For information:

Working Clearance = Dedendum - Addendum

Working Depth = Addendum * 2

Tooth Depth = Addendum + Dedendum

Each gear tooth is in contact with another gear tooth as it moves through the meshing position.

The Contact-Ratio gives the number-of-teeth that are in contact, on average, as they pass through the meshing point. A contact ratio between 1 and 2 means that contact alternates between two and one pairs of teeth in contact at any one time. Gears that have a high contact-ratio are smoother and quieter. The contact-ratio of an Internal Gear-Pair is higher than that of a similar External Gear-air, even greater than 2.

If the Contact-Ratio is too low, then consider these options:

•Decrease the pressure-angle

•Increase the number-of-teeth

•Increase the working-depth

Pitch Diameter

Module, m, number-of-teeth, N

D = mN

Circular Pitch

Module

pc = m.π = D.π  ∕  N

Module

Diametrical Pitch, Pd

m = 25.4  ∕  Pd

Number-of-Teeth

Module, m, Pitch Diameter, D

N = D  ∕  m

Addendum

Module, m

a = m

Dedendum

Module, m

b = 1.25m

Outside Diameter

Module, m, Pitch Diameter, D, or number-of-teeth, N

Do = D + 2m = m (N + 2)

Root Diameter

Pitch Diameter, D, Module, m

DR = D – 2.5m

Base Circle Diameter

Pitch Diameter & Pressure Angle

Db = D cos μ

Base Pitch

Module, m, & Pressure Angle, μ

pb = m π cos μ

Tooth Thickness at

Standard Pitch Diameter

Module, m

Tstd = π. m  ∕ 2

center Distance

Module, m, number-of-teeth, N

C = m . (N1 + N2) ∕ 2

Contact Ratio for Spur Gears

( 1 < CR < 2 )

Outside Radii, Base Circle Radii, center Distance, Pressure Angle

CR = (√R012 – Rb12 + √R022 – Rb22 – C sin μ)  ∕  m π cos μ

Backlash (linear)

Change in center Distance, ΔC

B = 2( ΔC )tan μ

Backlash (linear)

Change in Tooth Thickness, ΔT

B = ΔT

Backlash (linear) along

Line-of-action

Linear Backlash along Pitch Circle, B

BLA = B cos μ

Backlash, Angular

Linear Backlash, D

Ba = 6880 B ∕ D (arc minutes)  

Min. No. of Teeth

for No Undercutting

Pressure Angle, μ

Nc = 2 ∕ sin2 μ

Nc (20º) = ~17 Teeth

Addendum:

the height of the gear tooth above the pitch circle diameter

Backlash:

the angle the output shaft of the gearbox can move without the input shaft moving

Base Circle:

an imaginary circle used in involute gearing to generate the involutes that form the tooth profiles

Bevel Gears:

used for right-angle applications. There are two types of bevel gears which are straight and spiral

center distance:

distance between the axes of two meshed gears - Length of the Line-of centers

Circular Thickness:

the thickness of the tooth on the pitch circle.

Dedendum:

the depth of the tooth below the diameter of the pitch circle.

Diametrical Pitch:

the teeth per inch of the diameter of the pitch circle

Differential Gear:

a bevel gear which allows two shafts to rotate at a different speed.

Gear:

a wheel with teeth that meshes with another wheel with teeth to translate motion.

Gear center:

the center of the pitch circle.

Gear Train:

two or more gears meshed by their teeth. A gear train generates power speed through the meshed gears rotating

Gear Ratio:

the ratio between the numbers of teeth of meshing gears.

Helical Gear:

gear with the gear teeth cut at angles

Line of Contact:

the line or curve along which two tooth surfaces are tangent to each other

Involute:

the curve which describes a line which is unwound from the circumference of the gear

Pinion:

a small cogwheel which fits into a larger gear or track.

Pitch Circle:

the curve of intersection of a pitch surface of revolution and a plane of rotation

Pitch Diameter:

the diameter of the pitch circle

Pitch Radius:

the radius of the pitch circle

Planetary Gears:

a system that consists of three components: the sun gear, ring gear, and two or more planet gears. The sun gear is in the center, the ring gear is the outermost gear, and the planet gears are the gears surrounding the sun gear inside the ring gear.

Pressure Angle:

the angle between the line-of-action and the normal (90º, perpendicular) to the surface of the tooth

Spiral Bevel Gears:

shafts whose axes are perpendicular (90º) to each other and are used in right-angle applications

Spur Gear:

connect parallel shafts which have involute teeth that are parallel to the shaft

Sun Gear:

a gearwheel that rotates around its own axis and has other gears (planet gears) that rotate around it

Torsional Strength:

the measure of the amount of torque that a radial shaft can sustain during its rotation in a mechanical system

Working Depth:

the max depth a tooth of one gear extends into the tooth gear of a mating gear

Worm Gear:

a gear with one or more teeth with screwed threads

Crowning:

End-Relief

Topping and Semi-Topping

End Radius and Edge Radius/End Relief

Top Round/Semi-topping

Definition of Circular Pitch, p

Circular Pitch  = pitch circle circumference(pi.d) / number of teeth(z) ; p = Π.d / z

Module = Pitch Diameter(d) / Number of Teeth(z) ; m = d/z

Circular Pitch(p) / Module(m) = pi ; p/m = Π

Pitch Diameter(d) = module(m)*number of teeth(z) ; d = m.z