Interesting discussion gents... here are some of my observations regarding clamping shoes:
On some lathes, they are just a flat plate with a hole to receive the clamping bolt. Some have a better design with ribs on the bottom of the plate to improve stiffness and resist bending. It is this bending under load that actually is the problem of the TS sliding.
This is what most decent TS shoes look like - flat and coplanar clamping surfaces
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and the assembly at rest
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and under load (clamped)
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due to bending of the shoe, there is only a small contact area. The harder you clamp, the smaller it gets and thus the easier the TS slides under load.
A better design would be to slightly incline the clamping surfaces so as you apply force, the bending actually increases the contact area and thus a greater axial force is required to slide the TS away.
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I have not modified my TS shoes to this design yet. I would only mill about thou or so off the inside of the flats to begin with to give them a very small angle.
I have found that when my TS slips, I have overtorqued it and / or am using tools that are dull. At least one of my live centres has internal expansion compensating features that allow the part to expand without it pushing the TS back, thus maintaining relatively constant center pressure. I can’t find it right now, but an expanding part puts a huge axial load on any supporting center and easily overcomes most TS clamping forces. It is actually a good thing that the TS slides back (if you don’t have temp comped centres) otherwise you would bend the lathe bed while turning. And possibly overload your spindle bearings.