ISO/TR 10064-5:2005
(Main)Code of inspection practice — Part 5: Recommendations relative to evaluation of gear measuring instruments
Code of inspection practice — Part 5: Recommendations relative to evaluation of gear measuring instruments
ISO/TR 10064-5:2005 provides additional information and examples to support the implementation of ISO 18653. It proposes evaluation and calibration procedures for involute, helix, pitch, runout, and tooth thickness measurement processes. Methods are given for evaluation of the condition and alignments of instrument elements such as centres, guideways, probe systems, etc. Recommendations are included for establishment of a proper environment and for statistical data evaluation procedures. It also covers the application of gear artefacts to the estimation of U95 measurement process uncertainty. Guidance on the application of measurement processes to the inspection of product gears is provided, including fitness for use and the recommended limits for U95 uncertainty based upon the accuracy tolerances of product gears to be inspected. Many of its recommendations may also be applicable to the measurement of worms, worm wheels, bevel gears and gear cutting tools
Code pratique de réception — Partie 5: Recommandations relatives à l'évaluation des instruments de mesure des engrenages
L'ISO/TR 10064-5:2005 propose des informations et des exemples supplémentaires destinés à faciliter la mise en oeuvre de l'ISO 18653. Il fournit des modes opératoires d'évaluation et d'étalonnage des procédés de mesurage de la développante, de l'hélice, du pas, du faux-rond et de l'épaisseur des dents. Des méthodes d'évaluation de l'état et de l'alignement d'éléments d'instrument tels que des axes, des glissières, des systèmes de palpeurs, etc., ainsi que des recommandations concernant la mise en place d'un environnement approprié et des modes opératoires statistiques d'évaluation des données sont proposés. Il couvre également l'application d'artéfacts d'engrenage à l'estimation de l'incertitude du mesurage, U95. Des conseils sont fournis sur l'application des procédés de mesurage à la réception d'engrenages de production, y compris l'aptitude à l'emploi et les limites recommandées de l'incertitude U95 en fonction des tolérances d'exactitude des engrenages de production à inspecter. De nombreuses recommandations peuvent s'appliquer également au mesurage de vis, de roues à vis, de roues coniques et des outils de taillage d'engrenages.
Valjasti zobniki – Smernice za pregledovanje – 5. del: Priporočila za vrednotenje merilne negotovosti instrumentov za merjenje zobnikov
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-maj-2006
9DOMDVWL]REQLNL±6PHUQLFH]DSUHJOHGRYDQMH±GHO 3ULSRURþLOD]DYUHGQRWHQMH
PHULOQHQHJRWRYRVWLLQVWUXPHQWRY]DPHUMHQMH]REQLNRY
Cylindrical gears - Code of inspection practice -- Part 5: Recommendations relative to
evaluation of gear measuring instruments
Code pratique de réception -- Partie 5: Recommandations relatives à l'évaluation des
instruments de mesure des engrenages
Ta slovenski standard je istoveten z: ISO/TR 10064-5:2005
ICS:
21.200 Gonila Gears
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
TECHNICAL ISO/TR
REPORT 10064-5
First edition
2005-04-15
Cylindrical gears — Code of inspection
practice —
Part 5:
Recommendations relative to evaluation
of gear measuring instruments
Engrenages cylindriques — Code pratique de réception —
Partie 5: Recommandations relatives à l'évaluation des instruments de
mesure des engrenages
Reference number
©
ISO 2005
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ii © ISO 2005 – All rights reserved
Contents Page
Foreword. v
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 2
4 Instrument environment. 2
4.1 Environment . 2
4.1.1 Important parameters . 2
4.1.2 Practical guidelines . 3
4.1.3 Workshop environment. 3
4.2 Effect of temperature on gears and artifacts . 4
4.2.1 Profile temperature effect calculation. 4
4.2.2 Helix temperature effect calculation . 5
4.2.3 Tooth thickness temperature effect calculation . 5
5 Measurement system condition . 5
5.1 Evaluation procedure for generative instruments. 6
5.1.1 Verification of mounting centres. 6
5.1.2 Axial measuring slide verification. 10
5.2 Evaluation procedures for CMM type measuring instruments . 14
5.2.1 Performance test according to ISO 10360. 14
5.2.2 Ball plate test. 15
5.2.3 Rotary tables . 16
5.3 Probe system. 16
5.3.1 Stylus. 16
5.3.2 Data recording system . 17
5.4 Filtering . 21
5.4.1 Mechanical filtering. 21
5.4.2 Electrical filtering . 21
5.4.3 Mathematical filtering . 22
5.5 Uncertainty estimation . 22
6 Artifacts. 22
6.1 Mounting reference features. 22
6.2 Suggested master artifacts. 22
6.2.1 Integral base circle involute master. 23
6.2.2 Helix artifact. 23
6.2.3 Pitch variation, total cumulative pitch variation and runout artifact . 24
6.2.4 Tooth thickness artifacts. 25
6.2.5 Workpiece-like artifacts. 25
6.3 Modified base circle involute artifact testing. 27
6.4 Non-involute — Pin (cylindrical), plane (flank) and ball (spherical) artifacts . 27
6.4.1 Types of non-involute artifacts. 27
6.4.2 Non-involute artifact function. 29
6.4.3 Plane artifact calibration . 30
6.4.4 Pin or ball artifact calibration . 30
6.4.5 Probe-tip effects when calculating reference curve. 30
6.4.6 Measurement location . 31
6.4.7 Non-involute master interpretation . 31
6.5 Helix artifact testing. 31
6.5.1 Modified-lead helix artifact testing. 31
6.5.2 Non-involute helix masters . 32
6.6 Modified eccentricity pitch artifact testing .32
7 Uncertainty estimation guidelines.32
7.1 Uncertainty estimation methods.32
7.1.1 General methods .32
7.1.2 Comparator methods .33
7.2 Calculation of U measurement uncertainty .33
7.3 Measurement parameters.34
7.3.1 Line-fit parameters .34
7.3.2 Band-fit parameters.35
7.3.3 Pitch parameters .35
8 Measurement procedures.35
8.1 Traceability.35
8.2 Operating conditions .35
8.2.1 Conditions for bias determination.35
8.2.2 Conditions for standard uncertainty estimation .35
8.2.3 Conditions for combined determinations.36
8.3 Measurements .36
8.4 Calibration procedure .36
8.4.1 Initial set-up and adjustments.36
8.4.2 Initial calibration procedure .36
8.4.3 Ongoing calibration procedure.37
8.4.4 Tooling and gauges.37
9 Comparator measurement uncertainty estimation guidelines .37
9.1 Direct comparator example A .37
9.2 Comparator approach, expanded for workpiece characteristic influence.39
9.2.1 Comparator example B .39
9.2.2 Comparator example C .41
9.3 Comparator approach, expanded for workpiece characteristic and geometry similarity
influences.43
10 Statistical process control .43
10.1 Definitions .43
10.2 Constructing the X and MR chart .43
10.3 Criteria for evidence of lack of control.44
10.4 When control chart data fails one or more criteria according to 10.3 .46
11 Instrument fitness for use .46
11.1 Limiting measurement uncertainty.46
11.1.1 GPS Tolerance reduction method .46
11.1.2 Tolerance ratio method.48
11.1.3 Instrument uncertainty guidelines.48
11.2 Measurement uncertainty sources.49
11.3 Reducing measurement uncertainty .50
11.3.1 Following a different calibration procedure .50
11.3.2 Reducing uncertainty of the reference master certification .50
11.3.3 Improving the measuring process.50
12 Measurement process (instrument) correlation.51
12.1 Basis for comparison.51
12.2 Correlation of measurement .51
Annex A (informative) Effect of temperature on gears and artifacts .52
Annex B (informative) Modified involute, helix, pitch artifact testing .58
Annex C (informative) Non-involute pin, ball, or plane (flank) artifact interpretation.69
Bibliography.89
iv © ISO 2005 – All rights reserved
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each 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, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 10064-5 was prepared by Technical Committee ISO/TC 60, Gears.
ISO/TR 10064 consists of the following parts, under the general title Cylindrical gears — Code of inspection
practice:
Part 1: Inspection of corresponding flanks of gear teeth
Part 2: Inspection related to radial composite deviations, runout, tooth thickness and backlash
Part 3: Recommendations relative to gear blanks, shaft centre distance and parallelism of axes
Part 4: Recommendations relative to surface texture and tooth contact pattern checking
Part 5: Recommendations relative to evaluation of gear measuring instruments
TECHNICAL REPORT ISO/TR 10064-5:2005(E)
Cylindrical gears — Code of inspection practice —
Part 5:
Recommendations relative to evaluation of gear measuring
instruments
1 Scope
This part of ISO/TR 10064 provides additional information and examples to support the implementation of
ISO 18653. It proposes evaluation and calibration procedures for involute, helix, pitch, runout, and tooth
thickness measurement processes.
Methods are given for evaluation of the condition and alignments of instrument elements such as centres,
guideways, probe systems, etc. Recommendations are included for establishment of a proper environment
and for statistical data evaluation procedures.
It also covers the application of gear artifacts to the estimation of U measurement process uncertainty.
Guidance on the application of measurement processes to the inspection of product gears is provided,
including fitness for use and the recommended limits for U uncertainty based upon the accuracy tolerances
of product gears to be inspected.
Many of its recommendations may also be applicable to the measurement of worms, worm wheels, bevel
gears and gear cutting tools.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 1328-1:1995, Cylindrical gears — ISO system of accuracy — Part 1: Definitions and allowable values of
deviations relevant to corresponding flanks of gear teeth
ISO 1328-2:1997, Cylindrical gears — ISO system of accuracy — Part 2: Definitions and allowable values of
deviations relevant to radial composite deviation and runout information
ISO/TR 10064-1:1992, Cylindrical gears — Code of inspection practice — Part 1: Inspection of corresponding
flanks of gear teeth
ISO/TR 10064-2:1996, Cylindrical gears — Code of inspection practice — Part 2: Inspection related to radial
composite deviations, runout, tooth thickness and backlash
ISO/TR 10064-3:1996, Cylindrical gears — Code of inspection practice — Part 3: Recommendations relative
to gear blanks, shaft centre distance and parallelism of axes
ISO 10360-1:2000, Geometrical Product Specifications (GPS) — Acceptance and reverification tests for
coordinate measuring machines (CMM) — Part 1: Vocabulary
ISO/TS 14253-1:1998, Geometrical Product Specifications (GPS) — Inspection by measurement of
workpieces and measuring equipment — Part 1: Decision rules for proving conformance or non-conformance
with specifications
ISO/TS 14253-2:1999, Geometrical Product Specifications (GPS) — Inspection by measurement of
workpieces and measuring equipment — Part 2: Guide to the estimation of uncertainty in GPS measurement,
in calibration of measuring equipment and in product verification
ISO 18653:2003, Gears — Evaluation of instruments for the measurement of individual gears
Guide to the expression of uncertainty in measurement (GUM), BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML,
1st edition 1993, corrected and reprinted in 1995
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 1122-1, ISO 1328-1, ISO 1328-2
and ISO 18653 apply.
