Measuring principles for geometrical tolerances - Volvo · Standard STD 112-0004 Volvo Group Issue...
Transcript of Measuring principles for geometrical tolerances - Volvo · Standard STD 112-0004 Volvo Group Issue...
Standard STD 112-0004 Volvo Group
Issue date January 2017 Issue 3 Page 1 (41)
The English language version is the original and the reference in case of dispute.
Measuring principles for geometrical tolerances Indication, definitions and system structure
Orientation
This standard establishes the rules that apply in the Volvo Group when measuring principles are specified
together with geometrical tolerances.
There is no international equivalent to this standard, although there are similarities with the technical
report ISO/TR 5460:1985 Verification principles and methods, published as Swedish standard
SS 2650. The technical report ISO/TR 5460 was withdrawn in 2013, but the Swedish standard
SS 2650 still exists.
All basic definitions of tolerance zones, single features, etc., can be found in ISO 1101 Geometrical
tolerances – Tolerances of form, orientation location and run-out.
This version differs from issue 2 in that the reference to STD 112-0003 in the section “Orientation” and in
section 1 “Scope and field of application” has been changed to ISO 1101. Text has also been added in
the section “Orientation” stating that the technical report ISO/TR 5460 was withdrawn in 2013.
Contents
1 Scope and field of application ......................................................................................................... 2
2 Definitions of concepts..................................................................................................................... 2
3 Indication ........................................................................................................................................... 5
4 Measuring principles – measuring-technical rules, system description and examples ........... 5 4.1 Measuring-technical rules ................................................................................................................... 5 4.2 System description .............................................................................................................................. 6 4.3 Examples of the system ...................................................................................................................... 7
5 Guidelines for selecting measuring principle .............................................................................. 11 5.1 Form tolerances ................................................................................................................................ 12 5.2 Orientation tolerances ....................................................................................................................... 13 5.3 Location tolerances ........................................................................................................................... 14 5.4 16
6 Definitions of measuring principles .............................................................................................. 18 6.1 Form tolerances ................................................................................................................................ 18 6.2 Orientation tolerances ....................................................................................................................... 21 6.3 Location tolerances ........................................................................................................................... 29 6.4 Run-out tolerances ............................................................................................................................ 37
7 Reference to this standard ............................................................................................................. 41
Standard STD 112-0004 Volvo Group
Issue 3 Page 2 (41)
1 Scope and field of application
The tolerance definitions used in this standard are defined in ISO 1101.
Geometrical tolerances shall, together with measuring principles, be specified with regard to the functional
requirements. Manufacturing and inspection requirements may also influence the way in which the
geometrical tolerances are specified and which measuring principles are chosen.
The purpose of the measuring principles is partly to provide fundamental ways of evaluating that better
can reflect the functional requirements and/or allow a simpler evaluation than that of the fundamental
tolerance definition, and partly to obtain an unambiguous interpretation when implementing different
geometrical tolerances in practice. ISO 1101 does not specify any procedure for evaluating tolerance
zones, which is necessary in order for a tolerance to be unambiguous and for the verification of it to be
repeatable.
The choice of measuring principle affects the measuring result.
The specification of geometrical tolerances together with the measuring principle does not mean that
there is a particular measuring or inspection method that must be used when manufacturing. However,
the specified measuring principle is decisive in case of dispute and thus takes precedence over the
theoretical definitions that can be found in ISO 1101.
The system of measuring principles can be summarized as follows:
– Normally, the measuring principle shall be indicated on the drawing. If no measuring principle is
specified, a measuring principle in accordance with the tolerance definition in ISO 1101 applies (this
means measuring principle 1 by default).
– In this standard, measuring principle refers to fundamental ways of evaluating the tolerance
requirement.
– All measuring principles with a number higher than 1 (2, 3, 4, etc.) are simplified measuring principles
and do not comply with the requirements in accordance with the tolerance definition. However, a
simplified measuring principle can better correspond to the function requirements than the tolerance
definition does.
– The specified measuring principle means that this principle is decisive for the interpretation of the
tolerance requirement.
– By specifying measuring principles, the geometrical tolerances can be connected to more functionally
correct and/or simpler, and thus more economical, methods of inspection.
2 Definitions of concepts
Feature
Portion of a part, such as a plane, a hole, etc.
Actual feature
Physical real feature on a part.
Comment: Generating lines, cylinder surfaces and planes are examples of actual features.
Abstract feature
An unreal feature made from one or several real surfaces.
Comment: Axes, symmetry planes and symmetry lines are examples of abstract features.
Standard STD 112-0004 Volvo Group
Issue 3 Page 3 (41)
Generating line
A straight line on the surface of a body, in the longitudinal direction of the body.
Comment: A generating line on a cylindrical feature is parallel to the axis of the feature.
Cylinder surface
The surface of a cylindrical feature, such as a shaft or a hole.
Comment: A cylinder surface consists of generating lines.
Parallel lines and surfaces
Straight lines and flat surfaces with equal distance between them.
Comment: Please note that the concept “parallel” is only used for straight lines and flat surfaces. See also
the term Equidistant lines and surfaces.
Equidistant lines and surfaces
Lines and surfaces with the same distance between them, but of another geometrical shape than straight
lines and flat surfaces.
Comment: See also the term Parallel lines and surfaces.
Measuring principle
Interpretation of a tolerance by describing principal origins for measuring a specific geometrical
characteristic.
Comment: One and the same measuring principle, e.g. verification of form by evaluating the diameter
variation with two-point measurement, can be accomplished with one or several measuring methods and
measuring devices.
Measuring method
Realization of a measuring principle in practical application by using various equipments and procedures.
Tangent plane
An imaginary plane of the theoretically exact geometric form which is tangent to an actual plane so that a
stable position for the tangent plane is obtained.
Comment: At least three contact points are required in order to obtain a stable position.
Superimposed plane
An imaginary plane of the theoretically exact geometric form which is tangent to an actual plane so that
the distance between the tangent plane and the actual plane is as small as possible at the point where
this distance is at its maximum.
Comment: Superimposed planes are used to simulate contact between two planes where there is no
stable position for a tangent plane. A superimposed plane can have one contact point.
Tangent line
An imaginary line which is tangent to an actual line so that a stable position for the tangent line is
obtained.
Comment: At least two contact points are required in order to obtain a stable position.
Superimposed line
An imaginary line which is tangent to an actual line so that the distance between the tangent line and the
actual line is as small as possible at the point where this distance is at its maximum.
Comment: Superimposed lines are used to simulate contact between two lines where there is no stable
position for a tangent plane. A superimposed plane can have one contact point.
Least squares method, LS
A mathematical calculation method to adapt a feature of the theoretically exact geometric form to a
number of actual measuring points.
Standard STD 112-0004 Volvo Group
Issue 3 Page 4 (41)
Comment: With the least squares method, the associated feature is calculated so that the sum of the
squares of the deviation between individual measuring points from the associated feature is the least
possible. Calculation of an associated feature by the least squares method is a measuring principle which
can be applied to all geometrical features.
Maximum inscribed cylinder, MI
The maximum cylinder of the theoretically exact geometric form that can be contained in an internal
actual cylinder.
Comment: Evaluation of an internal cylinder as the maximum inscribed cylinder is a measuring principle
that can be applied via mechanical measuring equipment, or by calculation based on individual measuring
points on the actual cylinder. The maximum inscribed cylinder function constitutes contact feature in an
internal cylinder.
The two-dimensional equivalence to the maximum inscribed cylinder is the maximum inscribed circle.
Minimum circumscribed cylinder, MC
The minimum cylinder of the theoretically exact geometric form that can be placed around an external
actual cylinder.
Comment: Evaluation of an external cylinder as the minimum circumscribed cylinder is a measuring
principle that can be applied via mechanical measuring equipment, or by calculation based on individual
measuring points on the actual cylinder. The minimum circumscribed cylinder function constitutes contact
feature on an external cylinder.
The two-dimensional equivalence to the minimum circumscribed cylinder is the minimum circumscribed
circle.
Minimum zone, MZ
The minimum distance between two geometrically perfect features in which a given feature can be
contained.
For axes, it is the minimum cylinder of geometrically perfect shape in which the entire axis can be
contained.
Comment: For form tolerances, the minimum zone is the applicable tolerance in accordance with the
tolerance definition.
Two-point measurement
Measurement of a dimension when the measurement is made as the distance between two points,
situated opposite each other, for a dimension relating to external or internal surfaces in the same plane.
Comment: Measuring the diameter of a sphere with a micrometer is an example of two-point
measurement. By measuring the dimensional variation with a number of two-point measurements, certain
types of form deviations can be detected.
Three-point measurement
Measurement of a round object where the measurement is made as a diameter on a circle which passes
through three points on the object.
