The effect of oblique tool angle on surface integrity in ultraprecision machining of germanium

Transmissive infrared (IR) optics are manufactured from brittle materials such as single crystal germanium (Ge) and silicon (Si). Ultraprecision diamond machining with a negative rake diamond tool is the dominant manufacturing process for IR optical surfaces. The negative orthogonal rake angle directs the cutting force vector into the bulk material, increases the hydrostatic stress, and suppresses brittle fracture relative to shear deformation. Surfaces with optical integrity can be generated, but surface integrity is strongly correlated to the direction of the cutting force vector. This paper studies the effect of an oblique angle of the rake face (e.g., from tool misalignment or surface slope) on surface integrity in machining single crystal (100)Ge. Forces and geometric surface parameters are measured as a function of the oblique angle. A new observation is made. The cutting mechanics and the surface integrity change markedly with small changes in the angle of the rake face (order ±2.5°). The scientific contribution of the paper is to connect time-domain cutting mechanics, as represented by the direction of the cutting force vector, to spatial-domain surface integrity (surface roughness parameters) through a fundamental theoretical analysis of slip and fracture systems in crystals. A new force-mapping technique emphasizes the connection between the temporal and spatial domains and the ability of the theory to predict the number and prominence of damaged lobes caused by changes in the cutting direction as the crystal rotates during turning. The model material for the study is Ge, but the methodology is expected to provide new insights into the cutting of other brittle crystals and non-crystalline materials. The work is practically relevant to the productive machining of IR optics in brittle materials by emphasizing the importance of tool alignment on surface integrity.