Per Bennich, Ph.D.

Dr. Bennich is the chairman of ISO TC 213 "Dimensional and geometrical

product specifications and verification - GPS," the technical committee
responsible for the standards covered in this book. He has held this position
since the Technical Committee was started in 1996. From 1993 to 1996 he
was the Chairman of the precursor to ISO TC 213, ISOfTC 3-10-57/JHG
"Joint Harmonization Group" for geometrical product specifications (GPS).
He has participated in international standardization since 1980.

Dr. Bennich received a M.Sc. in Mechanical Engineering in 1970 and a

Ph.D for a thesis on metal forming in 1975 from the Technical University of
Denmark in Copenhagen.

From 1973 to 1990 Dr. Bennich was the Manager of the Branch for
Mechanical Processing of Materials at IPU, the Institute for Product
Development, a private consulting company located at the Technical
University of Denmark.

In 1990 Dr. Bennich started his own consulting business, PB Metrology

Consulting, specializing in:

Engineering metrology, calibration and testing of measuring

equipment and products
Quality assurance of industrial measurement and calibration
Certification and accreditation
GPS Dimensioning and tolerancing on engineering drawings.

He teaches public seminars on all of these subjects through various

organizations as weil as customized in-house company seminars. Over the
last 10 years he has taught GPS in 3-4 day public and company specific
seminars to more than 1000 people from over 20 companies.

From 1980 to 1999 Dr. Bennich taught a 300 hour curriculum in geometrical
metrology for industrial metro log ist students (an 18 month associate
program) at the Slageise Technical College.

Dr. Bennich is also the founder and chairman of The Danish Society for
Engineering Metrology - FVM (founded 1982). The Society has 700 member
companies from Denmark and other Scandinavian countries. The society
puts on 3 one day symposia each year.
Foreword

The GPS Pocket Book, First Edition , wh ich is the tille of this book , gives a Fund .
brief presentation of the most important and the most frequently used toler- Global
ance symbols in GPS tolerancing.
Dirn.
Tol.
The GPS Pocket Book also presents the most common rules and the most
basic grammar related to the GPS symbol language. Datum
TED
The GPS Pocket Book is not intended for stand alone use. It does not give a
complete and exhaustive presentation of GPS. The purpose of the GPS Pocket Geom.
Tol.
Book is to be a memory aid for people who are using GPS in their daily work.

The GPS Pocket Book is intended for use together with the more than one
hundred GPS standards issued by ISO. Only very few of these are refer-
enced and mentioned in the text. The fact that a standard is mentioned does
not mean that it is the most important, only that it is the most obvious place to
look for that particular issue. Q

It can be quite dillicult to find all the information and rules that apply to a 1.
specific GPS drawing indication or type of requirement. Therefore, our website ,
www.lfGPS.com contains a database that allows you to search for the GPS // ~
standards that apply to a given subject.
@
Standards not yet issued by ISO on the issue date of this pocket guide are -=t
marked with the symbol , a, before the designation.
l
The GPS Pocket Book is published by the Institute for Geometrical Product
U
Specifications. It is available in several languages. For more information, see
www.lfGPS.com.
®
Authors: ®
®
Per Bennich, Ph.D. , PB Metrology Consulting
www.bennich.dk

and L
;r-
Henrik Nielsen, Ph.D. HN Metrology Consulting Gen.
www.HN-Metrology.com Tol.

Y14.5

ISBN 0-9763032-0-5
© 2004 Per Bennich and Henrik Nielsen
 Fundamental and Global GPS Rules
Geometrical Product Specilications (GPS) used on drawings are based on the lollowing
principles and rules, which ~ apply il GPS tolerance symbols are used on the drawing.

GPS matrix system hierarchy - ISOITR 14638

GPS standards are organized in a hierarchy: Fundamental, Global, General, and
Complementary standards. Principles and rules given in Fundamental standards apply for all
other standards. Principles and rules given in Global standards apply lor General and
Complementary standards. Principles and rules given in General standards apply lor
Complementary GPS standards. There mayaiso be hidden principles and rules il you do not
know the GPS matrix system.

Operator principle - ISOITS 17450-1 and-2

An operator is adefinition of a geometrical characteristic based upon operations. GPS
standards define specification operators, which are controlled unambiguously by the indication
on the drawing . Specilication operators are formulated as virtual measuring procedures. The
verification operator is the physical implementation 01 the specilication operator in a measuring
procedure.

Ouality principle - ISOITS 17450-1 and -2

The Ouality principle states that the specification operator defines the requirement on the
drawing. The specification operator on the drawing is defined independently 01 any measuring
procedure or measuring equipment. If the verification operator (measuring procedure) is a
theoretically perfect implementation 01 the specilication operator, the measurement result is
without measurement uncertainty. The deviation 01 the verilication operator from the
specification operator indicated on the drawing is a contribution to the measurement uncertainty.

Independency principle - ISO 8015 J elSO 14659

Any specilication on a drawing is independent of all other specifications, and all specifications
shall be met without any influence from other specifications unless it is explicitly indicated
otherwise on the drawing. Only two such exceptions exist, the maximum material requirement
(MMR) and the minimum material requirement (LMR). indicated by ® and CD respectively.

