Training Material

GD&T, Version:1, Nov 2003World Class Manufacturing Solutions (WCMS)

Geometric Dimensioning and Tolerancing (GD&T)

Training Kit

2GD&T, Version:1, Nov 2003World Class Manufacturing Solutions (WCMS)

Introduction to GD&T

Concept of Function and Relationship

ASME Y14.5 Rules

GD&T Symbols

Form Control

Flatness, Straightness, Roundness, Cylindricity

Orientation Control

Perpendicularity, Angularity, Parallelism

Day – 1 Agenda


Composite Controls

Circular Runout and Total runout

Position Controls

Position, Symmetry and Concentricity

Profile Controls

Profile of Line and Profile of Surface

Day – 2 Agenda


Table of Contents

144 - 151Profile Controls – Profile of Line and Profile of Surface

133 - 143Composite Controls – Circular Runout and Total Runout

90 - 132Location Controls – Position, Symmetry and Concentricity

69 - 89Orientation Controls – Perpendicularity, Angularity and Parallelism

43- 68Form Controls – Flatness, Straightness, Roundness and Cylindricity

16 - 42GD&T Fundamentals

5-15Introduction to GD&T

4Table of Contents

2-3Agenda

PageChapter Description


1. Introduction to GD&T


The following are the guidelines followed in developing this material

a) Principles of United states standard ASME Y14.5M- 1994 is followedb) All the drawings are in third angle projectionc) Most of the units are in “inches”



• A method to specify the “Shape” of a piece of hardware on an engineering drawing

• Helps in standardizing • Helps as a common technical drawing language

for the designer, Tool manufacturer, Gage manufacturer, Process engineer

• Based on engineering and manufacturing principles



• Let us better understand what GD&T does to a part by studying the drawing given in the next slide

• The drawing given in the next slide in the “co-ordinate system”




• The following questions are left unanswered in the drawing given – What does the “size tolerance” mean. Does it mean

that the individual feature can depart in the shape also by the same extent as the size

– In the feature, 0.820, can a “bow” or bend is allowed. If not, how is this represented in the drawing

– In such a case, a micrometer used for measurement would accept the part



– With regard to the diameters .980, .315, 1.375, and 2.75 diameters, are they expected to be in the same axis. If there isdeviation allowed, by how much

– Do the overall length of the part adequately depict the requirement

– Does the 1.750 face need to be flat– What is the basis for the 45 deg angle tolerance and the 2.125

dia tolerancing. Is it based on scientific calculation or based on “atmospheric analysis”

• These questions are not answered in the Co-ordinate system of the drawing



• GD&T are based on “FUNCTION” and “RELATIONSHIP” as the fundamental principles

• FUNCTION and RELATIONSHIP are the key words in GD&T

• Its use saves money by– Ensuring less rejections– Ensuring integrity of design requirements– Ensuring interchangeability– Providing uniformity of interpretation– Adapts and facilitate CAD, CAM applications



• Let us now, analyze these two principles using the Flange mount drawing given on the next slide

• Next slide gives the assembly drawing of the flange mounting

• Relationship of key features between the assembled parts and also individual parts are clearly shown in the assembly drawing

• GD&T ensures that these functions and relationships are not lost and are translated in the drawing and in manufacturing




2. GD&T Fundamentals


GD&T fundamentals

For effective implementation of geometrics following are the major fundamentals to be understood1) Geometric characteristics & their symbols 2) Other related symbols3) Feature control frame & datum feature symbol4) General rules5) Maximum & least material condition, Regardless of feature size6) Distinction between form, orientation, profile, run-out & location type tolerances7) Tolerance zones8) Virtual condition


1. Characteristics and their Symbols

• Geometric tolerances are divided into five categories– Form control– Orientation control– Location control– Composite Control– Profile controls


1. Characteristics and Symbols

StraightnessFlatness Roundness Cylindricity

Perpendicularity( Squareness) Angularity Parallelism

Position Symmetry Concentricity

Form Controls

Orientation Controls

Location Controls


1. Characteristics and SymbolsComposite Controls

Profile Controls


2. Other related symbols and terms


3. Feature Control frame and Datum feature frame

Ex.

Geometric char.Geometric tol.Tolerance zone shapeDatum referenceModifier

0.006 M A B0.002

It comprises of a pictorial note which includes a) Kind of controlb) Geometric tolerancec) Any modifiers ( i.e. M or L ) d) Datum references & any datum reference modifiers ( i.e. M or L )


--In feature frame control, there can be more than one Datum reference letters. Reading from left to right , these reference letters indicate an order of precedence of the datum feature so identified.Ex.

0.006 M A B C

Primary datum

Secondary datum

Tertiary datum

--When two datum letters are separated by a dash it indicates a common data& is established by two datum features. There fore, there is noprecedence between the two but together they create a common datum.

Ex.

Primary datum

Secondary datum

Tertiary datum

0.002 A-B

Here A-B indicate common datum


3. Feature control frame and Datum feature frame


3. Feature control frame and Datum feature frame


4. Standard Rules

ASME Y14.5 rules

Rule#1 - Limits of size ruleWhere only a tolerance of size is specified, the limits of size of the individual feature describe the extent to which variation inthe geometric forms as well as size are allowed

The actual local size of an individual feature at any cross section shall be within the specified tolerance of size


4. Standard Rules


4. Standard Rules

ASME Y14.5 rules

The control of geometric form based on size is not applicable to the following:

a) Stock such as bars, sheets, tubing's, structural shapes

The forms of these shall be as per the industry standard norms


4. Standard Rules

ASME Y14.5 rules

Rule#2 a) - Material condition RuleFor all applicable geometric tolerances, RFS applies with respect to the individual tolerance, datum reference or both, where no modifying symbol is specified.

