Chapter Six - Geometrical Tolerances

7/31/2019 Chapter Six - Geometrical Tolerances

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Chapter six

GEOMETRICAL TOLERANCES

6.1 Introduction

Geometrical tolerances are applied over and above normal dimensional tolerances when it

is necessary to control more precisely the form or shape of some feature of a manufactured part,

because of the particular duty that the part has to perform. In the past, the desired qualities would

have been obtained by adding to drawings such expressions as surface to be true with one another,

surfaces to be square with one another, surfaces to be flat and parallel, etc., and leaving it to

workshop tradition to provide a satisfactory interpretation of the requirements.

Geometrical tolerances are used to transmit in a brief and precise manner complete

geometrical requirements on engineering drawings. They should always be considered for

surfaces which come into contact with other parts, especially when close tolerances are applied to

the features concerned.

Caution. It must be emphasized that geometrical tolerances should be applied only when

real advantages result, when normal methods of dimensioning are considered inadequate to

ensure that the design function is kept, especially where repeatability must be guaranteed.

Indiscriminate use of geometrical tolerances could increase costs in manufacture and inspection.

Tolerances should be as wide as possible, as the satisfactory design function permits.

The use of geometrical tolerances does not involve or imply any particular method of

manufacture or inspection.

6.2 Relationship between tolerances of size, form and position

According to current standards there are two possibilities ofmaking indications on technical

drawings in accordance with:

a) the principle of independence according to DIN ISO 8015 where tolerances of size, form

and position must be adhered to independent ofeach other, i.e. there is no direct relation

between them.

b) the envelope requirements according to DIN 7167, according to which the tolerances of size,

form and parallelism are in direct relation with each other, i.e. that the size tolerances limit

the form and parallelism tolerances.


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6.3 Application; general explanations

Feature is a general term applied to a physical portion of a part, such as a surface, hole, or

slot. A geometrical tolerance applied to a feature defines the tolerance zone within which the

feature is to becontained

.According to the characteristic which is to be tolerated and the manner in which it is

dimensioned, the tolerance zone is one of the following:

- the area within a circle;

- the area between two concentric circles;

- the area between two equidistant lines or two parallel straight lines;

- the space within a cylinder;

- the space between two coaxial cylinders;

- the space between two parallel planes;

- the space within a parallelepiped.

The toleranced feature may be ofany form orientation within this tolerance zone, unless a

more restrictive indication is given. Unless otherwise specified, the tolerance applies to the whole

length or surface of the considered feature.

A datum is a theoretically, perfect geometric shape or form from which a dimensional

measurement is made. A perfect point, line, flat plane, circle, or cylinders are all examples of

possible datums. The datum feature is a part feature that contacts a datum.

6.4 Tolerance frame

The tolerance requirements are shown in a rectangular frame which is divided into two or more

compartments. These compartments contain, from left to right, in the following order (Fig.6.1):

Fig.6.1 Tolerance frame.

- the symbol for the characteristic to be toleranced;

- the tolerance value in the unit used for linear dimensions. This value

is preceded by the sign if the tolerance zone is circular or

cylindrical;

- if appropriate, the capital letter or letters identifying the datum

feature or features.


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Table 1. Geometric characteristic symbols.

Arrowheads may be filled or not filled.

Table 2. Additional symbols.


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Remarks referred to the tolerance, for example 6 holes, 4 surfaces, or 6 x shall be

written above the frame (Fig.6.2a). If it is necessary to specify more than one tolerance

characteristic for a feature, the tolerance specifications are given in tolerance frames one below the

other (Fig.6.2b).

a) b)

Fig.6.2 Other tolerance frames.

6.5 Toleranced features

The tolerance frame is connected to the toleranced feature by a leader line terminatingwith an arrow in the following way:

a) b)

c) d)

e)

Fig.6.3 Toleranced features.

- on the outline of the feature or an extension of the

outline (but clearly separated from the dimension line)

when the tolerance refers to the line or surface itself

(Fig.6.3 a and b);

- as an extension of a dimension line when the

tolerance refers to the axis or median plane defined by

the feature so dimensioned (Fig.6.3 c and d); the

dimension line and frame leader line are drawn in line.

- on the axis or the median plane when the tolerance

refers to the common axis or median plane of two

features (Fig.6.3 e).

Note: Whether a tolerance should be applied to the contour of a cylindrical or symmetrical feature or

to its axis or median plane depends on the functional requirements.


