This document lists 14 formulae related to spur gear design parameters. The key parameters include: 1) Angular velocity and speed ratio calculations based on number of teeth and RPM. 2) Calculation of circular pitch, module, and pitch circle radius based on diameter and number of teeth. 3) Addendum, dedendum, and path of contact dimensions. 4) Calculations for maximum path of approach and recess, and sliding velocities during engagement based on angular velocities. 5) Minimum number of teeth required to avoid interference based on gear dimensions.

1. List of Formulae (Spur gear)
1. Angular velocity = 𝜔 =
2𝜋𝑁
60
rad/s
2. Speed Ratio / RPM ratio =
𝜔1
𝜔2
=
𝑖1
𝑖2
=
𝑁1
𝑁2
=
𝑑2
𝑑1
=
𝑟2
𝑟1
=
𝑧2
𝑧1
1 always corresponds to pinion
2 always corresponds to gear
3. Circular pitch = 𝑝 =
𝜋𝑑
𝑧
mm
4. Module m =
𝑑
𝑧
Also, p=𝜋 𝑚 mm
5. Pitch circle radius = r =
𝑚𝑧
2
mm
Pitch circle radius of pinion = r1 =
𝑚𝑧1
2
mm
Pitch circle radius of gear = r2 =
mz2
2
mm
6. Addendum = a = mm
7. Dedendum = b = mm
8. Path of Contact = mm
If the diameter of pinion and gear are same/equal mm
9. Path of approach =
10. Path of recess =
11. Maximum Path of approach ≤
12. Maximum Path of recess ≤
13. Velocity of sliding during approach = (𝜔1 + 𝜔2) x Path of approach
14. Velocity of sliding during recess = (𝜔1 + 𝜔2) x Path of recess
mm

2. Minimum No. of teeth to avoid interference
Maximum addendum circle radius of gear to avoid interference =
mm
Minimum number of teeth to avoid interference =
If number of teeth on pinion and gear are equal =
Addendum of gear = mm