AfM Technology Volumetric Compensation of machine tools

The Engineering & 

Calibration Service Company 

for 

Volumetric Compensation of machine tools / CMM 

Linear and rotary axis calibration of machine tools / CMM 

© AfM Technology GmbH / Wolfram Meyer 

Page 1

Aachen colloquium for 5-Axis precision machining 

Agenda 

• Geometric deviations of machine tools 

• Metrological parameter aquisition 

• Compensation in the CNC control 

• Limitations in aquisition and compensation 

• Trends and challenges 


Page 2


Geometric deviations of machine tools 


Page 3

Influences on machine tool accuracy 

Drives 

Dynamic 

Geometry 

• Component 

deviations 

• Location deviations 

• Model fitness 

• Machine coordinate 

system 

Thermal 

influences 


Page 4

Geometric deviations on a linear machine axis 

Each linear guide has 6 degrees of freedom, 3 translational und 3 rotational 

translational movement 

(transverse to the guide axis) / EZX 

translational movement 

(transverse to the guide axis) EYX 

support 

rotational movement: 

around X = roll / EAX 

around Y = pitch / EBX 

around Z = yaw / ECX 

guide 

translational movement (position) / EXX 

© AfM Technology GmbH / Horst Eckersberger 

Page 5

Geometric deviations on a rotary machine axis 

Each rotary axis has 6 degrees of freedom, 3 translational und 3 rotational 

translational movement (axial runout in Z) / EZC 

translational movement (radial runout in Y) / EYC 

support 

rotational movement: 

around X = wobble / EAC 

around Y = wobble / EBC 

around Z = position / ECC 

Rotary table 

translational movement (radial runout in X) / EXC 


Page 6

Kinematic chain of a machine tool 

Kinematic chain 

t – S – A – B – Y – Z – MB – X – C – MT – w 

Spindle 

Tool 

Machine 

base 

Work 

piece 

© AfM / Keppler 

Component dev. 

location dev. 

• 3 linear axes 

• 3 rotary axes 

• 1 spindle 

3 x 6 = 18 

3 x 6 = 18 

1 x 5 = 5 

3 x 3 = 9 

3 x 5 = 15 

1 x 4 = 4 

∑ = 69 

deviations 

• coordinate system 

- 6 

• Effective deviations 

41 

28 


Page 7

Resulting errors at the tool center point (linear axes) 

Geometric errors 

• positioning error 

• straightness 

• roll 

• yaw 

• pitch 

• squareness 

Resulting error 

at TCP 


• orientation error 

Programmed 

tool position 

and 

tool orientation 

Real 

tool 

orientation 

Real 

TCP 

position 

The geometrical errors of the linear axes of a 3-axes machine tool cause spatial errors of the TCP 

concerning position and orientation. 


Page 8

Resulting errors at the tool center point (rotary axes) 

Geometric errors 

• runout 

• wobble 

• position 

• location of axis 

• orientation of axis 

• zero position 

Resulting error 

at TCP 

Real 

tool 

orientation 

Real 

TCP 

position 


• orientation error 

The component and location errors of the radial axes of a 4/5/6-axes machine tool causes also 

spatial errors of the TCP concerning position and orientation. 


Page 9


Metrological parameter aquisition 


Page 10

Measurement methods for error parameters 

Direct Measurement 

Indirect Measurement 

Component 

deviations 

• Laserinterferometer 

• Straightness artefact 

& indicator (Wire / 

Stone) 

• Levels 

• Reference encoders 

Reference scales 

• Autokollimator 

Location 

deviations 

• Laserinterferometer 

• 90° stone angle, 

calibration cube & 

dial indicator 

• Levels 

• Test mandrel & dial 

indicator 

Component and location 

deviations 

• Ball bar, ball plate, Tetraeder 

• Reference parts 

• Circular test 

• Ball & 3D-Probe 

• Lasertracker 

• LaserTRACER 


Page 11

Direct measurement of linear axis with single-purpose tools 

• A great variety of tools is used 

Levels 

Reference scales 

Straightness laser 

Autokollimator 

Straightness artefact & indicator (Wire / Stone) 


Page 12

Direct measurement of linear axis with laser interferometer 

• Laserinterferometer available with 1 up to 6 DOF 

Renishaw (1-DOF) 

• High accurate, long range 

• Alignment effort, particularly for vertical and 

straightness measurement is high 

TSK (3-DOF) 

API (6-DOF) 

HP Agilent (1-DOF) 

© TSK 


Page 13

Direct measurement of rotary axis 

Test mandrell 

HEIDENHAIN Reference encoder RON 905 

& 

dial indicator 

Laserinterferometer with Renishaw RX10 

API Swivelcheck 


Page 14

Indirect measurement of linear axis with ball bars 

Renishaw QC-20W 

• Fast and easy measurement 

• Geometric and drive analysis 

• Applicable in any plane 

• Mind the volume size 

Dreier RoundCheck VA 

API Ballbar 


Page 15

Indirect measurement of component and location deviation 

• Ball bars (1D), ball plates (2D), Tetraeder (3D) 

