Page 370 - The Mechatronics Handbook

18.10 Eccentricity

The ideal relationships for gears, pulleys, and chain drives assume that the point of gear contact remains
at a fixed distance from the center of rotation for each gear. In reality, the true center of the gears pitch
circle and the center of rotation will be separated by a small amount, known as the eccentricity. Small
tooth-to-tooth errors can also cause local variations in the pitch circle radius. The combination of these two
effects can lead to a nonlinear geometrical relationship between two gears like that of Fig. 18.7, where
the nonlinear behavior is greatly exaggerated for clarity. Eccentricity impacts the accuracy of position
measurements made on the input side of the gear pair, as the output gear is not exactly where the sensor
measurement indicates.

18.11 Backlash

If two otherwise perfect gears are not mounted on a center-to-center distance that exactly matches the
sum of the pitch radii, there will be a small clearance, or backlash, between the teeth. When the input
gear reverses direction, a small rotation is required before this clearance is removed and the output gear
begins to move. Gear backlash is just one of many phenomena that can be characterized as hysteresis,
as shown in Fig. 18.8. Clearance between shafts and bearings can cause hysteretic effects also. Backlash
exhibits effects similar to those for eccentricity, i.e., a loss of repeatability, particularly when approaching
a measured point from different directions. The gear backlash problem is so prevalent and potentially
harmful that many manufacturers go to great lengths to minimize or reduce the effect:
• gears mounted closer together than the theoretically ideal spacing,
• split “anti-backlash” gears that are spring loaded to force teeth to maintain engagement at all times,
• external spring-loaded mounts for one of the gears to force engagement, or
• specially designed gears with anti-backlash features.

FIGURE 18.7 Gear eccentricity.

FIGURE 18.8 Gear backlash.

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