# Gearing Backlash Arcsine to Arc minutes

SevenToFive
Working on a project at work for backlash in a gearbox. I need to know the amount of backlash in arc minutes that this particular ratio has. Wondering if my approach is on the right path.
So can calculate the loose tolerance by the amount of end play in the input shaft and output shaft, add the input tolerance and output shaft tolerance together, divide by the gear pitch diameter, then divide by 2 for the radius. That should give me the sine of the degree, if I take the arc sine (sin^-1) of that value it will give me the degrees that I can multiply by 60 to get arc minutes. Does my approach sound correct?

Thanks for the help.

Gold Member
The end play will affect the radial backlash with helical, herring bone, or worm gearing. With straight cut gears it has no effect. Even then endplay contribution could be in addition to the backlash from the tooth clearences. Also, realize that for a multi-stage gear train, the backlash from each stage will be multiplied by the gear ratios of each succeding stage.

Your formula using arcsin is valid for straight cut gears as far as it goes. If not straight cut, account for the end play at each stage because it will contribute to the effective tooth clearence.

Cheers,
Tom

SevenToFive