Gearbox Backlash: Adding Values for Output?

[Shady99]

hello,i wanted to ask if we have integrated two spur gearboxes with different backlash values.How will the backlash add up at the output.Should i multiply the two backlash values,add them or there is a another relationship for it.Thanks

 

[JBA]

You should multiply the first unit's backlash by the input/output ratio of the second unit and then add that result to the of the second unit's backlash.

 

[Shady99]

Jba thnks for the reply...can u tell me how u gathered that?...or may be a link where i can read abt it more?

 

[JBA]

I can't give you any references, it simply comes from my general knowledge of gear assemblies.

Think of it this way: Backlash is simply a small rotational output movement of the first gearbox with its input shaft static; and, any input from that first gearbox is multplied by the ratio of the second second gearbox. On the other hand, backlash in the second gearbox is a direct measurement of the rotation of its output shaft with respect a nonrotating input shaft. With that said: then "oscillation i.e. backlash" can be substituted for "rotation" in the both of the above statements; thereefore, total backlash at the output shaft of the second gearbox = (the backlash of the first gearbox x the ratio of the second gearbox) + the direct backlash of the second gearbox.

Does this help you understand any better?