B
•To simulate datum feature A, an adjustable gage/fixture is required.
•No relative movement allowed between datum feature A and its simulator.
Ref Slide 268
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Comparison of Datum Precedence – Case D
Case d
•The axis of two small holes shall be perpendicular to datum feature B
•To simulate datum feature A, a fixed gage/fixture of dia 16.0 is required.
•relative movement allowed between datum feature A and its simulator. Such relative movement could cause the two small holes to shift more wrt to datum axis A Ref Slide 268
iiii2222304
TGC Types
As we have already seen, each type of
datum feature has corresponding TGC. Each TGC has either no size,
adjustable size or fixed size depending
upon type of datum feature and
referenced material condition.
Also, TGC is either restrained or unrestrained depending on datum
precedence
iiii2222310
Adjustable Size TGC : Primary Datum (axis) at RFS
Adjustable Chuck to Simulate datum
feature A
Datum Axis A. Same as axis of
chuck
Stepped Shaft Example
iiii2222311
Adjustable Size TGC : Primary Datum (axis) at RFS
Expandable mandrel used to simulate datum feature B
iiii2222312
Adjustable Size TGC : Primary Datum (centerplane) at RFS
Adjustable Vice to Simulate datum feature
C
iiii2222313
Adjustable Size TGC : Primary Datum (centerplane) at RFS
Expandable plates to Simulate datum feature
D
iiii2222315
Adjustable Size TGC : Secondary Datum (Axis) at RFS + Tertiary
Datum (Centerplane) at RFS Example
Surface plate to Simulate datum feature E
Expandable mandrel to simulate datum feature F
Datum axis F
Datum centerplane G
Expandable width to simulate datum feature G
iiii2222318
Fixed Size TGC
For features of size and
bounded features referenced as datums at MMC or LMC, the TGCs include MMC and LMC boundaries of perfect form,
MMC and LMC virtual boundaries, and MMC and LMC profile boundaries.
Each of these TGCs have fixed size and/or fixed shape.
iiii2222325
Fixed Size TGC (contd…)
Dia 89.61(=VCB size of H) fixed size opening in gage/fixture to simulate Hmmmm
iiii2222339
Effect of Datum Shift on hole location ..
• Datum shift can result in an additional tolerance for a geometric control
• Datum shift is only permissible when a modifier is shown in datum compartment of a feature control frame
• Datum shift results when the AME of the datum feature departs from given material condition (in this case MMC
• The maximum allowable datum shift is the difference between the gage size (for the datum feature) and LMC size of the datum feature.
iiii2222340
DRF Displacement Example 2
When a special-case FOS datum is referenced at MMC, datum shift may be possible when the datum feature is at MMC
Datum Shift = Fixed gage size – AME of Datum feature
iiii2222345
DRF Displacement Example 6 : Datum Axis MMC
Secondary, Datum Centerplane MMC Tertiary
A gage pin of dia = VCB of datum feature F = MMC-GTol = (58.73 - 0.25) - 0.2 = 58.28
A gage block of width = VCB of datum feature G = MMC-GTol = (18.76 - 0.25) -0.2 = 18.31
Both the simulators will be perpendicular to datum E. Center plane of G will align with datum axis F
iiii2222346
DRF Displacement Example 7 : Datum Axis from a
Pattern of Holes, MMC Secondary.
B
4 Pins of dia = VCB of one small hole = 10.5 – 0.2 = 10.3
1 Pin of dia = VCB of center hole = 18.3 – 0.15 = 18.15
A
iiii2222384
Orientation Tolerance (Level3 Control)
Orientation is feature’s angular relationship to a DRF. An Orientation tolerance
controls this relationship without meddling in location control.
Thus, an orientation tolerance is useful for relating one datum feature to another and for refining the orientation of a feature already controlled with a positional tolerance.
iiii2222385
How to apply Orientation Tolerance?
An orientation tolerance is specified using a feature control frame one of the three orientation characteristic symbols.
The symbol used depends on the basic orientation angle as follows:
0o or 180o– “parallelism” symbol
90o or 270o– “Perpendicularity” Symbol
Any other angle – “Angularity” Symbol
All three symbols work exactly same. The only difference is that where angularity symbol is used, basic angle should be explicitly specified. Where the parallelism or perpendicularity is used, the basic angle is implied by the drawing view that shows parallel or perpendicular relationship.
The feature control frame includes the orientation tolerance value followed by one or two datum references.
iiii2222386
Datums for Orientation Control
Orientation control requires a DRF. A primary datum plane or axis always establishes
rotation about two axes of the DRF and usually the only reference needed for orientation control.
However in some cases, rotation it may be necessary to restrain rotation about third
axis and in such case, secondary datum is needed to orient/locate tolerance zone plane for controlling elements of feature
iiii2222388
Angularity Tolerance applied to a Width-Type FOS
When an orientation tolerance FCF is placed as
per options (a) or (d) in previous table (associated
with a diameter or width dimension), the tolerance
controls the orientation of the cylindrical or width
type of feature.
