Just let we know what you want, and we will get in touch with you as soon as possible!
Here's a focused, engineer-ready reference for the pulley shell (drum): design purpose, sizing rules, materials, fabrication, lagging options, inspection, balancing and drawing/QA notes. Use this as a checklist for engineering, procurement and workshop handover.

The pulley shell (or drum) is the cylindrical outer part of the pulley that contacts the belt (or the lagging). It:
Core design goals: adequate stiffness (limit deformation), long fatigue life, good wear resistance, easy manufacture and serviceability.
Exact design requires structural analysis; practical rules-of-thumb used in industry for preliminary sizing:
Ensure radial deformation under full belt load won't exceed belt tracking/tensioning limits (typical maximum rim deflection often < 0.5–1.5 mm depending on belt system). Use beam-on-elastic-foundation or FEA for accurate deflection.
If you want, I can run a worked thickness calculation for your pulley if you give D, face width, belt load (radial) and material.

Lagging improves traction, protects the shell and increases life. Options:
Design note: lagging thickness typically 6–12 mm; account for it in pulley diameter and balancing.
If you want, I can:
run a shell thickness & stiffener calculation for a pulley (give me D, face width, radial belt load, material),
Tell me which and I'll do it right away.
Just let we know what you want, and we will get in touch with you as soon as possible!