Modifiers for “Maximum material condition” and “Least material condition” must be specified on the drawing where it isrequired

0.006 M A B C


4. Standard Rules – Rule #2

• Characteristics and Controls which can be applicable to “Size” features and thus to which RFS applies under Rule # 2 unless modified to MMC or LMC are:

• Straightness

•Perpendicularity

•Angularity

•Parallelism

•Position

•Characteristics and controls which are always applicable at RFS under Rule # 2 and due to the nature of the requirement cannot be applied at MMC or LMC are:

•Circular Runout

•Total Runout

•Concentricity

•Symmetry

•Flatness

•Roundness

•Cylindricity

•Profile of line

•Profile of Surface


4. Standard Rules

Rule #2 b) – Pitch Diameter RuleEach tolerance of orientation or position and datum reference specified for a screw thread applies to the axis of the thread derived from the pitch cylinderWhere an exception to this is necessary, it has to be mentioned below as MAJOR or MINOR

Each tolerance of orientation or location and datum reference specified for gears, splines must designate the specific feature of the gear to which it applies (PITCH, MAJOR DIA, MINOR DIA)


4. Standard Rules

Rule #2 c) – Datum/Virtual Condition Rule

A virtual condition exists for a datum feature of size where its axis or center plane is controlled by a geometric tolerance. In such cases, the datum feature applies at its virtual condition even though it is referenced in a feature control frame as MMC or LMC


5. MMC, LMC and RFS


5. MMC, LMC and RFS


5. MMC, LMC and RFS


6. Form, Orientation, Location

a) Surface w.r.t Surfaceb) Axis w.r.t Surface

(RFS)c) Axis w.r.t Surface

(MMC)d) Axis w.r.t Axis

a) Surface

a) Surface

a) Straightness of surfaceb) Straightness of axis

(RFS)c) Straightness of axis

(MMC)

a) Surface (Plane)

Types of controls

Perpendicularity

Cylindricity

Roundness (Circularity)

Straightness

Flatness

Control

YesOrientation

NoForm

NoForm

NoForm

NoForm

DatumSymbolType



a) Same as above

a) Surface w.r.t axisb) Surface w.r.t between

centersc) Surface w.r.t Two

functional diametersd) Surface w.r.t one Face

and one Diameter

a) Surface w.r.t Surfaceb) Axis w.r.t Surface (RFS)c) Axis w.r.t Surface (MMC)

a) Surface w.r.t Surfaceb) Axis w.r.t Surface(RFS)c) Axis w.r.t Surface (MMC)d) Axis w.r.t Axis (MMC)

Types of controls

Total Runout

Circular Runout

Angularity

Parallelism

Control

YesComposite

YesComposite

YesOrientation

YesOrientation

DatumSymbolType



a) Axis to Axis

a) Feature to Surface

a) Floating Fastener (Between holes)

b) Fixed Fastener (Between holes)

c) Position w.r.t to edges (as pattern) and Position within Pattern (Holes)

d) Position w.r.t another feature – Hole (as pattern) and Position within pattern (Holes)

e) Position between Coaxial features

f) Position between non-cylindrical features

Types of controls

Concentricity

Symmetry

Position

Control

YesLocation

YesLocation

YesLocation

DatumSymbolType



a) Surface to Surface

a) Line to Surface

Types of controls

Profile to Surface

Profile of Line

Control

YesProfile

YesProfile

DatumSymbolType

To Summarize, there are 35 different types of Geometric controls that can be designed using the 14 geometric characteristics


7. Tolerance Zones

• Tolerance zone describes numerically as well as pictorially, represent the extent of the permissible deviation from the desired form, orientation, location, profile or runout

• If the diameter symbol is used before the numerical value, it means it is a diametrical tolerance zone (always used in axis control), otherwise it is the distance between parallel lines.

0.006 M A B C


8. Virtual Condition

• Refer to Rule # 2c for the definition of Virtual Condition


Exercise # 1 – GD&T fundamentals

• Complete the exercise for Chapter - 2

Paired comparison


Geometric Controls detailed explanation


3. Form Controls

StraightnessFlatness Roundness Cylindricity


Form Controls - Application

• Purpose of these form controls are– To control features critical to fit, function or

interchangeability– Tolerances of size do not provide adequate control– Other geometrical tolerance controls are to be refined


Flatness

• Definition:• Flatness is the condition of a surface having all elements in one

plane.• Flatness tolerance – specifies a tolerance zone defined by two

parallel planes within which the surface must lie.

• Flatness tolerance must be less than the associated size tolerance ( and often more logically, less than one-half of the size tolerance)

• The flatness tolerance is applied in a view of the drawing where the surface elements to be controlled are shown as a straight line ( the side view of the plane)

• The feature control frame is shown on an extension line of the surface, or attached to a leader directed to the surface.


Flatness

– Flatness tolerance does not associate with a datum reference ; the actual surface relates to a perfect counterpart of itself, a plane; thus, no datum is needed nor proper.

– Flatness tolerance relates to a surface with area but no size; therefore , MMC or RFS principles can not be applied to flatness.

– Flatness tolerance is normally applied to uninterrupted surfaces; for coplanar surfaces see profile tolerancing.

– The concerned surface must also be within the specified limits of size and the boundary of perfect form at MMC.


Flatness


Straightness

• The following are the different controls that can be defined for Straightness – Straightness of surface– Straightness of Axis (RFS)– Straightness of Axis (MMC)


Straightness of Surface

• The straightness tolerance is applied in a view of the drawing where the feature to be controlled are shown as a straight line

• All elements of the surface are to be within the specified size tolerance and the boundary of perfect form at MMC

• Each longitudinal element of the surface must lie between parallel lines the stated tolerance apart and in a plane common with the nominal axis (cylindrical part) or a longitudinal plane normal to the surface (flat part)

• The straightness tolerance must be less than the size tolerance (generally less than ½ of the size tolerance)

• Straightness of surface elements related to a line which has no size, therefore MMC or RFS principles cannot be applied

• Since boundary of perfect form at MMC must not be violated, waisting or barreling may prevent the use of the full straightness tolerance


Straightness of surface


Straightness of an axis(RFS)

• The diameter symbol precedes the tolerance value in the feature control frame

• The boundary of perfect form may be exceeded to the extent of the stated tolerance (rule #1 does not apply)

• An outer or inner boundary results i.e. collective effect of the MMC size plus (for shafts) and minus (for holes) the straightness tolerance

• In this case, the straightness tolerance can be greater than the size tolerance where necessary

• Each circular element (actual local size) must be within the specified limits of size

• The derived median must be within the straightness tolerance zone, RFS


Straightness of an axis(RFS)


Straightness of an axis (MMC)

• The straightness tolerance is applied in a view of the drawing where the axis to be controlled is shown .

• The feature controlled frame is placed with the size dimension in the same view.

• The diameter symbol precedes the tol. Value in feature controlled frame .

• The boundary of perfect form may be exceeded to the extent of the stated tolerance .

• A virtual condition results i.e the collective effect of the MMC size ,plus (for shafts), minus (for holes) , the straightness tolerance



• The straightness tolerance applies at MMC , as the actual size of the feature frame controlled departs from MMC , the tolerance increases to the amount of that departure.

• The straightness tolerance may be greater than the size tolerance where necessary .

• Each circular element must be within specified limit of size

• Straightness tolerance does not associate with datum reference

• Straightness tolerance of this variety deals with a feature of size , therefore , the principles of MMC(RFS) is usable.

• Straightness of an axis applied on an MMC is effective when dealing with mating parts (pin in hole etc) and captures part function and interface




Straightness of a center plane (RFS or MMC)



• Definition: Circularity is a condition of a surface of revolution • Where w.r.t to a cylinder or cone , all points of the surface intersected by

any plane perpendicular to a common axis are equidistant from that axis .

• Where w.r.t a sphere , all points of the surface intersected by any plane passing through a common center are equidistant from that centre

• The circularity tolerance is applied in either view of the drawing , whichever is most convenient .

• The feature control frame is attached to the concerned surface by a leader .

• All elements of the surface are to be within the specifiedsize tolerance and the boundary of a perfect form at MMC.



• Each circular element of the cylindrical surface must lie in a tolerance zone between 2 concentric circles the stated tolerance apart and in a plane perpendicular to the part nominal axis.

• The circularity tol. must be less than the size tolerance .

• Circularity tolerance does not associate with the datum reference , each circular element relates to a perfect counterpart of itself , a circle thus no datum is needed nor proper .

• Circularity of each circular element compares the form of each element to a circle . Since the control of the surface itself is of concern , its size variation is irrelevant to the form . Therefore , MMC or RFS principles cannot be applied .



• Part size may vary within its size tolerance , yet the circularity tolerance remains the same . Where size of the produced part approaches LMC , the roundness tolerance proportionately diminishes .

• Circularity tolerance may be applied to any part which is circular in cross section .

• Verification with a conventional v block methods must recognize the variable involved i.e the lobing effect on the part , angle of the V-BLOCK ,

out of straightness of the longitudinal axis etc.




Circularity of Cone

• The circularity tolerance is applied in the side view on the drawing . The feature control frame is attached to the conical surface by a leader .

• All elements of the conical surface must lie within the specified size tolerances.

• Each circular element of the conical surface must lie in a tolerance zone between 2 concentric circles the stated tolerance apart and in a plane perpendicular to the nominal axis of the conical surface .

• The circularity tolerance must be less than the controlling size tolerances, logically , les than one half the controlling size tolerances .


Circularity of Cone


Cylindricity

• Definition :• Is a condition of surface of revolution in which all points of the surface are

equidistant from a common axis .

• Cylindricity tolerance (C.T) specifies a tolerance zone bounded by two concentric cylinders within which the surface must lie .

• The Cylindricity tolerance must be less than the feature size tolerance .

• Cylindricity tolerance is a composite control of form which includes circularity , straightness & taper .

• Cylindricity tolerance differs from circularity tolerance in that it applies to the total surface (entire length) simultaneously .

• All the elements of the surface controlled are to be within the specified size tolerance and the boundary of perfect form at MMC .


Cylindricity

• C.T relates to the control of the surface form which is irrelevant to size , therefore RFS or MMC principle cannot be applied.

• C.T is applicable only to cylindrical features , either inside or outside cylinders.

• C.T does not associate with a datum reference , the cylindrical elements relate to a perfect counterpart of itself, a cylinder , thus no datum is needed , nor proper.

• Part size may vary within its size tolerance , yet the cylindricity tolerance remains the same . Where the size of the product approaches LMC, C.T proportionately diminishes .


Cylindricity


Quick reference for Form tolerances

NoNoComposite checking

< ½ of the size tolerance

Cylindricity of the surfaceCylindricity

No

Yes

Yes

No

No

MMC applicable

Roundness tester

Functional gage

Dial

Dial

Dial

Inspection method


Based on the fitment (Clearance 0 and interchangeability

Based on the function and fitment



Calculation of tolerances

Roundness of the surface

Straightness of the axis (MMC)

Straightness of the axis (RFS)

Straightness of the surface

a) Surface (Plane)

Types of tolerancing

Roundness

Straightness

Straightness

Straightness

Flatness

Control

No

No

No

No

No

DatumSymbol


Exercise # 2 – Form Tolerances


Paired comparison


4. Orientation Controls

Perpendicularity( Squareness) Angularity Parallelism


Orientation Controls - Application

• Orientation controls are applied when– Relationship of features (surfaces or size features) are

required but which do not include location controls– A refinement tolerance control of orientation within a

location control for the feature or features is required– Where otherwise anticipated controls like workmanship,

standards etc. are insufficient

Orientation controls always require a datum


Datum Features - Application

• Definition ;• Is theoretically exact point , axis , or plane derived from true geometric

counterpart of a specified datum feature . A datum is the origin from which the location or geometric characteristics of features of part is established .

• A datum is established from an actual part feature .

• A datum feature refers to actual part feature and thus includes all the inaccuracies and irregularities of produced feature.

• A datum feature is indicated on drawing by appropriately attaching or relating the datum feature symbol to the desired feature .

• In manufacturing or verification , reference cannot be made fromtheoretical plane or axis.

• Therefore such a reference is referred to as simulated datum feature and is assumed to exist in the precise manufacturing or inspection equipment such as fixtures , gage pins , surface plates , collets , chucks , mandrels etc. , the datum feature simulators .


Datum Features - Application


Perpendicularity

• Perpendicularity is the condition of a surface , median plane , or a axis at a right angle (90°) to a datum plane or axis

• A perpendicularity tolerance specifies one of the below:– A tolerance zone defined by two parallel planes perpendicular to a

datum plane or axis within which a surface or median plane of the considered feature must lie

– A tolerance zone defined by two parallel lines perpendicular to a datum axis within which the axis of the considered feature must lie

– A cylindrical tolerance zone perpendicular to a datum plane within which the axis of the considered feature must lie

– A tolerance zone defined by two parallel lines perpendicular to a datum plane or axis within which an element of the surface must lie

• Perpendicularity controls can be of the following types:– Surface to Surface– Axis to Surface (RFS)– Axis to Surface (MMC)– Axis to Axis


Perpendicularity (Surface to Surface)

• Perpendicularity is often referred to as ‘Squareness’

• A Perpendicularity tolerance always requires a datum reference , a relationship of a feature in its orientation to datum feature .

• A Perpendicularity tolerance applied to a surface also controls the flatness of the controlled surface to the extent of the stated tolerance .

• The concerned feature must be within the specified limits of size .

• Perpendicularity tolerance to a surface should be applied in a view of the drawing where the relationship appears .

• The collective effect of the size dimension and the perpendicularity tolerances should be considered in the part assembly and other relationships

• The datum feature error is not accumulative to the related feature being controlled , the relationship is from the datum plane


Perpendicularity (Surface to Surface)


Perpendicularity (Axis to Surface RFS)

• The Perpendicularity tolerance zone for a cylindrical feature of size , such as pin which projects from a surface , is a tolerance zone of the stated tolerance and perpendicular to the datum plane .Where the Perpendicularity tolerance is specified on RFS basis , the tolerance indicated is maximum regardless of the actual mating size of the produced feature . The derived axis of the produced feature must lie within that tolerance zone .

• The controlled feature must be within the specified limits of size and within the specified tolerance of location . Therefore Perpendicularity control of a size feature is normally a refinement of another control ( I.e position) in terms of its orientation relative to the specified datum

• The diameter symbol is normally included preceding the perpendicularity tolerance value in the feature control frame where a feature of size, such as a pin, is related to a datum surface only. However without the diameter symbol, the derived meaning could be assumed the same i.e the tolerance zone would be between two parallel planes of infinite rotation , thus developing a cylindrical zone tolerance .

• The collective effect of the MMC size of the controlled feature such as a pin , and its perpendicularity tolerance develop an outer boundary . This collective effect of the possible feature error is considered as necessary in the relationship with other parts in the design requirements . This consideration usually is a factor in determining that a perpendicularity tolerance is necessary and in establishing the permissible amount of such a tolerance


Perpendicularity (Surface to Axis RFS)


Perpendicularity (Axis to Surface - MMC)

• The Perpendicularity tolerance zone for a cylindrical feature of size , such as pin which projects from a surface , is a tolerance zone of the stated tolerance and perpendicular to the datum plane .Where the Perpendicularity tolerance is applied on MMC basis , the permissible perpendicularity tolerance increases an amount equal to the produced feature actual mating size departure from MMC size . The axis of the produced feature must lie within that tolerance zone .

• Where functional interface of mating parts is involved , the MMC principle should be considered . In terms of perpendicularity, such a tolerance is usually determined by the clearance between pin and mating part hole .

• Functional gaging is possible and practical when MMC principles are invoked . Such gaging is usually a simulation of the mating part interface . The virtual condition and gage member size are synonymous

• The controlled feature must be within the specified limits of size and within the specified tolerance of location . Therefore Perpendicularity control of a size feature is normally a refinement of another control ( i.e position) in terms of its orientation relative to the specified datum .


Perpendicularity (Surface to Axis MMC)


Perpendicularity (Non-cylindrical feature)


Angularity

• Angularity is the condition of the surface , axis or the median plane which is at a specified angle ( other than 90°) from a datum plane or axis .

• Angularity tolerance always requires a datum reference , it is control of a feature in its orientation to a datum feature .

• Angularity tolerance always requires that the desired angle be indicated as a basic angle .

• The angular relationship of the controlled feature ( surface or axis ) is not affected by the surface irregularities of the datum feature since the relationship is from the datum plane or axis .

• Angularity tolerance applied to a surface includes a control of flatness to the extent of the stated angularity tolerance

• Angularity tolerance is independent of the size tolerance and is verified separately . The part must also meet all size requirements .Aspects of the controlled angular surface ( I.e corner ) , which is also dimensioned and toleranced as a separate requirement , must also meet such requirements .


Angularity


Parallelism of surface

• The considered feature surface must lie within a tolerance zone between two parallel planes, the stated tolerance apart, which is Parallel to the datum plane.

• Parallelism tolerance always requires a datum reference; it is the control of a feature in its orientation to a datum feature.

• Parallelism tolerance is shown in the view of the drawing where the parallel relationship is seen. An appropriate feature control frame is used.

• The parallelism tolerance must be must be less than the associated • Size dimension ( and more appropriately less than one-half the size

tolerance).

• Parallelism tolerance applied to a surface includes a control of flatness to the extent of the stated parallelism tolerance.

• The parallelism tolerance and the size tolerance is verified separately. The surface must be within the specified size limits


Parallelism of Surface


Parallelism of Axis to Surface


Parallelism of Axis to Axis


Quick reference for Orientation tolerances

YesNoDialBased on the function

Surface to SurfaceAngularity

YesYesDialBased on the function and relation with other parts

Axis to Surface (RFS)Angularity

YesYesFunctional gageBased on fitment and clearances required for fitment

Axis to Surface (MMC)Angularity

Yes

Yes

No

MMC applicable

Functional gage

Dial

Dial

Inspection method

Based on fitment and clearances required for fitment

Based on the function and relation with other parts

Based on the function


Axis to Surface (MMC)

Axis to Surface (RFS)

Surface to Surface


Perpendicularity

Perpendicularity

Perpendicularity

Control

Yes

Yes

Yes

DatumSymbol


Quick reference for Orientation tolerances

YesYesFunctional gageBase don the fitment and clearances

Axis to Axis (MMC)Perpendicularity

Yes

Yes

No

MMC applicable

Functional gage

Dial

Dial

Inspection method

Based on fitment and clearances required for fitment

Based on the function and relation with other parts

Based on the function


Axis to Surface (MMC)

Axis to Surface (RFS)

Surface to Surface


Perpendicularity

Perpendicularity

Parallelism

Control

Yes

Yes

Yes

DatumSymbol


Exercise # 3 – Orientation Tolerances


Paired comparison


5. Location Controls

Position Symmetry Concentricity


Location Controls - Application

• Location tolerances are used to control the following types of relationship– Center distances between features such as pins, holes,

projections etc..– Location of features as a group relative to a datum or

datums– Co-axiality between a feature or features relative to a

datum axis– Centrality between a non-cylindrical feature or features

relative to a datum center-plane


Position tolerance

• Following controls are possible in position tolerance– Center distance between holes – Fixed Fastener– Center distance between holes - Floating Fastener– Position with respect to edges (as pattern) and Position within pattern

(Holes) - Composite– Position with respect to another feature – Hole (as pattern) and

Position within pattern (Holes) – Position between Coaxial features – Mating parts– Position between non Cylindrical features – Mating parts


Datum reference frame (Three plan concept)


Datum reference frame (Three plan concept)


Datum Targets


Positional Tolerance Theory


Positional Tolerance Theory


Center Distance between holes –Floating Fastener

• Position tolerancing is effective when controlling location of mating part features

• Where both mating parts have clearance holes to accommodate a fastener as means of assembly, the “floating fastener” method ofcalculation can be used to determine the position tolerance

• The size of the fastener is selected and the appropriate size of the clearance holes are then determined and specified as based upon the designer discretion or as per standard

• The MMC of both the mating features are used to calculate the positional tolerance

• Formula is T = H- F (H – Hole F – Fastener) Both at are MMC

• Where datum references are required to ensure orientation control of the holes relative to the respective mating surfaces, they are used

• Functional gage principles are utilized where MMC are specified. Gage Pin size is determined as P = H – T

• Soft gaging (CMM) may also be used for inspection


Center Distance between holes –Floating Fastener


Center Distance between holes –Fixed Fastener

• Where one part has clearance hole to accommodate fixed pins (or fasteners) on the mating part or assembly, the “fixed fastener” method of calculation is used to determine the position tolerances

• The sizes of the mating features are determined as per the standard or designer discretion

• The tolerance is calculated as follows; T = (H-F)/2 both at MMC• Where desirable to select a more suitable distribution of tolerance

between the parts, the calculated total tolerance may be dividedbetween the parts

• Functional gage is used to verify the position of the holes. Gage Pin size is given by the formula P = H – T


Center Distance between holes –Fixed Fastener


Position Tolerance – Datum reference


Center Distance and Relation to Edges

• Where a position tolerance is applied to the features in a pattern (i.e. holes) and the pattern relationship to outside part edges (or other features) is less critical, the composite position tolerance method may be used. In such applications the required precision in pattern ( feature relating tolerance) can be stated, yet the pattern ( as a unit) may be separately stated with more lenient control relative to the part edges ( datum features) with a pattern location tolerance. The MMC principle is usually most appropriate in such applications.

• Where the composite positional tolerancing method is used, datum's are required. The datum reference frame and datum precedence is also used. This will ensure proper functional interface with the component or part which mounts to the located features ( i.e. holes) and on the indicated surface (datum). Although rare , it is permissible to omit datum's in the feature relating tolerance callout

• The features (holes) on the example shown may individually vary from their true position within the specified “feature relating” position tolerance & the established t zones at each true position and as oriented to datum A. The hole pattern relative to the specified datum's (i.e. A, B & C) may shift/rotate from true position within the specified “Pattern locating” position tolerance. These two requirements are both applicable to the feature pattern but are separate requirements.

• The feature control frame is constructed as a composite symbol with the “pattern locating” position tolerance in the upper portion and the “feature relating” position tolerance in the lower portion of the symbol. There is no significance as to whether each portion is in the upper or lower segment; the datum indicators and the tolerance values are the key criteria. The method shown is standard.

• It should be noted that in the composite positional tolerancing method , one control (i.e. position) is used on both portions of the requirement. The discipline of the datum reference frame ensures clarity of design intent and production uniformity.


• Orientation of the features (holes) in the pattern and their location with respect to true position and one another must be within the “feature relating” position tolerance ( i.e. Ø.008). To ensure that this requirement clearly indicates an orientation relationship ( if required per the design), the primary datum is stated.

• Functional gaging techniques may be used when composite positional tolerance is applied on an MMC basis. Two separate gages would normally be used. The gage for the “pattern-locating”

• Positional tolerance (i.e. Ø.030) would include pick-up of the datum surfaces in an appropriate manner & with the virtual condition & nominal gage member size determined by MMC size of the feature (hole) minus the stated positional tolerance; the formula is

• GP = H – T (Ø.198 = Ø.206 – Ø.030)• The gage for the “in-the-pattern” positional tolerance (Ø.008) would include a pick up of

the primary datum (only) & with the virtual condition and the nominal gage member size determined by MMC size of the feature (hole) minus the stated positional tolerance; the formula is

• GP = H – T (Ø.198 = Ø.206 – Ø.008)



Note that the nominal gage pin sizes are the virtual conditions sizes of the holes developed from their respective position tolerances. Described above are “hard gages." Soft gaging” principles, using computer or electronic means to accomplish the same task via CMM data, software programs & mathematical manipulation, are in common use as well.

Composite tolerance principles may be extended to numerous other applications. For ex., if it is desired to maintain an orientation of the “feature relating” tolerance datum reference frame to both datums A & B the Called out would be:

The added datum B gives orientation to the pattern true positions ( i.e. parallel to secondary datum B) but not location. The functional gage principles for the “feature relating” pattern would then require an added sliding rail similar to that shown in Slide no.

Ø.030

Ø.008

A B C

A B





Center Distance and Relation to anotherFeature (Hole)

• Where a position tolerance is applied to features in a pattern (i.e. holes) and the pattern relationship is to another feature, such as a pilot hole, that feature can be indicated as a locating datum. In such a case, the location of the surrounding feature (holes) pattern relative to the pilot hole is the critical requirement. A mating part situation with a pilot pin surrounded by its counterpart features (pins, tapped holes) can be envisioned as the mating part interface.

• The pilot hole feature may first be specified with a more lenient positional tolerance relative to the selected outside features. Where necessary , a refinement in orientation (i.e. a perpendicularity tolerance) may be necessary to ensure the proper pilot hole orientation ( squareness) & the pilot pin mating part interface. Since the datum feature (the pilot hole) is a “size” feature the MMC principle can be applied if appropriate to the design requirement; for ex., if there is to be a clearance fit between the pilot hole & pilot pin at assembly.

• Where the surrounding holes are to interface with mating part features (i.e. pins, tapped holes) their positional tolerance is calculated using the “fixed fastener” formula and maximum material condition is specified. The location dimensions for the surrounding holes are specified relative to the pilot hole.

• The datum references specified with the surrounding holes are, first, the orientation (squareness ) datum ( top surface) as the primary datum, the location datum ( pilot hole) as the secondary datum, and an outside surface as the tertiary datum.



• As indicated by the Datum/Virtual Condition Rule, the pilot hole ( the secondary & locating datum), is implied at its virtual condition. That is, the pilot hole has been permitted orientation tolerance in its control. This, therefore, must be recognized in its “pick-up” in fixturing & inspection and as pertinent to the part function.

• Where MMC is specified to the surrounding holes and also to the pilot hole, the full advantages of MMC are realized. Part function is assured, additional production tolerance is available, and functional gaging techniques may be used. As each surrounding hole actual mating size departs from its MMC in production, an increase in the hole position tolerance is realized to the extent of that departure; as the pilot hole actual mating size departs from its MMC in production , the shift of the surrounding hole pattern as a group is permissible relative to the pilot hole.

• Functional gaging is permissible ( but not required ) when MMC is specified . Functional gaging would simulate the mating part interface , expedite inspection operations, and effectively capture the subtle interplay between feature size and location . Feature sizes must be verified separately and independently . Open set up measuring techniques can , of course be used in lieu of the functional gaging with uniform results




Position Tolerance – Co-axial features

• Position tolerancing is particularly practical and effective when controlling location of coaxial mating part features on an MMC basis .

• Where one part has clearance holes ( bores , counterbores etc. ) and the mating part has corresponding features ( pins shafts etc.) , the ‘fixed fastener ‘ method of calculation can be used to determine the position tolerances on both part mating features

• The sizes of the mating features are determined and specified as based upon the designer discretion or as selected from standards recommendations .

• The MMC sizes of the mating features i.e the shaft and related hole , are used to calculate the position Tolerance for these features on both parts .

• The results of the ‘ fixed fastener’ calculation derives the positional tolerance for both parts using the formula T =( H-S)/2

• i.e ( Ø 0.0025 = (Ø 0.711- Ø 0.706)/2)



• H = hole MMC S = shaft MMC

• Where there is a relationship of only one feature to the datum feature on each part , an extension of the fixed fastener method maybe used to directly derive maximum tolerance and yet assure function and assembly using the formula T= ( ( H-S) + ( D2-D1)) / 2i.e Ø 0.005 = ((Ø 0.711- Ø 0.706) + (Ø 0.905- Ø 0.900) ) /2

• D1 =Datum shaft MMC D2 = Datum hole MMC

• Where desirable to select a more suitable distribution of tolerance between the mating part features , the calculated total tolerance may be divided between parts i.e where Ø 0.01 is the total tolerance to be distributed , such combinations as 0.006 and 0.004 , 0.007 and 0.003 etc .This is done at the design stage before release to production .

• Where MMC is specified , the stated positional tolerances on each part are individually increased an amount equal to the actual mating size departure from MMC size as the holes and shafts are produced




Position Tolerance –Design of Co-axial gages


Position Tolerance –Composite control of Co-axial features


Position Tolerance – Non cylindrical features

• Position tolerancing is particularly practical and effective when controlling location of non cylindrical mating part features on an MMC basis .

• Where one part has slots and the mating part has external width features , the ‘fixed fastener ‘ method of calculation can be used to determine the position tolerances on both part mating features

• The sizes of the mating features are determined and specified as based upon the designer discretion or as selected from standards recommendations .

