Precision machining of automotive industrial parts is a highlighted topic in mechanical engineering due to the increased need for efficient and high-quality machining processes. This study is aimed to contribute to the field of surface topography evaluation by analyzing tribology-related topography parameters parallelly and finding connections between them. Hard machining experiments were carried out for the widely applied case-hardened material 16MnCr5 and the 3D topography of the machined surfaces was measured and analyzed. Based on a comprehensive design of experiments cubic response functions were determined for the analyzed parameters and the coefficients of determination were calculated. It was found that the cubic response function is reliable for predicting the topography parameter values and there are strong relationships between counterpart parameters under certain circumstances The findings could help clarify the roles of the analyzed parameters in some tribological properties within the analyzed cutting circumstances.