Impact of Surface Roughness on Pantograph-Catenary Current Collection Quality

In the pantograph-catenary system, the change of the surface roughness of pantograph sliding plate directly affects the current collection quality of electric locomotive. In this paper, a large number of current-carrying friction experiments have been carried out on the self-developed high-performance sliding electric contact experimental machine, and the effects of the surface roughness of the sliding friction pair on important performance parameters have been studied, including pantograph-catenary contact resistance (<inline-formula> <tex-math notation="LaTeX">$R_{j}$ </tex-math></inline-formula>), current carrying efficiency (<inline-formula> <tex-math notation="LaTeX">$\eta$ </tex-math></inline-formula>), current collection stability (<inline-formula> <tex-math notation="LaTeX">$\delta$ </tex-math></inline-formula>) and the friction coefficient (<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>). Further, the current conduction mechanism is revealed by the microscopic approach. In order to quantitatively reveal the effect of roughness on each evaluation index of current collecting performance, the paper formulates the functional relationship between <inline-formula> <tex-math notation="LaTeX">$R_{a}$ </tex-math></inline-formula> (arithmetic mean height of contour) and <inline-formula> <tex-math notation="LaTeX">$R_{j}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> by nonlinear fitting. On this basis, a comprehensive evaluation equation is established by the entropy weight method, and then the optimal <inline-formula> <tex-math notation="LaTeX">$R_{a}$ </tex-math></inline-formula> value is derived for the best pantograph-catenary current collecting performance. The experimental results show that with the increase of the surface roughness <inline-formula> <tex-math notation="LaTeX">$R_{a}$ </tex-math></inline-formula> of the sliding plate, <inline-formula> <tex-math notation="LaTeX">$R_{j}$ </tex-math></inline-formula> decreases first and then increases, while <inline-formula> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula> increases first and then decreases, <inline-formula> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula> increases monotonically, and <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> gradually increases. The optimal pantograph-catenary current collection condition can be achieved by reconciliation of these indices. The research results of this paper provide a theoretical basis for improving the current collection quality of pantograph-catenary systems, and is useful for material selection or new type design of pantograph sliding plates.

tric energy transmission of electric locomotive. In the cur- 23 rent collection process, changes of the surface roughness 24 of the sliding plate will greatly change the contact state 25 between the sliding friction pairs, which directly affects the 26 power transmission quality of the high-speed railway, and 27 The associate editor coordinating the review of this manuscript and approving it for publication was Harikrishnan Ramiah . also shortens the service life of sliding plates. Appropriate 28 roughness will reduce friction loss and the contact resis-29 tance between friction pairs, and improve the current collec-30 tion efficiency and stability of pantograph-catenary systems. 31 Therefore, it is important to study the impact of surface 32 roughness of sliding friction pairs on the current collection 33 performance of pantograph-catenary systems and determine 34 the optimal roughness value. 35 In recent decades, domestic and foreign scholars have 36 conducted a lot of research work on how to improve the cur-37 rent collection quality of pantograph-catenary systems from 38 the two aspects of experimental simulation and simulation 39 resistance by proposing the concept of similarity index. How-96 ever, these documents have not comprehensively considered 97 the influence of roughness on the current collection indicators 98 of pantograph-catenary systems. 99 According to the existing literature, the research on the cur-100 rent collection characteristics of pantograph-catenary mainly 101 focuses on the macro experimental conditions, while the 102 research on the roughness characteristics of friction pair 103 materials is relatively few, and the optimal roughness value is 104 not given. In this paper, a large number of experiments have 105 been carried out to clarify the variation rule between the sur-106 face roughness of the pantograph sliding plate and the current 107 collection evaluation indexes, reveal the current transmission 108 mechanism from the microscopic approach. And on this 109 basis, a comprehensive evaluation equation is established, 110 and the optimal roughness value is obtained, under which the 111 current collection performance is the best.