The drawing is definitive principle - elSO 14659

What is not specilied on a drawing can not be required. A GPS requirement only exists if it is
explicitly indicated on the drawing or if it is defined in a GPS standard.

Oefault principle - ISOITS 17450-2

A complete specification operator can be indicated by the shortest indication for a GPS
characteristic, the basic GPS specification. The basic GPS specification results in the default
definition of the specification operator, which can be seen in standards only, it is not visible on
the drawing.

Reference cenditien principle - ISO 1, ISOJR 1938, el SO 14659

Oefault values for physical inlluence quantities are defined. II not otherwise indicated, the
relerence temperature lor the tolerances on the drawing is 20°C. The work piece is not

2
 Fundamental and Global GPS Rules
inlluenced by external lorces, not even the lorce of gravity. Other influence quantities
shall be delined on the drawing.

Uncertainty principle - ISOfTS 17450-2

Doubt and deviations result in uncertainties in the sense given in GUM (ENV 13005).
In the GPS matrix system several different types of uncertainties are delined:

Measurement uncertainty: the result 01 the difference between the specification

operator on the drawing and the chosen actual verification operator. The person
•
Dirn.
Tol.

Datum
TED
Geom.
who chooses the verilication operator is in control of the magnitude of the measure-
Tol.
ment uncertainty (see ISOfTS 14253-2). The measurement uncertainty is the re-
sponsibility 01 the metro log ist.

Specilication uncertainty: the uncertainty due to the range of allowed interpretations

of a GPS specilication given on a drawing when it is applied to the real work
piece with lorm and angular deviations Irom the nominal geometry. The
specification uncertainty is the range 01 values that will be obtained by the different
interpretations of the specification. The specification uncertainty is the Cl
responsibility 01 the designer. The supplier is allowed to take advantage 01 the ..1
specilication uncertainty. The supplier may choose any interpretation in the range
allowed by the specification uncertainty. The result is an extension of the tolerance
given on the drawing, with the size 01 the specilication uncertainty at both tolerance //~
limits.

Correlation uncertainty: the uncertainty quantifying how weil the specifications -=, @

on the drawing express (simulate) the lunction 01 the work piece.

Conformance/non-conformance rule - ISO 14253-1

tJ'
The measurement uncertainty always works against the party who shall prove
conformance or non-conlormance with a specification. When conformance with a ®
specilication shall be proven, the measurement uncertainty, U, reduces the
specification to the conlormance zone at both tolerance limits. When non-
conformance shall be proven , the measurement uncertainty, U, expands the tolerance
at both tolerance limits.

Rule lor non indicated decimals in tolerances - olSO 14659

Non indicated decimals in a tolerance indication are zeros, e.g 0,2 is the same as
0,20000000000 ....... 0000. L
r
Interpretation rules lor specilications indicated on a drawing - olSO 14659 Gen.
A drawing shall always be interpreted according to the rules given in the GPS Tol.
standards that were in lorce when the drawing was made. The main rule is that the
acceptance date 01 the drawing is the key to the interpretation of the specifications
on the drawing. Only when the symbols used to express the specilications are either Y14.5
newer or older than the acceptance date, do they alter the interpretation rule.

3
 Tolerancing by Dimensions
Linear size (the diameter of a cylinder or the distance between two parallel
flat opposite surfaces). ISO 129, ISO 286-1, ISO 1938, ISO 8015 and alSO
14405.

Two methods for unambiguous tolerancing of size exist. The two methods do
not result in the same tolerance limits:

Method #1 - ISO 8015, ±tolerances and envelope requirement ®

Method #2 - ISO 286-1 and ISO/R 1938 - Tolerance code

Explanations:
-L---I-----,I]
L " Lmax, distance between two parallel tangential planes or the diameter of
the minimum circumscribed cylinder. L" Lmin, two-point distance er diame-
ter. The two-point distance/diameter and the direction are defined in
ISO 14660-2.

Linear size indicated by ±tolerance without indication of operator

A linear size indicated by a ±tolerance without supplementary indication (mod-
ifier symbol) according to method 1 or 2 above is not defined on the real work

1 I]I
piece.

0=1
alSO 14405 will include a number of symbols (modifiers) in addition to ®,
which can specify wh ich diameter definition (specification operator) is required
by the drawing , e.g.: @, @, @, @ and @ID .

4
 Tolerancing by Dimensions
Angular size - ISO 8015 (The definition is only active if a reference is made Fund.

•
to ISO 8015 on the drawing - otherwise angular size has no operator defini- Global
tion). The angle between two tangential lines in the surfaces .

Angular size between two flat opposing surfaces of approximately the same
size:
Datum
TED
Geom.
Tol.

Dimension indication for non linear size

All other types of dimensions, except size, with ± tolerances, see examples a) Cl
through f), are not defined on the real work piece. The result is specification ..1
uncertainty. Dimension tolerancing with ± tolerances , therefore , should not
be used on new drawings. Use geometrical tolerances instead.
//~
I I I 20 ±O,~

n
10 ±O,l 30 ±0,2
@
I I ~;

CJ 1.,111 1 ~~
I i
tJ'
a) b) c)
®
28° ±Q 1°
®

M f)1 fj
®

d) e) f) L
~
a Linear distance between two integral features (step height) Gen.
b Linear distance between an integral and a derived feature Tol.
c Linear distance between two derived features
d Radial distance for an integral or a derived feature Y14.5
e Angular distance between an integral and a derived feature
f Angular distance between two derived features

5
 Datums, Datum Systems, and TED Patterns
Datum - Associated theoretically perfect feature (point, straight line or plane) as a
reference for the toleranced feature - ISO 5459.