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6.6 Tolerance zones

The tolerance zone is the zone within which all the points of a geometric feature (point,

line, surface, median plane) must lie. The width of the tolerance zone is in the direction of the

arrowof the

leaderline

joiningthe tolerance

frameto the feature which is toleranced, unless the

tolerance value is preceded by the sign (Fig.6.4 a, b).

a) b) c)

Fig.6.4 Tolerance zone.

Where a common tolerance zone is applied to several separate features, the requirement is

indicated by the words common zone above the toleranced frame (Fig.6.4 c).

6.7 Datums and datum systems

Datum features are features according to which a workpiece is aligned for recording the

tolerated deviations.

6.7.1 Datum

When a toleranced feature is referred to a datum, this is generally shown by datum

letters. The same letter which defines the datum is repeated in the tolerance frame.

Fig.6.5 Datum.

To identify the datum, a capital letter enclosed in a

frame is connected to a solid datum triangle (Fig.6.5).


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If a datum system the sequence oftwo or more datum features is important. The datum

letters are to be placed in different compartments, where the sequence from left to right shows the

order ofpriority, and the datum letter placed first should refer to the directional datum feature.

(Fig.6.9 a, b and c).

a) b) c)

Fig.6.9 Datum features.

6.7.2 Datum system

A datum system is a group oftwo or more datums to which one toleranced feature refers

in common. A datum system is frequently required because the direction of a short axis cannot be

determined alone.

- datum formed by two features (common datum) (Fig.6.8 c);

- datum system formedby two datums (short axis A and directional datum B (Fig.6.9 b);

- datum system formed by one plane and one perpendicular axis of a cylinder: datum A is the

plane formed by the plane contact surface; datum B is the axis of the largest inscribed cylinder,the axis being at right angles with datum A (Fig.6.9 c).

6.8 Theoretically exact dimensions

(a)

b)

Fig.6.10 Theoretically exact position.

Iftolerances ofposition or angularity are prescribed

for a feature, the dimensions determining the theoretically

exact position or angle shall not be toleranced.

These dimensions are enclosed, for example .

The corresponding actual dimensions of the part are subject

only to the position tolerance or angular tolerance specified

within the tolerance frame (Fig.6.10a and b).


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6.9 Detailed definitions of tolerances

Symbol Definition of the tolerance zone Indication and interpretation

6.9.1 Straightness tolerance

The tolerance zone when projectedin a plane is limited by two parallelstraight lines a distancet apart.

Fig.6.11

Any line on the upper surface parallel to the planeof projection in which the indication is shownshall be contained between two parallel straightlines 0,1 apart.

Fig.6.12

Any portion of length 200 of any generator of the

cylindrical surface indicated by the arrow shall becontained between two parallel straight lines 0,1apart in a plane containing the axis.

Fig.6.13The tolerance zone is limited by aparallelepiped of section t1.t2 if thetolerance is specified in twodirections perpendicular to each

other.

Fig.6.14

The axis of the bar shall be contained within aparallelepipedic zone of width 0,1 in the verticaland 0,2 in the horizontal direction.

Fig.6.15

The tolerance zone is limited by acylinder of diameter t if thetolerance value is preceded by thesign .

Fig.6.16

The axis of the cylinder to which the tolerance isconnected shall be contained in a cylindrical zoneof diameter 0,08.

Fig.6.17


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6.9.2 Flatness tolerance

The tolerance zone is limited by twoparallel planes a distancet apart.

Fig.6.18

The surface shall be contained between twoparallel planes 0,08 apart.

Fig.6.19

6.9.3 Circularity tolerance (roundness)

The tolerance zone in the consideredplane is limited by two concentriccircles a distancet apart.

Fig.6.20

The circumference of each cross-section of theoutside diameter shall be contained between twoco-planar concentric circles 0,03 apart.

Fig.6.21

The circumference of each cross-section shall becontained between two co-planar concentric

circles 0,01 apart.

Fig.6.22

6.9.4 Cylindricity tolerance

The tolerance zone is limited bytwo coaxial cylinders a distance tapart.

Fig.6.23

The considered surface area shall be containedbetween two coaxial cylinders 0,1 apart.

Fig.6.24


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6.9.5 Profile tolerance

6.9.5.1 Profile tolerance of any line

(a) BilateralThe tolerance zone is limited by twolines enveloping circles of adiameter t,the centres of which aresituated on a line having thetheoretically exact geometricalform.