Ball plate 

• Fixed grid, limited dimension, handling complex 

Ball bar 

© Prof. Knapp ETH Zürich 

Tetraeder 

© IBS Precision Engineering 

© Dr. Trapet 


Page 16

Indirect measurement of linear axis with laser interferometer 

Optodyne MCV 500 

© Dr. Trapet 


Page 17

Indirect measurement by multilateration with LaserTRACER 

• Linear axis calibration 

• Rotary axis calibration 

• Acceptance test according 

to ISO 230-2/4/6 and ISO 

10360-2 

LaserTRACER MT 

LaserTRACER 


Page 18

Online multilateration with LaserTRACER 

What is Multilateration? 

• Ideal realization of the Abbe Principle: All measurement 

lines pass directly through the measurement point. 

• Principle is used in Global Positioning System (based on 

time of flight measurement). 

• With LaserTRACERs, the principle can be downscaled to 

submicron accuracy in a medium measurement volume. 

© Etalon 

• If four LaserTRACERs are used, the system is self calibrating 

Characteristics 

• Mobile, Self calibration 

• Contactless, 3D measure 

• Working volume up to 10 m x 10 m x 10 m. 

• Direct traceability by stabilized laser interferometer. 

• Highest resolution and accuracy (down to sub-micron range) 


Page 19

3D Messung mit LaserTracker 

Moving 

Active Target (AT) 

Lasertracker 

Stationary 

T3 Laser Tracker 

(with Pan & Tilt) 

© API 


Page 20

Rotary axis calibration with ball and 3D probe 

• Rotary and swivel axis as well as trunion table are 

supported 

Trunion Table Calibration 

• Fixed ball, moved probe or fixed probe and moved ball 

• Fast, easy and automatic cycle 

Up to 3 rotary axis at once 

Fork Head Calibration 

© HEIDENHAIN 

© Fidia 

© IBS Engineering Precision 


Page 21


Compensation in the CNC control 


Page 22

Geometric compensations in CNC controllers 

Geometric compensations (stand alone or as combination) 

• Linear encoder error compensation (slope) 

• Non linear encoder error compensation (arbitrary form) 

• Cross error compensation 

• Grid compensation 

• Volumetric compensation 

Stand alone or as part of geometric compensation 

• Backlash compensation 


Page 23

deviation [µm] 

0 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

2000 

2200 

2400 

2600 

2800 

3000 

3200 

3400 

Linear and non linear encoder error compensation 

linear encoder error compensation (slope) 

100,0 

Position deviation y-axis 

80,0 

60,0 

40,0 

20,0 

0,0 

-20,0 

-40,0 

yTy / EYY 

Linear (yTy / EYY) 

Non linear encoder error compensation (arbitrary form) 


Page 24

Cross error compensation 

• Crosstalk of any axis combination can be compensated 

• Compensation of straightness and squareness 

© HEIDENHAIN 


Page 26

3D Grid compensation 

• The volume is divided in cubes or a spherical grid 

• Each corner of the cube is represent by an error vector 

• Used for linear axis as well as rotary axis 

∆X i 

∆Y i = f(A,C) 

∆Z i 

© Bosch Rexroth 

© Siemens © FANUC 


Page 27

Volumetric compensation 

E = T e + R em * P m + R et * P t 


Page 28

Backlash compensation 

Backlash compensation 

Backlash U / U1 

As single axis parameter 

z.B. Siemens 840D sl 

MD 32450 Backlash compensation 

$MA_BACKLASH[0]=0.002 mm 

As data set along the axis 

Position deviation B-Axis (forward & backward travel) 

20,0 

10,0 

0,0 

-29,0 -24,0 -19,0 -14,0 -9,0 

-10,0 

-4,0 1,0 6,0 11,0 16,0 21,0 26,0 

-20,0 

-30,0 

-40,0 

without CEC [0,001°] with CEC [0,001°] 

without CEC [0,001°] with CEC [0,001°] 


Page 29


Limitations in aquisition and compensation 


Page 33

Limitation by model fitness (I) 

EZY (y,z) 

yTz (y,z) 

EAY (y,z) 

yRx (y,z) 

Crosstalking from Z-axis to Y-axis 

Y 

Z 

yTz = yTz(y) + Ytz(y,z) *z 

Z 

Y 

Z 

yRx = yRx(y) + yRxz(y,z) * z 

Y 

EZY = EZY(y) + EZYZ(y,z) *z 

EAY = EAY(y) + EAYZ(y,z) * z 

21 Error Model 

23 Error Model 

900 

800 

700 

600 

500 

400 

300 

200 

100 

0 

±3s ≈ ±30,6 µm 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

±3s ≈ ±18,3 µm 


Page 34

deviation [µrad] 

deviation [µm/m] 

