Abstract
Auxiliary fixtures are widely used to enhance the rigidity of cylindrical thin-walled workpieces (CTWWs) in the machining process. Nevertheless, the accurate and efficient prediction of frequency response function (FRF) for the workpiece-fixture system remains challenging due to the complicated contact constraints between workpiece and fixture. This paper proposes an analytical solution for the comprehensive FRF analysis of the CTWW-fixture system. Firstly, based on the vector mechanics, the mode shape functions of the workpiece are presented using the classical theory of thin shell. The variable separation method is utilized to deal with the inter-mode coupling of the workpiece. Secondly, the motion equation of the CTWW with fixture constraints is established using analytical mechanics from the viewpoint of energy balance. Finally, the FRFs of the CTWW-fixture system are derived by means of modal superposition. Experimental modal tests verify that the predicted FRFs are in good agreement with the measured curves.
Highlights
Cylindrical thin-walled parts such as engine casings are widely used in aerospace industries
The main objective of this paper is to develop a comprehensive analytical solution to predict the frequency response function (FRF) of the system so as to investigate the effects of fixture support on the dynamic characteristics of cylindrical thin-walled workpieces (CTWWs)
Adding fixture support can effectively improve the rigidity of the CTWWs, which makes the modeling and analysis of the system more complicated. erefore, it is necessary to focus on the establishment of the motion equation of the workpiece-fixture system, which is the basis for investigating the effects of fixture support on workpiece dynamic characteristics
Summary
Cylindrical thin-walled parts such as engine casings are widely used in aerospace industries. Many factors such as nonlinear behavior [27], stiffness [28], friction damping [29], and so on should be considered, which have great influence on the dynamics of rigid bodies In this way, the fixturing stability of the system [30] and the optimal design of the fixture [19] can be effectively analyzed. It was necessary to divide very fine grids and set complex equivalent boundary conditions to ensure the accuracy of the results, which would cause a significant reduction in calculation efficiency [36] To solve this problem, the analytical method focusing on thinwalled plate or frame structures [37, 38] is widely used to analyze the effects of fixture on the dynamic characteristics of the workpiece.
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