112
The paper consists of four sections. The definition of exper-113 imental system, experimental scheme and evaluation indexes 114 are introduced in Section II. In Section III, the variation rules 115 of different roughness parameters and evaluation indexes are 116 discussed, and nonlinear fitting of the experimental results 117 is performed. In Section IV, the comprehensive evaluation 118 equation of pantograph-catenary current collection quality is 119 established by using entropy weight method, and the optimal 120 roughness value for best current collection performance is 121 calculated by using mathematical method. Finally, Section V 122 concludes this paper.

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A. SLIDING ELECTRIC CONTACT EXPERIMENTAL SYSTEM 125 A high-performance pantograph-catenary sliding electric 126 contact experimental machine developed by the research 127 group is used to carry out the current carrying friction experi-128 ment. The structural diagram of the experimental system is 129 shown in FIGURE 1. In order to adjust the contact pres-130 sure F N between sliding friction pairs and truly simulate the 131 ''zigzag'' trajectory of pantograph -catenary in actual opera-132 tion, the experimental machine is equipped with horizontal 133 and vertical sliding platforms. In addition, the size of the 134      plate, is selected in the Geometric Product Specification 172 (GPS) ISO4287-1997 standard as a characteristic parameter 173 to measure the surface roughness of sliding friction pairs. 174 R a value not only reflects the change of surface roughness 175 of friction pairs, but also contains important information 176 related to pantograph-catenary current collection character-177 istics. As shown in FIGURE 2: R a is the average arithmetic 178 deviation from the contour curve to the least square centerline 179 within the sampling length l, which can be calculated by 180 formula (1). Its unit is µm.
where Z i is the distance from a point on the evaluation curve 183 to the center line. It can be seen that the larger the R a value 184 is, the rougher the surface of the sliding plate is.

185
In the experiment, the surface roughness R a of the sliding 186 plate is directly measured by SJ-210 roughness measuring 187 instrument (the accuracy is 0.001um, and the actual measured 188 contour measurement curve is shown in FIGURE 3). The 189 temperature rise of the sliding plate surface is obtained by 190 real-time measurement and average of the whole experiment 191 with FLIRT530 infrared thermal imager.

192
In the process of electric energy transmission of high-193 speed railway, contact resistance, current carrying efficiency, 194 current receiving stability and friction coefficient are the 195 key indicators to measure the current receiving quality of 196 pantograph-catenary system. They directly reflect the quality 197 of electric contact performance between friction pairs and 198 VOLUME 10, 2022 pantograph-catenary system. Therefore, it is very necessary 200 to study the influence of surface roughness of sliding friction 201 pair on these four current receiving indexes.

202
The contact resistance value R j is the averaged value com-203 puted from instantaneous voltage and current values mea-204 sured by the data acquisition card, according to Ohm's law. 205 Its value directly reflects the electrical contact performance 206 between friction pairs [20], and it is the key factor affecting 207 the current collection condition of pantograph-catenary sys-208 tems.

209
Current carrying efficiency of pantograph-catenary η is the 210 ratio of the averaged dynamic current carrying value I to the 211 static given current I S , calculated from formula (2) [21].
The relative stability of contact current between sliding 214 friction pairs is denoted by the relative stability coefficient δ 215 of contact current, and its calculation formula is shown in (3).
where S I is the standard deviation of dynamic contact current.

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The higher the value of δ, the better the current collection 219 stability of the pantograph-catenary system.

220
The friction coefficient µ is indirectly calculated by mea-221 suring the torque of the disc table of the experimental 222 machine, and its calculation formula is derived as follows [5]:   change trend of the four fitting curves, with the increase of 246 the roughness value R a , the contact resistance first decreases 247 and then increases, which is approximate to the ''V'' shape 248 change trend. When R a = 6 µm, R j reaches the minimum 249 of about 0.54 . Among the four fitting curves, the fitting 250  On the other hand, according to the G-W statistical contact 273 model, the total conductivity G of the expected contact of the 274 friction pair is [22]: where N is the total number of micro convex bodies of the 277 friction pair, ρ is the resistivity, β is the radius of curvature 278 of the micro convex body, d is the distance between the two 279 reference planes, φ(z) is the probability density of the distri-280 bution of the surface micro convex body, and z is the height 281 expected to contact any rough body; When other conditions 282 remain unchanged, the increase of R a and the effect of plate 283 temperature rise will affect ρ and z in the model, so that the 284 contact resistance first decreases and then increases with the 285 increase of roughness R a .