4 Instrument environment
4.1 Environment
The stability of the environment will affect accuracy of the calibration process and measurement of production
parts. The measurement temperature should be maintained as a constant. It is recommended that the
temperature be 20 °C. Standards or instrument manufacturer’s recommendations often require an
environment controlled to the extent necessary to assure continued measurements of required accuracy
considering temperature, humidity, vibration, cleanliness and other controllable factors affecting precision
measurement.
4.1.1 Important parameters
1)
The following parameters are of primary importance :
the cooling (heating) medium, usually air;
flow rate, distribution and velocity of the cooling (heating) medium;
frequency and amplitude of temperature variations of the cooling (heating) medium;
temperature gradients within the cooling (heating) medium;
vibrations;
electrical power supply quality.
1) A more thorough discussion of the effects may be found in such standards as ASME B89.6.2, Temperature and
Humidity Environment for Dimensional Measurement R(2002).
2 © ISO 2005 – All rights reserved
4.1.2 Practical guidelines
The following are practical guidelines for gear measurement. However, compliance with these guidelines does
not guarantee measurements to a specific accuracy.
Artifact temperature. Tooling, artifacts and other test pieces should be left for an adequate period to
stabilize to ambient temperature. Artifact temperature ideally should be the temperature at which it was
calibrated.
Mean temperature variation. The instrument manufacturer’s temperature variation guidelines for the
desired accuracy should be consulted. If this information is not available, it is recommended that the
mean temperature should not change more than 1 °C per hour, with a maximum change of 3.5 degrees
per day.
Temperature cycles. The temperature may cycle ± 2 °C, centred on the mean temperature, every 5 min
or faster. The thermal inertia of most mechanical systems will allow for rapid cyclic temperature
undulations within these guidelines for the stated accuracy. If a temperature cycle of the instrument
approaches 1 °C in 15 min, serious effects on the measuring system accuracy may occur. Many people
use an air conditioner in an attempt to achieve thermal control. The temperature sensors in these units
may be very slow to respond to temperature changes. If the response is slower than 5 min, serious
effects on measurement accuracy may be noted.
Temperature gradient. The temperature should be within 0,5 °C over the entire area of the instrument
surface. The best way to do this is with a high air flow. Air flow must be uniform throughout the room to
prevent dead spots and gradients. To accomplish this, diffuse the air coming in to the room and, if
possible, design multiple air returns to further diffuse the air uniformly in the room. The goal is to have all
air moving uniformly in the room and at the same temperature. Moving air must remove heat from
electronic controls, computers, motors, hydraulics, people, lights, etc., to prevent gradients.
Vibrations caused by instrument movements should not be allowed to interfere with measurements. Also,
vibrations from the surrounding environment should be observed or measured. If they are affecting
instrument accuracy, vibration isolation of the instrument or a suitable foundation may be necessary.
Electrical power supply. Power fluctuation may cause some electronic instruments and computers of
numerical control positioning systems to malfunction.
4.1.3 Workshop environment
It is recommended that measuring instruments be situated in a temperature controlled room. However, many
measuring instruments are placed in a workshop environment where it is difficult to maintain a process
measurement uncertainty of 5 microns. Accumulation of dirt or other contaminants on the ways of the
instrument can cause inaccuracies as well as premature wear.
If an instrument must be used in this kind of environment, care must be taken to avoid certain conditions, such
as
local radiant heat sources such as space heaters or sunlight through nearby windows that may distort the
instrument,
roof vents that allow cold air to drop on the instrument, and
cooling systems or open windows that cause a draft to hit one side of the instrument.
The formulae in 4.2.1 and 4.2.2 may also be used for estimating the effect of a stable, but consistent,
difference in instrument temperature from the standard temperature (20 °C). If the formulae are used, CTE
should be the instrument material or encoder scale value and the sign of the resulting compensation should
be changed. The user should be aware that the results might vary depending upon the location of temperature
measurement.
4.2 Effect of temperature on gears and artifacts
Temperature can have a significant effect on the geometry of gears and artifacts. Temperature effects upon
involute profile slope, f , helix slope, f , and tooth thickness measurements of external gears and artifacts
Hα Hβ
can be predicted using the following formulae. Such calculations assume uniform temperature of the given
test piece; localized temperature variations cannot be conveniently modelled. Temperature of the measuring
instrument is not considered in these calculations.
The temperature of the measuring instrument is not considered in these calculations, but a difference between
standard temperature (20 °C) and the instrument temperature will also cause errors in measurement result.
It may be desirable to correct profile and helix slope measurement values for temperature effect. Such
corrections are required by U estimation methods described in Clause 7 of this document.
Uniform temperature variations of a gear or artifact are not considered to have an effect upon pitch or runout
(tooth position) parameters.
4.2.1 Profile temperature effect calculation
For involute profile measurement, the effect of temperature can be modelled by considering the associated
change in the base circle diameter. The effect upon profile slope f can be calculated as follows:
Hα
a) Given (typical) data:
z is number of teeth;
m is normal module;
n
β is helix angle;
α is normal pressure angle;
n
L is roll length to the start of profile analysis;
αs
L is roll length to the end of profile analysis;
αe
−6 −1
CTE is coefficient of thermal expansion (approximately 11,5 × 10 C for steel).
NOTE When profile analysis start and end points are specified in roll angle degrees (ξ ), conversion to roll
y
length can be done with the following formula:
ξ
y
Ld=π (1)
()
yb
b) Calculate the slope change due to the temperature difference:
∆fL=−L t−t CTE (2)
( )( )
Heαα αsas
where
t is the actual (measured) temperature;
a
t is the standard temperature (20 °C).
s
See Annex A for an example and further information.
4 © ISO 2005 – All rights reserved
4.2.2 Helix temperature effect calculation
For helix measurement, the effect of temperature can be modelled by considering the associated change in
the lead. The effect upon helix slope, f , can be estimated as follows.
Hβ
a) Given (typical) data in 4.2.1 a), plus:
L is helix evaluation range;
β
b) Calculate the base helix angle, β :
b
β = arcsin sinβcosα (3)
( )
bn
c) Calculate the slope change due to the temperature difference:
∆fL=− tanβt −t CTE (4)
( )
Hββ ba s
See Annex A for an example and further information.
4.2.3 Tooth thickness temperature effect calculation
In addition to involute profile and helix, tooth thickness may be significantly affected by temperature. These
effects can be modelled by considering the associated change in the tooth section intersecting the pitch
diameter, where tooth thickness is usually measured. The effect of temperature upon normal tooth thickness
of an external gear can be estimated as follows.:
a) Given (typical) data in 4.2.1 a), plus:
s is normal tooth thickness at the reference pitch diameter, d:
n
b) Calculate the reference pitch diameter, d:
m
n
dz= (5)
cosβ
c) Calculate the change in normal circular tooth thickness at the reference pitch diameter of an external gear
due to the temperature difference:
∆sd=−tanα t t CTE (6)
( )
n na s
See Annex A for an example and further information.
5 Measurement system condition
Many factors affect the accuracy of gear measuring instruments. These include squareness and parallelism of
the instrument guideways to each other and to the rotary table, straightness of the guideways, linear
positioning errors, and angular motion errors (pitch, roll and yaw) of the moving components of the instrument.
Errors caused by electronic components, scales, controls, and software may also adversely effect the
accuracy of a measuring instrument. There are various methods of measuring these errors. While a complete
discussion of machine kinematics and electronic controls is beyond the scope of this document, it is
recommended that users of these instruments be aware of the many possible sources of inaccuracy.
Some manufacturers of measuring instruments provide detailed procedures for periodically verifying their
product’s conformance to original factory specifications. The generalized tests and recommended tolerances
found in this section are for use in the absence of, or in addition to, the instrument manufacturer’s
recommended procedures. These tests are not to be considered a replacement for the manufacturer’s
procedures.
Gear accuracy grade and parameters to be tested should be identified prior to starting verification procedures.
The actual work envelope should also be known. Results of all procedures should be recorded to document
this verification work and to provide data for statistical analysis.
5.1 Evaluation procedure for generative instruments
Proper operation of important components of gear measuring instruments can be verified by the procedures
outlined in the following. This verification procedure should begin with a visual inspection of the instrument to
assure that no obvious detrimental conditions exist that would impair proper operation. Centres, drivers and
measuring probe styli that are subject to wear and damage should be checked. Confirm also that
environmental conditions meet the requirements of 4.1.
The probe systems and indicators that measure instrument errors should be calibrated and have an
appropriate discrimination (1 µm or less is recommended). The user should note that data capture rates and
filters will affect the measurement results. See 5.4 for further information.
5.1.1 Verification of mounting centres
Inspection of gear geometry by generative methods requires mounting the gear such that its datum axis of
rotation is coincident with the instrument’s main spindle axis. See ISO/TR 10064-3. Any eccentricity or non-
parallelism of this mounting will cause an error in measurement results. See Figure 1.
Between-centres mounting of test gears is a common practice. Most gear testing instruments are fitted with
centres, one on the main spindle and one on a tailstock assembly. Misalignment and runout of these centres
are common. Verification of instruments used for testing should therefore begin with the observation of these
mounting centres.
Key
1 between-centres axis
2 workspindle axis
3 error
Figure 1 — Alignment error of the spindle axis and the between-centres axis
6 © ISO 2005 – All rights reserved
5.1.1.1 Centre runout
Using an indicator with an appropriate discrimination, measure the runout (TIR) of the main spindle centre in a
direction normal to the surface. This measurement of runout should be within the manufacturer’s
specifications or the guidelines listed in Table 1. It is advisable to measure runout of each centre at the small
and large end to detect bent or skewed centres.
a
Table 1 — Recommended guidelines for deviations when checking instrument alignment
Accuracy grade Runout of centres Z-axis parallelism with spindle axis in any Alignment of top
to be tested (TIR) measured 200 mm region centre with spindle
µm axis (TIR) per 200
b c
ISO 1328-1
A B d
mm
ISO 1328-2
µm µm
2 1 1 2 2
3 1 2 2 2
4 1 2 3 3
5 2 3 4 4
6 2 4 6 6
7 3 5 6 6
8 4 5 6 6
9 5 7 6 6
10 7 10 8 8
11 10 10 12 12
12 10 10 12 12
a
The guidelines are for multi-purpose instruments. Single-purpose instruments may only require one or more of the parameters.
b
In the measuring (base tangent) plane. See Figure 5.
c
Perpendicular to the measuring plane. See Figure 6.
d
Alignment tolerance is the greater of 2 µm or the table tolerance per 200 mm of the length, R, in Figures 3 and 4.
