Mathematical Modeling and Numerical Simulation of Fixtures for Fork-Type Parts Manufacturing

Abstract

The chapter presents the mathematical models of free and forced oscillations of the comprehensive mechanical system “fixture–workpiece” describing the proposed adjustable locating-and-clamping module with a high level of flexibility for providing CNC multiaxis machining operation. With the aim to increase the fixture rigidity and detuning from a resonance mode, the eigenfrequencies and maximum displacements are determined using the numerical simulation model realized by the ANSYS software. The proposed mathematical model is proved by the results of numerical simulation on the example of fork-type parts considering contact stiffness of functional elements and values of clamping and cutting forces and moments. As a result, the advantage of the proposed manufacturing process in comparison on the typical one is justified. Particularly, the first eigenfrequency for the proposed manufacturing process is 1.64 times more than the same frequency for the typical manufacturing process. Additionally, the rigidity of a new fixture design is significantly increased, as well as detuning from a resonance mode is ensured. The proposed methodology allows estimating physical parameters of the proposed mathematical model by the results of numerical simulation and experimental research for ensuring dynamic stability of the highly complicated mechanical system “CNC machine tool–flexible fixture–spatial workpiece–precise cutting tool.”