Questo rapporto tecnico descrive la taratura di un segmento di anello di un cuscinetto a sfere. L’INRIM ha progettato il segmento di anello che è stato quindi prodotto dalla MG Marposs S.p.a. di Torino. La taratura è stata eseguita con la macchina a coordinate CMM/ST001 dell’INRIM.

Questo lavoro si colloca all’interno del Progetto DriveTrian (ENG56) come deliverable 2.2.3.This technical report describes the calibration of a ball bearing ring segment. INRIM designed the ring segment to be representative of bearing rings Ø > 1 m and MG Marposs S.p.a. (Turin, Italy) manufactured the workpiece. The calibration has been performed with the coordinate measuring machine CMM/ST001 at INRIM.

The present work is related to the deliverable 2.2.3 of Drive Train Poject (ENG56)

Balsamo, Alessandro

Corona, Davide

CINECA IRIS Institutional Research Information System

 
 
 
 
 
 
 
 
 
 
 
 
A. Balsamo, D. Corona,  
 
Calibration of a Master Gear   
 
T.R. 19/2017                                  September 2017 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
I.N.RI.M. TECHNICAL REPORT 
Abstract   
This technical report describes the calibration of a master gear provided by Newcastle University. The 
calibration has been performed with the coordinate measuring machine CMM/ST001 at INRIM, with the 
master gear mounted on the workpiece table (no rotary table) and a star configuration of the stylus system. 
The present work is related to the deliverable 2.1.9 of Drive Train Poject (ENG56). 
 
 
Questo rapporto tecnico  descive la taratura di un Master Gear fornito dall’università di Newcastle. La 
taratura è stata condotta con la macchina a coordinate CMM/ST001 dell’INRIM nella configurazione con il 
Master Gear montato sulla tavola (non rotante) e con un tastatore a stella. 
Questo lavoro si colloca all’interno del Progetto DriveTrian (ENG56) come deliverable 2.1.9. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Pag. 1 / 5 
 
1. MEASURAND, MEASUREMENT PROCEDURE AND CONDITIONS 
 
1.1 Measurands 
 
The measurands are the profile parameters (fH, ff, F) and lead parameters (fH, ff, F) of the left and 
right flanks of teeth 1, 9, 17 and 25, the pitch parameters (fp, Fp) and the runout (Fr) [1, 2]. 
 
The nominal parameters of the gear are summarised in the following table. 
 
Diameter Facewidth Teeth Helix angle 
Normal 
Module 
Pressure 
angle 
Base 
diameter 
d b z  mn n db 
390.048 mm 100 mm 32 35° RH 10 mm 20° 356.994 
 
The profile parameters are evaluated in the range (377 – 407) mm of the length or roll. The lead 
parameters are evaluated along the facewidth with exclusion of 10 mm on each side (i.e. in the range 
(10 – 90) mm of the axial coordinate, while the full facewidth scans (0 – 100) mm). 
The diameter of the theoretical sphere used to evaluate the runout is 18 mm. 
 
1.2 Procedure 
 
The calibration is performed with the coordinate measuring machine CMM/ST001, with the master 
gear mounted on the workpiece table (no rotary table) and a star configuration of the stylus system.  
 
 
Figure 1: Mounting arrangement. 
 
1,2,3,4: probe tips used to scan the gear surfaces (the vertical one is for alignment only). 
3,4: thermometers. 
 
The calibration is done in two steps with different measurands: a preliminary calibration (hereafter 
referred to as precalibration) and the actual calibration. 
 
 Precalibration. Two radial and an axial features of the master gear are calibrated by comparison 
with calibrated gauge blocks (see figure 2): 
Pag. 2 / 5 
 
o Two orthogonal point-to-point external diameters of the upper shoulder, lx and ly, aligned to the 
CMM x and y axes, respectively; they are calibrated by comparison with the calibrated 400 mm 
gauge block CEJ s/n 750004. 
o The average of two point-to-point distances of the upper to the lover shoulders, lz1 and lz2, in the 
axial direction, in two point pairs opposite to the gear axis
1
; each distance is calibrated by 
comparison with the calibrated 100 mm gauge block CARY 100 s/n 40077. 
 Actual calibration. All measurands of the master gear are measured while the precalibrated 
features are remeasured. The (x,y,z) coordinates of all sampled points are multiplied by three 
global scale factors, respectively and independently for each axis, equal to the ratios of the 
pre-calibrated values to the currently measured ones. This way the actual values of the 
precalibrated features are brought back to their traceable precalibrated values; as the same scale 
factors are applied to all sampled points, the traceability is extended to all measurands. 
 
