A complete - and first ever at INRIM - calibration of a master gear is described. This includes the evaluation of the uncertainty of measurement, which is particularly challenging for this type of complex calibration

Balsamo, A.

Corona, D.

A. Balsamo

D. Corona

Archivio istituzionale della ricerca - INRIM

MacroScale  Recent developments in traceable dimensional measurements   Calibration of a 400 mm helical master gear at INRIM  Alessandro Balsamo1,*, Davide Corona1 1 INRIM – Istituto Nazionale di Ricerca Metrologica – Torino (Italy)  * Corresponding author: a.balsamo@inrim.it  Keywords : gear, calibration, lead, profile, pitch  Abstract Gears are extremely important mechanical components in very many manufactured products, and crucial in powertrain applications: whenever mechanical power is to be transmitted and/or transformed in angular speed and/or rotation axis, gears enter the game. Just as any other mechanical component, gears range the full scale of size and requirements. Of interest here are the ones with the topmost quality, i.e. bearing the strictest tolerances. In particular, gear masters are intended to provide measurement traceability to gears, and are then required the highest accuracy. In spite of the very large economic impact of gears, only seven NMI’s world-wide (three in Euramet) have CMC’s registered in the KCDB in this calibration field, and not all covering all areas. In particular, only four (one in Euramet) have got CMC’s for lead masters. The European project Drivetrain (EMRP ENG56, ending on August 2017) is about large drivetrain components particularly for wind energy systems. Among its objectives, it aims at improving the gear calibration infrastructure, providing committed project partners – including the INRIM – with the opportunity of investigating and exercise. A project deliverable was the calibration of a 400 mm helical master gear. The measurands were the profiles and the leads of four selected teeth angularly spaced 90° about the gear axis, and the pitch and runout. The calibration occurred at the INRIM in December 2016 and January 2017 and was done with a CMM (Leitz PMM-C 12107) not equipped with a rotary table. Because of that, the stylus system was set up with four horizontal equally spaced styli. A fifth vertical stylus was added for alignment of the master – thus completing the conventional star set up (see figure).  The calibration was carried out in two steps, following common practice at INRIM for calibrations by means of coordinate metrology. MacroScale  Recent developments in traceable dimensional measurements  1. The first step was intended to introduce traceability. Three mutually orthogonal elementary features of the master, each aligned to a CMM axis, were calibrated. As these calibrations were done prior to the rest, they were referred to as pre-calibrations. The features were two point-to-point internal diameters of the upper flange (along x and y) and the axial separation of the upper and lower faces (along z). Because the shaft seat prevented a direct axial measurement and for sake of symmetry, the face separation was defined more precisely as the mean separation of two corresponding point pairs on the upper and lower flanges, symmetrically to the gear axis. Each feature was calibrated by comparison with an aligned calibrated gauge block of similar length. 2. The second step performed the full measurement of the master, as well as a repetition of the measurement of the three pre-calibrated features. The x coordinates of all measured points were stretched (i.e. multiplied by a common factors close to unity) to make the repeated measurement value of the pre-calibrated x feature match the pre-calibrated value. The same was done separately for y and z. This way, the traceability brought in by the pre-calibrated features was extended to all other features. The first step only suffered uncertainty due to thermal expansion, as the stretches occurring in the second automatically recovered any expansion (no thermal compensation done in the second step). The evaluation of the uncertainty was particularly challenging (more details in the presentation): • The input uncertainties were evaluated based on experimental data or expert judgment. The important effect of the scanning probing was evaluated experimentally by scanning a reference sphere: paths were selected accurately to have normal directions to the material mimicking those of the actual tooth measurement, separately for profile and lead scans. • The geometric complexity of the teeth prevented a rigorous analytic derivation of the sensitivity coefficients as partial derivatives. Simplified intuitive models were considered but not used, as this calibration was the first ever in the laboratory and no previous experience was available to validate any simplification. The sensitivity coefficients most difficult to predict were derived by adapting the suggestion given in [1] § 5.1.3 Note 2. The measured points were collectively perturbed in software to simulate each individual error of a known amount (e.g. a 50 µrad rotation about the axis x to simulate the effect of a poor establishment of the coordinate system), the gear re-evaluated, and the sensitivity coefficients derived as incremental ratios. The exercise was not a formal comparison. Nevertheless, the results were compared with reference calibration values provided by the NGML (GB). The comparison was satisfactory, with all normalized errors less than unity but one isolated case slightly in excess. The uncertainty achieved was in line with other NMIs’ holding gear CMC’s. This poses the basis for submitting a new CMC. Not using a rotary table for the calibration cleared from a number of table-related uncertainty components. On the other hand, the scanning probing system was exercised over a range of spatial directions, instead of essentially a single direction as in the case of the rotary table. It was no surprise that the uncertainty budget resulted dominated by the scanning probing system.  [1] JCGM 100:2008 Evaluation of measurement data — Guide to the expression of uncertainty in measurement 

Calibration of a 400 mm helical master gear at INRIM

CINECA IRIS Institutional Research Information System

MacroScale  
Recent developments in traceable dimensional measurements 
 
 
Calibration of a 400 mm helical master gear at INRIM 
 
Alessandro Balsamo1,*, Davide Corona1 
1 INRIM – Istituto Nazionale di Ricerca Metrologica – Torino (Italy) 
 
