ISO 4291:1985
(Main)Methods for the assessement of departure from roundness — Measurement of variations in radius
Methods for the assessement of departure from roundness — Measurement of variations in radius
Establishes types of contact (stylus) instruments to be used, recommendations for their use, procedures for calibration of instruments and verification of their characteristics. Applies to a profile transformation, obtained under reference conditions. Departures from roundness of the measured profile, procedure, calibration and determination of systematic errors of rotation are dealt with in annexes A to D, respectively. Annex E gives rules for plotting and reading polar graphs. The position of the least squares centre can be calculated from a simple explicit equation given in annex F.
Méthodes d'évaluation des écarts de circularité — Mesurage des variations de rayon
Metode za ugotavljanje odstopka od krožnosti – Meritev sprememb polmera
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International Standard
INTERNATIONAL ORGANIZATION FOR STANDARDIZATION.ME)I(CiYHAPO,QHAF OPf-AHM3ALWl I-IO CTAH,QAPTM3ALWl.ORGANISATlON INTERNATIONALE DE NORMALISATION
Methods for the assessment of departure from
Measurement of variations in radius
roundness -
- Mesurage des variations de rayon
MS thodes d’kvalua tion des Ecarts de circularite
First edition - 19850945
Ref. No. ISO 4291-1985 (EI
UDC 531.717
w
-
Descriptors : surface conditions, roundness measurement, measuring instruments, Profile meters, error analysis.
Price based on 18 pages
---------------------- Page: 1 ----------------------
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of
national Standards bodies (ISO member bedies). The work of preparing International
Standards is normally carried out through ISO technical committees. Esch member
body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, govern-
mental and non-governmental, in liaison with ISO, also take patt in the work.
Draft International Standards adopted by the technical committees are circulated to
the member bodies for approval before their acceptance as International Standards by
the ISO Council. They are approved in accordance with ISO procedures requiring at
least 75 % approval by the member bodies voting.
International Standard ISO 4291 was prepared by Technical Committee ISO/TC 57,
Metrology and properties of surfaces.
0 International Organkation for Standardization, 1985
Printed in Switzerland
---------------------- Page: 2 ----------------------
INTERNATIONAL STANDARD ISO 42914985 (E)
Methods for the assessment of departure from
Measurement of variations in radius
roundness -
1 Scope and field of application digital representation of the Profile (generally 7 % to 15 % of its mean
radius, see annex EI, the Position of the measured section or sections
relative to some feature of the workpiece.
This International Standard specifies a method for determining
departures from roundness by measuring variations in radius by
means of contact (stylus) instruments.
2 Reference
It establishes
ISO 6318, Measurement of roundness - Terms, definitions
a) types of instruments and general requirements; and Parameters of roundness.
b) recommendations for the use of instruments;
3 Definitions
c) procedures for calibration of instruments and verifica-
tion of their characteristics.
For the purposes of this International Standard, the definitions
given in ISO 6318 apply.
This International Standard applies to the assessment of the
departures from ideal roundness of a workpiece through the
medium of a Profile transformation, obtained under reference
4 Instruments
conditions, expressed with respect to any one of the following
centres :
4.1 Instrument types and geheral requirements
a) centre of the least squares circle;
Instruments of the stylus type employed for the determination
of departures from ideal roundness may be of one of two
b) centre of the minimum zone circle;
types :
c) centre of the minimum circumscribed circle;
a) a stylus and transducer rotating round a stationary
workpiece;
d) centre of the maximum inscribed circle.
b) a rotating workpiece engaged by a stationary stylus and
Esch of these centres may have its own particular application.
transducer.
The Position of the least squares centre tan be calculated from
a simple explicit equation given in annex F.
According to the nature of the output information, instruments
for the measurement of roundness fall into two groups :
Departures from roundness of the measured Profile, procedure,
calibration and determination of systematic errors of rotation
a) Profile recording;
are dealt with in annexes A to D, respectively. Annex E gives
rules for plotting and reading polar graphs.
b) with direct display of the values of the Parameters.
NOTES
Both groups may be combined in one instrument.
1 Profile transformation is defined in ISO 6318.
Stylus instruments should comply with the requirements of
2 Reference conditions include the stylus, frequency limitations of an
4.1.1 to 4.1.3.
electric wave filter (if used), permissible eccentricity of the graphical or
1
---------------------- Page: 3 ----------------------
ISO 42914985 (El
The dimensions r and R of the various styli shall be selected
4.1.1 Stylus types and dimensions
from the following values :
The surface characteristics of the part under examination are of
-
0,25; 0,8; 2,5; 8 and 25 mm.
primary importante in the choice of stylus. Variations to meet
different requirements, depending upon the nature and
magnitude of the irregularities which are to be taken into
4.1.2 Stylus static forte
account, are permitted as shown in figures 1 to 4 (see also
clause B .3) E
The forte shall be adjustable up to 0,25 N and in use shall be
adjusted down to the lowest value that will ensure continuous
contact between the stylus and the surface being measured.
4.1.3 Instrument response for sinusoidal undulations
The range of periodic sinusoidal undulations per revolution
(upr) (i.e. per 360”) of the workpiece to which the instrument
responds shall be terminated by values taken from the table.
