面向六自由度机械手的机电产品多学科协同优化设计研究
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摘要
产品设计是一个复杂的过程，它涉及多门学科、多个子系统。多学科设计优化是近二十年发展起来的一种系统优化方法，它利用各学科或子系统间的相互耦合产生的协同效应，获得系统的整体最优解，缩短设计周期，是解决复杂机电产品设计的有效方法，已在航空航天领域得到长足发展和广泛应用，而在复杂机械系统领域的研究才刚刚起步，本文以6自由度机械手为研究对象，着重研究基于带精英策略的改进遗传算法和目标级联的优化设计问题，以及不确定性环境下的产品可靠性分析及优化设计问题。将六西格玛设计、改进遗传算法和目标级联法相结合，建立了协同优化模型，并用算例验证了该方法的可行性。具体工作如下：
1、在对国内外多学科设计优化研究深入分析的基础上，通过对MDO各技术要素的整合，归纳总结出面向复杂机械产品的多学科设计优化技术体系，给出了具有指导意义的应用框架。
2、总结分析了机构的有限元模态分析的数学模型、模态提取方法，采用了基于montecarlo的贝叶斯模型缩减的特征值和特征向量的灵敏度分析方法，并且将网格技术引入到协同设计领域中，从而有效提高优化的执行效率，为协同设计领域中遇到的大型计算问题提供了一种新的解决思路，并且具有很好的扩展性和可移植性。
3、在6自由度机械手的实例基础上，对柔性机器人机构的刚体运动对弹性运动的影响和其弹性运动对刚体的影响的同时进行了研究，以确保机构在大范围刚体运动的同时，尽可能抑制其振动，它是基于完全逆动力学分析的运动控制方法，为进一步的动态分析与优化提供了明确的和强有力的证据。
4、在分析6自由度机械手的多体动力学、运动学学科时，解决了机构运动学初始条件的初值相容性问题；解决了复杂多体系统直接采用广义坐标计算时所面临大规模稀疏矩阵的乘法运算问题，提高了计算效率；解决了运动学分析中，全局法建模所带来的方程规模较大，求解效率低的问题；解决了通常拓扑法采用速度转换矩阵，并且将虚位移和加速度关系式直接代入由全局建模法组建的系统运动方程，运动方程矩阵组装后仍面临大规模稀疏矩阵的乘法运算而同样引起求解效率较低的问题；在分析机械手的动力学特性时，考虑了机构构件及关节弹性变形产生的影响，解决了机械手的构件和关节作为刚柔耦合体的问题；使用修正的Newton-Raphson迭代校正公式求解非线性的动力学方程，解决了一般用Newmark法加Newton-Raphson法求解时需要求矩阵和向量的导数，比较复杂同时计算量也大的问题。
5、在对伺服控制系统的仿真研究背景及对混合式步进电机的工作原理和分析原理研究的基础上，推导了两相混合式步进电动机在动坐标系下的数学模型，并根据此建立了6自由度机械手的开环仿真控制模型，为动力学/运动学的分析提供了理论支持，并为后续的协同优化设计奠定了基础。
6、研究了6自由度机械手系统的分解协调技术；MDO的数学模型；优化求解策略，并且利用了全局灵敏度方程，对耦合因素的灵敏度信息进行了简化处理，构造了系统近似模型，然后运用优化算法寻找系统近似模型的最优解，直至收敛；多学科协同设计优化空间的搜索策略，以及多学科设计优化算法的实施思想和理论；耦合系统的基于隐函数原理推导出的全局灵敏度方程；对多目标决策及多目标优化结果的满意评价分析；结合遗传算法、ATC、六西格玛的主要特点，提出了一种基于带精英策略的遗传算法的结合ATC和六西格玛的可提高可靠性和鲁棒性的优化方法。
Product design is an intricated process, which involves multiple disciplines, and multiplesubsystems. Multidisciplinary design optimization(MDO) is a system optimization method，itexplorts the synergistic effects generated by the mutual coupling between the variousdisciplines or subsystems, to obtain the overall optimal solution, and to shorten the designcycle, which is an effective way to solve complex mechatronic system design. It has beendeveloped rapidly and widely over the past two decades in the field of aerospace, but has juststarted in the research field of complex engineering mechanical systems. This paper studiesthe issues of improved genetic algorithm with elitist strategy, design co-optimization withAnalytical Target Cascading (ATC), and product reliability analysis and optimal design underuncertainty. Co-optimization model is set up based on the Six Sigma design method,improved genetic algorithm and ATC, and is verified with a6-DOF manipulator as anexample. And main work in this paper is as following:
1. Sum up and put forward a technology system of optimal design for complexmechanical product based on the indepth study achievements made at home and abroad, andon the basis of integration of the technical elements of the MDO, which gives an applicationframework of significance.