 
Figure 2: Features of the master gear precalibrated at step 1, to introduce traceability. 
 
To minimise the effects of the CMM geometry errors, the calibrated gauge blocks used at step 1 are 
aligned parallel and fixtured as close as possible to the features under precalibration. This way the 
effects of the CMM geometry errors are second order and neglected. 
 
The deviation of the mean temperatures of the gear and of the calibrated gauge blocks from the 
standard reference temperature (20 °C [3]) is relevant to the precalibration and is compensated for. 
On the contrary, it is not to the actual calibration as the scale factors applied to all sampled points 
already include and compensate for thermal expansion effects. 
 
1.3 Environmental conditions 
 
The gear and gauge blocks temperatures varied during the measurement in the range 
(19.84 - 20.26) °C. The value of the thermal expansion coefficient (CTE) of the gear was assumed at 
(11.5 ± 2.5) × 10
-6
 K
-1
. 
 
 
 
 
 
 
 
 
 
 
 
 
                                                          
1
 The average is taken for sake of symmetry, as the gear seat makes the central portion of the gear 
unavailable. 
l
y
 
l
x
 
l
z1
 l
z2
 
Pag. 3 / 5 
 
2. MEASUREMENT RESULTS AND ASSOCIATED UNCERTAINTIES 
 
2.1 Results 
 
The calibration values and their uncertainties are reported in the two tables below. 
 
Flank Left Right Uncertainty 
Tooth 25 17 9 1 1 9 17 25 U 
fH 2.85 4.44 2.30 0.87 6.97 7.54 6.56 7.89 1.0 
F 3.71 4.75 3.05 2.57 7.49 8.07 6.72 7.99 1.0 
ff 1.55 1.57 1.56 2.47 2.23 2.54 1.97 2.05 1.0 
fH -2.87 -5.78 -2.83 2.47 2.76 -4.79 -7.71 -4.47 1.0 
F 4.37 6.84 3.70 4.02 2.83 5.54 8.29 5.27 1.0 
ff 2.02 1.15 1.56 4.13 1.25 1.63 0.93 1.20 1.0 
All values in micrometres (apart from the tooth numbering) 
 
   Uncertainty 
Flank Left Right U 
fp 5.23 4.13 0.6 
Fp 12.40 23.27 2.7 
Fr 26.27 1.9 
All values in micrometres 
 
The graphical report of a measurement repetition is given in the attachment. 
  
2.2 Uncertainty 
 
The uncertainty of measurement is summarised in the following tables. 
 
Precalibration 
Input uncertainty 
u(xi) 
Sensitivity 
ci 
Standard 
component 
ui(y)/µm 
Gauge block calibration 0,025 µm 1 
 
0,025 
Gauge block temperature 0,023 K 1,150 µm/K 0,027 
Gauge block CDT 0,577 × 10
-6
/K -0,010 K m -0,006 
Gear temperature 0,023 K -1,448 µm/K -0,033 
Gear CDT 1,443 × 10
-6
/K 0,019 K m 0,028 
resolution 0,014 µm 2 
 
0,029 
Probe unidir. reproducibility 0,058 µm 2 
 
0,115 
Overall repeatability 0,074 µm 1 
 
0,074 
 
   
u(y) 0,151 
 
Pag. 4 / 5 
 
Actual calibration       fH     F     ff   
  
 
ci ui(y) ci ui(y) ci ui(y) 
   u(xi)      /µm     /µm     µm 
Scale factor, x 0.67 × 10
-6
 0.019 m 0.01 0.017 m 0.01 0.000 m 0.00 
Scale factor, y 0.71 × 10
-6
 0.018 m 0.01 0.016 m 0.01 -0.001 m 0.00 
Scale factor, z 1.20 × 10
-6
 -0.002 m 0.00 -0.001 m 0.00 0.000 m 0.00 
Axis localisation, x 0.17 µm -0.096  -0.02 0.018 
 
0.00 -0.002 
 
0.00 
Axis localisation, y 0.17 µm -0.089  -0.02 0.020 
 
0.00 0.001 
 
0.00 
Axis localisation. z 0.17 µm 0.000  0.00 0.000 
 
0.00 0.000 
 
0.00 
Axis orientation. about x 3.92 µrad 0.002 m 0.01 -0.005 m -0.02 0.000 m 0.00 
Axis orientation. about y 3.92 µrad 0.006 m 0.02 0.006 m 0.02 -0.001 m 0.00 
Temperature variations 0.087 K 0.175 µm/K 0.02 0.155 µm/K 0.01 0.004 µm/K 0.00 
Probing anisotropy 0.44 µm 1 
 