Figure 1 - Spherical stylus
Table - Limiting values of upr
8
Filters transmitting from
Filters rejecting
Q=
1 upr up to below
I I
rt
Figure 2 - Cylindrical stylus
The response at the rated termination of the band shall be 75 %
of the maximum transmission within the band except for 1 upr
which represents direct mechanical coupling between input
and output. [See note 2~1.1
The transmission characteristics of the filter shall be equivalent
to those produced by two independent C-R 1) networks of equal
time constant (see figure 5). These curves show only the
amplitude attenuation characteristics and do not take Phase
shift into account. A Phase corrected filter of known
characteristics giving the same rate of attenuation may be used
provided that these characteristics are indicated in the test
report.
NOTES
Figure 3 - Toroidal (hatchet) stylus
1 When a fitter attenuating high frequencies is required, the two C-R
form will generally be acceptable, distortion of the transmitted Profile
due to Phase shift of the high relative to the low frequencies being
generally unimportant.
When a filter attenuating low frequencies is required, distortion due to
Phase shift may be more significant and have to be taken into account,
or avoided by using a Phase corrected filter.
2a) lt is necessary to distinguish clearly between the undulations per
revolution (i.e. per 360°) of the workpiece and the response of elec-
tronic circuits in the instrument in hertz?)
The frequency, in hertz, generated by the instrument will be given by
the number of sinusoidal undulations per 360° of the workpiece
multiplied by the number of revolutions per second of the spindle.
2b) Eccentricity will count as 1 upr. A sinusoidal component of 1 upr
will be found when the periphery of the workpiece is assessed from a
Figure 4 - Ovoidal stylus centre other than the centre of the least squares circle.
-~-
“C” Stands for “capacitive”, “R” for “resistive”.
1)
2) 1 Hz = 1 cycle per second
2
---------------------- Page: 4 ----------------------
ISO 4291-1985 (El
5 15 50 150
Number of undulations per revolution, upr
Figure 5 - Typical transmissions showing rate of attenuation given by two independent C-R networks
of equal time constant
2c) When electronie circuits of instruments are required to respond
ing on a perfectly flat test piece set perfectly perpendicular
down to 1 upr, they are often made responsive down to zero frequency
to the reference axis of rotation.
(0 Hz), this being a natura1 way of avoiding Phase distortion and per-
mitting calibration by static means.
NOTE - The components of errors of rotation are vector quantities
and should not therefore be algebraically added to the measured value
of a roundness Parameter in an attempt to allow for errors of rotation.
4.2 Instrument errors
4.2.3 Statements of errors of rotation
4.2.1 Overall instrument error
The rotating member tan exhibit, within the confines of its
This is the differente between the value of the Parameter in-
bearings, combinations of
dicated, displayed or recorded by the instrument and the true
value of this Parameter. The value of this error is determined
a) radial displacements parallel to itself;
when measuring a test piece. The Overall instrument error shall
be expressed as a percentage of the upper limiting value of the
b) axial displacements parallel to itself;
measuring range used. This error comprises systematic and
random components from the spindle error, electric noise,
c) tilt.
Vibration, magnification, etc.
The magnitude of the radial instrument error, measured at the
4.2.2 Errors of rotation of the instrument stylus, depends on the Position of the measurement plane
along the axis of rotation. The magnitude of the axial instru-
The errors of rotation are determined under reference condi- ment error depends on the radius at which the flat test piece is
tions at assigned positions of measurement : measured. The axial and radial positions selected for test shall
therefore be stated.
a) radial instrument error - the value of the roundness
Parameter which would be indicated by the instrument The radial instrument error shall be expressed at two stated and
well separated positions along the axis or at one Position
when measuring a perfectly round and perfectly centred
section of a test piece, in a direction perpendicular to the together with the rate of Change of the radial instrument error
reference axis of rotation; along the axis.
b) axial instrument error - the value derived from the The axial instrument error shall be expressed on the axis and at
one stated radius.
zonal Parameter displayed by the instrument when measur-
3
---------------------- Page: 5 ----------------------
ISO 42914985 (El
Annex A
Departure from roundness of the measured Profile of the workpiece
In this International Standard, the departure from ideal round- The largest and smallest radii, in each case, are commonly used
ness is assessed as the differente between the largest and the
to define a concentric Zone. The width of the zone may be
smallest radii of the measured Profile of the workpiece,
designated by AZ, with a subscript denoting its centre. For the
measured from one or other of e following centres : International Standard, the following
purposes of this
subscripts are used :
a) least squares centre (LSC) - the centre of the least
squares mean circle (see figure 6); least squares subscript q, thus AZ,
b) minimum zone centre (MZC) - the centre of the minimum width
subscript z, thus AZ,
minimum zone circle (sec figure 7);
minimum circumscribed subscript c, thus AZ,
c) minimum circumscribed circle centre (MCC) - the
centre of the minimum circumscribed circle for external sur-
maximum inscribed subscript i, thus AZi
faces (see figure 8);
NOTE - The use of circles drawn on the Chart to represent circles fit-
d) maximum inscribed circle centre (MIC) - the centre of
ting the Profile of the workpiece assumes that the workpiece is suffi-
the maximum inscribed circle for internal surfaces (sec
ciently well centred on the axis of the instrument (see 6.1 .l, figure 10
figure 9). and annex F).
Figure 6 - Assessment of roundness from least squares centre, AZ,
4
---------------------- Page: 6 ----------------------
ISO 4291-1985 (El
Figure 7 - Assessment of roundness from minimum zone centre, AZ,
t( Deviation z roundness$ \/
= 2,87 pm
\\ \\ I I
Assessment of roundness from centre of minimum circumscribed circle, AZ,
Figure 8 -
---------------------- Page: 7 ----------------------
ISO 4291-1985 (El
Figure 9 - Assessment of roundness from centre of maximum inscribed circle, AZi
---------------------- Page: 8 ----------------------
ISO 4291-1985 (EI
Annex B
Procedure
(This annex gives general guidance on setting up and measurement.)
