What is the end application as this will dictate the size and the type of alumina? Why would you consider making your own when they are freely available in the marketplace?
Google (Scholar) and YouTube are your friends. See, for example:
D.W. Luks, "Method for producing spheroidal ceramics", US 4,407,967, Oct. 4, 1983.
L. Boulanger, S. Desiles, "Billes de broyage et leur procédé de fabrication", EP 1 713 743 B9, 16.09.2009; idem, idem, EP 1 564 196 A1, 17.08.2005"; idem, "Grinding balls and production method thereof", WO 2005/075375 A1; idem, "Grinding balls and their manufacturing method", US 2008/0245912 A1, Oct. 9, 2008; idem, idem, US 7487,928 B2, Feb. 10, 2009.