geometrical tolerancing

Geometrical Tolerancing

Reference Standards

BS ISO 1101:1983 Technical Drawings - Geometrical tolerancing - Tolerancing of form, orientation, location and run-out - Generalities, definitions, symbols, indications on drawings

BS ISO 5459:1981 Technical Drawings - Geometrical tolerancing - Datums and datum-systems for geometrical tolerances

Introduction

The notes below relate to use of geometric tolerances on drawing. The notes are outline in nature to provide general guidance. This subject is complex and it is wise to consult the standards and have a clear understanding of what is required when including geometric tolerances on technical drawings. There are clear differences between ANSI Y14.5 and the above noted ISO standard. The notes below do not address this difference or refer to the ANSI standard in any way.

Geometric Tolerances

Geometric tolerances specify the maximum variation that is allowed in form or position from true geometry. The geometric tolerance is, in essence, the width or diameter of tolerance zone within which a surface or axis of hole or cylinder can lie which results in resulting feature being acceptable for proper function and interchangeability.

If a tolerance of form is not specified on a drawing for a feature, then the feature as made will be acceptable regardless of form variation. The tolerances of form control straightness, flatness, parallelism, angular displacement etc. etc.

The tolerance zone will be one of the following:

The area within a circle The area between two circles The area between two equidistant lines or between two parallel

straight lines The space within a cylinder The space between two coaxial cylinders The space between two equidistant surfaces or two parallel planes The space within a bent pipe

Tolerance Frame with Symbol identifications

Indication of datum

Supplimentary Symbols

Notes on supplimentary symbols are provided on webpage Geometrical Tolerancing Notes

Tolerance Frame Variations

The tolerance frame can be divided into two or more compartments. These compartments include from left to right

The symbol for the feature to be toleranced The tolerance value..If the tolerance zone is circular or

cylinderical it is preceded with a Letters for datums when the toleranced feature is specified in

relation to one, or more datums.

When multiple datums are referenced in the tolerance box they are indicated as below:

Maximum Material Indication in Tolerance Frame

The maximum material condition, when used, is indicated by a symbol placed after the tolerance value, after the datum letter, or both.

See the figures below:

Additional Frames- Notes

If a single frame cannot convey sufficient information it is acceptable to stack additional frames and/or provide additional notes..

Positioning of Frames /Datum triangles

The datum triangle is placed on a feature or on an extension of the outline ( but clearly separated from the dimension line) when the datum feature is the line or surface itself

The datum triangle is place on the extension of a dimension arrow when the datum feature is the axis or medium line.When two datums are indicated they relate to the common axis of the two features

The datum triangle can replace a dimension arrow if there is not enough room.

The datum can be located on the axes or median line when

The axis or median line is clearly for a single feature The axis or median line is clearly formed by two features

Examples of Form Control

Examples of Maximum Material Condition

Examples of Profile Tolerancing

Flatness

Roundness

Straightness

Angularity

Squareness

Symmetry

Examples of parallelism

Examples of position

Examples of Concentricity

Examples of Cylindricity

Examples of Runout

Note: Runout is a composite tolerance including the effects of Cylindricity, and Concentricity.

Example of Total Runout

Note: Total runout is a composite tolerance including the effects of cylindricity, and concentricity, co-axiality, straightness and parallism along the axis.

Hardness Measurement

Brinell ...... Vickers ...... Rockwell ...... Superficial Rockwell...... Scleroscope......

Knoop...... Jominy...... Moh...... Shore (Durometer)

Equivalent Hardness Table (harder scales)...... Equivalent Hardness Table (softerr scales)

Hardness Comparison chart...... Typical component Surface Hardness......

Methods of Measuring Hardness

Brinell Hardness Test

In this test a hardened steel ball is pressed into the surface of the test material using a prescribed ball. The ball and load have to be selected to suit the material being tested.

The Brinell hardness test consists of indenting the test material with a 10 mm diameter hardened steel or carbide ball subjected to a load of 3000 kgf (29 430 N). For softer materials the load can be reduced to 1500 kgf (14 715 N) or 500 kgf (4 905 N ) to avoid excessive indentation. The full load is normally applied for 10 to 15 seconds for harder ferrous metals and for 30 seconds or more for other metals softer metals. The diameter of the indentation left in the test material is measured with a microscope.

The Brinell hardness number is calculated by dividing the load applied by the surface area of the indentation.