B.l Guidance on setting up Prior to measurement BA.3 Inclination of the axis of the workpiece to the axis of
rotation will Cause a perfectly round cylinder to appear ellip-
The workpiece shall be set up so that the section to be tical. If D is the diameter of the workpriece, 0 the angle of incli-
measured is sufficiently well centred on the axis of rotation to nation (sec figure 11) and M the magnification, the diametral
avoid excessive distortion due to eccentricity, and with its axis differente on the Chart will be MD (l-sec 0).
sufficiently parallel to the axis of rotation to avoid excessive
inclination errors. Conversely, appropriate inclination tan Cause an elliptical cylin-
der to appear to be round.
Several kinds of distortion result from polar plotting because,
on the Chart, only the variations in radius of the workpiece,
together with the eccentricity, and not the radius itself, are
highly*magnified.
In the direction of eccentricity, the radius of the eccen-
B.1.1
tric plot is independent of the eccentricity, but in the perpendi-
cular direction the radius is slightly increased in proportion to
the Square of the eccentricity (sec figure 10). Strictly, the
eccentric plot of a perfett circle has the form of a limacon;
Dsec 8
however, this is hardly perceptible as such when the eccen-
tricity is very small. Graphical compensation is sometimes poss-
ible; compensation by electrical methods is widely practised,
Figure 11 - Inclination of the axis of the workpiece to
and elimination of the distortion by digital correction is in
the axis of rotation
course of development.
B.1.4 Some guiding rules for plotting and reading polar
E2
‘.
graphs are given in annex E.
2R
B.2 Direction of measurement
circle
B.2.1 When the workpiece is a cylinder, its roundness will be
assessed in a Cross-section perpendicular to the axis of rotation
of the instrument, the direction of measurement will be perpen-
dicular to this axis, and the traced Profile which is plotted and
measured will be that of the Cross-section. This forms the nor-
mal basis of roundness measurement and assessments.
E ’
B.2.2 When the workpiece is conical or toroidal, the question
,-
of which is the more significant functional direction shall be
determined by details of the application and the direction in
L- Eccentric circle
which the surface is likely to be operative. Furthermore, the
question tan arise as to whether the direction of measurement
should be perpendicular to the axis or normal to the surface
Figure 10 - Slight increase of the radius of the
(sec figure 12). If the direction of measurement is normal to the
eccentric plot in the perpendicular direction
surface, the Profile will be that formed by the intersection of the
workpiece with a perfett, nominally coaxial cone of com-
plementary semi-angle, along the generators of which the
Kl.2 The circumferential Se
...
SLOVENSKI STANDARD
SIST ISO 4291:1995
01-november-1995
Metode za ugotavljanje odstopka od krožnosti – Meritev sprememb polmera
Methods for the assessement of departure from roundness -- Measurement of variations
in radius
Méthodes d'évaluation des écarts de circularité -- Mesurage des variations de rayon
Ta slovenski standard je istoveten z: ISO 4291:1985
ICS:
17.040.20 Lastnosti površin Properties of surfaces
SIST ISO 4291:1995 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
SIST ISO 4291:1995
---------------------- Page: 2 ----------------------
SIST ISO 4291:1995
International Standard
INTERNATIONAL ORGANIZATION FOR STANDARDIZATION.ME)I(CiYHAPO,QHAF OPf-AHM3ALWl I-IO CTAH,QAPTM3ALWl.ORGANISATlON INTERNATIONALE DE NORMALISATION
Methods for the assessment of departure from
Measurement of variations in radius
roundness -
- Mesurage des variations de rayon
MS thodes d’kvalua tion des Ecarts de circularite
First edition - 19850945
Ref. No. ISO 4291-1985 (EI
UDC 531.717
w
-
Descriptors : surface conditions, roundness measurement, measuring instruments, Profile meters, error analysis.
Price based on 18 pages
---------------------- Page: 3 ----------------------
SIST ISO 4291:1995
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of
national Standards bodies (ISO member bedies). The work of preparing International
Standards is normally carried out through ISO technical committees. Esch member
body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, govern-
mental and non-governmental, in liaison with ISO, also take patt in the work.
Draft International Standards adopted by the technical committees are circulated to
the member bodies for approval before their acceptance as International Standards by
the ISO Council. They are approved in accordance with ISO procedures requiring at
least 75 % approval by the member bodies voting.
International Standard ISO 4291 was prepared by Technical Committee ISO/TC 57,
Metrology and properties of surfaces.
0 International Organkation for Standardization, 1985
Printed in Switzerland
---------------------- Page: 4 ----------------------
SIST ISO 4291:1995
INTERNATIONAL STANDARD ISO 42914985 (E)
Methods for the assessment of departure from
Measurement of variations in radius
roundness -
1 Scope and field of application digital representation of the Profile (generally 7 % to 15 % of its mean
radius, see annex EI, the Position of the measured section or sections
relative to some feature of the workpiece.
This International Standard specifies a method for determining
departures from roundness by measuring variations in radius by
means of contact (stylus) instruments.
2 Reference
It establishes
ISO 6318, Measurement of roundness - Terms, definitions
a) types of instruments and general requirements; and Parameters of roundness.
b) recommendations for the use of instruments;
3 Definitions
c) procedures for calibration of instruments and verifica-
tion of their characteristics.
