basic gd&t course

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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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About iSquare …

iSquare

(InterOperability & InterChangeability Solutions)

Pune, 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.

[email protected]

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Relationships …

• InterChangeability:

• With Dimensional Control Systems Inc., USA having more than 15

years of experience in Dimensional Control Techniques, Solutions

and Services.

[email protected]

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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


24hrs(3 days)

Introduction to Dimensioning and Tolerancing Principles for Gages and Fixtures Based on ASME Y14.43:2003

6


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


24hrs(3 days)

Tolerance Stack-up Analysis using Co-ordinate System of Dimensioning and GD&T : A practical Approach to Solve

Assembly Build Problems3


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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That’s about iSquare

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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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GD&T

Geometric Dimensioning and Tolerancing

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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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Expressing Size Limits

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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

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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

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Exercise 1

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Part Features

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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

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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.

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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)

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Exercise 2

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GD&T Symbols

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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… !!

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Form and Proportions of GD&T Symbols

h = size of letter

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Feature Control Frames (FCF)

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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

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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

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Modifying / Modifier Symbols

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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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Run a leader from the frame to the feature.

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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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Attach either side or either end of the frame to an extension of the dimension line pertaining to a

feature of size.

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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?

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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

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Four Fundamental Levels of Control for FOS

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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

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Level 1 : ‘Size’ Control

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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

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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

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Level 2 : ‘Form’ Control

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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.

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�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

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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’

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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

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Rule #1 Example (External FOS)

Every Cross-sectional measurement must be

within limits of Size

Part shall be always contained within MMC

Envelope

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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

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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.

iiii2222163

VCB of Location for Internal FOS controlled at MMC

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

iiii2222165

VCB of Location for External 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

iiii2222176

Actual Mating Envelope/SizeBonus Tolerance

Actual Minimum Material Envelope/Size

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

iiii2222191

Level 3 : ‘Orientation’ Control

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

iiii2222194

Level 4 : ‘Position’ Control

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.


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!!


iiii2222210

Derived Elements

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

iiii2222215

When to Use MMC / LMC / 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

iiii2222220

Exercise 3

iiii2222221

Form Tolerances

StraightnessFlatness

CircularityCylindricity

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:


– 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 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 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

iiii2222246

Exercise 4

iiii2222247

Datums

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

iiii2222252

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.

iiii2222256

How to Identify Datum Features and Apply Symbols?

iiii2222257

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.

iiii2222259

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

iiii2222261


( 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

iiii2222262


(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

iiii2222263

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

iiii2222264

Introduction to True Geometric Counterpart (TGC)

iiii2222268

Datum Features and their TGCs

Go Slide 300

Go Slide 301

Go Slide 302

iiii2222270

Datum Reference Frame (DRF)

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

iiii2222274

Datum Reference Frame (DRF) (contd…)

iiii2222279

Degree of Freedom (DOF)

iiii2222294

DRF Development Examples

iiii2222295

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?

)

iiii2222296


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?

iiii2222297


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?

iiii2222299

Comparison of Datum Precedence

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

iiii2222301

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

iiii2222302

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

iiii2222303

TGC Types

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

iiii2222317

Adjustable Size TGC : Datum Axis from Co-Axial diameters RFS

Primary Example

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.

iiii2222324

Fixed Size TGC (contd…)

Dia 89.31 fixed size opening in gage/fixture to simulate Hmmmm

iiii2222325

Fixed Size TGC (contd…)

Dia 89.61(=VCB size of H) fixed size opening in gage/fixture to simulate Hmmmm

iiii2222338

DRF Displacement Example 1

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

iiii2222383

Orientation Tolerance

Perpendicularity

Angularity

Parallelism

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.

iiii2222396

Parallelism with Tangent Plane Modifier

iiii2222457

Concentricity

Symmetry

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

iiii2222464

Runout Tolerance

Circular Runout

Total Runout

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?

iiii2222491

Profile 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.

iiii2222519

GD&T Reference Chart

iiii2222520

Dimensioning Habits (?)

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:

basic gd&t course

Documents

customized

tolerance

encroaches

central tolerance

annular tolerance

tolerance

downstream

dimensional