Friction and Wear Performance of Pantograph-Catenary System in Electrified Railways: State of the Art
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摘要:
针对电气化铁路弓网正常和异常状态的接触副，分析受电弓滑板磨耗周期内的摩擦磨损性能差异性，特别是受电弓滑板的磨耗率和磨耗型面的差异性，包括：发生异常磨损时受电弓滑板磨损率数倍甚至数十倍的增长差异，以及局部偏磨、波浪型磨耗和贯穿性凹坑等磨耗型面差异；着重归纳不同弓网系统载流摩擦磨损试验台的特点及异同，总结磨耗检测接触式测量方法与非接触式测量方法的优劣；分析弓网系统结构及参数、列车运行参数、弓网系统载流参数及外界环境等因素的影响，归纳总结弓网载流摩擦磨损特性的演变规律. 在此基础上，综合分析弓网系统磨耗机理分析模型和数据拟合模型的研究现状和进展，并给出弓网系统载流摩擦磨损性能在后续研究中所需重点关注的研究方向和发展趋势，包括：弓网摩擦副的真实服役工况在实验室条件下的等效模拟；弓网磨耗性能的在线高精度检测；复杂气候条件及多物理场耦合作用下弓网磨耗性能的仿真和优化；结合大数据和智能算法的弓网磨耗预测，以及智能运维策略和全生命周期的能力保持技术等.
Abstract:For pantograph-catenary contact pairs in electrified railways operating in normal and abnormal states, the friction and wear performance of pantograph strip differentiates in a wear cycle, highlighted by differences in wear rate and wear profile. When abnormal wear occurs, the wear rate of pantograph strip will have a multifold increase or even dozens of times increase, but the wear profile acts differently, revealing partial eccentric wear, wavy wear, and penetrating wear. The similarities and differences in current-carrying friction and wear platforms are summarized for pantograph-catenary systems, as well as the advantages and disadvantages of contact and non-contact detection methods. The influential factors and evolution law are analyzed in view of the structure and parameters, train operation parameters, current-carrying parameters and external environment of pantograph-catenary system. Following above work, the state of the art of pantograph-catenary wear models, including mechanism analysis model and data fitting model, are analyzed extensively, and the prospective direction and development trend are put forward, such as, the equivalent simulation of a pantograph-catenary friction pair in real service under laboratory conditions, online high-precision detection of pantograph-catenary wear performance, simulation and optimization of pantograph-catenary wear performance in complex climatic conditions and multi-physical field coupling, pantograph-catenary wear prediction using big data and intelligent algorithms, intelligent operation and maintenance strategies, and capability maintenance in the whole life cycle.
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纤维增强复合材料（FRP）轻质、高强，且热膨胀系数与混凝土相近，可与混凝土变形协调，具有裁剪不易松散变形、易于浸溃、施工便捷等优点[1-2]. 超高性能混凝土（UHPC）是一种高强、高韧和高耐久性的新型水泥基复合材料，具有优异的力学性能和耐久性[3-4]. 用FRP侧向约束UHPC，可以充分发挥UHPC和FRP的优点，提高核心UHPC的强度和变形能力[5].
Lam等[6]对18个FRP约束UHPC短柱进行了轴压试验研究发现，在FRP约束下UHPC短柱的极限强度和应变显著提高. Guler[7]对碳纤维增强复合材料（CFRP）、玻璃纤维增强复合材料（GFRP）和芳纶纤维增强复合材料（AFRP）约束UHPC圆柱进行了轴向加载，并对不同纤维增强复合材料对UHPC圆柱极限强度和应变的提升程度做了对比分析. Wang等[8]对FRP约束UHPC的轴压性能进行研究，并比较FRP对UHPC、高强混凝土和普通混凝土约束性能，结果表明，由于FRP约束的UHPC具有超高强度和独特的微观结构，比FRP约束的NSC和HSC表现出更多的脆性. 邓宗才等[9-10]对FRP约束UHPC圆柱进行轴心抗压试验，结果表明，约束比和侧向约束刚度是影响试件极限强度和极限应变的关键参数，FRP的约束作用对核心UHPC的强度和延性具有提高效果. 黄美珍[11]基于细观力学方法对UHPC本构模型受钢纤维掺量的影响进行研究发现，适量的钢纤维能够显著提高UHPC的峰值应变与轴心抗压强度. 田会文等[12]利用LS-DYNA建立FRP约束UHPC圆柱细观有限元模型，研究FRP厚度、纤维缠绕角度和钢纤维体积掺量对其轴压性能的影响，结果表明，FRP显著提高核心UHPC的极限强度和延性.
