Spline-Based Framework for Microscopic Contact Zone Modeling in Lubricated Orthogonal Cutting

Accurately predicting the coefficient of friction between tool, chip, and workpiece during machining is essential for a reliable and cost-effective process. In this context, current numerical methods are often based on homogenized approaches with friction models that use constant friction coefficients; thus, failing to capture local effects. In addition, often neither the effect of lubricants nor the local tool and chip topographies is accounted for. Towards improving the state of the art in both respects, in this paper, we present a micro-scale friction model that can be coupled with a meso-scale chip formation model. The micro model determines a local friction coefficient based on local temperature, contact pressure, cutting speed, and lubricant wetting. It also incorporates the experimentally determined tool and chip topography. A key assumption of the model is that the main contribution to the friction coefficient is the interlocking of local roughness peaks. Our numerical implementation uses a combination of isogeometric analysis (IGA) for the chip and finite elements with spline-based boundaries for the fluid. This approach ensures a smooth, conformal interface between the cooling fluid and the chip, allowing for direct spatial coupling. Temporally, a Robin–Neumann coupling is used, which is critical for handling fully enclosed fluid pockets. The direct contact between the tool and the chip is modeled using a mortar knot-to-surface approach. To ensure computational affordability in this multi-query FE² scenario, a surrogate model for the micro-scale model is created using Gaussian process regression.