Several types of datums exist:

Single datum - One datum used alone.

Common datum - Two or more single datums used together as a single

datum.

Datum system - Two or more single datums or common datums used as a

coordinate system.

Datum target(s) - Part(s) of a datum feature used as a basis for a single

datum .

Datum indication on the drawing

A datum indicator on the contour line or the extension line indicates the surface to be
used as the basis for a datum.

Indication of the axis of a cylinder or the median plane between two surfaces as a
datum.

R
 Datums, Datum Systems, and TED Patterns
Datums and datum systems are described in ISO 1101 and ISO 5459 Fund.
Global
A tolerance can refer to a datum or a datum system in the following ways:
Dim.
~ Reference to a single datum. Tol.

~ Reference to a common datum of A and B. •

I I lAIBlei Reference to a datUm system - A is the primary datum, B Geom.

is the secondary datum and C is the tertiary datum . Tol.

fiiJ fiiJ fiiJ ~A1.2.3 Datum target indicators.

Example of a datum system

~+I4>O,2IAIBI~

Drawing:
Interpretation:
Datum B is the axis in the
largest inscribed eylinder
®
®

L
~
Gen.
The real work piece is positioned and oriented in the datum system
Tol.
according to the rules of priority for the datums in the datum systems .

Y14.5

7
 Datums, Datum Systems, and TED Patterns
The use 01 geometrical characteristic requirements, datums, and datum systems

There are 14 different geometrical characteristics, each represented by its own symbol ,
that can be used to deline requirements to the leatures 01 a workpiece or to the relation-
ship between leatures. The 14 symbols indicate only the type 01 characteristic. The toler-
ance symbol in the drawing can contain additional symbols which contra I the details 01
the delinition 01 the tolerance zone.
.. Independent cf datum I

-OOtl"oL//~+-=-@t tJ
Dependent of datum(s)

The tolerance zone has the shape 01 and usually extends to the area 01 the nominal
leature shown in the drawing.

Geometrical characteristic requirements independent 01 datums

For a pure lorm requirement where the symbol does not relerence a datum or a datum
system, there are no constraints on the location and orientation 01 the tolerance zone
lram other leatures 01 the work piece. Roundness, straightness, cylindricity, and Ilatness
are examples 01 pure lorm requirements.

Geometrical characteristic requirements dependent on a datum or a datum sys-

tem
A tolerance zone has 6 degrees 01 Ireedom (3 translations and 3 rotations). Any number
and combination 01 these 6 degrees 01 Ireedom can be constrained as necessary lor the
lunctional requirements by indicating a relationship to a datum or a datum system in the
drawing indication.

1+lo,osIBII+lo,osIBIAII+lo,osIBIAlcl
TED - Theoretically Exact Dimension (ISO 1101 and ISO 5458)
TEDs can only be used lor geometrical tolerancing. TEDs are indicated in the drawing
by showing the dimension (linear or angular) in a rectangular Irame placed on a dimen-
sion line.

.. ..
TEDs are used to indicate the theoretically exact dimension between tolerance zones or
between one or more tolerance zones and a datum or a datum system.

8
 Datums, Datum Systems, and TED Patterns
TED patterns (1505458) Fund.
TED patterns consist of a graphical representation in the drawing of the fea- Global
tures that are part of the pattern and one or more TEDs to indicate the dimen-
sions of the pattern. TED patterns have implicit theoretical properties, e.g. 0° Dim.
and 90° angles and equal division of a full 360° circle. Tol.

TED pattern as a floating datum system

A TED pattern where TEDs are only indicated between !wo or more features (no
TEDs refer to a datum or a datum system) and where datum letters have not Geom.
been used in the tolerance indicators is a floating TED system in the workpiece. Tol.
None of the relative degrees of freedom between the TED pattern and the rest
of the workpiece is locked. The only requirements are to the theoretically exact
location and orientation of the tolerance zones indicated in the drawing for the
features that are part of the TED pattern (relative to the other features in the
TED pattern).
Q

-.l
I/i
@
-= !

TED pattern related to a datum or a datum system ul

The 6 degrees of freedom of a TED pattern can be locked as necessary, by
relating the TED pattern to a datum or a datum system. The relation to the ®
datum or the datum system is shown in the relevant tolerance indicators by
using the relevant datum leiters and TEDs. In this way the overall TED pattern
can be located and/or oriented relative to the chosen datum or datum system .
The relations between the features that are part of the TED pattern are main-
tained as for the floating TED pattern.

L
r
8 Gen.
Tol.

Y14.5

9
 Geometrical Tolerancing
Toleranced feature - tolerance zones - ISO 1101
The tolerance zone shall contain the real feature in its entirety. Geometrical character-
istics can be subdivided in:
Form.
Orientation.
Location.
Run-out.