目前，国内外对FRP约束UHPC圆形短柱轴心受压力学性能的研究大多都是基于FRP层数、混凝土强度等变量的研究，对钢纤维影响短柱轴压性能的研究相对较少. 同时，现有研究多集中于单一变量对短柱轴压性能的影响，对多个变量耦合作用的研究较少，且缺少多个变量下短柱轴压性能的对比分析. 此外，现有研究中对FRP约束UHPC本构模型的理论分析也有待深入.
为此，本文以FRP层数、FRP种类和钢纤维体积掺量为变量，研究FRP约束UHPC圆形短柱的轴压性能及变量的影响规律；并在考虑钢纤维体积掺量的影响下，提出FRP约束UHPC圆形短柱抗压强度和极限应变的计算模型，并进一步给出FRP约束UHPC的本构模型.
1. 试验方案
1.1 试件设计
试验共设计制作21组FRP约束UHPC圆形短柱和3组UHPC圆形短柱，所有试件的高度均为200 mm，直径均为100 mm. 试件编号见表1，表中：首字母“P”代表无约束试件，“G”表示GFRP约束UHPC圆形短柱，“C”表示CFRP约束UHPC圆形短柱，N为试件的峰值荷载；ɛy为试件的轴向极限应变.
表 1 试件编号及试验结果Table 1. Specimen numbering and experimental results试件
编号钢纤维掺量/% FRP 层数/层 N/kN ɛy 试件
编号钢纤维掺量/% FRP 层数/层 N/kN ɛy P1 1 805.0 0.0024 G32 3 2 1392.2 0.0088 P2 2 874.2 0.0029 G33 3 3 1511.9 0.0120 P3 3 917.3 0.0029 G34 3 4 1657.5 0.0148 G11 1 1 1197.1 0.0044 C11 1 1 1312.9 0.0056 G12 1 2 1318.1 0.0063 C12 1 2 1546.4 0.0087 G13 1 3 1409.6 0.0082 C13 1 3 1787.3 0.0138 G14 1 4 1532.8 0.0106 C21 2 1 1336.0 0.0073 G21 2 1 1239.3 0.0061 C22 2 2 1675.7 0.0125 G22 2 2 1351.6 0.0080 C23 2 3 1931.9 0.0176 G23 2 3 1469.5 0.0109 C31 3 1 1375.4 0.0084 G24 2 4 1620.4 0.0136 C32 3 2 1696.8 0.0145 G31 3 1 1283.1 0.0075 C33 3 3 2065.1 0.0210 1.2 材料性能
UHPC的配合比见表2. 根据T/CECS864−2021《超高性能混凝土试验方法标准》[13]对UHPC进行抗压强度试验，试件制作时浇筑3组边长为100 mm、钢纤维体积掺量分别为1%、2%和3%的UHPC立方体，立方体的尺寸符合GB/T 50081—2016《普通混凝土拌合物性能试验方法标准》[14]的有关规定. 测得3组立方体的平均抗压强度分别为129.2、144.5、153.3 MPa. FRP力学性能指标见表3.
表 2 UHPC的配合比Table 2. Mix proportion of UHPCkg/m3 名称 水胶比 水泥 硅灰 石英砂 粉煤灰 配合比 0.15 1.00 0.32 1.46 0.30 表 3 FRP的性能指标Table 3. Performance index of FRP型号 抗拉强度/MPa 弹性模量/GPa 伸长率/% GFRP 2381 114 2.7 CFRP 3961 240 1.8 1.3 加载方案及测点布置
试验采用的加载设备为200 t压力试验机，如图1. 加载前，应先进行预压，以保证试件轴心受压，并对位移传感器和应变片进行检查和校正；正式加载时，加载速率控制为1.5 kN/s；当荷载达到试件计算强度的90%时，加载速率控制为0.5 kN/s；直到试件破坏后，卸载.
