A graph-based modelling methodology for high-pressure networks applied on waterjet machining S. Niederberger a,b,∗ , R. Orjuela a,∗∗ , P. Schleuniger b , R. Anderegg b , M. Basset a a Universit´ e de Haute-Alsace, IRIMAS (EA 7499), 12 rue des Fr` eres Lumire, Mulhouse, 68093 France b University of Applied Sciences Northwestern Switzerland, Institute of Automation, Klosterzelgstrasse 2, Windisch, 5210 Switzerland Abstract 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. Keywords: High-pressure network modelling, graph network, lumped parameter model, varying parameter model, waterjet machining 1. Introduction Nowadays, waterjet machining is used in metal, composite, textile, food and many other industries. It is the first choice for contour cutting and surface stripping causing minimal thermal stress and is devoid of chemicals. Besides various pure water applications, abrasive waterjet cutting is often used to increase the material removal rate when machining hard and brittle materials [1]. These applications demand operating pressures in a range of 100 to 400 MPa. A pressure of 700 MPa has been reported to further increase the productivity of waterjet cutting [2]. Future research should improve the energy efficiency of entire waterjet facilities. Hence, mathematical modelling is needed to provide valuable numerical simulations that further enhance the performance of waterjet cutting. The present work was initiated by a recently developed, directly driven piston pump. These modular piston pumps allow the realization of a new class of scalable high-pressure networks for waterjet machining. The industry needs a modelling methodology to optimally design future high-pressure networks of next-generation waterjet facilities. This modelling approach is also used to efficiently research distributed control concepts and managing algorithms for various decentralized pump setups. In this respect, different modelling approaches can already be found in the field of waterjet cutting [3] - [6] and in related fields [7] - [10] to model specific high-pressure systems. In general, the principles of continuity and momentum conservation appear to be the most prevalent approach when modelling high-pressure generation. For waterjet machining, Tremblay et al., 1999 [3] presented a model for intensifier pumps with attenuators. Their experimental studies reveal the effect of bulk modulus, fluid density and other parameters on pressure fluctuations at 153.4, 181.0 and 215.5 MPa. More than a decade later, Fabien et al., 2010 [4] ∗ Corresponding author ∗∗ Principal corresponding author Email address: stefan.niederberger@uha.fr (S. Niederberger ) Preprint submitted to Elsevier March 14, 2019