The surface roughness of a part during external cylindrical grinding is directly impacted by cutting force and vibration, which are intermediate parameters. To improve the quality of finished parts, studying and controlling these parameters is essential. In this research, the Taguchi method combined with ANOVA analysis was utilized to analyse the effects of feed rate, cutting depth, and rotational speeds on cutting force and vibration amplitude. The test material used was SKH2 steel, which was heat-treated to a hardness of 60 HRC. The research aimed to investigate the relationship between cutting force, vibration, and surface roughness. The study concludes with an analysis of the influence of cutting force and vibration on the surface roughness of parts during external cylindrical grinding. The results show that as cutting force and vibration increase, the surface roughness of the workpiece in external grinding will also increase, and conversely when cutting force and vibration decrease, the surface roughness will decrease.