0.44 1 
 
0.44 1 
 
0.44 
CMM geometry (over a profile) 0.2 µm 1 
 
0.20 1 
 
0.20 1 
 
0.20 
Reproducibility fH 0.16 µm 1 
 
0.16   
 
0.00   
 
0.00 
Reproducibility F 0.17 µm   
 
0.00 1 
 
0.17   
 
0.00 
Reproducibility ff 0.17 µm   
 
0.00   
 
0.00 1 
 
0.17 
      uc(y) 0.51   uc(y) 0.51   uc(y) 0.51 
(k = 2)   
 
Uc(y) 1.02  Uc(y) 1.03  Uc(y) 1.02 
 
Actual calibration       fH     F     ff   
  
 
ci ui(y) ci ui(y) ci ui(y) 
   u(xi)      /µm     /µm     µm 
Scale factor. x 0.67 × 10
-6
  0.000 m  0.00 0.000 m 0.00 0.000 m 0.00 
Scale factor. y 0.71 × 10
-6
 0.000 m 0.00 0.000 m 0.00 0.000 m 0.00 
Scale factor. z 1.20 × 10
-6
 0.000 m 0.00 0.000 m 0.00 0.000 m 0.00 
Axis localisation. x 0.17 µm 0.000 
 
0.00 0.000 
 
0.00 0.000 
 
0.00 
Axis localisation. y 0.17 µm 0.000 
 
0.00 0.000 
 
0.00 0.000 
 
0.00 
Axis localisation. z 0.17 µm 0.000 
 
0.00 -0.092 
 
-0.02 0.000 
 
0.00 
Axis orientation. about x 3.92 µrad 0.038 m 0.15 0.000 m 0.00 -0.001 m 0.00 
Axis orientation. about y 3.92 µrad 0.014 m 0.05 0.025 m 0.10 0.002 m 0.01 
Temperature variations 0.087 K 0.001 µm/K 0.00 0.003 µm/K 0.00 0.004 µm/K 0.00 
Probing anisotropy 0.45 µm 1 
 
0.45 1 
 
0.45 1 
 
0.45 
CMM geometry (over a lead) 0.15 µm 1 
 
0.20 1 
 
0.20 1 
 
0.20 
Reproducibility fH 0.10 µm 1 
 
0.10   
 
0.00   
 
0.00 
Reproducibility F 0.16 µm   
 
0.00 1 
 
0.16   
 
0.00 
Reproducibility ff 0.09 µm   
 
0.00   
 
0.00 1 
 
0.09 
      uc(y) 0.51   uc(y) 0.51   uc(y) 0.48 
(k = 2)     Uc(y) 1.02   Uc(y) 1.02   Uc(y) 0.96 
 
Actual calibration       fp     Fp     fr   
  
 
ci ui(y) ci ui(y) ci ui(y) 
   u(xi)      /µm     /µm     µm 
Scale factor. x 0.67 × 10
-6
 0.033 m  0.02 0.127 m  0.09 0.062 m 0.04 
Scale factor. y 0.71 × 10
-6
 0.024 m 0.02 0.126 m 0.09 0.014 m 0.01 
Scale factor. z 1.20 × 10
-6
 0.000 m 0.00 0.000 m 0.00 0.000 m 0.00 
Axis localisation. x 0.17 µm 0.169 
 
0.03 1.947 
 
0.34 1.094 
 
0.19 
Axis localisation. y 0.17 µm 0.206 
 
0.04 2.024 
 
0.35 1.580 
 
0.27 
Axis localisation. z 0.17 µm 0.000 
 
0.00 0.000 
 
0.00 0.000 
 
0.00 
Axis orientation. about x 3.92 µrad 0.020 m 0.08 0.237 m 0.93 -0.020 m -0.08 
Axis orientation. about y 3.92 µrad 0.027 m 0.11 0.159 m 0.62 0.128 m 0.50 
Temperature variations 0.087 K 0.271 µm/K 0.02 1.188 µm/K 0.10 0.422 µm/K 0.04 
Probing anisotropy 0.35 µm  0.342 
 
0.12  0.342 
 
0.12  1 
 
0.35 
CMM geometry (over full section) 0.2 µm 1 
 
0.20 1 
 
0.20  1 
 
0.20 
Reproducibility fp 0.14 µm 1 
 
0.14   
 
0.00   
 
0.00 
Reproducibility Fp 0.51 µm   
 
0.00 1 
 
0.51   
 
0.00 
Reproducibility fr 0.59 µm   
 
0.00   
 
0.00 1 
 
0.59 
      uc(y) 0.31   uc(y) 1.35   uc(y) 0.94 
(k = 2)     Uc(y) 0.61   Uc(y) 2.71   Uc(y) 1.87 
 
The input uncertainty due to the probe anisotropy is evaluated experimentally (type A). A reference 
sphere with negligible form error is scanned along a path designed to mimic the exact directions of 
contact when scanning the gear. This is done separately for the profile and the lead measurements. 
 