Load the spindle assemblies by mounting an arbor between centres. The length, accuracy, or configuration of
this arbor is not significant. See Figure 2.
Key
1 tailstock live centre
2 work spindle centre
Figure 2 — Centre runout test
5.1.1.2 Tailstock centre positioning
A testing practice often called sweeping can be used to effectively evaluate the position of the tailstock centre
relative to the main spindle axis. Sweeping the tailstock centre at only one location on the tailstock slide
verifies its positioning for testing gears at that location only. Sweeping the tailstock centre at two significantly
separated tailstock slide locations verifies both lateral positioning and angular alignment of the tailstock slide
with the main spindle axis. If straightness of travel of the tailstock slide has been confirmed to be within
manufacturer’s specifications by other methods, a two-location test will verify tailstock centre positioning at all
locations. Otherwise, sweeping of the tailstock centre at a minimum of three significantly separated locations
within its range of operation is required. For high-quality gears, it is recommended sweeping of the tailstock be
done for each unique configuration before inspection.
Two sweeping test set-ups will be described.
a) The first is recommended only for instruments with a vertical main spindle axis. Figure 3 provides an
example of this set-up. The spindle assemblies are loaded by mounting an arbor between centres. The
accuracy and configuration of this arbor is not significant as the indicator and arbor rotate together.
A minimum of two such sweeping tests, each using different length arbors, is normally required.
Instruments that use base discs should be tested with a base disc contacting the base tangent slide to
ensure spindle clearance effects are included. The lengths of the two arbors should be selected to be
toward opposite ends of the range of tailstock operation.
An indicator with an appropriate discrimination is mounted so as to be carried by the rotating main spindle
and simultaneously to measure in a radial direction the alignment (TIR) of the arbor near the tailstock
centre. These measurements of the tailstock centre alignment with the spindle axis should be within the
value listed in Table 1.
The value is stated as a ratio of permissible centre alignment (TIR) to the axial distance of that
measurement from the main spindle centre. The recommended value therefore changes with
measurement location and should be adjusted accordingly. The tolerance value is the greater of 2 µm or
the table tolerance per 200 mm of the length, R, in Figure 3.
8 © ISO 2005 – All rights reserved
Key
1 between-centres axis
2 work spindle axis
3 error
Figure 3 — Tailstock alignment measurement method (vertical axis instruments only)
b) The second sweeping test set-up is recommended for instruments with a horizontal main spindle axis, but
may also be used for vertical instruments. Figure 4 provides an example of this set-up. This figure shows
the sweeping set-up made at two locations, L and L . As before, the spindle assemblies are loaded by
1 2
mounting different length arbors between centres at the two locations.
In this case, an indicator with appropriate discrimination is mounted so as to be carried by the rotating test
arbor and to measure in an axial direction the alignment (TIR) of a fixture carried by the rotating main
spindle. These alignment measurements of the tailstock centre with the spindle axis should be within the
value listed in Table 1.
The value is stated as a ratio of permissible centre alignment (TIR) to the axial distance of that
measurement from the main spindle centre. The recommended value therefore changes with
measurement location and should be adjusted accordingly. The tolerance value is the greater of 2 µm or
the table tolerance per 200 mm of the length, R, in Figure 4.
Key
1 work spindle
2 tailstock
3 driver pin (clearance in hole)
Figure 4 — Tailstock centre alignment fixture for horizontal or vertical work spindles
5.1.2 Axial measuring slide verification
Parallelism of the path of the axial measuring slide with the main spindle axis should be confirmed. A parallel
mandrel is required for this evaluation. Alternatively, an accurately manufactured mandrel can be used in
conjunction with a self-proving, reversal-method. This verification should apply to the length of the work
envelope, or at minimum 80 % of the full travel, see Figures 5 and 6.
5.1.2.1 Centre-mounted mandrel
The mandrel may be mounted between centres. In this case, its orientation concentric with the main spindle
axis should be confirmed by two observations. First, its concentricity near the main spindle centre and near
the tailstock centre can be confirmed by measuring its radial runout near those centres. Second, its
concentricity near the tailstock centre can be confirmed by sweeping the mandrel. If the sweeping set-up
recommended for vertical axis instruments is used, the test indicator should be positioned near the tailstock
centre. It is recommended that this mounting of the test mandrel be optimized before observation of axial
measuring slide parallelism. This may include minimizing runout of the main spindle centre, runout of the
tailstock spindle centre, and alignment error of the tailstock slide assembly at this test location.
10 © ISO 2005 – All rights reserved
Key
1 rotary direction
2 radial direction
3 axial direction (Z)
4 tangential direction
Figure 5 — Z-axis to between-centres axis alignment verification
axial plane parallel to the measuring (base tangent) plane
Key
1 rotary direction
2 radial direction
3 axial direction (Z)
4 tangential direction
Figure 6 — Z-axis to between-centres axis alignment verification, perpendicular to measuring plane
5.1.2.2 Direct mounted mandrel
Alternatively, the test mandrel can be attached directly to the main spindle, thereby eliminating adverse
influences of mounting centres. In this case, its orientation concentric with the main spindle axis must be
confirmed by observation of radial runout near each end of the mandrel. Centring and tilting adjustments will
be required to optimize this mounting before observation of axial measuring slide parallelism.
5.1.2.3 Axial slide parallelism testing
Once a calibrated mandrel has been properly oriented on the instrument, it should be tested by traversing its
length with the measuring probe carried by the axial measuring slide. This will reveal errors of straightness
and alignment of the axial slide. The observation should be made in a radial direction within two different axial
planes:
a) the plane parallel with the measuring plane (the base tangent plane);
b) the plane perpendicular to the measuring plane.
See Figures 5 and 6.
These measurements of axial measuring slide parallel
...
TECHNICAL ISO/TR
REPORT 10064-5
First edition
2005-04-15
Cylindrical gears — Code of inspection
practice —
Part 5:
Recommendations relative to evaluation
of gear measuring instruments
Engrenages cylindriques — Code pratique de réception —
Partie 5: Recommandations relatives à l'évaluation des instruments de
mesure des engrenages
Reference number
©
ISO 2005
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ii © ISO 2005 – All rights reserved
Contents Page
Foreword. v
1 Scope. 1
2 Normative references . 1
3 Terms and definitions. 2
4 Instrument environment. 2
4.1 Environment . 2
4.1.1 Important parameters . 2
4.1.2 Practical guidelines . 3
4.1.3 Workshop environment. 3
4.2 Effect of temperature on gears and artifacts . 4
4.2.1 Profile temperature effect calculation. 4
4.2.2 Helix temperature effect calculation . 5
4.2.3 Tooth thickness temperature effect calculation . 5
5 Measurement system condition . 5
5.1 Evaluation procedure for generative instruments. 6
5.1.1 Verification of mounting centres. 6
5.1.2 Axial measuring slide verification. 10
5.2 Evaluation procedures for CMM type measuring instruments . 14
5.2.1 Performance test according to ISO 10360. 14
5.2.2 Ball plate test. 15
5.2.3 Rotary tables . 16
5.3 Probe system. 16
5.3.1 Stylus. 16
5.3.2 Data recording system . 17
5.4 Filtering . 21
5.4.1 Mechanical filtering. 21
5.4.2 Electrical filtering . 21
5.4.3 Mathematical filtering . 22
5.5 Uncertainty estimation . 22
6 Artifacts. 22
6.1 Mounting reference features. 22
6.2 Suggested master artifacts. 22
6.2.1 Integral base circle involute master. 23
6.2.2 Helix artifact. 23
6.2.3 Pitch variation, total cumulative pitch variation and runout artifact . 24
6.2.4 Tooth thickness artifacts. 25
6.2.5 Workpiece-like artifacts. 25
6.3 Modified base circle involute artifact testing. 27
6.4 Non-involute — Pin (cylindrical), plane (flank) and ball (spherical) artifacts . 27
6.4.1 Types of non-involute artifacts. 27
6.4.2 Non-involute artifact function. 29
6.4.3 Plane artifact calibration . 30
6.4.4 Pin or ball artifact calibration . 30
6.4.5 Probe-tip effects when calculating reference curve. 30
6.4.6 Measurement location . 31
6.4.7 Non-involute master interpretation . 31
6.5 Helix artifact testing. 31
6.5.1 Modified-lead helix artifact testing. 31
6.5.2 Non-involute helix masters . 32
6.6 Modified eccentricity pitch artifact testing .32
7 Uncertainty estimation guidelines.32
7.1 Uncertainty estimation methods.32
7.1.1 General methods .32
7.1.2 Comparator methods .33
7.2 Calculation of U measurement uncertainty .33
7.3 Measurement parameters.34
7.3.1 Line-fit parameters .34
7.3.2 Band-fit parameters.35
7.3.3 Pitch parameters .35
8 Measurement procedures.35
8.1 Traceability.35
8.2 Operating conditions .35
8.2.1 Conditions for bias determination.35
8.2.2 Conditions for standard uncertainty estimation .35
8.2.3 Conditions for combined determinations.36
8.3 Measurements .36
8.4 Calibration procedure .36
8.4.1 Initial set-up and adjustments.36
8.4.2 Initial calibration procedure .36
8.4.3 Ongoing calibration procedure.37
8.4.4 Tooling and gauges.37
9 Comparator measurement uncertainty estimation guidelines .37
9.1 Direct comparator example A .37
9.2 Comparator approach, expanded for workpiece characteristic influence.39
9.2.1 Comparator example B .39
9.2.2 Comparator example C .41
9.3 Comparator approach, expanded for workpiece characteristic and geometry similarity
influences.43
10 Statistical process control .43
10.1 Definitions .43
10.2 Constructing the X and MR chart .43
10.3 Criteria for evidence of lack of control.44
10.4 When control chart data fails one or more criteria according to 10.3 .46
11 Instrument fitness for use .46
11.1 Limiting measurement uncertainty.46
11.1.1 GPS Tolerance reduction method .46
11.1.2 Tolerance ratio method.48
11.1.3 Instrument uncertainty guidelines.48
11.2 Measurement uncertainty sources.49
11.3 Reducing measurement uncertainty .50
11.3.1 Following a different calibration procedure .50
11.3.2 Reducing uncertainty of the reference master certification .50
11.3.3 Improving the measuring process.50
12 Measurement process (instrument) correlation.51
12.1 Basis for comparison.51
12.2 Correlation of measurement .51
Annex A (informative) Effect of temperature on gears and artifacts .52
Annex B (informative) Modified involute, helix, pitch artifact testing .58
Annex C (informative) Non-involute pin, ball, or plane (flank) artifact interpretation.69
Bibliography.89
iv © ISO 2005 – All rights reserved
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each 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, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 10064-5 was prepared by Technical Committee ISO/TC 60, Gears.