* Corresponding author: a.balsamo@inrim.it 
 
Keywords : gear, calibration, lead, profile, pitch 
 
Abstract 
Gears are extremely important mechanical components in very many manufactured products, 
and crucial in powertrain applications: whenever mechanical power is to be transmitted and/or 
transformed in angular speed and/or rotation axis, gears enter the game. Just as any other 
mechanical component, gears range the full scale of size and requirements. Of interest here are 
the ones with the topmost quality, i.e. bearing the strictest tolerances. In particular, gear masters 
are intended to provide measurement traceability to gears, and are then required the highest 
accuracy. 
In spite of the very large economic impact of gears, only seven NMI’s world-wide (three in 
Euramet) have CMC’s registered in the KCDB in this calibration field, and not all covering all 
areas. In particular, only four (one in Euramet) have got CMC’s for lead masters. 
The European project Drivetrain (EMRP ENG56, ending on August 2017) is about large 
drivetrain components particularly for wind energy systems. Among its objectives, it aims at 
improving the gear calibration infrastructure, providing committed project partners – including 
the INRIM – with the opportunity of investigating and exercise. A project deliverable was the 
calibration of a 400 mm helical master gear. The measurands were the profiles and the leads 
of four selected teeth angularly spaced 90° about the gear axis, and the pitch and runout. 
The calibration occurred at the INRIM in December 2016 and January 2017 and was done with 
a CMM (Leitz PMM-C 12107) not equipped with a rotary table. Because of that, the stylus 
system was set up with four horizontal equally spaced styli. A fifth vertical stylus was added 
for alignment of the master – thus completing the conventional star set up (see figure). 
 
The calibration was carried out in two steps, following common practice at INRIM for 
calibrations by means of coordinate metrology. 
MacroScale  
Recent developments in traceable dimensional measurements 
 
1. The first step was intended to introduce traceability. Three mutually orthogonal 
elementary features of the master, each aligned to a CMM axis, were calibrated. As 
these calibrations were done prior to the rest, they were referred to as pre-calibrations. 
The features were two point-to-point internal diameters of the upper flange (along x 
and y) and the axial separation of the upper and lower faces (along z). Because the shaft 
seat prevented a direct axial measurement and for sake of symmetry, the face separation 
was defined more precisely as the mean separation of two corresponding point pairs on 
the upper and lower flanges, symmetrically to the gear axis. Each feature was calibrated 
by comparison with an aligned calibrated gauge block of similar length. 
2. The second step performed the full measurement of the master, as well as a repetition 
of the measurement of the three pre-calibrated features. The x coordinates of all 
measured points were stretched (i.e. multiplied by a common factors close to unity) to 
make the repeated measurement value of the pre-calibrated x feature match the 
pre-calibrated value. The same was done separately for y and z. 
This way, the traceability brought in by the pre-calibrated features was extended to all other 
features. The first step only suffered uncertainty due to thermal expansion, as the stretches 
occurring in the second automatically recovered any expansion (no thermal compensation done 
in the second step). 
The evaluation of the uncertainty was particularly challenging (more details in the 
presentation): 
• The input uncertainties were evaluated based on experimental data or expert judgment. 
The important effect of the scanning probing was evaluated experimentally by scanning 
a reference sphere: paths were selected accurately to have normal directions to the 
material mimicking those of the actual tooth measurement, separately for profile and 
lead scans. 
• The geometric complexity of the teeth prevented a rigorous analytic derivation of the 
sensitivity coefficients as partial derivatives. Simplified intuitive models were 
considered but not used, as this calibration was the first ever in the laboratory and no 
previous experience was available to validate any simplification. The sensitivity 
coefficients most difficult to predict were derived by adapting the suggestion given in 
[1] § 5.1.3 Note 2. The measured points were collectively perturbed in software to 
simulate each individual error of a known amount (e.g. a 50 µrad rotation about the 
axis x to simulate the effect of a poor establishment of the coordinate system), the gear 
re-evaluated, and the sensitivity coefficients derived as incremental ratios. 
The exercise was not a formal comparison. Nevertheless, the results were compared with 
reference calibration values provided by the NGML (GB). The comparison was satisfactory, 
with all normalized errors less than unity but one isolated case slightly in excess. The 
uncertainty achieved was in line with other NMIs’ holding gear CMC’s. This poses the basis 
for submitting a new CMC. 
Not using a rotary table for the calibration cleared from a number of table-related uncertainty 
components. On the other hand, the scanning probing system was exercised over a range of 
spatial directions, instead of essentially a single direction as in the case of the rotary table. It 
was no surprise that the uncertainty budget resulted dominated by the scanning probing system. 
 
[1] JCGM 100:2008 Evaluation of measurement data — Guide to the expression of 
uncertainty in measurement 


English

https://iris.inrim.it/retrieve/handle/11696/56785/17266/2017-10%20Macroscale%20-%20taratura%20master%20gear.pdf

Calibration of a 400 mm helical master gear at INRIM

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