铜材三个力学性能指标的概率分布研究  

Probability Distribution of Three Mechanical Properties of Copper

作　　者：杨帆[1] 华滨 陈帆[1] 陈刚[1] 刘兵[1] 张红卫[1] 刘小宁[1] Yang Fan;Hua Bin;Chen Fan;Chen Gang;Liu Bing;Zhang Hongwei;Liu Xiaoning(School of Mechanical Engineering,Wuhan Vocational College of Software and Engineering,Wuhan 430205,Hubei)

机构地区：[1]武汉软件工程职业学院机械工程学院,湖北武汉430205

出　　处：《武汉工程职业技术学院学报》2022年第4期25-31,共7页Journal of Wuhan Engineering Institute

基　　金：武汉市知识创新专项曙光计划项目(2022010801020439)。

摘　　要：应用概率论与数理统计知识,建立了单个试验数据有效性与两组试验数据同质性的分析模型;基于两个企业关于TP2铜材三个力学性能指标的90个试验数据,对其抗拉强度、维氏硬度与延伸率的概率分布进行了探索,得到如下结论。1)双侧置信度为98%时,两个企业关于TP2铜材抗拉强度试验数据具有有效性与同质性;显著度为0.05时,抗拉强度是基本符合正态分布的随机变量;抗拉强度在双侧置信度为98%时的均值不小于236.1 MPa且不大于240.1 MPa,标准差不小于3.411 MPa且不大于6.361 MPa。2)双侧置信度为98%时,两个企业关于TP2铜材维氏硬度试验数据分别具有有效性,但不具有同质性;显著度为0.05时,两个企业得到的维氏硬度指标分别是基本符合正态分布的随机变量,但是分布参数不同;在双侧置信度为98%时,一个企业得到的维氏硬度的均值不小于51.18且不大于54.82,标准差不小于1.795且不大于4.489;另一个企业得到的维氏硬度的均值不小于47.56且不大于51.84,标准差不小于2.114且不大于5.287。3)双侧置信度为98%时,两个企业关于TP2铜材延伸率试验数据具有有效性与同质性,但是在显著度为0.05时的分析表明,延伸率的概率分布与生产企业存在较大的关系,应具体问题具体分析。The analysis model of the validity of single test data and the homogeneity of two groups of test data is established on the basis of probability theory and mathematical statistics.Based on 90 test data of three mechanical properties of TP2 copper from two enterprises,the probability distribution of tensile strength,Vickers hardness and elongation was explored,and therefore the following conclusions were obtained.1)When the bilateral confidence is 98%,the tensile strength test data of TP2 copper are effective and homogeneous;When the significance is 0.05,the tensile strength is a random variable basically conforming to normal distribution.The mean value of tensile strength is between 236.1 MPa and 240.1 MPa,and the standard deviation is between 3.411 MPa and 6.361 MPa when the bilateral confidence is 98%.2)When the two-sided confidence is 98%,the Vickers hardness test data of TP2 copper are respectively valid,but not homogeneous;When the significance is 0.05,the Vickers hardness indexes obtained by the two enterprises are random variables basically conforming to normal distribution,but the distribution parameters are different.When the two-sided confidence is 98%,the mean value of Vickers hardness obtained by an enterprise is no less than 51.18 and no more than 54.82,and the standard deviation is between 1.795 and 4.489.The mean of Vickers hardness obtained by another firm is no less than 47.56 and no more than 51.84,and the standard deviation is within 2.114 and 5.287.3)When the bilateral confidence is 98%,the test data of TP2 copper elongation of the two enterprises are valid and homogeneous,but the analysis when the significance is 0.05 shows that the probability distribution of the elongation is closely related to different manufacturers,so it should be analyzed on a case-specific basis.

关 键 词：TP2铜材 抗拉强度 维氏硬度 延伸率 概率分布 试验数据 有效性与同质性 

分 类 号：TH142.3[一般工业技术—材料科学与工程]