2 *

Study on Improvement Methods of CMM (Coordinate Measuring Machine) in Workshop Environment – Correction of Squareness Error –

Tohru OHNISHI, Shotoku TAKASE and Kiyoshi TAKAMASU

In recent years, the CMM (Coordinate Measuring Machine) quickly has been spreading in the manufacturing industry. With this phenomenon, the environmental condition and installation site of CMMs has been changed from the temperature control room to the workshop environment and the production line without air conditioning. However, even in severe environment the demand to high accuracy measurements by CMM has been enhancing still more. Therefore, the methods to evaluate and realize the high accuracy measurements by CMM in workshop environment have been investigated. In this paper, we propose the evaluation and correction method of squareness errors using MCG (Machine Checking Gauge). Additionally the performances of CMM in workshop environment and temperature-controlled room are tested and corrected experimentally. From these results, we confirmed the availability of the proposed methods.

Key words: CMM, coordinate measuring machine, workshop environment, squareness error correction

1.

Coordinate Measuring MachineCMM

CMM

CMM

1) 2)

CMMCMM

CMM

CMM

CMM

1

2 CMM

3

1)

CMM 21

CMM

3)~6)

CMM CMMX Y Z

* 18 12 14 **

1-1-12*** 7-3-1

精密工学会誌，73（7），2007，818-822

4)~6)

Double Ball BarDBB

7)~10) DBB

DBB CMMMachine

Checking Gauge MCG6)

MCG CMMCMM

CMM CMMMCG

2. MCG CMM

2.1 MCG1 MCG MCG 4 mm

3

1.0 × 10-6/ 11

CMM

R x, y,z R 101 mm 151 mm 226 mm 380 mm 532 mm 685 mm

2 45 845 45 8 24

3 72R

CMM

CMM1 20

2.2 MCG72 xi, yi, zi

x0, y0, z0 txy, tzx, tzy

1 Sc

CMM 3 3CMM x, y, z

X, Y, Z X xxy XY y

Y txy z Z X

tzx z Z Y tzy 3

2 3 Sqr

n

iiiic rzzyyxxS

1

220

20

20 )()()( (1)

zttzttzZ

ztytztyYztytxtztyxX

zyzxzyzx

zyzyxy

zxxyzxxy

coscostantan1

sincossinsin

22

(2)

222

1

2 rztzytztyxS izyii

n

izxixyiiq (3)

2.3 MCG 100 mm 3

Fig. 1 Construction and set up of Machine Checking Gauge (MCG), R is length between centers of pivot ball and stylus ball 11)

Fig. 2 Location of measuring positions by MCG; 8 positions on 3 difference Z levels (+45º, 0º, -45º) 11)

Y

Z

plane

Fig. 3 Coordinate systems and squareness errors by 3 angle error parameters txy, tzx and tzy; XYZ is coordinate system without squareness errors and xyz is machine coordinate system with squareness errors.

R

probe

stylus ball

pivot ball

Kinematic pivot location

精密工学会誌，73（7），2007，818-822

0 4545 XY

4 4 a b45 txy

4 a c e 45 45X tzy 4 c d

e 45 45 Ytzx

3 SqMCG

3. CMM MCG

3.1CMM-1 CMM-2

MCG 1CMM CMM-1 CMM

CMM-2 CMM

5 CMM-1 CMM-2 MCG 101 mm 151 mm 226 mm 380 mm

CMM-2 380 mm CMM-1

tzx 101 mm 380 mm 3 sec

CMM-2 txy tzy tzxtzx 5 sec

CMM 1.5 sec 3.26 CMM-1 1

7 1

(µm

02468

10+Y

+X

-Y

-X

0°+45°-45°

(µm

02468

10+Y

+X

-Y

-X

0°+45°-45°

(µm

02468

10+Y

+X

-Y

-X

0°+45°-45°

(a) txy = 10 sec, tzy = 0 sec, tzx = 0 sec (b) txy = 10 sec, tzy = 1 sec, tzx = 2 sec (c) txy = 0 sec, tzy = 10 sec, tzx = 0 sec

(µm

02468

10+Y

+X

-Y

-X

0°+45°-45°

(µm

02468

10+Y

+X

-Y

-X

0°+45°-45°

(µm

02468

10+Y

+X

-Y

-X

0°+45°-45°

(d) txy = 0 sec, tzy = 0 sec, tzx = 10 sec (e) txy = 10 sec, tzy = 10 sec, tzx = 0 sec (f) txy = 10 sec, tzy = 10 sec, tzx = 5 sec

Fig. 4 Simulations of output geometrical errors from MCG measurements on different squareness errors

