Machinability and optimization are the two objectives of researchers who guide us to enhance the manufacturing industry. Examining and analyzing the parameters such as surface roughness, tool wear, and cutting force during the processing would be beneficial that are used in various fields in the manufacturing industires. This study examined the effect of cutting forces to surface roughness on the material surface. Experimental studies were carried out by using constant feed rate (0.1 mm/rev), depth of cut (1 mm), three different coolants (CO₂, minimum quantity lubrication, and dry), and cutting speeds (100, 140, 180, 220 m/min). In this study, grey relational analysis modeling and analysis of relationships between F _x , F _y , and F _z forces on the surface roughness of Inconel 718 material, which is an important alloy in aviation, is examined. The influence of machinability parameters on F _top and R _a was calculated using variance analysis, which determined that cutting speed was the most significant machining parameters.