Gear Terminologies

Gear Definitions and Formulas

Active Profile ndash is that part a gear tooth that actually comes into contact with its mating tooth along the line of action

Addendum (a) ndash is the radial or perpendicular distance between the pitch circle and the top of the teeth

Spur Gears - a = 1 Pd (Pd = Diametral Pitch)

Helical Gears - a = 1 Pnd (Pnd = Normal Diametral Pitch)

Angular Bevel Gears ndash are bevel gears in which the axes are not at a right angle

Angular Pitch (θN) ndash is the angle subtended by the circular pitch

Arc of Approach (Qt) ndash is the arc of the pitch circle through which a tooth travels from the time it first makes contact with a mating tooth until it is in contact at the pitch point

Arc of Recession (Qr) ndash is the arc of pitch circle through which a tooth travels from the time it is in contact with a mating tooth at the pitch point until contact ceases

Axial Direction ndash A direction parallel to an axes

Axial Pitch (Px) ndash is the distance in an axial plane surface between corresponding adjacent tooth profiles

Px = Pt Tan Ψ (Pt = Transverse Circular Pitch Ψ = Helix Angle)

Axial Pressure Angle (Φx) ndash is the angle between the tangent to the tooth profile in an axial plane at the pitch surface and a line perpendicular to the axis

Axial Runout ndash is the runout measured in a direction parallel to the axes of rotation

Backlash (B) ndash is the amount by which the width of a tooth space exceeds the thickness of the engaging tooth on the pitch circles

Backlash Variation ndash is the difference between the maximum and minimum backlash occurring in one revolution of the larger of a pair of mating gears

Base Circular Thickness (tb) ndash is the length of arc on the base circle between two involute curves forming the profiles of a tooth

Base Cylinder ndash is the cylinder of the same diameter as the base circle

Base Lead Angle (λb) ndash is the lead angle at the base cylinder

Base Diameter (Db) ndash is the diameter of the circle from which the involute form is generated

Db = D Cos Φ (D = Pitch Diameter Φ = Pressure Angle

Base Helix Angle (Ψb) ndash is the helix angle at the base cylinder

Base Pitch (Pb) ndash is the circular pitch in the plane of rotation at the base circle

Pb = Cos Φ π Pd (Φ = Pressure Angle Pd = Diametral Pitch)

Base Radius (rb) ndash is the radius of the circle from which the involute form is generated

Base Tooth Thickness (Tb) ndash is the distance on the base circle in the plane of rotation between involutes of the same pitch

Bevel Gears ndash are gears of conical form designed to operate on intersecting axes

Bore Diameter ndash is the diameter of the hole in a gear

Bottom Land ndash is the surface of a gear between the flanks of two adjacent teeth For external gears it is measured in the root and for internal gears it is measured at the minor tip of the tooth

Center Distance (C) ndash is the radial distance from the center of a gear to the center of its mating gear

Chordal Addendum (ac) ndash is the radial distance from the circular tooth thickness chord to the top of the tooth

Chordal Thickness (tc) ndash is the length of the chord subtended by the circular tooth thickness arc

Circular Pitch (P) ndash is the distance on the circumference of the pitch circle between corresponding points of adjacent teeth

P = π Pd (Pd = Diametral Pitch)

Circular thickness (t) ndash is the thickness of the tooth on the pitch circle

t (Basic) = 5 P (P = Circular Pitch)

Clearance (c) ndash is the radial distance between the top of a tooth and the bottom of the mating tooth space

c = 157 Pd (Pd = Diametral Pitch)

Composite Action ndash is the variation in center distance when two gears are rolled in tight mesh

Contact Ratio (mc) ndash is the ratio of the arc of action to the circular pitch

mc = sqrt(Ro1sup2 - Rb1sup2) + sqrt(Ro2sup2 - Rb2sup2-C SIN Φ )

P COS Φ

(Ro1 and Ro2 = Outside Radius of gear 1 and Gear 2)

(Rb1 and Rb2 = Base Radius of Gear 1 and Gear 2)

(C = Center Distance P = Circular Pitch Φ = Pressure Angle)