ISO/TR 10064 consists of the following parts, under the general title Cylindrical gears — Code of inspection
practice:
Part 1: Inspection of corresponding flanks of gear teeth
Part 2: Inspection related to radial composite deviations, runout, tooth thickness and backlash
Part 3: Recommendations relative to gear blanks, shaft centre distance and parallelism of axes
Part 4: Recommendations relative to surface texture and tooth contact pattern checking
Part 5: Recommendations relative to evaluation of gear measuring instruments
TECHNICAL REPORT ISO/TR 10064-5:2005(E)
Cylindrical gears — Code of inspection practice —
Part 5:
Recommendations relative to evaluation of gear measuring
instruments
1 Scope
This part of ISO/TR 10064 provides additional information and examples to support the implementation of
ISO 18653. It proposes evaluation and calibration procedures for involute, helix, pitch, runout, and tooth
thickness measurement processes.
Methods are given for evaluation of the condition and alignments of instrument elements such as centres,
guideways, probe systems, etc. Recommendations are included for establishment of a proper environment
and for statistical data evaluation procedures.
It also covers the application of gear artifacts to the estimation of U measurement process uncertainty.
Guidance on the application of measurement processes to the inspection of product gears is provided,
including fitness for use and the recommended limits for U uncertainty based upon the accuracy tolerances
of product gears to be inspected.
Many of its recommendations may also be applicable to the measurement of worms, worm wheels, bevel
gears and gear cutting tools.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 1328-1:1995, Cylindrical gears — ISO system of accuracy — Part 1: Definitions and allowable values of
deviations relevant to corresponding flanks of gear teeth
ISO 1328-2:1997, Cylindrical gears — ISO system of accuracy — Part 2: Definitions and allowable values of
deviations relevant to radial composite deviation and runout information
ISO/TR 10064-1:1992, Cylindrical gears — Code of inspection practice — Part 1: Inspection of corresponding
flanks of gear teeth
ISO/TR 10064-2:1996, Cylindrical gears — Code of inspection practice — Part 2: Inspection related to radial
composite deviations, runout, tooth thickness and backlash
ISO/TR 10064-3:1996, Cylindrical gears — Code of inspection practice — Part 3: Recommendations relative
to gear blanks, shaft centre distance and parallelism of axes
ISO 10360-1:2000, Geometrical Product Specifications (GPS) — Acceptance and reverification tests for
coordinate measuring machines (CMM) — Part 1: Vocabulary
ISO/TS 14253-1:1998, Geometrical Product Specifications (GPS) — Inspection by measurement of
workpieces and measuring equipment — Part 1: Decision rules for proving conformance or non-conformance
with specifications
ISO/TS 14253-2:1999, Geometrical Product Specifications (GPS) — Inspection by measurement of
workpieces and measuring equipment — Part 2: Guide to the estimation of uncertainty in GPS measurement,
in calibration of measuring equipment and in product verification
ISO 18653:2003, Gears — Evaluation of instruments for the measurement of individual gears
Guide to the expression of uncertainty in measurement (GUM), BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML,
1st edition 1993, corrected and reprinted in 1995
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 1122-1, ISO 1328-1, ISO 1328-2
and ISO 18653 apply.
4 Instrument environment
4.1 Environment
The stability of the environment will affect accuracy of the calibration process and measurement of production
parts. The measurement temperature should be maintained as a constant. It is recommended that the
temperature be 20 °C. Standards or instrument manufacturer’s recommendations often require an
environment controlled to the extent necessary to assure continued measurements of required accuracy
considering temperature, humidity, vibration, cleanliness and other controllable factors affecting precision
measurement.
4.1.1 Important parameters
1)
The following parameters are of primary importance :
the cooling (heating) medium, usually air;
flow rate, distribution and velocity of the cooling (heating) medium;
frequency and amplitude of temperature variations of the cooling (heating) medium;
temperature gradients within the cooling (heating) medium;
vibrations;
electrical power supply quality.
1) A more thorough discussion of the effects may be found in such standards as ASME B89.6.2, Temperature and
Humidity Environment for Dimensional Measurement R(2002).
2 © ISO 2005 – All rights reserved
4.1.2 Practical guidelines
The following are practical guidelines for gear measurement. However, compliance with these guidelines does
not guarantee measurements to a specific accuracy.
Artifact temperature. Tooling, artifacts and other test pieces should be left for an adequate period to
stabilize to ambient temperature. Artifact temperature ideally should be the temperature at which it was
calibrated.
Mean temperature variation. The instrument manufacturer’s temperature variation guidelines for the
desired accuracy should be consulted. If this information is not available, it is recommended that the
mean temperature should not change more than 1 °C per hour, with a maximum change of 3.5 degrees
per day.
Temperature cycles. The temperature may cycle ± 2 °C, centred on the mean temperature, every 5 min
or faster. The thermal inertia of most mechanical systems will allow for rapid cyclic temperature
undulations within these guidelines for the stated accuracy. If a temperature cycle of the instrument
approaches 1 °C in 15 min, serious effects on the measuring system accuracy may occur. Many people
use an air conditioner in an attempt to achieve thermal control. The temperature sensors in these units
may be very slow to respond to temperature changes. If the response is slower than 5 min, serious
effects on measurement accuracy may be noted.
Temperature gradient. The temperature should be within 0,5 °C over the entire area of the instrument
surface. The best way to do this is with a high air flow. Air flow must be uniform throughout the room to
prevent dead spots and gradients. To accomplish this, diffuse the air coming in to the room and, if
possible, design multiple air returns to further diffuse the air uniformly in the room. The goal is to have all
air moving uniformly in the room and at the same temperature. Moving air must remove heat from
electronic controls, computers, motors, hydraulics, people, lights, etc., to prevent gradients.
Vibrations caused by instrument movements should not be allowed to interfere with measurements. Also,
vibrations from the surrounding environment should be observed or measured. If they are affecting
instrument accuracy, vibration isolation of the instrument or a suitable foundation may be necessary.
Electrical power supply. Power fluctuation may cause some electronic instruments and computers of
numerical control positioning systems to malfunction.
4.1.3 Workshop environment
It is recommended that measuring instruments be situated in a temperature controlled room. However, many
measuring instruments are placed in a workshop environment where it is difficult to maintain a process
measurement uncertainty of 5 microns. Accumulation of dirt or other contaminants on the ways of the
instrument can cause inaccuracies as well as premature wear.
If an instrument must be used in this kind of environment, care must be taken to avoid certain conditions, such
as
local radiant heat sources such as space heaters or sunlight through nearby windows that may distort the
instrument,
roof vents that allow cold air to drop on the instrument, and
cooling systems or open windows that cause a draft to hit one side of the instrument.
The formulae in 4.2.1 and 4.2.2 may also be used for estimating the effect of a stable, but consistent,
difference in instrument temperature from the standard temperature (20 °C). If the formulae are used, CTE
should be the instrument material or encoder scale value and the sign of the resulting compensation should
be changed. The user should be aware that the results might vary depending upon the location of temperature
measurement.
4.2 Effect of temperature on gears and artifacts
Temperature can have a significant effect on the geometry of gears and artifacts. Temperature effects upon
involute profile slope, f , helix slope, f , and tooth thickness measurements of external gears and artifacts
Hα Hβ
can be predicted using the following formulae. Such calculations assume uniform temperature of the given
test piece; localized temperature variations cannot be conveniently modelled. Temperature of the measuring
instrument is not considered in these calculations.
The temperature of the measuring instrument is not considered in these calculations, but a difference between
standard temperature (20 °C) and the instrument temperature will also cause errors in measurement result.
It may be desirable to correct profile and helix slope measurement values for temperature effect. Such
corrections are required by U estimation methods described in Clause 7 of this document.
Uniform temperature variations of a gear or artifact are not considered to have an effect upon pitch or runout
(tooth position) parameters.
4.2.1 Profile temperature effect calculation
For involute profile measurement, the effect of temperature can be modelled by considering the associated
change in the base circle diameter. The effect upon profile slope f can be calculated as follows:
Hα
a) Given (typical) data:
z is number of teeth;
m is normal module;
n
β is helix angle;
α is normal pressure angle;
n
L is roll length to the start of profile analysis;
αs
L is roll length to the end of profile analysis;
αe
−6 −1
CTE is coefficient of thermal expansion (approximately 11,5 × 10 C for steel).
NOTE When profile analysis start and end points are specified in roll angle degrees (ξ ), conversion to roll
y
length can be done with the following formula:
ξ
y
Ld=π (1)
()
yb
b) Calculate the slope change due to the temperature difference:
∆fL=−L t−t CTE (2)
( )( )
Heαα αsas
where
t is the actual (measured) temperature;
a
t is the standard temperature (20 °C).
s
See Annex A for an example and further information.
4 © ISO 2005 – All rights reserved
4.2.2 Helix temperature effect calculation
For helix measurement, the effect of temperature can be modelled by considering the associated change in
the lead. The effect upon helix slope, f , can be estimated as follows.
Hβ
a) Given (typical) data in 4.2.1 a), plus:
L is helix evaluation range;
β
b) Calculate the base helix angle, β :
b
β = arcsin sinβcosα (3)
( )
bn
c) Calculate the slope change due to the temperature difference:
∆fL=− tanβt −t CTE (4)
( )
Hββ ba s
See Annex A for an example and further information.
4.2.3 Tooth thickness temperature effect calculation
In addition to involute profile and helix, tooth thickness may be significantly affected by temperature. These
effects can be modelled by considering the associated change in the tooth section intersecting the pitch
diameter, where tooth thickness is usually measured. The effect of temperature upon normal tooth thickness
of an external gear can be estimated as follows.:
a) Given (typical) data in 4.2.1 a), plus:
s is normal tooth thickness at the reference pitch diameter, d:
n
b) Calculate the reference pitch diameter, d:
m
n
dz= (5)
cosβ
c) Calculate the change in normal circular tooth thickness at the reference pitch diameter of an external gear
due to the temperature difference:
∆sd=−tanα t t CTE (6)
( )
n na s
See Annex A for an example and further information.
5 Measurement system condition
Many factors affect the accuracy of gear measuring instruments. These include squareness and parallelism of
the instrument guideways to each other and to the rotary table, straightness of the guideways, linear
positioning errors, and angular motion errors (pitch, roll and yaw) of the moving components of the instrument.