BHN = 2.F / (.D .(D - (D2-D1)

D = Diameter of BallD1 = Diameter of indentationF = applied force

Vickers Hardness Test

In this test a Diamond Indenter is pressed into the surface of the material being tested. Standard loads used include 5, 10, 20, 30, 50, and 100 kgf. (49,05, 98,1 196,2 490,5 and 981 N).The load is stated in specifying the hardness number i.e HD(10) = 100. the indenter is a square based pyramid (136o included angle )to suit the material being tested

The Hardness Number HD = 1.844 x Load/ Average diagonal length of indentation

Rockwell Hardness Test

In this test a Hard Steel Ball or a Diamond Cone Indenter is pressed into the surface of the material being tested/ The result of the test is read directly from machine.

The indenter is forced into the test material under a preliminary minor load (98N)and after equilibrium are achieved an indicating device, which follows the movements of the indenter, is set to the datum position. An additional major load is then applied with resulting increase in penetration. The conditions are then allowed to stabilise and then the additional major load is removed,leaving the minor load in place. The resulting permanent penetration esulting from the application and removal of the additional major load is used to calculate the Rockwell hardness number.

HR = E - e F1 = additional major e = permanent increase in depth of penetration due to major load , measured in units of

0.001 mmE = a constant of 100 units for diamond and ball indenters

HR = Rockwell hardness numberD = diameter of steel ball

Scale

Indenter

Major LoadF1N

E Applications

A120oDiamond cone

490.5 100Sheet steel ; shallow case hardened

B 1/16" steel ball 882.9 130

Copper, Aluminium alloys, Low Carbon Steel

C120oDiamond cone

1373.4 100

Most Widely Used -Hardened Steels, Cast irons etc

D120oDiamond cone

882.9 100Thin but hard steels, Ductile Iron (Pearlitic

E 1/8" steel ball 882.9 130Cast Iron, Aluminium, Bearings alloys

F 1/16" steel ball 490.5 130Annealed copper alloys , Soft thin metals

G 1/16" steel ball 1373.4 130

Phosphor bronze, beryllium copper, malleable irons, Lead etc

H 1/8" steel ball 490.5 130Soft Metals Plastics etc

K 1/8" steel ball 1373.4 130Soft bearing metals, Plastics, soft materials.

L 1/4" steel ball 490.5 130Soft bearing metals, Plastics, soft materials.

M 1/4" steel ball 882.9 130Soft bearing metals, Plastics, soft materials.

P 1/4" steel ball 1373.4 130Soft bearing metals, Plastics, soft materials.

R 1/2" steel ball 490.5 130Soft bearing metals, Plastics, soft materials.

S 1/2" steel ball 882.9 130Soft bearing metals, Plastics, soft materials.

V 1/2" steel ball 1373.4 130Soft bearing metals, Plastics, soft materials.

Superficial Rockwell Hardness Test

A more surface sensitive measurement of hardness than for the regular Rockwell scales. This technique is useful for samples with hardness gradients at the surface, to test small areas, and for thin samples. Superficial Rockwell hardness scales are N and T for metals and W, X, and Y for non-metallic materials and coatings. The Superficial Rockwell hardness test method consists of indenting the test material with a diamond cone (N scale) or hardened steel ball indenter. The indenter is forced into the test material under a preliminary minor (29.43N) and the conditions are allowed to settle. Then the indicating device that follows the movements of the indenter is set to a datum position. An additional major load, is applied with resulting increase in penetration . The conditions are allowed to settle again and then the additional major load is removed. The permanent increase in depth of penetration, resulting from the application and removal of the additional major load is used to calculate the Rockwell Superficial hardness number.

HR = E - e

e = permanent increase in depth of penetration due to major load F1, measured in units of 0.001 mmE = a constant of 100 units for diamond and ball indentersHR = Rockwell hardness numberD = diameter of steel ball

Scale

Indenter

Major Load( N )

EApplication

15N120o Diamond cone

117.72

100

Similar to C scale, but for thin materials


264.87

100Same as 15N


412 100Same as 15N

15T 1/16" steel ball117.72

100

Similar to B scale, but for thin materials

30T 1/16" steel ball264.87

100Same as 15T

45T 1/16" steel ball 412 100Same as 15T

15W

1/8" steel ball117.72

100For very soft materials

30W

1/8" steel ball264.87


45W

1/8" steel ball 412 100For very soft materials

15X 1/4" steel ball117.72


30X 1/4" steel ball264.87


45X 1/4" steel ball 412 100For very soft materials

15Y 1/2" steel ball117.72


30Y 1/2" steel ball264.87


45Y 1/2" steel ball 412 100For very soft materials

The Shore (Scleroscope ) Hardness Test

The Scleroscope test consists of dropping a diamond tipped hammer, which falls inside a glass tube under the force of its own weight from a fixed height, onto the test specimen. The height of the rebound travel of the hammer is measured on a graduated scale. The harder the material, the higher the rebound. The scale of the rebound is arbitrarily chosen and consists on Shore units, divided into 100 parts, which represent the average rebound from pure hardened high-carbon steel. The scale is continued higher than 100 to to allow for metals having greater hardness.

