2011

12-1

12-1

(precision)

(accuracy)repeatability

12.1 A A1 a1

a1

100mm 99.95mm

0.05mm 0.05mm

A A

A

2011

12-2

A A

50 100.02mm

100.11mm 99.92mm 100.02mm-100.00mm=0.02mm

100.11mm-99.92mm=0.19mm

12-1

A

(standard deviation)A A

A(12.1)(12.2) n

n 6 50

=

=+++=n

iinA An

nAAA1

211/)( L (12.1)

=

=n

iAiA An 1

2)(1 (12.2)

A 50

2011

12-3

12.1 12-2 A B

A

A B

B

12-2

(size tolerance)(form tolerance)

(position tolerance)

2011

12-4

12-2

(basic dimension)

(tolerance zone)12-3

12-3 [CNS B1002-1]

12-2-1

2011

12-5

(ISO)

(IT grade)

IT01IT0IT1IT2IT16

18

DDi 001.045.0 3 += (12.3)

D mmi m (1m=0.001mm)

12-1 500mm

64mm i

64001.06445.0 3 + =1.864m 11 100i=

186.4m = 0.1864mm 6 10i=18.64m=

0.01864mmIT 6

10 IT16

IT17 1600iIT18 2500i

12-1 IT5 IT16 IT 4

12-2 D mmi m IT 2 IT 4

IT 1 IT 5

12-1 500mm IT 5 IT 16 [CNS B1002-1]

IT 5 IT6 IT7 IT8 IT9 IT10 IT11 IT12 IT13 IT14 IT15 IT16

7i 10i 16i 25i 40i 64i 100i 160i 250i 400i 640i 1000i

2011

12-6

12-2 500mm IT 01IT 0 IT 1 [CNS B1002-1]

IT 01 IT 0 IT 1

0.3 +0.008D 0.5 +0.012D 0.8 +0.020D

12-1 12-2 500mm

500mm IT6 IT16

12-3 I

I m D mm 12-1

12-3 10

IT16

I=0.004D+2.1 (12.4)

12-3 500mm 3150mm IT6 IT16 [CNS B1002-1]

IT6 IT7 IT8 IT9 IT10 IT11 IT12 IT13 IT14 IT15 IT16

10I 16I 25I 40I 64I 100I 160I 250I 400I 640I 1000I

12-4

D

A12-1 500mm A12-2 500mm

3150mm 64mm

18.64m 19m

A12-150 80 6

19m A12-1 A12-2

2011

12-7

12-4[CNS B1002-1]

- 3

80 120 80

100 100 120

3 6 120 180

120 140 160

140 160 180

6 10

10 18 10 14

14 18

180 250 180 200 225

200 225 250

18 30 18 24

24 30

250 315 250 280

280 315

30 50 30 40

40 50

315 400 315 355

355 400

50 80 50 65

65 80

400 500 400 450

450 500

12-2-2

12-3

12-4

100-0.1/-0.2 50+0.3/+0

100+0.1/-0.2

2011

12-8

12-4

es ei

12-5

a h

es a bcd

h 0 k zc ei

0

es ei=es-

js ei=es=(/2)

64mm g -10m A12-1

500mm 19m 64g6 -10m

-10m-19m= -29m 64g6 029.0010.0

64

971.63990.63

CNS B1002-1A12-3

500mm

64mm g

2011

12-9

12-5[CNS B1002-1]

ES EI

12-6

A H

EI A

BCD H 0 K ZC

ES 0

ES EI=ES-

A H EI= -es J ZC ES= -ei

A12-3 500mm

2011

12-10

64mm H 0 A12-1 30m

64H7 0m 0+30m= 30m 000.0030.0

64

12-6[CNS B1002-1]

12-3

12-2 12-7

64mm

2011

12-11

g H

64g6 64H7-0.010mm -0.029mm

63.990mm 63.971mm

0.030mm 0mm 64.030mm

64.000mm

12-7 [CNS B1002-1]

64 H7/g6 64 H7-g6 64 67gH

H7g6

H8d9H7f8 G7h6

2011

12-12

12-8(a) 12-8(b)

12-8(c)

(a) (b) (c)

12-8

()

2011

12-13

12-9

h 12-9

H

12-9[CNS B1002-1]

64H7g6 12-5

H

cdef g

IT9 IT6

5 ISO CNS JIS

12-5

H9c9

()

H8d9H9d9

2011

12-14

H7e7H8e8H9e9

H6f6H7f7H8f7H8f8

H6g5H7g6

12-4

12-10

D0

2011

12-15

12-10

D0

12-10 D0 D1

D2 D3 D4 D0 (loop)

12-10 (dimensional chain)

D0 D0 ( D1D2

D4)( D3)

D0+D1+D2-D3+D4=0 (12.5)

D0=D3-D1-D2-D4 (12.6)

D0 D1D2D3 D4

D1D2D3 D4 T1T2T3 T4

D0 T0 (12.6)

(12.7)

T0=T1+T2+T3+T4 (12.7)

(12.6) D1D2D3 D4

(12.7)

2011

12-16

[1995]

DR(12.8) vi+1 -1

Di DR

01

==

m

iii Dv (12.8)

DR

(12.9)

=

=1

1

m

iiiR DvD (12.9)

= =+++=

1

1121

m

iimR TTTTT L (12.10)

(12.10)(12.9)