Contact Ratio Total (mf) ndash is the ratio of the sum of the arc of action and the face advance to the circular pitch

Crowned Teeth ndash are teeth having modified surfaces in the lengthwise direction to prevent contact at their ends

Dedendum (b) ndash is the radial or perpendicular distance between the pitch circle and the bottom of the tooth space

b = 1157 Pd (Pd = Diametral Pitch)

Diametral Pitch (Pd) ndash is the ratio of the number of teeth per inches of pitch diameter

Pd = π P (P = Circular Pitch)

Pd = N D (N = Number of Teeth D = Pitch Diameter)Pd = N + 2 Do (Do = Outside Diameter)

Pd = (Pb Cos Φ) π (Pb = Base Pitch Φ = Pressure Angle)

Pd = 254 m (m = Module)

Double Helical Gear ndash is a gear of cylindrical form with two sections of teeth one right hand and the other left hand that engage simultaneously with teeth of a similarly designed mating gear

Effective Face Width (Fe) ndash is the width of face that actually comes into contact with a mating gear

External Gear ndash is a gear with teeth formed on the outer surface of a cylinder or cone

Face Width (F) ndash is the width of the pitch surface

Fillet Curve ndash is the concave portion of the tooth profile where it joins the bottom of the tooth space

Fillet Radius (rt) ndash is the radius of a circular arc approximating the fillet curve

Form Diameter (TIF) - is the diameter of the circle beyond which the tooth profile must conform to the specified involute curve

Full Depth Teeth ndash are teeth in which the working depth equals 20 divided by the Diametral pitch

Gear(s) ndash are machine elements that transmit motion by means of successively engaging teeth

Gears Center ndash is the center of the pitch circle

Gear Ratio (mG ndash is the ratio of the number of teeth in a mating set of gears

Helical Gear ndash is a cylindrical gear with helical teeth

Helix Angle (Ψ) ndash is the angle between a tangent to the helix and an element of the cylinder Usually the pitch helix is referred to

Hub Diameter ndash is the diameter of the central part of the gear body surrounding the bore and extending beyond the web spokes or body

Hub Extension ndash is the distance that the hub extends beyond the face of the gear body

Interference ndash is the contact between mating teeth at some other point than along the line of action

Inside Diameter (Di) ndash is the diameter of the circle which contains the tops of the teeth of an internal gear

Involute ndash is the curve that is described by the end of a line which is unwound from the circumference of a circle

Involute function of an angle ndash is the difference between its Tangent and its angular value in radians

Inva=tan(a)-(a (π 180)) (a = An angle in degrees)

Involute Polar Angle (θ) ndash is the angle between a radius vector to a point on an involute curve and a radial line to the point where the curve touches the base circle

Involute Roll Angle (ε) ndash is an angle whose arc on the base circle of radius unity equals the tangent of the pressure angle at a selected point on the involute

K Factor (K) ndash Is the ratio of tooth thickness change to the measurement overbetween pins change

Lead (L) ndash is the axial advance of a helix for one complete turn as in the threads of cylindrical worms and teeth of helical gears

L = π D Tan Ψ (D = Pitch Diameter Ψ = Helix Angle)

Lead Angle (λ) ndash is the angle between a tangent to the pitch helix and a plane of rotation

Length of Action (Z) ndash is the distance on an involute line of action through which the point of contact moves during the action of the tooth profiles

Line of Action ndash is that portion of the common tangent to the base circles along which contact between the mating involute teeth occurs

Line of Centers ndash is the straight line through the center of tangent pitch circles

Line of Contact ndash is the line or curve along which two tooth surfaces are tangent to each other

Long and Short addendum teeth ndash are the teeth of engaging gears (on a standard designed center distance) one of which has a long addendum and the other has a short addendum

Module (Metric) (m) ndash is the ratio of the pitch diameter in millimeters to the number of teeth

m = 254 Pd (Pd = Diametral Pitch)

Normal Base Pitch (Pnb) ndash is the circular pitch taken along the base circle normal to the gear helix angle

Pnb = Pn Cos Φn (Pn = Normal Circular Pitch Φn = Normal Pressure Angle)

