Do the hole patterns drilled in laps really help ensure uniform expansion and contraction?

Some laps have patterns of holes drilled into them - two examples are below. In both cases the user claims that the holes (among other techniques) help ensure that the laps stays close to round when they're adjusted. I've seen it in enough places that I'm willing to believe there's some truth to it. Beyond vaguely saying that it redistributed the stress, I just don't see how though.

How do these hole patterns help ensure roundness when the lap changes sizes?

Examples of the claims (time to start on the relevant sentence):

Examples of the laps:

3 Answers

You can think of the top picture as two semicircular curved beams joined at one end and with equal and opposite forces applied by the clamp at the other end.

If you apply a force at the end of a uniform cantilever beam, it doesn't bent into a circular arc but part of a cubic curve with more curvature at the root than at the tip. This will give an more constant curvature along the length of the "beam".

To counteract that, the holes are smaller at the "root" of the beam than at the tip, which is equivalent to a change in the moment of inertia along the length of the beam - greater at the root (small holes) and smaller at the tip (large holes).

For the second picture, a solid ring with no slots would simply be far too stiff to deform it by expanding the center. The slots and holes mean that the only continuous material which can support hoop stress is a thin ring at the outside of the disk.

The function of the laps is diferent looking both vídeos.

The first lap is for external diameter.
The external piece (part with holes) distribute evenly the stress like you said. And the internal piece (tubing with a cut) redistributes the stress more evenly (in the vídeo he said the helical cut is better than a straight cut because the straight can get oval).

The way the geometry works is similar to bicicle wheels. The hub and rim are conected by the spokes and remain centered. This lap works exactly like this. Using the screw in the external part will change the diameter of the rim, the spokes remain with the same distance, so the iner part (hub) need to acomodate the new geometry. The spokes apply exactly the same force, so the inner part adjusts equaly.

The second lap is for internal diameter (this one I think the geometry is not perfect).
When you apply stress evenly the outer ring will open (looks like not a perfect round part, but definetly closer).
In 15:40 of the vídeo he says that lapping like he's doing the position of the piece need to change time from time to compensate if geometry is not perfect.

You need to remember that laping is used to very precise and minimal changes in diameter, so the diference in tool geometry will be closely to zero.

For an object as "chunky" as a solid lap, tightening the adjustment screw will deform it out of flat because of Poisson's ratio (squeeze it one way, it swells up another way). By drilling those holes, the lap deforms more like a hoop and less like a solid mass because they prevent compressive stresses from being transmitted towards the central axis.