Technical

Supplement (Basic and Technical Data) 1

Supplem ent (Basic and Technical Data)

Table of Contents ■ Operating Conditions ......................................... 3 ■ Selection Table of Bearings ................................ 4 ■ Friction Characteristics ..................................... 5 ■ Installation ........................................................ 6 ■ Calculations of Punching Force ........................... 7 ■ Steel Materials .................................................. 8 ■ Non-ferrous Materials ......................................... 9 ■ Quenching / Surface Treatment and Hardness Tests ................................................. 10 ■ Conversion Table of Hardness ............................ 11 ■ Surface Roughness ........................................... 13 ■ General Dimensional Tolerance of Cutting ........... 15 ■ Tolerances of Commonly Used Hole Fits ............. 16 ■ Tolerances of Commonly Used Shaft Fits ............. 17 ■ Oilless Bearings ............................................... 18 ■ Areas of Plane Figures ....................................... 23 ■ Volumes, Surface Area, Centers of Gravity of Solids ............................... 24 ■ SI Units ............................................................ 26 ■ Table of Unit Conversion Factors ........................ 32 ■ Hexagon Socket Head Cap Screw ...................... 33 ■ Compression and Extension Coil Spring Design Data ..................... 34 ■ Coefficients of Linear Thermal Expansion ........... 36 ■ Average Specific Gravity ................................... 36

Supplement (Basic and Technical Data) 2

Operating Conditions ■ Note - ( ) Static allowable loads (without sliding or very low speed) - (Sl4): Solid lubricant for underwater or extremely high load application Properties

Products

Allow able Range Lubrication status

Allowable Pressure (kgf/cm )

Allowable Velocity (m/min)

Allowable PV value (kgf/cm ㆍ m/min)

Allowable Temperature (℃ )

300

(1,000)

30

1,000

＋300

500(SL4)

(1,000)

15

1,000

＋ 80

300

(1,000)

60

2,000

＋150

No Lubrication

#500SP Periodic Lubrication No Lubrication

150(500)

50

600

＋400

Periodic Lubrication

150

100

1,000

＋150

No Lubrication

50(750)

50

500

＋400

Periodic Lubrication

80

100

1,000

＋150

#100

No Lubrication

200

70

1,500

＋ 80

#200A+Gr

No Lubrication

200

25

1,000

＋ 80

#200A

Periodic Lubrication

200

100

1,500

＋120

#200B

Underwater

150

1,000

3,000

＋ 60

LB Series

No Lubrication

500(2,800)

30

1,080(2,160)

＋270

LX Series

Periodic Lubrication

500(1,400)

70

1,080(2,760)

＋110

LI

Series

Periodic Lubrication

350(1,000)

120

2,500

＋150

LD Series

Periodic Lubrication

300

150

2,000

＋150

#500B

#500F

Supplement (Basic and Technical Data) 3

Selection Table of Bearings ●: Excellent , ○: Good , △: Possible, ×: Not Good

Products

DDU01 (LB)

DBX01 (LX)

#500SP

#200

#100

LI & LD

Medium Speed

○ ○ ● ● ● ● △

○ ○ ● ○ ○ ● ●

● ○ ● ● ● ● △

× × ● ● ○ ● ○

○ ○ ● ● ● ○ ●

High Speed

×

○

×

△ ● ● ● ● ● ○ ○

△

○

High/Load Temperature

Reduction/Transmission

○ ○ △ × ● ○ ● ● ● ● ○ ○ △ ○ ○ ● ● ● ● ● × ○ ○ △

× × × × ○ ○ ○ ○ ○ ○ ○ △ △ ○ △ ● ● ○ ○ ○ × × ○ ●

● ● ○ ○ △ × △ × ● ● ○ ● ● ● ● ○ ○ ● ● ○ ● ● ● ○

× ○ ● ○ △ × ○ × ● ● ○ ● ○ × × ○ △ △ ○ ● ○ ● ● △

× × ○ × ● ● ○ ● × × △ × × × × ○ ○ △ × ○ × × × ×

× △ △ × ○ △ ● ○ ○ ○ ○ ○ △ △ △ ○ ● ○ ○ ○ × × ○ ○

Waste-water Treatments/Water Pumps

×

×

○

●

×

×

○ ● ○ ● ●

● ○ ○ ● ●

● △ ● ● ○

● ○ ○ △ ○

○ ● ○ △ ●

● ○ ○ ● ●

Applications High Load Impact/Oscillating Load Rotational Motion Reciprocating Motion Angular Rocking Motion

Operating Conditions

Low Speed

Chemical Resistance Underwater(marine) Harsh Environments Automobiles Home Appliances Agricultural Machinery Office Equipments Transportation Machinery Construction Machinery Machine Tools Vessels Water Gates/Generators Steel Mills

Machinery

Press Dies(Stamping Tools) Textile Machinery Printing/Packaging Machinery Injection Molding Machinery Tire Manufacturing Hydraulic/Pneumatic Machinery Bridges/Structures Chemical Machinery Paper Mills

With Lubrications Price

Miscellaneous

Dimension Stability Standard Size Light Weight/Compact Design

(Water)

Supplement (Basic and Technical Data) 4

Friction Characteristics

Supplement (Basic and Technical Data) 5

Installation ■ Bearing Retention Please use following methods when retaining bushings within a housing.

■ Press Fit -A screw or hydraulic press is used for press fitting. -Press fitting is accomplished by using a jig, which is perpendicular to the center of bushing. -Insert-end of housing ID is chamfered to 15˚ ~20˚.

15 ~20

˚

O.D (H7)

O.D

I.D

I.D

-0.1 ~ -0.2

˚

Force

3.2

(Jig-Mandrel)

(Bushing)

(Press Fitting)

(Housing)

■ Conversion Table of Units Indication

Conversion

Length

1mm = 0.03937inch,

1inch = 25.4mm

Mass

1kg = 2.2046lb

1lb = 0.4536kg

Force

1N = 1.0197 × 10 -1 kgf 1N = 0.2248lbf,

1Kgf = 9.8N 1lbf = 4.448N

Pressure

1N/mm 2 = 1Mpa = 1.0197 × 10kgf/cm 1kgf/cm 2 = 9.8 × 10 -2 N/mm 2 1N/mm 2 = 145psi

Velocity

1m/sec = 60m/min, 1m/sec = 196.85f/min,

2

= 10bar

1m/min = 0.01667m/sec 1f/min = 0.00508m/sec

Revolutions per Minute

1S

-1

= 60RPM

1RPM = 0.01667S

Frequency

1S

-1

= 60CPM

1CPM = 0.01667S

Angle Temperature

1rad = ℉ =

180°

π

9 ℃＋ 32 5

1° = ℃ =

π 180 5 9

-1

-1

rad

( ℉－ 32)

■SI Units : Consistent unit recommended and adopted in the general meeting of weights and measures.

Supplement (Basic and Technical Data) 6

Calculations of Punching Force

P=

<Meaning of Symbols >

ℓ×t×τ 1000

P : Punching Force (KN)

ℓ : Punching profile length (mm) t : Material Thickness (mm)

τ: Shearing Strength of Material

(N/mm2)

■ Shearing and Tensile Strength of Various Materials Shearing Strength (N/mm )

Material Lead

Tensile Strength (N/mm )

Soft

Hard

Soft

Hard

20 ~ 30

-

25 ~ 40

-

Tin

30 ~ 40

-

40 ~ 50

-

Aluminum

70 ~ 110

130 ~ 160

80 ~ 120

170 ~ 220

120

200

150

250

Copper

180 ~ 220

250 ~ 300

220 ~ 280

300 ~ 400

Brass

220 ~ 300

350 ~ 400

280 ~ 350

400 ~ 600

Bronze

320 ~ 400

400 ~ 600

400 ~ 500

500 ~ 750

Nickel Silver

280 ~ 360

450 ~ 600

350 ~ 450

550 ~ 700

190

-

260

-

Zinc

Silver Hot-Rolled Soft Steel Plates, Sheets, Strips

260 over

280 over

Cold-Rolled Carbon Steel Plates, Sheets, Strips

260 over

280 over

330 ~ 420

410 ~ 520

Steel Plates for structural use (SS400) Steel (0.1% C)

250

320

320

400

Steel (0.2% C)

320

400

400

500

Steel (0.3% C)

360

480

450

600

Steel (0.4% C)

450

560

560

720

Steel (0.6% C)

560

720

720

900

Steel (0.8% C)

720

900

900

1100

Steel (1.0% C)

800

1050

1000

1300

Stainless Steel

520

560

650 ~ 700

-

Nickel Steel

250

-

440 ~ 500

570 ~ 630

Supplement (Basic and Technical Data) 7

Steel Materials Korea Industrial Standards Name(No.) Rolled Steels for General Structural Use (KS D 3503) Carbon Steels Bars for General Structural Use (KS D 3566) Carbon Steels Bars for Machine Structural Use (KS D 3517)

Code

Tensile Elongation Hardness Strength (%) (HB) (N/mm )

JIS

AISI ㆍ ASTM

DIN

SS400

400~510

17~24

-

SS400

ASTM 45~65

St44-2, -3

SPS400

400 over

23 over

-

STK400

-

St44-2

STKM11A 290 over

30 over

-

STKM11A

ASTM 1008

St34-2

SM20C

400 over

28 over

116~174

S20C

AISI 1020

CK22

SM45C

570 over

20 over

167~229

S45C

AISI 1045

CK45

Nickel-Chromium Steels (KS D 3708)

SNC415

780 over

17 over

-

SNC415

-

-

SNC418

980 over

12 over

-

SNC418

-

-

Chromium-Molybde num Steels (KS D 3711)

SCM420

830 over

14 over

262~352

SCM420

-

-

SCM435

930 over

15 over

269~331

SCM435

AISI 4135

34CrMo4

SCM440

980 over

12 over

285~352

SCM440

AISI 4140

42CrMo4

STC1

-

-

217 under

SK1

ASTM W1-13

-

STC3

-

-

212 under

SK3

ASTM W1-10

C105W1

-

207 under

SK5

ASTM W1-8

C80W1

269 under

SKH3

ASTM T4

S18-1-2-5 S12-1-4-5

Carbon Steels for Machine Structural Use (KS D 3752)