Comments: Often a standard is required for setting purposes, e.g. if the measurement is made with two
contact points and one measuring point for instance when using a V-yoke and a dial indicator to measure
out-of-roundness. Also internal measurements with a three-point micrometer refer to three-point
measurement. A lobed form of triangular shape can be detected with three-point measurement.
Standard STD 112-0004 Volvo Group
Issue 3 Page 5 (41)
3 Indication
The measuring principles are indicated with the symbol MP 1, MP 2, MP 3, or MP 4 and stated next to the
tolerance frame, see example in figure 1. This indication replaces the previous indication of measuring
principles using Roman numerals in the tolerance frame.
MP 2
MP 1 MP 3
MP 2
MP 1
MP 3
Figure 1
4 Measuring principles – measuring-technical rules, system description and examples
4.1 Measuring-technical rules
General measuring-technical rule
The general rule is that measuring of geometrical requirements shall be carried out in such a way that
the result of the measurement is influenced only by the geometrical shape of the toleranced feature and
by the geometrical shape of the specified datums. In other words, other features must not be used as
“auxiliary datums” or similar since this can affect the measuring result. Therefore, it is important to
specify alignment surfaces and similar as datum features when this is actually required.
Tolerance zone extension
Unless otherwise specified, the tolerance applies to the entire extension of the actual feature, excluding
an edge zone of 0,01 x the length of the feature, where sections pointing downwards are not included.
Surface defects such as burrs and similar are not covered by the geometrical tolerance.
See examples in figures 2 - 3.
Standard STD 112-0004 Volvo Group
Issue 3 Page 6 (41)
10 45
0,1
MP 1
10
65
0,1
MP 1
Figure 2 Figure 3
The straightness tolerance applies to the
specified area, gauge length 45.
The straightness tolerance applies to the entire
feature. However, “negative” deviations, that is
downward relief, within the area 0,01 x 65 on
each side are not included. Upward-directed
material peaks that cannot be referred to as
surface defects shall be included even if they are
within the edge zone.
Measuring force
Geometrical tolerances apply with the theoretical measuring force 0. Unless otherwise specified, the
maximum measuring force at inspection with indicating instrument is 1 N.
When fixed measuring devices such as function gauges are used at the inspection, the measuring force
is given by the intrinsic mass of the gauge. If it can be assumed that the measuring force can influence
the measuring result to a non-negligible degree, the effect of the measuring force’s influence shall - in
both cases - be recalculated with this in mind.
For soft objects, non-contact measurement is recommended.
4.2 System description
The basic structure below is valid regardless to which tolerance symbol the measuring principle has
been stated.
Measuring principle 1 = The evaluation shall comply with the tolerance definition as per ISO 1101.
The principle can normally be complied with by using computerized or mechanical measuring methods.
Measuring principle 1 means that form deviations are included in the tolerance limitation for both actual
and abstract features regardless of tolerance type. This measuring principle is suitable for many form
requirements and also for run-out requirements. It is also suitable for positional and orientation
tolerances when tolerances apply to an actual feature.
Measuring principle 2 = Evaluation of all features shall be made according to the least squares (LS)
method. This principle requires computer evaluation.
Measuring principle 2 provides a quick measurement in computerized equipment which also often has a
high repeatability.
However, the measuring principle is often not correct functionally, unless it is a question of slender
parts, which take the shape of the mating part when assembled.
Standard STD 112-0004 Volvo Group
Issue 3 Page 7 (41)
No form deviations are included for this measuring principle other than for form tolerances.
Measuring principle 3 = Evaluation shall be made with actual contact features. The principle can
normally be complied with by using computerized or mechanical measuring methods.
Measuring principle 3 is often the most functionally correct definition. Note that this measuring principle
corresponds to measuring principle 1 in the previous Volvo standard STD 5062,2E if the tolerance is
orientation and location tolerances for an abstract feature. It is thus important to specify this principle for
such function requirements where measuring principle 1 was previously indicated, or where no
indication of measuring principle was previously made if conformity between old and new drawings shall
be obtained.
No form deviations are included for this measuring principle, other than for form tolerances.
Measuring principle 4 and higher = Evaluation adapted to shop-floor measurements. The principle
can normally be complied with by using mechanical measuring methods, but in some cases
computerized evaluations can also be used.
Different measuring principles can be combined.
4.3 Examples of the system
4.3.1 Examples for form tolerance
Ø 2
5 h
7
0,01
Figure 4 Roundness requirement Figure 5 Actual appearance
Measuring principle 1: The circumference in every cross-section shall be contained between two
concentric circles a radial distance 0,01 apart.
When verifying in accordance with measuring principle 1, the centre of these two circles is determined
according to the MZ method, the centre giving the least possible distance between the tolerance circles.
Figure 6 Roundness according to measuring principle 1
Measuring principle 2: The circumference in every cross-section shall be contained between two
concentric circles a radial distance 0,01 apart. The tolerance circles are concentric with a median circle
calculated according to the least squares (LS) method.
When verifying in accordance with measuring principle 2, the centre of a median circle is calculated with
the LS method and, on the basis of the centre of this circle, the radial distance between two tolerance
circles containing the circumference is determined.
Standard STD 112-0004 Volvo Group
Issue 3 Page 8 (41)
Figure 7 Roundness according to measuring principle 2
Measuring principle 3: The circumference in every cross-section shall be contained between two
concentric circles a radial distance 0,01 apart. The tolerance circles are concentric with the minimum
circumscribed circle.
When verifying in accordance with measuring principle 3, the centre of the minimum circumscribed
circle is determined according to the MC method and, on the basis of the centre of this circle, the radial
distance between two tolerance circles containing the circumference is determined.
Note: If the tolerance refers to an internal circle, use instead the maximum inscribed circle according to the MI
method.
Figure 8 Roundness according to measuring principle 3
4.3.2 Examples for orientation tolerance
Ø 25 h7 Ø 0,05 A
A
Figure 9 Perpendicularity requirement Figure 10 Actual appearance
Measuring principle 1: The axis, formed by the centre points for all sections, shall be contained within a
cylinder of diameter 0,05. The tolerance cylinder is perpendicular to datum feature A.
When verifying in accordance with measuring principle 1, the centre of the requisite number of sections
is determined according to the MZ method, and the diameter of the cylinder perpendicular to datum
feature A circumscribing these centre sections is determined.
Standard STD 112-0004 Volvo Group
Issue 3 Page 9 (41)
Figure 11 Perpendicularity according to measuring principle 1
Measuring principle 2: The axis of a median cylinder determined according to the least squares method
shall be contained within a cylinder of diameter 0,05 mm. The tolerance cylinder is perpendicular to
datum feature A.
When verifying in accordance with measuring principle 2, the toleranced feature is measured as a
median cylinder and the perpendicularity deviation for the axis of the median cylinder is evaluated.
Figure 12 Perpendicularity according to measuring principle 2
Measuring principle 3: The axis of the minimum circumscribed cylinder shall be contained within a
cylinder of diameter 0,05 mm. The tolerance cylinder is perpendicular to datum feature A.
When verifying in accordance with measuring principle 3, the toleranced feature is evaluated as
circumscribed cylinder and the perpendicularity deviation of the axis of the circumscribed cylinder is
evaluated.
Note: If the tolerance refers to an internal cylinder, use the maximum inscribed cylinder instead.
Standard STD 112-0004 Volvo Group
Issue 3 Page 10 (41)
Figure 13 Perpendicularity according to measuring principle 3
4.3.3 Examples for positional tolerance
Ø 25 h7 Ø 0,1 C
A
B C
25 15
B A
Figure 14 Positional requirement Figure 15 Actual appearance
Measuring principle 1: The axis, formed by the centre points for all sections, shall be contained within a
cylinder of diameter 0,1 mm. The tolerance cylinder is perpendicular to datum feature A and situated in
the theoretically exact position in relation to datum features B and C.
When verifying in accordance with measuring principle 1, the centre for the requisite number of sections
is determined according to the MZ method and the position of these sections is evaluated. The centre of
all sections shall be within tolerance in order for the entire axis to be within the tolerance cylinder.
25
Figure 16 Position according to measuring principle 1
Measuring principle 2: The axis of a median cylinder determined according to the least squares method
shall be contained within a cylinder of diameter 0,1 mm. The tolerance cylinder is perpendicular to
datum feature A and situated in the theoretically exact position in relation to datum features B and C.
When verifying in accordance with measuring principle 2, the toleranced feature is measured as a
median cylinder and the positional deviation for the axis of the median cylinder is evaluated.
Standard STD 112-0004 Volvo Group
Issue 3 Page 11 (41)
25
Figure 17 Position according to measuring principle 2
Measuring principle 3: The axis of the minimum circumscribed cylinder shall be contained within a
cylinder of diameter 0,1 mm. The tolerance cylinder is perpendicular to datum feature A and situated in
the theoretically exact position in relation to datum features B and C. When verifying in accordance with
measuring principle 3, the toleranced feature is measured as circumscribed cylinder and the positional
deviation for the axis of the circumscribed cylinder is evaluated.
