基于欧拉-伯努利梁理论,构建了谐振管式液体密度计长直管谐振子工作的非齐次偏微分方程,并进行求解,给出了谐振子灵敏度的解析式。依据谐振子灵敏度解析式,结合ANSYS Workbench湿模态仿真分析了谐振子灵敏度在不同结构尺寸与工作模态下的变化规律。根据分析结果,选择加工了13根不同结构尺寸的长直管谐振子,并采用力锤模态分析法进行实验,验证了解析式的有效性。结果表明,通过减小有效长度,增大内半径,将壁厚取临界值及提高工作模态阶数,可以显著提升长直管谐振子的灵敏度,最高可达-1.904Hz·kg-1·m3。
Abstract
Based on Euler-Bernoulli beam theory, an inhomogeneous partial differential equation describing the resonator of vibrating tube densitometer is constructed and solved. An analytical equation for computing the sensitivity of the resonator is given. Based on the analytical equation and combined with the wet modal analysis of ANSYS Workbench, the variation rule of resonator sensitivity under different structural sizes and working modes is analyzed. According to the analysis results, 13 straight tube samples with different structure sizes were selected and fabricated. The validity of the analytical formula was verified by experiments on these samples using force hammer modal analysis method. It is found that the sensitivity of the straight tube resonator can be significantly improved by a series of measures including reducing the effective length, increasing the inner radius and taking the wall thickness to the critical value, up to -1.904Hz·kg-1·m3
关键词
计量学 /
液体密度计 /
长直管谐振子 /
锤击法 /
湿模态 /
灵敏度
Key words
metrology;densitometer /
resonator of vibrating straight tube;hammering method /
wet modal /
sensitivity
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