The sensitivity coefficients for the scale factors and the axis localisation and orientation are evaluated 
by simulation: arbitrary scale factors and an arbitrary rototranslation is applied to all scanned points 
and then the derived values are evaluated again. These variations are imposed one at a time to 
identify individual effects. 
 
Pag. 5 / 5 
 
The reported expanded uncertainty of measurement U is stated as the standard uncertainty of 
measurement multiplied by the coverage factor k = 2, which for a normal distribution corresponds to a 
coverage probability of approximately 95%.  
 
In the evaluation of the standard uncertainty, the long-term stability of the object under measurement 
has not been considered.  
 
REFERENCES 
[1] ISO 701:1998 International gear notation – Symbols for geometrical data 
[2] ISO 1328-2:1997 Cylindrical gears – ISO system of flank tolerance classification – Part 1: 
Definitions and allowable values of deviations relevant to flanks of gear teeth 
[3] EN ISO 1:2016 Geometrical product specifications (GPS) – Standard reference temperature for 
the specification of geometrical and dimensional properties 
 
ATTACHED DOCUMENTS 
 
Annex A: Graphical report of a measurement repetition. 
 
 
 
 
 
 
 
 
 
+ +
+ +
Prog.Name:
Type:
Drawing No.:
Notes:
Part/Mach. No.:
Meas.Device:
Q-Type: Unit:
Operator:
No. of teeth
Module m
Pressure angle
Helix angle
Base circ.dia. db
Base Helix angle
Date:
Face Width
Length Ev. La
Length  Ev. Lb
Addend.mod.fact.
Stylus dia.
Filter
Cylindrical Gear Profile/Helix
left rightPROFILE
Tip
Root Tooth
Ref. left rightHELIX
Top
Bottom Tooth
meas.[um]  Qual. meas.[um]  Qual.Tolerance
Qua.fHAm
fHA
FA
ffA
fHßm
fHß
Fß
ffß
um
um
mm
mm
QUINDOS
GEAR
 1
  0.8
  2.7
  2.3
  78.57
 100.82
  97.73
  60.59
  0/  0   0/  00 0
  0   00 0
  0   00 0
Va
1000:1
 10
Vb
1.5:1
6.6
 1
  6.9
  7.3
  2.0
  78.57
 100.82
  97.73
  60.59
fHß/80% fHß/80%
 1
  2.6
  4.0
  4.1
100.00
 90.00
 50.00
 10.00
  0.00
  0/  0   0/  00 0
  0   00 0
  0   00 0
Va
1000:1
 10
Vb
0.8:1
12.8
 1
  2.7
  2.8
  1.2
100.00
 90.00
 50.00
 10.00
  0.00
 9
  2.3
  2.9
  1.7
 9
  7.8
  7.9
  2.3
 9
 -2.7
  3.6
  1.6
 9
 -4.8
  5.3
  1.7
17
  4.6
  5.0
  1.7
17
  6.4
  6.7
  1.9
17
 -5.9
  7.0
  1.2
17
 -7.8
  8.4
  0.9
25
  2.9
  3.7
  1.7
25
  8.1
  8.1
  1.9
25
 -2.8
  4.5
  1.9
25
 -4.5
  5.4
  1.3
DRIVETRAIN
Master gear
PMC 12 10  7 #216
mmDIN 3962 + VDI
DC 09-JAN-2017 09:07:56
 32
 10.0000mm
 20.0000
 35.0000
356.9943mm
 32.6146
100.000mm
x  -0.030
  3.000mm
G50  1.33mm / G50  3.33mm
 37.140mm
 80.000mm
   2.6
 4
 3
 1
   7.3
 6
 5
 1
  -2.2
 5
 4
 3
  -3.6
 6
 5
 1
+   10.0 m
-   10.0 m
Fpi (left flank)
Fp    fu
Act   12.6   10.0
Qua.  3  5
Tol.   0.0    0.0
Qua. 0 0
+   10.0 m
-   10.0 m
fpi (left flank)
Rp    fp
Act   10.0    5.4
Qua.  4
Tol.   0.0    0.0
Qua. 0
+   10.0 m
-   10.0 m
Fpi (right flank)
Fp    fu
Act   24.0    5.3
Qua.  5  4
Tol.   0.0    0.0
Qua. 0 0
+   10.0 m
-   10.0 m
fpi (right flank)
Rp    fp
Act    8.4    4.2
Qua.  4
Tol.   0.0    0.0
Qua. 0
+   10.0 m
-   10.0 m
Runout  Fri
Fr
Act   25.6
Qua.  6
Tol.   0.0
Qua. 0
Dimension over balls nom (  0.0000,  0.0000) Probe Diam. 18.0000
RMd  0.0129 max  416.3035(   4,  20) min  416.2906(  12,  28) Aver.  416.2976
Effective Tooth Thickness (Spline) = 18.5429 nom ( 0.0000, 0.0000)
Result : o.k.      n.o.k. A.       W.       R.
QUINDOS
GEAR
Order No.   :
Identity No.:
Comment     :
Title       :
Part No.    :
Inspect/Date:
No. of teeth:
Norm. Module:
Press. Angle:
Helix Angle :
Hand of Lead:
Facewidth   :
NGML - DriveTrain
400 Msster Gear
Master gear
DC/09-JAN-2017/09:52
  32
 10.0000
 20.0000
 35.0000
 right
100.0000
Q-Type: DIN 3962