Note: If the tolerance refers to an internal cylinder, use maximum inscribed cylinder instead.
25
Figure 18 Position according to measuring principle 3
5 Guidelines for selecting measuring principle
The following matrix is for guidance in selecting measuring principle. It gives general recommendations
for selecting measuring principles and does not contain any clear limits of what is considered low or
high requirements. The aim of the matrix is only to provide support in the form of general guidelines for
how the different measuring principles are intended to be used.
Standard STD 112-0004 Volvo Group
Issue 3 Page 12 (41)
5.1 Form tolerances
Tolerance MP 1
In accordance
with the tole-
rance definition
MP 2
Mean value
evaluation [LS]
MP 3
Actual contact
features
MP 4 and higher
Adapted to production,
verified during production.
Often used if the process is
stated and thus the poss-
ible types of deviations are
known
Straightness
For generating line For high requirements, as for bearing fits and the like
Slender parts which take the shape of the mating part and for generators with low to medium requirements
For sealing surfaces and stable contact faces
For axis When the maxi-mum material principle can be permitted
For axes with low to medium requirements
For cylinder axes where sealing requirements are important
For verification of bar materials, etc.
Flatness Mating sur-faces, for high form require-ments, and for median planes where the maxi-mum material principle can be allowed
Slender flange which is connecting plane and takes the shape of the mating part when used, and for contact surfaces with low to medium form requirements
Sealing surfaces and contact faces with high requirements
Roundness For high requirements, as for bearing fits and the like
Slender parts which take the shape of the mating part and for parts with low requirements
For parts where high sealing requirements are important
For shop-floor inspection where the type of round-ness deviation is known
Cylindricity For high requirements, as for bearing fits and the like
Slender parts that take the shape of the mating part and for parts with low requirements
For parts where high sealing requirements are important
For shop-floor inspection where the type of cylind-ricity deviation is known
Profile of any line When checking against a digital shape model
Not recommended When checking against a profile template
Profile of any surface When checking against a digital shape model
Not recommended When checking against a digital shape model
For shop-floor inspection
Standard STD 112-0004 Volvo Group
Issue 3 Page 13 (41)
5.2 Orientation tolerances
Tolerance MP 1
In accordance
with the tole-
rance definition
MP 2
Mean value
evaluation [LS]
MP 3
Actual contact
features
MP 4 and higher
Adapted to production,
verified during production.
Often used if the process is
stated and thus the poss-
ible types of deviations are
known
Parallelism
For axis When the maxi-mum material principle can be permitted
For low to medium requirements
For parts with high requirements on parallelism such as bearing fits and the like
Parallelism
For plane For high requirements on parallelism when the flatness requirements are not specified separately
For slender surfaces which take the shape of the mating part when used, and for surfaces with low to medium high requirements
For contact surfaces with medium to high requirements and where flatness requirements are specified separately, and sealing surfaces where flatness requirements are specified separately
For slender surfaces which take the shape of the mating part when used, and where the limitation of the thickness variation is a primary function requirement, e.g. slender washers
Perpendicularity
For axis When the maxi-mum material principle can be permitted
For low to medium requirements
For parts with high requirements on perpendicularity, such as bearing fits and the like
For plane For high re-quirements on perpendicularity when the flat-ness require-ments are not specified separately
For slender surfaces which take the shape of the mating part when used, and for surfaces with low to medium requirements
For contact surfaces with medium to high requirements and where flatness requirements are specified separately, and sealing surfaces where flatness requirements are specified separately
Standard STD 112-0004 Volvo Group
Issue 3 Page 14 (41)
Tolerance MP 1
In accordance
with the tole-
rance definition
MP 2
Mean value
evaluation [LS]
MP 3
Actual contact
features
MP 4 and higher
Adapted to production,
verified during production.
Often used if the process is
stated and thus the poss-
ible types of deviations are
known
Angularity
For axis When the maxi-mum material principle can be permitted
For low to medium requirements
For parts with high angularity requirements concerning fits
Angularity
For plane For high re-quirements on angularity when the flatness requirements are not specified separately
For slender surfaces which take the shape of the mating part when used, and for surfaces with low to medium requirements
For contact surfaces with medium to high requirements and where flatness requirements are specified separately, and sealing surfaces where flatness requirements are specified separately
5.3 Location tolerances
Tolerance MP 1
In accordance
with the tole-
rance definition
MP 2
Mean value
evaluation [LS]
MP 3
Actual contact
features
MP 4 and higher
Adapted to production,
verified during production.
Often used if the process is
stated and thus the poss-
ible types of deviations are
known
Position
For centre point in a plane
When the maxi-mum material principle can be permitted for circle
For circles with low positional tolerance requirements
For circles with high positional tolerance requirements
For centre point in a sphere
Not recommended
For spheres with low to medium requirements on positional tolerance
For spheres with high requirements on positional tolerance
Standard STD 112-0004 Volvo Group
Issue 3 Page 15 (41)
Tolerance MP 1
In accordance
with the tole-
rance definition
MP 2
Mean value
evaluation [LS]
MP 3
Actual contact
features
MP 4 and higher
Adapted to production,
verified during production.
Often used if the process is
stated and thus the poss-
ible types of deviations are
known
For axis When the maxi-mum material principle can be permitted
For axes with low requirements on positional tole-rances, e.g. screw holes, and for clearance dia-meters, oil ducts etc.
For fits with high requirements on positional tolerances, e.g. bearing races
For plane For high requirements on positional tolerance when flatness requirements are not specified separately
For slender surfaces which take the shape of the mating part when used, and for surfaces with low to medium requirements
For contact surfaces with medium high to high requirements and where flatness requirements are specified separately, and sealing surfaces where flatness requirements are specified separately
Position of any profile
When checking against a digital shape model
Not recommended When checking against a profile template
Position of any surface
When checking against a digital shape model
Not recommended When checking against a surface template
Concentricity If the maximum material principle can be permitted for a circle
For circles with low concentricity requirements
For circles with high concentricity requirements
For shop-floor inspection where the limitation of variation in edge distance is a primary functional requirement
Coaxiality When the maximum material principle can be permitted
For axes with low requirements on coaxiality, e.g. screw holes, and for clearance diameters, oil ducts, etc.
For fits with high requirements on coaxiality, e.g. bearing races
For shop-floor inspection where the limitation of variation in edge distance is a primary functional requirement
Symmetry
For axis When the maxi-mum material principle can be permitted
For axes with low requirements on symmetry, e.g. screw holes, and for clearance diameters, oil ducts, etc.
For fits with high requirements on symmetry
For shop-floor inspection where the limitation of variation in edge distance is a primary functional requirement
Standard STD 112-0004 Volvo Group
Issue 3 Page 16 (41)
Tolerance MP 1
In accordance
with the tole-
rance definition
MP 2
Mean value
evaluation [LS]
MP 3
Actual contact
features
MP 4 and higher
Adapted to production,
verified during production.
Often used if the process is
stated and thus the poss-
ible types of deviations are
known
For median plane When the maxi-mum material principle can be permitted
For median planes with high requirements on symmetry, at clearance, etc.
For median planes with high requirements on symmetry and fit function, e.g. key ways
For shop-floor inspection where the limitation of variation in edge distance is a primary functional requirement
5.4 Run-out tolerances
Tolerance MP 1
In accordance
with the tole-
rance definition
MP 2
Mean value
evaluation [LS]
MP 3
Actual contact
features
MP 4 and higher
Adapted to production,
verified during production.
Often used if the process is
stated and thus the poss-
ible types of deviations are
known
Circular run-out
Radial For general radial run-out requirements
Use concentricity instead
Use concentricity instead
For shop-floor inspection where the type of round-ness deviation is known
Axial For general axial run-out requirements
For low axial run-out requirements where the design of the part requires measuring with measuring machine
For low axial run-out requirements where the design of the part requires measuring with measuring machine and where the resulting run-out on the mating part is functionally essential
For shop-floor inspection where the type of round-ness deviation on datums is known
Total run-out
Radial For general radial run-out requirements when only measuring one section at a time is not enough
Use coaxiality instead
Use coaxiality instead
For shop-floor inspection where the type of round-ness deviation is known
Standard STD 112-0004 Volvo Group
Issue 3 Page 17 (41)
Tolerance MP 1
In accordance
with the tole-
rance definition
MP 2
Mean value
evaluation [LS]
MP 3
Actual contact
features
MP 4 and higher
Adapted to production,
verified during production.
