Authors: Yu.V. Pipkin, A.M. Zinchenko, S.V. Kuberskii

Title of the article: Transition from the pole graph of a mechanical system to the signal-flow graph on the example of a milling workholding fixture

Year: 2024, Issue: 5, Pages: 5-18

Branch of knowledge: 2.5.6. Engineering technology

Index UDK: 62-229.3:621.914:531:004.942:519.171.2

DOI: 10.26730/1999-4125-2024-5-5-18

Abstract: To improve milling workholding fixtures using mathematical modeling, it is convenient to use graph theory as a mathematical apparatus that naturally reflects the connections between structural elements or parameters of a technical system. However, modern systems for computer-aided design of structures in mechanical engineering do not have the appropriate functionality. The development of algorithms that ensure the application of graph theory is relevant for the research of workholding fixtures. Using the example of research the force closure of a milling workholding fixture, the article examines the use of two sections of graph theory - pole graphs and signal-flow graphs. The capabilities of pole graphs are used to create a mathematical model of the structural organization of a design in the form of equivalent circuits of a translational mechanical system and a transition is made to the description of the equations of the mathematical model in the form of a signal-flow graph that clearly reflects the relationships between the parameters and variables of the technical system. The performed transformations made it possible to obtain a description of the force closure of a milling workholding fixture in the form of a closed sequence of variables, which is considered as a theoretical prerequisite for studying the adaptive properties of the system. Based on empirical initial data, a mathematical model in the form of a signal-flow graph, implemented in the SimInTech software package, was verified. A conclusion is made about the applicability of the force closure model in the form of a signal-flow graph for further research and practical implementation

Key words: force closure a milling workholding fixture mechanical translational system system with lumped components pole graph system signal-flow graph

Receiving date: 05.06.2024

Approval date: 29.09.2024

Publication date: 24.10.2024

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