试件应变测点的布置如图2所示，在试件的中部布置4个轴向应变片测量其轴向应变，并将4个环向应变片垂直于轴向应变片布置，用以测量试件的环向应变. 此外，轴向位移通过固定装置两侧的位移传感器获得，荷载由数据采集系统自动采集.
2. 试验结果及分析
2.1 试件破坏特征
2.1.1 GFRP约束UHPC的破坏特征
GFRP约束UHPC圆形短柱的破坏形态如 图3（a）～（d）所示. 在加载初期，试件变形微小，导致GFRP未对其产生约束作用；随着荷载的增加，GFRP发出噼啪裂开的声音；当荷载接近极限强度的90%时，UHPC圆形短柱中部的GFRP逐渐断裂；当试件加载至极限强度时，爆裂声响加剧，试件中部的GFRP断裂频率加快，直至整节断裂，试件破坏.
2.1.2 CFRP约束UHPC的破坏特征
CFRP约束UHPC圆形短柱的破坏形态如图3（e）～（h）所示. 在加载初期，试件无明显变形，CFRP未对其产生约束作用；随着荷载的逐步增加，偶尔听到CFRP破裂的声音，且UHPC圆形短柱中部开始膨胀，CFRP对其约束力也逐渐增强；直至荷载达到试件极限强度的90%时，试样发生显著变形，CFRP从拐角处逐渐断裂，开始与UHPC圆形短柱剥离；当试件加载至极限强度时，CFRP发出爆响，随即被拉断，试件强度急剧下降，此时，UHPC圆形短柱表面产生纵向裂缝，且裂缝贯通至整个试件，轴向应变和环向应变迅速增大，试件破坏.
由图3可知，随着FRP层数增加，其断裂面积逐渐减小. 钢纤维沿裂缝面被拔出，但由于钢纤维在UHPC内部多向分布，发挥了桥接作用，有效阻止了混凝土内部裂缝的扩大和延伸，因此，试件内部的UHPC并没有完全破碎. 钢纤维能够在一定程度上改善FRP约束UHPC圆形短柱的脆性破坏.
2.2 荷载-应变曲线
图4为FRP约束UHPC圆形短柱的荷载-应变曲线（应变大于0为轴向应变，小于0为环向应变）. 从图中可以看出，荷载-轴向应变曲线可分为3个阶段：在加载初期，各试件荷载-应变曲线的变化趋势基本相同，此时试件变形较小，FRP对UHPC圆形短柱产生的约束作用不明显，约束试件的荷载-轴向应变曲线与未约束试件的相似，均呈线性增长；随着荷载的进一步增大，UHPC圆形短柱中部开始膨胀，FRP产生的约束应力随之增加，试件的强度不断提高，此阶段的约束应力不断变化，试件的曲线呈非线性发展；在加载后期，FRP对UHPC圆形短柱的约束应力达到极限，试件的荷载-轴向应变曲线基本呈水平发展趋势，该阶段为试件的强化阶段，对比发现，FRP提高了UHPC圆形短柱的强度和变形能力.
FRP约束UHPC圆形短柱的荷载-环向应变曲线同样可分为3个阶段：在初期加载阶段，其与荷载-轴向应变曲线相似，FRP基本没有对试件产生明显的约束作用，曲线呈线性增长趋势，同时，各约束试件在此阶段的荷载-环向应变曲线基本重合，未受到FRP层数的影响；随着荷载的增加，约束试件的中部开始膨胀，环向应变的增长速率加快，同时，UHPC圆形短柱承受较大荷载，FRP的约束力不断增加，此阶段约束试件的荷载-环向应变曲线呈非线性增长；随着荷载的持续增加，FRP的约束应力达到极限，环向应变迅速增大，直至试件破坏.
2.3 荷载-应变曲线影响因素分析
2.3.1 约束比
定义FRP对UHPC圆形短柱的约束应力与无约束UHPC圆形短柱抗压强度的比值为约束比[10]. 不同约束比下试件的承载及变形性能如表1和图4所示. 可以看出：试件C12、C22和C32的极限强度相较于C11、C21和C31分别提高了17.8%、25.4%和23.4%，极限应变分别提高了55.4%、71.2%和72.6%；试件G12、G22和G32的极限强度相较于G11、G21和G31分别提高了10.1%、9.1%和8.5%，极限应变分别提高了43.2%、31.1%和17.3%. 由此可得，随着FRP层数的增加，试件的轴向极限强度和极限应变均得到提高，但极限应变的提高幅度更加明显.
