Higher-Order Models for Resonant Viscosity and Mass-Density Sensors

Abstract

Advanced fluid models relating viscosity and density to resonance frequency and quality factor of vibrating structures immersed in fluids are presented. The numerous established models which are ultimately all based on the same approximation are refined, such that the measurement range for viscosity can be extended. Based on the simple case of a vibrating cylinder and dimensional analysis, general models for arbitrary order of approximation are derived. Furthermore, methods for model parameter calibration and the inversion of the models to determine viscosity and/or density from measured resonance parameters are shown. One of the two presented fluid models is a viscosity-only model, where the parameters of it can be calibrated without knowledge of the fluid density. The models are demonstrated for a tuning fork-based commercial instrument, where maximum deviations between measured and reference viscosities of approximately ±0.5% in the viscosity range from 1.3 to 243 mPas could be achieved. It is demonstrated that these results show a clear improvement over the existing models.

Electromechanical resonators for sensing fluid density and viscosity—a review

“…Using dimensional analysis (see, e.g. [175]) shows that the complex-valued fluid drag force F(ω) acting on a vibrating structure can be written as…”

“…Viscous damping acting on vibrating fluid sensors reduces the Q-factor (e.g. to 6.1 for a QTF in a fluid with ρ f = 834.1 kg m −3 and η = 242.9 mPa s [175]) which impairs the accuracy of the determined resonance parameters. Higher dampings cause broader resonance characteristics and lower amplitudes, such that in the presence of noise, the frequency peak is not as clearly localized as for high-Q resonances.…”

“…Furthermore, the signal amplitude is reduced, causing a reduced signal-to-noise ratio. Both effects translate to standard deviations σ ρ and σ η of estimated density and viscosity featuring approximate proportionalities of σ ρ ∝ 1/Q 2 and σ η ∝ 1/Q 3 for the QTF [175]. Accurate determination of resonance parameters in order to give accurate viscosity and density readings is therefore more demanding in higher viscous fluids.…”

Engine oil quality deterioration estimation using an integrated sensory system

“…39 Higher-order model analysis is advantageous in the viscosity and density calculation from measured resonance parameters. 40 Various existing research in the wider literature has been explored. Published literature includes a study conducted on a few civilian vehicles under typical urban traffic conditions.…”

“…39 Higher-order model analysis is advantageous in the viscosity and density calculation from measured resonance parameters. 40…”