Gears

Drawing Gear Teeth Spur Gears

Drawing Gear Teeth

The involute System

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

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

16 17 18 19 20 21 22 23 24

Number of Teeth

12 13 14 15

14 1/2 degrees R r

2.87

3.02

.079

.088

3.17

3.31

.097

1.06

3.46

3.60

3.74

3.88

4.02

4.16

4.29

4.43

4.57

1.16

1.26

1.36

1.46

1.56

1.66

1.77

1.87

1.98

20 degrees R r

3.21

3.40

1.31

1.45

3.58

3.76

1.60

1.75

3.94

4.12

4.30

4.48

4.66

4.84

5.02

5.20

5.37

1.90

2.05

2.20

2.35

2.51

2.66

2.82

2.89

3.14

Construction of the tooth profile Draw 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)/P Drawing 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)/P Drawing 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 teeth The remaining tooth profiles can be constructed using the same process, constructing a tooth profile through every other mark on the pitch circle.