The shore scleroscope test does not normally mark the material under test. The Shore Scleroscope measures hardness in relation to the elasticity of the material.

Advantages of this method are portability and non-marking of the test surface.

Knoop

The Knoop indenter has a polished rhombohedral shape with an included longitudinal angle of 172° 30’ and an included transverse angle of 130° 0’. The narrowness of the indenter makes it ideal for testing specimens with steep hardness gradients and coatings. Knoop is a better choice for hardness testing of hard brittle materials.

Jominy Hardenability

The Jominy test involves heating a test specimen of steel 25mm diameter and 100mm long to an austenitising temperature and quenching from one end with a controlled and standardized jet of water. After quenching, the hardness is measured at intervals taken form the quenched end. The hardness gradient along the test surface provides an indication of the material’s hardenability.

Moh's Hardness Scale

The Moh's hardness scale consists of 10 minerals arranged in order from 1 to 10. Diamond is rated as the hardest and is indexed as 10; talc as the softest with index number 1. Each mineral in the scale will scratch all those below it as follows:

Diamond

10

Corundum

9

Topaz 8Quartz 7Orthoclase (Feldspar)

6

Aptite 5Fluorite 4Calcite 3Gypsum 2Talc 1

Shore (Durometer) test

The hardness testing of plastics is most commonly measured by the Shore (Durometer)

test. This test measures the resistance of the plastic toward indentation. The scale provide an empirical hardness value that doesn't relate directly to the mechanical properties of the material being tested. Shore Hardness, using either the Shore A or Shore D scale, is the preferred method for rubbers/elastomers and is also commonly used for 'softer' plastics such as polyolefins, fluoropolymers, and vinyls. The Shore A scale is used for 'softer' rubbers while the Shore D scale is used for 'harder' rubbers.

The Shore hardness is measured with an apparatus known as a Durometer and consequently is also known as 'Durometer hardness'. The hardness value is determined by the penetration of the Durometer indenter foot into the sample. If the indenter completely penetrates the sample, a reading of 0 is obtained, and if no penetration occurs, a reading of 100 results. Because of the resilience of rubbers and plastics, the hardness reading my change over time - so the indentation time is sometimes reported along with the hardness number. The test method is identified in standard ISO 868.

The results obtained from this test are a useful measure of relative resistance to indentation of various grades of polymers. However, the Shore Durometer hardness test does not serve well as a predictor of other properties such as strength or resistance to scratches, abrasion, or wear, and should not be used alone for product design specifications.

Tables showing the comparative hardness numbers between scales is provided at site the following sites.....

1. Gordon England..... 2. Corrosion Products Handbook

Equivalent Hardness Conversion Tables

Harder Scales

VPNROCKWELL SCALES

ROCKWELL Superficial

BRINELLSCLERO-SCOPE

U.T.S.