Errors caused by electronic components, scales, controls, and software may also adversely effect the
accuracy of a measuring instrument. There are various methods of measuring these errors. While a complete
discussion of machine kinematics and electronic controls is beyond the scope of this document, it is
recommended that users of these instruments be aware of the many possible sources of inaccuracy.
Some manufacturers of measuring instruments provide detailed procedures for periodically verifying their
product’s conformance to original factory specifications. The generalized tests and recommended tolerances
found in this section are for use in the absence of, or in addition to, the instrument manufacturer’s
recommended procedures. These tests are not to be considered a replacement for the manufacturer’s
procedures.
Gear accuracy grade and parameters to be tested should be identified prior to starting verification procedures.
The actual work envelope should also be known. Results of all procedures should be recorded to document
this verification work and to provide data for statistical analysis.
5.1 Evaluation procedure for generative instruments
Proper operation of important components of gear measuring instruments can be verified by the procedures
outlined in the following. This verification procedure should begin with a visual inspection of the instrument to
assure that no obvious detrimental conditions exist that would impair proper operation. Centres, drivers and
measuring probe styli that are subject to wear and damage should be checked. Confirm also that
environmental conditions meet the requirements of 4.1.
The probe systems and indicators that measure instrument errors should be calibrated and have an
appropriate discrimination (1 µm or less is recommended). The user should note that data capture rates and
filters will affect the measurement results. See 5.4 for further information.
5.1.1 Verification of mounting centres
Inspection of gear geometry by generative methods requires mounting the gear such that its datum axis of
rotation is coincident with the instrument’s main spindle axis. See ISO/TR 10064-3. Any eccentricity or non-
parallelism of this mounting will cause an error in measurement results. See Figure 1.
Between-centres mounting of test gears is a common practice. Most gear testing instruments are fitted with
centres, one on the main spindle and one on a tailstock assembly. Misalignment and runout of these centres
are common. Verification of instruments used for testing should therefore begin with the observation of these
mounting centres.
Key
1 between-centres axis
2 workspindle axis
3 error
Figure 1 — Alignment error of the spindle axis and the between-centres axis
6 © ISO 2005 – All rights reserved
5.1.1.1 Centre runout
Using an indicator with an appropriate discrimination, measure the runout (TIR) of the main spindle centre in a
direction normal to the surface. This measurement of runout should be within the manufacturer’s
specifications or the guidelines listed in Table 1. It is advisable to measure runout of each centre at the small
and large end to detect bent or skewed centres.
a
Table 1 — Recommended guidelines for deviations when checking instrument alignment
Accuracy grade Runout of centres Z-axis parallelism with spindle axis in any Alignment of top
to be tested (TIR) measured 200 mm region centre with spindle
µm axis (TIR) per 200
b c
ISO 1328-1
A B d
mm
ISO 1328-2
µm µm
2 1 1 2 2
3 1 2 2 2
4 1 2 3 3
5 2 3 4 4
6 2 4 6 6
7 3 5 6 6
8 4 5 6 6
9 5 7 6 6
10 7 10 8 8
11 10 10 12 12
12 10 10 12 12
a
The guidelines are for multi-purpose instruments. Single-purpose instruments may only require one or more of the parameters.
b
In the measuring (base tangent) plane. See Figure 5.
c
Perpendicular to the measuring plane. See Figure 6.
d
Alignment tolerance is the greater of 2 µm or the table tolerance per 200 mm of the length, R, in Figures 3 and 4.
Load the spindle assemblies by mounting an arbor between centres. The length, accuracy, or configuration of
this arbor is not significant. See Figure 2.
Key
1 tailstock live centre
2 work spindle centre
Figure 2 — Centre runout test
5.1.1.2 Tailstock centre positioning
A testing practice often called sweeping can be used to effectively evaluate the position of the tailstock centre
relative to the main spindle axis. Sweeping the tailstock centre at only one location on the tailstock slide
verifies its positioning for testing gears at that location only. Sweeping the tailstock centre at two significantly
separated tailstock slide locations verifies both lateral positioning and angular alignment of the tailstock slide
with the main spindle axis. If straightness of travel of the tailstock slide has been confirmed to be within
manufacturer’s specifications by other methods, a two-location test will verify tailstock centre positioning at all
locations. Otherwise, sweeping of the tailstock centre at a minimum of three significantly separated locations
within its range of operation is required. For high-quality gears, it is recommended sweeping of the tailstock be
done for each unique configuration before inspection.
Two sweeping test set-ups will be described.
a) The first is recommended only for instruments with a vertical main spindle axis. Figure 3 provides an
example of this set-up. The spindle assemblies are loaded by mounting an arbor between centres. The
accuracy and configuration of this arbor is not significant as the indicator and arbor rotate together.
A minimum of two such sweeping tests, each using different length arbors, is normally required.
Instruments that use base discs should be tested with a base disc contacting the base tangent slide to
ensure spindle clearance effects are included. The lengths of the two arbors should be selected to be
toward opposite ends of the range of tailstock operation.
An indicator with an appropriate discrimination is mounted so as to be carried by the rotating main spindle
and simultaneously to measure in a radial direction the alignment (TIR) of the arbor near the tailstock
centre. These measurements of the tailstock centre alignment with the spindle axis should be within the
value listed in Table 1.
The value is stated as a ratio of permissible centre alignment (TIR) to the axial distance of that
measurement from the main spindle centre. The recommended value therefore changes with
measurement location and should be adjusted accordingly. The tolerance value is the greater of 2 µm or
the table tolerance per 200 mm of the length, R, in Figure 3.
8 © ISO 2005 – All rights reserved
Key
1 between-centres axis
2 work spindle axis
3 error
Figure 3 — Tailstock alignment measurement method (vertical axis instruments only)
b) The second sweeping test set-up is recommended for instruments with a horizontal main spindle axis, but
may also be used for vertical instruments. Figure 4 provides an example of this set-up. This figure shows
the sweeping set-up made at two locations, L and L . As before, the spindle assemblies are loaded by
1 2
mounting different length arbors between centres at the two locations.
In this case, an indicator with appropriate discrimination is mounted so as to be carried by the rotating test
arbor and to measure in an axial direction the alignment (TIR) of a fixture carried by the rotating main
spindle. These alignment measurements of the tailstock centre with the spindle axis should be within the
value listed in Table 1.
The value is stated as a ratio of permissible centre alignment (TIR) to the axial distance of that
measurement from the main spindle centre. The recommended value therefore changes with
measurement location and should be adjusted accordingly. The tolerance value is the greater of 2 µm or
the table tolerance per 200 mm of the length, R, in Figure 4.
Key
1 work spindle
2 tailstock
3 driver pin (clearance in hole)
Figure 4 — Tailstock centre alignment fixture for horizontal or vertical work spindles
5.1.2 Axial measuring slide verification
Parallelism of the path of the axial measuring slide with the main spindle axis should be confirmed. A parallel
mandrel is required for this evaluation. Alternatively, an accurately manufactured mandrel can be used in
conjunction with a self-proving, reversal-method. This verification should apply to the length of the work
envelope, or at minimum 80 % of the full travel, see Figures 5 and 6.
5.1.2.1 Centre-mounted mandrel
The mandrel may be mounted between centres. In this case, its orientation concentric with the main spindle
axis should be confirmed by two observations. First, its concentricity near the main spindle centre and near
the tailstock centre can be confirmed by measuring its radial runout near those centres. Second, its
concentricity near the tailstock centre can be confirmed by sweeping the mandrel. If the sweeping set-up
recommended for vertical axis instruments is used, the test indicator should be positioned near the tailstock
centre. It is recommended that this mounting of the test mandrel be optimized before observation of axial
measuring slide parallelism. This may include minimizing runout of the main spindle centre, runout of the
tailstock spindle centre, and alignment error of the tailstock slide assembly at this test location.
10 © ISO 2005 – All rights reserved
Key
1 rotary direction
2 radial direction
3 axial direction (Z)
4 tangential direction
Figure 5 — Z-axis to between-centres axis alignment verification
axial plane parallel to the measuring (base tangent) plane
Key
1 rotary direction
2 radial direction
3 axial direction (Z)
4 tangential direction
Figure 6 — Z-axis to between-centres axis alignment verification, perpendicular to measuring plane
5.1.2.2 Direct mounted mandrel
Alternatively, the test mandrel can be attached directly to the main spindle, thereby eliminating adverse
influences of mounting centres. In this case, its orientation concentric with the main spindle axis must be
confirmed by observation of radial runout near each end of the mandrel. Centring and tilting adjustments will
be required to optimize this mounting before observation of axial measuring slide parallelism.
5.1.2.3 Axial slide parallelism testing
Once a calibrated mandrel has been properly oriented on the instrument, it should be tested by traversing its
length with the measuring probe carried by the axial measuring slide. This will reveal errors of straightness
and alignment of the axial slide. The observation should be made in a radial direction within two different axial
planes:
a) the plane parallel with the measuring plane (the base tangent plane);
b) the plane perpendicular to the measuring plane.
See Figures 5 and 6.
These measurements of axial measuring slide parallelism with the main spindle axis should be within the
guidelines listed in Table 1. Two such guideline values are provided: one for observations parallel with the
measuring plane, and one for those that are perpendicular to the measuring plane. These value(s) apply to
any measured 200 mm region of the axial measuring slide.
5.1.2.4 Change in alignment with heavy load
Ideally, tests should be carried out with the instrument head placed at the limits of the measuring capacity
[i.e. with the tangential slide length at ± the maximum length of roll (4-axis instruments only) and radial slide at
the limiting base radius], see Figure 7.
12 © ISO 2005 – All rights reserved
a) Four-axis measuring instrument b) Three-axis measuring instrument
Key
1 tangential
2 radial
3 axial
4 rotary
5 load
Figure 7 — Position of the base tangent slide during the deflection tests
( ±±±± maximum length of roll for the verified measuring volume)
The measuring instrument table or table centre should be loaded with a test gear or artifact that provides a
tooth geometry that satisfies the measuring volume as mentioned above. Weights are then to be added in
increments to represent the maximum weight capacity expected in service or the instrument’s work spindle
weight capacity as stated by the original equipment manufact
...