0 

0 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

2000 

2200 

2400 

2600 

2800 

3000 

3200 

3400 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

2000 

2200 

2400 

2600 

2800 

3000 

3200 

3400 

deviation [µrad/m] 

0 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

2000 

2200 

2400 

2600 

2800 

3000 

3200 

3400 

Limitation by model fitness (II) 

20,0 

15,0 

10,0 

5,0 

0,0 

-5,0 

-10,0 

-15,0 

-20,0 

-25,0 

Pitch y-axis 

yRx / EAY with 21 model 

yRx / EAY with 23 model 

Squareness yWz / AOZ 

1,000000 

0,000000 

deviation [µrad] 

yWz/AOZ 

yWz/AOZ 

with 23 model 

Bending of Column 

Yaw of Column 

100,0 

90,0 

80,0 

70,0 

60,0 

50,0 

40,0 

30,0 

20,0 

10,0 

0,0 

-10,0 

30,0 

25,0 

20,0 

15,0 

10,0 

5,0 

0,0 

-5,0 

YTZZ with 21 model 

YTZZ with 23 model 

YRXZ with 21 model 

YRXZ with 23 model 


Page 35

-0,0300 

-0,0270 

-0,0240 

-0,0210 

-0,0180 

-0,0150 

-0,0120 

-0,0090 

-0,0060 

-0,0030 

0,0000 

0,0030 

0,0060 

0,0090 

0,0120 

0,0150 

0,0180 

0,0210 

0,0240 

0,0270 

0,0300 

Limitation by volumetric backlash 

Volumetric backlash analysis 

Position 1 Position 2 Position 3 Position 4 Position 5 Position 6 Total 

Maximum 0,0187 0,0290 0,0170 0,0271 0,0142 0,0087 0,0087 

Minimum -0,0281 -0,0234 -0,0255 -0,0183 -0,0149 -0,0153 -0,0153 

Range 0,0468 0,0524 0,0426 0,0454 0,0290 0,0240 0,0240 

Std. dev. σ 0,0101 0,0119 0,0089 0,0092 0,0056 0,0061 0,0061 

±3σ (99,73%) 0,0607 0,0717 0,0532 0,0549 0,0338 0,0369 0,0369 

Drift 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 

x̅ + 3σ 0,0303 0,0358 0,0266 0,0275 0,0169 0,0184 0,0184 

Average x̅ 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 

x̅ - 3σ -0,0303 -0,0358 -0,0266 -0,0275 -0,0169 -0,0184 -0,0184 

180 

160 

140 

120 

100 

80 

60 

40 

20 

0 

Backlash distribution 

0,040 

0,030 

0,020 

0,010 

0,000 

-0,010 

-0,020 

-0,030 

-0,040 

Backlash single values 

1 26 51 76 101 126 151 176 201 226 251 

x̅ - 3σ x̅ + 3σ Pos1 Pos2 

Pos3 Pos4 Pos5 Pos6 

© AfM Technology GmbH / Wolfram Meyer Volumetric Compensation of machine tools 

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Limitation by temperature conditions 

Temperature over time 

22,0 

21,0 

Calibration 

with AC-Head 

Calibration 

With AC-Head 

Verification 

With AC-Head 

Calibration 

W-Axis 

Verification 

W-Axis 

Calibration 

With Quill 

Verification with Quill 

20,0 

19,0 

18,0 

17,0 

16,0 

15,0 

14,0 

13,0 

X-Achse (min) [°C] X-Achse (max) [°C] Z-Achse [°C] Y-Achse (min) [°C] Y-Achse (max) [°C] Luft [°C] 

© AfM Technology GmbH / Wolfram Meyer Volumetric Compensation of machine tools 

Page 37


Trends and challenges 


Page 38

Trends and challenges 

Kinematic measurement at once 

Dynamic data collection 

Online connection 

Thermal models for machines 

MPE for volumetric accuracy 

Advanced kinematic error models 


Page 39

Thank you for your attention 

Vielen Dank für Ihre Aufmerksamkeit 

Grazie per la vostra attenzione 

AfM Technology Italia Srl 

Via Giotto 25 / Giotto Straße 25 

39100 Bolzano / Bozen / Italy 

Fon/ Fax: +39 0471 911953 

Mobile: +39 348 4221124 

www.afm-tec.it • info@afm-tec.it 

AfM Technology GmbH 

Gartenstraße 133 

73430 Aalen / Germany 

Fon: +49 (0)7361 889608-0 

Fax: +49 (0)7361 889608-99 

www.afm-tec.de • info@afm-tec.de 


Page 40

AfM Technology Volumetric Compensation of machine tools

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