DPHHV/10

A B C D G 15N 30N 45NBHN500kg

BHN3000kg

MPa

1865 92 80 87 97 92 87

1787 92 79 86 96 92 87

1710 91 78 85 96 91 86

1633 91 77 84 96 91 85

1556 90 76 83 96 90 84

1478 90 75 83 95 89 83

1400 89 74 82 95 89 82

1323 89 73 81 95 88 81

1245 88 72 80 95 87 80

1160 87 71 80 94 87 79

1076 87 70 79 94 86 78 101

1004 86 69 78 94 85 77 99

940 86 68 77 93 84 75 97

900 85 67 76 93 84 74 95

865 85 66 75 93 83 73 92

832 84 65 75 92 82 72 739 91

800 84 64 74 92 81 71 722 88

772 83 63 73 91 80 70 705 87

746 83 62 72 91 79 69 688 85

720 82 61 72 91 79 68 670 83

697 81 60 71 90 78 67 654 81 2206

674 81 59 70 90 77 66 634 80 2137

653 80 58 69 89 76 64 615 78 2069

633 80 57 69 89 75 63 595 76 2000

613 79 56 68 88 74 62 577 75 1944

595 79120

55 67 88 73 61 560 74 1889

577 78120

54 66 87 72 60 543 72 1834

560 78119

53 65 87 71 59 523 71 1772

544 77119

52 65 86 70 57 512 69 1689

528 77118

51 64 86 69 56 496 68 1648

513 76117

50 63 86 69 55 481 67 1607

498 75117

49 62 85 68 54 469 66 1565

484 75116

48 61 85 67 53 455 64 1524

471 74116

47 61 84 66 51 443 63 1496

458 74115

46 60 84 65 50 432 62 1462

446 73115

45 59 83 64 49 421 60 1420

434 73114

44 59 83 63 48 409 58 1379

423 72 11 43 58 82 62 47 400 57 1351

3

412 72113

42 57 82 61 46 390 56 1317

402 71112

41 56 81 60 44 381 55 1289

392 71112

40 55 80 60 43 371 54 1255

382 70111

39 55 80 59 42 362 52 1220

372 70110

38 54 79 58 41 353 51 1193

363 69110

37 53 79 57 40 344 50 1165

354 69109

36 52 78 56 38 336 49 1138

345 68109

35 52 78 55 37 327 48 1103

336 68108

34 51 77 54 36 319 47 1076

327 67108

33 50 77 53 35 311 46 1048

318 67107

32 49 76 52 34 301 44 1014

310 66106

31 48 91 76 51 33 294 43 993

302 66105

30 48 91 75 50 31 286 42 965

294 65104

29 47 89 75 50 30 279 41 945

286 65104

28 46 88 74 49 29 271 41 917

279 64103

27 45 87 73 48 28 264 40 889

272 64103

26 45 86 73 47 27 258 39 869

266 63102

25 44 85 72 46 26 253 38 855

260 63101

24 43 84 72 45 24 247 37 834

254 62100

23 42 83 71 44 23 201 240 36 814

248 62 99 22 42 81 71 43 22 195 234 35 793

243 61 98 21 41 79 70 42 21 189 228 35 772

238 61 97 20 40 78 69 42 20 184 222 34 752

VPNROCKWELL SCALES


BRINELL SCLERO-SCOPE

U.T.S.

DPHHV/10

A B C D G 15N 30N 45N BHN500kg

BHN3000kg

MPa

Softer Scales

VPNROCKWELL SCALES


BRINELLSCLERO-SCOPE

U.T.S.