For the purposes of this International Standard, the definitions
given in ISO 6318 apply.
This International Standard applies to the assessment of the
departures from ideal roundness of a workpiece through the
medium of a Profile transformation, obtained under reference
4 Instruments
conditions, expressed with respect to any one of the following
centres :
4.1 Instrument types and geheral requirements
a) centre of the least squares circle;
Instruments of the stylus type employed for the determination
of departures from ideal roundness may be of one of two
b) centre of the minimum zone circle;
types :
c) centre of the minimum circumscribed circle;
a) a stylus and transducer rotating round a stationary
workpiece;
d) centre of the maximum inscribed circle.
b) a rotating workpiece engaged by a stationary stylus and
Esch of these centres may have its own particular application.
transducer.
The Position of the least squares centre tan be calculated from
a simple explicit equation given in annex F.
According to the nature of the output information, instruments
for the measurement of roundness fall into two groups :
Departures from roundness of the measured Profile, procedure,
calibration and determination of systematic errors of rotation
a) Profile recording;
are dealt with in annexes A to D, respectively. Annex E gives
rules for plotting and reading polar graphs.
b) with direct display of the values of the Parameters.
NOTES
Both groups may be combined in one instrument.
1 Profile transformation is defined in ISO 6318.
Stylus instruments should comply with the requirements of
2 Reference conditions include the stylus, frequency limitations of an
4.1.1 to 4.1.3.
electric wave filter (if used), permissible eccentricity of the graphical or
1
---------------------- Page: 5 ----------------------
SIST ISO 4291:1995
ISO 42914985 (El
The dimensions r and R of the various styli shall be selected
4.1.1 Stylus types and dimensions
from the following values :
The surface characteristics of the part under examination are of
-
0,25; 0,8; 2,5; 8 and 25 mm.
primary importante in the choice of stylus. Variations to meet
different requirements, depending upon the nature and
magnitude of the irregularities which are to be taken into
4.1.2 Stylus static forte
account, are permitted as shown in figures 1 to 4 (see also
clause B .3) E
The forte shall be adjustable up to 0,25 N and in use shall be
adjusted down to the lowest value that will ensure continuous
contact between the stylus and the surface being measured.
4.1.3 Instrument response for sinusoidal undulations
The range of periodic sinusoidal undulations per revolution
(upr) (i.e. per 360”) of the workpiece to which the instrument
responds shall be terminated by values taken from the table.
Figure 1 - Spherical stylus
Table - Limiting values of upr
8
Filters transmitting from
Filters rejecting
Q=
1 upr up to below
I I
rt
Figure 2 - Cylindrical stylus
The response at the rated termination of the band shall be 75 %
of the maximum transmission within the band except for 1 upr
which represents direct mechanical coupling between input
and output. [See note 2~1.1
The transmission characteristics of the filter shall be equivalent
to those produced by two independent C-R 1) networks of equal
time constant (see figure 5). These curves show only the
amplitude attenuation characteristics and do not take Phase
shift into account. A Phase corrected filter of known
characteristics giving the same rate of attenuation may be used
provided that these characteristics are indicated in the test
report.
NOTES
Figure 3 - Toroidal (hatchet) stylus
1 When a fitter attenuating high frequencies is required, the two C-R
form will generally be acceptable, distortion of the transmitted Profile
due to Phase shift of the high relative to the low frequencies being
generally unimportant.
When a filter attenuating low frequencies is required, distortion due to
Phase shift may be more significant and have to be taken into account,
or avoided by using a Phase corrected filter.
2a) lt is necessary to distinguish clearly between the undulations per
revolution (i.e. per 360°) of the workpiece and the response of elec-
tronic circuits in the instrument in hertz?)
The frequency, in hertz, generated by the instrument will be given by
the number of sinusoidal undulations per 360° of the workpiece
multiplied by the number of revolutions per second of the spindle.
2b) Eccentricity will count as 1 upr. A sinusoidal component of 1 upr
will be found when the periphery of the workpiece is assessed from a
Figure 4 - Ovoidal stylus centre other than the centre of the least squares circle.
-~-
“C” Stands for “capacitive”, “R” for “resistive”.
1)
2) 1 Hz = 1 cycle per second
2
---------------------- Page: 6 ----------------------
SIST ISO 4291:1995
ISO 4291-1985 (El
5 15 50 150
Number of undulations per revolution, upr
Figure 5 - Typical transmissions showing rate of attenuation given by two independent C-R networks
of equal time constant
2c) When electronie circuits of instruments are required to respond
ing on a perfectly flat test piece set perfectly perpendicular
down to 1 upr, they are often made responsive down to zero frequency
to the reference axis of rotation.
(0 Hz), this being a natura1 way of avoiding Phase distortion and per-
mitting calibration by static means.
NOTE - The components of errors of rotation are vector quantities
and should not therefore be algebraically added to the measured value
of a roundness Parameter in an attempt to allow for errors of rotation.
4.2 Instrument errors
4.2.3 Statements of errors of rotation
4.2.1 Overall instrument error
The rotating member tan exhibit, within the confines of its
This is the differente between the value of the Parameter in-
bearings, combinations of
dicated, displayed or recorded by the instrument and the true
value of this Parameter. The value of this error is determined
a) radial displacements parallel to itself;
when measuring a test piece. The Overall instrument error shall
be expressed as a percentage of the upper limiting value of the
b) axial displacements parallel to itself;
measuring range used. This error comprises systematic and
random components from the spindle error, electric noise,
c) tilt.
