# Research on Testing Method of Oil Characteristic Based on Quartz Tuning Fork Sensor
## 2 Fluid Property Sensing
### Measurement Principle  
The fluid property sensor measurement is based on a tuning fork flexural resonator. This resonator is composed of quartz, a piezoelectric material capable of being deformed upon the application of a voltage and reciprocally electrically polarized under the action of mechanical stress. The two times of the fork oscillate and generate a response indicative of the physicochemical and electrical properties of the fluid in which the sensor is immersed.  
A sinusoidal excitation voltage applied to the tuning fork's thin electrodes causes mechanical stress and periodic elastic deformation. This vibration produces a corresponding current through the electrodes. The ratio of the excitation voltage to the induced current allows measurement of the impedance of the system, and this process will be dependent on the excitation frequency, the elastic properties of the piezoelectric material, and the properties of the fluid. The quartz tuning fork impedance response in air has a sharp resonance at approximately 31 kHz. In a fluid, the resonance frequency and amplitude are reduced due to the increased mass load and frictional forces in the system [25; 26].  
As described in Figure 5, the calculation of the fluid properties is allowed through the use of a tuning fork equivalent electrical model.  
Figure 4: AD5933 peripheral circuit diagram.  
Figure 5: Tuning fork equivalent electrical model.  
The tuning fork complex impedance in air is modeled using the following formula:  
\[Z_{TF}(\omega)=R_{P}//C_{P}//\left(R_{0}+i\omega L_{0}+\frac{1}{i\omega C_{s}}\right) \tag{1}\]  
Serial capacitance (C\({}_{s}\)), resistance (R\({}_{0}\)) and inductance (L\({}_{0}\)) depend only on geometrical tuning fork parameters. Fluid impact is described by an additional term:  
\[Z_{(\omega)}\ =\ \mathrm{A}\ \mathrm{i}\ \omega\ \rho+\mathrm{B}\sqrt{\omega\ \rho\ \eta}(1+i) \tag{2}\]  
where \(\omega\) is the excitation frequency, \(\eta\) is the dynamic viscosity, \(\rho\) is the density, and \(\mathrm{A}\) and \(\mathrm{B}\) are constants that depend on the resonator geometry [27].  
The dielectric constant \(\varepsilon\) and the electrical resistivity \(\mathrm{P}\) are measured with the parallel capacitance (C\({}_{p}\)) and resistance (R\({}_{p}\)) [28; 29]:  
\[C_{P(\varepsilon)}=(\varepsilon-1)\frac{\partial C_{P}}{\partial\varepsilon}+ C_{P\ \mathrm{yaccum}} \tag{3}\]  
\[R_{P}(P)=P\frac{\partial(R_{P})}{\partial P} \tag{4}\]  
After a calibration step required to calculate each parameter, the fluid property sensor is used to measure the dynamic viscosity, density, dielectric constant, and R\({}_{p}\), an indication of resistivity, of the unknown fluid in which it is immersed.  
For measuring the density \"\(\rho\)\", the principle is that when the quartz tuning fork is immersed in the oil medium, its surface that is attached to the oil medium experiences effective mass changes, resulting in a reduction in resonance frequency; the use of density and effective mass of the relationship can be realized to measure the density of the oil medium. The principle of measuring viscosity (\(\eta\)) is that when the quartz tuning fork is used as the sensitive element, the impedance characteristics of its equivalent circuit will change due to the influence of viscosity. The purpose of online viscosity monitoring can be achieved by real-time monitoring of impedance. The measured temperature (T) is measured using a resistance temperature detector (RTD). The dielectric constant (\(\varepsilon\)) is calculated from the temperature measured by the RTD and the oil-related constant. The resistivity of a medium, \(P\), refers to the resistance encountered by free carriers when moving in the medium under the action of an electric field. The resistivity of the oil depends on the viscosity of the fluid, the density of free charge carriers, and the specific chemical composition of the oil. Resistivity (P) can be modeled in a simple linear form: \(P=H+I\), where T is the temperature measured by the RTD, and H and I are constants related to oil.