基于Stewart平台的并联风洞天平设计理论及应用研究
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摘要
天平是风洞测力实验的最关键的测量设备。本文研究了基于 Stewart 平台的并联风洞天平的若干基本设计理论及在风洞中的应用,主要工作如下:
首先系统地总结风洞天平的作用、分类、应用领域、国内外研究发展现状及基于 Stewart 平台的并联风洞天平优点与国内外研究现状。
将并联机构的六根可伸缩杆替换为六个一维弹性敏感元件,由此提出了一种全新的 6-SS 并联天平概念,分析该类天平的位置正、逆解,提供了并联天平应用研究的基本理论依据。依据天平工作时处于相对静平衡的特点,利用空间力变换关系,研究天平的六维感受力与被测力基本变换原理,直接推导出感测力的六维雅可比矩阵,同时给出其结构参数的解析表达形式。
以力雅可比矩阵条件数为目标函数对天平进行结构优化设计,推导出雅可比矩阵条件数关于五个基本结构参数的解析关系表达式。依据雅可比矩阵条件数最小原则,先利用 ADAMS 软件对目标函数和系统结构参数的关系进行定性分析,再基于矩阵的 F-范数利用数学软件 Mathematica 进行定量分析,应用数值法找到八种满足天平精度最高的优化结构,并计算出天平的设计中心。
基于 Kane 方法研究天平的动力学及模态,通过线性化动力学方程建立天平的固有频率方程,依据振动理论推导出并联天平的六阶固有频率及其对应的振型,同时研究了天平的六阶固有频率随敏感单元刚度系数及上平台质量的变化规律,并用有限元法验证理论计算结果的正确性。
最后,依据以上形成的设计理论和结构优化方法,根据应用要求确定了天平设计量程,设计出应变式敏感元件、柔性球铰、数据采集系统及数据处理系统等软件,并设计制造出并联天平样机与标定装置。对天平进行实验研究,运用单元标定与综合标定方法计算出标定矩阵和天平的精度、准度、分辨率及线性度,同时在低速风洞中进行 CAARC 建筑标模试验验证天平的性能,取得了令人满意的结果,证明了本文研究的有效性。
Balance is a key measurement equipment in the wind tunnel testing. The elementary design method and application are studied in the thesis for the parallel wind tunnel balance based on the Stewart platform, and the main research work is as following:
The function, classification ,applicational field and the state-of-art for the wind tunnel balance are summarized systematically,and the advantages and research status of wind tunnel balance based on Stewart platform are also included.
Presented a novel conception of 6-SS parallel wind tunnel balance.Firstly, the design theory of the balance is provided by analyzing the forward kinematics and the inverse kinematics of the Stewart platform. According to characteristic of static equilibrium, the relationship between forces and torques applied to the testing model and given six leg forces is derived by using of spatial force transformation, from which obtains the force Jacobian matrix for the balance, and its analytical expression is also obtained based on elementary structural parameters. The condition number of Jacobian matrix of parallel balance is studied by the F-norm based on the force Jacobian matrix, the condition number is used as objective function to design a optimal parallel balance, and the analytical relationship is derived between objective function and the five elementary architectural parameters. According to the minimum Jacobian matrix condition number theory, the minimum of the objective function about intermediate variables is provided by using of numerical method, which is validated by the 2-norm of the force Jacobian matrix, and the derived result is applied to achieve eight optimal architectures for good parallel balance accuracy. The design center of the balance is also provided.
The equations of dynamics for the balance are established by Kane’s method, from which derives the characteristic equation of natural frequency by means of linearization of dynamic equations, and the six natural frequencies being developed according to the theory of vibration. The law of the six natural frequencies varying with mass of the upper platform and the stiffness of the elastic element are presented,and the Finite Element Method(FEM) is employed to testify the validity of theoretical results.
In the end, the range of measurement, the strain sensitive unit, the flexible spherical joint, and the software of data processing and collection are designed based
on the design theory and architectural optimal method above. Further more, the model of the parallel balance and the calibration equipment are fabricated. Calibration method of single-component and multi-componet are put to use to work out the calibration matrix, accuracy, precision ,resolution and linearity for the parallel balance. In order to testify the design performance of the balance, standard model is used to compare the experimental data with theoretical data in low speed wind tunnel and the result is satisfactory, which confirms the validity of the thesis.