Vibration, magnification, etc.
The magnitude of the radial instrument error, measured at the
4.2.2 Errors of rotation of the instrument stylus, depends on the Position of the measurement plane
along the axis of rotation. The magnitude of the axial instru-
The errors of rotation are determined under reference condi- ment error depends on the radius at which the flat test piece is
tions at assigned positions of measurement : measured. The axial and radial positions selected for test shall
therefore be stated.
a) radial instrument error - the value of the roundness
Parameter which would be indicated by the instrument The radial instrument error shall be expressed at two stated and
well separated positions along the axis or at one Position
when measuring a perfectly round and perfectly centred
section of a test piece, in a direction perpendicular to the together with the rate of Change of the radial instrument error
reference axis of rotation; along the axis.
b) axial instrument error - the value derived from the The axial instrument error shall be expressed on the axis and at
one stated radius.
zonal Parameter displayed by the instrument when measur-
3
---------------------- Page: 7 ----------------------
SIST ISO 4291:1995
ISO 42914985 (El
Annex A
Departure from roundness of the measured Profile of the workpiece
In this International Standard, the departure from ideal round- The largest and smallest radii, in each case, are commonly used
ness is assessed as the differente between the largest and the
to define a concentric Zone. The width of the zone may be
smallest radii of the measured Profile of the workpiece,
designated by AZ, with a subscript denoting its centre. For the
measured from one or other of e following centres : International Standard, the following
purposes of this
subscripts are used :
a) least squares centre (LSC) - the centre of the least
squares mean circle (see figure 6); least squares subscript q, thus AZ,
b) minimum zone centre (MZC) - the centre of the minimum width
subscript z, thus AZ,
minimum zone circle (sec figure 7);
minimum circumscribed subscript c, thus AZ,
c) minimum circumscribed circle centre (MCC) - the
centre of the minimum circumscribed circle for external sur-
maximum inscribed subscript i, thus AZi
faces (see figure 8);
NOTE - The use of circles drawn on the Chart to represent circles fit-
d) maximum inscribed circle centre (MIC) - the centre of
ting the Profile of the workpiece assumes that the workpiece is suffi-
the maximum inscribed circle for internal surfaces (sec
ciently well centred on the axis of the instrument (see 6.1 .l, figure 10
figure 9). and annex F).
Figure 6 - Assessment of roundness from least squares centre, AZ,
4
---------------------- Page: 8 ----------------------
SIST ISO 4291:1995
ISO 4291-1985 (El
Figure 7 - Assessment of roundness from minimum zone centre, AZ,
t( Deviation z roundness$ \/
= 2,87 pm
\\ \\ I I
Assessment of roundness from centre of minimum circumscribed circle, AZ,
Figure 8 -
---------------------- Page: 9 ----------------------
SIST ISO 4291:1995
ISO 4291-1985 (El
Figure 9 - Assessment of roundness from centre of maximum inscribed circle, AZi
---------------------- Page: 10 ----------------------
SIST ISO 4291:1995
ISO 4291-1985 (EI
Annex B
Procedure
(This annex gives general guidance on setting up and measurement.)
B.l Guidance on setting up Prior to measurement BA.3 Inclination of the axis of the workpiece to the axis of
rotation will Cause a perfectly round cylinder to appear ellip-
The workpiece shall be set up so that the section to be tical. If D is the diameter of the workpriece, 0 the angle of incli-
measured is sufficiently well centred on the axis of rotation to nation (sec figure 11) and M the magnification, the diametral
avoid excessive distortion due to eccentricity, and with its axis differente on the Chart will be MD (l-sec 0).
sufficiently parallel to the axis of rotation to avoid excessive
inclination errors. Conversely, appropriate inclination tan Cause an elliptical cylin-
der to appear to be round.
Several kinds of distortion result from polar plotting because,
on the Chart, only the variations in radius of the workpiece,
together with the eccentricity, and not the radius itself, are
highly*magnified.
In the direction of eccentricity, the radius of the eccen-
B.1.1
tric plot is independent of the eccentricity, but in the perpendi-
cular direction the radius is slightly increased in proportion to
the Square of the eccentricity (sec figure 10). Strictly, the
eccentric plot of a perfett circle has the form of a limacon;
Dsec 8
however, this is hardly perceptible as such when the eccen-
tricity is very small. Graphical compensation is sometimes poss-
ible; compensation by electrical methods is widely practised,
Figure 11 - Inclination of the axis of the workpiece to
and elimination of the distortion by digital correction is in
the axis of rotation
course of development.
B.1.4 Some guiding rules for plotting and reading polar
E2
‘.
graphs are given in annex E.
2R
B.2 Direction of measurement
circle
B.2.1 When the workpiece is a cylinder, its roundness will be
assessed in a Cross-section perpendicular to the axis of rotation
of the instrument, the direction of measurement will be perpen-
dicular to this axis, and the traced Profile which is plotted and
measured will be that of the Cross-section. This forms the nor-
mal basis of roundness measurement and assessments.
E ’
B.2.2 When the workpiece is conical or toroidal, the question
,-
of which is the more significant functional direction shall be
determined by details of the application and the direction in
L- Eccentric circle
which the surface is likely to be operative. Furthermore, the
question tan arise as to whether the direction of measurement
should be perpendicular to the axis or normal to the surface
Figure 10 - Slight increase of the radius of the
(sec fi
...