RAPPORT ISO/TR
TECHNIQUE 10064-5
Première édition
2005-04-15
Engrenages cylindriques — Code
pratique de réception —
Partie 5:
Recommandations relatives à l'évaluation
des instruments de mesure des
engrenages
Cylindrical gears — Code of inspection practice —
Part 5: Recommendations relative to evaluation of gear measuring
instruments
Numéro de référence
©
ISO 2005
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ii © ISO 2005 – Tous droits réservés
Sommaire Page
Avant-propos. v
1 Domaine d'application. 1
2 Références normatives . 1
3 Termes et définitions. 2
4 Environnement de l'instrument. 2
4.1 Environnement. 2
4.1.1 Paramètres importants. 2
4.1.2 Recommandations pratiques . 3
4.1.3 Environnement de l'atelier . 3
4.2 Effet de la température sur les engrenages et les artéfacts . 4
4.2.1 Calcul de l'effet de la température sur le profil. 4
4.2.2 Calcul de l'effet de la température sur l'hélice. 5
4.2.3 Calcul de l'effet de la température sur l'épaisseur des dents. 5
5 État du système de mesure . 6
5.1 Mode d'évaluation des instruments génératifs . 6
5.1.1 Vérification des pointes de montage. 6
5.1.2 Vérification du coulisseau de mesurage axial. 10
5.2 Modes opératoires d'évaluation pour les instruments de mesure de type MMT . 14
5.2.1 Essai de performances selon l'ISO 10360. 14
5.2.2 Essai par plateau à boules. 15
5.2.3 Plateaux tournant. 16
5.3 Système de palpage . 17
5.3.1 Stylet . 17
5.3.2 Système d'enregistrement des données. 18
5.4 Filtrage . 21
5.4.1 Filtrage mécanique . 22
5.4.2 Filtrage électrique. 22
5.4.3 Filtrage mathématique. 22
5.5 Estimation de l'incertitude . 22
6 Artéfacts . 22
6.1 Caractéristiques de référence du montage. 23
6.2 Artéfacts étalons suggérés. 23
6.2.1 Étalon de développante à cercle de base intégral . 23
6.2.2 Artéfact d'hélice . 24
6.2.3 Artéfact de variation de pas, de variation totale cumulative de pas et de faux-rond . 25
6.2.4 Artéfacts d'épaisseur des dents. 26
6.2.5 Artéfacts de type pièce de fabrication. 26
6.3 Essais des artéfacts de développante à cercle de base modifié. 29
6.4 Artéfacts de broche (cylindrique), de plan (flanc) et de bille (sphérique) de forme autre
que de développante . 29
6.4.1 Types d'artéfacts de forme autre que de développante . 29
6.4.2 Fonction des artéfacts de forme autre que de développante . 31
6.4.3 Étalonnage d'un artéfact de plan . 32
6.4.4 Étalonnage d'un artéfact de broche ou de bille. 32
6.4.5 Effets de l'extrémité du palpeur lors du calcul de la courbe de référence . 32
6.4.6 Emplacement de mesure . 33
6.4.7 Interprétation des étalons de forme autre que de développante. 33
6.5 Essais des artéfacts d'hélice. 33
6.5.1 Essais des artéfacts d'hélice à pas hélicoïdal modifié . 33
6.5.2 Étalons d'hélice de forme autre que de développante. 34
6.6 Essais des artéfacts de pas à excentricité modifiée . 34
7 Directives relatives à l'estimation de l'incertitude. 34
7.1 Méthodes d'estimation de l'incertitude. 34
7.1.1 Méthodes générales. 35
7.1.2 Méthodes par comparaison . 35
7.2 Calcul de l'incertitude de mesure U . 36
7.3 Paramètres de mesure. 36
7.3.1 Paramètres d'ajustement de courbe . 37
7.3.2 Paramètres d'ajustement de bande. 37
7.3.3 Paramètres de pas . 37
8 Modes opératoires de mesure . 38
8.1 Traçabilité . 38
8.2 Conditions de fonctionnement . 38
8.2.1 Conditions relatives à la détermination du biais . 38
8.2.2 Conditions relatives à l'estimation de l'incertitude type. 38
8.2.3 Conditions relatives aux déterminations combinées. 38
8.3 Mesurages. 38
8.4 Mode opératoire d'étalonnage . 39
8.4.1 Configuration initiale et ajustements. 39
8.4.2 Mode opératoire d'étalonnage initial. 39
8.4.3 Mode opératoire d'étalonnage en continu. 39
8.4.4 Outillage et jauges . 40
9 Lignes directrices relatives à l'estimation de l'incertitude de mesure par comparaison. 40
9.1 Exemple de comparaison directe A . 40
9.2 Approche par comparaison, étendue à l'influence des caractéristiques de la pièce de
fabrication. 42
9.2.1 Exemple de comparaison B . 42
9.2.2 Exemple de comparaison C . 43
9.3 Approche par comparaison, étendue à l'influence des caractéristiques de la pièce de
fabrication et de la similarité de la géométrie. 45
10 Contrôle statistique du procédé. 46
10.1 Définitions. 46
10.2 Construction des cartes X et MR. 46
10.3 Critères indiquant un manque de contrôle. 47
10.4 Non-respect d'un ou de plusieurs critères de 10.3. 49
11 Aptitude à l'emploi d'un instrument. 49
11.1 Limitation de l'incertitude de mesure . 49
11.1.1 Méthode GPS de réduction de la tolérance. 49
11.1.2 Méthode du rapport de tolérance . 51
11.1.3 Ligne directrices relatives à l'incertitude de l'instrument. 51
11.2 Sources d'incertitude de mesure . 52
11.3 Réduction de l'incertitude de mesure . 53
11.3.1 Suivre un mode d'étalonnage différent. 53
11.3.2 Réduire l'incertitude de la certification de l'étalon de référence . 53
11.3.3 Améliorer le mode de mesure. 53
12 Corrélation entre les modes de mesure (instrument) . 54
12.1 Base de comparaison . 54
12.2 Corrélation entre mesurages . 54
Annexe A (informative) Effet de la température sur les engrenages et les artéfacts. 55
Annexe B (informative) Essais d'artéfacts de développante, d'hélice et de pas modifiés . 61
Annexe C (informative) Interprétation des artéfacts de broche, de bille ou de plan (flanc) en forme
autre que de développante. 72
Bibliographie . 92
iv © ISO 2005 – Tous droits réservés
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux de
normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est en général confiée
aux comités techniques de l'ISO. Chaque comité membre intéressé par une étude a le droit de faire partie du
comité technique créé à cet effet. Les organisations internationales, gouvernementales et non
gouvernementales, en liaison avec l'ISO participent également aux travaux. L'ISO collabore étroitement avec
la Commission électrotechnique internationale (CEI) en ce qui concerne la normalisation électrotechnique.
Les Normes internationales sont rédigées conformément aux règles données dans les Directives ISO/CEI,
Partie 2.
La tâche principale des comités techniques est d'élaborer les Normes internationales. Les projets de Normes
internationales adoptés par les comités techniques sont soumis aux comités membres pour vote. Leur
publication comme Normes internationales requiert l'approbation de 75 % au moins des comités membres
votants.
Exceptionnellement, lorsqu'un comité technique a réuni des données de nature différente de celles qui sont
normalement publiées comme Normes internationales (ceci pouvant comprendre des informations sur l'état
de la technique par exemple), il peut décider, à la majorité simple de ses membres, de publier un Rapport
technique. Les Rapports techniques sont de nature purement informative et ne doivent pas nécessairement
être révisés avant que les données fournies ne soient plus jugées valables ou utiles.
L'attention est appelée sur le fait que certains des éléments du présent document peuvent faire l'objet de
droits de propriété intellectuelle ou de droits analogues. L'ISO ne saurait être tenue pour responsable de ne
pas avoir identifié de tels droits de propriété et averti de leur existence.
L'ISO/TR 10064-5 a été élaboré par le comité technique ISO/TC 60, Engrenages.
L'ISO/TR 10064 comprend les parties suivantes, présentées sous le titre général Engrenages cylindriques —
Code pratique de réception:
— Partie 1: Contrôle relatif aux flancs homologues de la denture
— Partie 2: Contrôle relatif aux écarts composés radiaux, au faux-rond, à l'épaisseur de dent et au jeu entre
dents
— Partie 3: Recommandations relatives au corps de roues, à l'entraxe et au parallélisme des axes
— Partie 4: Recommandations relatives à la rugosité de surface et au contrôle de la marque de portée
— Partie 5: Recommandations relatives à l'évaluation des instruments de mesure des engrenages
RAPPORT TECHNIQUE ISO/TR 10064-5:2005(F)
Engrenages cylindriques — Code pratique de réception —
Partie 5:
Recommandations relatives à l'évaluation des instruments de
mesure des engrenages
1 Domaine d'application
La présente partie de l'ISO/TR 10064 propose des informations et des exemples supplémentaires destinés à
faciliter la mise en œuvre de l'ISO 18653. Il fournit des modes opératoires d'évaluation et d'étalonnage des
procédés de mesurage de la développante, de l'hélice, du pas, du faux-rond et de l'épaisseur des dents.
Des méthodes d'évaluation de l'état et de l'alignement d'éléments d'instrument tels que des axes, des
glissières, des systèmes de palpeurs, etc., ainsi que des recommandations concernant la mise en place d'un
environnement approprié et des modes opératoires statistiques d'évaluation des données sont proposés.
Il couvre également l'application d'artéfacts d'engrenage à l'estimation de l'incertitude du mesurage, U . Des
conseils sont fournis sur l'application des procédés de mesurage à la réception d'engrenages de production, y
compris l'aptitude à l'emploi et les limites recommandées de l'incertitude U en fonction des tolérances
d'exactitude des engrenages de production à inspecter.
De nombreuses recommandations peuvent s'appliquer également au mesurage de vis, de roues à vis, de
roues coniques et des outils de taillage d'engrenages.
2 Références normatives
Les documents de référence suivants sont indispensables pour l'application du présent document. Pour les
références datées, seule l'édition citée s'applique. Pour les références non datées, la dernière édition du
document de référence s'applique (y compris les éventuels amendements).
ISO 1122-1:1998, Vocabulaire des engrenages — Partie 1: Définitions géométriques
ISO 1328-1:1995, Engrenages cylindriques — Système ISO de précision — Partie 1: Définitions et valeurs
admissibles des écarts pour les flancs homologues de la denture
ISO 1328-2:1997, Engrenages cylindriques — Système ISO de précision — Partie 2: Définitions et valeurs
admissibles des écarts composés radiaux et information sur le faux-rond
ISO/TR 10064-1:1992, Engrenages cylindriques — Code pratique de réception — Partie 1: Contrôle relatif
aux flancs homologues de la denture
ISO/TR 10064-2:1996, Engrenages cylindriques — Code pratique de réception — Partie 2: Contrôle relatif
aux écarts composés radiaux, au faux-rond, à l'épaisseur de dent et au jeu entre dents
ISO/TR 10064-3:1996, Engrenages cylindriques — Code pratique de réception — Partie 3:
Recommandations relatives au corps de roues, à l'entraxe et au parallélisme des axes
ISO 10360-1:2000, Spécification géométrique des produits (GPS) — Essais de réception et de vérification
périodique des machines à mesurer tridimensionnelles (MMT) — Partie 1: Vocabulaire
ISO/TS 14253-1:1998, Spécification géométrique des produits (GPS) — Vérification par la mesure des pièces
et des équipements de mesure — Partie 1: Règles de décision pour prouver la conformité ou la non-
conformité à la spécification
ISO/TS 14253-2:1999, Spécification géométrique des produits (GPS) — Vérification par la mesure des pièces
et des équipements de mesure — Partie 2: Guide pour l'estimation de l'incertitude dans les mesures GPS,
dans l'étalonnage des équipements de mesure et dans la vérification des produits
ISO 18653:2003, Engrenages — Évaluation des instruments de mesure des engrenages individuels
Guide pour l'expression de l'incertitude de mesure (GUM), BIPM, CEI, IFCC, ISO, IUPAC, IUPAP, OIML,
3 Termes et définitions
Pour les besoins du présent document, les termes et définitions donnés dans l'ISO 1122-1, l'ISO 1328-1,
l'ISO 1328-2 et l'ISO 18653 s'appliquent.
