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BS ISO 21771-1:2024 Cylindrical involute gears and gear pairs - Concepts and geometry, 2024
- undefined
- Foreword
- 1 Scope
- 2 Normative references
- 3 Terms, definitions, symbols, subscripts and units [Go to Page]
- 3.1 Terms and definitions
- 3.2 Symbols
- 3.3 Subscripts
- 3.4 Units and conventions [Go to Page]
- 3.4.1 Units
- 3.4.2 Conventions
- 4 Individual cylindrical gears [Go to Page]
- 4.1 General
- 4.2 Concepts for an individual gear [Go to Page]
- 4.2.1 Gear, cylindrical gear, external gear and internal gear
- 4.2.2 Tooth system, external teeth and internal teeth
- 4.2.3 Tooth and tooth space
- 4.2.4 Tooth system parameters
- 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
- 4.3 Reference surfaces, datum lines and reference quantities [Go to Page]
- 4.3.1 Reference surface and datum face
- 4.3.2 Reference rack
- 4.3.3 Basic rack tooth profile for involute gear teeth
- 4.3.4 Reference cylinder, reference circle and reference diameter
- 4.3.5 Gear axis
- 4.3.6 Sections through a cylindrical gear
- 4.3.7 Module
- 4.3.8 Diametral pitch
- 4.3.9 Facewidth
- 4.3.10 Profile shift, profile shift coefficient and sign of profile shift
- 4.4 Involute helicoids [Go to Page]
- 4.4.1 Generator of involute helicoids
- 4.4.2 Base cylinder, base circle and base diameter
- 4.4.3 Transverse pressure angle at a point and transverse pressure angle
- 4.4.4 Normal pressure angle at a point and normal pressure angle
- 4.4.5 Involute function
- 4.4.6 Lead
- 4.4.7 Helix angle and lead angle
- 4.4.8 Hand of helix
- 4.4.9 Roll angle of the involute
- 4.4.10 Radius of curvature of the involute and length of roll
- 4.4.11 Length of involute profile, Lyt
- 4.5 Angular pitch and pitches [Go to Page]
- 4.5.1 Angular pitch
- 4.5.2 Pitches on the reference cylinder
- 4.5.3 Pitches on any cylinder
- 4.5.4 Axial pitch
- 4.5.5 Base pitch
- 4.6 Diameters of gear teeth [Go to Page]
- 4.6.1 General
- 4.6.2 V-cylinder and V-circle diameter
- 4.6.3 y-cylinder and y-circle diameter
- 4.6.4 Tip alteration coefficient
- 4.6.5 Tip cylinder, tip circle and tip diameter
- 4.6.6 Profile control diameter, dCf
- 4.6.7 Root cylinder, root circle and root diameter
- 4.7 Gear tooth depth [Go to Page]
- 4.7.1 Tooth depth
- 4.7.2 Addendum, working addendum, dedendum and working dedendum
- 4.8 Tooth thickness and space width [Go to Page]
- 4.8.1 General
- 4.8.2 Transverse tooth thickness
- 4.8.3 Transverse tooth thickness half angle
- 4.8.4 Transverse space width
- 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 in different planes
- 4.10 Tilt angle of contact line
- 5 Parallel axis cylindrical gear pairs [Go to Page]
- 5.1 General
- 5.2 Concepts for a gear pair [Go to Page]
- 5.2.1 Mating gear and mating flank
- 5.2.2 Working flank and non-working flank
- 5.2.3 External gear pair
- 5.2.4 Internal gear pair
- 5.3 Mating quantities [Go to Page]
- 5.3.1 Gear ratio
- 5.3.2 Driving gear, driven gear and transmission ratio
- 5.3.3 Line of centres and centre distance
- 5.3.4 Working transverse pressure angle
- 5.3.5 Working pitch point, pitch cylinders, pitch circles, pitch diameter and pitch axis
- 5.3.6 Working helix angles
- 5.3.7 Working depth
- 5.3.8 Tip clearance
- 5.3.9 Calculation of tip alteration coefficient k (for parallel axis gear)
- 5.4 Calculation of the sum of the profile shift coefficients
- 5.5 Tooth engagement [Go to Page]
- 5.5.1 General
- 5.5.2 Active area of the tooth flanks, start of active profile and active tip diameters
- 5.5.3 Plane of action, zone of action and contact line
- 5.5.4 Line of action, path of contact and point of contact
- 5.5.5 Form over dimension
- 5.5.6 Designations and values relating to the line of action
- 5.5.7 Radii of curvature of the tooth flanks in a transverse plane
- 5.5.8 Tooth interference
- 5.5.9 Mesh geometry parameters
- 5.5.10 Contact line and sum of the contact line lengths
- 5.6 Backlash [Go to Page]
- 5.6.1 General
- 5.6.2 Transverse backlash
- 5.6.3 Circumferential backlash
- 5.6.4 Normal backlash
- 5.6.5 Radial backlash
- 5.6.6 Angular backlash
- 5.7 Velocities and sliding conditions at the tooth flanks [Go to Page]
- 5.7.1 Angular velocity
- 5.7.2 Circumferential velocity
- 5.7.3 Normal velocity
- 5.7.4 Rolling velocity
- 5.7.5 Sliding velocity
- 5.7.6 Sliding factor
- 5.7.7 Specific sliding
- 6 Crossed axis cylindrical gear pairs [Go to Page]
- 6.1 General
- 6.2 Concepts for a gear pair
