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Spur Gear Formulas

To Get

Having

Rule

Formula

Diametral Pitch

The circular pitch

Divide 3.1416 by the circular pitch

Pd = 3.1416 / CP

Diametral Pitch

  • Pitch diameter
  • Number of teeth

Divide the number of teeth by the pitch diameter

Pd = N / D

Diametral Pitch

  • Outside diameter
  • Number of teeth

Divide number of teeth + 2 by the outside diameter

Pd = (N+2) / OD

Diametral Pitch

  • Base pitch
  • Pressure angle

Divide the base pitch by the cosine of the pressure angle then divide by 3.1416

Pd = (BP / Cos PA) / 3.1416

Pitch Diameter

  • Number of teeth
  • Diametral pitch

Divide the number of teeth by the diametral pitch

D = N / Pd

Pitch Diameter

  • Number of teeth
  • Outside diameter

Divide the product of the outside diameter + number of teeth by the number of teeth + 2

D = (OD x N) / (N+2)

Pitch Diameter

  • Outside diameter
  • Diametral pitch

Subtract 2 divided by the diametral pitch from the outside diameter

D = OD - (2/ Pd)

Pitch Diameter

  • Addendum
  • Number of teeth

Multiply addendum by the number of teeth

D = A x N

Pitch Diameter

  • Base diameter
  • Pressure angle

Divide the base diameter by the cosine of the pressure angle

D = BD / (Cos Pa)

Outside Diameter

  • Number of teeth
  • Diametral pitch

Divide number of teeth + 2 by the diametral pitch

OD = (N+2) / Pd

Outside Diameter

  • Pitch diameter
  • Diametral pitch

Two divided by the diametral pitch plus pitch diameter

OD = (2 / Pd) + D

Outside Diameter

  • Pitch diameter
  • Number of teeth

Number of teeth + 2, divided by the quotient of number of teeth divided by the pitch diameter

OD = (N+2) / (N / D)

Outside Diameter

  • Number of teeth
  • Addendum

Multiply the number of teeth + 2 by the addendum

OD = (N + 2) x A

Number Of Teeth

  • Pitch diameter
  • Diametral pitch

Multiply the pitch diameter by the diametral pitch

N = D x Pd

Number Of Teeth

  • Outside diameter
  • Diametral pitch

Multiply the outside diameter by the diametral pitch and subtract 2

N = (OD x Pd) - 2

Thickness Of Tooth

  • Diametral pitch

Divide 1.5708 by the diametral pitch

t = 1.5708 / Pd

Addendum

  • Diametral pitch

Divide 1 by the diametral pitch

a = 1 / Pd

Dedendum

  • Diametral pitch

Divide 1.157 (or 1.25) by the diametral pitch

b = 1.157 / Pd

Working Depth

  • Diametral pitch

Divide 2 by the diametral pitch

hk = 2 / Pd

Whole Depth

  • Diametral pitch

Divide 2.157 (or 2.25) by the diametral pitch

ht = 2.157 / Pd

Clearance

  • Diametral pitch

Divide .157 (or .250) by the diametral pitch

c = .157 / Pd

Clearance

  • Diametral pitch

Divide thickness of tooth at the pitchline by 10

c = t / 10

Operating Diametral Pitch

  • C.D. between both gears
  • Number of teeth in each

Add the number of teeth in both gears and divide by 2 then divide by the center distance

PdO = ((n1 + n2)/2) / C

Center Distance

  • Normal diametral pitch
  • Number of teeth in both gears

Add the number of teeth in both gears and divide by 2 then divide by the normal diametral pitch

C = ((n1 + n2)/2) / Pnd

Operating Center Distance

  • Operating diametral pitch
  • Number of teeth in both gears

Add the number of teeth in both gears and divide by 2 then divide by the operating diametral pitch

Co = ((n1 + n2)/2) / Pod

Base Diameter

  • Pitch diameter
  • Pressure angle

Multiply the pitch diameter by the cosine of the pressure angle

Db = PD x (cos PA)

Pressure Angle

  • Base diameter
  • Pitch diameter

Divide the base diameter by the pitch diameter

cosPA = Db / D

Pressure Angle

  • Base pitch
  • Diametral pitch

Divide Pi by the diametral pitch, then divide by the base pitch

cosPA = (3.1416 / Pd) / Pb

Base Pitch

  • Diametral pitch
  • Pressure angle

Divide the diametral pitch by Pi, then multiply by the cosine of the pressure angle

Pb = (Pd / 3.1416) x (cos PA)


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