Normal Chordal Addendum (anc) ndash is the chordal addendum the normal plane

Normal Chordal Thickness (tnc) ndash is the length of the normal thickness chord between pitch line elements of a tooth

Normal Circular Thickness (tn) ndash is the circular thickness in a plane normal to the helix angle

tn = tt Cos Ψ (tt = Transverse Circular Tooth Thickness Ψ = Helix Angle)

tn = 5 Pn (Pn = Normal Circular Pitch)

Normal Circular Pitch (Pn) ndash (Normal to the helix angle) is the shortest distance on the pitch surface between corresponding pitch line elements of adjacent teeth

Pn = Pt Cos Ψ (Pt = Transverse Circular Pitch Ψ = Helix Angle)

Pn = π Pnd (Pnd = Normal Diametral Pitch)

Normal Diametral Pitch (Pnd) ndash is the diametral pitch corresponding to the normal circular pitch and calculated in the normal plane

Pnd = Pd CosΨ (Pd = Transverse Diametral Pitch Ψ = Helix Angle)

Normal Helix ndash is the helix on a pitch cylinder normal to the pitch helix

Normal Plane (n) ndash is the plane perpendicular to a given straight line or to a tangent to a curved line

Normal Pressure Angle (Φn) ndash is the pressure angle in a plane normal to the pitch line element

Tan Φn = Tan Φt Cos Ψ (Φn = Normal Pressure Angle Ψ = Helix Angle)

Normal Profile Angle ndash is the profile angle in a normal plane of a helical or spiral tooth

Number of teeth ndash Number of gear teeth

N = Pd D (Pd = Diametral Pitch D = Pitch Diameter)

Operating Pitch Diameters (dp) ndash are the pitch diameters determined from the numbers of teeth and the center distance at which gears operate

dp = Db Cos Φ (Db = Base Circle Diameter Φ = Pressure Angle)

Outside Diameter (Do) ndash is the diameter of the circle that contains the tops of the teeth of an external gear

Do = N + 2 Pd (N = Number Of Teeth Pd = Diametral Pitch)

Do = D + 2 Pd (D = Pitch Diameter Pd = Diametral Pitch)

Outside Cylinder ndash is the surface which coincides with the tops of the teeth of an external cylindrical gear

Outside helix Angle (Ψo) ndash is the helix angle at the outside Cylinder

Outside Lead Angle (λo) ndash is the lead angle at the outside cylinder

Outside Radius (Ro) ndash is the radius of the circle which contains the tops of the teeth of external gears

Pinion ndash is a gear with a small number of teeth Of two mating gears the one with the smaller number of teeth is called the pinion

Pitch Circle ndash is the circle through the pitch point having its center at the axis of the gear

Pitch Cylinder ndash is the imaginary cylinder in a gear that rolls without slipping on a pitch cylinder or pitch plane of another gear

Pitch Diameter (D) ndash is the diameter of the pitch circle

D = N Pd (N=Number of teeth Pd = Diametral Pitch)

D = N 3183 P (P = Circular Pitch)

D = N Pd (Pd = Diametral Pitch or Transverse Diametral Pitch for helicals)

Pitch Radius (R) ndash is the radius of the pitch circle

R = 5 D (D = Pitch Diameter)

Pitch Point ndash is the intersection between the axes of the line of centers and the line of action

Pitch Range ndash is the difference between the longest and the shortest pitches on a gear

Point of Contact ndash is the point at which two profiles touch each other

Plane of Rotation ndash is any plane perpendicular to a gear axis

Pressure Angle (Φ) ndash is the angle between a tangent to the tooth profile and a line perpendicular to the pitch surface

Cos Φ = Db D (Db = Base Diameter D = Pitch Diameter)

Cos Φ = Pb (π Pd) (Pb = Base Pitch Pd = Diametral Pitch)

Profile Control Diameter ndash is the diameter of the circle beyond which the tooth profile must conform to the specified involute curve

Rack ndash is a gear with teeth spaced along a straight line and suitable for straight-line motion It is also described as a gear with an infinite number of teeth

Right Hand Helical Gear ndash is a gear in which the teeth twist clockwise as they recede from an observer looking along the axis

