基于最小范数原理的夹紧力优化设计算法  被引量:5

An Optimal Method to Clamping Force Determination Based on the Minimum Norm Principle

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作  者:秦国华[1,2] 张卫红[2] 

机构地区:[1]南昌航空大学航空与机械工程学院,江西南昌330063 [2]西北工业大学中法并行工程联合实验室,陕西西安710072

出  处:《中北大学学报(自然科学版)》2011年第4期442-447,共6页Journal of North University of China(Natural Science Edition)

基  金:航空科学基金资助项目(2006ZE56006);中国博士后科学基金资助项目(20070411142);国家自然科学基金资助项目(10676028);江西省教育厅科学技术基金资助项目(2007-172);南昌航空大学博士启动基金资助项目(EA200503139)

摘  要:合理地确定夹紧力是夹具设计过程极为重要的环节,为此对工件处于稳定状态的约束条件进行了系统研究,提出了夹紧力的优化设计算法.首先,基于螺旋理论建立了工件稳定性模型.其次,基于最小范数原理,提出了夹紧力的优化设计模型.在摩擦锥线性转化以及变量非负转换的基础上,提出了夹紧力的优化设计松弛为线性规划问题的求解方法.最后,以典型的"3-2-1"定位方案为例,分析了其夹紧力优化设计的全过程.分析结果表明:基于最小范数原理的夹紧力优化算法简便易行,实验数据可靠,不但改变了一般工艺中夹具设计的经验性方法,而且也丰富了夹具设计的基础理论.It is important to determine the clamping forces correctly in the fixture design task.Therefore,constraint conditions of the workpiece stability were systematically investigated.Simultaneously,the optimal algorithm of clamping forces was proposed.Firstly,the mathematical model of workpiece stability was established on the basis of the screw theory.Secondly,the optimization of clamping forces was formulated according to the minimum norm principle.Based on the linear approximation of the friction cone and non-negative variable transformation,the solution technology was proposed by slacking the optimization of clamping forces into the constrained linear programming problem.Finally,took example for the typical "3-2-1" locating scheme,the optimal design procedure of clamping forces was illustrated.The analytical results show that the minimum norm principle based algorithm to clamping force optimization is effective and feasible,and the experimental data are verified to be reliable.The proposed method not only changes the experiential approach to fixture design in the traditional process planning,but also enriches the basic theory of fixture design.

关 键 词:最小范数原理 摩擦锥 线性规划 夹紧力 

分 类 号:TG75[金属学及工艺—刀具与模具]

 

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