2. Summarize and analyze the mathematical model of finite element modal analysis,modal extraction method, using the sensitivity analysis method combined with reducedeigenvalues and eigenvectors from Bayesian model based on monte carlo, and introducesGrid technology into the field of collaborative design, so as to improve the efficiency of theimplementation of the tasks effectively, and shorten the product development cycle. Itprovides a new solution for large-scale computation encountered in the field of collaborativedesign, and has a very good expansibility and portability.
3. Reseach on the impact of the rigid-body motion of the flexible robot mechanism onelastic motion and elastic motion on a rigid body at the same time with an example of a6-DOF robot, to suppress vibration during the process of the machanism running a wide rangeof rigid-body motion, which is based on the completely inverse dynamics analysis. And itprovides clear and powerful evidence for further dynamic analysis and optimization.
4. Solves the initial value compatibility issues from kinematics initial conditions whenanalysing the knowledge of computing multi-body dynamics and kinematics for the model of 6-DOF manipulator; solve the problem of large-scale sparse matrix multiplication for thecomplex multi-body system using generalized coordinates directly, which improvscomputational efficiency; solve the problem of low efficiency from large-scale equation byglobal modeling method for kinematics analysis, and by usual topological method using speedconversion matrix with virtual displacement and acceleration substituted into the equations ofmotion of the system set up by the global modeling method directly; consider elasticdeformation from the impact of the mechanism components and joint of the robot as arigid-flexible coupling body; sovle the intricacy and huge computaion problems fromderivating of the matrix and vector by Newmark and Newton-Raphson method usingmodified Newton-Raphson iteration correction formula for solving nonlinear dynamicsequations.
5. Deduce a mathematical model of the two-phase hybrid stepping motor in the dqcoordinate system, on the theory basis of servo control system simulation and hybrid steppingmotor working principle, and build the6-DOF manipulator open loop simulation controlmodel, which provides a theoretical support for the dynamics/kinematics analysis, and lays afoundation for subsequent collaborative optimization.
6. Research on decomposition&coordination technology, MDO mathematicaltheoretical model, Optimization strategies, and simplify the sensitivity information ofcoupling factors, construct processing system approximation model using global sensitivityequation, and then use optimization algorithm to find the optimal solution for the systemapproximation model till convergence; investigate on searching strategy for MDO space, aswell as its implementation ideas and theories, global sensitivity equation of coupled systembased on the principle of implicit function, satisfaction evaluation analysis for multi-objectivedecision and multi-objective optimization results; propose a combination optimization methodof genetic algorithm with elitist strategy, ATC and Six Sigma, which can improve thereliability and robustness.
1、在对国内外多学科设计优化研究深入分析的基础上，通过对MDO各技术要素的整合，归纳总结出面向复杂机械产品的多学科设计优化技术体系，给出了具有指导意义的应用框架。
2、总结分析了机构的有限元模态分析的数学模型、模态提取方法，采用了基于montecarlo的贝叶斯模型缩减的特征值和特征向量的灵敏度分析方法，并且将网格技术引入到协同设计领域中，从而有效提高优化的执行效率，为协同设计领域中遇到的大型计算问题提供了一种新的解决思路，并且具有很好的扩展性和可移植性。
3、在6自由度机械手的实例基础上，对柔性机器人机构的刚体运动对弹性运动的影响和其弹性运动对刚体的影响的同时进行了研究，以确保机构在大范围刚体运动的同时，尽可能抑制其振动，它是基于完全逆动力学分析的运动控制方法，为进一步的动态分析与优化提供了明确的和强有力的证据。
4、在分析6自由度机械手的多体动力学、运动学学科时，解决了机构运动学初始条件的初值相容性问题；解决了复杂多体系统直接采用广义坐标计算时所面临大规模稀疏矩阵的乘法运算问题，提高了计算效率；解决了运动学分析中，全局法建模所带来的方程规模较大，求解效率低的问题；解决了通常拓扑法采用速度转换矩阵，并且将虚位移和加速度关系式直接代入由全局建模法组建的系统运动方程，运动方程矩阵组装后仍面临大规模稀疏矩阵的乘法运算而同样引起求解效率较低的问题；在分析机械手的动力学特性时，考虑了机构构件及关节弹性变形产生的影响，解决了机械手的构件和关节作为刚柔耦合体的问题；使用修正的Newton-Raphson迭代校正公式求解非线性的动力学方程，解决了一般用Newmark法加Newton-Raphson法求解时需要求矩阵和向量的导数，比较复杂同时计算量也大的问题。
5、在对伺服控制系统的仿真研究背景及对混合式步进电机的工作原理和分析原理研究的基础上，推导了两相混合式步进电动机在动坐标系下的数学模型，并根据此建立了6自由度机械手的开环仿真控制模型，为动力学/运动学的分析提供了理论支持，并为后续的协同优化设计奠定了基础。
6、研究了6自由度机械手系统的分解协调技术；MDO的数学模型；优化求解策略，并且利用了全局灵敏度方程，对耦合因素的灵敏度信息进行了简化处理，构造了系统近似模型，然后运用优化算法寻找系统近似模型的最优解，直至收敛；多学科协同设计优化空间的搜索策略，以及多学科设计优化算法的实施思想和理论；耦合系统的基于隐函数原理推导出的全局灵敏度方程；对多目标决策及多目标优化结果的满意评价分析；结合遗传算法、ATC、六西格玛的主要特点，提出了一种基于带精英策略的遗传算法的结合ATC和六西格玛的可提高可靠性和鲁棒性的优化方法。