4 Environnement de l'instrument
4.1 Environnement
La stabilité de l'environnement influe sur l'exactitude de l'étalonnage et sur le mesurage des pièces de
fabrication. Il convient que la température de mesure soit maintenue constante. Il est recommandé que la
température soit de 20 °C. Les normes ou les recommandations du fabricant de l'instrument exigent souvent
que l'environnement soit suffisamment régulé pour que des mesurages en continu atteignent l'exactitude
requise compte tenu de la température, de l'humidité, des vibrations, de la propreté et d'autres facteurs
contrôlables ayant un effet sur un mesurage de précision.
4.1.1 Paramètres importants
1)
Les paramètres suivants sont d'une importance primordiale :
⎯ milieu de refroidissement (de chauffage), habituellement de l'air;
⎯ débit, distribution et vitesse du milieu de refroidissement (de chauffage);
⎯ fréquence et amplitude des variations de température du milieu de refroidissement (de chauffage);
⎯ gradients de température au sein du milieu de refroidissement (de chauffage);
⎯ vibrations;
⎯ qualité de l'alimentation électrique.
1) On trouvera une discussion plus complète sur les effets de ces paramètres dans des normes telles que l'ASME
B89.6.2, Temperature and Humidity Environment for Dimensional Measurement R(2002).
2 © ISO 2005 – Tous droits réservés
4.1.2 Recommandations pratiques
On trouvera ci-dessous des recommandations pratiques concernant le mesurage des engrenages. Le respect
de ces recommandations ne garantit cependant pas qu'une exactitude spécifique des mesurages soit obtenue.
⎯ Température des artéfacts. Il convient d'accorder à l'outillage, aux artéfacts et aux autres éprouvettes
un temps suffisant pour que leur température se stabilise à la température ambiante. Dans l'idéal, il
convient que la température d'un artéfact soit celle à laquelle il a été étalonné.
⎯ Variation de température moyenne. Il convient de consulter les directives du fabricant de l'instrument
concernant les variations de température pour l'exactitude recherchée. Si cette information n'est pas
disponible, il est recommandé que la température moyenne ne varie pas plus de 1 °C par heure avec un
changement maximal de 3,5 degrés par jour.
⎯ Cycles de température. La température peut effectuer un cycle de ± 2 °C autour de la température
moyenne, toutes les 5 min ou plus rapidement. L'inertie thermique de la plupart des systèmes
mécaniques permet des ondulations cycliques rapides de la température dans le cadre des présentes
directives pour l'exactitude indiquée. Si le cycle de température de l'instrument approche de 1 °C en
15 min, de graves effets sur l'exactitude du système de mesurage peuvent apparaître. De nombreuses
personnes utilisent un climatiseur pour tenter d'obtenir un contrôle thermique. Les capteurs de
température de ce genre d'appareils peuvent être très lents à répondre aux changements de température.
Si la réponse prend plus de 5 min, on peut noter de graves effets sur l'exactitude de mesure.
⎯ Gradient de température. Il convient que le gradient de température soit inférieur à 0,5 °C sur toute la
surface de l'instrument. La meilleure manière de l'obtenir est d'utiliser un grand écoulement d'air.
L'écoulement d'air doit être uniforme dans tout le local pour éviter les angles morts et les gradients. Pour
l'obtenir, diffuser l'air arrivant dans le local et, dans la mesure du possible, prévoir des retours d'air
multiples afin de diffuser l'air plus uniformément dans le local. Le but est d'obtenir que tout l'air se déplace
de manière uniforme dans le local et qu'il soit à la même température. L'air en mouvement doit évacuer la
chaleur des commandes électroniques, des ordinateurs, des moteurs, des systèmes hydrauliques, des
personnes, des lampes, etc., afin d'éviter les gradients.
⎯ Vibrations. Il convient de ne pas laisser les vibrations causées par les mouvements de l'instrument
gêner les mesurages. Il convient également d'observer ou de mesurer les vibrations provenant de
l'environnement. Si elles affectent l'exactitude de l'instrument, il peut être nécessaire d'isoler ce dernier
des vibrations ou de lui donner un socle approprié.
⎯ Alimentation électrique. Des fluctuations de l'alimentation peuvent perturber le fonctionnement de
certains instruments électroniques et des ordinateurs des systèmes de positionnement à commande
numérique.
4.1.3 Environnement de l'atelier
Il est recommandé d'installer les instruments de mesure dans un local à température contrôlée. De nombreux
instruments de mesure se trouvent cependant dans un environnement de type atelier où il est difficile de
maintenir une incertitude de 5 microns dans les mesurages de procédé. L'accumulation de poussière ou
d'autres contaminants sur les glissières de l'instrument peut provoquer des imprécisions de même qu'une
usure prématurée.
Si un instrument doit être utilisé dans un environnement de ce genre, il faut prendre soin d'éviter certaines
situations, telles que
⎯ sources locales de chaleur radiante capables de déformer l'instrument, telles que des chaufferettes ou la
lumière solaire traversant des fenêtres proches;
⎯ évents de toiture faisant tomber de l'air froid sur l'instrument;
⎯ systèmes de refroidissement ou fenêtres ouvertes provoquant un courant d'air frappant un côté de
l'instrument.
Les formules de 4.2.1 et de 4.2.2 peuvent être utilisées aussi pour estimer l'effet d'une différence stable mais
constante de la température de l'instrument par rapport à la température normale (20 °C). Si les formules sont
utilisées, il convient que le coefficient de dilatation thermique (CET) soit celui du matériau de l'instrument ou la
valeur de l'échelle du codeur et il convient que le signe de la compensation résultante soit changé. Il convient
que l'utilisateur sache que les résultats sont susceptibles de varier en fonction de l'emplacement où est lue la
température.
4.2 Effet de la température sur les engrenages et les artéfacts
La température peut avoir un effet marqué sur la géométrie des engrenages et des artéfacts. Les effets de la
température sur les mesurages de l'inclinaison du profil en développante, f , de l'inclinaison d'hélice, f , et
Hα Hβ
de l'épaisseur des dents des roues à denture extérieure et des artéfacts peuvent être prévus à l'aide des
formules ci-dessous. De tels calculs supposent une température uniforme de l'éprouvette donnée; il n'est pas
facile en pratique de modéliser des variations localisées de la température. Ces calculs ne tiennent pas
compte de la température de l'instrument de mesure.
Il n'est pas tenu compte de la température de l'instrument de mesure dans ces calculs mais une différence
entre la température normale (20 °C) et la température de l'instrument provoque elle aussi des erreurs dans le
résultat de mesure.
Il peut être souhaitable de corriger les valeurs du mesurage de l'inclinaison du profil et de l'hélice en fonction
de l'effet de la température. De telles corrections sont requises par les méthodes d'estimation de U décrites
dans l'Article 7 du présent document.
On considère que des variations uniformes de la température d'un engrenage ou d'un artéfact n'ont pas d'effet
sur les paramètres de pas ou de faux-rond (position des dents).
4.2.1 Calcul de l'effet de la température sur le profil
Pour le mesurage du profil en développante, l'effet de la température peut être modélisé en considérant le
changement associé du diamètre du cercle de base. L'effet sur l'inclinaison du profil f peut être calculé
Hα
comme suit:
a) Données fournies (typiques):
z est le nombre de dents;
m est le module normal;
n
β est l'angle d'hélice;
α est l'angle de pression normal;
n
L est la longueur de roulement au début de l'analyse de profil;
αs
L est la longueur de roulement à la fin de l'analyse de profil;
αe
−6 −1
CET est le coefficient de dilatation thermique (approximativement 11,5 × 10 C pour l'acier).
NOTE Quand les points de départ et de fin de l'analyse de profil sont spécifiés en degrés d'angle de roulement
(ξ ), la conversion en longueur de roulement peut être effectuée à l'aide de la formule suivante.
y
ξ
⎛⎞
y
Ld= π (1)
()
yb⎜⎟
⎝⎠
b) Calculer le changement d'inclinaison dû à la différence de température:
∆=fL()−L(t−t)CTE (2)
Heαα αsas
4 © ISO 2005 – Tous droits réservés
où
t est la température réelle (mesurée);
a
t est la température normale (20 °C).
s
Voir l'Annexe A pour un exemple et des informations supplémentaires.
4.2.2 Calcul de l'effet de la température sur l'hélice
Pour le mesurage de l'hélice, l'effet de la température peut être modélisé en considérant le changement
associé du pas hélicoïdal. L'effet sur l'inclinaison de l'hélice, f , peut être estimé comme suit:
Hβ
a) Données (typiques) fournies en 4.2.1 a), plus:
L est la plage d'évaluation de l'hélice;
β
b) Calculer l'angle d'hélice de base, β :
b
ββ= arcsin()sin cosα (3)
bn
c) Calculer le changement d'inclinaison dû à la différence de température:
∆βfL=− tan t −t CTE (4)
()
Hbββ as
Voir l'Annexe A pour un exemple et des informations supplémentaires.
4.2.3 Calcul de l'effet de la température sur l'épaisseur des dents
Outre le profil en développante et l'hélice, l'épaisseur des dents peut être affectée de manière notable par la
température. Il est possible de modéliser ces effets en envisageant le changement associé de la section de la
dent qui coupe le diamètre primitif de fonctionnement, endroit où l'épaisseur des dents est habituellement
mesurée. L'effet de la température sur l'épaisseur normale des dents d'une roue à denture extérieure peut
être estimé comme suit:
a) Données (typiques) fournies en 4.2.1 a), plus:
s est l'épaisseur normale des dents au niveau du diamètre primitif de fonctionnement de référence, d;
n
b) Calculer le diamètre primitif de fonctionnement de référence, d:
m
n
dz= (5)
cosβ
c) Calculer le changement de l'épaisseur circulaire normale des dents au niveau du diamètre primitif de
fonctionnement de référence d'une roue à denture extérieure dû à la différence de température.