Fig.6.25

In each section parallel to the plane of projectionthe considered profile is to be contained betweentwo lines enveloping circles of diameter 0,04 thecentres of which are situated on a line oftheoretically exact geometrical profile.

Fig.6.26

(b) Unilateral

The tolerance zone is limited by twolines enveloping circles of diametert, one line being the theoreticallyexact profile.

Fig.6.27

In any section parallel to the plane of projection ofthe drawing, the actual profile is to lie between thetheoretical profile and a line which envelops aseries of circles 0,1 diameter.

Fig.6.28


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6.9.5.2 Profile tolerance of any surface

a) Bilateral

The tolerance zone is limited by two

surfaces enveloping spheres ofdiameter t, the centres of which aresituated on a surface having thetheoretically exact geometrical form.

Fig.6.29

The considered surface is to be contained betweentwo surfaces enveloping spheres of diameter 0,02

the centres of which are situated on a surface oftheoretically exact geometrical form.

Fig.6.30

b) Unilateral

The tolerance zone is limited by twosurfaces enveloping spheres ofdiameter t, one being thetheoretically exact profile.

Fig.6.31

The considered surfaces is to lie between twosurfaces which envelop a series of spheres, 0,02diameter, one surface being theoretically exact.

Fig.6.32


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6.9.6 Parallelism tolerance

6.9.6.1 Parallelism tolerance of a line with reference to a datum line

The tolerance zone when projectedin a plane is limited by twoparallel straight lines a distance tapart and parallel to the datumline, if the tolerance zone is onlyspecified in one direction.

Fig.6.33

Fig.6.34

The toleranced axis shall be contained between twostraight lines 0,1 apart, which are parallel to thedatum axis A and lie in the vertical direction(Fig.6.35 and 6.36).

Fig.6.35 Fig.6.36

The toleranced axis shall be contained between twostraight lines 0,1 apart, which are parallel to thedatum axis A and lie in the horizontal direction.

Fig.6.37The tolerance zone is limited by aparallelepiped of section t1.t2 andparallel to the datum line if thetolerance is specified in two planesperpendicular to each other.

Fig.6.38

The toleranced axis shall be contained in aparallelepipedic tolerance zone having a width of 0,2in the horizontal and 0,1 in the vertical direction andwhich is parallel to the datum axis A (Fig.6.39 and6.40).

Fig.6.39 Fig.6.40


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6.9.6.2 Parallelism tolerance of a line with reference to a datum line (continued)The tolerance zone is limited by a

cylinder of diameter t parallel tothe datum line if the tolerancevalue is preceded by the sign .

Fig.6.41

The toleranced axis shall be contained in a

cylindrical zone of diameter 0,03 parallel to thedatum axis A (datum line).

Fig.6.42

6.9.6.3 Parallelism tolerance of a line with reference to a datum surfaceThe tolerance zone is limited bytwo parallel planes a distance tapart and parallel to the datumsurface

Fig.6.43

The toleranced axis of the hole shall be containedbetween two planes 0,01 apart and parallel to thedatum surface B

Fig.6.44

6.9.6.4 Parallelism tolerance of a surface with reference to a datum lineThe tolerance zone is limited bytwo parallel planes a distance tapart and parallel to the datumline.

Fig.6.45

The toleranced surface shall be contained betweentwo planes 0,1 apart and parallel to the datum axisC of the hole.

Fig.6.46


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6.9.6.5 Parallelism tolerance of a surface with reference to a datum surfaceThe tolerance zone is limited by twoparallel planes a distancet apart and

parallel to the datum surface.

Fig.6.47

The toleranced surface shall be contained betweentwo parallel planes 0,01 apart and parallel to the

datum surface D (Fig.6.48).

Fig.6.48 Fig.6.49

All the points of the toleranced surface in a lengthof 100, placed anywhere on this surface, shall becontained between two parallel planes 0,01 apart

and parallel to the datum surface A (Fig.6.49).

6.9.7 Perpendicularity tolerance (squareness)6.9.7.1 Perpendicularity tolerance of a line with reference to a datum line

The tolerance zone when projectedin a plane is limited by two parallelstraight lines a distance t apart andperpendicular to the datum line.

