摘要
压力传感器是一种重要的压力信号感测和能量转换装置。近两百年来，历经了机械式量测、非电量电测、微机械系统（MEMS）、光学压力传感器等多次技术进步和性能提升的发展历程，当前向体积和结构微型化、功能智能化、制造工艺和材料多样化方向迅速发展。相对于微观结构的MEMS压力传感器，基于激光位移测量（LDM）的光学压力传感器采用宏观结构的压力腔、压力应变膜和激光探针，具有极小的差异性和精确的数学模型，结合了激光位移测量系统的高精度和高可靠性，对专用工艺装备的依赖性较弱，易于搭建压力传感器的模型验证实验平台等特点。本文对LDM光学压力传感器的位移模型、压力模型、光学压力传感器设计、压力信号分析、压力信号处理、标定方法等部分进行研究，主要研究成果如下：
（1）提出LDM压力传感器的压力调和模型和最优调和参数变步长搜索算法。分析周边固支、均布载荷条件下压力应变圆膜的应变元，利用调和方程及其边界条件建立圆膜的位移函数和应力函数，选择调和参数为λ的幂函数exp[λ(1-r/a)]，对圆膜的挠度进行非线性调制，采用Bubnov Galerkin变分方法，推导压力应变圆膜的最大挠度和挠度函数，建立LDM压力传感器的调和模型，分析调和参数λ对调和模型的影响。利用调和参数对调和模型的调制特性，以S.Timoshenko的挠度函数作为参考模型，将参考模型与调和模型在归一化条件下达到等挠度条件时，等挠度区间内的挠度模型误差获得最小二乘解，得到相对半径所对应的调和参数范围和调和裕量。提出最优调和参数变步长搜索算法，对归一化挠度误差在圆膜的相对半径范围内进行积分，以积分结果判断积分阈值终止条件，设计S形搜索加速模式修改步长因子，并更新搜索步长。当满足积分阈值终止条件时，停止搜索，获得最优调和参数。
（2）提出LDM光学压力传感器的反射型激光三角法测量模型，制定总体方案并分步进行结构设计，搭建实验平台。反射型激光三角法测量模型将压力应变圆膜的最大挠度位移量放大4.7669倍，利用7mW、650nm的半导体激光管，像元间距为8um、3648个有效像元数的线阵CCD图像传感器，优化布置激光管、聚焦透镜、反射镜和CCD传感器，设计并调试激光管驱动电路、CCD时序电路、模拟前端电路。分别以厚度为50um和10um、弹性模量为130GPa和205GPa的材料进行组合，设计四种压力应变圆膜及其压力腔，使激光探针的最大挠度测量范围达到0~6.12mm。分析CCD传感器的像元成像偏移，提出查找表式像元成像偏移补偿方法；
（3）研究压力信号的特性，推导LDM光学压力传感器的压力-像元解析模型，并采用最大三阶相关峭度反卷积算法对亚像元峰值位置进行盲提取。分析表面粗糙度对光强度信号的影响，测试光强度信号的偏度和峭度，以四组光强度信号的观测序列为Weibull概率分布的样本数据，采用极大似然估计法，对样本数据进行参数估计和Weibull概率分布测试，分析光强度信号的高斯分布、亚高斯分布和超高斯分布特性对亚像元峰值位置的影响。结合压力-挠度调和方程和挠度-位移方程，推导推导出压力-像元解析模型，分析LDM光学压力传感器的结构参数、调和参数、材料参数等对输入输出特性的影响。以三阶相关峭度最大为判定准则，推导反卷积逆滤波器的迭代解及其收敛性和稳定条件，仿真验证算法的收敛性；
（4）进行标定实验和压力实验。利用伺服电机、滚珠丝杠副、标定块和激光探针，搭建激光位移标定实验平台，电机拖动激光探针总成，向激光探针输入6mm范围内、0.25mm等间距微进给量的标定位移，获得激光探针的标定曲线和满量程±0.5218%的精度；之后，利用四种压力应变圆膜、压力腔和激光探针构成压力传感器标定平台，输入0~100KPa范围内压力间距为10KPa、100KPa~600KPa范围内压力间距为100KPa的压力载荷，进行压力标定实验，获得压力标定曲线和满量程±2.7055%的精度；最后，对LDM光学压力传感器进行压力实验，四种压力应变圆膜对应的压力分辨率分别达到109.723Pa/pixel、21.9466Pa/pixel、173.0247Pa/pixel和34.6049Pa/pixel。
As is an important pressure signal sensing and energy conversion device, in the previous twohundred years, pressure sensors have been gained the great improvement from the progress ofmechanical measurement, the non electrical quantity measurement, Microelectromechanicalsystems (MEMS) to optical pressure sensor so its performance were swiftly promoted tominiaturization with volume and structure, function of intelligence, diversification ofmanufacturing process and materials development. Compared with the MEMS pressuresensors, optical pressure sensor based on laser displacement measurement (LDM), whichconstructed with the pressure chamber, pressure strain diapgragm and laser probe macrostructure, have many better properties of minimal differences, precise mathematical model,and combined with the advantages of high precision and high reliability from the laserdisplacement measuring system. On the other hand, LDM optical pressure sensors wereindependent with special process equipments, and easy to complete the experimental platformfor calibration and real time measurement. In this paper, LDM optical pressure sensor’spressure harmonic model and displacement model, general scheme, signal analysis, signalprocessing, pressure calibration method of harmonic model, set up the pressure, have beenmade the overall implementation. The main research results are as follows:
(1) The harmonic model of LDM pressure sensor and the search algorithm for optimalharmonic parameter with variable step are proposed and tested. Strain element analysis ofcircular diaphragm with clamped edge under uniformly distributed load, using thedisplacement function and its boundary conditions of circular diaphragm to set up stressfunction and deflection function. The power function with parameter of lambda, exp [lambda(1-r/a)], was selected to modulate the nonlinear deflection of circular diaphragm. ApplyingBubnov Galerkin variational method, the maximum deflection function and deflectionfunction of circular diapgragm was deduced. The effect on harmonic model by harmonicparameter was examined. Using the harmonic parameters on the modulation characteristics ofharmonic model, the deflection function of S.Timoshenko was regarded as the referencemodel, and deflection error interval with least