We are printing on a heavy plastic sheet. When the sheets are removed from the delivery, we find rings and patterns that are rough to the touch. Is there a problem with the substrate or is it a process problem?

The roughness to the touch is most likely spray powder. The static electricity in the sheet can cause a magnetic field that creates rings of static electricity that attract spray powder. The spray powder concentrates and adheres to the wet ink or aqueous coating creating the feel of uneven roughness. The larger the grain size of the spray powder and the greater the amount of spray powder used, the more noticeable the difference in the texture will be to the touch. Printing this UV would eliminate the spray powder.