Fig.6.50

The toleranced axis of the inclined hole shall becontained between two parallel planes 0,06 apartand perpendicular to the axis of the horizontal holeA (datum line).

Fig.6.51

6.9.7.2 Perpendicularity tolerance of a line with reference to a datum surfaceThe tolerance zone when projectedin a plane is limited by two parallelstraight lines a distance t apart andperpendicular to the datum plane ifthe tolerance is specified only in onedirection.

Fig.6.52

The toleranced axis of the cylinder, to which thetolerance frame is connected, shall be containedbetween two parallel planes 0,1 apart,perpendicular to the datum surface.

Fig.6.53


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6.9.7.3 Perpendicularity tolerance of a line with reference to a datum surface (continued)

The tolerance zone is limited by aparallelepiped of section t1.t2 and

perpendicular to the datum surface ifthe tolerance is specified in twodirections perpendicular to eachother.

Fig.6.54

The toleranced axis of the cylinder shall becontained in a parallelepipedic tolerance zone of

2,01,0

which is perpendicular to the datumsurface.

Fig.6.55

The tolerance zone is limited by acylinder of a diameter tperpendicular to the datum surface ifthe tolerance value is preceded bythe sign .

Fig.6.56

The toleranced axis of the cylinder to which thetolerance frame is connected shall be contained ina cylindrical zone of diameter 0,01 perpendicularto the datum surface A.

Fig.6.57

6.9.7.4 Perpendicularity tolerance of a surface with reference to a datum surface

The tolerance zone is limited by twoparallel planes a distancet apart andperpendicular to the datum surface.

Fig.6.58

The toleranced surface shall be contained betweentwo parallel planes 0,08 apart and perpendicular tothe horizontal datum surface A.

Fig.6.59


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6.9.8 Angularity tolerance

6.9.8.1 Angularity tolerance of a line with reference to a datum linea) Line and datum line in the same

planeLine and datum line in the sameplane. The tolerance zone whenprojected in a plane is limited bytwo parallel straight lines a distancet apart and inclined at the specifiedangle to the datum line.

Fig.6.60

The toleranced axis of the hole shall be contained

between two parallel straight lines 0,08 apartwhich are inclined at 600 to the horizontal axis A-B (datum line).

Fig.6.61b) Line and datum line in different

planes

The tolerance zone is applied to theprojection of the considered line onthe plane containing the datum lineand parallel to the considered line.

Fig.6.62

The axis of the hole, projected on a planecontaining the datum axis, is to be containedbetween two parallel straight lines 0,08 apartwhich are inclined at 600 to the horizontal datumaxis A-B.

Fig.6.63


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6.9.8.2 Angularity tolerance of a line with reference to a datum surface

The tolerance zone, when projectedon a plane, is limited by two parallel

straight lines a distance t apart andinclined at the specified angle to thedatum surface.

Fig.6.64

The axis of the hole is to be contained betweentwo parallel planes 0,08 apart which are inclined at

60

0

to datum surface A.

Fig.6.65

6.9.8.3 Angularity tolerance of a surface with reference to a datum line

The tolerance zone is limited bytwo parallel planes a distance tapart and inclined at the specifiedangle to the datum line.

Fig.6.66

The inclined surface is to be contained betweentwo parallel planes 0,1 apart which are inclined at750 to datum axis A.

Fig.6.67

6.9.8.4 Angularity tolerance of a surface with reference to a datum surface

The tolerance zone is limited bytwo parallel planes a distance tapart and inclined at the specified

angle to the datum surface.

Fig.6.68

The toleranced surface shall be contained betweentwo parallel planes 0,08 apart which are inclined at400 to the datum surface A.

Fig.6.69


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6.9.9 Positional tolerance

6.9.9.1 Positional tolerance of a point

The tolerance zone is limited by acircle of diameter t, the centre ofwhich is in the theoretically exactposition of the considered point.

Fig.6.70

The actual point of intersection is to be containedwithin a circular zone of 0,3 diameter, the centreof which coincides with the theoretically exactposition of the considered point of intersection.

Fig.6.71

6.9.9.2 Positional tolerance of a line

The tolerance zone when projectedin a plane is limited by twoparallel straight lines a distance t

apart and disposed symmetricallywith respect to the theoreticallyexact position of the consideredline if the tolerance is specifiedonly in one direction.

Fig.6.72

Each of the toleranced lines shall be containedbetween two parallel straight lines 0,05 apartwhich are symmetrically disposed about the

theoretically exact position of the considered line,with reference to the surface A (datum surface).

