Backlash (gear)

From Academic Kids

Backlash is the amount of clearance between mated gear teeth in a gear pair. Some backlash is required to allow for lubrication, manufacturing errors, deflection under load and differential expansion between the gears and the housing .

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:

<math>b=b_t+b_c\;<math>

where:

  <math>b\;<math> = total backlash,
<math>b_t\;<math> = backlash due to tooth thickness modifications
<math>b_c\;<math> = backlash due to operating center distance modifications

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

<math>b_t=t_i-t_a\;<math>

where:

  <math>t_i\;<math> = tooth thickness on the pitch circle for ideal gearing (no backlash)
<math>t_a\;<math> = actual tooth thickness

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

<math>b_c=2(\triangle c)tan\phi<math>

where:

  <math>\triangle c\;<math> = difference between actual and ideal operating center distances
<math>\phi \;<math> = pressure angle

Standard practice is to make allowance for half the backlash in the tooth thickness of each gair. 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.

Antibacklash gear designs

In certain applications (for example, a radio tuning dial where one may make precise tuning movements both forwards and backwards) backlash is an undesireable characteristic and should be minimised. 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.

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