A geometrical tolerance is indicated by:

Aleader line and arrowhead pointing to the toleranced feature.
A tolerance indicator, which includes information about characteristics,
tolerance value and, if necessary, datum(s).

The direction of the width of the tolerance zone is perpendicular to the surface except
if the tolerance value is designated by 0 or S0, if the direction is specified specifically
by an angle, or if the direction is implicitly specified by a TED pattern.

Individual and common tolerance zone - ISO 1101

Individual tolerance zones

Drawing Interpretation

Common tolerance zones are indicated by CZ after the tolerance value

Drawing Interpretation

~ f1 ~·t 9
In the former editions of ISO 1101, CZ is placed outside the tolerance indicator and
spelled out fully: "Common zone".

10
 Geometrical Tolerancing
Indication of the toleranced feature surface - ISO 1101: Fund.
Global
On the contour line or on the extension line:
Dirn .
Tol.

Datum
Tolerance zone

•
TED

or

d o
..l
The leader line and arrowhead shall NQI be a continuation of the dimension
line. //~
@
Indication of median lines in cylinders and median surfaces between
two parallel surfaces as the toleranced feature - ISO 1101.
-=1
I
Median line: lj
Drawing Interpretation
®
®
®

Median surface:
Drawing Interpretation
,-L
Gen.
Tol.

Y14.5
The leader line and arrowhead shall be a continuation of the dimension line.

11
Symbol Example Interpretation

TF: Toleranced feature .

TZ: Tolerance zone.

EJ
CI)
TF: All lines in the upper surface
parallel with the projection plane
CI)
Ql of the view shall be straight.
c
1:
Ol
.~
D TZ: Two parallel lines with
(jj distance 0,2 mm in any section
plane of the surface parallel with
the projection plane of the view.

G
f - . -- -$-
TF: The median line in the
cyllnder.
TZ: A cylinder with diameter
0,1 mm.

TF: The flat surface.

TZ: The space between two

parallel planes with distance 0,5
D
CI)
CI)
Ql
c mm.
co
u::

TF: The intersection li ne between

[Q]~ any cross section plane and the

~ wB
cylinder.

TZ : The space between two

c concentric circles with the radial
"0
c distance 0 ,04 mm in a cross
::>
o section.
er:

12
Graphical Interpretation According to ISO 1101
Fund . .
Global

Dirn.
Tol.

Datum
TED

Geom.
Tol.

CI
Real median li ne
..L
4>0,1

//~
@
-=-,
I
tJ
Tolerance zone
Real surface ®
CD
/-::;:;:~::;?' Tolerance zone ®

Roundness profile
,,-L
0,04 Gen.
Roundness profiles Tol.

Y14.5

13
Symbol Example Interpretation
TF: Toleranced feature .
TZ: Tolerance zone .

~
TF: The cylindrical surface.

L=j TZ : The space between two

coaxial cylinders with radial
distance 0,2 mm.

TF: Any line in the curved surface

parallel with the projection plane
Q) of the view.
c
:.:J
eil TZ: Two lines in a plane parallel
Ci with the projection plane of the
E view. The lines are equidistant to
o
LL the nominal profile. The distance
between the limiting lines is
0,3 mm .

TF: The curved surface.

TZ: The space between two

Q)
ü surfaces. The surfaces are
eil
't: equidistant to the nominal
::J
(j) surface. The distance between
eil
the limiting surfaces is 0,05 mm.
Ci
E
o
LL

14
Graphical Interpretation According to ISO 1101

Fund.
Global

Dirn.
Tol.

Datum
TED
Geom.
Tol.

CI

1-
//~

L
~
Gen .
Tol.

Y14.5

15
Symbol Example Interpretation
TF: Toleranced feature.
§] TZ: Tolerance zone.

I
TF: The conical surface.
Q)
u
co TZ: The space between two
't:
:::J
(J)
coaxial conical surfaces. The
co surfaces are equidistant to the
Ö nominal conical surface. The
E distance between the limiting
Ci surfaces is 0,3 mm .
LL

TF: The flat surface.

TZ: The space between two

parallel planes with the distance
0,3 mm. The planes are
perpendicular to datum plane A.

TF: Median line in the cylinder.

TZ: The space in a cylinder with

diameter 0,1 mm. The axis of the
cylinder is perpendicular to datum
plane A.

16
Graphical Interpretation According to ISO 1101
Fund.
Global

Dirn.
Tal.

Datum
TED
Geom.
Tal.
Datum
plane B

®
®

Toterance zone
L
Real median Une ~
Gen.
Datu m plane A Tal.

Y14.5

17
Symbol Example Interpretation

TF: Toleranced feature.

TZ: Tolerance zone.

TF: The flat surface.

TZ: The space between two

parallel planes with distance
0,2 mm. The planes are inclined
64 Q to datum axis A.

TF: The median line in the smaller

cylindrical hole.

TZ: The space in a cylinder with

diameter 0,2 mm. The axis of the
cylinder is parallel to datum axis
A.

TF: The median line in the hole.

c TZ: The space in a cylinder with

o
..."
.üj diameter 0,1 mm. The axis of the
o cylinder is parallel to the planes
0...
of the datum system and located
on the position (30, 20) mm.

