摘要
基于负平方形式的加工成本-公差函数和田口质量损失函数,用方和根法建立装配精度约束条件,分别对两种公差优化数学模型采用拉格朗日方法进行求解:第一种模型仅以制造成本最小为目标;第二种模型以制造与质量损失的总成本最小为目标.分析了装配精度约束条件在以上两种公差优化模型求解过程中的作用:第一种模型的目标函数随着公差的增大而减小,因此装配精度必定为有效约束条件;第二种模型的目标函数未必随着公差的增大而减小,因此装配精度约束不一定是有效约束条件.推导了第二种模型在装配精度约束条件有效和无效两种情况下公差的解析最优解,并用实例验证了所提出方法的有效性.
Taking the reciprocal squared manufacturing cost-tolerance function and Taguchi quality loss function into con- sideration, two tolerance optimization mathematical models were built using the Lagrange Multiplier method, while the root sum square method was used to establish assembly constraint conditions. The objective of the first model was the minimiza- tion of manufacturing cost, and the objective of the second model was the minimum sum of manufacturing cost and quality loss cost. Researches were conducted to determine the effectiveness of the assembly constraint. In the first model, the objec- tive function decreased with the increase of component tolerance, and the assembly constraint condition was effective. In the second model, the objective function did not necessarily decrease with the increase of component tolerance, and the assembly constraint condition was not necessarily effective, either. Based on this analytical method, the optimum component tolerance obtained with the effectiveness of the assembly constraint conditions being considered. An example was presented to demon- strate the effectiveness of the proposed method.
出处
《天津科技大学学报》
CAS
2013年第5期70-74,共5页
Journal of Tianjin University of Science & Technology
基金
天津科技大学科学研究基金资助项目(20100226)
关键词
公差设计
制造成本
装配约束
解析解
tolerance design
manufacturing cost
assembly constraint
analytical solution