钢纤维体积掺量为1%时，被1层、2层和3层CFRP缠绕包裹的UHPC圆形短柱的极限强度比同条件下的GFRP缠绕包裹的分别提高了9.7%、7.8%和7.2%；钢纤维体积掺量为2%时，上述条件下试件的极限强度分别提高了17.3%、24%和21.9%，极限应变分别提高了38.1%、56.3%和64.8%. 可以看出，CFRP对UHPC圆形短柱极限强度和极限应变的改善程度要明显优于GFRP. 此外，FRP层数和种类的改变实质上反映的是约束应力的改变，由此可见，约束比是影响试件荷载-应变曲线的关键因素.
2.3.2 钢纤维体积掺量
不同钢纤维掺量下试件的极限强度及变形性能如表1和图4所示. 由不同钢纤维体积掺量下FRP约束UHPC圆形短柱的荷载-轴向应变曲线可知：随着钢纤维体积掺量的增加，荷载-轴向应变曲线在加载前期并没有受到影响；但在加载后期，试件的极限强度及极限应变均有一定幅度的提高. 而根据试件的荷载-环向应变曲线发现：钢纤维体积掺量为2%和3%时，试件在相同荷载下的环向应变明显比钢纤维体积掺量为1%的试件小，说明钢纤维的体积掺量越大，核心混凝土的极限强度和延性越大. 由此可知，随着加载荷载的增加，钢纤维在UHPC圆形短柱中产生了防止其自身横向膨胀的纤维约束力，在加载后期明显抑制了UHPC圆形短柱的横向变形；且钢纤维体积掺量越大，产生的约束作用越强.
3. FRP约束UHPC的本构模型
3.1 受力机理
在加载初期，FRP材料并未产生明显的约束作用. 随着荷载的持续增加，UHPC圆形短柱在受压状态下内部逐渐出现微裂纹，试件的变形逐渐增大并产生侧向膨胀，环向应变迅速增长，此时外包FRP开始参与工作，对核心混凝土提供有效约束，使核心混凝土处于三向受力状态，并限制其裂缝的产生和发展. 随着荷载继续增加，混凝土进入裂缝扩展阶段，其内部裂缝及侧向变形快速增大，FRP产生的约束应力不断提高，直至其达到极限抗拉强度，发生断裂，此时FRP约束UHPC圆形短柱的轴压荷载达到峰值. FRP约束UHPC圆形短柱受力状态如图5所示，图中：$ {{f}}_{{\rm{ccc}}}、{{f}}_{{\rm{coc}}} $（$ {{\varepsilon }_{{\rm{ccc}}}}、{{\varepsilon }_{{\rm{coc}}}}$）分别为约束试件、非约束试件的峰值应力（极限应变），${\sigma _{\rm{r}}}$为径向应力，$\sigma $为短柱的轴向应力，$\varepsilon $为短柱的环向应变.
3.2 抗压强度和极限应变计算公式
根据已有研究[15-16]可知，FRP是高性能单向材料，抗拉不抗压，因此在理论分析时仅考虑FRP的环向抗拉强度. 当FRP达到其极限抗拉强度时，将不会再对混凝土产生约束作用[17]，FRP约束UHPC圆形短柱时，其侧向受力均匀连续，如图6所示. 图中：ff为FRP的极限抗拉强度，θ 为约束力方向与x轴之间夹角的大小.
根据平衡原理积分可得侧向约束力为
∫π0d/2flsinθdθ=2fft， (1) 式中：fl为FRP对UHPC的约束力，如式（2）；d为UHPC 圆形短柱的直径；t为FRP的总厚度.
fl=2fft/d. (2) 考虑到钢纤维对UHPC圆形短柱轴压性能的影响，引入纤维约束力，如式（3）.
flf=α1Vflfdfτbond, (3) 式中：${\alpha _1}$为纤维影响系数，取值参考文献[18]；Vf为钢纤维掺量；lf为钢纤维的长度；df为钢纤维的直径；τbond为基体黏结强度.