18
Graphical Interpretation According to ISO 1101

Fund.
Global

Dirn.
Tol.

Datum
TED
circumscribe Geom.
ey!ffi<lee-- ·
Tol.

Cl

-.l
/Datum axis A 410,2 To lerance zone

Tolerance zone
'---/
~--r~~
Realsurfaces

L
Centre ~
o
N
of real
Gen.
hole
Tol.

30 Datum A Y14.5

19
Symbol Example Interpretation
TF: Toleranced feature.
TZ: Tolerance zone.

TF: The median li ne in the larger

cylinder.

TZ: The space in a cylinder with

diameter 0,8 mm. The axis of the
cylinder is coaxial with common
datum axis A-B.

~~~
TF: The median surface in the
notch.

it~J
TZ: The space between two
parallel planes with the distance .
0,8 mm. The limiting planes are
E symmetrical around datum plane
>-
CD
A.

TF: Any intersection line' betw~en

the cylinder and cross section
planes.

TZ: The space between two

concentric circleS in a cross
,section plane with radius distance
0,1 mm. The common centers are
. on datum axis A-B.

20
Graphicallnterpretation According to ISO 1101

Fund.
Global

Datum point A Datum point B

Dirn.
Tal.

Datum
TED
Geom.
Tal.

e:,

Real median surface .1

Datum plane A //~

I
tJ
®
~ [r0SS .
CD
P~ /
, P,
\.p sections
o .
p~
/-:;;;:~/ ®
Datum
~
Point on A- B
point B

[ross seeti on
profile
rL
0,1 Gen ,
Tal.

Datum axis A- B Y14.5

21
Symbol Example Interpretation
TF: Toleranced feature.
TZ: Tolerance zone.

TF: Any intersection line between

the real flat surface and a cylinder
coaxial to datum axis A.

TZ: The space between two

parallel circles - 0,2 mm apart -
on a cylinder. The circles are in
planes perpendicular to datum
axis A. The cylinder axis is coaxial
to datum axis A.

TF: The cylindrical surface.

:;
o
Co
:::J
er:
-- ] TZ: The space between two
coaxial cylinders with radius
distance 0,2 mm . The common
axis of the cylinders is coaxial to
datum axis A.
I9
~

TF: The flat surface.

TZ: The space between two

parallel planes with the distance
0,1 mm. The planes are
perpendicular to datum axis A.

22
Graphical Interpretation According to ISO 1101

Fund.
Global

Dirn.
Tol.

Datum
TED
Geom.
Tol.

...p===:::::,.-+> Tolerance zone

Real surface

axis A Least cir-

cumscribed
cylinder

Real surface
®
~""'~===-_> Tolerance zone
CE)
®
,/Real
1\ surface

L Oatu axisA ~ Least cir- ~

L

~ cylinder
._._._._- cumscribed

~
-
-;:P'" !Oler.ance
/1
Gen.
Tol.
zone
Y14.5

23
 Maximum Material Requirement
TF: Toleranced feature.
TZ: Tolerance zone.

TF: Two independent requirements. The

o surface of the cylinder and the median line
1ct>25 -O,l~ 1.1 1ct> 0,21 AI of the cylindrical surface.

DJ~
TZ: The diameter shall be larger than 24,9
mm (two point) and shall be smaller than
25,0 (envelope). The median line shall be
included in a cylinder with the diameter 0,2
mm. The axis of the tolerance cylinder IS
perpendicular to datum plane A.

NOTE: The envelope requirement can be

considered a special type 01 maximum ma-
terial requirement with no constraints on the
leeation and orientation of the maximum
material virtual condition

o TF: The surface of the cylinder only. Be-

1ct>25-0,l , 1.Ict>o,2@IAI cause 01 the maximum material require-
l ment,®.

DJ_~
TZ: The diameter of the cylinder shall be
larger than 24,9 (two point). The surface
shall be included in a cylinder. The axis of
the cylinder is perpendicular to datum plane
A. The diameter of the limiting cylinder is
the maximum material virtual condition size:
25,0 + 0,2 = 25,2 mm.

TF: The surface of the cylinder only. Be-

o cause 01 the maximum material require-
1,ct>25 -0,1'1' 1.1 ct> 0(8) 1AI ment,®.

DJ~
TZ: The diameter of the cylinder shall be
larger than 24,9 (two point). The surface
shall be included in a cylinder. The axis of
the cylinder is perpendicular to datum plane
A. The diameter of the limiting cylinder is
the maximum material virtual condition size:
25,0 + 0,0 = 25,0 mm.

24
 Graphical Interpretation According to ISO 2692

Fund,
Global

Dirn,
Real median tin Tol.

Datum
Maximum
eal surface TED
cylinder
Geom,
Real surfac Tol.

..L
DMM" = <P 25,2
MMve - Maximum material
vituel condition
//~
@
-=-,
Real surface

Datum plane A
t./
®
®
MMve - Maximum material
vituel condition

L
~
Real surfac
Gen ,
Datum plane A Tol.

Y14,5

25
 Tolerancing 01 Non-rigid Work Pieces
Tolerancing of non-rigid workpieces - ISO 10579

In the free state , non-rigid workpieces can be deformed, e.g. by the force of gravity. It
may be necessary to indicate two tolerances, one for the free state, CD, and another
for a defined restrained condition.

Example:

ISO 10579-NR
Restrained condition: The surface , datum A,
is restrained by 120 bolts M20 with a torque
of 18-20 NM. Datum B is restrained at the
corresponding maximum material limit.

Mandatory indication for non-rigid workpieces:

1. The indication ISO 10579-NR.

2. The conditions under which the work piece shall be restrained to

meet the drawing requirements.

3. Geometrical deviations, allowed in the free state shall be indicated

by the modifier, CD, after the geometrical tolerance.

4. The conditions under which the geometrical tolerance under free state
is achieved, such as direction of gravity, orientation of the work piece,
