Gears

Drawing Gear Teeth

Spur Gears

Drawing Gear Teeth

The involute SystemThe curved surface of the gear tooth profile must be of a definitegeometric form if the gears are to operate smoothly with a minimum ofnoise and vibration. The most common form in use today is the involuteprofile.

In the involute system, the shape of the tooth depends basically upon thepressure angle. The pressure angle is either 14 1/2 degrees or 20degrees. The pressure angle determines the size of the base circle. Theinvolute curve is generated from the base circle.

Construction of the Base Circle

Construction of the Base Circle

Draw the pitch circle, the addendum circle, and the root circle (Dedendum). Add the vertical and horizontal center lines.

Construction of the Base Circle

Mark point (P) at the intersection of the vertical center line and the pitch circle.

Construction of the Base Circle

Construct a line perpendicular to the pressure angle and passing through point (P).

Construction of the Base Circle

Mark this intersection as point (J).

Construction of the Base Circle

The base circle is constructed with the center being the center of the pitch circle and the radius equal to the distance from the center to point (J).

Construction of the tooth profileDraw the gear tooth face from point (P) to point (A) with a radius (R) derived from the Wellman's Involute Odontograph chart. The center of the radius is on the base circle. Do not use the radius values given directly from the chart. Each value must be divided by the Diametral Pitch (P) for the given gear.

Draw the flank portion from (P) to (O) with a radius of (r) derived from the Wellman's Involute Odontograph chart as described above. The center of the radius is on the base circle.

The portion of the tooth below the base circle is a straight line drawn to the gear center.

Drawing Gear Teeth

Wellman's Involute Odontograph Chart

Number of 14 1/2 degrees 20 degreesTeeth R r R r12 2.87 .079 3.21 1.3113 3.02 .088 3.40 1.4514 3.17 .097 3.58 1.6015 3.31 1.06 3.76 1.7516 3.46 1.16 3.94 1.9017 3.60 1.26 4.12 2.0518 3.74 1.36 4.30 2.2019 3.88 1.46 4.48 2.3520 4.02 1.56 4.66 2.5121 4.16 1.66 4.84 2.6622 4.29 1.77 5.02 2.8223 4.43 1.87 5.20 2.8924 4.57 1.98 5.37 3.14

Construction of the tooth profileDraw the gear tooth face from point (P) to point (A) with a radius (R) derived from the Wellman's Involute Odontograph chart. The center of the radius is on the base circle. Do not use the radius values given directly from the chart. Each value must be divided then the Diametral Pitch (P) for the given gear.

Drawing Radius (R) = Given radius from chart (R)/PDrawing Radius (R) = (4.02)/4 = 1.005

Construction of the tooth profile

Draw the flank portion from (P) to (O) with a radius of (r) derived from the Wellman's Involute Odontograph chart as described above. The center of the radius is on the base circle.

Drawing Radius (r) = Given radius from chart (r)/PDrawing Radius (r) = (1.56)/4 = 0.3900

Construction of the tooth profile

The portion of the tooth below the base circle is a straight line drawn to the gear center.

Construction of the gear teeth

The opposite tooth profile can be drawn through the remaining marks located on the pitch circle by mirroring the above construction process.

Construction of the gear teeth

Fillet the corners of the straight portion of the gear tooth and the root circle. The fillet radius can be derived from the following formulas:

Fillet Radius = 1 1/2 x Clearance

Fillet Radius = 1.5 (.157/P)

Clearance = .157/P

Clearance = B – A

Construction of the gear teethThe remaining tooth profiles can be constructed using the same process, constructing a tooth profile through every other mark on the pitch circle.