squares solution for the reference model and theharmonic model reached under the normalization condition to obtain the harmonic parameterrange and harmonic margin under the corresponding relative radius. The search algorithm ofoptimal harmonic parameter with variable steps was poposed with the integral of normalized deflection error which its relative radius was selected in the range of circular membrane, andthe integral result is judged by integral threshold termination condition. S-shaped searchacceleration mode was designed to modify the step size factor, and update the search step.When meet the integral threshold of the termination condition, the search progress stop socurrent harmonic parameter was the optimal one.
(2)The reflecting-type measurement model of laser triangulation for LDM optical pressuresensor is proposed and formulated. The structure design for the general scheme are carried outand built the experimental platform. The displacement measurement range for maximumdeflection of circular diaphragm is magnified4.7669times with reflecing-type opticalstructure. Semiconductor laser diode with power of7mW and with wave length of650nm, thelinear array CCD image sensor with pixel pitch of8um and effective pixel number of3648, afocusing lens and a reflector mirror are layouted with optimal placement. The driver circuitfor laser diode, the timing driver circuit for CCD sensor, and analog-front-end are designed.With the composition by different materials which have the thickness of50um and10um,130GPa and205GPa of the elastic modulus, four kinds of pressure strain circular diaphragmare designed. And, the pressure chamber is finished. As a result, the measurement range ofmaximum deflection for laser probe has0~6.12mm. The lookup-table are used to compensatethe pixel imaging offset of linear array CCD image sensor.
(3) Signal characteristics of LDM optical pressure sensor are researed and the laserdisplacement model is derived. The deconvolution algorithm with three order maximumcorrelation kurtosis is applied for blind extraction of sub-pixel peak position. Analysing theeffect of surface roughness on the laser intensity signal, skewness and kurtosis of laser signalintensity in the observation sequence are test. Four groups of the sample data with laserintensity signal which are regarded as Weibull probability distribution are used for parameterestimation with maximum likelihood estimation method. The impact of laser intensity signalto subpixel peak position is discussed with the Gauss distribution, sub-Gauss distribution andsuper-Gauss distribution characteristics. Combining the pressure deflection harmonic equationwith deflection displacement equation, the pressure-pixel analysis model is derived. Theinfluence on the characteristics of the input and output by the structural parameters, theharmonic parameters, material parameters are induced. The three order correlation kurtosismaximum criterion, iterative solution of deconvolution inverse filter, convergence andstability conditions, is derived and verified.
(4) Pressure calibration and test. Servo motor, ball screw, calibration block and laser probeare established an experiment platform to calibrate laser probe’s displacement measurement. The laser probe obtained the micro displacement of0.25mm per step, and calibration curveand the precision0.5218percentage in measurement range of6mm. And, a pressure chamberand a laser probe are used for pressure calibration platform for four kinds of pressure circulardiaphragm. Pressure calibration input loaded with10KPa per step in the range of0-100KPa,100KPa per step in the range of0-600KPa, and obtain the pressure calibration curve and fullrange calibration precision of2.7055perentage. Finally, LDM optical pressure sensor is carryout the pressure test with four kinds of pressure circular diaphragm which its resolutionreached109.723Pa/pixel,21.9466Pa/pixel,173.0247Pa/pixel and34.6049Pa/pixel,respectively.
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