Often used if the process is
stated and thus the poss-
ible types of deviations are
known
Axial For high requirements on axial total run-out when flatness requirements are not specified separately
For slender surfaces which take the shape of the mating part when used, and for surfaces with low to medium requirements
For contact surfaces with medium to high requirements and where flatness requirements are specified separately, and sealing surfaces where flatness requirements are specified separately
For shop-floor inspection where the type of round-ness deviation on datums is known
Standard STD 112-0004 Volvo Group
Issue 3 Page 18 (41)
6 Definitions of measuring principles
The various measuring principles for different geometrical tolerances are defined in the table below.
The abbreviation t refers to the size of the tolerance concerned in mm.
6.1 Form tolerances
Geometrical tolerances Measuring
principle
Definition
Straightness
Straightness of a
generating line
1 The generating line shall be contained between two parallel
lines a distance t apart.
" 2 The generating line shall be contained between two parallel
lines a distance t apart. These two lines are parallel with a
median line, calculated according to the least squares (LS)
method.
" 3 The generating line shall be contained between two parallel
lines a distance t apart. These two lines are parallel with a line
tangent to the generating line.
" 4 The generating line shall be contained between two parallel
lines a distance t apart. These two lines are parallel with an
alignment line through two points as far apart as possible on
the generating line.
Straightness of an axis,
cylindrical tolerance zone
1 The axis shall be contained in a cylinder of diameter t.
” 2 The axis shall be contained in a cylinder of diameter t. The size
and orientation of the tolerance cylinder is calculated as a
median cylinder according to the least squares (LS) method,
containing the centre points of all sections. The sections are
calculated as median circles according to the least squares
(LS) method.
“ 3 The axis shall be contained in a cylinder of diameter t. The axis
of toleranced features consists of a line passing through the
centre points of all the sections. These centre points are set
according to the MC method (minimum circumscribed cylinder)
for sections on an external diameter and according to the MI
method (maximum inscribed cylinder) for sections on an
internal diameter.
" 4 The axis shall be contained in a cylinder of diameter t. The
radial difference when rotating with support against two
tangent points is considered as the size of the tolerance
cylinder.
Standard STD 112-0004 Volvo Group
Issue 3 Page 19 (41)
Geometrical tolerances Measuring
principle
Definition
Flatness
Flatness 1 The toleranced plane shall be contained between two parallel
planes a distance t apart.
" 2 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two planes are parallel to a
median plane, calculated according to the least squares (LS)
method.
Flatness 3 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two planes are parallel to a
plane tangent to the toleranced one.
" 4 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two planes are parallel to an
alignment plane through three points as far apart as possible
on the toleranced plane.
Roundness
Roundness 1 The circumference in every cross-section shall be contained
between two concentric circles a radial distance t apart.
" 2 The circumference in every cross-section shall be contained
between two concentric circles a radial distance t apart. These
two circles are also concentric with a median circle calculated
according to the least squares (LS) method.
" 3 The circumference in every cross-section shall be contained
between two concentric circles a radial distance t apart. These
two circles are also concentric with a circle determined by the
contact points, the minimum circumscribed circle for an
external circle is set according to the MC method, and the
maximum inscribed circle for an internal circle is set according
to the MI method.
" 4 The diameter variation in every cross-section, measured with
two-point measurement, may amount to maximum twice the
stated tolerance t.
" 5 The diameter variation in every cross-section, measured with
three-point measurement and with 120° between the
measurement points, may amount to maximum twice the
stated tolerance t.
Cylindricity
Cylindricity 1 The whole cylinder surface shall be contained between two
coaxial cylinders a radial distance t apart.
" 2 The whole cylinder surface shall be contained between two
coaxial cylinders a radial distance t apart. In addition, these
two cylinders are also coaxial with a median cylinder calculated
according to the LS method.
Standard STD 112-0004 Volvo Group
Issue 3 Page 20 (41)
Geometrical tolerances Measuring
principle
Definition
" 3 The whole cylinder surface shall be contained between two
coaxial cylinders a radial distance t apart. These two cylinders
are also coaxial with a cylinder determined by the contact
points, the minimum circumscribed circle for an external
diameter is set according to the MC method and the maximum
inscribed circle for an internal circle is set according to the MI
method.
“ 4 The diameter variation over the whole cylinder, measured with
two-point measurement, may amount to maximum twice the
stated tolerance t.
Cylindricity 5 The diameter variation over the whole cylinder, measured with
three-point measurement and with 120° between the
measurement points, may amount to maximum twice the
stated tolerance t.
Profile of any line
Profile of any line 1 The profile shall be contained between two equidistant lines
tangent to all circles of diameter t, and whose centres lie on a
line of the theoretically exact geometric form. Measurement
against a digital shape model, where a theoretical profile is
fitted against the measured points, belongs to this measuring
principle.
" 2 The measuring principle presupposes that features can be
created with the least squares (LS) method. Such features
exist normally only for very simple profiles of lines. This is why
measuring principle 2 is not recommended.
" 3 The profile shall be contained between two equidistant lines
tangent to all circles of diameter t, and whose centres lie on a
line of the theoretically exact geometric form. These two
equidistant lines are equidistant to a line tangent to an actual
profile of the theoretically exact geometric form.
Profile of any surface
Profile of any surface 1 The surface shall be contained between two equidistant
surfaces tangent to all circles of diameter t, and whose centres
lie on a surface of the theoretically exact geometric form.
Measurement against a digital shape model, where the
theoretical surface is fitted against measured points, belongs to
this measuring principle.
“ 2 This measuring principle presupposes that features can be
created with the least squares (LS) method. Such features
exist normally only for very simple profiles of surfaces. This is
why measuring principle 2 is not recommended.
Standard STD 112-0004 Volvo Group
Issue 3 Page 21 (41)
Geometrical tolerances Measuring
principle
Definition
" 3 The surface shall be contained between two equidistant
surfaces tangent to all spheres of diameter t, and whose
centres are on a surface of the theoretically exact geometric
form. These two equidistant surfaces are equidistant to a
surface tangent to an actual surface of the theoretically exact
geometric form.
“ 4 Deviations in profile of surface are considered as a deviation in
profile of line in two directions, at a 90° angle to each other.
The maximum distance between surface and profile template
is considered surface profile deviation.
6.2 Orientation tolerances
Geometrical tolerances Measuring
principle
Definition
Parallelism
Parallelism of a line in
relation to a datum line, in
a plane
1 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
parallel to the datum feature. The datum line is set as tangent
line if it consists of a generating line and as axis for the
maximum inscribed cylinder or the minimum circumscribed
cylinder if it consists of an axis for an internal or external
diameter respectively.
” 2 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
parallel to the datum line. The toleranced line and the datum
line are calculated as median features according to the least
squares (LS) method.
" 3 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
parallel to the datum line. The datum line is set as the tangent
line if it consists of a generating line and as an axis for the
maximum inscribed cylinder and the minimum circumscribed
cylinder if it consists of an axis for an internal or external
diameter respectively.
Parallelism of a line in
relation to a datum line in
all directions, cylindrical
tolerance zone
1 The line shall be contained in a cylinder of diameter t. This
cylinder is parallel to the datum line. The toleranced line is
calculated using the required number of centre sections in a
cylinder. These centres are set as centres for circles according
to the minimum zone (MZ) method. The datum line is set as an
axis for the maximum inscribed cylinder or the minimum
circumscribed cylinder if it consists of an axis for an internal or
external diameter respectively.
Standard STD 112-0004 Volvo Group
Issue 3 Page 22 (41)
Geometrical tolerances Measuring
principle
Definition
" 2 The line shall be contained in a cylinder of diameter t. This
cylinder is parallel to the datum line. The toleranced line is
calculated as the median line of the cylinder according to the
least squares (LS) method. The datum line is calculated as the
axis for the median cylinder according to the least squares (LS)
method.
“ 3 The line shall be contained in a cylinder of diameter t. This
cylinder is parallel to the datum line. The toleranced line is set
as axis for the maximum inscribed cylinder for a hole and as
minimum circumscribed cylinder for a shaft according to the MI
and MC method respectively. The datum line is set as the
maximum inscribed cylinder for a hole and as the minimum
circumscribed cylinder for a shaft according to the MI and MC
method respectively.
Parallelism of a line in
relation to a datum plane
1 The line shall be contained between two parallel planes a
distance t apart. These two tolerance planes are parallel to the
datum plane. The toleranced line is calculated using the
required number of centre sections in a cylinder. These centres
are set as centres for circles according to the minimum zone
(MZ) method. The datum plane is set as tangent plane.
" 2 The line shall be contained between two parallel planes a
distance t apart. These two tolerance planes are parallel to the
datum plane. The toleranced line and the datum plane are
calculated as median features according to the least squares
(LS) method.
" 3 The line shall be contained in a cylinder of diameter t. This
cylinder is parallel to the datum plane. The toleranced line is
set as axis for the maximum inscribed cylinder for a hole and
as the minimum circumscribed cylinder for a shaft according to
the MI and MC method respectively.
The datum plane is set as tangent plane.
