allowable taper when turning a shaft

savarin

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I'm making an extended cross slide leadscrew for my generic 9x20 lathe.
I've re-alligned the tail stock and have obtained the following dimensions over a 150mm long length of stainless after turning, testing adjusting etc to remove as much taper as possible.
Starting at the head stock and using a micrometer every 35mm I get :-
12.46, 12.47, 12.44, 12.40
Using the vernier I get :-
11.85, 11.85, 11.84, 11.84
Is this reasonable or should I aim for a closer match?
Thanks.
 
A variation in diameter will have an effect on the class of fit along the length of the lead screw. If you are turning an Acme thread, the thread angle will be 14.5º per side. An increase of .1mm in diameter will decrease the thread clearance by about .026mm measured along the axis of the screw. If you adjust your thread nut for a tight fit at the maximum screw diameter, it will amount to about .26mm of play for every .1mm decrease in diameter. The effect would be similar to wear in the lead screw.

I would normally trust micrometer readings over those obtained with a caliper. From your micrometer readings, your total variation is .07 mm which would be about .18mm along the screw axis. This, added to any backlash associated with the thrust bearing and the lead screw nut, would be a theoretical worst case backlash.

I would be more concerned about the discrepancy between the micrometer and caliper readings. The average difference is .60mm. The micrometer and caliper should agree to within the resolution of the instruments. I would want to resolve that before cutting any thread.

My guess would be the caliper is the errant reading. A caliper can give a low reading if the adjustment of the beam is too loose. The far side of the movable jaw will lift with applied pressure which tends to pull the jaw away from the measured piece, giving a low reading.
 
Is it not the pitch diameter that is critical? Unless the screw threads will be bottoming in the nut threads, the o.d. of the shaft can vary slightly.
I suspect that getting zero deflection when cutting the ACME threads is the main objective.
 
Definitely as RJ said you need to resolve the discrepancy between micrometer and caliper, or, using a test piece confirm which one is correct, then only use it.

Interestingly the measurements with the vernier are quite consistent over the length, only .01 difference, this I would think is quite acceptable if it is in fact correct, so first you have to confirm which measuring tool is correct, one of them definitely has a problem, and like RJ I would tend to suspect the vernier, but you need to confirm it.
 
I know the calipers under report but are pretty consistent, the mic seems spot on but I'm not a good user. (never used one before and I might not be reading it correctly)
I revisited the tail stock adjustment and used a dial gauge to get the taper as best ever.
It now reads only 0.04mm difference over a 240mm length instead of 0.06 over 150mm, I'm calling that done. With the micrometer.
I will be cutting M10x1 standard metric fine for the lead screw
 
Is it not the pitch diameter that is critical? Unless the screw threads will be bottoming in the nut threads, the o.d. of the shaft can vary slightly.
I suspect that getting zero deflection when cutting the ACME threads is the main objective.
The pitch diameter is the important parameter but my concern is that for whatever reason, the diameter is varying, it could also vary when you are cutting the thread. This would cause a varying pitch diameter.

Just looking at the micrometer readings and using the assumption that the tailstock is used for support, the following should be true. Deflection due to tool pressure should be minimal at the two ends of the shaft. This would result in a barrel shaped piece. If taper was also present, the piece could take on a bullet shape. Here is a drawing of the surface with the axial distance compressed by a factor of 100 to illustrate the point.Taper Curve.JPG
While the curve is greatly exaggerated, the curvature would be sufficient to cause difficulties with backlash in the lead screw.

If I were trying to adjust taper of the cut, I would make my measurements as close to the headstock and tailstock as I could. In this case, it looks like the tailstock is too close to the front by .06/2 or .03mm.

The other concern is the bowing of the workpiece. Going from a 12.4mm diameter to a 10mm diameter will make the bowing worse. Definitely, a follower is is recommended.
 
Thanks Bob, I plead a seniors moment that I didnt think of searching for that. Doh! Looks like I did get it correct after all but need way more practice holding it square.
Thanks RJ, I've only used a follower once before and it was not a happy experience.
I will be turning the shaft down to 10mm using the tail stock and a travelling steady to get as accurate as possible but cutting a thread with the steady will be my main challenge.
The first cuts to get to size yesterday without the steady took 4 spring passes to get to size.
I think I will set up the steady with the fingers on the left hand side of the work and the tool bit exactly opposite the fingers and have more shaft spare on the right hand side that can be removed once the length of thread required is cut to size.
As its a left hand thread I think this will work.
My biggest worry is the roughness of the cuts wearing the brass fingers. I've read somewhere that running a file after every pass mitigates this.
But, as its a metric thread being cut with an imperial lead screw on the lathe so hopefully there will be sufficient space and time to do this on the return without disconnecting the half nuts.
so much to think about.
 
I've always found it interesting how some people prefer micrometers over verniers and vice versa. When I trained back in the early 60's I was taught micrometers,

Only the senior toolmakers used the verniers. A few years later, late 60's, when I went to sea, and initially on Swedish ships, I was expected to learn to use vernier calipers, it was a bit of a learning curve but eventually got there, and over time preferred the calipers for speed, but when it comes to real accuracy I still prefer the micrometer.

By the early 70's I came back to Australia, and started working on Australian ships, and again I found the majority preferred the micrometer. Eventually with the electronic digital calipers becoming popular and affordable a lot are changing over, as they are quicker, and nearly as accurate as a micrometer. I would still prefer a micrometer for any thing better than 0.001" My old Moore & Wright from 1961 still reads to 0.0001
 
Since you want an M10x1 thread a pretty popular size why don't you just buy a length, not the rubbish from the hardware shop but get a good quality from a machinery suppliers?
 
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