单一平面电容传感器数学模型及有限元解法研究  

Research on the mathematical model of a uniplanar capacitance sensor and its finite element solution

作　　者：刘少刚[1] 安进华[1] 罗跃生[2] 葛杨[1] 王珏[2] 王士成[1] 

机构地区：[1]哈尔滨工程大学机电工程学院,黑龙江哈尔滨150001 [2]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2011年第1期79-84,共6页Journal of Harbin Engineering University

基　　金："948"国家林业局引进项目(2003-4-29)

摘　　要：单一平面电容传感器是木材含水率高精度测量仪器的核心装置,是任意结构形状电容传感器的特例.为了得到单一平面电容传感器数学模型的数值解,该文以一种设定了具体尺寸的单一平面电容传感器为例,描述了将前期研究中所建立的偏微分方程数学模型转换成三维状态下的有限元方程的具体过程.在有限元分析软件FlexPDE环境下对偏微分方程进行求解,得到了木材介电常数与传感器电容值的关系.该结果可应用于工程实际,可以方便地推广到具有一般尺寸和结构的单一平面电容传感器上去.The uniplanar capacitance sensor is the core device of high-precision equipment applied to measure wood moisture content and presents a special case of capacitance sensors of unspecific form.In order to obtain a numerical solution for the mathematical model of the uniplanar capacitance sensor,a sensor of a specific size was taken as an example.The specific process that converts the partial differential equations established in previous studies into three-dimensional finite element equations was introduced.Next,the partial differential equations were solved and the relationship between the permittivity of wood and the capacitance value of the sensor was obtained based on Flex-PDE.The result can be applied to engineering practices and the presented method is easily extended to a uniplanar capacitance sensor of general size and structure.

关 键 词：电容传感器 木材含水率 数学模型 有限元法 FlexPDE 

分 类 号：TP212[自动化与计算机技术—检测技术与自动化装置]