柔性机构拓扑优化方法及其在微机电系统中的应用
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摘要
柔性机构是一种依靠构件自身弹性变形来输出全部或部分运动、力和能量的新型装置。由于柔性机构为无铰链机构,因而具有无运动间隙和无摩擦磨损等优点,在微机电系统、精密定位机构和智能结构等领域有广阔的应用前景。本文对柔性机构的拓扑优化设计方法进行了系统的研究,并应用该方法设计制造夹持毛细管的压电式微夹钳和电热驱动的二维微执行器。
针对连续体结构拓扑优化中出现的棋盘格式等数值计算不稳定性现象,本文提出了一种以节点密度作为设计变量的优化方法,它确保了设计区域内的密度场函数具有C_0连续性,从拓扑优化数学模型描述的本质上克服了棋盘格式问题。算例表明该方法能够有效消除拓扑优化中的棋盘格和网格依赖等数值计算不稳定性现象,而且计算量小于滤波方法,具有良好的实用价值。
基于互能原理,建立了以互能和应变能比值作为目标函数的柔性机构拓扑优化数学模型,推导了基于节点密度法的柔性机构敏度计算的解析表达式。对热致动器这一多物理场拓扑优化问题进行了研究,建立了相应的数学模型,运用伴随矩阵法完成敏度分析。应用节点密度法对典型算例进行了拓扑优化计算,计算结果表明不需要借助滤波处理,节点密度法就能够得到具有清晰拓扑结构的优化结果,真实地反映了机构的结构细节。
利用所研究的柔性机构拓扑优化求解理论和算法,设计研制了用于夹持毛细玻璃管的压电驱动式微夹钳,并对其进行了实验测试。实验结果表明,实验值与有限元计算值有较好的吻合性,位移和夹持力与控制电压呈良好的线性关系。
利用多工况柔性机构拓扑优化方法设计了可用于微平台的二维微执行器,以此为基础,并考虑微加工工艺的限制,确定了其最终的结构尺寸。利用SU-8光刻胶制备电铸模和微电铸工艺,制造了二维微执行器原型。显微立体成像微操作系统上测试了二维微执行器的位移性能。试验结果表明该微执行器基本达到了设计要求。
本文研究工作表明连续体结构拓扑优化技术在MEME器件的优化设计中有着重要的方法论的作用,具有广阔的应用前景。
Compliant mechanisms are the type of mechanisms that use elastic deformation of flexible members to transfer force, motion or energy. These devices have good prospects in areas such as Micro-Electro-Mechanical Systems, precision position and smart structures due to their advantages such as elimination of friction and wear. In this dissertation, the topology optimization method of compliant mechanisms is deeply investigated. Based on topology optimization method, piezoelectric driven micro-gripper and thermal micro actuator is designed and tested.In this dissertation, a new method using nodal density as design variable of continuum topology optimization is proposed to resolve the checkerboard pattern. This method ensures C_0 continuity of density field in a fixed design domain, which prevents the checkerboard pattern problem from mathematical model in essence. Numerical examples are presented to support the proposed design method which can effectively eliminate the numerical instabilities, such as checkerboard and mesh-dependency in topology optimization results. The calculate speed of the proposed method is faster than the filter method. Therefore, it can be widely used in application.The mathematical model of topology optimization for compliant mechanisms is established based on the principle of mutual energy, in which, the ratio of mutual energy to strain energy of the mechanism is regarded as the objective function. The analytical expression of sensitivity based on nodal density for compliant mechanisms is deduced in detail. The design of thermal actuator is deeply researched, which is a coupling multi-physics problem. The mathematical model of thermal actuator is established based on the nodal density method. The adjoint method is applied to sensitivity analysis of design of thermal actuator. The results of representative numerical examples show that the mechanisms obtained by the nodal density method have clear topology structures which actually reflect
the structures of the mechanisms without any filtering schemes.The above theory and algorithm for topology optimization of compliant mechanisms is applied on the study of MEMS component. The microgripper used in the assembly of the electrophoresis chip is designed and manufactured. The experimental results of piezoelectric micro gripper show that displacement and clamping fore of gripper are coincident with the FEM results and linear with the control voltage.The 2D micro actuator that can be used in micro stage is designed by using topology optimization of compliant mechanisms with multi load cases. Based on the topology optimization results and restrictions of micro fabrication technology, the size of the micro actuator is finally determined. The prototype of the micro actuator is fabricated by means of micro electroforming and SU-8 photolithography techniques. The displacement of the micro actuator is measured by using the stereo vision micromanipulation systems. The experimental results show that properties of the micro actuator can be fulfilled the designing demand.It can be seen that the topology optimization of compliant mechanisms plays an important methodological role in the optimal design of MEMS component, which will be applied in wide fields.