Parallelism of a surface in
relation to a datum line
1 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
parallel to the datum line. The datum line is set as tangent line
if it consists of a generating line and as axis for the maximum
inscribed cylinder or the minimum circumscribed cylinder if it
consists of an axis for an internal or external diameter
respectively.
" 2 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
parallel to the datum line. The toleranced plane and the datum
line are calculated as median features according to the least
squares (LS) method.
Standard STD 112-0004 Volvo Group
Issue 3 Page 23 (41)
Geometrical tolerances Measuring
principle
Definition
" 3 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
parallel to the datum plane. The toleranced plane is set as
tangent plane. The datum line is set as tangent line if it
consists of a generating line and as axis for the maximum
inscribed cylinder or the minimum circumscribed cylinder if it
consists of an axis for an internal or external diameter
respectively.
Parallelism of a surface in
relation to a datum
surface
1 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
parallel to the datum plane. The datum plane is set as tangent
plane.
" 2 A toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
parallel to the datum plane. The toleranced plane and the
datum plane are calculated as median features according to
the least squares (LS) method.
“ 3 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
parallel to the datum plane. The toleranced plane and the
datum plane are set as tangent planes.
Parallelism of a surface in
relation to a datum
surface
4 The dimensional variation, measured with two-point measure-
ment, between the toleranced plane and the datum plane may
amount to maximum t. This measuring principle is applicable to
plane-parallel surfaces where two-point measurement can be
applied.
Perpendicularity
Perpendicularity of a line
in relation to a datum line
1 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
perpendicular to the datum feature. The datum line is set as
tangent line if it consists of a generating line and as an axis for
the maximum inscribed cylinder or the minimum circumscribed
cylinder if it consists of an axis for an internal or external
diameter respectively.
" 2 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
perpendicular to the datum line. The toleranced line and the
datum line are calculated as median features according to the
least squares (LS) method.
" 3 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two lines are
perpendicular to the datum line. The toleranced line and the
datum line are set as tangent lines if they consist of generating
lines and as axes for the maximum inscribed cylinder or the
minimum circumscribed cylinder if they consist of axes for an
internal or external diameter respectively.
Standard STD 112-0004 Volvo Group
Issue 3 Page 24 (41)
Geometrical tolerances Measuring
principle
Definition
Perpendicularity of an
axis in relation to a datum
plane in all directions,
cylindrical tolerance zone
1 The line shall be contained in a cylinder of diameter t. This
cylinder is perpendicular to the datum plane. The toleranced
line is set using the required number of centre sections in a
cylinder. These centres are set as centres for circles according
to the minimum zone (MZ) method. The datum plane is set as
tangent plane.
" 2 The line shall be contained in a cylinder of diameter t. This
cylinder is perpendicular to the datum plane. The toleranced
line is set as median line by the least squares (LS) method,
using the required number of centre sections in a cylinder.
These centres are calculated as centres for circles according
to the least squares (LS) method. The datum plane is
calculated as median plane according to the least squares
method.
" 3 The line shall be contained in a cylinder of diameter t. This
cylinder is perpendicular to the datum plane. The toleranced
line is set as axis for the maximum inscribed or the minimum
circumscribed cylinder if they consist of axes for an internal or
an external diameter respectively according to the MI and MC
method respectively. The datum plane is set as tangent plane.
Perpendicularity of a line
in relation to a datum
plane in one direction
1 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
perpendicular to the datum feature. The datum plane is set as
tangent plane.
” 2 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
perpendicular to the datum feature. The toleranced line and the
datum line are calculated as median features according to the
least squares (LS) method.
" 3 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
perpendicular to the datum feature. The toleranced line is set
as tangent line if it refers to a generating line. If it refers to an
axis, it is set as axis for the maximum inscribed or the
minimum circumscribed cylinder when the tolerance refers to
an internal or external diameter, according to the MI and the
MC method respectively. The datum plane is set as tangent
plane.
Standard STD 112-0004 Volvo Group
Issue 3 Page 25 (41)
Geometrical tolerances Measuring
principle
Definition
Perpendicularity of a
surface in relation to a
datum line
1 The toleranced plane shall be contained between two parallel
lines a distance t apart. These two tolerance planes are
perpendicular to the datum feature. The datum line is set as
tangent line if it consists of a generating line and as axis for the
maximum inscribed or the minimum circumscribed cylinder if it
consists of an axis for an internal or external diameter
respectively.
" 2 The toleranced plane shall be contained between two parallel
lines a distance t apart. These two tolerance planes are
perpendicular to the datum feature. The toleranced plane and
the datum line are calculated as median features according to
the least squares (LS) method.
" 3 The toleranced plane shall be contained between two parallel
lines a distance t apart. These two tolerance planes are
perpendicular to the datum feature. The toleranced plane is set
as tangent plane. The datum line is set as tangent line if it
consists of a generating line and as axis for the maximum
inscribed or the minimum circumscribed cylinder if it consists of
an axis for an internal or external diameter respectively.
Perpendicularity of a
surface in relation to a
datum surface
1 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
perpendicular to the datum feature. The datum plane is set as
tangent plane.
Note: If no secondary datum feature is indicated, the part may be
turned around the datum plane to the smallest possible difference in
dimensions.
Perpendicularity of a
surface in relation to a
datum surface
2 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
perpendicular to the datum feature. The toleranced plane and
the datum plane are calculated as median features by the least
squares (LS) method.
Note: If no secondary datum feature is indicated, the part may be
turned around the datum plane to the smallest possible difference in
dimensions.
" 3 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
perpendicular to the datum feature. The toleranced plane and
the datum plane are set as tangent planes.
Note: If no secondary datum feature is indicated, the part may be
turned around the datum plane to the smallest possible difference in
dimensions.
Standard STD 112-0004 Volvo Group
Issue 3 Page 26 (41)
Geometrical tolerances Measuring
principle
Definition
Angularity
Angularity of a line in a
plane in relation to a
datum line
1 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
aligned with the specified angle in relation to the datum
feature. The datum line is set as tangent line if it consists of a
generating line and as axis for the maximum inscribed or the
minimum circumscribed cylinder if it consists of an axis for an
internal or external diameter respectively.
” 2 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
aligned with the specified angle in relation to the datum
feature. The toleranced line and datum line are calculated as
median features according to the least squares (LS) method.
" 3 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
aligned with the specified angle in relation to the datum
feature. If it refers to a generating line, the toleranced line is set
as tangent line. If it refers to an axis, it is set as axis for the
maximum inscribed or the minimum circumscribed cylinder
according to the MI and MC method respectively.
The datum line is set as tangent line if it consists of a
generating line and as axis for the maximum inscribed or the
minimum circumscribed cylinder if it consists of an axis for an
internal or external diameter respectively.
Angularity in all directions
of an axis in relation to a
datum line
1 The line shall be contained in a cylinder of diameter t. This
tolerance cylinder is aligned with the specified angle in relation
to the primary datum feature and parallel to the secondary
datum feature. The toleranced line is set using the required
number of centre sections in a cylinder. These centres are set
as centres for circles according to the minimum zone (MZ)
method. The datum line is set as tangent plane if it consists of
an axis and as axis for the maximum inscribed or the minimum
circumscribed cylinder if it consists of an axis for an internal or
external diameter respectively.
Angularity in all directions
of an axis in relation to a
datum line
2 The line shall be contained in a cylinder of diameter t. This
tolerance cylinder is aligned with the specified angle in relation
to the primary datum feature and parallel to the secondary
datum feature. The toleranced line and datum feature are
calculated as median features according to the least squares
(LS) method.
Standard STD 112-0004 Volvo Group
Issue 3 Page 27 (41)
Geometrical tolerances Measuring
principle
Definition
” 3 The line shall be contained in a cylinder of diameter t. This
tolerance cylinder is aligned with the specified angle in relation
to the primary datum feature and parallel to the secondary
datum feature. The toleranced line is set as the maximum
inscribed or minimum circumscribed cylinder if it consists of an
axis for an internal or external diameter respectively.
The datum line is set as tangent line if it consists of a
generating line and as axis for the maximum inscribed or the
minimum circumscribed cylinder if it consists of an axis for an
internal or external diameter respectively.
Angularity of a line in
relation to a datum
surface
1 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
aligned with the specified angle in relation to the primary datum
feature. The datum plane is set as tangent plane.
" 2 In a projection plane, the line shall fit between two parallel lines
a distance t apart. These two tolerance lines are aligned with
the specified angle in relation to the primary datum feature.
Toleranced line and datum plane are calculated as median
features by the least squares (LS) method.
” 3 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
aligned with the specified angle in relation to the primary datum
feature. If it refers to a generating line, the toleranced line is set
as tangent plane. But if it refers to an axis, it is set as axis for
the maximum inscribed cylinder for a hole or the minimum
circumscribed cylinder for a shaft according to the MI and MC
method respectively.
