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
Lin C T, Zhu X M, Chen W C. Measurement of fluid pressure and density based on Hall Effect［J］. Experiment Technology and Management, 2014(8):69-71.
［18］
胡倩. 基于力锤激励法的振动时效系统设计与实现［D］. 哈尔滨:哈尔滨工业大学, 2012.
［2］
张欲晓, 樊尚春. 液体密度传感器［J］. 计测技术, 2006, 26(1):1-3, 20.
［8］
Kratky O, Leopold H, Stabinger H. Device for density determination: US3523446［P］. 1970-08-11.
Zhang Y X, Fan S C. Liquid density sensors［J］. Metrology and Measurement Technology, 2006, 26(1):1-3, 20.
Wei C Z,Pan J,Song X H,et al.Apparatus for Density Measurement with Direct-driven Vibrating Tube Method［J］.Acta Metrologica Sinica, 2021, 42(10):1294-1298.
Fan Y M, Zhang Y, Li X H, et al. Design of cylinder shell resonant liquid density sensor［J］. Nanotechnology and Precision Engineering, 2007, 5(2):134-138.
［1］
Schmidt H, Wolf H, Hassel E. A method to measure the density of seawater accurately to the level of 10-6［J］. Metrologia, 2016, 53(2):770-786.
［7］
张桂铭. 微机械悬臂梁谐振传感器的关键技术与应用研究［D］. 西安:西安交通大学, 2014.
［9］
Picker P, Tremblay E, Jolicoeur C. A high-precision digital readout flow densimeter for liquids［J］. Journal of solution Chemistry, 1974, 3(5):377-384.
［10］
Albert H J, Wood R H. High precision flow densimeter for fluids at temperatures to 700 K and pressures to 40 MPa［J］. Review of scientific instruments, 1984, 55(4):589-593.
Han L L, Cao X, Wang Q, et al. Study on the measurement of liquid density by supporting resonance method［J］. Acta Metrologica Sinica, 2018, 39(2):197-200.
［15］
李兴华. 密度· 浓度测量［M］. 北京: 中国计量出版社, 1991.
Cai K L, Liu Y H, Zhu Y Q, et al. Wet modal tests and numerical simulation for a rigid-liquid-flexible coupled structure［J］. Journal of Vibration and Shock, 2020, 39(23): 128-134, 147.
Luo S W, Le Y F, Peng Y, et al. Design of a High Linearity Two-Dimensional Uncoupled Nanometer Piezoelectric Displacement System［J］. Acta Metrologica Sinica, 2021, 42(8): 977-985.
Li S X, Gong J W, Yu G Y. Study on measuring method of liquid density by a vibrating tube sensor［J］. Transactions of The Chinese Society, 1999, 30(1):77-83.
2023, Vol. 44 