- 6.3 Mating quantities [Go to Page]
- 6.3.1 Gear ratio
- 6.3.2 Driving gear, driven gear and transmission ratio
- 6.3.3 Working pitch surfaces and working pitch point
- 6.3.4 Line of centresa and working centre distance
- 6.3.5 Skew angle
- 6.3.6 Intermeshing racks at working pitch cylinders
- 6.3.7 Working transverse pressure angles
- 6.3.8 Working transverse tooth thicknesses
- 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
- 6.3.12 Working conditions at minimum centre distance
- 6.3.13 Working conditions with backlash
- 6.3.14 Working depth
- 6.3.15 Tip clearance
- 6.3.16 Calculation of tip alteration coefficient k (for crossed axis gear)
- 6.4 Tooth engagement [Go to Page]
- 6.4.1 General
- 6.4.2 Line of action, path of contact and point of contact
- 6.4.3 Active area of the tooth flanks, start of active profile and active tip diameters
- 6.4.4 Form over dimension
- 6.4.5 Designations and values relating to the line of action
- 6.4.6 Tooth interference
- 6.4.7 Mesh geometry parameters
- 6.5 Backlash [Go to Page]
- 6.5.1 General
- 6.5.2 Normal base backlash
- 6.5.3 Backlash angle and circumferential backlash
- 6.6 Sliding conditions at the tooth flanks [Go to Page]
- 6.6.1 General
- 6.6.2 Angular velocities vectors
- 6.6.3 Velocity vectors of a point of contact along path of contact
- 6.6.4 Sliding velocity
- 7 Principal radii of curvature of the tooth flanks [Go to Page]
- 7.1 General
- 7.2 Angle between the principal radius of curvature at point of contact
- 7.3 Particularities for crossed axis helical involute gear
- 7.4 Equivalent radii of curvature at point of contact
- 8 Tooth flank modifications [Go to Page]
- 8.1 General
- 8.2 Tooth modifications which restrict the usable flank [Go to Page]
- 8.2.1 Pre-finish flank undercut
- 8.2.2 Tip corner chamfering, tip corner rounding
- 8.3 Transverse profile modifications [Go to Page]
- 8.3.1 General
- 8.3.2 Tip and root relief, Cαa Cαf
- 8.3.3 Transverse profile slope modification, CHα
- 8.3.4 Profile crowning (barrelling), Cα
- 8.4 Flank line (helix) modifications [Go to Page]
- 8.4.1 Flank line end relief, CHβ
- 8.4.2 Helix angle modification, CHβ
- 8.4.3 Flank line (helix) crowning, Cβ
- 8.5 Flank face modifications [Go to Page]
- 8.5.1 Topographical modifications
- 8.5.2 Triangular end relief
- 8.5.3 Flank twist
- 8.6 Descriptions of modifications by functions
- 9 Geometrical limits [Go to Page]
- 9.1 General
- 9.2 Counterpart rack tooth profile and rack tool profile [Go to Page]
- 9.2.1 Counterpart rack tooth profile
- 9.2.2 Rack tool profile
- 9.3 Machining allowance
- 9.4 Limits of normal tooth thickness
- 9.5 Generating profile shift, generating profile shift coefficient
- 9.6 Generated root diameter
- 9.7 Usable area of the tooth flank, tip and root form diameter
- 9.8 Undercut
- 9.9 Overcut
- 9.10 Minimum tooth thickness at the tip circle of a gear
- 10 Start of involute for hob or rack type cutters [Go to Page]
- 10.1 Formulae of involute and trochoid
- 10.2 Undercut conditions
- 10.3 Determination of start of involute
- 10.4 Determination of radius of curvature of trochoid
- 11 Start of involute calculation in case of pinion-type cutter [Go to Page]
- 11.1 Geometry of pinion-type cutter [Go to Page]
- 11.1.1 General
- 11.1.2 Pinon-type cutter without protuberance
- 11.1.3 Pinon-type cutter with protuberance
- 11.2 Undercut condition
- 11.3 Determination of start of involute when no undercut exists
- 11.4 Start of involute when there is undercut [Go to Page]
- 11.4.1 Residual fillet undercut (transverse plane)
- 11.4.2 Angle centre line of gear pair to centre point of tooth tip rounding:
- 11.4.3 Point Q (tangent point of cutter tip fillet and generated gear root fillet)
- 11.4.4 Determination of start of involute
- 11.4.5 Determination of radius of curvature of trochoid
- Annex A (informative) Form diameters when a circular arc in a transverse plane is used for tooth tip corner radius or tooth root fillet radius
- Annex B (informative) Tip form radius when tooth tip corner radius is defined on normal surface with pinion type cutter
- Annex C (informative) Supplementry information for crossed axes cylindrical gears
- Annex D (informative) Geometry of surfaces in contact
- Annex E (informative) Projection of transverse profile of the tooth to other planes
- Annex F (informative) Interface for geometry of involute worms defined with ISO 10828
- Bibliography [Go to Page]