etc.

The work piece shall comply with both tolerances, in the free state as weil as re-
strained conditions.

26
 Projected Tolerance Zone
Projected tolerance zone - ISO 10578 Fund.
Global
It is possible to indicate a projected tolerance zone, as illustrated with the
modifier, ®, followed by the dimension of the projection, and the modifier, ® , Dim.
Tol.
after the geometrical tolerance. The projected feature is represented by a
long dash double-dot line. Datum
TED
Drawing:
Geom.
Tol.

o
-.L
//~
@
Projected tolerance zone - interpretation -=-1
The toleranced feature is the extension of the real feature, here the median ljl
line of the cylindrical hole. The following illustration shows the extreme con-
sequences of the tolerancing in the hole itself.
</J0.3
®
Interpretation:

L
~

Gen.
Tol.

Y14.5
Projected tolerance allows the possibility to indicate special functions of the
work piece after assembly.

27
 Tolerancing 01 Surface Texture
Delault indication 01 surface texture - ISO 1302

yiRZü.4 Indicates: The requirement shall be met by removing material

~ Indicates: Removal 01 material is not allowed.

~ Indicates: Any method is permitted

- removal or no removal 01 material.

The surface texture specilication operator always consists 01 the lollowing specilica-
tion elements. When the delault indication is used, most 01 the specilication elements
are not visible:

_.:::... EJ EJ
. . . . . :':'.== EJ ... "'" EJ
~catlonlirm
Uorl
F~1ype ·...'" ~::=.
biond Pn>Ch.lrac-
file ter1slic:
lenglh ""'.
16%ormax
Limltvalue

11 \ \\ \ \ \
U "X" 0,08-0,8 / Rz8max 3,3
ground
08-0,8 / Rz8max 3,3

Example 01 a special surface texture indication based on a delault. What is not wanted
in the delault is changed by direct indication in the symbol:

vi 0,008-2,S/Rz3 0,4
II the delault delinition 01 the operator does not simulate the lunction 01 the surface,
the correct total specilication operator shall be indicated on the drawing.

28
 Tolerancing of Surface Texture
The operations in the default specifieation operators are given in the following Fund.
standards : Global

Parameters from ISO 4287 in: ISO 3274, 4288,11562 , ete. Dim.
Tol.
Parameters from ISO 12085 in: ISO 12085
Datum
TED
Parameters from ISO 13565-series in: ISO 3274, 4288 , 11562, 13565-1 ,
ete. Geom.
Tol.
P-parameter default definitions, are also ineluded in the standards above.

Waviness parameters - no default operators are defined . Therefore, the total

speeifieation operator for waviness shall always be indieated on the drawing.

Surfaee texture ineludes three different groups of parameters:

c::.
ISO 4287 parameters are defined for the roughness profile , R, the waviness ..1
profile, W, and the primary profile , P, e.g.:

Rz, Wz, Ps, Ra , Wa, Pa, Rt, Wt, Pt , ete .

//~
@
ISO 12085 - Motif-parameters are defined for R- and W-profile , e.g: -=1
R, W, Rx , Wx, AR, AW, ete. l
U
ISO 13565 series parameters
®
- ISO 13565-2 parameters are defined for the R-profile :

Rpk, Rk and Rvk - (Rpke , Rke and Rvke)

- ISO 13565-3 parameters are defined for R-profile and P-profile:

Rpq , Rvq , Rmq - Ppq , Pvq, Pmq L

r
Note: Surfaee texture only ineludes the texture from the manufaeturing proeess .
Gen.
Seratehes, pores, and other errors in the surfaee are exeluded . See Toleraneing
Tol.
of Surfaee Imperfeetions.
Y14.5

29
 Tolerancing 01 Surface Imperfeetions
Tolerancing 01 surface imperfections - ISO 8785

These tolerances limit surface errors, e.g. scratches , pores, their size (depth D, Height
H, length S) , area, number, etc. Surface errors or imperfections are not covered by
surface texture requirements, but only by surface imperfection requirements.

Combined imperfection: Single (One sided) imperfection:

s
I 'I
Q<y]

Parameters are :

SIMe Surface imperfection length

SIMw Surface imperfection width

SIMsd Single surface imperfection depth

SIMcd Combined surface imperfection depth

SIMsh Single surface imperfection height

SIMch Combined surlace imperfection height

SIMa Surface imperfection area

SI Mt Total surface imperfection area

SIMn Surface imperfection number

SIMn/A Number 01 surface imperfections per unit area

30
 Tolerancing of Edges
Edge tolerancing - ISO 13715 Fund.
Global
Can only be used for tolerancing of external and internat edges that have no
work piece functions. The shape of the edge can not be specified , only how Dim.
much is missing or how much the edge extends the nominal edge can be Tol.
specified. If the edge has a function, use geometrical tolerancing. Datum
TED
In the examples: a) Drawing indication, b) Upper limit and c) lower limit.
Geom.
Examples: Tol.

.~'~ 4
~
[:.0,8

'.,,/
~mL
L~8
a) b) L c) a) b) c)

External edge - both sides Internal edge - both sides

One-sided tolerance - Inwards One-sided tolerance - Outwards

-.0,2

"'~a) b) L

External edge - both sides

c)
~~i~l
~ ~8~
j~ .
a) b)

Internal edge - both sides

c)

®
®
Two-sided tolerance - Inwards Two-sided tolerance - Outwards

a) b) c)
~
~ ~~"':;0/'
}'!; ;
.' Y
'l,
I/Shar p
Gen.
Tol.
a) b) c)

External edge - only one side Internal edge - only one side Y14.5