The datum plane is set as tangent plane.
Angularity of a surface in
relation to a datum line
1 The toleranced plane shall be contained between two parallel
lines a distance t apart. These two tolerance lines are aligned
with the specified angle in relation to the datum feature. The
datum line is set as tangent line if it consists of a generating
line and as axis for the maximum inscribed or the minimum
circumscribed cylinder if it consists of an axis for an internal or
external diameter respectively.
Note: If no secondary datum feature is indicated, the part may be
turned around the datum line to the smallest possible difference in
dimensions.
Angularity of a surface in
relation to a datum line
2 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance lines are
aligned with the specified angle in relation to the datum
feature. The toleranced plane and the datum line are
calculated as median features by the least squares (LS)
method.
Note: If no secondary datum feature is indicated, the part may be
turned around the datum line to the smallest possible difference in
dimensions.
Standard STD 112-0004 Volvo Group
Issue 3 Page 28 (41)
Geometrical tolerances Measuring
principle
Definition
" 3 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance lines are
aligned with the specified angle in relation to the datum
feature. The datum line is set as tangent line. The datum line is
set as tangent line if it consists of a generating line and as axis
for the maximum inscribed or the minimum circumscribed
cylinder if it consists of an axis for an internal or external
diameter respectively.
Note: If no secondary datum feature is indicated, the part may be
turned around the datum line to the smallest possible difference in
dimensions.
Angularity of a surface in
relation to a datum
surface
1 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance lines are
aligned with the specified angle in relation to the datum
feature. The datum plane is set as tangent plane.
Note: If no secondary datum feature is indicated, the part may be
turned around the datum line to the smallest possible difference in
dimensions.
“ 2 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
aligned with the specified angle in relation to the datum
feature. The toleranced plane and the datum plane are
calculated as median features according to the least squares
(LS) method.
Note: If no secondary datum feature is indicated, the part may be
turned around the datum line to the smallest possible difference in
dimensions.
" 3 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
aligned with the specified angle in relation to the datum
feature. The toleranced plane and datum plane are set as
tangent planes.
Note: If no secondary datum feature is indicated, the part may be
turned around the datum line to the smallest possible difference in
dimensions.
Standard STD 112-0004 Volvo Group
Issue 3 Page 29 (41)
6.3 Location tolerances
Geometrical tolerances Measuring
principle
Definition
Position
Position in all directions
of a point in a plane
1 The toleranced point shall be contained in a circle of diameter
t. The centre point of this tolerance circle is situated in the
theoretically exact position in relation to stated datums. If it is a
centre point, the position of the toleranced features is set as
position for a circle calculated according to the minimum zone
(MZ) method
The datum feature is set as tangent plane, inscribed circle or
cylinder, or circumscribed circle or cylinder, depending on what
the datum feature is made up of.
" 2 The toleranced point shall be contained in a circle of diameter
t. The centre point of this tolerance circle is situated in the
theoretically exact position in relation to stated datums. If it is a
centre point, the position of the toleranced features is set as
position for a median circle calculated according to the least
squares (LS) method
The datum feature is calculated as median feature according to
the least squares (LS) method.
“ 3 The toleranced point shall be contained in a circle of diameter
t. The centre point of this tolerance circle is situated in the
theoretically exact position in relation to stated datums. If it is a
centre point, the position of the toleranced features is set as
position for an inscribed or circumscribed circle according to
the MI and MC method respectively.
The datum feature is set as tangent plane, inscribed circle or
cylinder, or circumscribed circle or cylinder, depending on what
the datum feature is.
Position in all directions
of a point, spherical
tolerance zone
1 The toleranced point shall be contained in a circle of diameter
t. The centre point of this tolerance circle is situated in the
theoretically exact position in relation to stated datums. If it is a
centre point, the position of the toleranced features is set as
position for a circle calculated according to the minimum zone
(MZ) method.
The datum feature is set as tangent plane, inscribed circle or
cylinder, or circumscribed circle or cylinder, depending on what
the datum feature is.
“ 2 The toleranced point shall be contained in a sphere of diameter
t. The centre point of this tolerance sphere is situated in the
theoretically exact position in relation to stated datums. If it is a
centre point, the position of the toleranced features is set as
position for a median sphere calculated according to the least
squares (LS) method
The datum feature is calculated as median feature according to
the least squares (LS) method.
Standard STD 112-0004 Volvo Group
Issue 3 Page 30 (41)
Geometrical tolerances Measuring
principle
Definition
Position in all directions
of a point, spherical
tolerance zone
3 The toleranced point shall be contained in a sphere of diameter
t. The centre point of this tolerance sphere is situated in the
theoretically exact position in relation to stated datums. If it is a
centre point for an internal sphere, the position of the tole-
ranced feature is set as position for an inscribed sphere
according to the MI method and if it is an external sphere, it is
set as position for a circumscribed sphere according to the MC
method.
The datum feature is set as tangent plane, inscribed circle or
cylinder, or circumscribed circle or cylinder, depending on what
the datum feature is.
Position of a line in one
direction
1 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
symmetrically disposed around the theoretically exact position
in relation to the datum feature. The reference feature is set as
tangent plane, inscribed circle or cylinder or circumscribed
circle or cylinder depending on what the datum feature is.
" 2 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
symmetrically disposed around the theoretically exact position
in relation to the datum feature. The toleranced line is
calculated as median line according to the least squares
method if it consists of a generating line and as an axis for a
median cylinder according to the least squares method if it
consists of a cylinder axis.
The datum feature is calculated as median feature according to
the least squares (LS) method.
“ 3 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
symmetrically disposed around the theoretically exact position
in relation to the datum feature. The toleranced line is set as
tangent line if it consists of a generating line and as the
maximum inscribed cylinder or minimum circumscribed
cylinder if it consists of an internal or external cylinder
respectively.
The datum feature is set as tangent plane, inscribed circle or
cylinder, or circumscribed circle or cylinder depending on what
the datum feature is.
Standard STD 112-0004 Volvo Group
Issue 3 Page 31 (41)
Geometrical tolerances Measuring
principle
Definition
Position of a line in all
directions
1 The line shall be contained in a cylinder of diameter t. The axis
of this tolerance cylinder lies in the theoretically exact position
in relation to the datum feature.
The datum feature is set as tangent plane, inscribed circle or
cylinder, or circumscribed circle or cylinder depending on what
the datum feature is.
" 2 The line shall be contained in a cylinder of diameter t. The axis
of this tolerance cylinder lies in the theoretically exact position
in relation to the datum feature.
The toleranced feature consists of the axis for a cylinder
calculated according to the least squares method. The datum
feature is set as median feature according to the least squares
(LS) method.
Position of a line in all
directions
3 The line shall be contained in a cylinder of diameter t. The axis
of this tolerance cylinder lies in the theoretically exact position
in relation to the datum feature.
The toleranced feature consists of the axis for a cylinder set as
the maximum inscribed cylinder or the minimum circumscribed
cylinder if it consists of an internal or external cylinder
respectively.
The datum feature is set as tangent plane if it consists of a
plane, as tangent line if it consists of a line, and as the
maximum inscribed cylinder or the minimum circumscribed
cylinder if it consists of an internal or external cylinder
respectively.
Position of a flat surface
or a median plane 1 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
symmetrically disposed around the theoretically exact position
in relation to the datum feature.
The datum feature is set as tangent plane. If the tolerance
consists of a median plane, it is set as median plane for two
planes which have been set as tangent plane for those planes
that make up the datum feature.
“ 2 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
symmetrically disposed around the theoretically exact position
in relation to the datum plane.
The toleranced plane and the datum plane are calculated as
median features according to the least squares (LS) method. If
the tolerance consists of a median plane, it is set as median
plane for two planes which have been calculated as median
planes for those planes that make up the datum feature.
Standard STD 112-0004 Volvo Group
Issue 3 Page 32 (41)
Geometrical tolerances Measuring
principle
Definition
" 3 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
symmetrically disposed around the theoretically exact position
in relation to the datum plane. The toleranced plane and the
datum plane are set as tangent planes.
If the tolerance consists of a median plane, it is set as median
plane for two planes set as tangent planes for those planes
that make up the datum feature.
Position of any profile
Position of any profile 1 The profile shall be contained between two equidistant lines
enveloping all circles of diameter t, and whose centres lie on a
line of the theoretically exact geometric form and are disposed
in the theoretically exact position. Measurement against digital
shape model, where the position of the measured points is
related to the correct position on the model, belongs to this
measuring principle.
“ 2 This measuring principle presupposes that features can be
created with the least squares method. Such features exist
normally only for very simple profile of lines. This is why
measuring principle 2 is not recommended.
Position of any profile 3 The profile shall be contained between two equidistant lines
enveloping all circles of diameter t, and whose centres lie on a
line of the theoretically exact geometric form and are disposed
in the theoretically exact position. The profile is set against a
line of the theoretically exact geometric form tangent to an
actual profile.
