This paper proposes a graph-based methodology that models high-pressure networks of various topologies. Therefore, a mathematical modelling of a supply network for waterjet machining will be introduced. High-pressure components are assigned to homogeneous segments, each representing a local pressure state as a differential equation. Segments are subsequently interconnected along the fluid flow path as an algebraic equation that allocates a fluid flow to the interconnections, resulting in a lumped parameter model. For this purpose, a graph network description has been used to approximate the spatially distributed high-pressure system. In this way, the proposed methodology offers a flexible modelling to cope with different network topologies. Moreover, a variable fluid compressibility has also been introduced so that a wide operating range can be included. This modelling methodology has been applied to a supply network for waterjet machining. The resulting mathematical model has been verified by measurements from a test bench with a pressure range of 100 to 400 MPa. It was shown that a variable fluid compressibility improves the model's accuracy and that modelling errors can be reduced in comparison to other existing methodologies.
In the wire sawing process, a silicon brick is fed into a moving wire web, thus deflecting the wires. By considering static deflections only, the wire displacement and the contact forces between wire and brick may be computed by minimizing the potential energy of the wire, which introduces a constrained quadratic optimization problem. In a time-domain simulation, the continuously changing contour inside the kerf requires the optimization problem to be solved recurringly. This work aims at reducing the optimization-related computational effort by applying multi-parametric quadratic programming.
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