Where tolerance is modified to LMC/MMC, it
establishes a level3 virtual condition boundary as
described earlier. Alternatively the “center method”
discussed earlier may be applied to an orientation
tolerance at MMC/LMC.
Unmodified, tolerance zone applies RFS and
establishes a central tolerance zone as described
earlier within which the features axis or center
plane shall be contained
When applied to feature of size, orientation
tolerance provides no additional form control
beyond level2
In the figure at left, the center plane of the slot is
held within the central parallel plane tolerance zone
iiii2222389
Angularity Tolerance applied to a Cylindrical FOS
Y14.5 also allows orientation of axis to be
controlled within a parallel plane tolerance zone,
however this would not prevent axis from
revolving like a compass needle between two
parallel planes, such application usually
accompanies a larger positional tolerance.
In the figure left, a “diameter” symbol precedes
the orientation tolerance value. Here the tolerance
zone is bounded by a cylinder having dia. equal to
tolerance value. This is more like a positional
tolerance except the orientation zone is not
basically located from the datums.
A positional tolerance also controls orientation for
a feature of size to the same degree as an equal
orientation tolerance. Thus for a feature of size, an
orientation tolerance equal to or greater than its
positional tolerance is meaningless.
Conversely, when engineer needs to maximize
positional tolerance while protecting
orientation, a generous positional tolerance can
be teamed up with more restrictive orientation
tolerance.
iiii2222458
Concentricity Tolerance
Concentricity is that condition where median points
of all diametrically opposed elements of figure of revolution (or correspondingly located
elements of two or more radially disposed
features) are congruent with the axis (or center
point) of a datum feature.
Concentricity tolerance is a cylindrical (or spherical)
tolerance zone whose axis (or center point) coincides with the axis (or center point) of
datum feature(s)
The median points of all correspondingly located
feature(s) being controlled, regardless of
feature size, must lie within the cylindrical (pr spherical) tolerance zone. The specified
tolerance and datum references can apply on
RFS basis only.
Concentricity tolerance requires the establishment
and verification of features’ median points
Irregularities in the form of a actual feature to be inspected may make it
difficult to establish the location of that features’ median point. For
example a nominally cylindrical surface of revolution may be bowed or out
of round in addition to being displaced from its datum axis, in such cases
finding median point may be very time consuming. Therefore unless there
is definite need to establish median points, it is recommended to use
position or runout tolerance.
iiii2222459
Difference between Coaxiality and Concentricity Controls
Both parts are acceptable from coaxiality
control inspection.
iiii2222460
Difference between Coaxiality and Concentricity Controls
This is the one part configuration acceptable
under concentricity control.
While parts as shown in previous slide may
get rejected when inspected from
concentricity viewpoint, if their median points
do not lie in 0.4 central tolerance zone
cylinder. Note that there are no material modifiers specified for tolerance value as
well as for datum feature reference.
iiii2222462
Symmetry Tolerance
Symmetry control is same as Concentricity control. The difference is that while concentricity is used on surface of revolution, symmetry is used on planar feature of Size
iiii2222465
Runout Tolerance
� Runout is the oldest and simplest concepts used in GD&T
� Runout is a composite form, location and orientation control of
permissible error in the desired part surface during a complete revolution
of part around datum axis
iiii2222466
Runout Tolerance – Why we use it?
In precision assemblies runout causes
misalignment and/or alignment problems.
As shown in figure at left, runout of ring groove
diameters relative to pistons’ diameter may
cause rings to squeeze unevenly around the
piston or force the piston off center in its bore.
A motor shaft that runs out relative to its bearing
journals will cause motor to run out of balance
shortening its working life.
A designer can control such wobble by
specifying runout control.
There are two levels of runout :
Circular Runout
Total Runout
iiii2222469
Datums for Runout Control
�A runout tolerance controls surface elements of a
round feature relative to a datum axis. Every runout tolerance shall reference a datum axis.
�In the figure above, since designer wish to control
the runout of surface as directly as possible, its
important to select the functional feature to establish
a datum axis.
�During inspection for the part shown above, the
datum feature might be placed on V block or fixtured
in a precision spindle so that the part can be rotated
about the axis of datum features’ TGC.
�This requires datum feature be long enough and its
form be well controlled (by own size limits or separate
form tolerance (level2 control)). In addition datum
feature should be accessible for fixturing and probing.
iiii2222472
Circular Runout Tolerance
�Circular runout tolerance can also be applied
to a face or a face groove that is perpendicular to datum axis.Here, the surface
elements are circles of various diameters,
each concentric to the datum axis and each
evaluated separately from the others.
iiii2222473
Total Runout Tolerance
Total runout is greater level of control. Its tolerance applies to the FIM while the indicator sweeps over the entire controlled surface. Rather than each circular element being evaluated separately, the total runout FIM encompasses the highest and lowest of allreadings obtained at all circles
For a nominal cylindrical feature, the indicators body shall be swept parallel to the datum axis, covering the entire length of controlled feature, as the part is rotated 360o about the datum axis. Any taper or hourglass shape in the controlled feature will increase FIM
For a nominally flat surface perpendicular to datum axis, the indicators body shall be swept in a line perpendicular to the datum axis, covering entire breadth of controlled feature, Any conicity, wobble in the controlled feature will increase FIM. The control
imposed by this type of total runout control is identical to
that of an equal perpendicularity tolerance with a RFS
datum reference.
iiii2222474
� Runout tolerance is especially suited for parts that revolve about a datum axis in an assembly,
and where alignments and dynamic balances are critical.
