Backlash (engineering)
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In mechanical engineering, backlash is purposeful clearance between mating components, sometimes described as the amount of lost motion due to clearance or slackness when movement is reversed and contact is re-established. For example, in a pair of gears, backlash is the amount of clearance between mated gear teeth. This gap means that when a gear-train is reversed the driving gear must be turned a short distance before all the driven gears start to rotate. A similar effect is the taking up of slack when a train starts to pull away at the station and each car bumps as its link becomes tight. 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.
Backlash is an unavoidable property of all reversing mechanical couplings, and may or may not be desirable, depending on the application. Some backlash is required to allow for lubrication, manufacturing errors, deflection under load and differential expansion between the gears and the housing.
Gear couplings use backlash to allow for angular misalignment. The looseness of railroad car couplings is another type of backlash which is deliberate; when starting a train from a dead stop, the engine starts each following car rolling in turn as the couplings engage, instead of having to start all the cars at once, thus efficiently overcoming the initial inertia and static friction with less force over a longer time.
Backlash is undesirable in precision positioning applications such as machine tool tables. It can be minimized by tighter design features such as ballscrews instead of leadscrews, and by using preloaded bearings. A preloaded bearing uses a spring or other compressive force to maintain bearing surfaces in contact despite reversal of direction.
[edit] Math
Backlash is created when the tooth thickness of either gear is less than the tooth thickness of an ideal gear, or the zero backlash tooth thickness. Additional backlash is created when the operating center distance of the gear pair is less than that for two ideal gears. The total backlash is defined as:
where:
 |
= total backlash, | |
 |
= backlash due to tooth thickness modifications | |
 |
= backlash due to operating center distance modifications |
Backlash due to tooth thickness changes is typically measured along the pitch circle and is defined by:
where:
 |
= 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:
- bc = 2(Δc)tanφ
where:
 |
= 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, there are applications where this may not be advisable. For example, if the pinion (the smaller of the two gears) is too small or has few teeth, the engineer may elect to not modify the pinion teeth and instead, take the total backlash out of the gear teeth.
[edit] Antibacklash gear designs
In certain applications, backlash is an undesirable characteristic and should be minimised; for example, a radio tuning dial where one may make precise tuning movements both forwards and backwards. Specialised gear designs allow this. One of the more common designs splits the gear into two gears, each half the thickness of the original. One half of the gear is fixed to its shaft while the other half of the gear is allowed to turn on the shaft, but pre-loaded in rotation by small coil springs that rotate the free gear relative to the fixed gear. In this way, the spring tension rotates the free gear until all of the backlash in the system has been taken out; the teeth of the fixed gear press against one side of the teeth of the pinion while the teeth of the free gear press against the other side of the teeth on the pinion.
Loads smaller than the force of the springs do not compress the springs and with no gaps between the teeth to be taken up, backlash is eliminated.
In mechanical computers a more complex solution is required, namely a frontlash gearbox.[1] This works by turning slightly faster when the direction is reversed to 'use up' the backlash slack.