Carbon Tool Steels (K S D 3751) High-Speed Tool Steels (KS D 3522)

Alloy Tool Steels (KS D 3753) Spring Steels (KS D 3071) High Carbon Chromium Steels (KS D 3525) Carbon Steel Castings (KS D 4101) Gray Iron Castings (KS D 4301) Spheroidal Graphite Iron Castings (KS D 4302)

STC5

-

SKH3

-

SKH10

-

-

285 under

SKH10

ASTM T15

SKH55

-

-

277 under

SKH55

-

S6-5-2-5

SKH59

-

-

277 under

SKH59

ASTM M42

S2-10-1-8 105WCr6

STS2

-

-

217 under

SKS2

-

STD11

-

-

255 under

SKD11

ASTM BD2

-

STD6

-

-

299 under

SKD6

ASTM H11

X38CrMoV51

SPS3

1226 over

9 over

341~401

SUP3

AISI 1075

-

SPS7

1230 over

9 over

363~429

SUP7

AISI 9260

-

SPS9

1230 over

9 over

363~429

SUP9

-

55Cr3

STB2

-

-

217 under

SUJ2

ASTM 52100

100Cr6

STB3

-

-

217 under

SUJ3

-

-

SC450

450 over

19 over

-

SC450

ASTM 65-35

GS-45

GC200

200 over

-

223 under

FC200

ASTM Class35

-

GC250

250 over

-

241 under

FC250

ASTM Class40

-

GCD450

450 over

10 over

143~217

FCD450

ASTM 65-45-12

GGG-45

GCD600

600 over

3 over

192~269

FCD600

ASTM 80-55-06

GGG-60

Supplement (Basic and Technical Data) 8

Nonferrous Metal Materials ● ( ) : Old Codes Tensile Strength (N/mm )

Elongation (%)

Hardness (HB)

CAC202 (YBsC2)

195 over

20 over

CAC203 (YBsC3)

245 over

CAC301 (HBsC1)

Korea Industrial Standards Name(No.) Brass Castings (KS D 6024)

High Strength Brass Castings (KS D 6024)

Bronze Castings (KS D 6024)

Phosphor Bronze Castings (KS D 6024)

Lead Bronze Castings (KS D 6024)

Aluminium Bronze Castings (KS D 6024)

Silicon Bronze Castings (KS D 6024)

Code

Related to Foreign Standards JIS

UNS(ASTM)

DIN

-

CAC202

C85400

CuZn33Pb

20 over

-

CAC203

C85700

CuZn37Pb

430 over

20 over

90 over

CAC301

C86500

CuZn35Al1

CAC302 (HBsC2)

490 over

18 over

100 over

CAC302

C86400

CuZn34Al1

CAC303 (HBsC3)

635 over

15 over

165 over

CAC303

C86200

CuZn25Al5

CAC304 (HBsC4)

755 over

12 over

200 over

CAC304

C86300

CuZn25Al5

CAC401 (BC1)

165 over

15 over

-

CAC401

C84400

-

CAC402 (BC2)

245 over

20 over

-

CAC402

C90300

-

CAC403 (BC3)

245 over

15 over

-

CAC403

C90500

CuSn10Zn

CAC406 (BC6)

195 over

15 over

-

CAC406

C83600

CuSn5ZnPb

CAC407 (BC7)

215 over

18 over

-

CAC407

C92200

-

CAC502A (PBC2)

195 over

5 over

60 over

CAC502A

-

CuSn10

CAC502B (PBC2B)

295 over

5 over

80 over

CAC502B

C90700

CuSn12

CAC503B (PBC3B)

265 over

3 over

90 over

CAC503B

C91000

CuSn12

CAC602 (LBC2)

195 over

10 over

65 over

CAC602

-

CuPb5Sn

CAC603 (LBC3)

175 over

7 over

60 over

CAC603

C93700

CuPb10Sn

CAC604 (LBC4)

165 over

5 over

55 over

CAC604

C93800

CuPb15Sn

CAC605 (LBC5)

145 over

5 over

45 over

CAC605

-

CuPb20Sn

CAC701 (AIBC1)

440 over

25 over

80 over

CAC701

C95200

CuAl10Fe

CAC702 (AIBC2)

490 over

20 over

120 over

CAC702

C95400

CuAl9Ni

CAC703 (AIBC3)

590 over

15 over

150 over

CAC703

C95800

CuAl10Ni

CAC704 (AIBC4)

590 over

15 over

160 over

CAC704

C95700

-

CAC801 (SzBC1)

345 over

25 over

-

CAC801

C87400

-

CAC802 (SZBC2)

440 over

12 over

-

CAC802

C87500

CuZn15Si4

CAC803 (SzBC3)

390 over

20 over

-

CAC803

-

-

Supplement (Basic and Technical Data) 9

■ Heat Treatment for Steels Type

Vickers Hardness (HV)

Quenching Depth (mm)

Strain

Applicable Material

Typical Material

Quenching

Max.750

Full Depth

Varies according to material

High Carbon Steels (C＞0.45%)

STB2 SKH55 STC4 SM45C

Max.750

Standard:0.5 Max.:2

Moderate

Low Carbon Steel (C＜0.3%)

SCM415 SNCM220

Carburizing and Quenching

High Frequency Quenching

Max.500

1~2

High

Medium Carbon Steel (0.3%＜0.5%)

SM45C

Remarks * Not recommended ded for long or precision parts * Quenching depth and area specified on drawings * Applicable to precision parts * Quenching depth and area specified on drawings * Expensive in small volume * Good Strain resistance * Applicable to precision parts

Nitriding

900~1000

0.1~0.2

Nitralloy Steel

Low

SACM645

* Obtains highest hardness of all quenching techniques * Applicable to spindles for radial bearings * Low temperature annealing

Bluing

-

-

-

Wire Rods

SWP-B

* Removes internal stress in forming to enhance elasticity

■ Hardness Tests and Applicable Parts Test Method

Principles

Brinell Hardness

* A known load applied through a harden steel ball will make permanent indentation in the metal. The Brinell hardness number is found as a number equal to the applied load divided by the spherical surface area of indentation

Rockwell Hardness

* The Rockwell hardness tester will measure hardness by determining the depth of penetration of penetrator, a steel ball or a diamond spheroconical penetrator, into specimen under certain fixed condition of test

Vickers Hardness

* Similar in principle to the Brinell hardness test. The standard Vickers penetrator is a square-based diamond pyramid with 136. The Vickers hardness number equals the applied load in kilograms divided by the area of pyramidal impression

Applicable Heat Treated Parts * Annealed Parts

Characteristics * Applicable to uneven materials due to large indentation

* Normalized Parts * Not applicable to small or thin specimens * Quenched-Tempered Parts

* Hardness number is obtained very quickly

* Carburized/Nitrided Surfaces

* Suitable for intermediate test to actual products

* Thin Sheets, such as Copper, Brass, Bronze, etc.

* Be cautious because various types of tests are available

* Parts with High Frequency quenching

* Applicable to small and thin specimens

* Harden layer depth in carburized/nitrided parts

* Applicable to all materials because of diamond penetrators

Supplement (Basic and Technical Data) 10

Conversion Table of Hardness ■ Conversion table for approximate values for steel according to Rockwell hardness 'C' scale ①

Rockwell C-Scale Hardness (HRC)

Brinell Hardness (HB) Load: 3000kgf, 10mm Ball Vickers Hardness (HV)

③

Standard Ball

Tungsten Carbide Ball

Rockwell Hardness ③ A-Scale D-Scale B-Scale 60-kgf Load 100-kgf Load 100-kgf Diamond Diamond Load 1.6mm Conical Conical (1/16 inch) Penetrator Penetrator Ball (HRB) (HRA) (HRD)

Shore Hardness (HS)

Tensile Strength (Approximate value) Mpa (kgf/mm2) ②

Rockwell C-Scale Hardness (HRC) ③

68

940

-

-

85.6

-

76.9

97

-

68

67

900

-

-

85.0

-

76.1

95

-

67

66

865

-

-

84.5

-

75.4

92

-

66

65

832

-

(739)

83.9

-

74.5

91

-

65

64

800

-

(722)

83.4

-

73.8

88

-

64

63

772

-

(705)

82.8

-

73.0

87

-

63

62

746

-

(688)

82.3

-

72.2

85

-

62

61

720

-

(670)

81.8

-

71.5

83

-

61

60

697

-

(654)

81.2

-

70.7

81

-

60

59

674

-

(634)

80.7

-

69.9

80

-

59

58

653

-

615

80.1

-

69.2

78

-

58

57

633

-

595

79.6

-

68.5

76

-

57

56

613

-

577

79.0

-

67.7

75

-

56

55

595

-

560

78.5

-

66.9

74

2075 (212)

55

54

577

-

543

78.0

-

66.1

72

2015 (205)

54

53

560

-

525

77.4

-

65.4

71

1950 (199)

53

52

544

(500)

512

76.8

-

64.6

69

1880 (192)

52

51

528

(487)

496

76.3

-

63.8

68

1820 (186)

51

50

513

(475)

481

75.9

-

63.1

67

1760 (179)

50

49

498

(464)

469

75.2

-

62.1

66

1695 (173)

49

48

484

451

455

74.7

-

61.4

64

1635 (167)

48

47

471

442

443

74.1

-

60.8

63

1580 (161)

47

46

458

432

432

73.6

-

60.0

62

1530 (156)

46

45

446

421

421

73.1

-

59.2

60

1480 (151)

45

44

434

409

409

72.5

-

58.5

58

1435 (146)

44

43

423

400

400

72.0

-

57.7

57

1385 (141)

43

42

412

390

390

71.5

-

56.9

56

1340 (136)

42

41

402

381

381

70.9

-

56.2

55

1295 (132)

41

40

392

371

371

70.4

-

55.4

54

1250 (127)

40

39

382

362

362

69.9

-

54.6

52

1215 (124)

39

Supplement (Basic and Technical Data) 11

Conversion Table of Hardness

Rockwell C-Scale Vickers Hardness Hardness (HRC) (HV) ③

Brinell Hardness (HB) Load: 3000kgf, 10mm Ball

Rockwell Hardness ③

Standard Ball

Tungsten Carbide Ball

A-Scale 60-kgf Load Diamond Conical Penetrator (HRA)