-8.0

-6.0

-4.0-2.0

0.02.0

4.06.0

8.0

101 151 226 380length of arm mm

txytzytzx

(a) CMM-1: normal accuracy and moving bridge type CMM

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

101 151 226 380length of arm mm

txytzytzx

(b) CMM-2: high accuracy and fixed bridge type CMM

Fig. 5 Relationship of length of MCG arm and squareness errors for 2 types of CMM (CMM-1 and CMM-2)

精密工学会誌，73（7），2007，818-822

1 0.6 sec 1

txy 1.1 sec tzy 2.5 sec tzx 0.5 sec

8

txy 0.07 sec/ tzy0.20 sec/ tzx 0.03 sec/

tzy 9CMM-1 tzy Z

X Y-bridge

tzy tzxZ X Z

CMM 1 sec 10 µmCMM

3 10

4 1 sec

2 1

4.

22 mm 25 83 mm 5 5

Retter

113 forward

13 1backward 12)~14) 1 30

XY YZ XZ5

CMM-1CMM-2 XZ MCG

52

CMM-1 4.4 sec 0.5 sec

10 CMM-1 XY CMM-2XZ

CMM-1 7.3 µm

Table 1 Specifications of CMM-1 and CMM-2

CMM-1 CMM-2 Modes of operation CNN CNN

Type of CMM Moving bridge Fixed bridge Measurement range (XYZ mm) 850 1000 600 700 550 400

Indicating digit (µm) 0.1 0.1 Type of probing system Touch trigger Parallel twin

Error of indication E (µm) 3.9 + 5L/1000 0.8 + L/800 Type of room ( ) Workshop 20±0.5

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

9:40 11:00 12:20 13:40 15:00time

14

16

18

20

22

24

26

28

30

txy tzytzx room

Fig. 6 Variation of squareness errors and room temperature in a day on CMM-1

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

Feb-04 Apr-04 Jun-04 Aug-04 Oct-04 Dec-04 Feb-05month

14

16

18

20

22

24

26

28

30

txy tzytzx room

Fig. 7 Variation of squareness errors and room temperature in a year on CMM-1

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

15 18 21 24 27 30

room temperture C

txytzytzx

Fig. 8 Relationship between room temperature and squareness errors

Fig. 9 Position of supporting air-bearings of CMM-1 (moving bridge type CMM)

X

Y

Z

Y-bridge

(X-column and Z-column) supporting air-bearingZ-column

精密工学会誌，73（7），2007，818-822

2.2 µm CMM-2 8.2 µm 2.8 µm

CMMCMM MCG

5.

CMMMCG

CMM MCG

1 MCG CMM

2 CMM CMM

3 MCG

CMM

1)1

73 2 2007 270. 2) 40 11 2001

801. 3) M. Abbe K. Takamasu S. Ozono Reliability on calibration of CMM

Measurement 33 2003 359. 4) W. Knapp, U. Tschudi, A. Bucher: Comparison of different artefacts

for interim coordinate-measuring machine checking, Precision

Engineering, 13, 4 1991 277. 5) P.C. Miguel, T. King, J. Davisc: CMM verification: a survey,

Measurement 17, 1 1996 1. 6) P.C. Miguel, T. King: Co-ordinate measuring machines Concept,

classification and comparison of performance tests, International Journal of Quality & Reliability Management, 12, 8 1995 48.

7) NC1 DBB

52 7 1986 1193. 8) NC

2 DBB52 10 1986 1739.

9)3 DBB

51 6 1986 1244. 10) Emmett Curran et al. Quick check error verification of coordinate

measuring machines, Journal of Materials Processing Technology, 155-156 2004 1207.

11) RENISHAW Catalog: The Machine Checking Gauge. 12) E. Trapet et al. Traceability of Coordinate Measurements According

to the Method of the Virtual Measuring Machine, PTB, 1998 .13)

67 2 2001 256. 14)

8 2005 .

Table 2 Result of squareness errors before and after squareness errors correction

type of CMM CMM-1 CMM-2plane XY YZ XZ XZ

before correction 4.4 4.1 -1.0 -4.9 winter after correction -0.2 -0.3 -0.3 -0.1 before correction 3.6 2.6 -0.8 - summer after correction -0.3 -0.5 0.2 -

before correction after correction

before correction after correction

(a) XY plane on CMM-1 in winter

before correction after correction

(b) XZ plane on CMM-2

Fig. 10 Positional errors of 25 sphere centers of ball plate before and after squareness errors correction

1div=10µm 1div=10µm

1div=10µm 1div=10µm

精密工学会誌，73（7），2007，818-822