Thus the sensor’s sensitivity is determined by the physical dimensions of the flow channel. In addition, the flow sensor is operated with high speed fluid in the dispensing system, so it is important to know its dynamic behavior for predicting the time dependent signal from the flow and pressure. A lumped electric element analogy of the flow sensor was used to estimate the working range, as shown in Figure 3.Figure 3.Electric analogy of the flow sensor.From Figure 3 the transfer function and resonance frequency fhyd of the LRC circuit can be deduced as in (2) and (3). Then it can be concluded that it is possible to increase fhyd by reducing Chyd and Lhyd so as to obtain a higher dynamic range. Due to the square membrane deflection under a pressure load, liquid can be accumulated.
The hydraulic capacity of the sensor is expressed in (4). The inertance of the sensor caused by the acceleration of liquid mass can be defined as in (5):Ghyd=11+j��RhydChyd?��2LhydChyd(2)fhyd=12��LhydChyd(3)Chyd=0.28(a/2)6Eh3(1?v2)(4)Lhyd=��lA(5)where L is the channel length, A is the channel cross section, E is the modulus of elasticity, v is the Poisson constant, �� is the density, a is the membrane width, h is the membrane thickness. It can be seen that the dynamic behavior is influenced by the stiffness of the membrane and the dimension of the channel.Based on the principles above, the sensor prototype was designed. It consists of two square silicon membranes with dimensions of 50 ��m thick �� 2,000 ��m wide �� 2,000 ��m long, and the Chyd value is around 1.60��10-17m5/N.
Simulation of a single membrane by ANSYS (general purpose finite element analysis software) is shown in Figures 4(a) and 4(b), and the stresses and strains on X-axis path are shown in Figures 4(c) and 4(d). From the results we can see that the stress at maximum system pressure (15 psi) is 2.5��107 Pa, which is less than the limit value 80 MPa, and the maximum deflection is 1.3 ��m, which is far smaller than the membrane thickness of 50 ��m. Therefore the membranes stay in elastic deformation stage. In the liquid dispensing system, the required liquid flow rate is about several 10 ��L/s. So the channel is designed as 2,005 ��m long and 30 ��m deep. For a 2,000 ��m wide channel, the resistance to water is 3.36��1011 Ns/m5 with an inertia of 3.2��107 kg/m4.
Besides, the resonance frequency is 7,019 Hz, and then the sensor can work well with a fluid frequency up to 1 kHz.Figure 4.Simulation shows the stress and strains for single membrane under 15 psi pressure.The sensor fabrication consists of an industrial piezo-resistive GSK-3 process with the additio
High precision accelerometers find many applications such as acoustic measurement, seismology and navigation. Micro-machined accelerometers have been developed with different working principles [1-3].