Fig.6.73


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6.9.9.3 Positional tolerance of a line (continued)When the tolerance is specified intwo directions perpendicular toeach other the tolerance zone is

limited by a parallelepiped ofsection t1.t2 the centre line ofwhich is in the theoretically exactposition of the considered line.

Fig.6.74

Each of the axes of the eight holes is to becontained within a parallelepipedic zone ofwidth0,05 in the horizontal and 0,2 in the vertical

direction the centre line of which is in thetheoretically exact position of the considered holeaxis.

Fig.6.75

When the tolerance value ispreceded by the diameter symbolthe tolerance zone is limited by acylinder of diameter t the axis ofwhich is in the theoretically exactposition of the considered line.

Fig.6.76

The axis of the hole is to be contained within acylindrical zone of diameter 0,08 the axis of whichis in the theoretically exact position of theconsidered line, with reference to the datumsurfaces A and B.

Fig.6.77

Each of the axes of the eight holes is to becontained within a cylindrical zone of diameter 0,1the axis of which is in the theoretically exactposition of the considered hole axis.

Fig.6.78


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6.9.9.4 Positional tolerance of a flat surface or a median plane

-

The tolerance zone is limited by

two parallel planes a distance t

apart and disposed symmetrically

with respect to the theoretically

exact position of the considered

surface.

Fig.6.79

The inclined surface shall be contained between

two parallel planes which are 0,05 apart and

which are symmetrically disposed with respect to

the theoretically exact position of the considered

surface with reference to the datum surface A

and the axis of the datum cylinder B (datum

line).

Fig.6.80

6.9.10 Concentricity and coaxiality tolerance

6.9.10.1 Concentricity tolerance of a point

The tolerance zone is limited bya circle of diameter t the centreof which coincides with thedatum point.

Fig.6.81

The centre of the circle, to which the toleranceframe is connected, shall be contained in a circleof diameter 0,01 concentric with the centre ofthe datum circle A.

Fig.6.82


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6.9.10.2 Coaxiality tolerance of an axis

The tolerance zone is limited by a

cylinder of diameter t, the axis of

which coincides with the datum axis

if the tolerance value is preceded by

the sign .

Fig.6.83

The axis of the cylinder, to which the tolerance

frame is connected, shall be contained in a

cylindrical zone of diameter 0,08 coaxial with the

datum axis A-B.

Fig.6.84

6.9.11 Symmetry tolerance

6.9.11.1 Symmetry tolerance of a median plane

The tolerance zone is limited by twoparallel planes a distancet apart anddisposed symmetrically to themedian plane with respect to thedatum axis or datum plane.

Fig.6.85

The median plane of the slot shall be containedbetween two parallel planes, which are 0,08 apartand symmetrically disposed about the medianplane with respect to the datum feature A.

Fig.6.86


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6.9.11.2 Symmetry tolerance of a line or an axis

The tolerance zone when projectedin a plane is limited by two parallel

straight lines a distance t apart anddisposed symmetrically with respectto the datum axis, if the tolerance isspecified only in one direction.

Fig.6.87

The axis of the hole shall be contained betweentwo parallel planes which are 0,08 apart and

symmetrically disposed with respect to the actualcommon median plane of the datum slots a and B.

Fig.6.88

The tolerance zone is limited by a

parallelepiped of sectiont1.t, the axisof which coincides with the datumaxis if the tolerance is specified intwo directions perpendicular to eachother.

Fig.6.89

The axis of the hole shall be contained in a

parallelepipedic zone of width 0,1 in thehorizontal and 0,05 in the vertical direction andthe axis of which coincides with the datum axisformed by the intersection of the two medianplanes of the datum slots A-B and C-D.

Fig.6.90


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6.9.12 Circular run-out tolerance

6.9.12.1 Circular run-out tolerance - radial

The tolerance zone is limited withinany plane of measurementperpendicular to the axis by twoconcentric circles a distance t apart,the centre of which coincides withthe datum axis.

Fig.6.91

Note: Run-out normally applies tocomplete revolutions about the axisbut could be limited to apply to apart of a revolution.

The radial run-out shall not be greater than 0,1 inany plane of measurement during one revolutionabout the datum axis A-B.