English

Calibration of a Master Gear

Questo rapporto tecnico descrive la taratura di un segmento di anello di un cuscinetto a sfere. L’INRIM ha progettato il segmento di anello che è stato quindi prodotto dalla MG Marposs S.p.a. di Torino. La taratura è stata eseguita con la macchina a coordinate CMM/ST001 dell’INRIM.
Questo lavoro si colloca all’interno del Progetto DriveTrian (ENG56) come deliverable 2.2.3.This technical report describes the calibration of a ball bearing ring segment. INRIM designed the ring segment to be representative of bearing rings Ø > 1 m and MG Marposs S.p.a. (Turin, Italy) manufactured the workpiece. The calibration has been performed with the coordinate measuring machine CMM/ST001 at INRIM.
The present work is related to the deliverable 2.2.3 of Drive Train Poject (ENG56)

BALSAMO, ALESSANDRO

CORONA, DAVIDE

Archivio istituzionale della ricerca - INRIM

            A. Balsamo, D. Corona,   Calibration of a Master Gear    T.R. 19/2017                                  September 2017                       I.N.RI.M. TECHNICAL REPORT Abstract   This technical report describes the calibration of a master gear provided by Newcastle University. The calibration has been performed with the coordinate measuring machine CMM/ST001 at INRIM, with the master gear mounted on the workpiece table (no rotary table) and a star configuration of the stylus system. The present work is related to the deliverable 2.1.9 of Drive Train Poject (ENG56).   Questo rapporto tecnico  descive la taratura di un Master Gear fornito dall’università di Newcastle. La taratura è stata condotta con la macchina a coordinate CMM/ST001 dell’INRIM nella configurazione con il Master Gear montato sulla tavola (non rotante) e con un tastatore a stella. Questo lavoro si colloca all’interno del Progetto DriveTrian (ENG56) come deliverable 2.1.9.                       Pag. 1 / 5  1. MEASURAND, MEASUREMENT PROCEDURE AND CONDITIONS  1.1 Measurands  The measurands are the profile parameters (fH, ff, F) and lead parameters (fH, ff, F) of the left and right flanks of teeth 1, 9, 17 and 25, the pitch parameters (fp, Fp) and the runout (Fr) [1, 2].  The nominal parameters of the gear are summarised in the following table.  Diameter Facewidth Teeth Helix angle Normal Module Pressure angle Base diameter d b z  mn n db 390.048 mm 100 mm 32 35° RH 10 mm 20° 356.994  The profile parameters are evaluated in the range (377 – 407) mm of the length or roll. The lead parameters are evaluated along the facewidth with exclusion of 10 mm on each side (i.e. in the range (10 – 90) mm of the axial coordinate, while the full facewidth scans (0 – 100) mm). The diameter of the theoretical sphere used to evaluate the runout is 18 mm.  1.2 Procedure  The calibration is performed with the coordinate measuring machine CMM/ST001, with the master gear mounted on the workpiece table (no rotary table) and a star configuration of the stylus system.    Figure 1: Mounting arrangement.  1,2,3,4: probe tips used to scan the gear surfaces (the vertical one is for alignment only). 3,4: thermometers.  The calibration is done in two steps with different measurands: a preliminary calibration (hereafter referred to as precalibration) and the actual calibration.   