The elusive backlash

I now have a second DTI, so it's time to take another look at the backlash on the Z axis. This has been grieving me for the past few weeks and I am determined to work out if it there is anything I can do to improve it or if I just have to assess it and live with it.

I already had a 10um / div Baty DTI and the new DTI is a Mitutoyo 10um / div Series 1 (only £35 or so, ie not much more expensive than a China special, so why buy cotton when you can have silk?).

I'd already seen that if I set up a DTI right next to the ballnut, the backlash on the nut is of the order of 3um, including any hysteresis and noise in the servo system. That's pretty amazing for a machine of this age. The handwheel / MPG generates one pulse per um and the nut moves within typically 3 pulses after a change of direction. And the DTIs agree with the DRO.

But if I watch the movement at the bottom of the quill (that excludes the spindle bearings, to keep it simple), there is the best part of 100um of lost movement. Call it backlash or mechanical hysteresis if you like but however you look at it, that's 0.1mm of slop. And annoyingly it's between the ballnut and the quill.

So how come I have pretty much zero backlash at the ballnut, yet almost 0.1mm of backlash at the quill? That's particularly puzzling when you consider that the yoke is mounted directly on to the quill.

There seem to be only a limited number of possible explanations (root causes):

1. The yoke is not securely mounted on the quill.
2. There is sufficient radial wear between the quill and the cylindrical bore it runs in that the quill can move radially when the ballnut applies a load. 
3. Surely that's it?

One downside of the ballscrew / yoke arrangement is that the quill load generates a relatively significant radial load. The yoke is cantilevered out from the quill with the ballnut on the end. So either of these causes are entirely plausible.

I previously removed the yoke, cleaned it up and refitted it, ensuring the bolts were torqued up to an appropriate setting. Annoyingly this made no obvious difference. That doesn't mean the yoke is not the problem but it would have been nice if the backlash had been fixed all the same.

So that still leaves radial movement of the quill to check for. With 2 DTIs at play, it's possible to show that the quill has NO discernible radial play going on while the 100um of backlash is happening. Furthermore, that's true no matter where you measure it on the quill. "No discernible play" means less than a few microns, compared to as much as 100 lost movement.

No need to post loads of videos and pics to document the tests (although I'll do so anyway) but it is pretty clear that the yoke MUST be moving relative to the quill, despite being firmly torqued down. The yoke shows no backlash at the ballnut end - and significant backlash at the quill end. Meanwhile, the quill only moves axially. 

One DTI set up at the ballnut, the other at the quill nose:

And again:

Here it is in action. Bugger all backlash:

If you look carefully, you can see the front of the yoke has sod all backlash, while the back is a different story:

Both DTIs checking radial movement on the quill - nothing measurable, ie of the order of microns, not hundreds of microns:

So......time to take the yoke off again. And possibly the quill too? But at least there seems to be the possibility of substantially reducing it.

Later:
Mounted a DTI directly onto the quill and looked for movement of the ballnut end of the yoke, like this: 

The amount of backlash is clearly visible with this method. So yes, the yoke isn't secure, despite being fully torqued up. Some scraping and filing required....