One-sided tolerance - Outwards One-sided tolerance - Inwards

31
 General Tolerances
General dimensional tolerances - ISO 2768-1

Four classes: fine

m medium
c coarse
v very coarse

Covers linear and angular dimensions, radii, and chamfers heights on external edges.
Tables for ± tolerances are given in ISO 2768-1. Indicated on the drawing as shown in
the figure below. Should QLlhc.be used as an exception and QLlhc.with great care.

ISO 2768- m

General geometrical tolerances - ISO 2768-2

Three classes: H, K, and L. Covers only some of the characteristics in ISO 1101.
Tables for tolerance values are given in ISO 2768-2. The use of general geometrical
tolerances has incalculable consequences . Use is strongly discouraged!!! Indica-
tion as illustrated.

ISO 2768-K

80th general dimensional and geometrical tolerances - ISO 2768-1 & -2

80th general dimensional and geometrical tolerances used on the drawing. The use
has incalculable consequences. Use is strongly discouraged!!! Indication as illus-
trated.

ISO 2768-m-K

32
 Application of GPS
How to apply GPS tolerancing on a drawing Fund.
Global
1. A functionally correct main datum system shall be established. The main
datum system shall position and orient the work piece , as if it were al ready Dirn.
assembled with the rest of the product. This datum system is an Tol.
absolute precondition for achieving the advant ag es of GPS
Datum
tolerancing
TED
A second precondition: Dimensioning shall ONLY be used for size, e.g. Georn.
diameter and thickness. Tol.

2. All features of size are toleranced. It is necessary either to use codes,

e.g. h6 and K8, or 10 indicate how the ±tolerance shall be interpreted by
adding a modifier.

3. All features shall be positioned relative to the main datum system andl
or to a single datum in the work piece by TEDs and location requirements . Cl

..1
Note: The location tolerance zones are also setting up requirements for
the orientation of the features with the same tolerance value. //~
4. The features , which need smaller orientational tolerance than established @
by the location tolerances are toleranced with orientation tolerances. -=1
Note: The orientation tolerance zones are also setting up requirements VI
for the form of the features with the same tolerance value.

5. The features , wh ich Med smaller form tolerance than established by ®

the location or orientation tolerances, are toleranced with form tolerances.
®
6. Form tolerances are supplemented as needed by surface texture ®
tolerances (roughness, waviness, etc.) to take care of the short and
medium wave band in the surfaces.

7. Surfaces are toleranced as needed with surface imperfeetion tolerances. L

•
~
8. All edges are toleranced .

Y14.5

33
 ASME Y14.5M-1994
Dillerences between ISO GPS standards and the ASME Y14.5M-1994 standard

There are a number 01 differences in indication and interpretation between the ISO
GPS standards and the US national standard ASME Y14.5M-1994 (Y14 .5). A number
01 these differences are minor and usually it is not difficult to interpret the intent 01 a
drawing made using Y14.5 conventions il you are lamiliar with the ISO GPS standards.
However, in some cases the same or similar indications are interpreted differently in
the two standard systems. In the 101l0wing, some 01 the major differences are discussed.
This discussion is by no means intended to be exhaustive and il the exact meaning 01
a requirement is important, the applicable standard should be consulted .

Applicability 01 standards
ISO GPS standards apply to technical product documentation (engineering drawings)
without any special indication. II GPS symbols are used, the ISO standards apply by
delault. To invoke Y14.5, a relerence has to be made on the drawing or in a document
relerenced on the drawing. The relerence shall state ASME Y14.5M-1994. In other
words , the ISO GPS rules apply, unless the Y14.5 standard is explicitly relerenced.

Exclusion 01 surface texture

The ASME Y14.5.1M-1994 standard (Y14 .5.1), wh ich can be viewed as an integral
part 01 Y14.5 containing mathematical delinitions 01 the Y14.5 principles, states that
all requirements apply after the "smoothing lunctions" delined in ANSI B46.1-1985,
Surlace Texture , have been applied. In other words, surlace texture has to be
disregarded when evaluating work pieces using Y14.5.

The ISO GPS standards currently do not state whether surface texture should be
included or excluded when geometrical requirements are evaluated. This can make a
very signilicant difference, as size and lorm tolerances are reduced to the point where
the amplitude 01 the surface texture becomes a substantial Iraction 01 these tolerances.

Delinition 01 datums
In the case where a datum is shaped such that the part can "rock" on the datum (e.g .
il the datum leature is a convex surface), the rule in ISO GPS standards is to "equalize
the rock", such that an "average" position and orientation is used lor the datum. Each
requirement relating to the datum is evaluated individually to this datum. These rules