针对连续体结构拓扑优化中出现的棋盘格式等数值计算不稳定性现象,本文提出了一种以节点密度作为设计变量的优化方法,它确保了设计区域内的密度场函数具有C_0连续性,从拓扑优化数学模型描述的本质上克服了棋盘格式问题。算例表明该方法能够有效消除拓扑优化中的棋盘格和网格依赖等数值计算不稳定性现象,而且计算量小于滤波方法,具有良好的实用价值。
基于互能原理,建立了以互能和应变能比值作为目标函数的柔性机构拓扑优化数学模型,推导了基于节点密度法的柔性机构敏度计算的解析表达式。对热致动器这一多物理场拓扑优化问题进行了研究,建立了相应的数学模型,运用伴随矩阵法完成敏度分析。应用节点密度法对典型算例进行了拓扑优化计算,计算结果表明不需要借助滤波处理,节点密度法就能够得到具有清晰拓扑结构的优化结果,真实地反映了机构的结构细节。
利用所研究的柔性机构拓扑优化求解理论和算法,设计研制了用于夹持毛细玻璃管的压电驱动式微夹钳,并对其进行了实验测试。实验结果表明,实验值与有限元计算值有较好的吻合性,位移和夹持力与控制电压呈良好的线性关系。
利用多工况柔性机构拓扑优化方法设计了可用于微平台的二维微执行器,以此为基础,并考虑微加工工艺的限制,确定了其最终的结构尺寸。利用SU-8光刻胶制备电铸模和微电铸工艺,制造了二维微执行器原型。显微立体成像微操作系统上测试了二维微执行器的位移性能。试验结果表明该微执行器基本达到了设计要求。
本文研究工作表明连续体结构拓扑优化技术在MEME器件的优化设计中有着重要的方法论的作用,具有广阔的应用前景。
Compliant mechanisms are the type of mechanisms that use elastic deformation of flexible members to transfer force, motion or energy. These devices have good prospects in areas such as Micro-Electro-Mechanical Systems, precision position and smart structures due to their advantages such as elimination of friction and wear. In this dissertation, the topology optimization method of compliant mechanisms is deeply investigated. Based on topology optimization method, piezoelectric driven micro-gripper and thermal micro actuator is designed and tested.In this dissertation, a new method using nodal density as design variable of continuum topology optimization is proposed to resolve the checkerboard pattern. This method ensures C_0 continuity of density field in a fixed design domain, which prevents the checkerboard pattern problem from mathematical model in essence. Numerical examples are presented to support the proposed design method which can effectively eliminate the numerical instabilities, such as checkerboard and mesh-dependency in topology optimization results. The calculate speed of the proposed method is faster than the filter method. Therefore, it can be widely used in application.The mathematical model of topology optimization for compliant mechanisms is established based on the principle of mutual energy, in which, the ratio of mutual energy to strain energy of the mechanism is regarded as the objective function. The analytical expression of sensitivity based on nodal density for compliant mechanisms is deduced in detail. The design of thermal actuator is deeply researched, which is a coupling multi-physics problem. The mathematical model of thermal actuator is established based on the nodal density method. The adjoint method is applied to sensitivity analysis of design of thermal actuator. The results of representative numerical examples show that the mechanisms obtained by the nodal density method have clear topology structures which actually reflect
the structures of the mechanisms without any filtering schemes.The above theory and algorithm for topology optimization of compliant mechanisms is applied on the study of MEMS component. The microgripper used in the assembly of the electrophoresis chip is designed and manufactured. The experimental results of piezoelectric micro gripper show that displacement and clamping fore of gripper are coincident with the FEM results and linear with the control voltage.The 2D micro actuator that can be used in micro stage is designed by using topology optimization of compliant mechanisms with multi load cases. Based on the topology optimization results and restrictions of micro fabrication technology, the size of the micro actuator is finally determined. The prototype of the micro actuator is fabricated by means of micro electroforming and SU-8 photolithography techniques. The displacement of the micro actuator is measured by using the stereo vision micromanipulation systems. The experimental results show that properties of the micro actuator can be fulfilled the designing demand.It can be seen that the topology optimization of compliant mechanisms plays an important methodological role in the optimal design of MEMS component, which will be applied in wide fields.
引文
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