Theoretical models for surface roughness in turning considering inclination and rake angles

New analytical four-parameter models for surface roughness are proposed based on the feed rate, nose radius as well as the inclination and rake angles. These models were derived to determine the maximum peak-to-valley roughness Rt and arithmetic average roughness Ra using homogeneous transformation matrices and are verified by digital simulation. The model for Rt was used to study two sequential effects of introducing the inclination and rake angles. The Rt and Ra values obtained from the four-parameter models and the existing two-parameter models, based on nose radius and feed rate, were compared. The comparison shows maximum percentage differences of 8.18% and 10.98% in Rt and Ra, respectively. The results demonstrate that the inclination and rake angles can influence the surface roughness by affecting the tool-workpiece contact geometry. The proposed four-parameter model can be employed for a more accurate theoretical surface roughness evaluation compared to the existing two-parameter models.