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BSI 23/30459716 DC:2023 Edition

BSI 23/30459716 DC:2023 Edition

$24.66

BS ISO 21771-1. Gears. Cylindrical involute gears and gear pairs. Concepts and geometry – Part 1. Concepts and geometry

Published By Publication Date Number of Pages
BSI 2023 160
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PDF Catalog

PDF Pages PDF Title
9 Foreword
11 1 Scope
2 Normative references
3 Symbols, subscripts and units
3.1 Symbols
17 3.2 Subscripts
18 3.3 Units
19 4 Individual cylindrical gears
4.1 General
4.2 Concepts for an individual gear
4.2.1 Gear, cylindrical gear, external gear, internal gear
4.2.2 Tooth system, external teeth, and internal teeth
4.2.3 Tooth and space
4.2.4 Tooth system parameters
20 4.2.5 Number of teeth and sign of number of teeth
4.2.6 Tooth number
4.2.7 Top land and bottom land
4.2.8 Tooth flanks and flank sections
21 4.3 Reference surfaces, datum lines and reference quantities
4.3.1 Reference surface, datum face
4.3.2 Reference rack
22 4.3.3 Basic rack tooth profile for involute gear teeth
23 4.3.4 Reference cylinder, reference circle, reference diameter
4.3.5 Gear axis
4.3.6 Sections through a cylindrical gear
24 4.3.7 Module
4.3.8 Facewidth
4.3.9 Profile shift, profile shift coefficient and sign of profile shift
25 4.4 Involute helicoids
4.4.1 Generator of involute helicoids
26 4.4.2 Base cylinder, base circle, base diameter
4.4.3 Transverse pressure angle at a point, transverse pressure angle
27 4.4.4 Normal pressure angle at a point, normal pressure angle
4.4.5 Involute function
4.4.6 Lead
28 4.4.7 Helix angle, lead angle
29 4.4.8 Flank direction
30 4.4.9 Roll angle of the involute
4.4.10 Radius of curvature of the involute, length of roll
4.4.11 Length of involute profile, Lyt
4.5 Angular pitch and pitches
4.5.1 Angular pitch
4.5.2 Pitches on the reference cylinder
32 4.5.3 Pitches on any cylinder
4.5.4 Axial pitch
4.5.5 Base pitch
33 4.6 Diameters of gear teeth
4.6.1 General
4.6.2 V-cylinder, V-circle diameter
4.6.3 Y-cylinder, Y-circle diameter
4.6.4 Addendum modification coefficient
4.6.5 Tip cylinder, tip circle, tip diameter
4.6.6 Profile control diameter, dcf
4.6.7 Root cylinder, root circle, root diameter
34 4.7 Gear tooth height
4.7.1 Tooth depth
4.7.2 Addendum, working addendum, dedendum, working dedendum
4.8 Tooth thickness, space width
4.8.1 General
4.8.2 Transverse tooth thickness
35 4.8.3 Transverse tooth thickness half angle
36 4.8.4 Space width
37 4.8.5 Transverse space width half angle
4.8.6 Normal tooth thickness
4.8.7 Normal space width
4.9 Radii of curvature of the tooth flanks
39 4.10 Tilt angle of contact line
40 5 Parallel Axis Cylindrical gear pairs
5.1 General
5.2 Concepts for a gear pair
5.2.1 Mating gear, mating flank
5.2.2 Working flank, non-working flank
5.2.3 External gear pair
5.2.4 Internal gear pair
41 5.3 Mating quantities
5.3.1 Gear ratio
5.3.2 Driving gear, driven gear, transmission ratio
5.3.3 Line of centres, centre distance
42 5.3.4 Working transverse pressure angle
5.3.5 Working pitch point, working pitch cylinders, working pitch circles, working pitch diameter, working pitch axis
44 5.3.6 Working helix angles:
5.3.7 Working depth
5.3.8 Tip clearance
45 5.3.9 Calculation of addendum modification coefficient k (for parallel axis gear)
46 5.4 Calculation of the sum of the profile shift coefficients
5.5 Tooth engagement
5.5.1 General
47 5.5.2 Active area of the tooth flanks, start of active profile and active tip diameters
48 5.5.3 Plane of action, zone of action, contact line
5.5.4 Line of action, path of contact, point of contact
49 5.5.5 Form over dimension
5.5.6 Designations and values relating to the line of action
50 5.5.7 Tooth interference
52 5.5.8 Overlaps
54 5.5.9 Contact line, sum of the contact line lengths
56 5.6 Backlash
5.6.1 General
5.6.2 Transverse backlash
5.6.3 Circumferential backlash
5.6.4 Normal backlash
5.6.5 Radial backlash
57 5.6.6 Backlash angle
58 5.7 Velocities and sliding conditions at the tooth flanks
5.7.1 Angular velocity