B-Scale 100-kgf Load 1.6mm (1/16 inch) Ball (HRB)

D-Scale 100-kgf Load Diamond Conical Penetrator (HRD)

Shore Hardness (HS)

Tensile Strength Rockwell (Approximate C-Scale value) Hardness 2 Mpa (kgf/mm ) (HRC) ②

③

38

372

353

353

69.4

-

53.8

51

1180 (120)

38

37

363

344

344

68.9

-

53.1

50

1160 (118)

37

36

354

336

336

68.4

(109.0)

52.3

49

1115 (114)

36

35

345

327

327

67.9

(108.5)

51.5

48

1080 (110)

35

34

336

319

319

67.4

(108.0)

50.8

47

1055 (108)

34

33

327

311

311

66.8

(107.5)

50.0

46

1025 (105)

33

32

318

301

301

66.3

(107.0)

49.2

44

1000 (102)

32

31

310

294

294

65.8

(106.0)

48.4

43

980 (100)

31

30

302

286

286

65.3

(105.5)

47.7

42

950 (97)

30

29

294

279

279

64.7

(104.5)

47.0

41

930 (95)

29

28

286

271

271

64.3

(104.0)

46.1

41

910 (93)

28

27

279

264

264

63.8

(103.0)

45.2

40

880 (90)

27

26

272

258

258

63.3

(102.5)

44.6

38

860 (88)

26

25

266

253

253

62.8

(101.5)

43.8

38

840 (86)

25

24

260

247

247

62.4

(101.0)

43.1

37

825 (84)

24

23

254

243

243

62.0

100.0

42.1

36

805 (82)

23

22

248

237

237

61.5

99.0

41.6

35

785 (80)

22

21

243

231

231

61.0

98.5

40.9

35

770 (79)

21

20

238

226

226

60.5

97.8

40.1

34

760 (77)

20

(18)

230

219

219

-

96.7

-

33

730 (75)

(18)

(16)

222

212

212

-

95.5

-

32

705 (72)

(16)

(14)

213

203

203

-

93.9

-

31

675 (69)

(14)

(12)

204

194

194

-

92.3

-

29

650 (66)

(12)

(10)

196

187

187

-

90.7

-

28

620 (63)

(10)

(8)

188

179

179

-

89.5

-

27

600 (61)

(8)

(6)

180

171

171

-

87.1

-

26

580 (59)

(6)

(4)

173

165

165

-

85.5

-

25

550 (56)

(4)

(2)

166

158

158

-

83.5

-

24

530 (54)

(2)

(0)

160

152

152

-

81.7

-

24

515 (53)

(0)

Note) ① The values in correspond to Table 1 of ASTM E 140 (Adjusted by SAE, ASM, and ASTM in collaboration) ② The values and units in parentheses have been converted from psi based on conversion tables of JIS Z 8413 and Z 8438 ③ The Values in parentheses are beyond the normal range and are given for reference only

Supplement (Basic and Technical Data) 12

Surface Roughness ■ Typical methods for measuring surface roughness

m

Rv

Rmax

Rp

ℓ

Rmax=Rp+Rv

Supplement (Basic and Technical Data) 13

Surface Roughness ■ Reference : Relationship between arithmetical mean roughness(Ra) and conventional symbols Max. height (Rmax)

Arithmetical mean roughness (Ra) Preferred number series 0.012a

Cut-off

π

value C(mm)

Indication of surface texture on drawings

0.08

Ten-point mean roughness (Rz)

Preferred number series 0.05s

0.05z

0.1s

0.1z

0.2s

0.2z

Standard length of Rmaxㆍ Rz (mm)

Triangular indication

0.08 0.025a 0.25 0.05 a

0.012

~

0.2

0.25 0.1

a

0.4s

0.4z

0.2

a

0.8s

0.8z

0.4

a

1.6s

1.6z

0.8

0.8 0.8

a

1.6

a

3.2

a

0.4

0.25 6.3

a

12.5

a

3.2

12.5 25

a

50

a

100

a

~

1.6

~

3.2s

3.2z

6.3s

6.3z

2.5s

12.5z

25s

25z

50s

50z

100s

100z

200s

200z

400s

400z

6.3

~

2.5

25

8

8

50 -

~

100

~ -

■ The interdependence for 3 classes is not strictly enforced. ■ The evaluation lengths of Ra, Rmax and Rz : Five times the cut-off value and standard length respectively.

Supplement (Basic and Technical Data) 14

General Dimensional Tolerance of Cutting 1. General dimensional tolerance of cutting (excluding chamfered parts) Length dimensional tolerance

unit : mm

Degree

Symbol

Standard Dimension

Explanation

0.5(') to 3 incl.

Over 3 to 6 incl.

Over 6 Over 30 to to 30 incl. 120 incl.

Over 120 to 400 incl.

Over 400 Over 1000 Over 2000 to to to 1000 incl. 2000 incl. 4000 incl.

Tolerance

f

Fine

± 0.05

± 0.05

± 0.1

± 0.15

± 0.2

± 0.3

± 0.5

-

m

Medium

± 0.1

± 0.1

± 0.2

± 0.3

± 0.5

± 0.8

± 1.2

± 2

c

Coarse

± 0.2

± 0.3

± 0.5

± 0.8

± 1.2

± 2

± 3

± 4

■ Note (') : Tolerance for standard dimensions of less than 0.5mm shall be specified individually.

2. Length dimensional tolerance in chamfered parts (corner roundness or chamfer dimension) Degree

unit : mm

Standard Dimension

Symbol

Explanation

f

Fine

m

Medium

c

Coarse

0.5(') to 3 incl.

Over 3 to 6 incl.

Over 6

Tolerance

± 0.2

± 0.5

± 1

± 0.4

± 1

± 2

■ Note (') : Tolerance for standard dimensions of less than 0.5mm shall be specified individually.

3. Tolerance of angle dimension Degree Symbol

unit : mm Shorter Side of Corner

Explanation

10 or less

Over 10 to 50 incl.

Over 50 to 120 incl.

Over 120 to 400 incl.

Over 400

Tolerance f

Fine

m

Medium

c

Coarse

± 1°

± 30'

± 20'

± 10'

± 5'

± 1 ° 30'

± 1°

± 30'

± 15'

± 10'

Supplement (Basic and Technical Data) 15

Tolerances of Commonly Used Hole Fits ■ Tolerances of holes to be used in commonly used fits Basic Over Size Step or (mm) less

―

3

6

10

14

18

24

3

6

10

14

18

24

30

+188 +208 B10 +180 +140 +140 +150

30

40

50

65

80

100

120

140

160

180

200

225

250

280

315

355

400

450

40

50

65

80

100

120

140

160

180

200

225

250

280

315

355

400

450

500

+220 +150

+244 +160

+270 +280 +310 +320 +360 +380 +420 +440 +470 +525 +565 +605 +690 +750 +830 +910 +1010 +1090 +170 +180 +190 +200 +220 +240 +260 +280 +310 +340 +380 +420 +480 +540 +600 +680 +760 +840

+100 +116 +70 +80

+138 +95

+162 +110

+182 +192 +214 +224 +257 +267 +300 +310 +330 +355 +375 +395 +430 +460 +500 +540 +595 +120 +130 +140 +150 +170 +180 +200 +210 +230 +240 +260 +280 +300 +330 +360 +400 +440

+635 +480

+118 +138 C10 +100 +60 +70 +80

+165 +95

+194 +110

+220 +230 +260 +270 +310 +320 +360 +370 +390 +425 +445 +465 +510 +540 +590 +630 +690 +120 +130 +140 +150 +170 +180 +200 +210 +230 +240 +260 +280 +300 +330 +360 +400 +440