Product design is an intricated process, which involves multiple disciplines, and multiplesubsystems. Multidisciplinary design optimization(MDO) is a system optimization method，itexplorts the synergistic effects generated by the mutual coupling between the variousdisciplines or subsystems, to obtain the overall optimal solution, and to shorten the designcycle, which is an effective way to solve complex mechatronic system design. It has beendeveloped rapidly and widely over the past two decades in the field of aerospace, but has juststarted in the research field of complex engineering mechanical systems. This paper studiesthe issues of improved genetic algorithm with elitist strategy, design co-optimization withAnalytical Target Cascading (ATC), and product reliability analysis and optimal design underuncertainty. Co-optimization model is set up based on the Six Sigma design method,improved genetic algorithm and ATC, and is verified with a6-DOF manipulator as anexample. And main work in this paper is as following:
1. Sum up and put forward a technology system of optimal design for complexmechanical product based on the indepth study achievements made at home and abroad, andon the basis of integration of the technical elements of the MDO, which gives an applicationframework of significance.
2. Summarize and analyze the mathematical model of finite element modal analysis,modal extraction method, using the sensitivity analysis method combined with reducedeigenvalues and eigenvectors from Bayesian model based on monte carlo, and introducesGrid technology into the field of collaborative design, so as to improve the efficiency of theimplementation of the tasks effectively, and shorten the product development cycle. Itprovides a new solution for large-scale computation encountered in the field of collaborativedesign, and has a very good expansibility and portability.
3. Reseach on the impact of the rigid-body motion of the flexible robot mechanism onelastic motion and elastic motion on a rigid body at the same time with an example of a6-DOF robot, to suppress vibration during the process of the machanism running a wide rangeof rigid-body motion, which is based on the completely inverse dynamics analysis. And itprovides clear and powerful evidence for further dynamic analysis and optimization.
4. Solves the initial value compatibility issues from kinematics initial conditions whenanalysing the knowledge of computing multi-body dynamics and kinematics for the model of 6-DOF manipulator; solve the problem of large-scale sparse matrix multiplication for thecomplex multi-body system using generalized coordinates directly, which improvscomputational efficiency; solve the problem of low efficiency from large-scale equation byglobal modeling method for kinematics analysis, and by usual topological method using speedconversion matrix with virtual displacement and acceleration substituted into the equations ofmotion of the system set up by the global modeling method directly; consider elasticdeformation from the impact of the mechanism components and joint of the robot as arigid-flexible coupling body; sovle the intricacy and huge computaion problems fromderivating of the matrix and vector by Newmark and Newton-Raphson method usingmodified Newton-Raphson iteration correction formula for solving nonlinear dynamicsequations.
5. Deduce a mathematical model of the two-phase hybrid stepping motor in the dqcoordinate system, on the theory basis of servo control system simulation and hybrid steppingmotor working principle, and build the6-DOF manipulator open loop simulation controlmodel, which provides a theoretical support for the dynamics/kinematics analysis, and lays afoundation for subsequent collaborative optimization.
6. Research on decomposition&coordination technology, MDO mathematicaltheoretical model, Optimization strategies, and simplify the sensitivity information ofcoupling factors, construct processing system approximation model using global sensitivityequation, and then use optimization algorithm to find the optimal solution for the systemapproximation model till convergence; investigate on searching strategy for MDO space, aswell as its implementation ideas and theories, global sensitivity equation of coupled systembased on the principle of implicit function, satisfaction evaluation analysis for multi-objectivedecision and multi-objective optimization results; propose a combination optimization methodof genetic algorithm with elitist strategy, ATC and Six Sigma, which can improve thereliability and robustness.
引文
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