通过改变试件的约束比及钢纤维体积掺量，研究其对试件峰值参数的影响，各试件的峰值荷载及其对应的轴向极限应变如表1所示. 以试件约束比（fL/fco，其中：fL为FRP约束力fl与钢纤维约束力flf之和，fco为非约束柱的极限强度）为控制因素，通过对试验数据进行回归分析，得到FRP约束UHPC峰值应力及峰值应变拟合曲线，如图7所示.
图7中：y=（fccc/fcoc）−1，x=fL/fcoc，代入方程最终得FRP约束UHPC的极限抗压强度计算公式，如式（4）；y1=（ɛccc/ɛcoc）−1，代入方程得到极限应变的计算公式，如式（5）.
fccc/fcoc=1+2.45(fL/fcoc)0.92, (4) εccc/εcoc=1+21.75(fL/fcoc)1.62. (5) 3.3 计算值与试验值对比分析
为更好地验证所提出模型的合理性，收集文献[10,19-20]中的试验数据进行验证. 表4为文献中FRP约束UHPC柱极限强度及峰值应变的计算值与试验值的对比，其中，fcc和ɛcc分别为极限强度和极限应变的试验值.
表 4 试件极限强度和极限应变计算值与试验值对比Table 4. Comparison between calculated and test results of ultimate strength and ultimate strain of specimens参考文献 试件编号 Vf/% fcc/MPa ɛcc fccc/MPa ɛccc fccc/fcc ɛccc/ɛcc 文献[10] 2 130.7 0.0078 175.2 0.0082 1.340 1.047 2 180.8 0.0116 217.2 0.0155 1.201 1.332 2 148.8 0.0073 185.3 0.0097 1.245 1.325 2 162.3 0.0094 211.1 0.0102 1.301 1.085 2 156.5 0.0065 172.7 0.0078 1.103 1.202 2 191.4 0.0104 211.8 0.0144 1.107 1.382 文献[19] 2 226.6 0.0086 264.8 0.0075 1.168 0.874 2 273.5 0.0106 281.8 0.0090 1.030 0.853 2 298.9 0.0115 298.2 0.0107 0.998 0.934 2 254.1 0.0068 267.4 0.0077 1.052 1.138 2 372.2 0.0105 319.7 0.0133 0.859 1.263 文献[20] UHPC-1C 1 168.0 0.0068 178.1 0.0057 1.060 0.836 UHPC-2C 1 180.8 0.0073 194.2 0.0071 1.074 0.970 UHPC-3G 1 171.5 0.0076 195.0 0.0072 1.137 0.942 UHPC-5G 1 182.0 0.0073 214.5 0.0094 1.178 1.291 通过上述计算方法所得极限强度计算值与试验值比值的平均值与标准差分别为1.124和0.123，极限应变计算值与试验值比值的平均值与标准差分别为1.098和0.191，这表明计算方法得到的极限应力、极限应变的计算值与试验值较为吻合，考虑钢纤维体积掺量影响后所得的计算公式能够较好地预测FRP约束UHPC的峰值应力和应变.
3.4 本构模型
通过对已有模型分析，选用Mander[21]本构方程作为FRP约束UHPC圆形短柱的主动约束模型，将fcc和ɛcc代入Mander[21]本构方程，以此得到FRP约束UHPC的本构模型，如式（6）所示.
σ=fccxcr/(r−1+xrc)， (6) 式中：xc = ɛc/ɛcc，ɛc为约束柱的轴向应变；r =Ec/（Ec−Esec），Esec为约束柱达到极限强度时的割线模量，Esec =fcc/ɛcc，Ec为UHPC的弹性模量.
从21个约束试件中选取6个试件，分别采用Lam模型[22]、Zohrevand模型[19]、邓宗才模型[10]和本文建立的模型，计算得到相应的应力-应变全过程曲线，与试验结果进行对比，如图8所示.
图8中：曲线的前期阶段，所有模型与试验结果无较大差异，后期阶段则差异化明显. 综合对比下，本文建立的模型与试验结果吻合程度较好.
4. 结 论
1） 随着FRP层数的增加，UHPC圆形短柱的极限抗压强度和极限应变均提高，但极限应变的提高幅度更加明显. 试件C12、C22和C32的极限强度相较于试件C11、C21和C31分别提高了17.8%、25.4%和23.4%，极限应变分别提高了55.4%、71.2%和72.6%；试件G12、G22和G32的极限强度相较于试件G11、G21和G31分别提高了10.1%、9.1%和8.5%，极限应变分别提高了43.2%、31.1%和17.3%.
