Abstract
The presented paper focuses to rotating components of mechanical constructions. The problem of the spatial combined bending-gyratory vibration and calculation of the Eigen frequencies is studied. The model of Cardan Mechanism is solved by the transfer matrix method. Transfer matrices were derived for shaft, concentrated mass and elastic bearing. The physical and mechanical properties of each part of the mechanism are hidden in these matrices. A procedure for calculating Eigen frequencies was proposed.
Highlights
IntroductionThe most endangered parts are rotating components, e.g. shafts [1]
In mechanical constructions, the most endangered parts are rotating components, e.g. shafts [1]
Using the transfer matrix method is relatively easy to get a solution to the whole system
Summary
The most endangered parts are rotating components, e.g. shafts [1]. In the vicinity of resonance, there is an enormous increase in the amplitudes of the state variables and reaching of the yield strength of a material These conditions often occur with the coupling shafts of Cardan mechanisms. Using the transfer matrix method is relatively easy to get a solution to the whole system (the whole Cardan mechanism) Another advantage is that it can be combined with the method of the imaginary slice, which analytically solves the differential equations of motion for a smooth shaft (smooth continuum - a constant diameter), the transfer matrices for the shaft, matrices of concentrated mass and the elastic bearing, which are the basic structural elements of a dynamic model of shafts, are derived. This paper is devoted to studying the problem spatial combined bending-gyratory vibration and calculation of the Eigen frequencies using the transfer matrix method
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