Position of any surface
Position of any surface 1 The surface shall be contained between two equidistant
surfaces enveloping all spheres of diameter t, and whose
centres lie on a surface of the theoretically exact geometric
form and are disposed in the theoretically exact position.
Measurement against digital shape model, where the position
of the measured points is related to the correct position on the
model, belongs to this measuring principle.
" 2 This measuring principle presupposes that features can be
created with the least squares method. Such features exist
normally only for very simple profile of surfaces. This is why
measuring principle 2 is not recommended.
“ 3 The surface shall be contained between two equidistant
surfaces tangent to all spheres of diameter t, and whose
centres lie on a line of the theoretically exact geometric form
and are disposed in the theoretically correct position. The
profile is set against a line of the theoretically exact geometric
form tangent to an actual profile.
Standard STD 112-0004 Volvo Group
Issue 3 Page 33 (41)
Geometrical tolerances Measuring
principle
Definition
Concentricity
Concentricity of a point 1 The toleranced point shall be contained in a circle of diameter
t. The centre point of this tolerance circle coincides with the
centre point of the datum. The position of the toleranced
feature is set as the position of a circle calculated in
accordance with the minimum zone (MZ) method.
The datum feature is set as maximum inscribed circle or
minimum circumscribed circle depending on whether it consists
of an internal or external circle.
“ 2 The toleranced point shall be contained in a circle of diameter
t. The centre point of this tolerance circle coincides with the
centre point of the datum. The position of the toleranced
feature is set as position of a median circle calculated
according to the least squares (LS) method.
The datum feature is calculated as median circle according to
the least squares (LS) method.
“ 3 The toleranced point shall be contained in a circle of diameter
t. The centre point of this tolerance circle coincides with the
centre point of the datum. The position of the toleranced
feature and the position of the datum feature are set as
position of the maximum inscribed circle or the minimum
circumscribed circle depending on whether it applies to an
internal or external circle.
Concentricity of a point 4 The toleranced point shall be contained in a circle of diameter
t. The centre point of this tolerance circle coincides with the
centre point of the datum.
The size of the tolerance circle corresponds to the variation in
two-point measurement when measuring the cylinder surface
of the toleranced feature and the datum feature. The variation
is measured in one section.
Coaxiality
Coaxiality of an axis 1 The line shall be contained in a cylinder of diameter t. The axis
of this tolerance cylinder coincides with the datum feature or its
extension. The datum feature is set as the maximum inscribed
cylinder or the minimum circumscribed cylinder depending on
whether it applies to an internal or external cylinder.
If the primary datum consists of a plane and the secondary
datum consists of a cylinder, the primary datum is set as
tangent plane and the secondary datum as the maximum
inscribed cylinder, which is perpendicular to the primary datum
if the secondary datum consists of an internal cylinder and as
minimum circumscribed cylinder, perpendicular to the primary
datum, if the secondary datum consists of an external cylinder.
Standard STD 112-0004 Volvo Group
Issue 3 Page 34 (41)
Geometrical tolerances Measuring
principle
Definition
“ 2 The line shall be contained in a cylinder of diameter t. The axis
of this tolerance cylinder coincides with the datum feature or its
extension. The toleranced axis is calculated as the axis of a
median cylinder according to the least squares method. The
datum feature is set as the axis of a median cylinder.
If the primary datum consists of a plane and the secondary
datum consists of an internal cylinder, the primary datum is
calculated as median plane according to the least squares
method and the secondary datum as the maximum cylinder,
perpendicular to the primary datum, that can be inscribed
within the median cylinder of the secondary datum which is
calculated according to the least squares method.
If the primary datum consists of a plane and the secondary
datum consists of an external cylinder, the primary datum is
calculated as median plane by the least squares method and
the secondary datum is calculated by the least squares method
as the minimum cylinder, perpendicular to the primary datum,
that can be circumscribed around the median cylinder of the
secondary datum which is calculated according to the least
squares method.
Coaxiality of an axis 3 The line shall be contained in a cylinder of diameter t. The axis
of this tolerance cylinder coincides with the datum feature or its
extension. The toleranced feature is calculated as the axis of a
cylinder set as the maximum inscribed cylinder or the minimum
circumscribed cylinder if it consists of an internal or external
cylinder respectively.
The datum feature is set as the maximum inscribed cylinder or
the minimum circumscribed cylinder depending on whether it
applies to an internal or external cylinder respectively.
If the primary datum consists of a plane and the secondary
datum consists of an internal cylinder, the primary datum is set
as tangent plane and the secondary datum as the maximum
inscribed cylinder, which is perpendicular to the primary datum
if the secondary datum consists of an internal cylinder, and as
minimum circumscribed cylinder, perpendicular to the primary
datum, if the secondary datum consists of an external cylinder.
" 4 The line shall be contained in a cylinder of diameter t. The axis
of this tolerance cylinder coincides with the datum feature.
The size of the tolerance cylinder corresponds to the variation
in two-point measurement when measuring the cylinder
surface of the toleranced feature and the datum feature. The
variation is measured over the entire length of the feature.
Standard STD 112-0004 Volvo Group
Issue 3 Page 35 (41)
Geometrical tolerances Measuring
principle
Definition
Symmetry
Symmetry of an axis 1 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
symmetrically disposed around the datum line or the datum
plane.
If the datum feature consists of a cylinder axis it is set as the
maximum inscribed cylinder or minimum circumscribed
cylinder depending on whether it applies to an internal or
external cylinder respectively.
If the datum consists of a median line, it is set as median line
for two lines set as tangent lines for those lines that make up
the datum feature. If the datum feature consists of a median
plane, it is set as tangent plane for the planes that make up the
datum feature.
“ 2 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
symmetrically disposed around the datum line or the datum
plane.
A toleranced line is calculated as axis for a median cylinder
according to the least squares method if it consists of a
cylinder axis.
If the datum feature consists of a cylinder axis, it is calculated
as median cylinder axis according to the least squares method.
If the datum feature consists of a median line, it is set as
median line for two lines set as median lines for those lines
that make up the datum feature. If the datum feature consists
of a median plane, it is set as median plane for two planes set
as median plane for the planes that make up the datum
feature.
Symmetry of an axis 3 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
symmetrically disposed around the datum line or the datum
plane.
The toleranced feature is set as axis for a cylinder set as the
maximum inscribed cylinder or the minimum circumscribed
cylinder if it consists of an internal or external cylinder
respectively.
If the datum feature consists of a cylinder axis it is set as
maximum inscribed cylinder or the minimum circumscribed
cylinder depending on whether it applies to an internal or
external cylinder respectively.
If the datum feature consists of a median line, it is set as
median line for two lines set as tangent lines for those lines
that make up the datum feature. If the datum feature consists
of a median plane it is set as median plane for two planes set
as tangent plane for those planes that make up the datum
feature.
Standard STD 112-0004 Volvo Group
Issue 3 Page 36 (41)
Geometrical tolerances Measuring
principle
Definition
” 4 In a projection plane, the line shall be contained between two
parallel lines a distance t apart. These two tolerance lines are
symmetrically disposed around the datum line or the datum
plane.
If the datum feature consists of an axis, the distance variation
between the cylinder surface of a toleranced cylinder and the
cylinder surface of the datum feature, measured by two-point
measurement, is considered as symmetry deviation and must
not exceed the tolerance t.
If the datum feature consists of symmetry plane, the distance
variation between the cylinder surface of a toleranced cylinder
and the cylinder surface of any surfaces constituting the datum
feature, measured by two-point measurement, is considered as
symmetry deviation and must not exceed the tolerance t.
This measuring principle can be regarded as variation in
distance to the edge.
Symmetry of a median
plane
1 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two toleranced planes are
symmetrically disposed around the datum feature.
The datum feature is set as median plane for two planes set as
tangent planes for those planes that make up the datum
feature.
“ 2 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two toleranced planes are
symmetrically disposed around the datum plane.
The toleranced plane and the datum plane are set as median
planes for the two planes respectively, which in turn are set as
median planes for those planes that make up the toleranced
feature or the datum feature.
Symmetry of a median
plane
3 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two toleranced planes are
symmetrically disposed around the datum plane.
The toleranced plane and the datum plane are set as median
planes for two planes respectively, which in turn are set as
tangent planes for those planes that make up the toleranced
feature or the datum feature.
“ 4 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two toleranced planes are
symmetrically disposed around the datum plane.
The distance variation between the surfaces forming the
toleranced feature and surfaces forming the datum feature,
measured by two-point measurement, is considered as
symmetry deviation and must not exceed the tolerance t.
The measuring principle can be considered as a variation in
distance to the edge.