DPHHV/10

A B C E F G H K15T

30T

45T

BHN500kg

BHN3000kg

MPa

23460

97

19

77

92 80 69 181 218 34 738

23059

96

18

76

92 80 68 179 214 33 731

22659

96

17

75

92 80 68 177 210 33 717

22258

95

16

74

92 79 67 175 208 32 703

21758

95

15

73

92 79 67 171 205 31 690

21358

94

14

73

91 79 66 169 203 31 683

20857

93

13

71

91 78 66 167 200 30 676

20457

92

12

70

100

91 78 65 163 195 30 662

20056

92

11

69

100

91 77 64 162 193 29 655

19656

91

10

68

100

90 77 64 160 190 28 641

19256

90

966

99 90 76 63 157 185 27 627

18855

89

864

98 90 76 62 154 180 26 607

18454

88

763

97 90 75 61 151 176 26 593

180 5 8 6 6 97 89 75 60 148 172 26 579

4 7 1

17653

86

559

96 89 74 59 145 169 25 572

17253

85

458

95 89 74 58 142 165 25 558

16852

84

356

94 88 73 57 140 162 25 545

16451

83

254

93 88 72 56 137 159 24 538

16051

82

153

92 88 72 55 135 156 24 524

15650

81

051

91 87 71 54 133 153 24 517

15250

80

49

91 87 70 53 130 150 503

14849

79

48

90 87 70 52 128 147

14449

78

46

89 86 69 51 126 144

14148

77

44

88 86 68 50 124 141

13947

76

43

87 86 68 49 122 139

13747

75

100

41

86 85 67 49 120 137

13546

74

9939

85 85 66 48 118 135

13246

73

9938

85 85 66 47 116 132

13045

72

9836

84 84 65 46 114 130

12745

71

100

9835

83 84 64 45 112 127

12544

70

100

9733

82 84 64 44 110 125

12344

69

99 9631

81 83 63 43 109 123

12043

68

98 9630

80 83 62 42 107 121

11843

67

98 9528

79 83 62 41 106 119

11642

66

97 9527

78 82 61 40 104 117

11542

65

96 9425

78 82 60 39 102 116

11442

64

96 9424

77 82 60 38 101 114

11341

63

95 9322

76 81 59 37 99 112

11241

62

95 9221

75 81 58 36 98 110

11140

61

94 9219

74 81 57 35 96 108

11040

60

93 9118

73 81 57 34 95 107

10839

59

93 9116

72 80 56 32 94 106

10739

58

92 9015

71 80 55 31 92 104

10638

57

91 9013

71 80 55 30 91 102

10538

56

91 8912

70 79 54 29 90 101

10438

55

90 8810

69 79 53 28 89 99

10337

54

90 88 9 68 79 53 27 87

10237

53

89 87 7 67 78 52 26 86

10136

52

88 87 6 66 78 51 25 85

10036

51

88 86 4 65 78 51 24 84

10035

50

87 86 3 65 77 50 23 83

9935

49

87 85 64 77 49 22 82

9835

48

86 85 63 77 49 21 81

9734

47

85 84 62 76 48 20 80

9634

46

85 83 61 76 47 19 79

9533

45

84 83 60 76 46 18 79

9533

44

84 82 59 75 46 17 78

9432

43

83 82 58 75 45 16 77

93 3 4 82 81 58 75 44 15 76

2 2

9231

41

82 81 57 74 44 14 75

9131

40

81 80 56 74 43 13 74

9031

39

80 79 55 74 42 11 74

9030

38

80 79 54 73 42 10 73

8930

37

79 78 53 73 41 9 72

8829

36

79 78100

52 73 40 8 71

8829

35

78 77100

52 72 40 7 71

8728

34

77 77 99 51 72 39 6 70

8728

33

77 76 99 50 72 38 5 69

8628

32

76 75 99 49 71 38 4 68

8627

31

76 75 98 48 71 37 3 68

8527

30

75 74 98 47 71 36 2 67

8526

29

74 74 98 46 70 36 1 66

8426

28

74 73 97 45 70 35 66

8425

27

73 73 97 45 70 34 65

8325

26

73 72 97 44 69 33 65

8324

25

72 71 96 42 69 33 64

8224

24

71 71 96 42 69 32 64

8224

23

71 70 96 41 68 31 63

8123

22

70 70 95 40 68 31 63

8123

21

70 69 95 39 68 30 62

8022

20

69 69 95 38 68 29 62

8022

19

68 68 94 38 67 29 61

7921

18

68 67 94 37 67 28 61

7921

17

67 67 93 36 67 27 60

7821

16

67 66 93 35 66 26 60

7820

15

66 66 93 34 66 26 59

7714

65 65 92 33 66 25 59

7713

65 65 92 32 65 24 58

7612

64 64 92 32 65 24 58

7611

64 64 91 31 65 23 57

7510

63 63 91 30 64 22 57

75 9 62 62 91 29 64 22 56

74 8 62 62 90 28 64 21 56

74 7 61 61 90 27 63 20 56

73 6 61 61 90 26 63 20 55

73 5 60 60 89 26 63 19 55

72 4 59 60 89 25 62 18 55

72 3 59 59 88 24 62 17 54

71 2 58 58 88 23 62 17 54

71 1 58 58 88 22 61 16 53

70 0 57 57 87 21 61 15 53

VPNROCKWELL SCALES


BRINELLSCLERO-SCOPE

U.T.S.

DPHHV/10

A B C E F G H K15T

30T

45T

BHN500kg

BHN3000kg

MPa

Table of Components showing relevant surface Hardness values

Important Notes:Values below are typical of high specification components.. Lower values are likely in

more general applications...

Component Hardness Scale

Hardened Track for Roller 670-840 HV

Hardened Machine slideway

70-75 HS

Surface Hardened Gear (High spc'n)

58-63 RC

Modern Rails (Used for Normal traffic)

300-340 HV

Modern Rails (High Duty) 340 -420 HV

Shear Blades 81-85 RC

Carbide Dies (Drawing , Forming etc)

80-92 RA

Mild steel components 120 HV

Wrought iron 102 HV

Axe 600 HV

Fork/Rake 700 HV

Kitchen knife 680 HV

Stainless table knife 550 HV

Hammer Face 660 HV

Chisel 600 HV

File 60-61 RC

Drill Bit HSS 63-65 RC

Drill Bit Cobalt 66-67 RC

geometrical tolerancing

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