Precalibration. Two radial and an axial features of the master gear are calibrated by comparison with calibrated gauge blocks (see figure 2): Pag. 2 / 5  o Two orthogonal point-to-point external diameters of the upper shoulder, lx and ly, aligned to the CMM x and y axes, respectively; they are calibrated by comparison with the calibrated 400 mm gauge block CEJ s/n 750004. o The average of two point-to-point distances of the upper to the lover shoulders, lz1 and lz2, in the axial direction, in two point pairs opposite to the gear axis1; each distance is calibrated by comparison with the calibrated 100 mm gauge block CARY 100 s/n 40077.  Actual calibration. All measurands of the master gear are measured while the precalibrated features are remeasured. The (x,y,z) coordinates of all sampled points are multiplied by three global scale factors, respectively and independently for each axis, equal to the ratios of the pre-calibrated values to the currently measured ones. This way the actual values of the precalibrated features are brought back to their traceable precalibrated values; as the same scale factors are applied to all sampled points, the traceability is extended to all measurands.   Figure 2: Features of the master gear precalibrated at step 1, to introduce traceability.  To minimise the effects of the CMM geometry errors, the calibrated gauge blocks used at step 1 are aligned parallel and fixtured as close as possible to the features under precalibration. This way the effects of the CMM geometry errors are second order and neglected.  The deviation of the mean temperatures of the gear and of the calibrated gauge blocks from the standard reference temperature (20 °C [3]) is relevant to the precalibration and is compensated for. On the contrary, it is not to the actual calibration as the scale factors applied to all sampled points already include and compensate for thermal expansion effects.  1.3 Environmental conditions  The gear and gauge blocks temperatures varied during the measurement in the range (19.84 - 20.26) °C. The value of the thermal expansion coefficient (CTE) of the gear was assumed at (11.5 ± 2.5) × 10-6 K-1.                                                                       1 The average is taken for sake of symmetry, as the gear seat makes the central portion of the gear unavailable. ly lx lz1 lz2 Pag. 3 / 5  2. MEASUREMENT RESULTS AND ASSOCIATED UNCERTAINTIES  2.1 Results  The calibration values and their uncertainties are reported in the two tables below.  Flank Left Right Uncertainty Tooth 25 17 9 1 1 9 17 25 U fH 2.85 4.44 2.30 0.87 6.97 7.54 6.56 7.89 1.0 F 3.71 4.75 3.05 2.57 7.49 8.07 6.72 7.99 1.0 ff 1.55 1.57 1.56 2.47 2.23 2.54 1.97 2.05 1.0 fH -2.87 -5.78 -2.83 2.47 2.76 -4.79 -7.71 -4.47 1.0 F 4.37 6.84 3.70 4.02 2.83 5.54 8.29 5.27 1.0 ff 2.02 1.15 1.56 4.13 1.25 1.63 0.93 1.20 1.0 All values in micrometres (apart from the tooth numbering)     Uncertainty Flank Left Right U fp 5.23 4.13 0.6 Fp 12.40 23.27 2.7 Fr 26.27 1.9 All values in micrometres  The graphical report of a measurement repetition is given in the attachment.   2.2 Uncertainty  The uncertainty of measurement is summarised in the following tables.  Precalibration Input uncertainty u(xi) Sensitivity ci Standard component ui(y)/µm Gauge block calibration 0,025 µm 1  0,025 Gauge block temperature 0,023 K 1,150 µm/K 0,027 Gauge block CDT 0,577 × 10-6/K -0,010 K m -0,006 Gear temperature 0,023 K -1,448 µm/K -0,033 Gear CDT 1,443 × 10-6/K 0,019 K m 0,028 resolution 0,014 µm 2  0,029 Probe unidir. reproducibility 0,058 µm 2  0,115 Overall repeatability 0,074 µm 1  0,074     u(y) 0,151  Pag. 4 / 5  Actual calibration       fH     F     ff      ci ui(y) ci ui(y) ci ui(y)    u(xi)      /µm     /µm     µm