# Nonlinear Suppression of a Dual-Tube Coriolis Mass Flowmeter Based on Synchronization Effect
## 4 Experiment and Analysis  
Figure 7 shows the hardware configuration of the experimental platform, which included a dual U-tube CMF, an acceleration sensor distributed on the flowmeter, a signal acquisition system, and a computer. The flowmeter was horizontally suspended on the beam by a steel rope, and four accelerometers were rigidly connected to the bottoms of four beams of the flowmeter measuring tube. One accelerometer was rigidly connected to the base centre. In Figure 7, the four points a, b, c, and d indicate the positions of the additional masses, which corresponded to \(l/2\), \(l\times 3/4\), \(l\) and actuation position(Aq), respectively for numerical analysis and were the exciting point of the CMF. The additional masses were made of mass blocks with a unit of 1 g and were pasted at the designated positions with 3M double-sided adhesive, with the direction in line with the motion equation. The signal acquisition system contained seven channels. Self-developed data acquisition cards were used. The signal output by the accelerometer is represented by 1-4 and 7, and 5 and 6 were the output signals of the detection point of the CMF closed-loop system, marked as 1 to 7  
Figure 6: Response spectrogram of coupled vibration model of double beams with asymmetric additional mass. (a-d) Asymmetric additional masses in beam 1 (m\({}_{01}\) = 30 g) with different locations (left to right \(l/4\), \(l/2\), \(l\times 3/4\), and \(l\)). (e-h) Asymmetric additional masses in beam 1 (m\({}_{01}\) = 70 g) with different locations (left to right \(l/4\), \(l/2\), \(l\times 3/4\), and \(l\)). (i-l) Asymmetric additional masses in beam 1 (m\({}_{01}\) = 200 g) with different location (left to right \(l/4\), \(l/2\), \(l\times 3/4\), and \(l\)).  
nonlinear frequency doubling phenomenon. However, the suppression of the nonlinear frequency doubling amplitude was affected: as the additional mass increased, the less the distance away from the base, the better the suppression effect of the nonlinear frequency doubling phenomenon and nonlinear frequency doubling amplitude.  
Same position but different masses: at \(l/2\), the greater the mass, the better the suppression effect of the nonlinear frequency doubling phenomenon and frequency doubling amplitude. Also, the less the random noise, the smoother the spectrogram: some impurity peaks gradually weakened or disappeared and had a good suppression effect on low-order frequency doubling. At \(l\times 3/4\), the nonlinear suppression effect of different masses showed little difference. However, as the mass increased, the high-frequency doubling was markedly suppressed; relatively, at \(l\), the smaller the mass, the better the suppression effect.  
Because the exciting unit of the CMF was arranged in the centre of the U tube, considering the effect of additional mass in the exciting unit, the experimental results showed that the additional mass had less effect on the nonlinear frequency doubling, but the random noise could be reduced by additional mass.  
Through the experiment on symmetric additional mass, the conclusion was in line with the numerical analysis. From the perspective of actual operation, to suppress the nonlinear low-frequency doubling of the coupling system, a small mass far from the base or a large mass close to the base was selected as a priority. To suppress the nonlinear high frequency, a symmetric additional mass was arranged at \(l\times 3/4\) as a priority, but the magnitude of the mass needed to be obtained by more dynamic balance experiments.  
Figure 10: Vibration spectrogram of coupling system with symmetric additional mass.