Norme internationale
INTERNATIONAL ORGANIZATION FOR STANDARDIZATION.MEIK~YHAPO.4HAR OPl-AHM3ALWlR l-IO CTAH~APTM3ALWl.ORGANlSATlON INTERNATIONALE DE NORMALISATION
Mbthodes d ’bvaluation des Gcarts de circularit -
Mesurage des variations de rayon
Methods for the assessment of departure from roundness - Measurement of variations in radius
Premiere hdition - 1985-09-15
CDU 531.717 Ref. no : IS0 4291-1985 (F)
Descripteurs : 6tat de surface, mesurage de la circularit& instrument de mesurage, profilomhtre, calcul d ’erreur.
Prix base sur 18 pages
---------------------- Page: 1 ----------------------
Avant-propos
L ’ISO (Organisation internationale de normalisation) est une federation mondiale
d ’organismes nationaux de normalisation (comites membres de I ’ISO). L/elaboration
des Normes internationales est confiee aux comites techniques de I ’ISO. Chaque
comite membre interesse par une etude a le droit de faire partie du comite technique
tree a cet effet. Les organisations internationales, gouvernementales et non gouverne-
mentales, en liaison avec I ’ISO, participent egalement aux travaux.
Les projets de Normes internationales adopt& par les comites techniques sont soumis
aux comites membres pour approbation, avant leur acceptation comme Normes inter-
nationales par le Conseil de I ’ISO. Les Normes internationales sont approuvees confor-
mement aux procedures de I ’ISO qui requierent I ’approbation de 75 % au moins des
comites membres votants.
La Norme internationale IS0 4291 a ete elaboree par le comite technique ISO/TC 57,
Me trologie et proprih t6s des surfaces.
0 Organisation internationale de normalisation, 1985 l
Imprim en Suisse
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NORME INTERNATIONALE IS0 4291-1985 (F)
Mbthodes d ’bvaluation des &arts de circularit -
Mesurage des variations de rayon
1 Objet et domaine d ’application
(en general, 7 a 15 % de son rayon moyen, voir annexe E), la position
de la section ou des sections mesurees, par rapport a un element carac-
teristique de la piece.
La presente Norme internationale specific une methode de
determination des &arts de circularite par mesurage des varia-
tions de rayon, au moyen d ’instruments a contact (palpeurs).
2 R6fGrence
Elle etablit
I SO 6318, Mesurage de la circularit& - Termes, dkfinitions et
a) les types d ’instruments et les prescriptions g&&ales;
param& tres de circularit&.
b) des recommandations pour I ’emploi des instruments;
3 Definitions
c) des methodes d ’etalonnage des instruments et de verifi-
cation de leurs caracteristiques.
Dans le cadre de la presente Norme internationale, les defini-
tions donnees dans I ’ISO 6318 sont applicables.
La presente Norme internationale fournit une evaluation des
&arts de circularite d ’une piece par rapport a la forme ideale
par le biais d ’une transformation du profil obtenue dans des
conditions de reference, et qui s ’exprime en fonction de I ’un
4 Instruments
quelconque des centres suivants :
4.1 Types d ’instruments et prescriptions
a) centre du cercle des moindres car&;
gh&ales
b) centre du cercle de zone minimale;
Les instruments du genre palpeur utilises pour determiner les
&arts par rapport a une circularite ideale peuvent etre de deux
c) centre du cercle circonscrit minimal;
types :
d) centre du cercle inscrit maximal.
a) a palpeur et capteur tournant, la piece etant maintenue
fixe;
Chacun des centres precedents peut avoir son domaine d ’appli-
cation. La position du centre des moindres car&s peut se cal-
b) a piece tournante, palpeur et capteur etant maintenus
culer $I partir d ’une formule simple et explicite donnee dans
fixes.
l ’annexe F.
Selon le caractere de I ’information fournie, les instruments de
L ’ecart de circularite du profil mesure, la methode, I ’etalonnage
mesure de la circularite se rangent en deux categories :
et la determination des erreurs systematiques de rotation sont
trait& dans les annexes A a D, respectivement. L ’annexe E
a) a enregistrement du profil;
concerne les regles de trace et de lecture des graphiques polai-
res.
b) 8 affichage direct des valeurs des parametres,
NOTES
les deux categories pouvant etre combinees en un seul instru-
1 La transformation du profil est definie dans I ’ISO 6318
ment.
2 Par conditions de reference on entend : le palpeur, les limitations
Les instruments a palpeur doivent repondre aux specifications
de frequence pour un filtre d ’ondes electrique (s ’il est utilise), I ’excen-
tricite admissible des representations graphique ou numerique du profil de 4.1.1 a 4.1.3.
1
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IS0 42914985 (F)
Les dimensions R et r des divers palpeurs sont a choisir parmi
4.1.1 Type et dimensions du palpeur
les valeurs suivantes :
Les caracteristiques de la surface de la piece a examiner sont
- 0,25; 0,8; 2,5; 8 et 25 mm.
d ’une importance capitale pour le choix du palpeur. Les varian-
tes indiquees aux figures 1 a 4 (voir aussi chapitre B.3) sont
admises suivant la nature et I ’ampleur des irregularites a pren-
4.1.2 Effort statique exerc6 par le palpeur
dre en consideration.
L ’effort doit etre reglable jusqu ’a 0,25 N et, en usage, reducti-
ble jusqu ’a la plus faible valeur garantissant un contact continu
entre le palpeur et la surface a mesurer.
