Backlash (due to tooth thickness changes)


In mechanical engineering, backlash, sometimes called lash or play, is clearance or lost motion in a mechanism caused by gaps between the parts. It can be defined as the maximum distance or angle through which any part of a mechanical system may be moved in one direction without applying appreciable force or motion to the next part in mechanical sequence, and is a mechanical form of deadband. An example, in the context of gears and gear trains, is the amount of clearance between mated gear teeth. It can be seen when the direction of movement is reversed and the slack or lost motion is taken up before the reversal of motion is complete. Another example is in a valve train with mechanical tappets, where a certain range of lash is necessary for the valves to work properly.

Depending on the application, backlash may or may not be desirable. It is unavoidable for nearly all reversing mechanical couplings, although its effects can be negated or compensated for. In many applications, the theoretical ideal would be zero backlash, but in actual practice some backlash must be allowed to prevent jamming. Reasons for the presence of backlash include allowing for lubrication, manufacturing errors, deflection under load, and thermal expansion.


Factors affecting the amount backlash required in a gear train include errors in profile, pitch, tooth thickness, helix angle and center distance, and run-out. 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 the formula shown here.

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 divided by the diametral pitch and the maximum 0.05 divided by the diametric pitch.
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.

Related formulas


btbacklash due to tooth thickness modifications (dimensionless)
titooth thickness on the pitch circle for ideal gearing (no backlash) (dimensionless)
taactual tooth thickness (dimensionless)