The shank of the mandrel must match the size of the power tool collet or drill chuck, and the pilot diameter must be compatible with the size of the cartridge roll.
3M 45116, Cartridge RoII Mandrel, 1/4 in x 1-1/2 in x 1/4 in, 7010328350
$4.58
Factory Stock, 7-10 Day Leadtime
3M Cartridge Roll Mandrel is a tool attachment that holds an abrasive cartridge roll (sold separately). Together, the mandrel and cartridge roll enable the user to grind or finish hard-to-reach areas of a workpiece, such as angles and curves. The mandrel attaches to a rotary tool such as a die grinder or drill, and comes in different sizes to fit a variety of cartridge roll sizes.

Dynabrade 40320 Dynafile II Abrasive Belt Tool
3M 22396, Roloc Disc 361F, 36 YF-weight, TR, 1-1/2 in, Die R150S, 7000045091
3M 22407, Roloc Disc 361F, 80 YF-weight, TR, 1-1/2 in, Die R150S, 7000045099
3M 77558, Cubitron II Hookit Cloth Disc 947A, 77558, 40+ to 120+, 6 in x NH, Die 600Z, 7100232737
3M 22409, Roloc Disc 361F, P120 XF-weight, TR, 1-1/2 in, Die R150S, 7000045103 
