The objective of this paper is to perform the innovative design for the new structures of cam-controlled planet SKD11 cold tool steel is a high-carbon and high-chromium alloy tool steel that is used to make cold work or hot work dressing dies, sides of rollers, screw lines, lines dies, transformer core stamping dies, rolled knives, steel tube forming rollers, special molding rollers, screw heading molds. The hardened SKD11 steel has a high hardness 58-62HRC good wear resistance and good toughness. Hard turning is an important process because all manufacturers are continually seeking ways to manufacture their parts with lower cost, higher quality, rapid setups, lower investment, and smaller tooling inventory while eliminating non-value-added activities. In where Surface roughness is an important parameter determining the accuracy and quality of parts. Analysis of surface roughness is presented by many researchers based on cutting conditions during hard turning. In this paper, analysis of surface roughness of SKD11 steel in hard turning with mixed ceramic inserts is performed based on variables like cutting speed, feed, and depth of cut. The feed rate is the most significant parameter affecting the surface roughness in the machining process. Prediction of surface roughness considering the simultaneous effect of cutting parameters is very difficult. Here, a mathematical model is developed based on the simultaneous effect of depth, cutting speed, and feed rate. Moreover, the developed model is validated using different sets of cutting conditions and found in close agreement with experimental results.