5.7.2 Circumferential velocity
5.7.3 Normal velocity
5.7.4 Rolling velocity
59 5.7.5 Sliding velocity
61 5.7.6 Sliding factor
5.7.7 Specific sliding
6 Crossed Axis External Cylindrical gear pairs
6.1 General
63 6.2 Concepts for a gear pair
6.3 Mating quantities
6.3.1 Gear ratio
6.3.2 Driving gear, driven gear, transmission ratio
6.3.3 Working pitch surfaces, working pitch point
6.3.4 Line of centres, working centre distance
64 6.3.5 Skew angle
6.3.6 Intermeshing racks at working pitch cylinders
66 6.3.7 Working transverse pressure angles
6.3.8 Working transverse tooth thicknesses
67 6.3.9 Basic rack profile to generate each part of the gear pair
6.3.10 Profile shift coefficients
6.3.11 Base space width half angle
68 6.3.12 Working conditions at minimum centre distance
6.3.13 Working conditions with backlash
69 6.3.14 Working depth
6.3.15 Tip clearance
6.3.16 Calculation of addendum modification coefficient k (for crossed axis gear)
6.4 Tooth engagement
6.4.1 General
6.4.2 Line of action, path of contact, point of contact
71 6.4.3 Active area of the tooth flanks, start of active profile and active tip diameters
72 6.4.4 Form over dimension
6.4.5 Designations and values relating to the line of action
73 6.4.6 Radii of curvature of the tooth flanks
77 6.4.7 Tooth interference
6.4.8 Meshing conditions
78 6.5 Backlash
6.5.1 General
6.5.2 Normal base backlash
6.5.3 Backlash angle, circumferential backlash
79 6.6 Sliding conditions at the tooth flanks
6.6.1 General
6.6.2 Angular velocities vectors
80 6.6.3 Velocity vectors of a point of contact along path of contact
81 6.6.4 Sliding speed
7 Tooth flank modifications
7.1 General
7.2 Tooth modifications which restrict the usable flank
7.2.1 Pre-finish flank undercut
82 7.2.2 Tip corner chamfering, tip corner rounding
83 7.3 Transverse profile modifications
7.3.1 General
7.3.2 Tip and root relief
84 7.3.3 Transverse profile slope modification, CHα
85 7.3.4 Profile crowning (barrelling), Cα
7.4 Flank line (helix) modifications
7.4.1 Flank line end relief
86 7.4.2 Flank line (helix) slope modification, CHβ
87 7.4.3 Flank line (helix) crowning, Cβ
7.5 Flank face modifications
7.5.1 Topographical modifications
88 7.5.2 Triangular end relief
89 7.5.3 Flank twist
90 7.6 Descriptions of modifications by functions
91 8 Geometrical limits
8.1 General
8.2 Counterpart rack tooth profile and rack tool profile
8.2.1 Counterpart rack tooth profile
94 8.2.2 Rack tool profile
98 8.3 Machining allowance
8.4 Deviations in normal tooth thickness
99 8.5 Generating profile shift, generating profile shift coefficient
101 8.6 Generated root diameter
8.7 Usable area of the tooth flank, tip and root form diameter
103 8.8 Undercut
8.9 Overcut
8.10 Minimum tooth thickness at the tip circle of a gear
9 Start of involute for hob or rack type cutters
9.1 Formulae of involute and trochoid
105 9.2 Undercut conditions
106 9.3 Determination of start of involute
108 9.4 Determination of radius of curvature of trochoid
111 10 Start of involute calculation in case of pinion-type cutter or shaper
10.1 Parameters of pinion-type cutter
10.2 Undercut condition
112 10.3 Calculation of trochoid line point
10.3.1 Helix angle on the circle of radius rM0
10.3.2 Residual fillet undercut
113 10.3.3 Angle between centre line of gear pair and centre point of tooth tip rounding of pinion-type cutter: 
10.4 Determination of start of involute
10.5 Determination of radius of curvature of trochoid
116 Annex€A (informative) Form diameters for tip and root radius in the transverse plane for involute cylindrical gear teeth
124 Annex€B (Informative) Tip form radius when tip radius is defined in normal plane
132 Annex€C (Informative) Explanation for Cross Axes cylindrical gear
140 Annex€D (Informative) Geometry of surfaces in contact
150 Annex€E (Informative) Projection of transverse profile of the tooth to other planes
158 Annex€F (Informative) Interface for geometry of worms defined with ISO 10828
160 Bibliography

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