关于J.Warburton方法的钢丝交叉磨痕体积计算及误差分析

Calculation and Error Analysis of J.Warburton’s Method to Calculate Wear Scar Volumes in Crossed-Wire Fretting

以J.Warburton和R.Bradford的研究为基础,采用数值解的方法分析直线型钢丝接触、直线型钢丝与圆弧型钢丝接触时的磨痕体积和误差。分析显示:当直线型钢丝交叉时,因为被省略的I项是一个负值,所以J.Warburton方法所得到的磨痕体积始终大于数值方法得到的磨痕体积,当磨痕深度达到2.5mm时,J.Warburton方法带来的误差为0.27%,之后随着磨痕深度的增大而急剧增大,当磨痕深度达到5mm时,J.Warburton方法省略I项所带来的误差为1.43%。因此当磨痕深度超过钢丝半径的一半时,J.Warburton方法所带来的体积误差将必须予以考虑。直线型钢丝与圆弧型钢丝接触的磨痕体积由V_(A)和V_(B)两部分来表达,J.Warburton方法总体积计算结果与数值方法相差甚远,最大误差超过10%,同时,反验证得出r^(*)和r_(3)^(*)呈现出截然相反的变化规律,所以r_(3)^(*)参与计算的V_(B)不能反映B磨痕的真实体积。所以,J.Warburton对B磨痕的体积计算方法持怀疑态度是正确的。本研究为计算直线型钢丝接触、直线型钢丝与圆弧型钢丝接触时的磨痕体积和误差分析提供理论依据。

Based on the research of J.Warburton and R.Bradford,the numerical solution method to analyze the fretting wear scar volume and error of crossed steel wires.The analysis shows that when two straight wires cross,because the omitted I term is a nega⁃tive value,the fretting wear scar volume obtained by Warburton’s method is larger than that obtained by the numerical method.The error in the previous method is 0.27%at a wear scar depth of 2.5mm,and increases sharply with increasing depth;The error is 1.43%when the depth reaches 5mm.This error must be considered when the depth of the wear scar exceeds half the radius of the wire.The fretting wear scar volume of a linear wire and circular arc-wire contains two parts.The total volume calculated with the Warburton’s method is far from that calculated with the numerical method,and the maximum error is more than 10%.Two radii of curvature show opposite trends,which means the equation for one portion of the volume in the previous research cannot reflect the true volume.Therefore,skepticism exists about that volume calculation.This study provides a theoretical basis for calculating wear scar volume and for error analysis when linear steel wires cross,or when a linear wire and circular arc wire are in contact.