+730 +480

C9

To leranc e Zo ne Cla ss of Ho le

Unit : ㎛

+85 +60

D8

+34 +20

+48 +30

+62 +40

+77 +50

+98 +65

+119 +80

+146 +100

+174 +120

+208 +145

+242 +170

+271 +190

+299 +210

+327 +230

D9

+45 +20

+60 +30

+763 +40

+93 +50

+117 +65

+142 +80

+174 +100

+207 +120

+245 +145

+285 +170

+320 +190

+350 +210

+385 +230

D10 +60 +20

+78 +30

+98 +40

+120 +50

+149 +65

+180 +80

+220 +100

+260 +120

+305 +145

+355 +170

+400 +190

+440 +210

+480 +230

E7

+24 +14

+32 +20

+40 +25

+50 +32

+61 +40

+75 +50

+90 +60

+107 +72

+125 +85

+146 +100

+162 +110

+182 +125

+198 +135

E8

+28 +14

+38 +20

+47 +25

+59 +32

+73 +40

+89 +50

+106 +60

+126 +72

+148 +85

+172 +100

+191 +110

+214 +125

+232 +135

E9

+39 +14

+50 +20

+61 +25

+75 +32

+92 +40

+112 +50

+134 +60

+159 +72

+185 +85

+215 +100

+240 +110

+265 +125

+290 +135

F6

+12 +6

+18 +10

+22 +13

+27 +16

+33 +20

+41 +25

+49 +30

+58 +36

+68 +43

+79 +50

+88 +56

+98 +62

+108 +68

F7

+16 +6

+22 +10

+28 +13

+34 +16

+41 +20

+50 +25

+60 +30

+71 +36

+83 +43

+96 +50

+108 +56

+119 +62

+131 +68

F8

+20 +6

+28 +10

+35 +13

+43 +16

+53 +20

+64 +25

+76 +30

+90 +36

+106 +43

+122 +50

+137 +56

+151 +62

+165 +68

G6

+8 +2

+12 +4

+14 +5

+17 +6

+20 +7

+25 +9

+29 +10

+34 +12

+39 +14

+44 +15

+49 +17

+54 +18

+60 +20

G7

+12 +2

+16 +4

+20 +5

+24 +6

+28 +7

+34 +9

+40 +10

+47 +12

+54 +14

+61 +15

+69 +17

+75 +18

+83 +20

H6

+6 0

+8 0

+9 0

+11 0

+13 0

+16 0

+19 0

+22 0

+25 0

+29 0

+32 0

+36 0

+40 0

H7

+10 0

+12 0

+15 0

+18 0

+21 0

+25 0

+30 0

+35 0

+40 0

+46 0

+52 0

+57 0

+63 0

H8

+14 0

+18 0

+22 0

+27 0

+33 0

+39 0

+46 0

+54 0

+63 0

+72 0

+81 0

+89 0

+97 0

H9

+25 0

+30 0

+36 0

+43 0

+52 0

+62 0

+74 0

+87 0

+100 0

+115 0

+130 0

+140 0

+155 0

H10 +40 0

+48 0

+58 0

+70 0

+84 0

+100 0

+120 0

+140 0

+160 0

+185 0

+210 0

+230 0

+250 0

JS6 ±3

±4

±4.5

±5.5

±6.5

±8

±9.5

±11

±12.5

±14.5

±16

±18

±20

JS7 ±5

±6

±7

±9

±10

±12

±15

±17

±20

±23

±26

±28

±31

K6

0 -6

+2 -6

+2 -7

+2 -9

+2 -11

+3 -13

+4 -15

+4 -18

+4 -21

+5 -24

+5 -27

+7 -29

+8 -32

K7

0 -10

+3 -9

+5 -10

+6 -12

+6 -15

+7 -18

+9 -21

+10 -25

+12 -28

+13 -33

+16 -36

+17 -40

+18 -45

M6

-2 -8

-1 -9

-3 -12

-4 -15

-4 -17

-4 -20

-5 -24

-6 -28

-8 -33

-8 -37

-9 -41

-10 -46

-10 -50

M7

-2 -12

0 -12

0 -15

0 -18

0 -21

0 -25

0 -30

0 -35

0 -40

0 -46

0 -52

0 -57

0 -63

N6

-4 -10

-5 -13

-7 -16

-9 -20

-11 -24

-12 -28

-14 -33

-16 -38

-20 -45

-22 -51

-25 -57

-26 -62

-27 -67

N7

-4 -14

-4 -16

-4 -19

-5 -23

-7 -28

-8 -33

-9 -39

-10 -45

-12 -52

-14 -60

-14 -66

-16 -73

-17 -80

P6

-6 -12

-9 -17

-12 -21

-15 -26

-18 -31

-21 -37

-26 -45

-30 -52

-36 -61

-41 -70

-47 -79

-51 -87

-55 -95

P7

-6 -16

-8 -20

-9 -24

-11 -29

-14 -35

-17 -42

-21 -51

-24 -59

-28 -68

-33 -79

-36 -88

-41 -98

-45 -108

R7

-10 -20

-11 -23

-13 -28

-16 -34

-20 -41

-25 -50

-30 -60

-32 -62

-38 -73

-41 -76

S7

-14 -24

-15 -27

-17 -32

-21 -39

-27 -48

-34 -59

-42 -72

-48 -78

-58 -93

-66 -77 -85 -93 -105 -113 -123 -101 -117 -125 -133 -151 -159 -169

-64 -94

-78 -91 -107 -119 -131 -113 -126 -147 -159 -171

T7

―

―

―

―

― -33 -54

-39 -64

-45 -70

-55 -85

U7

-18 -28

-19 -31

-22 -37

-26 -44

-33 -40 -54 -61

-51 -76

-61 -86

-76 -91 -111 -131 -106 -121 -146 -166

X7

-20 -30

-24 -36

-28 -43

-33 -38 -46 -56 -51 -56 -67 -77

―

―

―

-48 -88

-50 -90

-53 -93

-60 -63 -67 -74 -78 -87 -93 -103 -106 -109 -113 -126 -130 -144 -150 -166

-109 -172

―

―

―

―

―

―

―

―

―

―

―

―

―

―

―

―

―

Supplement (Basic and Technical Data) 16

Tolerances of Commonly Used Shaft Fits ■ Tolerances of Shafts to be used in commonly used fits Unit : ㎛ Basic Over Size Step (mm) or

less

b9 c9

To leranc e Zo ne Cla ss of Ho le

d8

―

3

6

10

14

18

24

3

6

10

14

18

24

30

-140 -140 -150 -165 -170 -186 -60 -70 -80 -85 -100 -116 -20 -30 -40 -34 -48 -62

30

40

40

50

50

65

65

80

-150 -193 -95 -138 -50 -77

-160 -212 -110 -162 -65 -98

-170 -180 232 -242 -120 -130 -182 -192 -80 -119

-190 -200 -264 -274 -140 -150 -214 -224 -100 -146

d9

-20 -45

-30 -60

-40 -76

-50 -93

-65 -117

-80 -142

-100 -174

e7

-14 -24

-20 -32

-25 -40

-32 -50

-40 -61

-50 -75

-60 -90

e8

-14 -28

-20 -38

-25 -47

-32 -59

-40 -73

-50 -89

-60 -106

e9

-14 -39

-20 -50

-25 -61

-32 -75

-40 -92

-50 -112

-60 -134

f6

-6 -12

-10 -18

-13 -22

-16 -27

-20 -33

-25 -41

-30 -49

f7

-6 -16

-10 -22

-13 -28

-16 -34

-20 -41

-25 -50

-30 -60

f8

-6 -20

-10 -28

-13 -35

-16 -43

-20 -53

-25 -64

-30 -76

g5

-2 -6

-4 -9

-5 -11

-6 -14

-7 -16

-9 -20

-10 -23

g6

-2 -8

-4 -12

-5 -14

-6 -17

-7 -20

-9 -25

-10 -29

h5

0 -4

0 -5

0 -6

0 -8

0 -9

0 -11

0 -13

h6

0 -6

0 -8

0 -9

0 -11

0 -13

0 -16

0 -19

h7

0 -10

0 -12

0 -15

0 -18

0 -21

0 -25

0 -30

h8

0 -14

0 -18

0 -22

0 -27

0 -33

0 -39

0 -46

0 -25 ±2 ±3 ±5

0 -30 ±2.5 ±4 ±6

0 -36 ±3 ±4.5 ±7

0 -43 ±4 ±5.5 ±9

0 -52 ±4.5 ±6.5 ±10

0 -62 ±5.5 ±8 ±12

0 -74 ±6.5 ±9.5 ±15

k5

+4 0

+6 +1

+7 +1

+9 +1

+11 +2

+13 +2

+15 +2

k6

+6 0

+9 +1

+10 +1

+12 +1

+15 +2

+18 +2

+21 +2

m5

+6 +2

+9 +4

+12 +6

+15 +7

+17 +8

+20 +9

+24 +11

m6

+8 +2

+12 +4

+15 +6

+18 +7

+21 +8

+25 +9

+30 +11

n5

+8 +4

+13 +8

+16 +10

+20 +12

+24 +15

+28 +17

+33 +20

n6

+10 +4

+16 +8

+19 +10

+23 +12

+28 +15

+33 +17

+39 +20

+12 +6 +16 +10 +20 +14

+20 +12 +23 +15 +27 +19

+24 +15 +28 +19 +32 +23

+29 +18 +34 +23 +39 +28

h9 js5 js6 js7

p6 r6 s6 t6 u6 x6

―

―

―

+24 +18 +26 +20

+31 +23 +36 +28

+37 +28 +43 +34

+35 +22 +41 +28 +48 +35 ― ― +54 +41 +44 +54 +61 +33 +41 +48 +51 +56 +67 +77 +40 +45 +54 +64

+42 +51 +26 +32 +50 +60 +62 +34 +41 +43 +59 +72 +78 +43 +53 +59 +64 +70 +85 +94 +48 +60 +66 +75 +76 +86 +106 +121 +60 +70 +87 +102 ―

―

80

100

120 140 160 180 200 225 250

280

100 120

140 160 180 200 225 250 280

315

-220 -240 -307 -327 -170 -180 -257 -267 -120 -174 -120 -207 -72 -107 -72 -126 -72 -159 -36 -58 -36 -71 -36 -90 -12 -27 -12 -34 0 -15 0 -22 0 -35 0 -54 0 -87 ±7.5 ±11 ±17

-260 -360 -200 -300

+18 +3 +25 +3 +28 +13 +35 +13 +38 +23 +45 +23 +59 +37 +73 +76 +51 +54 +93 +101 +71 +79 +113 +126 +91 +104 +146 +166 +124 +144 ―

-280 -310 -380 -410 -210 -230 -310 -330 -145 -208 -145 -245 -85 -125 -85 -148 -85 -185 -43 -68 -43 -83 -43 -106 -14 -32 -14 -39 0 -18 0 -25 0 -40 0 -63 0 -100 ±9 ±12.5 ±20

-340 -455 -240 -355

-380 -420 -459 -535 -260 -280 -375 -395 -170 -242 -170 -285 -100 -146 -100 -172 -100 -215 -50 -79 -50 -96 -50 -122 -15 -35 -15 -44 0 -20 0 -29 0 -46 0 -72 0 -115 ±10 ±14.5 ±23

+21 +3 +28 +3 +33 +15 +40 +15

+88 +63 +117 +92 +147 +122

―

― +60 +31 +79 +50 +109 +80 +159 +130

+93 +68 +133 +108 +171 +146

+106 +77 +151 +122

355

355

400

400

450

450

500

-480 -540 -610 -670 -300 -330 -430 -460 -190 -271 -190 -320 -110 -162 -110 -191 -110 -240 -56 -88 -56 -108 -56 -137 -17 -40 -17 -49 0 -23 0 -32 0 -52 0 -81 0 -130 ±11.5 ±16 ±26

-600 -680 -740 -820 -360 -400 -500 -540 -210 -299 -210 -350 -125 -182 -125 -214 -125 -265 -62 -98 -62 -119 -62 -151 -18 -43 -18 -54 0 -25 0 -36 0 -57 0 -89 0 -140 ±12.5 ±18 ±28

-760 -840 -915 -995 -440 -480 -595 -635 -230 -327 -230 -385 -135 -198 -135 -232 -135 -290 -68 -108 -68 -131 -68 -165 -20 -47 -20 -60 0 -27 0 -40 0 -63 0 -97 0 -155 ±13.5 ±20 ±31

+27 +4 +36 +4 +43 +20 +52 +20

+29 +4 +40 +4 +46 +21 +57 +21

+32 +5 +45 +5 +50 +23 +63 +23

―

―

―

+24 +4 +33 +4 +37 +17 +46 +17

+52 +27 +68 +43 +90 +65 +125 +100 +159 +134

315

+66 +73 +80 +34 +37 +40 +88 +98 +108 +56 +62 968 +113 +126 +130 +144 +150 +166 +172 +84 +94 +98 +108 +114 +126 +132 +169 ― ― ― +140

―

―

―

―

―

―

―

―

―

―

―

―

―

―

Supplement (Basic and Technical Data) 17

Oilless Bearings

■ The general concept and description of Bearing. Concept. All elements that transfer the power under the condition of rotation, linear motion, thrust load, or angular pitching motion using it's own sliding or rolling character with ball, roller or self lubricating character regardless it's shape and material.

