磨损套管抗内压强度的通用计算模型  

A general calculation model for wear casing burst strength

作　　者：陈占锋[1,2] 朱卫平[1,2] 狄勤丰[1,2] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072 [2]上海大学上海市力学在能源工程中的应用重点实验室,上海200072

出　　处：《应用力学学报》2015年第6期967-972 1101,1101,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51174130);上海市优秀学术带头人项目(12XD1402500);上海市部分地方院校能力建设重点项目(12160500200)

摘　　要：将承受内外压的偏心筒模型作为磨损套管的计算模型,以磨损引起的磨损率(偏心率)为磨损指标,根据弹塑性力学理论和Tresca强度理论,利用双极坐标系和应力函数法,得到偏心筒应力解析解和套管抗内压强度通用计算公式。结果表明:套管抗内压强度对磨损率较为敏感,随着磨损率的增大,套管抗内压强度减小;月牙形、槽形磨损套管的抗内压强度也可按本文公式计算,所得计算结果与现有的实验、理论、ISO10400标准、弹塑性有限元法结果相比,相对误差的平均值最大不超过7%。An eccentric cylinder model subjected to internal and external pressure is taken as the calculation model of worn casings, and the wear ratio(eccentricity caused by wearing) is regarded as the wear indicator. The analytical solution of stresses for the eccentric cylinder, as well as a general burst strength calculation formula, is obtained by using the stress function method in a bipolar coordinate system according to the principle of elastic-plastic mechanics and Tresca strength theory. Calculated results indicate that the strength of internally pressurized casing is sensitive to the eccentricity caused by wearing. The strength of casing without wear is equal to that in zero-eccentricity in the present model, and with the wear ratio increased by 10%, the strength will be decreased by about 10%. In addition, the strength of casing worn in a crescent or slot cross-section may also be calculated by the present model. Results by the present model are extensively compared with those of related existing experiments, ISO10400 standard formula, previous theoretical model and elastic-plastic finite element method, the maximum value of all average relative errors is less than 7%.

关 键 词：套管磨损 双极坐标系 Tresca强度理论 抗内压强度 解析解 应力函数法 

分 类 号：O343[理学—固体力学] TE931.2[理学—力学]