� Circular runout tolerance is often ideal for O ring grooves, where cylinder bore is datum.
Remember that the datum feature and controlled feature should be accessible for
fixturing/inspection as the case is. For example, circular runout tolerance applied to internal
groove with internal bore as datum feature makes groove inaccessible for inspection!
� Following equations pertain to the controls imposed by circularity, cylindricity, concentricity,
circular runout and total runout when applied to a revolute or cylindrical feature.
Circularity + Concentricity = Circular Runout
Cylindricity + Concentricity = Total Runout
When do we use a Runout Tolerance?
iiii2222492
Profile Control
What is Profile?
– A profile is outline of an object in a given plane (2D figure)
– Profiles are formed by projecting a 3D figure onto a plane or by taking cross sections
through the figure.
– Such profile can contains straight lines, arcs, curves.
– If the drawing specifies individual tolerances for elements or points of a profile, these
elements or points need individual verification
iiii2222493
Profile Tolerancing
� The profile tolerance specifies a uniform boundary along
the true profile within which the elements of surface must lie.
� It is used to control form or combination of size, form,
orientation or location. Where used as refinement of size,
the profile tolerance must be contained within the size
limits.
� Depending upon design requirements, the tolerance may be divided bilaterally to both sides of true profile or
applied unilaterally to both sides of profile.
� When an equally disposed bilateral tolerance is needed,
its necessary to show only FCF with leader directed to
surface.
� For an unequally disposed or unilateral tolerance,
phantom lines are drawn parallel to true profile to indicate
tolerance zone boundary
� Phantom line should extend only a sufficient distance to
make its application clear.
iiii2222494
Profile Tolerancing
Where a profile tolerance applies all
around the profile of a part, the symbol used to designate “all around” is placed on
the leader from the FCF.
iiii2222495
Profile Tolerancing
Where segments of profile have different
tolerances, the extent of each profile tolerance may be indicated by the use of
reference letters to identify the extreme
positions or limits of each requirement.
If some segments of profile are controlled by
a profile tolerance and other segments by individually toleranced dimensions, the
extend of profile tolerance must be indicated.
iiii2222503
Combining Profile Tolerance with other Controls
In this case, a part with profile of line
tolerance where size is controlled by a separate tolerance. Line elements of
the surface along the profile must lie
within the profile tolerance zone and
within a size limiting zone.
iiii2222505
Profile tolerance for Coplanar Surfaces
Coplanarity is the condition of two or more
surfaces having all elements in one
plane.
A profile of a surface tolerance may be used
where it is necessary to treat two or more
surfaces as a single interrupted or noncontinuous surface. In this case, the
control provided is similar to that achieved
by flatness tolerance applied to a single
planar surface.
As shown in figure at left, the profile of a
surface tolerance establishes a tolerance
zone defined by two parallel planes within
which considered surfaces must lie. No
datums are specified as in case of flatness as the considered surfaces themselves
establishes a plane
iiii2222506
Profile tolerance for Coplanar Surfaces
Where two or more surfaces are involved, it may be
desirable to identify specific surface(s) to be used as datum feature(s). Datum feature symbol is applied to
these surfaces with appropriate tolerance for their
relationship with each other.
Datum reference letters are added to the FCF for the
features being controlled. The tolerance zone thus established applies to all coplanar surfaces including
datum surfaces
iiii2222507
Profile tolerance for Plane Surfaces
Profile tolerance may be used to control form and
orientation of plane surfaces. In this case, profile of surface is used to control a plane surface inclined to a
datum feature.
iiii2222521
Suggested Readings & References …
� ASME Y14.5M-1994 Geometric Dimensioning and Tolerancing
� ASME Y14.5.1M-1994 Mathematical Definition of Dimensioning and Tolerancing Principals
� Geometrics IIIm - Lowell W. Foster
� Geometric Dimensioning and Tolerancing: Applications and Techniques for Use in Design, Manufacturing, and
Inspection - James D. Meadows
� Tolerance Design: A Handbook for Developing Optimal Specifications – Clyde M. Creveling –
� CAD/CAM Theory and Practice : Ibrahim Zeid
� Interpretation of Geometric Dimensioning and Tolerancing : Daniel Puncochar. Dimensioning & Tolerancing
Handbook : Paul Drake Jr.
� Fundamentals of GD&T : Alex Krulikowski
Credit is given and acknowledgement is made for certain references and
definitions derived from the following: