Form and Position

7/30/2019 Form and Position

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TOLERANCES OF FORM AND POSI TI ON

Introduct ion

In certain circumstances, tolerances of size are not alwayssufficient to provide the required control of form. Forexample, in Fig.1a, the shaft has the same diameter

measurement in all possible positions but is not circular, inFig.1 b the component has the same thickness throughoutbut is not flat, in Fig. 1c, the component is circular in allcross sections but is not straight. The forms of these

components can be controlled by means of geometricaltolerances. For an internal feature of a hole, the variation ofsize, form and position is illustrated in Fig. 2.


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(a) (b) (c)

Fig. 1 Errors of form


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Fig. 2 Geometric tolerances of internal feature

a - Error of Size b - Error of form c - Error of posit ion


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Form Var iat ion

It is a variation of the actual condition of a form feature(surface, line) from geometrically ideal form.

Posit ion Variat ion

It is a variation of the actual position of the form feature(surface, line) form the geometrically ideal position, withreference to another form feature, called datum feature.

Geomet r ical t oleranceGeometrical tolerance is defined as the maximum permissibleoverall variation of form or position of a feature.


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i. to specify the required accuracy in controlling the form ofa feature,

i. to ensure correct functional positioning of the feature,

ii. to ensure the interchangeability of components, and

iii. to facilitate the assembly of mating components.

Geometrical tolerances are used,


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The form of a single feature is deemed to be correct, when

the distance of its individual points from a superimposed

surface of ideal geometrical form is equal to or less than the

value of the specified tolerance. The orientation of the ideal

surface should be so chosen that the maximum distancebetween this and the actual surface of the feature concerned

is the least possible value. Referring Fig. 3, possible

orientation of ideal surface are A1 B1, A2 B2, A3 B3 and

the corresponding maximum distances are h1,h2, and h3.

The relation between the distance is h1 < h2 < h3.


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Fig. 3 Orientation of ideal surface


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Therefore, the orientation of the idealsurface is A1 B1 and h1 must beequal to or less than the specified

tolerance value. According to thefeature which is to be toleranced andthe manner in which it is dimensioned,the tolerance zone may be one of thefollowing:


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i. The area within a circleii. The area between two concentric circles

iii. The area between two parallel lines

iv. The space within a sphere

v. The space within a cylinder or between two co axialcylinders

vi. the space between two parallel surfacevii.The space within a parallelopiped.


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The feature may be of any form ororientation within this tolerance zone,unless a more restricted indication is

given by an explanatory note.Further, unless otherwise specified,the tolerance applies to the wholelength or surface of the featureconsidered.


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Tolerance Zone

It is an imaginary area or volume, within which the controlledfeature of the manufactured component must be completelycontained, as shown in Figs. 4 a and b.

Fig. 4

ElementTolerance zone

Tolerance zone

Element

a Tolerance area b Tolerance Volume


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Definitions

Datum

It is a theoretically exact geometric reference such as axes,

planes, straight lines, etc., to which the tolerance features arerelated (Fig. 5).

Datum Feature

A datum feature is a feature of a part, such as an edge,

surface or a hole, which forms the basis for a datum or is used

to establish its location (Fig. 5).

Datum Triangle

The datums are indicated by a leader line, terminating in a

filed or an open triangle (Fig. 5).


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Fig. 5


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Datum Let t er

To identify a datum for reference purpose, a capital letter is

enclosed in a frame, connected to the datum triangle (Fig. 5).

Datum System

Datum system is a group of two or more separated datums,

used as a combined reference for tolerance features. In this

case, the sequence of datums referred, has considerableinfluence on the result obtained ( Fig. 6).


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The datum feature is the feature to which the tolerance of

orientation, position and run out are related. Further, the

form of datum feature should be sufficiently accurate for its

purpose and it may therefore be necessary in some cases to

specify tolerances of form from the datum features. Table 1

gives the symbols which represent the feature

characteristics to be controlled by the tolerance.


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Fig. 6 Datum System


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I ndicat ion of geomet rical t olerances on adrawing

To eliminate the need for descriptive notes, geometricaltolerances are indicated on drawings by symbols, tolerancesand datums, all contained in compartments of a rectangularframe, as shown in Fig.5.

Advant ages of using geomet r ical t olerances

1. Geometrical tolerances convey very briefly and precisely,the complete geometrical requirements on engineeringdrawings.


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2. he use of symbols and boxes, eliminates the need for

lengthy descriptive notes and corresponding dimensions,because of which the drawings are much clearer to read.

3. he symbols used are internationally recommended. Hence,the language barrier is minimized and misunderstanding iseliminated.

4. One type of geometrical tolerance can control anotherform. For instance, squareness can correct flatness andstraightness.


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I ndicat ion of features cont rolled

The feature controlled by geometrical tolerance is

indicated by an arrow head at the end of aleader line, from the tolerance frame. The toleranceframe is connected to the tolerance feature by aleader line, terminating with an arrow in the following

ways:


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On the outline of the feature, on extension of theoutline, but not a dimension line, when thetolerance refers to the line or surface itself

( Fig.7 a,b,c), and

On the projection line, at the dimension line,when the tolerance refers to the axis or medianplane of the part so dimensioned ( Fig. 7d) or on

the axis, when the tolerance refers to the axis ormedian plane of all features, common to that axisor median plane ( Fig.7e).


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Fig. 7 Indication of feature controlled (outline or surface only)

a - correct

d - correct

b - correct c - Incorrect

e - correct


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I ndicat ion of Datum features

The datum features are indicated by a leader line, terminatingin a solid triangle, the base of which lies,

1. On the outline of the feature or an extension of the outline( but not a dimension line), when the datum feature is theline or surface itself (Fig. 8a), and

2. On the projection line, at the dimension line, when thedatum feature is an axis or median plane of the part sodetermined ( Fig. 8b), or on the axis or median plane of all

the features, common to that axis or median plane ( Fig.8c), if such an axis can be determined with sufficientaccuracy.


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Note : The leader line shown on the right hand side is to be

connected to the feature to the toleranced with reference tothat datum indicated.

Fig. 8 I ndicat ion of datum features

a b c


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If the tolerance frame cannot be connected in a clear andsimple manner with the datum feature, a capital letter(different for every datum feature) is used (Fig. 9). If thetolerance is applied to a specified length, lying any where, thevalue of this length should be added after the tolerance value

and separated from it by an oblique stroke (Fig.10).

Fig. 9 I dent ificat ion of a datum feature


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B0.01/100//

Fig. 10 Tolerance over specified length

In the case of a surface, the same indication is used. Thismeans that the tolerance is applied to all the lines of specifiedlength in any position and direction.


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Boxed dimensions

These dimension are enclosed as 40 , 20. When the

dimensions are boxed, the corresponding actual dimensions

of the part are subjected only to the position tolerance.

Profile tolerance, angularity tolerance and size tolerances are

not given to the dimension.


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Tolerances of form for single features

Tolerance of st raight ness

The tolerance or perfect straightness of a line on a surfacemay be defined as the condition in which the distance betweenany two points on that line is always the shortest possible,when measured along the line.

The tolerance zone for controlling errors of straightness is thearea between two parallel lines, and the tolerance value is thedistance between these lines.

The line on the surface of the feature in Fig. 11 a can take anyform, provided it lies in an axial plane between two parallel

straight lines, 0.02 mm apart, as shown in Fig. 11 b.


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Fig. 11 Tolerances of st raightness


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Tolerance of f latness

The theoretical or perfect flatness of a surface may be defined

as the condition in which the distance between any two pointson that surface is always the shortest possible, whenmeasured along that surface.

The tolerance zone for controlling errors of flatness is thespace between two parallel planes, and the tolerance value isthe distance between these planes.

The surface controlled as shown in Fig. 12 a can take anyform, provided it lies in the space between two parallel flatplanes, 0.04 mm apart, as shown in Fig. 12 b.


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Fig. 12 Tolerances of f lat ness

b - Interpretationa - Example


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Tolerances of Roundness

The theoretical or perfect roundness of a surface may bedefined as the condition in which the surface has the form of aperfect circle, i.e., the distance between any point on the

circumference and the centre is always equal to the radius ofthe circle.

The tolerance zone for controlling errors of roundness is theannular area between two concentric coplanar circles, and thetolerance value is the radial distance between these circles.

In Fig. 13 a, the circle controlled, which may represent theperiphery at any cross-section, perpendicular to the axis, cantake any form, provided it lies in the space between twoconcentric circles, 0.03 mm radially apart, as shown in Fig.13b.


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Fig. 13 Tolerance of roundness



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Tolerances of Cyl indr icit y

Theoretical or perfect Cylindricity may be defined as thecondition in which all cross sections of solid are perfect circles,

with their centres lying on a straight axis.

The tolerance zone for controlling errors of Cylindricity is theannular space between two perfect cylindrical surfaces lying onthe same straight axis, and the tolerance value is the radialdistance between these surfaces.

The surface controlled as shown in Fig. 14 a may take anyform provided it lies between two perfect concentric cylinders,0.03 mm apart, as shown in Fig.14 b


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Fig. 14 Tolerance of Cyl indr icit y



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Prof ile tolerance of a line

The theoretical or perfect form of a profile is defined byboxed dimensions, which locate the true position of any point

on the line.

The tolerance zone has a constant width equal to thetolerance value, normal to the theoretical profile and equally

disposed about it. The tolerance zone is the area betweentwo lines which envelope circles of diameter equal to thetolerance value.

The profile line controlled in Fig. 15 a can take any formprovided it lies between two lines 0.05 mm apart, as shownin Fig.15b.


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Fig. 15 Prof ile t olerance of a line



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Prof ile tolerances of a sur face

The theoretical or perfect form of a surface is defined byboxed dimensions which locate the true position of any point

on that surface.

The tolerance zone is the space between two surfaces, whichenvelope spheres of diameter equal to the tolerance value,with their centers lying on the theoretical surface of thecorrect geometrical shape.

The curved surface of the part controlled as shown in Fig. 16ais required to lie between two surfaces, as shown in Fig. 16b.


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Fig. 16 Prof ile tolerance of a sur face



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Tolerances of Or ientat ion ( related features)

Tolerances of parallelism

Theoretical or perfect parallelism may be defined as thecondition in which all the perpendicular distances between theline or the surface controlled and the datum feature arealways the same.

The tolerance zone for controlling errors of parallelism is thearea between two parallel straight lines or the space betweentwo parallel planes, which are parallel to the datum feature.The tolerance value is the distance between the lines or

planes.The controlled top surface of the part as shown in Fig. 17 a isrequired to lie between two planes, 0.06 mm apart andparallel to the datum line or surface, as shown in Fig.17b.


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Fig. 17 Tolerances of parallelism



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Tolerances of squareness

Theoretical or perfect squareness may be defined as thecondition in which the feature controlled is truly perpendicularto the datum feature.

The axis of the vertical pillar as shown in Fig. 18 a is requiredto be contained within a tolerance cylinder of 0.05 mm

diameter, the axis of which is perpendicular to the datumsurface A, as shown in Fig. 18 b. The tolerance value here ispreceded by the symbol .

The controlled end surface of the second component isrequired to lie between two planes, 0.06 mm apart andperpendicular to the axis of the left side cylindrical portion(datum axis B).


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Fig. 18 Tolerances of squareness


T l f A l i


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Tolerances of Angular it y

Theoretical or perfect angularity may be defined as thecondition in which the controlled feature is inclined to thedatum feature at a specified true angle.

The tolerance zone for controlling errors of angularity is thearea between two parallel straight lines or the space betweenthe parallel planes which are inclined to the datum feature at

a specified angle. The tolerance value is the distance betweenthe lines or planes.

The controlled inclined surface of the part in Fig. 19 a are tolie between two planes, 0.1 mm apart which are inclined at60o to the datum axis of the cylindrical portion or the datumsurface, as shown in Fig. 19b.


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Fig. 19 Tolerances of Angular it y



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Tolerances of locat ion for related features

Tolerances of posit ion

The theoretical position of a feature is the specified trueposition of the feature as located by boxed dimensions.

The actual point shown in Fig. 20 a is required to lie within atolerance circle, 0.1 mm diameter, centered on the specifiedtrue point of intersection, as shown in Fig. 20 b.

The axis of the hole is required to be contained within atolerance cylinder 0.08 mm diameter, centered on thespecified true position.


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Fig. 20 Tolerances of Posit ion


T l f C t i it


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Tolerances of Concent r icit y

Theoretical or perfect concentricity may be defined as thecondition in which the controlled features which may be circlesor cylinders lie truly on the same centre or axis, as the datum

features.

The tolerance zone for controlling errors of concentricity is acircle or cylinder within which the center or axis of the

controlled feature is to be contained. The tolerance value isthe diameter of the tolerance zone.

The axis of the right side cylindrical portion of the componentas shown in Fig.21a is to be contained within a cylinder, 0.08mm diameter and is to be co axial within the axis of the leftside portion, which is the datum, as shown in Fig. 21b.


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Fig. 21 Tolerance of Concent r icit y



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Tolerances of symmet ry

Theoretical or perfect symmetry may be defined as thecondition in which the position of the feature is specified by itsperfect symmetrical relationship to a datum.

The tolerance zone for controlling errors of symmetry is thearea between two parallel lines or the space between the

parallel planes, which are symmetrically disposed about thedatum feature.

The median plane of the slot controlled as shown in Fig.22a, is

required to lie between two parallel planes, 0.08 mm apart,which are symmetrically disposed about the datum plane, asshown in Fig.22b.


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Fig. 22 Tolerance of symmetry



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Tolerance of run out

Theoretical radius may be defied as the condition in which thecontrolled features lie truly on a cylinder, with the same centre

or axis as the datum features.

(i) Radial run out The tolerance zone in this case limitedwithin any plane, perpendicular to the axis, by two concentric

circles, a distance t apart.

The radial run out a shown in Fig. 23a, must not be greaterthan 0.1 mm in any measuring plane, during one completedrevolution about the common axis of the surfaces A andB.


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(ii) Axial run out The tolerance zone is limited for any

measuring point, by two circles, a distance t apart, lying

on the measuring cylinder.

The axial run out must not be grater than 0.1 mm in any

measuring cylinder, during one complete revolution, about

the axis of the surface in Fig. 23b.


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Fig. 23 Tolerance of run out

a Radial run - out

b Axial run - out

Form and Position

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