Make a base out of metal tubing. Use square tubing that is 2 inches by 3 inches and bend it into a square that is 2 feet by 3 feet. Make an identical square from the tubing. Using a metal saw, cut four upright posts from the tubing that are 15 inches high. Weld the posts to both rectangles to make a box. This will hold your motor.
Lay a 55-gallon plastic barrel on its side and cut it in half with a box cutter. This will be your tub. It's best to start with an unused barrel so that you won't have to deal with any contaminants. The cleanliness of your tub will determine how effective it is at deburring.
Weld eight springs to the base. These springs should be industrial strength so that they will stand up to repeated usage. The type of springs used on garage doors will work.
Make a cradle for the tub using the square metal tubing. This cradle will look exactly like the base, but the dimensions should allow the tub to sit down in the cradle. Weld this cradle on top of the springs and place the barrel in it.
Drill holes in the cradle and bolt a pillow block bearing to the cradle. Insert a 1-inch axle into the pillow block bearing and tighten the set screw to hold it in place.
Place a compressor motor with a motor shaft in the base.
Attach the end of the axle to the motor shaft using a shaft coupler. This coupler will have set screws in each end to hold the axle and the motor shaft tightly.
Fill the tub with enough deburring compound and water to immerse the part you're working on. Turn on the motor and allow it to shake the spring-mounted cradle for several minutes. This will remove imperfections from the part.