Standard STD 112-0004 Volvo Group
Issue 3 Page 37 (41)
6.4 Run-out tolerances
Geometrical tolerances Measuring
principle
Definition
Circular run-out
Circular radial run-out 1 The outline in a section shall be contained between two
concentric circles a radial distance t apart. The centre points of
these tolerance circles coincide with the axis of the datum shaft
or its elongation.
The datum feature is set as maximum inscribed cylinder or
minimum circumscribed cylinder depending on whether it
applies to an internal or external circle respectively.
If the primary datum consists of a plane and the secondary
datum consists of a cylinder, the primary datum is set as
tangent plane and the secondary datum is set as maximum
inscribed cylinder perpendicular to the primary datum if the
secondary datum consists of an internal cylinder, and as
minimum circumscribed cylinder perpendicular to the primary
datum if the secondary datum consists of an external cylinder.
" 2 Not relevant. Use concentricity/coaxiality if measuring principle
2 is required
" 3 Not relevant. Use concentricity/coaxiality if measuring principle
3 is required
Circular radial run-out 4 The outline in a section shall be contained between two
concentric circles a radial distance t apart. The centre points of
these tolerance circles coincide with the axis of the datum shaft
or its elongation.
The datum feature is evaluated by rotation in two 90° V-yokes
if the datum feature consists of two external circles or in a 90°
V-blocks if the datum feature consists of an external cylinder.
If the datum feature consists of internal circles or cylinders it
shall be rotated in a corresponding way with contact with two
points or lines on the datum feature. These contact points/lines
are at a 90° angle to each other.
Circular axial run-out 1 The outline in each cross-section of the same radius on the
surface shall be contained between two concentric circles of
the same radius and an axial distance t apart. The centres of
these tolerance circles coincide with the axis of the datum
feature or its elongation.
The datum feature is set as maximum inscribed cylinder or
minimum circumscribed cylinder depending on whether it
applies to an internal or external circle respectively.
If the primary datum consists of a plane and the secondary
datum consists of a cylinder, the primary datum is set as
tangent plane and the secondary datum is set as maximum
inscribed cylinder perpendicular to the primary datum if the
secondary datum consists of an internal cylinder, and as
minimum circumscribed cylinder perpendicular to the primary
datum if the secondary datum consists of an external cylinder.
Standard STD 112-0004 Volvo Group
Issue 3 Page 38 (41)
Geometrical tolerances Measuring
principle
Definition
“ 2 Each cross-section of the same radius on the surface shall be
contained between two concentric circles of the same radius
and an axial distance t apart. The centres of these tolerance
circles coincide with the axis of the datum shaft or its
elongation.
Each cross-section is calculated as a circular plane according
to the least squares (LS) method.
The datum feature is set as the axis of a median cylinder.
If the primary datum consists of a plane and the secondary
datum consists of an internal cylinder, the primary datum is set
as median plane by the least squares method and the
secondary datum is set as maximum cylinder perpendicular to
the primary datum that can be inscribed in the median cylinder
of the secondary datum, calculated according to the least
squares method.
If the primary datum consists of a plane and the secondary
datum consists of an external cylinder, the primary datum is set
as median plane according to the least squares method and
the secondary datum is calculated according to the least
squares method as the minimum cylinder perpendicular to the
primary datum that can be scribed around the median cylinder
of the secondary datum.
Circular axial run-out 3 Each cross-section of the same radius on the surface shall be
contained between two concentric circles of the same radius
and an axial distance t apart. The centres of these tolerance
circles coincide with the axis of the datum feature or its
elongation.
Each cross-section is set as a circular tangent plane.
The datum feature is set as maximum inscribed cylinder or
minimum circumscribed cylinder depending on whether it
applies to an internal or external cylinder respectively.
If the primary datum consists of a plane and the secondary
datum consists of a cylinder, the primary datum is set as
tangent plane and the secondary datum is set as maximum
inscribed cylinder perpendicular to the primary datum if the
secondary datum consists of an internal cylinder and as the
minimum circumscribed cylinder, perpendicular to the primary
datum if the secondary datum consists of an external cylinder.
“ 4 The outline in each cross-section of the same radius on the
surface shall be contained between two concentric circles of
the same radius and an axial distance t apart. The centres of
these tolerance circles coincide with the axis of the datum
feature or its elongation.
The datum feature is evaluated by rotation in two 90° V-yokes
if it consists of two external circles, or in two 90° V-blocks if it
consists of an external cylinder.
If the datum feature consists of internal circles or cylinders it
shall be rotated in a corresponding way with contact with two
points or lines on the datum feature. These contact points/lines
are at a 90° angle to each other.
Standard STD 112-0004 Volvo Group
Issue 3 Page 39 (41)
Geometrical tolerances Measuring
principle
Definition
Total run-out
Total radial run-out 1 The whole cylinder surface shall be contained between two
coaxial cylinders a radial distance t apart. The axis of these
tolerance cylinders coincides with the axis of the datum feature
or its extension.
The datum feature is set as maximum inscribed cylinder or
minimum circumscribed cylinder depending on whether it
applies to an internal or external cylinder.
If the primary datum consists of a plane and the secondary
datum consists of a cylinder, the primary datum is set as
tangent plane and the secondary datum as the maximum
inscribed cylinder, perpendicular to the primary datum if the
secondary datum consists of an internal cylinder, and as a
minimum circumscribed cylinder, perpendicular to the primary
datum, if the secondary datum consists of an external cylinder.
" 2 Not relevant. Use coaxiality if measuring principle 2 is required.
" 3 Not relevant. Use coaxiality if measuring principle 3 is required.
Total radial run-out 4 The whole cylinder surface shall be contained between two
coaxial cylinders a radial distance t apart. The axis of these
tolerance cylinders coincides with the axis of the datum feature
or its extension.
The datum feature is evaluated by rotation in two 90° V-yokes
if it consists of two external circles, or in two 90° V-blocks if it
consists of an external cylinder.
If the datum feature consists of internal circles or cylinders it
shall be rotated in a corresponding way with contact with two
points or lines on the datum feature. These contact points/lines
are at a 90° angle to each other.
Total axial run-out
Note: This tolerance is
identical to perpendicularity
for a surface with an axis as
datum.
1 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
perpendicular to the datum axis.
The datum axis is set as axis for the maximum inscribed
cylinder or the minimum circumscribed cylinder if it consists of
an axis for an internal and external diameter respectively.
If the primary datum consists of a plane and the secondary
datum consists of a cylinder, the primary datum is set as
tangent plane and the secondary datum as the maximum
inscribed cylinder perpendicular to the primary datum if the
secondary datum consists of an internal cylinder, and as the
minimum circumscribed cylinder perpendicular to the primary
datum if the secondary datum consists of an external cylinder.
Standard STD 112-0004 Volvo Group
Issue 3 Page 40 (41)
Geometrical tolerances Measuring
principle
Definition
“ 2 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
perpendicular to the datum feature. The toleranced plane and
the datum line are calculated as median features according to
the least squares (LS) method.
The datum shaft is set as axis for a median cylinder.
If the primary datum consists of a plane and the secondary
datum consists of an internal cylinder, the primary datum is
calculated as median plane according to the least squares
method and the secondary datum as the maximum cylinder
perpendicular to the primary datum that can be inscribed into
the median cylinder of the secondary datum, calculated
according to the least squares method.
If the primary datum consists of a plane and the secondary
datum consists of an external cylinder, the primary datum is
calculated as median plane according to the least squares
method, and the secondary datum is calculated according to
the least squares method as the minimum cylinder,
perpendicular to the primary datum, to be scribed around the
median cylinder of the secondary datum.
Total axial run-out 3 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
perpendicular to the datum feature. The toleranced plane is set
as tangent plane.
The datum axis is set as axis for the maximum inscribed
cylinder or the minimum circumscribed cylinder if it consists of
an axis for an internal or external diameter respectively.
If the primary datum consists of a plane and the secondary
datum consists of a cylinder, the primary datum is set as
tangent plane and the secondary datum is set as maximum
inscribed cylinder perpendicular to the primary datum if the
secondary datum consists of an internal cylinder, and as the
minimum circumscribed cylinder perpendicular to the primary
datum if the secondary datum consists of an external cylinder.
“ 4 The toleranced plane shall be contained between two parallel
planes a distance t apart. These two tolerance planes are
perpendicular to the datum feature. The datum feature is
evaluated by rotation in two 90° V-yokes if it consists of two
external circles, or in two 90° V-blocks if it consists of an
external cylinder.
If the datum feature consists of internal circles or cylinders, it
shall be rotated in a corresponding way with contact with two
points or lines on the datum feature. These contact points/lines
are at a 90° angle to each other.
Standard STD 112-0004 Volvo Group
Issue 3 Page 41 (41)
7 Reference to this standard
Reference to this standard on drawings or other engineering design documentation shall be made
through a reference standard or directly with the following note:
MEASURING PRINCIPLES STD 112-0004