Backgear - piece of cake is the phrase. Buy the gears from Myfords.
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but they're not good at the web. Phone them instead. Spend an hour, job done.
On the other question define "play". Axial, probably easy. Adjust the thrust bearing. Radial it's down to shims and possibly expensive stuff like spindles and headstock
Do you mean the back gear (bronze gear on pulley, pair of gears underneath, steel gear on mandrel or the tumble reverse gears at the end of the lathe? If the former, which of the four gears are damaged? Relatively simple to replace, but the shaft holding the retaining washer for the bottom pair will probably need heating up to undo it without snapping an allen key.
If it's the tumble reverse gears, it's only a few moments work to replace them.
In both cases, get the spares from Myfords:-
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Vertical play is adjusted be peeling leaves off the shims between the bearing caps and the headstock, then scraping the bearings to get the preferred fit. End play is adjusted by loosening the grub screw on the collar threaded on to the end of the mandrel and screwing it in to remove free play without binding.
Myfords will also supply the manual, which has such useful information in it.
Using the spindle lock Myford have very conveniently provided at the change gear end of the headstock. It's a plunger which fits into a hole in the largest pulley on the left. Just don't forget to disengage it before trying to engage the drive again (DAMHIKT!)
'Play' defined as when I stand in front of the lathe, if I grab the chuck, I can pull it towards me. I didn't notice any movement towards the tailstock.
I detected a definate movement but not really excessive. What would the 'spindles' be?
Moving from chuck towards change gears... you have spindle nose, front of headstock, backgear, another gear, bearing (I think), pulleys...
So, backgear is just inside the headstock just behind the chuck. There is a lever between the backgear location and chuck that brings the backgear into play (you can see the backgear move).
The two damaged gears are the first ones you get to coming from the chuck end and moving left.
I can see no such animal on my ML7 (K130898) nor anywhere it could be fitted. But then I may have misunderstood your description. On the spindle the 3 pulley cluster is free to rotate but locked to it by the 'tooth' which slides in the largest gear at the RHS of spindle. Largest pulley, at RH end of the cluster, is more or less in the middle of the headstock under the cover. From looking at the pictures on the 'lathes' site it might be that you are referring to ML7R or Super 7 which have the (4) pulley cluster the other way round Please prove me wrong as you've got me worrying about my back gears now!!
If the teeth took a pounding, hard enough to break off, chances are pretty good that the rest of the teeth may well have some "issues".
If you replace both of the sets of gears, you only replace one set (as damaged teeth on the remaining gear, can damage teeth on the new one, running) and you only have the lathe apart once.
Not a huge cost, in the scheme of things, as large as that cost may seem.
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