Spur gears are toothed wheels that transfer rotation and torque between parallel shafts. Their geometry controls how smoothly power moves from a driver gear to a driven gear. Engineers use standard dimensions such as module, pitch circle, pressure angle, and addendum so gears can mesh correctly.
A small error in tooth shape or spacing can cause noise, wear, vibration, or complete failure.
Key Facts
- Module relates tooth size to pitch diameter: m = d / N, where d is pitch diameter and N is number of teeth.
- Pitch diameter is found from tooth count and module: d = mN.
- Gear ratio from tooth counts is GR = N_driven / N_driver.
- For meshing spur gears with the same module, center distance is C = (d1 + d2) / 2 = m(N1 + N2) / 2.
- A common full-depth metric tooth uses addendum a = m and dedendum b ≈ 1.25m.
- The pressure angle is commonly 20 degrees and sets the direction of the contact force between meshing teeth.
Vocabulary
- Module
- Module is the pitch diameter divided by the number of teeth, and it describes the size of a gear tooth in metric units.
- Pitch circle
- The pitch circle is the imaginary circle where two gears roll together as if they were smooth cylinders.
- Pressure angle
- The pressure angle is the angle between the line of action of the tooth force and the tangent to the pitch circle.
- Addendum
- Addendum is the radial height of a tooth above the pitch circle.
- Involute profile
- An involute profile is the curved tooth shape that allows gears to keep a nearly constant speed ratio while teeth engage and disengage.
Common Mistakes to Avoid
- Mixing gears with different modules, which is wrong because their tooth spacing and size will not match properly for smooth meshing.
- Using outside diameter instead of pitch diameter in gear ratio calculations, which is wrong because speed ratio depends on pitch circles and tooth counts.
- Ignoring center distance, which is wrong because even correctly sized gears will bind or have excessive backlash if their shafts are placed incorrectly.
- Assuming bigger teeth always make a stronger gear, which is wrong because strength also depends on material, face width, load, lubrication, tooth count, and stress concentration.
Practice Questions
- 1 A driver gear has 20 teeth and a driven gear has 60 teeth. What is the gear ratio, and how many revolutions does the driven gear make when the driver makes 12 revolutions?
- 2 Two spur gears have module m = 2 mm. Gear 1 has 24 teeth and Gear 2 has 36 teeth. Find both pitch diameters and the required center distance.
- 3 Explain why an involute tooth profile helps two spur gears maintain a constant speed ratio even as the contact point moves along the tooth.