Description. -Rolling bearing It has more merits in velocity and load capacity under the general condition.

1. Ball bearing (Under high speed condition by using it's point contact working) 2. Roller bearing (Under high load condition by using it's line contact working)

● Spherical Roller (

)

● Tapered Roller (

)

● Cylindrical Roller (

)

● Needle Roller

)

(

3. Thrust Bearings (for Thrust Motion) ● Ball Thrust

● Tapered Roller Thrust

-Sliding B earing Operation proceed under contact onto Shaft or Sliding surface directly, small gap is required when it is working. It is more ideal than Ball & Roller bearing for a light and small shape, vibration and impact. 1. Oilless bearings (Using without oiling) 2. Simple oiling type sliding bearing (Oil or grease will be needed)

■ What is an oilless bearing A bearing which can improve productivity and enable the saving cost and time by using in condition of high & low temperature, corrosion environment, alien sub stance, impactive load, or by using in where oiling is not easy or useless. There are various kind of shape or material for oilless bearing such as various metal, wooden material, plastic and ceramic.

Supplement (Basic and Technical Data) 18

Oilless Bearings

■ Advantage & Disadvantage of Oilless bearing and Oiling method. General lubricating of oilless bearing ● Dry lubrication = Using solid lubricant

EX) DDU01 dry bearing (PTFE + lead compound lubricant) LuBo #500SP (natural graphite + PTFE lubricant)

* Solid lubricant : Powder or solid type lubricant that is supposed to be used in harsh environments such as high & low temperature, corrosion environment and where can not use oil or grease. Generally it is made with natural graphite, Mo S 2 , PTFE, Pb.

● Liquid lubricant (lubricating with oil or water)

EX) - Sintered metal bearing (Oiling into sintered metal) - LuBo #200B (Water lubricating by performing water film when it is using in the water.

■ Advantage & Disadvantage of each lubricating method Dry lub ricating (Using solid lubricant)

Advantage

Disadvantage

- Possible to being used in high & low temperature. - Possible to being used in corrosion environment - High load and low speed condition where oiling is useless, linear motion, angular pitching motion, impactive load, and ideal in discontinuous motion.

- Not supposed to be used in high speed when it is using in oilless condition. * Using it in high speed condition may occur melting or shorten life cycle of bearing because solid lubricant has higher friction coefficient than liquid lubricant.

Liquid lub ricating (Using oil or w ater) - Light or medium load and high speed * Liquid lubricating prevent friction between metal to metal by forming oil film with continuously rotating by centrifugal force in the clearance of shaft and housing. - Regular oiling is required - Can not be used in high & low temperature. - Can not be used in corrosion environment. - Not proper to be used in high load & low speed as oil film is hard to be formed, impactive load, angular pitching motion, discontinuous motion.

Supplement (Basic and Technical Data) 19

Oilless Bearings ■ Bearing life and wear amount The life of bearing is basically dependent on the acceptable amount of wear, which is mainly affected by friction conditions. Friction is influenced by load and velocity, foreign particles, condition of mating material, operational temperature, different modes of operation, type of lubricant used, etc. Therefore, it may not be possible to accurately estimate the life of bearing without sufficient application data. However, the wear amount may be estimated by the following method:

W : Wear amount (mm) V : Velocity (m/min) P : Surface pressure (kgf/cm ² ) T : Running time (hr) K : Coefficient of specific wear amount (mm / kgf/cm²ㆍ m/minㆍhr)

W=K.P.V.T

● Table (Experimental K value under different lubricating) Lubrication condition

K value

No lubricant (Dry)

1X10 -3~-5

Boundary lubrication under low speed (LuBo #500, DDU01 Dry Bearing)

1X10 -5~-7

Periodic lubrication (DX)

1X10 -6~-8

Continuous lubrication under water application (#200B, Miscellaneous)

1X10 -8~-10

■ PV value The PV value is a very important reference for selecting bearings and it can be obtained simply 2 by multiply P to V, where P is bearing surface pressure per unit area (Kgf/Cm , Estimation of bearing surface pressure per unit area will be obtained by multiply inner diameter to length), V is velocity per unit time.

● Rotary Motion Bushing

Pmax P PV-Value Limit

Thrust Washer

V (m/min) =

V m/min =

P (kgf/cm²) =

P kgf/cm²= PV kgf/cm²ㆍm/min =

PV (kgf/cm²ㆍ m/min) = V

max

W : Radial Load[kgf] L : Length[mm]

D : Outside-Dia.[mm]

N : RPM

d : Inside-Dia.[mm]

The allowable PV value is listed in the catalog. Please note that PV value can vary depending on its working condition temperature or lubrication. PV value of thrust washer & wear plate must not exceed 1/2 of bushing PV value.

Supplement (Basic and Technical Data) 20

Oilless Bearings ■ Frictional heat The frictional heat(Q) generated per unit time and unit area is as follows:

Q=

μㆍ P ㆍ V J

(kcal/min)

J : Heat equivalent of work (≒427kgf-m/kcal) μ: Coefficient of friction P : Pressure in kilograms per square centimeter (kgf/cm²) V : Velocity in meter per minute (m/min)

Since velocity is the main factor which limits bearing performance, the friction heat is mainly affected by velocity rather than pressure. Therefore, for similar PV values, additional lubrication should be considered for a higher velocity application to prevent damage to the bearing or the mating shaft.

■ Mating Shaft Type

Shaft Material

General use

General structural metal with S35C and higher strength

High Temperature

Stainless steel or Chrome plating

Corrosive Environment

Chrome plating

Hardness

Shaft Roughness

Rockwell "C 35" and above(higher strength material is recommended when foreign particles are present)

3~12 ㎛

* For applications above 100 C, the mating shaft dimensions should be reduced to account for the t hermal expansion of the material.

Thermal expansion= Thermal expansion coefficient( α)×diameter(d)×(application temperature-ambient temperature) -5 F or example) low carbon steel α :1.12×10 /℃ * 2, 3 Chrome plating is ideal for sea water and liquid medicine * Nitrification of the mating shaft effectively reduces friction for high load and low speed applications.

■ Additional Lubrication Additional lubrication with grease or oil reduces frictional heat and wear. Also it increases the bearing life and performance by reducing the amount of worn particles, preventing foreign particle interference (sealing effect), and reducing the noise as well as anti-rust effect of the shaft operation. Oil lubrication applied at the inner surface of a bearing in the installation stage, though no lubrication is required, reduces, the drastic wear th at occurs during initial operation.

Low load, High speed

Low Viscosity

Medium load, Medium speed

Medium Viscosity

8~17cst (30

High Load, Low speed

High Viscosity

) Spindle Oil, Miscellaneous

7~15cst (98.9 ) Motor Oil, Turbine Oil, Miscellaneous

100~1,000cst (37 ) Gear Oil, Cylinder Oil , Miscellaneous

* Grease containing MoS 2 that is highly recommended for the better life time and performance because this is very effective under high load, excessive wear, and high frictional heat condition.

Supplement (Basic and Technical Data) 21

Oilless Bearings ■ Oil groove and Lubrication h ole design - Oil g roove : Distribute the oil grooves around the maximum load point as shown below. The length of an oil groove is approximately 80% of the bearing length. The radius (R and r) and height (H) of an oil g roove is selected based on the inner diameter (ID) of the bearing as shown in the table below. Use a circular oil groove on the inner surface of a housing or the outer surface of the bearing when oil is supplied from outside of the housing. (Unit : mm)

Detail of A Oil Groove

R H

r

A

Lubricating Hole

I.D.

R

r

H

Q'ty

30 under

1.5

1.5

1.2

1~2

30 ~ 50

2.0

2.0

1.8

3

50 ~ 80

3.0

3.0

2.5

3

80 ~ 120

3.5

3.5

3.5

4

120 ~ 180

4.0

4.0

5.0

4

180 ~ 250

5.0

5.0

6.0

5

250 ~ 315

6.0

6.0

7.0

6

315 ~ 400

7.0

7.0

8.0

8

400 ~ 500

8.0

8.0

8.0

8

- Lubricating hole : One hole is recommended in an area where the load is not concentrated. Two holes on each side of the maximum load point are suggested for rotational motion. Use two holes along the length of each groove for longer bearing.

■ Edge(angle) chamfering It is ideal to chamfer the oilless bearing as the chart on the right. ID/Chamfering level

I.D.

Chamfer

ø80 under

0.5C

ø80 ~ 200

1.0C

ø200 ~ 300

1.5C

ø300 over

2.0C

■ The formula of calculating ideal thickness t = (0.05 ~ 0.07)d＋(2 ~ 5mm)

■ How to insert into the housing Per drawing on the right, you can insert the bushing into housing with a little pressure using a guide bar. It will be easier to oil after cutting the edge of OD and ID.

C

Inside-Dia. Chamfer

■ Attention - S haft must be ground. ( 3S ) - P lease follow the tolerance as shown at the dimension table in case of housing and shaft. - Please maintain the shaft horizontally to prevent the shaft from eccentricity. - Sealing is recommended because of possible inflow of foreign objects . - Hardening is not required, but the life of bearing will be extended if it is c hrome plated.

