Backlash (engineering) - Gears

Gears

Factors affecting the amount backlash required in a gear train include errors in profile, pitch, tooth thickness, helix angle and center distance, and runout. The greater the accuracy the smaller the backlash needed. Backlash is most commonly created by cutting the teeth deeper into the gears than the ideal depth. Another way of introducing backlash is by increasing the center distances between the gears.

Backlash due to tooth thickness changes is typically measured along the pitch circle and is defined by:

where:

 = backlash due to tooth thickness modifications = tooth thickness on the pitch circle for ideal gearing (no backlash) = actual tooth thickness

Backlash, measured on the pitch circle, due to operating center modifications is defined by:

where:

 = backlash due to operating center distance modifications = difference between actual and ideal operating center distances = pressure angle

Standard practice is to make allowance for half the backlash in the tooth thickness of each gear. However, if the pinion (the smaller of the two gears) is significantly smaller than the gear it is meshing with then it is common practice to account for all of the backlash in the larger gear. This maintains as much strength as possible in the pinion's teeth. The amount of additional material removed when making the gears depends on the pressure angle of the teeth. For a 14.5° pressure angle the extra distance the cutting tool is moved in equals the amount of backlash desired. For a 20° pressure angle the distance equals 0.73 times the amount of backlash desired.

As a rule of thumb the average backlash is defined as 0.04 divided by the diametral pitch; the minimum being 0.03 and the maximum 0.05.

In a gear train, backlash is cumulative. When a gear-train is reversed the driving gear is turned a short distance, equal to the total of all the backlashes, before the final driven gear begins to rotate. At low power outputs, backlash results in inaccurate calculation from the small errors introduced at each change of direction; at large power outputs backlash sends shocks through the whole system and can damage teeth and other components.