For vertical motor with radial tilting pads with a positioning jack-screw in back, we often set/ check the clearance between the back of the pad and the jack-screw rather than the gap between pad and runner.
The pad/jackscrew gap is fairly easy to access because it is something resembling convex/convex point contact. In contrast if you tried to measure between pad and runner you would face a convex/concave arc gap…. and the pad tends to stick to the runner due to oil surface tension, ….and you may damage babbit depending on you gap check/set tool (feeler gage or steel shim at this location would not be good).
Speaking of measuring tool… you mentioned lead wire. Could be used for checking. We often use feeler gage for checking. Actually the setting is more reliable process than the checking. We center the rotor, place desired gap thickness of steel shim between back of pad / jackscrew, tighten the jackscrews keeping the rotor centered. When all clearance is removed, the steel shim needs to be removed to recreate the clearance. Sometimes you can pull it out, other times you may back the jackscrew a carefully measured amount like ¼ turn to remove the shim, then re-tighen to get back where you were.
Above applies to checking clearances of installed pads. I’m not sure what you had in mind with mandrel.
Details may depend on machine construction.
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(2B)+(2B)' ?