Modeling of surface topography on diamond-turned spherical and freeform surfaces

Single-point diamond turning machines are capable of generating high-quality spherical and freeform surfaces. However, there are inevitable tool marks on the diamond-turned surfaces. Although several models have been proposed to describe the surface topography of a flat surface, there is a lack of a more general model to describe spherical and freeform surfaces. In this paper, we propose a model to estimate the surface topography of the diamond-turned spherical and freeform surfaces. The model takes into consideration the basic cutting parameters as well as the dominant relative vibration components between the diamond tool and the workpiece in both infeed and feeding directions. We first discuss the principles and create a model for spherical surfaces. The model is then extended to describe more general freeform surfaces. We also show how the micro-waviness of the diamond tool impacts the surface topography. Finally, we conduct a series of face cutting experiments and conclude that there is good correlation between the model and the experimental results.