Guide Bar

Bushing

Supplement (Basic and Technical Data) 22

Housing

Areas of Plane Figures Circular Sector

Hyperbola r × α× 3 .1 4 1 6 = 0.01745 r α 180 = 2A r 1 A = r ℓ = 0 .0 0 8 7 2 7 α r 2 2

ℓ=

α r

D b

ℓ

r = 2A

ℓ

=

C

c

α

r

h= r - 1 2

p 2

2x 2x p 1＋ p 2x 2x p ＋ 1＋ p

＋ ln y

A close approximation when x is small in proportion to y

c 2＋ 4 h2 , ℓ= 0 . 0 1 7 4 5 αr 8h

r=

ℓ =Length of Arc=

ℓ

h(2 r－h)

1 A = [ r ℓ－c ( r － h ) ] 2

h

y x a ＋ b

x

Parabola c = 2

xy ab ln 2 2

57.296 ℓ α

Circular Segment ℓ

A=

B

a

5 7 .2 9 6 ℓ r

α =

A = Area BCD

y

P/2

x

ℓ = y 1＋

57.296 ℓ 4 r 2 - c2 , α = r

2 3

또는

x y

2

-

2 5

y2＋

ℓ=

4

x y

4 2 x 3

Parabola

Circular Ring

A = Area A = π ( R2 - r 2 ) = 3 .1 4 1 6 ( R 2 - r 2 )

y

A=

2

D

d

R

r

= 3.1416(R + r ) ( R - r )

(The area is equal to two-third of a rectangle which has x for base and y for its height)

2

= 0 .7 8 5 4 ( D - d )

x

= 0.7854(D+d)(D-d)

Circular Ring Sector

Segment of Parabola

A = Area, α= Angle in Degree A=

α

R

D

D

A = Area

C

F

απ 2 2 (R - r ) 360

A = BFC 2 = ( Area of parallelogram BCDE)× 3 If FG is the height of the segment and measured at right angle to BC, then 2 A = BFC = BC ×FG 3

G E

2 2 = 0 .0 0 8 7 3 α( R - r ) απ 2 2 d (D ) = 4 ×360

d

2 xy 3

B

2 2 = 0 .0 0 2 1 8 α (D - d )

Cycloid

Spandrel or Fillet

A = Area

ℓ = Length of Cycloid

A = Area c

r

πr2 A= r24 = 0.1075c 2

A = 3 πr 2 = 9.454 8 r

ℓ = 0 .2 1 5 r 2

d r

Ellipse A = Area , P = Perimeter of circumference A = π a b = 3.1416a b Approximate formulas for P are: α

b

1. P = 3.1416

2 (α 2＋ b 2 )

2. P = 3.1416

2 ( α 2 ＋ b2 ) -

2

2

= 2.3562d = ( Area of generating circle )× 3 ℓ = 8r = 4d

(α - b)2 2.2

Supplement (Basic and Technical Data) 23

V= Volum S= Surface Area

As= Lateral Surface Area

Ab=Base Area

χ= Distance from the base to the center of gravity

Prizm (Regular Hexagon Base)

Square Prizm

Cubic

G d

1.7321a

G

a

h

d

a

a

h

G χ

χ

χ

b

a

a

a

2a V = αbh

V = α3 S = 6α

As = 4a

S = 5.196 3α2＋6 αh

As = 2h(α＋b) h χ= 2

2

α χ= 2 d=

V = 2.59 8 α2 h

S = 2 (αb＋αh＋ bh)

2

χ =

α2＋ b 2 ＋ h 2

d=

3 α = 1.7321 α

A s = 6 αh

h 2 h 2 ＋4 α2

d=

Cone

Frustum of Cone

ℓ

r

ℓ

h

h

G

h

χ

G

χ

R

χ

G

Ab V= V=

πR2 h 3

=

As = πR ℓ

ℓ=

h 4

2

πα ＋

χ=

h 4

2 1 πb 3

V=

α = R ＋r

b= R- r ,

χ = h 4

a

πh 2 ( R ＋ Rr ＋ r 2 ) 3

As = πℓ α ,

R2＋ h2

a

R

ℓ=

Ab =

b2＋ h2

χ=

R2＋ 2Rr ＋3 r 2 R2 ＋Rr ＋r 2

Ab h 3 3 3 α2 = 2.598α2 2 h 4

Spherical Segment

Sphere

Regular Polygon r

h

G

Length of side

d

χ

r

a

Number of sides Area of base

4 πr 3 = 4 .1 88 790 20 5r 3 3

V=

πh (3 α2 πh 2 (3 r - h) ＋h 2 ) = V= 3 6

πd 3 = 0.52359877d 3 6

=

As = 2 π r h = π ( α2＋ h 2 ) α2 = h (2r - h)

S = 4πr 2 = πd 2 r=

3

3v = 0.6 203 51 4π

3

V=

d 2

χ=

2 3 (2 r - h) 4 (3 r - h)

V = Ab h S = 2A b ＋ nh α A s = nhα h χ = 2

Supplement (Basic and Technical Data) 24

Cylinder/Hollow Cylinder

Portion of Cylinder

Frustum of Pyramid

A

D

G

h

h

h2

χ

h1 r

Ab

R

V = πr 2 h = Ash

r

χ= h

Frustum of Pyramid with retangular base

h ( A b＋ A b1＋ A b A b1 ) 3

As = πR( h1＋ h2)

Ab =

3 3 2 α = 2.59 8α2 2

χ =

h A b＋ 2 A b A b1＋3 A b1 4 A b＋ A b A b1＋A b1

4R2＋(h2- h1)2

Torus

Spherical Sector

R

R

h

b1

a1

r G

G χ

a r

b

χ

a

V=

D=

2

2

A b

h1＋h2 2

2 V = πR

= πht (2 r ＋t)

χ = h

G

R

= π ht ( 2R - t)

AS = 2πr h

χ

t

V = πh (R 2- r 2 )

S = 2πr (r ＋h)

h

b1

D a

h ( 2 α＋α1)b ＋ (2α ＋α) b 1 6 h αb = ＋( α＋α1) (b ＋b1)＋α1 b1 6

V=

χ = h αb ＋αb1＋α1b ＋ 3α1b1

2 2 αb ＋αb1＋α1b ＋2 α1b 1

V = 2π2 Rr 2 = 19.739 Rr 2

V=

1 2 2 π Dd = 2.4674Dd 2 = 4 S = 4π Rr = 39.478Rr 2

= π2 Dd = 9.8696Dd

= 2.09 439510 24r 2 h S = πr ( 2h ＋ α)

χ = 3 (2 r - h)

Spherical Zone b

h

a

r

V=

πh (3α2＋3b2 ＋h 2 ) 6

As = 2πr h r

2

= α2＋

α2 - b2 - h 2 2h

2πr 2 h 3

2

Supplement (Basic and Technical Data) 25

8

SI Units ■ Overview of the International System of Units (SI Units) th ' ' ' The International System of Units was established by the 11 Conference Generale des Poids et ' Mesures (CGPM) in 1960. Universally abbreviated SI (from the French Le Systeme International ' d'Unites), it is the modern metric system of measurement used throughout the world. It is the responsibility of the CGPM to ensure that SI is widely disseminated and that it reflects the latest advances in science and technology.

SI Units are currently divided into three classes, Base Units, Derived Units, and Supplementary Units, which together form what is called "the coherent system of SI units." The SI also includes prefixes to form decimal multiples and submultiples of SI units. Also certain units that are not part of SI units are essential and used so widely that they are accepted by the International Committee for Weights and Measures (CIPM) for use with SI units.

■ SI Units Base Units : The SI base units on which the SI is founded are seven base quantities assumed to be mutually independent. Table 1 gives the names, symbols, and definitions of SI base units. Supplementary Units : Table 2 gives the names, symbols, and definitions of the SI supplementary units. They are now interpreted as so-called dimensionless derived units. SI derived Units : The SI derived units are expressed algebraically in terms of base units or other derived units including two supplementary units. Table 3 gives examples of derived units expressed in terms of SI base units only. Table 4 gives certain SI derived units expressed in terms of other SI units, which have special names and symbols. Also example of SI derived units that can be expressed with the aid of SI derived units having special names and symbols are given in table 5 SI prefixes : Table 6 gives the SI prefixes that are used to form decimal multiples and submultiples of SI units. They allow very large or very small numerical values to be avoided. Units outside SI units : Table 7 shows examples of units that are not part of SI units but accepted for use with SI units because they are used so widely.

■ Rules and Style conventions for printing and using SI units and Values of Quantities (1) Print in roman (upright) type regardless of the type used in the surrounding text. But symbols for quantities and variables are printed in italic (Example: t=3 s (t time, s second)) (2) Print in lower-case letters except when the name of the unit is derived from the name of a person. (Examples: m (meter), Pa (pascal), s (second), lm (lumen), V (volt), Wb (weber)) (3) Unaltered in the plural. (Example: 1= 75 cm, but not 1 = 75 cms) (4) Not followed by a period unless at the end of a sentence. (5) Symbols for units formed from other units by multiplication are indicated by means of either a half-high (that is, centered) dot or a space. (Example: Nㆍm or N m )

Supplement (Basic and Technical Data) 26

SI Units (6) In the expression for the value of a quantity, the unit symbol is placed after the numerical value and a space is left between the numerical value and the unit symbol. The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle: ˚ , ' , and," respectively, in which case no space is left between the numerical value and the unit symbol. ( 7) Digits should be separated into groups of three, counting from the decimal marker towards the left and right, by the use of a thin, fixed space, not by a comma. (Examples: 76 483 522, 43 279.168 29 but not 76,483,522, 43,279.168 29) (8) Symbols for units formed from other units by division are indicated by means of a solidus -1 (oblique stroke, /), a horizontal line, or negative exponents. (Example : m/s, m s , or mㆍ s ) However, to avoid ambiguity, the solidus must not be repeated on the same line unless parentheses are used. 2

-2

(Examples: m/s or, m ㆍ s , but not: m/s/s) (9) Unit symbols and unit names are not used together. -1

(Example: C/kg or coulomb per kilogram, but not coulomb/kg, C/kilogram; coulombㆍ kg , C per kg, or coulomb/kilogram) (10) not permissible to use abbreviations for their unit symbols or names 3

(Example: sec (for either s or second), cc (for either cm or cubic centimeter), mins (for either min or minutes), amps(for either A or amperes))

■ Rules and Style conventions for SI prefixes (1) Prefix symbols are printed in roman (upright) type regardless of the type used in the surrounding text, and are attached to unit symbols without a space between the prefix symbol and the unit symbol. This last rule also applies to prefixes attached to unit names. (Examples: mL(milliliter), pm(picometer), THz(terahertz)) (2) Prefixes are normally printed in lowercase letters except for prefix symbols Y(yotta), Z (zetta), E(exa), P(peta), T(tera), G(giga), and M(mega) (3) Compound prefix symbols, that is, prefix symbols formed by the juxtaposition of two or more prefix symbols, are not permitted. This rule also applies to compound prefixes. (Example: nm (nanometer), but not m μ m (millimicrometer)) (4) Prefix symbols cannot stand-alone and thus cannot be attached to the number 1, the symbol for the unit one. (Example: the number density of Pb atoms is 5 x 106/m 3, but not the number density of Pb 3 atoms is 5 M/m ) (5) It is often recommended that, for ease of understanding, prefix symbols should be chosen in such a way that numerical values are between 0.1 and 1000 7

6

(Examples: 3.3 x 10 Hz, may be written as 33 x 10 Hz = 33 Mhz)

Supplement (Basic and Technical Data) 27

SI Units Table 1. SI base units Base Quantity

SI base units Name

Symbol

Definition

Length

Meter

m

The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.