∆αsd=−tan()t t CTE (6)
nnas
Voir un exemple et des informations supplémentaires en Annexe A.
5 État du système de mesure
De nombreux facteurs affectent l'exactitude des instruments de mesure des engrenages. Ils incluent
l'équerrage et le parallélisme des glissières de l'instrument l'une par rapport à l'autre et par rapport au plateau
tournant, la rectitude des glissières, les erreurs de positionnement linéaire et les erreurs de mouvement
angulaire (pas, roulis et lacet) des composants mobiles de l'instrument. Les erreurs causées par les
composants électroniques, les balances, les commandes et le logiciel peuvent avoir elles aussi des effets
négatifs sur l'exactitude d'un instrument de mesure. Il existe diverses méthodes permettant de mesurer ces
erreurs. Bien qu'une discussion complète sur la cinématique et les commandes électroniques des machines
sorte du cadre du présent document, il est recommandé aux utilisateurs de ces instruments d'être conscients
de l'existence des nombreuses sources possibles d'imprécision.
Certains fabricants d'instruments de mesure fournissent des modes opératoires détaillés pour la vérification
périodique de la conformité du produit aux caractéristiques d'usine d'origine. Les essais généralisés et les
tolérances recommandées que l'on trouve dans la présente section sont à utiliser en l'absence ou en sus de
modes opératoires recommandés par le fabricant de l'instrument. Ces essais ne doivent pas se substituer aux
modes opératoires du fabricant.
Il convient d'identifier la classe d'exactitude et les paramètres à vérifier sur les engrenages avant de
commencer les vérifications. Il convient que l'enveloppe de travail réelle soit elle aussi connue. Il convient
d'enregistrer le résultat de tous les essais afin de documenter ce travail de vérification et de recueillir des
données pour une analyse statistique.
5.1 Mode d'évaluation des instruments génératifs
Le bon fonctionnement des éléments importants des instruments de mesure des engrenages peut être vérifié
par les modes opératoires précisés dans le présent paragraphe. Il convient que cette vérification commence
par une inspection visuelle de l'instrument pour s'assurer de l'absence de toute condition préjudiciable
évidente capable de gêner le bon fonctionnement de ce dernier. Il convient de vérifier les pointes, les
entraînements et les stylets des palpeurs de mesurage qui peuvent s'user et être endommagés. Confirmer
également que les conditions environnementales répondent aux exigences de 4.1.
Il convient que les systèmes de palpeurs et les indicateurs qui mesurent les erreurs des instruments soient
étalonnés et qu'ils aient une résolution appropriée (il est recommandé que cette résolution soit inférieure ou
égale à 1 µm). Il convient que l'utilisateur note que les filtres et les taux de saisie des données influent sur le
résultat des mesures. Voir 5.4 pour des informations supplémentaires.
5.1.1 Vérification des pointes de montage
Pour inspecter la géométrie des engrenages par des procédés génératifs, il est nécessaire de monter
l'engrenage de manière que son axe de rotation de référence coïncide avec l'axe du fuseau principal de
l'instrument. Voir l'ISO/TR 10064-3. Toute excentricité ou absence de parallélisme de ce montage provoque
une erreur des résultats de mesure. Voir Figure 1.
Une pratique courante consiste à monter entre des pointes les engrenages à soumettre à essai. La plupart
des instruments de vérification d'engrenages sont équipés de pointes, l'une sur le fuseau principal et l'autre
sur un montage de contrepointe. Le mauvais alignement et le faux-rond de ces pointes sont fréquents. Il
convient donc que la vérification des instruments utilisés pour les essais commence par l'observation de ces
pointes de montage.
6 © ISO 2005 – Tous droits réservés
Légende
1 axe entre les pointes
2 axe du fuseau de travail
3 erreur
Figure 1 — Erreur d'alignement entre l'axe du fuseau et l'axe entre les pointes
5.1.1.1 Faux-rond des pointes
À l'aide d'un indicateur ayant une résolution appropriée, mesurer le faux-rond (TIR) de la pointe du fuseau
principal dans une direction normale par rapport à la surface. Il convient que ce mesurage de faux-rond soit
conforme aux spécifications du fabricant ou aux directives données dans le Tableau 1. Il est conseillé de
mesurer le faux-rond de chaque pointe au niveau du petit bout et du grand bout afin de détecter les pointes
courbées ou faussées.
Tableau 1 — Recommandations relatives aux écarts lors de la vérification
a
de l'alignement d'un instrument
Degré Parallélisme de l'axe Z avec l'axe du fuseau dans
Alignement de la
d'exactitude à toute région de 200 mm mesurée
pointe supérieure
Faux-rond de
vérifier
centres (TIR) avec l'axe du
b c
A B
fuseau (TIR) par 200
µm
ISO 1328-1
µm µm
d
mm
ISO 1328-2
2 1 1 2 2
3 1 2 2 2
4 1 2 3 3
5 2 3 4 4
6 2 4 6 6
7 3 5 6 6
8 4 5 6 6
9 5 7 6 6
10 7 10 8 8
Tableau 1 (suite)
Degré Parallélisme de l'axe Z avec l'axe du fuseau dans
Alignement de la
d'exactitude à toute région de 200 mm mesurée
Faux-rond de pointe supérieure
vérifier
avec l'axe du
centres (TIR)
b c
A B
µm fuseau (TIR) par 200
ISO 1328-1
µm µm
d
mm
ISO 1328-2
11 10 10 12 12
12 10 10 12 12
a
Les lignes directrices concernent des instruments polyvalents. Un ou plusieurs des paramètres peuvent suffire dans le cas
d'instruments spécialisés.
b
Dans le plan de mesure (tangente à la base). Voir Figure 5.
c
Perpendiculaire au plan de mesure. Voir Figure 6.
d
La tolérance d'alignement est la plus grande des deux valeurs suivantes: 2 µm ou la tolérance du tableau par 200 mm de la
longueur, R, dans les Figures 3 et 4.
Charger les fuseaux en montant un arbre entre les pointes. La longueur, l'exactitude et la configuration de cet
arbre ne sont pas importantes. Voir Figure 2.
Légende
1 pointe vive de la contrepointe
2 pointe du fuseau de travail
Figure 2 — Essai du faux-rond des pointes
5.1.1.2 Positionnement de la contrepointe
Lors des essais, une pratique souvent appelée balayage peut être utilisée pour évaluer efficacement la
position de la contrepointe par rapport à l'axe du fuseau principal. Un balayage de la contrepointe en un seul
emplacement sur le coulisseau de la contrepointe ne vérifie son positionnement pour les essais d'engrenages
qu'en cet emplacement. Un balayage de ce centre réalisé en plaçant le coulisseau de la contrepointe en deux
endroits nettement séparés permet de vérifier à la fois le positionnement latéral et l'alignement angulaire du
coulisseau de la contrepointe par rapport à l'axe du fuseau principal. S'il se confirme par d'autres procédés
8 © ISO 2005 – Tous droits réservés
que la rectitude du déplacement du coulisseau de la contrepointe respecte les spécifications du fabricant, un
essai en deux emplacements vérifie le positionnement de la contrepointe à tous les emplacements. Sinon, un
balayage de la contrepointe au moins en trois emplacements nettement séparés dans sa plage de
fonctionnement est nécessaire. Dans le cas d'engrenages de haute qualité, il est recommandé d'effectuer un
balayage de la contrepointe dans chaque configuration unique avant réception.
Deux montages d'essai de balayage vont être décrits.
a) Le premier n'est recommandé que pour des instruments ayant un axe de fuseau principal vertical. La
Figure 3 donne un exemple de ce montage. Les fuseaux sont chargés en montant un arbre entre les
pointes. L'exactitude et la configuration de cet arbre ne sont pas importants car l'indicateur et l'arbre
tournent ensemble. Il est normalement requis d'effectuer au moins deux essais de balayage de ce type,
en utilisant pour chacun des arbres de longueur différente. Dans le cas d'un essai sur un instrument qui
comporte un disque de base, il convient que l'essai soit réalisé avec un disque de base au contact du
coulisseau tangent à la base pour s'assurer que les effets du jeu du fuseau sont inclus. Il convient de
choisir la longueur des deux arbres vers les extrémités opposées de la plage de fonctionnement de la
contrepointe.
Un indicateur ayant une résolution appropriée est monté de manière à être porté par le fuseau principal
en rotation et à mesurer simultanément dans une direction radiale l'alignement (TIR) de l'arbre à
proximité de la contrepointe. Il convient que le mesurage de l'alignement de la contrepointe sur l'axe de la
broche soit conforme aux valeurs données au Tableau 1.
La valeur est indiquée en tant que rapport entre l'alignement admissible du centre (TIR) et la distance
axiale de ce mesurage par rapport à la pointe du fuseau principal. La valeur recommandée varie donc
avec l'emplacement du mesurage et il convient de l'ajuster en conséquence. La valeur de la tolérance est
la plus grande des deux valeurs suivantes: 2 µm ou la tolérance du tableau par 200 mm de la longueur, R,
à la Figure 3.
Légende
1 axe entre les pointes
2 axe du fuseau de travail
3 erreur
Figure 3 — Méthode de mesure de l'alignement de la contrepointe
(instruments à axe vertical seulement)
b) Le second dispositif d'essai de balayage est recommandé pour des instruments ayant un fuseau principal
dont l'axe est horizontal mais il peut être utilisé aussi pour des instruments verticaux. La Figure 4 donne
un exemple de ce dispositif. Cette figure montre le dispositif de balayage réalisé en deux emplacements,
L et L . Comme précédemment, les fuseaux sont chargés en montant des arbres de différentes
1 2
longueurs entre les pointes aux deux emplacements.
Dans ce cas, un indicateur ayant une résolution appropriée est monté de manière qu'il soit porté par
l'arbre d'essai en rotation et qu'il mesure en direction axiale l'alignement (TIR) d'un dispositif porté par le
fuseau principal en rotation. Il convient que les mesures de l'alignement de la contrepointe sur l'axe du
fuseau soient conformes aux valeurs données au Tableau 1.
La valeur est donnée comme le rapport entre l'alignement admissible des pointes (TIR) et la distance
axiale à partir de la pointe du fuseau principal. La valeur recommandée change donc avec l'emplacement
du mesurage et il convient de l'ajuster en conséquence. La tolérance est la plus grande des deux valeurs
suivantes: 2 µm ou la tolérance du tableau par 200 mm de la longueur, R, dans la Figure 4.
Légende
1 fuseau de tr
...
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