Fig.6.92

The radial run-out shall not be greater than 0,2 inany plane of measurement when measuring thetoleranced part of a revolution about the axis ofthe datum hole A.

Fig.6.93

Fig.6.94


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6.9.12.2 Circular run-out tolerance- axial

The tolerance zone is limited at anyradial position by two circles a

distancet apart lying in a circular ofmeasurement, the axis of whichcoincides with the datum axis.

Fig.6.95

The axial runout shall not be greater than 0,1 atany position of measurement during one

revolution about the datum axis D.

Fig.6.96

6.9.12.3 Circular run-out tolerance in any direction

Within any cone of measurementthe tolerance zone is limited bytwo circles a diameter t apart. Theaxis of the cone of measurementcoincides with the datum axis.

Unless otherwise specified thedirection of measurement isperpendicular to the surface.

Fig.6.97

The run-out in the direction indicated by the arrowis to be not greater than 0,1 in any cone ofmeasurement during one revolution about thedatum axis C.

Fig.6.98

The run-out in the direction perpendicular to thetangent of the curved surface is to be not greaterthan 0,1 in any cone of measurement during onerevolution about the datum axis C.

Fig.6.99


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6.9.12.4 Circular run-out tolerance in a specified direction

Within any cone of measurement of

the specified angle the tolerancezone is limited by two circles adistancet apart. The axis of the coneof measurement coincides with thedatum axis.

Fig.6.100

The run-out in the specified direction is to be not

greater than 0,1 in any cone of measurement

during one revolution about the datum axis C.

Fig.6.101

6.9.12.5 Total radial run-out tolerance

The tolerance zone is limited by twocoaxial cylinders a distance t apart,the axes of which coincide with thedatum axis.

Fig.6.102

The total radial run-out is to be not greater than0,1 at any point on the specified surface whilstrevolving about the datum axis A-B, and withrelative axial movement between workpiece andmeasuring instrument. With relative movement themeasuring instrument or the workpiece is to be

guided along a line having the theoretically exactform of the contour and being in its correctposition relative to the datum axis.

Fig.6.103


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6.9.12.6 Total axial run-out tolerance

The tolerance zone is limited bytwo parallel planes a distance tapart and perpendicular to thedatum axis.

Fig.6.104

The total run-out is to be not greater than 0,1 atany point on the specified surface whilst revolvingabout the datum axis D and with relative radialmovement between the measuring instrument andthe workpiece. With relative movement themeasuring instrument or the workpiece is to beguided along a line having the theoretically exactform of the contour and being in its correctposition relative to the datum axis.

Fig.6.105


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6.10 Additional explanations

Onecommon

area ofconfusion

within Geometrical Tolerances is thedifferences

betweenthe various ways of specifying how true a cylindrical surface or surface of revolution is:

circularity (roundness), cylindricity, concentricity, circular runout, and total runout.

As shown in Fig.6.106, circularity applies to individual circular cross sections of a surface

ofrevolution or of a sphere.

Fig.6.106 Circularity (Roundness).

Cylindricity, on the other hand, applies to all cross-sections of a cylindrical surface

simultaneously. The surface must lie between the two cylindrical surface which bound the

tolerance zone and are determined by a best-fit nominal cylinder. Fig.6.107 illustrates cylindricity.

Fig.6.107 Cylindricity.

Fig.6.108 Diametral measurement.

It is a common misconception that circularity and

cylindricity can be checked by taking diametral

measurements Fig.6.108 (as with a micrometer) or by

using an indicator and Vee block (Fig.6.110). A diametral

measurement doesjust what the words imply; it measures

the diameter. It does not check the shape of the surface

which is what circularity and cylindricity control.


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Fig.6.109 Measuring over the flat surface.

A dial indicator is positioned over

the surface to a reference height. The

part is then rolled underneath. The peak

height can then be compared to other

readings (Fig.6.109).

Fig.6.111

With this test the two readings shown

would indicate circularity, when in fact

this is not true (Fig.6.111). When using

the Flat Plane, the diameters can be

directly obtained.

Fig.6. 110 Measuring with Vee block.

A dial indicator is positioned over the surface to a

reference height. The part is then rolled underneath.

The peak height can then be compared to other

readings. The Vee support reduces the effect of a

single datum point (Fig.6.110).

Fig.6. 112

This test would exaggerate the circularity error such

that it would be greater than the actual error

(Fig.6.112). When using the Vee block, some

additional calculations are required to find the diameter

value.

