六维加速度传感器的性能建模及结构优化

Performance Modeling and Structure Optimizing of Six-Axis Accelerometer

针对目前六维加速度传感器的性能指标尚无规范的评价标准和理论计算模型的现状,从基频、灵敏度、误差区间宽度3个方面建立并求解系统的单性能数学模型;对传统理想点法进行改进,给出多性能目标关于矛盾参量的评价函数。研究表明:在六维加速度传感器样机设计阶段,通过以结构矩阵为乘子的矩阵迭代运算,可以得到系统的一阶固有模态;通过构建弹性体内的协调方程,可以解决灵敏度模型中涉及到的超静定反向动力学问题;通过给出经过证明的关于误差区间宽度的3个定理,可以揭示并量化传感器的误差传递关系;以提出的一种综合性能函数为指标,可以有效解决多目标优化过程中普遍存在的3大问题,并据此绘制六维加速度传感器的综合性能图谱。

According to the present situation that performance index of six-axis accelerometer has no normative evaluation standard and theoretical calculation model, mathematical models of three single performances including fundamental frequency, sensitivity and width of error interval are established. The function of multi-objective on contradictive parameters is given based on modified ideal point meth- od. The results show that at the design stage of six-axis accelerometer, first mode can be calculated u- sing matrix iteration method. The statically indeterminate reverse dynamics equations about sensitivity model are calculated by constructing compatibility equations. Considering the uncertain errors, three theorems about width of interval are proposed and proved to reveal the mechanism of error transmission which can be used to direct the improvement of measuring accuracy. With the function of comprehensive performance, three major issues of multi-objective optimization can be solved effectively, and the map of six-axis accelerometer can be drawn.