Scale factor, x 0.67 × 10-6 0.019 m 0.01 0.017 m 0.01 0.000 m 0.00 Scale factor, y 0.71 × 10-6 0.018 m 0.01 0.016 m 0.01 -0.001 m 0.00 Scale factor, z 1.20 × 10-6 -0.002 m 0.00 -0.001 m 0.00 0.000 m 0.00 Axis localisation, x 0.17 µm -0.096  -0.02 0.018  0.00 -0.002  0.00 Axis localisation, y 0.17 µm -0.089  -0.02 0.020  0.00 0.001  0.00 Axis localisation. z 0.17 µm 0.000  0.00 0.000  0.00 0.000  0.00 Axis orientation. about x 3.92 µrad 0.002 m 0.01 -0.005 m -0.02 0.000 m 0.00 Axis orientation. about y 3.92 µrad 0.006 m 0.02 0.006 m 0.02 -0.001 m 0.00 Temperature variations 0.087 K 0.175 µm/K 0.02 0.155 µm/K 0.01 0.004 µm/K 0.00 Probing anisotropy 0.44 µm 1  0.44 1  0.44 1  0.44 CMM geometry (over a profile) 0.2 µm 1  0.20 1  0.20 1  0.20 Reproducibility fH 0.16 µm 1  0.16    0.00    0.00 Reproducibility F 0.17 µm    0.00 1  0.17    0.00 Reproducibility ff 0.17 µm    0.00    0.00 1  0.17       uc(y) 0.51   uc(y) 0.51   uc(y) 0.51 (k = 2)    Uc(y) 1.02  Uc(y) 1.03  Uc(y) 1.02  Actual calibration       fH     F     ff      ci ui(y) ci ui(y) ci ui(y)    u(xi)      /µm     /µm     µm Scale factor. x 0.67 × 10-6  0.000 m  0.00 0.000 m 0.00 0.000 m 0.00 Scale factor. y 0.71 × 10-6 0.000 m 0.00 0.000 m 0.00 0.000 m 0.00 Scale factor. z 1.20 × 10-6 0.000 m 0.00 0.000 m 0.00 0.000 m 0.00 Axis localisation. x 0.17 µm 0.000  0.00 0.000  0.00 0.000  0.00 Axis localisation. y 0.17 µm 0.000  0.00 0.000  0.00 0.000  0.00 Axis localisation. z 0.17 µm 0.000  0.00 -0.092  -0.02 0.000  0.00 Axis orientation. about x 3.92 µrad 0.038 m 0.15 0.000 m 0.00 -0.001 m 0.00 Axis orientation. about y 3.92 µrad 0.014 m 0.05 0.025 m 0.10 0.002 m 0.01 Temperature variations 0.087 K 0.001 µm/K 0.00 0.003 µm/K 0.00 0.004 µm/K 0.00 Probing anisotropy 0.45 µm 1  0.45 1  0.45 1  0.45 CMM geometry (over a lead) 0.15 µm 1  0.20 1  0.20 1  0.20 Reproducibility fH 0.10 µm 1  0.10    0.00    0.00 Reproducibility F 0.16 µm    0.00 1  0.16    0.00 Reproducibility ff 0.09 µm    0.00    0.00 1  0.09       uc(y) 0.51   uc(y) 0.51   uc(y) 0.48 (k = 2)     Uc(y) 1.02   Uc(y) 1.02   Uc(y) 0.96  Actual calibration       fp     Fp     fr      ci ui(y) ci ui(y) ci ui(y)    u(xi)      /µm     /µm     µm Scale factor. x 0.67 × 10-6 0.033 m  0.02 0.127 m  0.09 0.062 m 0.04 Scale factor. y 0.71 × 10-6 0.024 m 0.02 0.126 m 0.09 0.014 m 0.01 Scale factor. z 1.20 × 10-6 0.000 m 0.00 0.000 m 0.00 0.000 m 0.00 Axis localisation. x 0.17 µm 0.169  0.03 1.947  0.34 1.094  0.19 Axis localisation. y 0.17 µm 0.206  0.04 2.024  0.35 1.580  0.27 Axis localisation. z 0.17 µm 0.000  0.00 0.000  0.00 0.000  0.00 Axis orientation. about x 3.92 µrad 0.020 m 0.08 0.237 m 0.93 -0.020 m -0.08 Axis orientation. about y 3.92 µrad 0.027 m 0.11 0.159 m 0.62 0.128 m 0.50 Temperature variations 0.087 K 0.271 µm/K 0.02 1.188 µm/K 0.10 0.422 µm/K 0.04 Probing anisotropy 0.35 µm  0.342  0.12  0.342  0.12  1  0.35 CMM geometry (over full section) 0.2 µm 1  0.20 1  0.20  1  0.20 Reproducibility fp 0.14 µm 1  0.14    0.00    0.00 Reproducibility Fp 0.51 µm    0.00 1  0.51    0.00 Reproducibility fr 0.59 µm    0.00    0.00 1  0.59       uc(y) 0.31   uc(y) 1.35   uc(y) 0.94 (k = 2)     Uc(y) 0.61   Uc(y) 2.71   Uc(y) 1.87  The input uncertainty due to the probe anisotropy is evaluated experimentally (type A). A reference sphere with negligible form error is scanned along a path designed to mimic the exact directions of contact when scanning the gear. This is done separately for the profile and the lead measurements.  