Roll Angle (Involute) (ε) ndash is an angle whose arc on the base circle of radius unity equals the tangent of the pressure angle at a selected point on the involute

Roll Angle to Form Diameter ndash Is the inactive angle of involute or the amount of roll in degrees from the base circle to the start of active profile

Root Diameter (DR) ndash is the diameter of the circle which contains the roots of the teeth

Root Radius (Rr) ndash is the radius of the root circle containing the bottoms of the tooth spaces

Tooth Face ndash is the surface between the pitch line element and the top of the tooth

Tooth Fillet ndash is the curved surface of the tooth flank joining it to the bottom land

Tooth Flank ndash is the surface between the pitch line and the bottom land including the fillet

Tooth Surface ndash is the total area including the tooth face and the tooth flank

Tooth to Tooth Composite Action ndash is the amount of composite action from one tooth to the next

Top Land ndash is the surface of the top of the tooth

Total Composite Action ndash is the total amount of composite action for an entire gear

Transverse Circular Pitch (Pt) ndash is the circular pitch in the transverse planePt = Pn Cos Ψ (Pn = Normal Circular Pitch Ψ = Helix Angle)

Pt = π Ptd (Ptd = Transverse Diametral Pitch)

Transverse Circular Thickness (tt) ndash is the circular thickness in the transverse plane

tt = tn Cos Ψ (tn = Normal Circular tooth Thickness Ψ = Helix Angle)

Transverse Contact Ratio (mp) ndash is the ratio of the arc of action to the transverse circular pitch

mp = sqrt(Ro1sup2 - Rb1sup2) + sqrt(Ro2sup2 - Rb2sup2-C SIN Φt )

Pt COS Φt



(C = Center Distance Pt = Transverse Circular Pitch Φt = Transverse Pressure Angle)

Transverse Diametral Pitch (Pd) ndash is the ratio of the number of teeth to inches of transverse pitch diameterPd = Pnd Cos Ψ (Pnd = Normal Diametral Pitch Ψ = Helix Angle)

Pd = π Pt (Pt = Transverse Circular Pitch)

Transverse Plane (t) ndash is perpendicular to the axial plane and to the pitch plane In parallel axis gears the transverse plane and the plane of rotation coincide

Transverse Pressure Angle (Φt) ndash is the pressure angle in the plane of rotationTan Φt = Tan Φn Cos Ψ (Φn = Normal Pressure Angle Ψ = Helix Angle)

Cos Φt = Db D (Db = Base Diameter D = Pitch Diameter)

True Involute Form Diameter (TIF) - is the diameter of the circle beyond which the tooth profile must conform to the specified involute curve

Undercut ndash is a condition in generated gear teeth when any part of the fillet curve lies inside of the line drawn tangent to the true involute form and its lowest point Undercut may be deliberately introduced to facilitate finishing operation

Whole Depth (ht) ndash is the radial distance between the outside circle and the root circle

ht = 2157 Pd (Pd = Diametral Pitch)

Working Depth (hk) ndash is the greatest depth to which a tooth of one gear extends into the tooth space of the mating gear

hk = 2 Pd (Pd = Diametral Pitch)

Axial Pressure Angle (Φx) ndash is the angle between the tangent to the tooth profile in an axial plane at the pitch surface and a line perpendicular to the axis

Axial Runout ndash is the runout measured in a direction parallel to the axes of rotation

Backlash (B) ndash is the amount by which the width of a tooth space exceeds the thickness of the engaging tooth on the pitch circles

Backlash Variation ndash is the difference between the maximum and minimum backlash occurring in one revolution of the larger of a pair of mating gears

Base Circular Thickness (tb) ndash is the length of arc on the base circle between two involute curves forming the profiles of a tooth

Base Cylinder ndash is the cylinder of the same diameter as the base circle

Base Lead Angle (λb) ndash is the lead angle at the base cylinder

Base Diameter (Db) ndash is the diameter of the circle from which the involute form is generated

Db = D Cos Φ (D = Pitch Diameter Φ = Pressure Angle

Base Helix Angle (Ψb) ndash is the helix angle at the base cylinder




















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Gear Terminologies

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