The Vee block method has particular disadvantages:

- a number of angles are required (the standard angle is 900);

- only suitable for regular odd lobed figures.


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Fig.6. 113 Measuring a part between centers.

The centre support method also has

disadvantages:

-the part may be bowed, or warped;

-off centre or degraded centre holes will

decreasereading

quality;

-the centres themselves can also affect

readings.

However, rotating a part between centers

(Fig.6.113) is not an acceptable method since it

relates the part surface to an axis, which

technically is a check of another geometric

tolerance called runout.

Since the circularity or cylindricity tolerance is a radial distance between concentric

boundaries, aradial method ofchecking the surface is necessary.

To truly check for the circularity or cylindricity of a surface without regard to the axis of

the part, the part must be rotated about the ultra-precision spindle of a specialized circularity

measuring machine. A probe contacts the surface and transcribes an enlarged profile of the

surface onto a polar graph. The profile is then checked against a clear overlay of concentriccircles to determine if it falls within the allowable tolerance zone.

Circularity is usually assessed by rotational techniques by measuring radial deviations

from a rotating datum axis; this axis remains fixed and becomes the main reference for all

measurements. There are two common ways of measuring circularity.

Fig.6.114 Component rotation.

One method involves rotation of the part while

keeping the measuring transducer fixed and the

other involves keeping the component fixed

while rotating the measuring transducer.

In fig.6.114 the component is rotated on a highly

accurate spindle that provides the reference for

the circular datum.


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Fig.6.115 Rotating stylus.

In Fig.6.115, the axis of the component is aligned

with the axis of the spindle, using a centering and

leveling table. A transducer is then used to

measureradial

variationsof the

componentwith

respect to the spindle axis.

Concentricity is the condition in which the axes ofall cross-sectional elements of a surface

of revolution are common to the axis of a datum feature (Fig.6.116). Because the location of the

datum axis is difficult to find, it is easier to inspect for cylindricity or runout.

Fig.6.116 Concentricity.

Eccenticity the Talyrond can also be used to detect concentricity. A simple example is a bearingrace shown below (Fig.6.117).

Fig.6. 117 The stylus measures the profile for both

the inside and outside, and then these can be

compared to determine concentricity. Fig.6.118 A trace from Talyrond.


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Avoid specifying concentricity. Concentricity requires deriving the median line of a

feature. All of the features shown below are concentric (Fig.6.119). Usually, designs require that a

feature be round as well as concentric like example A.

A better geometric control is usually circular runout. Circular runout controls circularity

(roundness) as well asconcentricity

.

Fig.6.119 Runout vs. concentricity.

Runout refers to the result ofplacing a solid of revolution on a spindle such as a lathe, and

rotating the part about its central axis while measuring with a dial indicator its surface deviation

from perfect circularity.

Fig.6.120 Circular runout.

With circular runout, the dial

indicator is not moved along the

direction of the axis of the part.

Circular runout is therefore applied

independently at each station along

the length of the part as the part is

rotated through 360 degrees (Fig.6.

120 ).


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Total runout involves moving the dial indicator along the length of the part while the part

is rotated, so that it controls the cumulative variations ofcircularity, cylindricity, straightness,

coaxiality, angularity, taper, and profile (Fig.6.121).

Fig.6.121 Total runout applies to all cross sections simultaneously.

Confusion continues to exist over the difference between circular runout (one arrow) and

total runout (two arrows). To inspect the two runouts illustrated below, an inspector could set up

the inspection as illustrated. While rotating the part on the pin, several slices along the part could be

inspected (Fig.6.122).

Fig.6.122 Circular runout vs. total runout.


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Fig.6.123 In this case the part would pass both runout

checks.

The worst circular runout error occurs at

the slice with the greatest variation.

In this case two slices vary a total of 0.03.

Totalrunout is the

differencebetween the

highest and lowest readings found over the

entire feature (Fig.6.123). The highest reading

was +0.02 and the lowest reading was -0.09.

Therefore, the total runout for the feature is

0.11, the difference between +0.02 and -0.09.


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a)

b)

a)

b)

a)

b)

Fig.6.124 a) Circular runout as is given; b) Interpretation.


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Example:

a)

b)Fig.6.125 Total runout: on drawing; b) interpretation.

Chapter Six - Geometrical Tolerances

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Transcript of Chapter Six - Geometrical Tolerances