1001

101 99

(the worst-case tolerance

analysis)

2011

12-17

0

0.1

0.2

0.3

0.4

0.5

12-1

(statistical tolerance analysis)

(12.2)D

D DiD

12-11 (normal distribution)D

D

DD

68.5% 68.5%D2DD3D

D4D 95.4%99.73% 99.99%

3D 99.7%

(drift)4.5D

Motorola 6D3D

12-11

3D3D

D

T

d

D

2011

12-18

variance(12.9)

(Root Sum Square;

RSS)

(12.11)

= =+++=

1

1

221

22

21

m

iimR TTTTT L (12.11)

(12.11)(12.10) Ti

(12.11) TR(12.10)

TR Ti

12-12 (Xerox)

11 12-6

12-13

12-12[Creveling, 1996 ]

2011

12-19

12-6

1 1

2 1

3 1

4 1

5 2

6 2

7 2

8 1

9 1

10 1

11 1

12-13

LA

2011

12-20

LA

LA = -(AB+BC+CD+DE+EF+FG) + GH - (HI+IJ+JK+KL) (12.12)

12-7

12-13 LA (12.12)

0. 3mm

LA

(12.10) 0.4mm LA

0.30.2mm 0.5mm 0.1mm

(12.11) LA

12-7 12-13 mm

AB 2.0 0.01

BC 0.3 0.03

CD 9.0 0.07

DE 2.5 0.05

EF 0.2 0.03

FG 0.6 0.04

GH 25.4 0.05

HI 0.2 0.03

IJ 0.3 0.03

JK 2.0 0.01

2011

12-21

KL 8.0 0.05

12-5

TR (error

budget) Ti

(tolerance allocation)(tolerance synthesis)

(inverse computation) 12-4

(12.9)(12.10)(12.11)

12-13

12-13 LA 0.3mm

12-7 CDDE

FGGHKL

12-7 LA 0.4mm

0.3mm

0.16mm

Ti = Tj ; i, j = 1, 2, ., n (12.13)

2011

12-22

(12.10) TCD=TDE=TFG=TGH=TKL=0.032mm

0.032mm

0.3mm

Ti/Di = Tj/Dj ; i, j = 1, 2, ., n (12.14)

(12.10) TCD=0.03mm ;

TDE=0.01mm ; TFG=0.002mm ; TGH=0.09mm ; TKL=0.03mm

12-2-1

(12.3)

D

33 // jjii DTDT = ; i, j = 1, 2, ., n (12.15)

12-13 (12.15)

TCD=0.036mm ; TDE=0.023mm ; TFG=0.015mm ; TGH=0.051mm ; TKL=0.035mm

2011

12-23

12-13

2011

12-24

1. CNS 4-1, B1002-1 2009

2. Creveling, C. M., Tolerance Design, A Handbook for Developing Optimal

Specifications, 1996, Addison Wesley.

3. ISO 286-1:1988 ISO system of limits and fits Part 1: Bases of tolerances, deviations and fits

4. ISO 286-2:1988 ISO system of limits and fits Part 2: Tables of standard tolerance grades and limit deviations for holes and shafts

5. Greenwood, W. H., and Chase, K. W., A New Tolerance Analysis Method for Designers and Manufactures, Journal of Engineering for Industry, No.109, 1987, pp.112-116.

6. Spotts, M. F., Allocation of Tolerances to Minimize Cost of Assembly, Journal

of Engineering for Industry, 1973, pp.762-764.

7.

1996 33-40

8.

2000

9.

2008

10.

2009

11.

1995731-740

2011

12-25

1. (12.3)12.18mm64mm500mm

iIT6IT712-

2. 64H7/g6

3. 100mm(12.1)(12.2)

101.3 101.0 101.4 100.9 99.6 100.3 99.7 100.0 100.7 99.6

100.7 98.4 101.2 99.6 99.1 99.5 100.6 98.8 100.5 99.2

99.3 100.2 100.5 100.8 98.2 101.5 101.0 100.4 98.7 101.4

100.0 98.5 100.6 99.4 100.1 101.2 100.6 98.3 100.4 99.4

99.8 100.8 98.5 99.5 100.9 99.2 100.2 98.6 99.5 103.0

101.9 100.1 102.1 99.3 101.5 99.7 99.3 99.4 100.8 99.0

99.4 100.7 99.8 99.4 99.6 100.5 98.6 101.8 100.3 101.3

100.9 99.0 99.0 99.3 99.5 101.7 100.0 100.9 100.6 100.5

102.0 100.5 100.3 100.5 99.8 99.9 100.0 99.7 100.0 99.5

100.7 100.5 101.5 98.5 98.9 101.5 100.5 101.1 99.2 98.4

4. ZX=100.3mmY=50.4mmZ

5. XYX=9.7mm9.8mm9.9mm10.0mm10.1mm10.2mm10.3mmY=4.8mm4.9mm5.0mm5.1mm5.2mmZ

6. 12-13 LA(12.12)(12.7)(12.11)LA

7. 12-13 LA 0.3mm12-7 (CD)(DE)(FG)

X Y

(Z)

2011

12-26

(GH)(KL)0.3mm 0.16mm

2011

12-27

A12-1 500mm [CNS-B1002-1]

2011

12-28

A12-2 500mm 3150mm [CNS-B1002-1]

2011

12-29

A12-3 500mm [CNS-B1002-1]