Mass

Kilogram

kg

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

Time

Second

s

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

Electric Current

Ampere

A

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 7 2 × 10 newton per meter of length.

Thermodynamic Temperature

Kelvin

K

The Kelvin, unit of thermodynamic temperature, is the fraction 1/273. 16 of the thermodynamic temperature of the triple point of water.

Amount of Substance

Mole

mol

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

Luminous Intensity

Candela

cd

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 12 540 × 10 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Table 2. SI supplementary units

Quantity

SI supplementary units Name

Symbol

Definition

Plane Angle

Radian

rad

The radian is the plane angle between two radii of a circle that cut off an the circumference an arc equal in the length to the radius

Solid Angle

Steradian

sr

The steradian is the solid angle that, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere

Supplement (Basic and Technical Data) 28

SI Units Table 3. Examples of SI derived units expressed in terms of SI base units SI derived units

Derived Quantity

Name

Symbol

square meter

m

2

cubic meter

m

3

meter per second

m/s

meter per second squared

m/s

Area Volume Speed, Velocity Acceleration

2

-1

Wave Number

reciprocal meter

m

Mass Density

kilogram per cubic meter

kg/m

Specific Volume

cubic meter per kilogram

3

m /kg

Electric Current Density

ampere per square meter

A/m

Magnetic Field Strength

ampere per meter

A/m

Molar Mass

kilogram per mole

kg/mol

mole per cubic meter

mol/m

candela per square meter

cd/m

Amount-of-substance concentration Luminance

3

2

3

2

Table 4. SI derived units with special names and symbols SI derived units Special Name

Special Symbol

Expression in terms of other SI units

Expression in terms of SI base units

hertz

Hz

-

s

Force

newton

N

-

Pressure, Stress

pascal

Pa

N/m

Derived Quantity

Frequency

-1 -2

m· kg· s 2

-1

-2

2

-2

2

-3

m · kg· s

Energy, Work, Quantity of Heat

joule

J

N· m

m · kg· s

Power, Radiant Flux

watt

W

J/s

m · kg· s

Electric Charge, Quantity of Electricity

coulomb

C

-

s· A

Electric Potential Difference, Electromotive Force

volt

V

W/A

m · kg· s · A

farad

F

C/V

m · kg · s · A

Capacitance Electric Resistance Electric Conductance

2

-3

-2

-1

2

-1

4

-3

2

-2

ohm

Ω

V/A

m · kg· s · A

siemens

S

A/V

m · kg · s · A

-2

-1

2

3

-2

2

-1

Magnetic Flux

weber

Wb

V· s

m · kg· s · A

Magnetic Flux Density

tesla

T

Wb/m2

kg· s · A

Inductance Celsius Temperature Luminous Flux Illuminance

henry

H

Wb/A

degree Celsius

°C

-

-2

2

-1

-2

-2

m · kg· s · A K 2

-2

lumen

lm

cd· sr

m · m · cd = cd

lux

lx

lm/m2

m · m · cd = m · cd

Supplement (Basic and Technical Data) 29

2

-4

-2

SI Units Table 5. SI derived units expressed with the aid of SI derived units having special names and symbols

Derived Quantity

SI derived units Name

Symbol

Dynamic Viscosity

pascal second

Pa· s

Moment of Force

newton meter

N· m

Surface Tension

newton per meter

N/m

Angular Velocity

radian per second

rad/s

radian per second squared

rad/s

watt per square meter

W/m

joule per kelvin

J/K

joule per kilogram kelvin

J/(kg· K)

joule per kilogram

J/kg

Thermal Conductivity

watt per meter kelvin

W/(m· K)

Energy Density

joule per cubic meter

J/m

volt per meter

V/m

coulomb per cubic meter

C/m

coulomb per square meter

C/m

Permittivity

farad per meter

F/m

Permeability

henry per meter

H/m

joule per mole

J/mol

Molar Entropy, Molar Feat Capacity

joule per mole kelvin

J/(mol· K)

Molar Entropy, Molar Heat Capacity

coulomb per kilogram

C/kg

gray per second

Gy/s

watt per steradian

W/sr

watt per square meter steradian

W/(m · sr)

Angular Acceleration Heat Flux Density, Irradiance Heat Capacity, Entropy Specific Heat Capacity, Specific Entropy Specific Energy

Electric Field Strength Electric Charge Density Electric Flux Density

Molar Energy

Absorbed Dose Rate Radiant Intensity Radiance

Supplement (Basic and Technical Data) 30

2

2

3

3

2

2

SI Units Table 6. SI prefixes SI prefixes

Factor 24

10

Name 3 8

= (10 )

3 7

1021 = (10 )

3 6

1018 = (10 )

3 5

1015 = (10 )

3 4

1012 = (10 )

3 3

109 = (10 )

3 2

106 = (10 )

3 1

103 = (10 ) 2

yotta zetta exa peta tera giga mega kilo hecto

10

1

deka

10

SI prefixes

Factor

Symbol

-1

Y

10

-2

Z E

10

-6

P

10

-9

T

10

-12

G

10

-15

M

10

-18

k

10

-21

h

10

-24

da

10

Symbol

deci

d

centi

c

3 -1

milli

m

3 -2

micro

µ

3 -3

nano

n

3 -4

pico

p

3 -5

femto

f

3 -6

atto

a

3 -7

zepto

z

3 -8

yocto

y

10 -3

Name

= (10 ) = (10 ) = (10 )

= (10 ) = (10 ) = (10 ) = (10 ) = (10 )

Table 7. Units accepted for use with SI units Name

Symbol

Value in SI units

Hour

h

1 h = 60 min = 3600 s

Day

d

1 d = 24 h = 86 400 s

Degree (Angle)

˚

1° = (/180) rad

Minute (Angle)

'

1'= (1/60)° = (/10 800) rad

Second (Angle)

"

1"= (1/60) = (/648 000) rad

Liter

L

1 L = 1 dm = 10

Metric Ton

t

1 t = 10 kg

Electron Volt

eV

Unified Atomic Mass Unit

u

3

-3

3

m

3

-19

1 eV = 1.602 18 x 10

-27

1 u = 1.660 54 x 10

Supplement (Basic and Technical Data) 31

J, approximately

kg, approximately

Table of Unit Conversion Factors ■ Table of Conversion Factors to SI Units Pa

Pressure

kgf/cm ²

bar

1

1X10

1X10

5

9.806 65X10

4

1.013 25X10

5

1.019 72X10

1 -1

1

1.013 25

2

-5

1.019 72

9.806 65X10

9.806 65 1.333 22X10

-5

atm

mmH 2 O

9.869 23X10

-6

9.869 23X10

-1

9.678 41X10

-1

1.033 23

1

9.806 65X10

-5

1.000 0X10

-4

1.333 22X10

-3

1.359 51X10

-3

9.678 41X10

-5

1.315 79X10

-3

mmHg or Torr

1.019 72X10

-1

7.500 62X10

-3

1.019 72X10

4

7.500 62X10

2

1.000 0X10

4

7.355 59X10

2

1.033 23X10

4

7.600 00X10

2

7.355 59X10

-2

1 1.359 51X10

1

Note) 1Pa=1N/m 2

Force

N

dyn

1

1X10

1X10

-5

kgf 5

1

9.806 65

9.806 65X10

1.019 72X10

-1

1.019 72X10

-6

5

Viscosity

1

Paㆍ s

cP

1

1X10

1X10

-3

1X10

-1

P 3

1X10

1

1X10

1X10

2

-2

1

Note) 1P=1dyn ㆍs/cm2=1g/cmㆍ s 1Pa ㆍ s=1N ㆍ s/m 2 1cP=1mPa ㆍ s

MPa or N/mm ²

Pa 1

Stress

1X10

1X10

6

9.806 6 5 X 1 0

6

9.806 6 5 X 1 0

4

1

1.019 7 2 X 1 0

1.019 7 2 X 1 0

-1

1.019 7 2 X 1 0

-2

1X10

1X10

kW ㆍ h 2.777 78X10

3.600X10

kgf/cm ²

-7

1

9.806 6 5 X 1 0

1

-2

1 2.724 07X10

-6

4.186 05X10

1.162 79X10

-3

2

kcal

1.019 72X10

-1

3.670 98X10

5

1

2.388 89X10

-4

8.600

2

0X10

2.342 70X10

4.268 58X10

-5

1

kgf ㆍ m -7

9.806 65

2

-3

1

1 W ㆍ h = 3600W ㆍ s 1cal = 4.18605J

Note) 1J = 1W ㆍ s

Thermal Conductivity

kgf/mm ² 1.019 7 2 X 1 0

9.806 65

J Work, Energy, Quantity of Heat

-6

W/(mㆍ K) 1

kcal */(mㆍ hㆍ℃ ) 8.600 0 X1 0

1.162 79

-1

1

kW kgf ㆍ m/s PS -1 Power, -3 1 1.359 62X 1 0 1.019 7 2 X 1 0 Heat -3 -2 1 1.333 3 3 X 1 0 Flow 9.806 6 5 X 1 0 1 Rate 7.5 X 1 0 1 7.3 5 5 X 1 0

