Analytical Modeling of A Micro Dual-mode Media Compatible Pressure Sensor*

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(1.College of Mechanical Engineering,Quzhou University,Quzhou 324000,China;2.The State Key Laboratory of Fluid Power Transmission and Control,Zhejiang University,Hangzhou 310027,China)

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Analytical Modeling of A Micro Dual-mode Media Compatible Pressure Sensor*

YUJianping1*,LIXin1,ZHANGYuliang1,YAOZhehe2,ZHOUZhaozhong1,2

(1.College of Mechanical Engineering,Quzhou University,Quzhou 324000,China;2.The State Key Laboratory of Fluid Power Transmission and Control,Zhejiang University,Hangzhou 310027,China)

This paper presents the analytical modeling of a novel micro dual-mode pressure sensor which is capable of measuring static and transient pressure simultaneously under corrosive environment.The sensor is compromised of a LTCC-based(low temperature co-fired ceramic)piezoresistive measurement unit and a PDMS-based(polydimethylsiloxane)capacitive measurement unit.The use of piezoresistive unit is to accomplish static pressure measurement,while the capacitive measurement unit realizes transient pressure measurement.Mathematical models of the proposed piezoresistive and capacitive transduction were calculated respectively.FE analyses were also performed to help in assessing the impacts of sensor structure on measurement characteristics in the prototyping explore.

piezoresistive;capacitive;pressure sensor;low temperature co-fired ceramic(LTCC);polydimethylsiloxane(PDMS)

Pressure measurement provides crucial information for broad application circumstances that ranges from industrial process control,advanced manufacturing to biomedical applications,etc.For now,piezoresistive sensor is still the major type of sensor for pressure measurement,it provides advantages as simple structure,inexpensive cost with high sensitivity and suitable for static pressure measurement[1-3].Other than piezoresistive sensor,capacitive sensor is growing as another alternative for pressure measurement due to some certain advantages as higher measurement sensitivity,decreased temperature sensitivity,reduced power consumption,better stability and particularly suitable for transient pressure measurement[4-5].

The majority of corrosive media compatible pressure sensors are based on piezoresistive transduction.A common feature among all these typical pressure sensors is the use of thick-film technology[6-7].Ceramic materials as the thick-film substrate allows applications in series harsh measuring conditions,such as high pressure,high temperature,direct contact to corrosive liquids,etc[8-9].However relatively high Young’s Modulus of ceramic materials and short gauge property of thick film resistors limit thick film ceramic sensors from wider applications.The typical prototype of media compatible pressure sensors based on capacitive transduction is the use of stainless steel(SS)as the material for diaphragm die and packaging housing.The use of SS provides the capability for measuring in harsh environments[10].For cost efficiency concern,most pressure sensors are still based on monolithic transduction.However,during recent years,there is a growing demand for static and transient pressure measurement at the same time,any pressure sensors of monolithic transduction would easily fall short for the requirement.

In this work,the analytical modeling of a novel micro dual-mode pressure sensor for harsh environment is presented.The intrinsic features of this reported sensor includes:(i)the use of piezoresistive and capacitive transductions allows static and transient pressure measurement simultaneously;(ii)the usage of low temperature co-fired ceramic(LTCC)[11-12]as sensor substrate reveals quite a few advantages over some other traditional ceramic materials,i.e.,the easy-machining for three-dimensional structure,relatively lower Young’s Modulus and rigid mechanical strength;(iii)the use of polydimethylsiloxane(PDMS)[13]as the capacitive membrane shows phenomenal sensing flexibility.

Fig.1 Cross-sectional schematic view of the dual-mode pressure sensor

1 Pressure Sensor Device Structure

Fig.1 illustrates the cross-sectional schematic view of the sensor.The sensor is compromised of a LTCC-based piezoresistive measurement unit and a PDMS-based capacitive measurement unit.

The piezoresistive measurement unit was designed as a monolithic LTCC structure with thin membrane,a cylindrical cavity and the channel for pressure inlet.Four resistors(R1,R2,R3andR4)are symmetrically positioned on the upper surface of the thin membrane as shown in Fig.2,and parallelly connected to a common node asR0in the centre of the membrane.The use of piezoresistive unit is to accomplish static pressure measurement.

Fig.2 Layout of resistors(R0,R1,R2,R3 and R4)on the upper surface of thin membrane

Fig.3 Top view of sensing electrodes of the capacitive measurement unit

The capacitive measurement unit realizes transient pressure measurement,which consists of two sensing electrodes on the bottom substrate,and one common electrode on the top PDMS flexible membrane as shown in Fig 3.Of some conventional designs,two sensing electrodes are patterned on the top membrane and bottom substrate respectively,however,the sensing electrode on the top membrane is quite fragile when the membrane is bent during measurement.Sensor structure in this paper on the other hand,would preclude this from happening.

Of this sensor,piezoresistive measurement unit is in direct contact to corrosive measuring environment,which requires reasonable rigid mechanical strength and anti-corrosive capability.While capacitive measurement unit is in direct contact to the top surface of thin membrane,during the measurement,which should be tightly fit to the membrane.Based on the analysis,LTCC of excellent anti-corrosive capability and PDMS of outstanding sensing flexibility are chosen to be the materials for piezoresistive and capacitive measurement units respectively.

2 Sensor Measurement Operation

Shown in Fig.4,four resistors(R1,R2,R3andR4)share the same initial resistance.When a force is applied on the thin membrane,the bending of the membrane will deform the resistors,which resulting in the force-induced resistance variations.On the other hand,common nodeR0is located in the middle of thin membrane,the bending of the membrane would not induce any deformation of which,as a result,resistance of common node will not change even with the bending of the membrane.

Fig.4 The schematic of the proposed piezoresistive measurement unit

Consider LTCC as an ideal material,then the resistance variation of the four resistors can be expressed as:

ΔR1=kpsR1

(1)

ΔR2=kpsR2

(2)

ΔR3=kpsR3

(3)

ΔR4=kpsR4

(4)

wherekrepresentstheresistivityofLTCCstructure,psisthestaticpressurevaluetobemeasured.

Sincethefourresistorsaresymmetricallypositioned,amoreprecisevalueofpscanbeachievedfromthefollowingequation:

(5)

Fig.5 illustrates the schematic of the proposed capacitive measurement unit.As the external pressure applied to the top membrane,the applied pressure can be detected by the capacitanceCtof the capacitive measurement unit:

1/Ct=1/Ct1+1/Ct2

(6)

whereCt1andCt2are the capacitances between the common electrode and two sensing electrodes.Since the two sensing electrodes are symmetrically patterned,the specific value of which can be defined as:

(7)

Fig.5 The schematic of the proposed capacitive measurement unit

whereais the radius of the PDMS membrane,ε0is the permittivity in vacuum,εrandt0is the relative permittivity and thickness of the insulating layer,gandw(r,pt)are the original value and variation of air gap distance respectively,ris the position of measuring point,ptis the transient pressure value.

In this design,the capacitive measurement unit is working in two different mode,including the normal mode and the touch mode.When the measurement is in low pressure range,before the top membrane reaches the bottom surface of the insulating layer,the capacitive measurement unit is operating in the normal mode.When the measurement is in ultra high pressure range,the top membrane would in direct contact to the insulating layer,the capacitive measurement unit is working in the touch mode.

In the normal mode,the deflection of air gap distance can be obtained from equation(8):

(8)

whereDrepresents the flexural rigidity of the membrane.In the touch mode,the variation of air gap distance can be approximately assumed as:

(9)

whereap(pt) is the radius of the touching surface.

3 FE Simulation Analysis

In this section,based on the presented sensor model,static analysis and modal analysis were investigated.In the static analysis,strain simulation and stress simulation were proposed.In the modal analysis,resonant frequency and resonant amplitude of the sensor were both calculated.

Static Analysis.The proposed sensor was in axial symmetrical model.Fig.6 and Fig.7 illustrated the equivalent strain and von mises stress distribution when the sensor was under 5kPa pressure,respectively.

Fig.6 Equivalent strain simulation results of the sensor structure under 5 kPa pressure

Fig.7 Von mises stress simulation results of the sensor structure under 5 kPa pressure

From the simulation results,it could be concluded that the largest equivalent strain was about 3.5×10-4,and centralized in some certain areas on the membrane.The largest von mises stress was about 6.7×106N/m2,which appeared in the middle of the membrane.

Modal Analysis.Modal analysis is the study of dynamic properties of structures under vibrational excitation.In this section,the natural mode shapes and frequencies of the proposed sensor during free vibration were determined.Fig.8 illustrated the first four mode shapes of this pressure sensor,as can be identified,the first four natural frequencies were 26 kHz,56 kHz,78 kHz and 97 kHz respectively,which should be avoid during the measuring.

Fig.8 Modal analysis of the proposed pressure sensor

4 Summary

A dual-mode pressure sensor was considered for media compatible applications.The LTCC-based piezoresistive unit with significant media compatible capability was designed for static pressure measurement.The PDMS-based capacitive unit of outstanding sensing flexibility was designed for transient pressure measurement.Mathematical models of the proposed pressure sensor were calculated in this paper.FE analyses were also performed to help in assessing the impacts of sensor structure on measurement characteristics in the prototyping step.

The novel proposed sensor was favorable for advanced industrial requirements.In the future,a testing prototype will be constructed,and sensor performance and reliability will be investigated.

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2014-11-06 修改日期:2014-12-20

微型雙模式耐蝕壓力傳感器設計及特性分析*

余建平1*,李 欣1,張玉良1,姚喆赫2,周兆忠1,2

(1.衢州學院機械工程學院,衢州 324000;2.浙江大學流體動力與機電系統(tǒng)國家重點實驗室,杭州 310027)

本文提出一種微型雙模式耐蝕壓力傳感器設計并分析其測試特性,能夠?qū)崿F(xiàn)靜態(tài)力和瞬時力的同步測量。該傳感器由基于低溫共燒陶瓷的壓阻測量單元和基于硅橡膠的電容測量單元構成。并由壓阻測量單元實現(xiàn)靜態(tài)力的測量,電容測量單元實現(xiàn)瞬時力的測量。文中分別計算了壓阻測量單元和電容測量單元的數(shù)學分析模型,并通過有限元仿真研究傳感器的靜態(tài)特性和模態(tài)響應,考量傳感器結構參數(shù)對其測量性能的影響。

壓阻式;電容式;壓力傳感器;低溫共燒陶瓷;硅橡膠

TH823

A

1004-1699(2015)02-0193-05

余建平(1986-),男,博士,衢州學院講師?，F(xiàn)主持國家自然科學基金1項,參與3項,主要研究方向為精密壓力檢測及多維微納位移測量,yujianping@zju.edu.cn;

周兆忠(1968-),男,博士,教授,衢州學院機械工程學院院長,浙江大學機械電子控制工程博士后。主要研究方向為機電一體化技術,精密、超精密加工技術與裝備,zzz_2227@163.com。

項目來源:國家自然科學基金項目(51405263,51275272)

C:7230

10.3969/j.issn.1004-1699.2015.02.008