4.1.3 R6ponse de ( ‘instrument aux ondulations
sinusoi ’dales
La gamme d ’ondulations sinusoidales periodiques par tour
Palpeur a pointe spherique
Figure 1 -
(upr) (c ’est-a-dire par 360 ”) de la piece auxquelles repond I ’ins-
trument doit etre limitee aux valeurs indiquees dans le tableau.
Tableau - Valeurs limites des u.p.r.
Filtres transmettant de Filtres rejetant en
1 upr 5 dessous de
15 15
50 50
150
150
500
Figure 2 - Palpeur cylindrique 500
La reponse a une limite nominale de bande doit correspondre 8
75 % de la transmission maximale a l ’interieur de la bande con-
sideree, sauf pour 1 upr qui represente la liaison mecanique
directe entre I ’entree et la sortie. [Voir note 2~1.1
Les caracteristiques de transmission du filtre doivent etre equi-
valentes a celles de deux reseaux C-W) independants de meme
constante de temps (voir figure 5). Les courbes ne representent
que les caracteristiques d ’attenuation de I ’amplitude et ne tien-
nent pas compte du dephasage. On peut utiliser un filtre a cor-
rection de phase, de caracteristiques connues, donnant le
meme taux d ’attenuation du moment que ses caracteristiques
sont mentionnees dans le rapport d ’essai.
NOTES
Figure3 - Palpeur toro ’idal (hachette)
1 Si I ’on a besoin d ’un filtre pour attenuer les hautes frequences, la
forme 2-CR est generalement admise, la distorsion du profil transmis
par dephasage des frequences elevees par rapport aux basses etant
generalement negligeable.
Si le filtre est necessaire pour attenuer les basses frequences, ia distor-
sion par dephasage peut etre plus significative et doit etre prise en
compte ou etre evitee par utilisation d ’un filtre 8 correction de phase.
2a) II est necessaire de distinguer clairement entre les ondulations par
tour de piece (c ’est-a-dire par 36OO) et la reponse des circuits electroni-
ques de I ’instrument en hertz?
La frequence en hertz produite par I ’instrument est donnee par le pro-
duit du nombre d ’ondulations sinusdidales par 360° de rotation de la
piece et du nombre de tours par seconde de la broche.
2b) L ’excentricite compte pour I ’upr. On trouve une composante
d ’upr sinusdidale lorsqu ’on evalue la peripherie de la piece a partir d ’un
Figure4 - Palpeur owoi ’de centre autre que le centre du cercle des moindres carres.
1) ((0) indiquant la capacite et c(R)) la resistance.
2) 1 Hz = 1 cycle par seconde
2
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ISO4291-1985(F)
Nombre d ’ondulations par tour, upr
Figure 5 - Transmission type indiquant le taux d ’atthuation de deux rheaux C-R indhpendants
de meme constante de temps
2c) Lorsque les circuits electroniques des instruments doivent repon- eprouvette parfaitement plane montee parfaitement perpen-
dre vers le bas jusqu ’a 1 upr ils sont souvent concus pour repondre
diculaire a I ’axe de rotation de reference.
jusqu ’a la frequence zero (0 Hz), ce qui est un moyen nature1 d ’eviter la
distorsion de phase et de permettre I ’etalonnage par des moyens stati-
NOTE - Les composants des erreurs de rotation sont des grandeurs
ques.
vectorielles qui ne peuvent done pas etre ajoutees algebriquement 2 la
valeur mesuree d ’un parametre de circularite pour essayer de tenir
compte des erreurs de rotation.
4.2 Erreurs instrumentales
4.2.3 Indication des erreurs de rotation
4.2.1 Erreur globale de I ’instrument
La piece en rotation peut presenter dans les limites de ses
C ’est la difference entre la valeur du parametre telle qu ’elle est
paliers, les mouvements combines suivants :
indiquee, affichee ou enregistree par l ’instrument et la valeur
vraie de celui-ci. La valeur de I ’erreur est determinee par mesu-
a) deplacements radiaux paralleles a elle-meme;
rage d ’une eprouvette. L ’erreur globale de l/instrument
s ’exprime en pourcentage de la valeur limite superieure de
b) deplacements axiaux paralleles a elle-meme;
I ’etendue de mesure retenue. Cette erreur englobe les compo-
santes systematiques et aleatoires, de I ’erreur de la broche, du
c) deversement.
bruit electrique, des vibrations, du grossissement, etc.
L ’ampleur de I ’erreur radiale de I ’instrument mesuree au niveau
du palpeur depend de la position du plan de mesure le long de
4.2.2 Erreur de rotation de I ’instrument
I ’axe de rotation. L ’ampleur de l ’erreur axiale de I ’instrument
depend du rayon auquel est mesuree I ’eprouvette plane. Les
Les erreurs de rotation sont determinees dans les conditions de
positions axiale et radiale choisies pour I ’essai doivent done &r-e
reference en des positions de mesure assignees :
mentionnees.
a) erreur radiale de I ’instrument -- valeur du parametre de
circularite qui serait indiquee par I ’instrument s ’il mesurait L ’erreur radiale de ( ‘instrument doit etre indiquee en deux posi-
tions distinctes indiquees le long de I ’axe, ou en une seule posi-
une section d ’eprouvette parfaitement circulaire et parfaite-
tion, si I ’on indique en meme temps le taux de variation de
ment centree, perpendiculairement a I ’axe de rotation de
reference; l ’erreur radiale le long de cet axe.
b) erreur axiale de l ’instrument - valeur derivee du para- L ’erreur axiale de l ’instrument doit etre indiquee sur I ’axe et ti
un rayon determine.
