Mathematical modeling of forced oscillations of manometric tubular springs

Abstract

Difficult working conditions, as well as vibrations of technological process units and unstable load intensity impose high demands on overpressure monitoring devices that ensure the required measurement accuracy and trouble-free operation of equipment. The use of pressure gauges today is a mandatory requirement for monitoring overpressure. The main type of pressure gauges uses manometric tubular springs (MTP) as elastic sensing elements. Therefore, the issue of calculating the motion of the MTP under the influence of external variable loads, in particular variable internal pressure, is relevant. Issues related to the influence of internal pressure pulsations and external periodically changing external forces remain unexplored. For successful operation, the strength and frequency characteristics of vibrations of tubular springs were previously investigated, the effects of cross-sectional shapes and basic geometric dimensions on their vibration characteristics were considered, and the process of vibration damping by liquid was analyzed. The paper presents a mathematical model of forced oscillations of the MTP based on Lagrange equations of the second kind. The MTP is considered as a mechanical system with two degrees of freedom, that is, defined by two generalized coordinates. They are a relative change in the main angle of the tube and an increase in the small semi-axis of the cross section. The model allows us to determine the nature of the movement of the MTP under the influence of periodically changing internal pressure. To implement it, a program has been developed in MATLAB, which makes it possible to determine the required characteristics of pressure monitoring devices that exclude the possibility of resonance. With the help of the developed program, the influence of geometric characteristics and internal pressure pulsations on the movements of the free end of the MTP is estimated. The presented model can be successfully used for dynamic calculations of manometric tubes, since it is a classical approach to solving problems of vibrations of mechanical systems. In addition, it will allow you to calculate the parameters of tubular elastic elements used in various mechanisms as power elements.