Connecting a Shaft to Servo Gearbox

It is difficult to answer without more specs, especially torque and speed. But, there are lots of suppliers. GlobalSpec is a good way to find some of those. You might start here

http://www.ruland.com/?gclid=CLfo0beG35oCFQJhnAodm2GWzw

If shaft sizes are odd, or very mismatched, many suppliers provide couplings with machineable ends.

my coupling dia is 15 mm.thise is connect with sprinklers , can i find thickness of coupling.

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There is a lot of different type of coupler in the market where you can select from it. Each type of coupling has different specification and application.

You can use two coupling to couple your gearbox and your shaft of 55 mm. One of your coupling, you had to machine 22mm diameter for your gearbox and the other coupling you need to machine 55mm diameter for your shaft.

Bodge it!