首先系统地总结风洞天平的作用、分类、应用领域、国内外研究发展现状及基于 Stewart 平台的并联风洞天平优点与国内外研究现状。
将并联机构的六根可伸缩杆替换为六个一维弹性敏感元件,由此提出了一种全新的 6-SS 并联天平概念,分析该类天平的位置正、逆解,提供了并联天平应用研究的基本理论依据。依据天平工作时处于相对静平衡的特点,利用空间力变换关系,研究天平的六维感受力与被测力基本变换原理,直接推导出感测力的六维雅可比矩阵,同时给出其结构参数的解析表达形式。
以力雅可比矩阵条件数为目标函数对天平进行结构优化设计,推导出雅可比矩阵条件数关于五个基本结构参数的解析关系表达式。依据雅可比矩阵条件数最小原则,先利用 ADAMS 软件对目标函数和系统结构参数的关系进行定性分析,再基于矩阵的 F-范数利用数学软件 Mathematica 进行定量分析,应用数值法找到八种满足天平精度最高的优化结构,并计算出天平的设计中心。
基于 Kane 方法研究天平的动力学及模态,通过线性化动力学方程建立天平的固有频率方程,依据振动理论推导出并联天平的六阶固有频率及其对应的振型,同时研究了天平的六阶固有频率随敏感单元刚度系数及上平台质量的变化规律,并用有限元法验证理论计算结果的正确性。
最后,依据以上形成的设计理论和结构优化方法,根据应用要求确定了天平设计量程,设计出应变式敏感元件、柔性球铰、数据采集系统及数据处理系统等软件,并设计制造出并联天平样机与标定装置。对天平进行实验研究,运用单元标定与综合标定方法计算出标定矩阵和天平的精度、准度、分辨率及线性度,同时在低速风洞中进行 CAARC 建筑标模试验验证天平的性能,取得了令人满意的结果,证明了本文研究的有效性。
Balance is a key measurement equipment in the wind tunnel testing. The elementary design method and application are studied in the thesis for the parallel wind tunnel balance based on the Stewart platform, and the main research work is as following:
The function, classification ,applicational field and the state-of-art for the wind tunnel balance are summarized systematically,and the advantages and research status of wind tunnel balance based on Stewart platform are also included.
Presented a novel conception of 6-SS parallel wind tunnel balance.Firstly, the design theory of the balance is provided by analyzing the forward kinematics and the inverse kinematics of the Stewart platform. According to characteristic of static equilibrium, the relationship between forces and torques applied to the testing model and given six leg forces is derived by using of spatial force transformation, from which obtains the force Jacobian matrix for the balance, and its analytical expression is also obtained based on elementary structural parameters. The condition number of Jacobian matrix of parallel balance is studied by the F-norm based on the force Jacobian matrix, the condition number is used as objective function to design a optimal parallel balance, and the analytical relationship is derived between objective function and the five elementary architectural parameters. According to the minimum Jacobian matrix condition number theory, the minimum of the objective function about intermediate variables is provided by using of numerical method, which is validated by the 2-norm of the force Jacobian matrix, and the derived result is applied to achieve eight optimal architectures for good parallel balance accuracy. The design center of the balance is also provided.
The equations of dynamics for the balance are established by Kane’s method, from which derives the characteristic equation of natural frequency by means of linearization of dynamic equations, and the six natural frequencies being developed according to the theory of vibration. The law of the six natural frequencies varying with mass of the upper platform and the stiffness of the elastic element are presented,and the Finite Element Method(FEM) is employed to testify the validity of theoretical results.
In the end, the range of measurement, the strain sensitive unit, the flexible spherical joint, and the software of data processing and collection are designed based
on the design theory and architectural optimal method above. Further more, the model of the parallel balance and the calibration equipment are fabricated. Calibration method of single-component and multi-componet are put to use to work out the calibration matrix, accuracy, precision ,resolution and linearity for the parallel balance. In order to testify the design performance of the balance, standard model is used to compare the experimental data with theoretical data in low speed wind tunnel and the result is satisfactory, which confirms the validity of the thesis.
引文
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