Abstract
Certain nonlinear influences are found in dual-tube Coriolis mass flowmeters (CMFs). According to experimentation, a nonlinearity dominated by frequency-doubling signals can be observed in the measuring signal. In general, such nonlinear effects are simplified as linear systems or neglected through processing. In this paper, a simplified model has been constructed for dual-beam CMFs based on the theory of nonlinear dynamics, with the spring–damper system as the medium for the dual-beam coupled vibrations. Next, the dynamics differential equation of the coupled vibrations is set up on the basis of the Lagrangian equation. Furthermore, numerical solutions are obtained using the Runge–Kutta fourth-order method. The study then fits discrete points of the numerical solutions, which are converted into the frequency domain to observe the existence of frequency-doubling signal components. Our findings show that frequency-doubling components exist in the spectrogram, proving that these nonlinear influences are a result of the motions of coupled vibrations. In this study, non-linear frequency-doubling signal sources are qualitatively analyzed to formulate a theoretical basis for CMFs design.
Highlights
AAbbssttrraacctt:: CCeerrttaaiinn nnoonnlliinneeaarr iinnfflluueenncceess aarree ffoouunndd iinn dduuaall--ttuubbee CCoorriioolliiss mmaassss fflloowwmmeetteerrss ((CCMMFFss))
Focusing on a single beam, this study applies the modal analysis method to derive the kinematic equation for a single beam under the condition of sinusoidal excitation
The equation verifies that no frequency-doubling signal is detected in the output
Summary
A spring–damper model is established for dual-beam coupled vibrations. On this basis, the generalized coordinates of the system are redefined as (q11, q21, z), and the vibration expression of tube i is represented by the following function: zi ≈ ∅j(x)qji(t) (i = 1, 2),. Differential equations for system motion should be obtained via the Lagrangian equation [31], the general form of which can be written as follows: d. Equations (25) and (26) are substituted into Equation (18) to obtain the differential equation of motion, as follows:. The system of dynamics differential equations of the dual-beam coupled vibration model can be obtained as follows: q1i (t) ∂t2 dx + EJq1i(t).
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