A Simplified Analysis Method for the Natural Frequency and Stability of Rotationally Symmetrical Structures

Abstract

The invention discloses a simplified analysis method for an inherent frequency and the stability of a rotational symmetric structure. The method comprises the steps of establishing a complete dynamic differential equation of a system, a dynamic differential equation adopting a no-extension hypothesis, and a dynamic differential equation adopting an extension hypothesis: establishing the complete dynamic differential equation of the system; establishing the dynamic differential equation adopting the no-extension hypothesis; establishing the dynamic differential equation adopting the extension hypothesis; introducing coordinate conversion for converting the three dynamic differential equations to a support follow-up coordinate system so as to obtain corresponding three constant coefficient partial differential dynamic equations; performing discrete processing on the three constant coefficient partial differential dynamic equations in the support follow-up coordinate system to obtain three constant differential matrix equations; obtaining an eigenvalue of the complete dynamic differential equation and eigenvalues of two simplified dynamic differential equations; and analyzing a parametrically excited vibration mode characteristic and a dynamic stability change law of the rotational symmetric structure according to the three eigenvalues. According to the method, a specific analysis expression of system eigenvalues can be obtained more clearly.

Description

technical field [0001] The invention relates to a method for analyzing the natural frequency and stability of a rotationally symmetrical structure. In particular, it involves a simplified analysis method for the natural frequencies and stability of rotationally symmetric structures. Background technique [0002] Rotating machinery widely exists in industrial production, especially in modern machinery industry. For example, internal meshing gear transmission, electronic stator / rotor system, plunger motor, jet engine, inner and outer rings of bearings and hydroelectric generator sets, etc. Such structures can usually be summarized as a rotationally symmetric structure. They will inevitably have vibration and noise problems in the industrial production process, especially in some high-speed, heavy-duty applications, which have become a key factor restricting the overall performance of the system. In the existing research on the natural frequency and dynamic stability analysi...

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Problems solved by technology

This has led to the existing technology being too complicated and cumbersome when directly analytically solving its dynamic equations, which increases the workload and fails to obtain the analytical expressions of the system eigenvalues

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