metre de zone affichee par l ’instrument mesurant une
3
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IS0 42914985 (F)
Annexe A
&art de circularit du profil mesur6 de la pike
Dans la pr&ente Norme internationale I&art de circularit par
Le rayon le plus grand ou le plus petit, selon le cas, est commu-
rapport aux conditions ideales est estiml! comme etant la diff&
nement utilisi! pour dbfinir une zone concentrique. La largeur
rence entre le rayon le plus grand et le rayon le plus petit du
de la zone peut &re rephee par AZ, accompagne d ’un suffixe
profil mesure de la pike, le mesurage etant effect& 5 partir de
indiquant le centre. On utilisera dans la prhente Norme inter-
I ’un quelconque des centres suivants :
nationale les suffixes suivants :
a) centre des moindres car& (LSC) - centre du cercle
moindres car& suffixe q, et done AZ,
des moindres car& (voir figure 6);
largeur minimale suffixe z, et done AZ,
b) centre de la zone minimale (MZC) - centre du cercle de
zone minimale (voir figure 7);
circonscrit minimal
suffixe c, et done AZ,
c)
centre du cercle circonscrit minimal (MCC) - centre du
inscrit maximal
suffixe i, et done AZi
cercle circonscrit minimal pour les surfaces exthieures (voir
figure 8);
NOTE - Les cercles dessiks sur le graphique pour repksenter les cer-
d) centre du cercle inscrit maximal (MIC) - centre du cer-
cles s ’ajustant au profil de la pike indiquant que la pike est convena-
cle inscrit maximal pour les surfaces inthieures (voir
blement centree sur I ’axe de I ’instrument (voir B. 1.1, figure 10 et
figure 9).
annexe F).
Figure 6 - ivaluation de la circularit 5 partir du centre des moindres cart&, AZ,
4
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IS0 4291-1985 (F)
Figure 7 - Evaluation de la circularit 5 partir de la zone minimale, AZ,
Figure 8 - haluation de la circularit 2 partir du cercle circonscrit minimal,
5
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IS0 4291-1985 (F)
Figure 9 - haluation de la circularit 5 partir du cercle inscrit maximal, AZi
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IS0 4291-1985 (F)
Annexe B
Methode
(La nresente annexe donne des indications g&r&ales sur le montage et le mesurage.)
B.l Indication sur le montage B.1.3 L ’inclinaison de I ’axe de la piece par rapport a l ’axe de
rotation donnera I ’impression qu ’un cylindre parfaitement cir-
La piece doit etre montee de telle sorte que la section a mesurer culaire parait elliptique. Soit D le diametre de la piece, 0 I ’angle
soit convenablement centree sur I ’axe de rotation pour empe-
d ’inclinaison (voir figure 11) et M le grossissement, la diffe-
cher une distorsion excessive due a I ’excentricite, et que son rence de diametre sur le graphique sera de MD (I-set 8).
axe soit suffisamment parallele a I ’axe de rotation pour eviter les
erreurs d ’inclinaison excessives.
Inversement, une inclinaison convenable peut faire paraitre cir-
culaire un cylindre eiliptique.
Plusieurs types de distorsion resultent de la representation gra-
phique polaire, car le graphique n ’amplifie considerablement
que les variations de rayon de la piece et I ’excentricite et non le
e
rayon lui-meme.
B.l .I Dans le sens de I ’excentricite, le rayon du cercle excen-
trique est independant de I ’excentricite, alors que dans le sens
perpendiculaire, le rayon augmente Iegerement avec le car6 de
I ’excentricite (voir figure 10). Au sens strict, la representation
excentrique d ’un cercle parfait prend la forme d ’un limacon, ce
qui est toutefois a peine perceptible en soi quand I ’excentricite
est tres faible. Une compensation graphique est quelquefois
possible. La compensation par des methodes electriques est
- lnclinaison de I ’axe de la pike par rapport
Figure 11
largement pratiquee et I ’on arrive actuellement a eliminer la dis-
B I ’axe de rotation
torsion par correction numerique.
B.1.4 L ’annexe E donne quelques directives pour tracer et lire
E2
-
les graphiques polaires.
2R
B-2 Direction de mesurage
B.2.1 Lorsque la piece est cylindrique, sa circularite doit etre
evaluee dans une section perpendiculaire a I ’axe de rotation de
I/instrument, la direction de mesurage etant perpendiculaire a
cet axe et le profil trace, enregistre et mesure etant celui de la
section en question. Ce pro&de constitue la base normale des
mesures et evaluations de la circularite.
B.2.2 Si la piece est conique ou torique, la question de savoir
quelle est la direction fonctionnelle la plus significative doit etre
tranchee a la lumiere des details d ’emploi, suivant la direction
\
Cercle excentrique
dans laquelle la surface a un role a jouer. La question peut aussi
se poser de savoir si la direction de mesurage doit etre perpen-
diculaire a I ’axe ou normale a la surface (voir figure 12). Si elle
Figure 10 - L6gGre augmentation du rayon du cercle
est normale a la surface, le profil sera celui que forme I ’intersec-
excentrique dans le sens perpendiculaire
tion de la piece avec un cone parfait nominalement co-axial et
de demi angle complementaire, le long des generatrices dont
on mesure les variations sur le profil consider& Sur le graphi-
que representant le profil, ces variations appara ’itront toutefois
B.1.2 L ’ecartement circonferentiel des saillies d ’un profil
comme si elles etaient des variations radiales normales et leur
periodique est superieur a celui des valllees, meme
...
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