Related Resources: gears

Spur Gear Design Tool Calculator

Gear Design and Selection Application

Spur Gear Design Tool Calculator per. ANSI B6.1

Formulas for Tooth Parts, 20-and 25-degree Involute Full-depth Teeth ANSI Coarse Pitch Spur Gear Tooth Forms.

The spur gear diametral pitch system isintended to provide a series of standard tooth sizes, the principle being similar to the standardization of screw thread pitches. Inasmuch as there must be a whole number of teeth on each gear, the increase in pitch diameter per tooth varies according to the pitch. For example, the pitch diameter of a gear having, say, 20 teeth of 4 diametral pitch, will be 5 inches; 21 teeth, 5 1⁄4 inches; and so on, the increase in diameter for each additional tooth being equal to 1⁄4 inch for 4 diametral pitch. Similarly, for 2 diametral pitch the variations for successive numbers of teeth would equal 1⁄2 inch, and for 10 diametral pitch the variations would equal 1⁄10 inch, etc.

Units in imperial (inches)

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Base Circle Diameter Equation

Circular Pitch Equation

Diametral Pitch Equation

Addendum Equation

Dedendum Perferred Equation

Dedendum Shaved or Ground Teeth: When gears are preshave cut on a gear shaper the dedendum will usually need to be increased to 1.40/P to allow for the higher fillet trochoid produced by the shaper cutter. This is of particular importance on gears of few teeth or if the gear blank configuration requires the use of a small diameter shaper cutter, in which case the dedendum may need to be increased to as much as 1.45/P. This should be avoided on highly loaded gears where the consequently reduced J factor will increase gear tooth stress
excessively.

Working Gear Tooth Depth Equation

Whole Depth Preferred Equation

Whole Depth Shaved or Ground Teeth Equation

Clearance Preferred Equation

Clearance Shaved or Ground Teeth Equation: A minimum clearance of 0.157/P may be used for the basic 20-degree and 25-degree pressure angle rack in the case of shallow root sections and use of existing hobs or cutters.

Fillet Radius Rack Equation: The fillet radius of the basic rack should not exceed 0.235/P for a 20-degree pressure angle rack or 0.270/P for a 25-degree pressure angle rack for a clearance of 0.157/P. The basic rack fillet radius must be reduced for teeth with a 25-degree pressure angle having a clearance in excess of 0.250/P.

Nomenclature:
φ = Pressure Angle
a = Addendum
a_G = Addendum of Gear
a_P = Addendum of Pinion
b= Dedendum
c= Clearance
C= Center Distance
D= Pitch Diameter
D_G = Pitch Diameter of Gear
D_P = Pitch Diameter of Pinion
D_B = Base Circle Diameter
D_O = Outside Diameter
D_R = Root Diameter
F = Face Width
h_k = Working Depth of Tooth
h_t = Whole Depth of Tooth
m_G = Gear Ratio
N = Number of Teeth
N_G = Number of Teeth in Gear
N_P = Number of Teeth in Pinion
p = Circular Pitch
P = Diametral Pitch

Related:

• Spur Gear Generator with Download Spur Gear Generator is unitless: you may choose inches, cm or millimeters when importing your DXF file as you will have the same value for D/P as it is set above or as imported (SI or imperial units).
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• Gear Design Equations and Formula | Circular Pitches and Equivalent Diametral Pitches Table
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• Elements of Metric Gear Design
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