Influence of damping on the amplitude and phase of oscillations of a system with gyroscopic connections

In connection with the development of a technique for determining the mass flow rate of liquid under conditions of a two-component liquid-gas flow, an attempt was made to estimate the effect of damping due to the presence of gas bubbles on the amplitudes and phases of oscillations of the measuring tube of a Coriolis flowmeter. A series of experimental studies was conducted, the results of which showed that an increase in the volume fraction of air in the fluid leads to an increase in the error in measuring the mass flow rate and the logarithmic decrement by tens of times. A beam finite element model of a Coriolis flowmeter with two curved measuring tubes was developed. A method for representing forced oscillations of a Coriolis flowmeter with a flowing liquid in the form of a superposition of the mode shapes of a system with a stationary fluidis proposed. Using a linear transformation, a transition to a system with two degrees of freedom with gyroscopic constraints is made, taking into account two oscillation modes. A computational study of the effect of damping on the amplitudes and phases of oscillations of the measuring coils of the Coriolis flowmeter was performed on this system. It is shown that an increase in the logarithmic decrement leads to a significantly smaller decrease in the time delay (and, accordingly, mass flow rate) than is observed in the experiment. It is explained that due to gyroscopic connections caused by the presence of a fluid, damping leads to a decrease in amplitudes, but has virtually no effect on the phase shift of the oscillations of the characteristic points of the flow meter, by which the mass flow rate is determined.