Тo date the question of development of effective highly productive machine-tool equipment is actual which allows to produce the high-quality tooling of spherical surfaces of details of machines.
     There is a great number of methods of receipt of spherical surfaces tooling (sharpening, polishing, milling et cetera), however to itself polishing methods, as most productive processes of finish treatment, which allow to provide not only high geometrical exactness but also high quality of superficial layer of the treated detail, come into the special notice exactly.
     Presently in the world there is a tendency of production of wares from non-metal and composition materials which all wider replace metals in many industries of industry. This tendency is related to the decline of unit cost at the simultaneous increase of their term of service, reliability and ecological cleanness. The special place among non-metal materials occupies керамика. Физико-механические properties of ceramics as compared to all of types of metals which are presently used as main materials for making of details of machines, have such distinguishing features, as a high temperature of melting, hardness, lightness, wearproofness, corrosive firmness, firmness against chemicals et cetera Thus физико-механические properties of ceramics are stable in the large interval of temperatures, that not unimportant at the use of it in the knots of friction and formation of high temperatures. From other side there is a lot of complications with tooling of ceramic materials, as they in fact are abrasives.