Note ) 1W = 1J/s PS : French Horsepower 1PS = 0.7355kW

Thermal Conductivity

ㆍ K) W/ (m ²

ㆍ h ㆍ℃ ) kcal */ (m²

1

8.600 0X10

1.162 79

Kinematic Viscosity

-1

1

m²/s

cSt

1

1X10

1X10

-6

1X10

-4

Note) 1St = 1cm ² /S

Supplement (Basic and Technical Data) 32

St 6

1 1X10 2

1X10 1X10 1

4

-2

Hexagon Socket Head Cap Screw ■ Nominal Length ( ℓ ) Nominal Size

Nominal Length

Nominal Size

Nominal Length

Nominal Size

Nominal Length

M1.6

2.5~16

M2

3~20

M2.5

4~25

M3

5~30

M4

6~40

M12

Nominal Size

Nominal Length

Nominal Size

Nominal Length

M5

8~50

(M14)

M6

10~60

M16

25~140

M24

40~200

(M39)

65~300

25~160

(M27)

45~300

M42

65~300

M8

12~80

(M18)

M10

16~100

M20

30~180

M30

45~300

(M45)

80~300

30~200

(M33)

55~300

M48

20~120

(M22)

80~300

40~200

M36

55~300

(M52)

90~300

Notes 1) The size shown in ( ) is non-preferred 2) Standard nominal length

2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 30, 35, 40, 45 50, 55, 60, 65, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 180, 200, 220, 240, 260, 280, 300

■ Dimensions of counter-boring and bolt hole for hexagon socket head cap screws D

D'

H

H'

H"

M3

3

3.4

5.5

6

3

2.7

3.3

M4

4

4.5

7

8

4

3.6

4.4

M5

5

5.5

8.5

9.5

5

4.6

5.4

M6

6

6.6

10

11

6

5.5

6.5

M8

8

9

13

14

8

7.4

8.6

M10

10

11

16

17.5

10

9.2

10.8

M12

12

14

18

20

12

11

13

M14

14

16

21

23

14

12.8

15.2

M16

16

18

24

26

16

14.5

17.5

M18

18

20

27

29

18

16.5

19.5

M20

20

22

30

32

20

18.5

21.5

M22

22

24

33

35

22

20.5

23.5

M24

24

26

36

39

24

22.5

25.5

M27

27

30

40

43

27

25

29

M30

30

33

45

48

30

28

32

M33

33

36

50

54

33

31

35

M36

36

39

54

58

36

34

38

M39

39

42

58

62

39

37

41

M42

42

45

63

67

42

39

44

M45

45

48

68

72

45

42

47

M48

48

52

72

76

48

45

50

M52

52

56

78

82

52

49

54

D'

D'

D

D

d1

H H"

d'

H

d₁

H'

Bolt Nominal Size (d)

d'

Supplement (Basic and Technical Data) 33

d1

d'

1. Symbols used in designing springs Symbol

Unit

Symbol

d

Diameter of wire

Meaning

mm

Load acting on spring

D₁

Inside diameter of coil

mm

P δ

D₂

Outside diameter of coil

mm

κ

Spring constant

N/mm(kgf/mm)

D

Mean diameter of coil:

τo

Tensional Stress

N/mm (kgf/mm )

Nt

Total number of turns

Na Nf Hs

D1＋D2 2

mm

Meaning

Unit N(kgf)

Deflection of spring

mm

τ

Corrected torsional stress

-

τi

Number of active turns

-

χ

Torsional stress due to initial tension Stress correction factor

Number of inactive turns

-

∫

Natural frequency

Solid Height

mm

u

Energy stored in spring

P

Pitch

mm

r

Weight per unit volume of wire

Pi

Initial Tension

W

Weight of Spring (Active Coils)

g*

Gravitational acceleration

D C= d

N (kgf)

Spring Index

-

2

2

2

2

2

N/mm (kgf/mm ) N/mm (kgf/mm ) Hz Nㆍmm (kgfㆍmm) 3

3

N/mm (kgf/mm ) N(kgf) mm/s

2

2

N/mm (kgf/mm2) 2

G

2

Modulus of elasticity in torsion

* Gravitational acceleration is round off as 9800mm/s in 2 designing springs though prescribed as 9.80665 m/s in the regulation of measure.

2. Basic formulas used in designing springs For compression springs and extension springs without initial tension α

For extension springs with initial tension (P>Pi)

δ=

8N D P Gd⁴

δ=

8Na D (P-Pⅰ) Gd⁴

κ=

P Gd⁴ = δ 8N αD³

κ=

P-Pⅰ Gd⁴ = δ 8N α D³

3

3

τ =

8DP π d³

τ =

8DP πd ³

τ=

Gdδ π NαD²

τ=

Gdδ ＋τⅰ π NαD²

0

0

0

0

τ= κ τ

τ = κτ

0

d =

3

8DP = πτ

3

0

8 κ DP πτ

d =

3

0

8DP = πτ

3

0

Nα=

Gd ⁴ δ 8 D³ P

Nα=

Gd ⁴ δ 8 D ³ (P-Pⅰ)

U =

Pδ 2

U =

(P ＋ Pⅰ)δ 2

8 κ DP πτ

■ Modulus of rigidity G Material

G N/mm 2 (kgf/mm2 )

Spring Steel

78X10 3 (8X10 3 )

Hard Drawn Steel Wire

78X10 3(8X10 3 )

Music Wire

78X10 3 (8X10 3)

Oil-Tempered Wire

78X10 3(8X10 3)

Material

G N/mm2 (kgf/mm2 )

Material

69X10 3 (7X10 3 )

Spring Brass Wire Phosphor Bronze Wire BerylliumCopper Wire

SUS 302 Stainless Steel Wire

SUS 304 SUS 316 SUS 631 J 1

74X10 3 (7.5X10 3 )

Supplement (Basic and Technical Data) 34

G N/mm2 (kgf/mm 2) 39X10 3 (4X10 3 ) 42X10 3 (4.3X10 3) 44X10 3 (4.5X10 3)

■ Number of Active Turns The number of active turns in designing springs should be chosen as equal to the number of free coils. For compression springs, N=N t ( x 1+ x 2), x1 and x 2 indicate each number of coils of both ends. When only the tip of the coil touches the next free coil, x 1= x 2 =1. therefore, N a=Nt 2 When only the tip of the coil does not touch the next free coil and the length of end turn part is 3/4 length, x 1= x 2 =0.75. 1.6

Stress correction factor ( χ )

therefore, N a=N t - 1.5 For extension springs, N a=N t

■ Stress correction factor (χ) Stress correction factor which corrects for both curvature and direct shear is given by following formula or graph at the right χ= (4c-1)/(4c-4) + 0.615/c Wahl's factor

■ Range of Spring Index

1.5 1.4

1.3 1.2 1.1

1.0 4

3

5

6

7

9

8

10 11 12 1 3 14 1 5 16 1 7 1 8 19 2 0 21 22

D spring index C= d

In general, it is recommended to have the spring index within the range of 4 and 22.

■ Range of Slenderness Ratio In general, it is recommended to have the slenderness ratio (the ratio of free height against average diameter of coil) within the range of 0.8 and 4.

■ Range of Number of Active Turns

220

In general, it is recommended to have the number of active turns of 4 or more.

■ Range of Pitch In general, it is recommended to have the pitch of 0.5D or less.

■ Solid Height The solid height of compression spring can be estimated by following formula.

200

(2 0)

180

(18)

160

(1 6)

140

(1 4)

120

(1 2)

100

(1 0)

80

(8 )

60

(6)

40

(4 )

20

(2) (0)

0

τ1

3

4

5

6

8

9

10 11 1 2 13 14 15 16 17 18 19 20 2 1 22

D spring index C= d

N/mm²

HS = (N t - 1)d＋χ

7

Note: x : Sum of the thickness of both ends of the coil

■ Initial Tension of Extension Spring The initial tension P i is generated in the solid-wound, cold-formed extension spring. In this case, the torsional stress due to the initial tension shall be within the shaded range shown in figure above. Pⅰ=

(Note) Following empirical formula can be applied to get P i and I

πd ³ τⅰ 8D

τⅰ =

πd³τⅰ G = Pi = 100c , 8D

Gd⁴ 255D²

■ Effect of Spring Surge To avoid surging, natural frequency of the spring should be selected not to resonate to the frequency of applied force. Natural frequency of spring is

∫= α

κg W

70d =α πNαD ²

G

ω

Example) Steel's G=78× 10 ³ N/mm ² (8 × 10 ³kgf/mm ² ) -6 -6 ω = 76.93 × 10 N/mm ³ (7.85 ×10 kgf/mm ³ ) For both ends are free or fixed, primary natural frequency f is

α=

ⅰ For both ends are free or fixed 2

α=

2ⅰ－1 For one end is fixed and the other end is free ⅰ= 1, 2, 3 4

∫ = 3.56 × 10

5

d NαD²

Supplement (Basic and Technical Data) 35

■ Linear Thermal Expansion Coefficients of Various Metals a (Linear Mean Coefficients for the Temperature Range 0~100˚C) Metal

X10

-4

Metal

X10 - 4

Zinc

0.263 ~ 0.582

Copper

0.167

Lead

0.276

Gold

0.139

Aluminum, Cast

0.222

Nickel

0.128

Tin

0.214

Soft Steel

0.119

Aluminum, Sheet

0.207

Antimony

0.110

Brass, Rod

0.193

Steel

0.105 ~ 0.110

Type Metal

0.190

Iron, Cast

0.102

Silver

0.188

Platinum

0.089

■ Linear Thermal Expansion Coefficients of Various Substances a (Linear Mean Coefficients for the Temperature Range 0~100˚C) Substance

X10

-4

Substance

X10 - 4 0.08 ~ 0.05

Rubber

0.77

Wood

Ebonite

0.64 ~ 0.77

Brick

0.055

Concrete

0.10 ~ 0.14

Masonry, Brick

0.04 ~ 0.07

Slate

0.104

Marble

0.035 ~ 0.044

Glass

0.088

Granite

0.083

Ceramic

0.036

Average Specific Gravity

Material

Material

Specific Gravity

Steel

7.85

Iron, Cast

7.25

Lead

11.4

Copper

8.9

Zinc

6.9

Aluminum

2.7

Brass, Bronze

8.6

Supplement (Basic and Technical Data) 36

Remark