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Just a few of the ways that we have recently helped our customers solve some of their problems.


COOLING TOWER REDUCER REPAIR


LARGE POWER GENERATION
REDUCER REPAIR

 

 

 

Spur Gear Formulas
For American Standard Flat Root Full Depth Teeth

This is a chart of formulas used in calculating spur gear information based on standard gearing practices. The spur gear formulas here are based on the "Diametral Pitch system (DP). These formulas can be used with Circular Pitch and Module systems by first converting them to the Diametral Pitch (Click here for a calculator).
  • To convert a circular pitch (CP) to DP - Divide 3.1416 by the circular pitch
  • To convert the module (Mod) to DP - Divide the 25.4 by the module

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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