The sensitivity coefficients for the scale factors and the axis localisation and orientation are evaluated by simulation: arbitrary scale factors and an arbitrary rototranslation is applied to all scanned points and then the derived values are evaluated again. These variations are imposed one at a time to identify individual effects.  Pag. 5 / 5  The reported expanded uncertainty of measurement U is stated as the standard uncertainty of measurement multiplied by the coverage factor k = 2, which for a normal distribution corresponds to a coverage probability of approximately 95%.   In the evaluation of the standard uncertainty, the long-term stability of the object under measurement has not been considered.   REFERENCES [1] ISO 701:1998 International gear notation – Symbols for geometrical data [2] ISO 1328-2:1997 Cylindrical gears – ISO system of flank tolerance classification – Part 1: Definitions and allowable values of deviations relevant to flanks of gear teeth [3] EN ISO 1:2016 Geometrical product specifications (GPS) – Standard reference temperature for the specification of geometrical and dimensional properties  ATTACHED DOCUMENTS  Annex A: Graphical report of a measurement repetition.          + ++ +Prog.Name:Type:Drawing No.:Notes:Part/Mach. No.:Meas.Device:Q-Type: Unit:Operator:No. of teethModule mPressure angleHelix angleBase circ.dia. dbBase Helix angleDate:Face WidthLength Ev. LaLength  Ev. LbAddend.mod.fact.Stylus dia.FilterCylindrical Gear Profile/Helixleft rightPROFILETipRoot ToothRef. left rightHELIXTopBottom Toothmeas.[um]  Qual. meas.[um]  Qual.ToleranceQua.fHAmfHAFAffAfHßmfHßFßffßumummmmmQUINDOSGEAR 1  0.8  2.7  2.3  78.57 100.82  97.73  60.59  0/  0   0/  00 0  0   00 0  0   00 0Va1000:1 10Vb1.5:16.6 1  6.9  7.3  2.0  78.57 100.82  97.73  60.59fHß/80% fHß/80% 1  2.6  4.0  4.1100.00 90.00 50.00 10.00  0.00  0/  0   0/  00 0  0   00 0  0   00 0Va1000:1 10Vb0.8:112.8 1  2.7  2.8  1.2100.00 90.00 50.00 10.00  0.00 9  2.3  2.9  1.7 9  7.8  7.9  2.3 9 -2.7  3.6  1.6 9 -4.8  5.3  1.717  4.6  5.0  1.717  6.4  6.7  1.917 -5.9  7.0  1.217 -7.8  8.4  0.925  2.9  3.7  1.725  8.1  8.1  1.925 -2.8  4.5  1.925 -4.5  5.4  1.3DRIVETRAINMaster gearPMC 12 10  7 #216mmDIN 3962 + VDIDC 09-JAN-2017 09:07:56 32 10.0000mm 20.0000 35.0000356.9943mm 32.6146100.000mmx  -0.030  3.000mmG50  1.33mm / G50  3.33mm 37.140mm 80.000mm   2.6 4 3 1   7.3 6 5 1  -2.2 5 4 3  -3.6 6 5 1+   10.0 m-   10.0 mFpi (left flank)Fp    fuAct   12.6   10.0Qua.  3  5Tol.   0.0    0.0Qua. 0 0+   10.0 m-   10.0 mfpi (left flank)Rp    fpAct   10.0    5.4Qua.  4Tol.   0.0    0.0Qua. 0+   10.0 m-   10.0 mFpi (right flank)Fp    fuAct   24.0    5.3Qua.  5  4Tol.   0.0    0.0Qua. 0 0+   10.0 m-   10.0 mfpi (right flank)Rp    fpAct    8.4    4.2Qua.  4Tol.   0.0    0.0Qua. 0+   10.0 m-   10.0 mRunout  FriFrAct   25.6Qua.  6Tol.   0.0Qua. 0Dimension over balls nom (  0.0000,  0.0000) Probe Diam. 18.0000RMd  0.0129 max  416.3035(   4,  20) min  416.2906(  12,  28) Aver.  416.2976Effective Tooth Thickness (Spline) = 18.5429 nom ( 0.0000, 0.0000)Result : o.k.      n.o.k. A.       W.       R.QUINDOSGEAROrder No.   :Identity No.:Comment     :Title       :Part No.    :Inspect/Date:No. of teeth:Norm. Module:Press. Angle:Helix Angle :Hand of Lead:Facewidth   :NGML - DriveTrain400 Msster GearMaster gearDC/09-JAN-2017/09:52  32 10.0000 20.0000 35.0000 right100.0000Q-Type: DIN 3962

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Calibration of a Master Gear

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