Backlash/Center distance

[jasnjules]

I am fairly new to gears and am trying to visualize the formula for figuring backlash from adjusted center distance between two gears. (2 X difference in center distance X tan P.A.)

measuring backlash perpendicular to P.A. why tan and not sine? I visualize the centerline distance as the hypotenuse and line of backlash as the opposite leg of P.A. The mentioned calculation works, but I am trying to understand it.

I like formulas, but I like visualizing them even more.
Thanks

 

[davidh729]

Not 100% sure on thhis but I think the tan comes from the equation of the involute. As the gears are seperated the tooth thins out. I think you're visualization only works if the teeth have no thickness.

Dave Hyman
iRobot Corp

http://www.irobot.com

 

[israelkk]

http://www.sdp-si.com/D190/HTML/D190T47.htm

There you can see where the sin is used and where the tan is used. For more thorough analysis try GEAR HANDBOOK for Darle Dudley or Buckingham books.

 

[Philrock]

Backlash is typically measured tangentially, in the transverse plane. This is represented by the common backlash checking setup of a dial indicator mounted on one shaft with its stylus registering against a stationary object at the pitch radius. It is also consistent with using tan rather than sin.

Note that if you want to adjust backlash by changing center distance, in calculations you must use OPERATING pressure angle and pitch radius rather than STANDARD pressure angle and pitch radius. The OPERATING and STANDARD parameters are typically slightly different if the gears have profile shift.

The Dudley and Buckingham books suggeted by israelkk are excellent references.