are currently under revision to make them more mathematically rigorous, but the "spirit"
01 the rule will remain the same .

Y14.5.1 introduces the concept 01 candidate datums instead. Every position that an
unstable datum can rock to (within some limitations) is a valid candidate datum. A set
01 candidate datum relerence Irames can be derived lor each set 01 requirements that
are relerenced to the same datum system, using the same precedence and the same

34
 ASME Y14.5M-1994
material conditions . These sets of requirements are by default evaluated Fund.
simultaneously to each candidate datum reference frame . If there exists a Global
candidate datum reference frame where all the requirements are fulfilled , the
work piece is acceptable with regards to these requirements , oth erwise it is Dim.
not acceptable. Tol.

Datum
These two sets of rules can lead to substantially different conclusion s, TED
especially if the form errors of the datum features are substantial. In general,
the Y14.5.1 system gets more permissive (accepts more work pieces) as the Geom.
form errors of the datum features increase. However, cases have also been Tol.
demonstrated where a work piece was acceptable based on the ISO GPS
rules, but not acceptable based on the Y14.5.1 rules. It should be noted that
no measuring equipment is currently available that will evaluate work pieces
strictly in accordance with either set of rules.

Size requirements
The ISO system of limits and fits defined in ISO 286-1 can be invoked by CI
using the defined tolerance codes , e.g. h7 for a shaft and K8 for a hole. ISO ..L
286-1 in turn references ISOfR 1938, wh ich describes the inspection of work
pieces for size requirements when the ISO tolerance codes are used. // ~
ISOf R1938 defines a system of "hard" gages, e.g. plug and ring gages, that @
are to be used when testing size tolerances . An allowance is made for wear of -=,
these gages, so in the extreme case a gage may wear beyond the tolerance
limit by up to 30% of the tolerance and still be acceptable. This means that
work pieces can be up to 30% out of tolerance on the maximum material size
(sm all hole or large shaft) and still be acceptable under the ISO limits and fits
1./
system. Additionally, the tolerance intervals for hard gages are placed ®
symmetrically around either the tolerance limit the gage is intended to test
(minimum material side) or the wear limit (maximum material side) , allowing
the gage to be outside the limit by half its tolerance. In other words, the
tolerances given in ISO 286-1 are not the real tolerances - the allowances
given in ISOfR 1938 have to be added . This problem can be avoided by writing
the tolerance explicitly instead of using tolerance codes , as ISO 286-1 is not
invoked in this case. However, it requires an indication of the size definition, L
e.g. envelope requirement, to ensure that the requirement is defined on the ~
actual workpiece See Tolerancing by Dimensions on page 4.
Gen.

•
Tol.
Y14.5 always interprets size tolerances according to "Rule number 1", which
is equivalent to the envelope requirement described in ISO 8015. There is no
additional allowance for wear of hard gages under the Y14.5 set of rules, so
the tolerance wriUen on the drawing is the true tolerance in this case .

35
For Notes

36
Henrik S. Nielsen, Ph.D.

Dr. Nielsen has been an expert serving on ISO TC 213 "Dimensional and
geometrical product specifications and verification - GPS ," and related
committees since 1988.

Dr. Nielsen has served as project leader and main author of several ISO
standards on subjects such as Surface Finish , Form, and Uncertainty
Concepts.

He was the convenor of TC 213 Working Group 1, "Roundness , Straightness,

Flatness, and Cylindricity" until it was disbanded when the standards were
submitted for publication. He is currently the convenor of TC 213 Advisory
group 11, "Underlying Concepts."

Dr. Nielsen received a M.Sc. in Mechanical Engineering in 1984 and a Ph.D .

in Metrology in 1988 from the Technical University of Denmark.

From 1987 to 1991 he worked as a consulting engineer at IPU , the Institute

for Product Development in Copenhagen .

From 1991 to 1998 Dr. Nielsen was the Technical Manager of Corporate
Standards at Cummins Engine Co. in Columbus, Indiana, USA.

Dr. Nielsen started his own consulting business HN Metrology Consulting

in 1998 and in 2001 he started HN Proficiency Testing (the first accredited
proficiency testing provider catering to calibration laboratories in the United
States).

Dr. Nielsen's areas of expertise include dimensional and geometrical

metrology, uncertainty estimation, and quality assurance for calibration
laboratories. He teaches public seminars on all of these subjects th rough
various organizations as weil as customized in-house company seminars.
Since 1999 over 1500 students have attended his seminars.

Dr. Nielsen is a Lead Calibration Assessor for A2LA , the American

Association for Laboratory Accreditation , and has assessed over 100
dimensional calibration and testing (inspection) laboratories since 1999.