• The MMC sizes of the mating features i.e the slots and related external width, are used to calculate the position Tolerance for these features on both parts .

• The results of the ‘ fixed fastener’ calculation derives the positional tolerance for both parts using the formula T =( SL - W)/2i.e ( 0.003 = ( 0.466- 0.460)/2)



• SL = slot MMC W = external width MMC

• Where there is a relationship of only one feature to the datum feature on each part , an extension of the fixed fastener method maybe used to directly derive maximum tolerance and yet assure function and assembly.

• Where desirable to select a more suitable distribution of tolerance between the mating part features , the calculated total tolerance may be divided between parts i.e where 0.006 is the total tolerance to be distributed , such combinations as 0.002 and 0.004 , 0.0025 and 0.0035 etc . This is done at the design stage before release to production .

• Where MMC is specified , the stated positional tolerances on each part are individually increased an amount equal to the actual mating size departure from MMC size as the slots & widths are produced .




Converting from Position to Co-ordinateand Vice-versa

• Conversion from stated positional tolerance on the drawing to equivalent ± tolerances maybe necessary for tool building , prototype parts manufactures , inspection etc.

• Tool designers , tool makers , machinists , model makers , inspectors etc. can convert positional tolerances to equivalent ± tolerances by the use of ‘ rule of thumb’

• Conversion from the stated coordinate (± ) tolerance to the equivalent positional tolerance can be useful to production engineers , inspectors etc. who may wish to isolate possible problem areas ; such as , where parts may assemble but have been previously rejected on the basis of the permissible coordinate tolerance on the drawing .This method may help’ trouble shoot ‘ problems in general .

• This is not the method used to determine positional tolerances in design .






Inspection methods for PositionTolerances


Translating Position toleranceto Tool tolerance


Positional TolerancingFunctional Gaging Design

• Functional gaging simulates individual part feature function and their interface with mating part features . IT ensures proper assembly and fulfillment of design requirements while also encouraging economic advantages to production and inspection .

• The MMC principle and methodology must be specified before functional gaging is permissible.

• Functional gaging verifies the geometric tolerances only ; feature size tolerances must individually and separately proven .Such exception would be when zero tolerancing method ( position , perpendicularity ) are used which permits the functional gage to be utilized also as a ‘go’ size gage if desired .

• The nominal gage member size for each control feature is synonymous with is virtual is developed from the MMC size and the geometric tolerances assigned. The formula to derive virtual condition & gage pin size for hole feature is

• gage pin = Hole (MMC) – Position tolerance


Positional TolerancingFunctional Gaging Design


Symmetry

• Symmetry is that condition where the median points of all opposed or correspondingly located elements of two or more feature surfaces are congruent within the axis or center plane of a datum feature.

• Symmetry tolerance – is the distance between two parallel planes equally disposed about the center plane of the datum feature.

• Symmetry tolerance is a variety of a locational tolerance & is always applied RFS.

• Where necessary, two datum features ( a primary and secondary datum) are specified to stabilize the part to two planes.

• Verification procedures require analysis of a necessary number of measurements at opposed elements of the controlled feature surfaces & differential or direct comparison of these measurements to determine the resultant feature median points. These median points must be within the tolerance zone about the datum center plane.

• All size tolerances must be met independent of the symmetry tolerance


Symmetry


Concentricity

• Concentricity is that condition where the median points of all diametrically opposed elements of a figure of revolution ( or correspondingly located elements of 2 or more radially disposed features ) are congruent with the axis ( or centre point ) of a datum feature .

• Concentricity tolerance - A Concentricity tolerance is a cylindrical ( or spherical ) tolerance zone whose axis ( or centre point ) coincides with the axis or centre point of the datum feature(s) . The median of all correspondingly located elements of the feature(s) being controlled , RFS must lie within the cylindrical or spherical tolerance zone . The specified tolerance and the datum reference can only apply on RFS basis

• Concentricity tolerance is an axis to axis type of control which can effectively relate coaxial features where part tolerance , uniform distribution of part feature mass in rotation , controlling the geometry of a non rigid rotational part , etc is required .

• Concentricity tolerance – is more restrictive and potentially costly requirement due to the possible need for detailed analysis of the part in verification .Before concentricity tolerance is selected , the options of position tolerance at MMC or runout tolerance tolerance should be considered .

• Concentricity tolerance considers in composite the effect of various surface errors such as out of straightness, out of circularity out of cylindricity , etc as the median points are determined .

• Concentricity verification requires a form of differential measurement at opposed elements of the surface , to determine the resultant feature median point .Where precision spindle machine methods are used, polar graph printout and analysis with overlay gages will achieve the same results . Computerization analysis is also used where such capability is available .

• Concentricity tolerance is always specified and implied on an RFS basis .If MMC principles are desired ,consider position tolerance .

• All size tolerance must be met independent of the concentricity tolerance .


Concentricity


Restrained Features

• Where a non-rigid part must be verified in condition which simulates part assembly or interface with mating parts , the part maybe restrained during such verification .

• Restraining part means that during verification the appropriate features , as indicated by the drawing symbols and notes , are mounted , held, or stabilized to conditions or forces which simulate the part function or assembly requirements. Suitable fixturing and measuring processes are introduced to achieve simulation .

• Appropriate geometric tolerance and datum symbols are placed on the drawing tospecify the relationship desired . A note describing the conditions under which these requirements are to met including the word RESTRAINED , is added to the drawing

• When the amount of the restraint is not specifically indicated the restraint implied isthat required to simulate part function or assembly .

• Restrained features are typically found on weldments, pressure vessels, fabricated sheet metal parts , bulkheads etc.