2） 钢纤维可在一定程度上改善FRP约束UHPC圆形短柱的脆性特征；适量的钢纤维还可提高试件的极限抗压强度与极限应变. 试件C31的极限强度和极限应变比试件C21（C11）的分别提高了2.9%和15.1%（4.7%和50.0%）.
3） 相同层数及钢纤维体积掺量下，CFRP对UHPC圆形短柱极限抗压强度和极限应变的提升幅度比GFRP更高. 试件C11、C12和C13的极限应变分别比试件G11、G12和G13的提高了27.3%、19.7%和12.0%.
4） 分析了FRP约束UHPC圆形短柱的受力机理，在考虑钢纤维体对UHPC约束的影响下，提出了FRP约束UHPC圆形短柱抗压强度和极限应变的计算模型，并进一步给出了FRP约束UHPC的本构模型，计算结果与试验结果吻合较好.
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图 1 销-盘式弓网载流摩擦磨损试验台
Figure 1. Pin-disc pantograph-catenary current-carrying friction and wear test bench
图 2 高速弓网载流摩擦磨损试验台
Figure 2. High-speed current-carrying pantograph-catenary test bench for friction and wear
图 8 弓网系统摩擦磨损性能的影响因素
Figure 8. Influence factors of friction and wear performance in pantograph-catenary system
图 13 接触线拉出值波浪形分布及滑板磨耗型面
Figure 13. Waveform distribution of stagger and wear profile of strip
图 12 接触线拉出值正态分布及滑板磨耗型面
Figure 12. Normal distribution of stagger and wear profile of strip
图 14 弓网运行参数对磨耗性能的影响关系
Figure 14. Influence of pantograph-catenary operation parameters on wear performance
图 18 受电弓滑板磨耗性能预测流程
Figure 18. Process of predicting wear performance for pantograph strip
表 1 滑板材料分类及优劣
Table 1. Classification, advantages and disadvantages of strip materials
滑板种类 优点 缺点 纯金属滑板 机械强度高、导电性能好、使用寿命长、成本低、取材方便、引发故障率低 对导线磨损严重，易与导线发生黏着效应、耐高温性能差、易熔融 粉末冶金滑板 机械强度较好、表面硬度适中、抗冲击性能、导电性能良好 对导线磨损严重 纯碳滑板 对导线磨耗小、较强的自润滑性能和减磨性能、电磁噪声小、耐高温 机械强度低、抗冲击性能差、易磨损、发生断裂和掉块 浸金属碳滑板 机械强度高、耐冲击、导热性能好、与导线接触电阻小、耐磨、使用寿命长、耐电弧烧蚀 抗冲击性能差、易掉块、维护成本高 复合材料滑板 良好的自润滑性、抗冲击性和抗折强度 易发生导电性能恶化、生产周期长，成本高 
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表 2 常见滑板的主要技术参数
Table 2. Main technical parameters of strip
滑 板 体积密度/
（g·cm−3）硬度 电阻率/
（μΩ·m）冲击韧性/
（J·cm−2）抗拉/抗折
强度/MPa抗压强度/MPa 磨损率/
（mm·万公里−1）粉末冶金
滑板（铁基）＜8.0 HBS≤140 ≤0.35 ≥7.00 抗拉≥140 ≥290 ≤9.0 粉末冶金
滑板（铜基）7.8～8.2 HBS：60～90 ≤0.35 ≥7.00 抗拉≥120 — ≤12.0 浸金属滑板 ≤3.0 HS≥85 ≤12.00 ≥0.25 抗折≥85 ≥280 ≤13.0 碳滑板 ≤1.8 HS：60～100 ≤40.00 ≥0.10 抗折≥30 ≥40 ≤12.0
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表 3 预测模型对比
Table 3. Comparison of prediction models
模型类型 优点 缺点 机理分析模型 精度较高、可通过实时数据对磨耗量实时预测 各影响因素贡献度量化较困难；机理分析阶段对设备精度要求较高 数据拟合模型 通过较短期试验量化各影响因素，且可保证较好的精度 拟合所需数据量较大；线路应用较困难
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