Planar random graph representations of spatiotemporal surface morphology: Application to finishing of 3-D printed components

Surface finishing processes consume 20–70% of the cycle time of the emerging additive manufacturing process chains. Effective representations of the spatiotemporal evolution of the surface morphology are imperative towards developing monitoring schemes to arrest cycle time overruns. We present a thermodynamically consistent random planar graph representation to monitor, via in situ imaging, the spatiotemporal evolution of surface morphology during finishing processes. Experimental investigations into the finishing of electron beam printed Ti-6Al-4V components to Sa < 20 nm roughness suggest that the proposed representation captures the complex interflow among neighbouring asperities during finishing, and establishes a radically new endpoint criterion, i.e., surface quality improves only until each asperity interflows with six neighbours.