Quick reference for Location tolerances

YesYesTwo functional gages/ CMM

T = H – F (for distance within features)

Center distance and distance from another feature

Position

YesYesFunctional gageT = (H-S)/2T = (H-S) +

(D2-D1)/2

Coaxial featuresPosition

YesYesFunctional gageT = (SL-W)/2Non cylindrical featuresPosition

Yes

Yes

Yes

MMC applicable

Two functional gages/ CMM

Functional gage/CMM

Functional gage/CMM

Inspection method

T = H – F (For distance within features)

T = (H – F)/2

T = H – F


Center distance and distance from edge

Center distance (Fixed fastener)

Center distance (Floating fastener)


Position

Position

Position

Control

Yes

Yes

Yes

DatumSymbol


Quick reference for Location tolerances

No

No

MMC applicable

Dial

Dial

Inspection method

Based on function

Based on fitment and function


Axis to Axis

Symmetry of Hole or slot with respect to surface


Concentricity

Symmetry

Control

Yes

Yes

DatumSymbol


Exercise # 4 – Location Tolerances


Paired comparison


5. Composite Controls


Composite Controls - Application

• Runout is the composite deviation from the desired form and orientation of a part surface of revolution during full rotation (360 deg) of the part on a datum axis

• Circular Runout contains the following composite errors– Circularity (Roundness)– Concentricity– Other surface errors

• Total Runout contains the following composite errors– Circularity – Concentricity– Straightness– Cylindricity– Taper– Other surface errors

• Runout tolerance indicates the permissible error of the controlled feature surface when rotated about a datum axis.

• Typical applications are on rotating shafts, shafts to bearings where more precise surface to axis relationship is required


Runout – Surface to Axis

• Circular runout is a less stringent requirement than the total runout as it controls only circular elements of a surface individually and independently from one another

• Runout always requires a datum reference. When the datum is an outside cylindrical feature, the simulated cylinder, and its derived axis, is established by the minimum circumscribed cylinder which will contact (closed upon) the extremities of the datum feature. A bearing mount to the datum feature would be a typical design requirement

• Runout tolerance is applicable only on an RFS basis


Runout – Surface to Axis


Runout – Between Centers

• Run-out tolerance can be related to a datum axis established by two part centers in such a case, the part function and final mounting is on the centers. The two centering features are individually specified as datum's thus establishing a common datum axis which the part rotates

• Where the datum axis is established from two internal centers, it is the maximum inscribed true cone which will contact the extremities of the two produced centers (cones); the two true cones can be represented by machining or inspection centers.

• Where total runout is specified, the concerned surface must be within the stated runout tolerance across the entire feature when rotated 360 deg about the datum axis


Runout – Between Centers


Runout – Between two functionalDiameters

• This is given for parts mounted to bearings. The bearing mount diameters are selected as the datum's

• Runout error can possibly accumulate between features where they are relative to the same datum. This error will be to the extent of the sum of the concerned runout tolerances

• Where accumulation of runout error may need to be controlled between specific features, one of the features should be selected and specified as datum feature. The second feature is then related to it with an appropriate feature control frame and referenced to that datum. In such cases, maximum runout error permitted between the two features is that stated on the drawing

• Runout can also be applied to surfaces at right angles to the datum axis. Such application can control perpendicularity, wobble etc..


Runout – Between two functionalDiameters


Runout – Face and one Diameter


Quick reference for Composite tolerances

YesNoDialBased on function in rotation

Surface to One functional diameter and face

Circular and total Runout

YesNoDialBased on function in rotation

Surface to Two functional diameters

Circular and Total Runout

No

No

MMC applicable

Dial

Dial

Inspection method

Based on function in rotation

Based on function in rotation


Surface to Between centers

Surface to Axis




Control

Yes

Yes

DatumSymbol


Exercise # 5 – Composite Tolerances


Paired comparison


5. Profile Tolerances


Profile Tolerances - Application

• Profile tolerance specifies a uniform boundary along the desired true profile within which the feature elements (surface or line) must lie

• Profile tolerance is a method used to specify a permissible deviation from the desired profile

• Profile tolerance is used to control form or combination of form, size, orientation and location of a feature

• Where profile is used as refinement of size, the profile tolerance must be less than the size tolerance

• The direction of arrow indicates whether it is Bilateral or Unilateral and if Unilateral, in which direction


Profile of a Surface

• This tolerance is a three dimensional zone and is the distance between two boundaries disposed about the desired true profile or entirely disposed on one side of the desired true profile( based on the position of the arrow)

• Where necessary for clarification, letter (i.e X and Y) are used to indicate the start and the end of the profile

• Profile of a surface control is usually a combination of size, form, orientation and sometimes location control

• Profile of surface control requires consideration of datum references to ensure proper relationship of the profile to mounting surfaces

• MMC principles are not applicable to profile control


Profile of a Surface


Profile of a Surface ( All-round)


Profile of a Surface (Coplanar surface)

• Profile of a surface can be used to control two or more surfaces where it is desired to specify interrupted or non-continuous surfaces in their co planarity

• Co planarity is the condition of the two or more surfaces have all elements in one plane

• In this case, profile tolerance provides a control similar to that as established by flatness on a single plane surface

• Profile of a surface tolerance, applied to control co planarity, defines a tolerance zone between two parallel planes within which the considered surfaces must lie

• Where two or more surfaces are involved, specified surfaces can be selected as datum's if pertinent to the part function. In such cases, the profile tolerance zone applies to all the coplanar surfaces including the designated surface features


Profile of a Surface (Coplanar surface)


Quick reference for Profile tolerances

YesNoDial/GageBased on fitment and function

Co planarity checkProfile of Surface

No

No

MMC applicable

Dial

Dial

Inspection method




Surface (Plane) with respect to another surface

Line element of the surface with respect to another surface


Profile of Surface

Profile of Line

Control

Yes

Yes

DatumSymbol

Documents

Training Material