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FIGURE 6 shows the relationship between the current carry-289 ing efficiency of pantograph-catenary systems and the surface 290 roughness R a of sliding plate. According to the distribution 291 of experimental data and the change trend of fitting curve, 292 it can be seen that with the increase of roughness R a , η first 293 increase and then decrease. And in the whole experimental 294 range, when R a is about 4.55 µm, the maximum value of η 295 obtained is 0.884. Then with the increase of R a , η gradually 296 decreases. According to the nonlinear curve fitting results, the 297 cubic polynomial has the highest goodness of fit, which can 298 better reflect the relationship between R a and η.

299
This is because the contact resistance is one of the key fac-300 tors affecting the current carrying efficiency of pantograph-301 catenary systems. When the roughness R a is small, the contact 302 resistance gradually decreases, and the deviation of dynamic 303 current from the static given current also decreases, and 304 hence the current carrying efficiency increases. When R a > 305 5 µm, the contact state of the friction pair surface becomes 306 worse, the number of micro convex body actually participat-307 ing in the current conduction on the plate surface decreases, 308 thus the current receiving area decreases. At the same time, 309 R a > 6 µm, the gradual increase of contact resistance also 310 makes the pantograph-catenary current collection efficiency 311 gradually reduce. As can be seen in FIGURE 7, the experimental data are rela-315 tively concentrated, and the overall change trend is obvious. 316 With the increase of roughness R a , the value of δ also gradu-317 ally increases, and the pantograph-catenary current collection 318 stability becomes worse. According to the fitting results of the 319 four curves, the goodness of fit of the exponential function 320 is the highest and the sum of squares of the residuals is the 321 smallest, δ varies approximately as an exponential function of 322 R a . That is, the increase of the surface roughness of the sliding 323 friction pair makes the current collection stability coefficient 324 VOLUME 10, 2022 smaller the curvature radius of the micro convex body is, and the worse the contact state of the friction pair is. The friction 363 factor is composed of three parts: the deformation component 364 µ d of the surface asperities, the plowing component µ p by 365 wear particles and hard asperities, and the adhesion compo-366 nent µ a of the flat portions of the sliding surface [23]. When 367 R a is small, the deformation component µ d of the micro 368 convex body is also small. According to the experimental 369 results, with the increase of roughness R a , due to the reduction 370 of shear resistance of micro convex body, the abrasive wear 371 and adhesion wear on the sliding plate surface are serious, 372 and the plowing component µ p increases, which makes the 373 friction coefficient gradually increase with the increase of 374 roughness R a on the sliding plate surface.

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After obtaining 59 sets of experimental data, this paper uti-378 lizes the entropy weight method to obtain the weight coeffi-379 cients of the relative changes of each current collection eval-380 uation index under different roughness conditions, and then 381 η, δ, µ and R a , so as to establish a comprehensive evaluation 382 equation of pantograph-catenary current collection. Entropy weight method is an objective weighting method 386 based on the dispersion degree of data itself. It calculates 387 the corresponding information entropy according to the vari-388 ation degree of each characteristic index, and then obtains 389 the entropy weight of R j , η, δ, µ, which is used to make 390 corrections to get more objective index weights. That is, the 391 more scattered the data, the smaller the entropy, the more 392 information contained in the index, and the greater the weight. 393 The specific calculation process of entropy weight method is 394 shown in FIGURE 10.

395
In order to eliminate the unit differences among the indica-396 tors, the data need to be processed forward. Because R j , δ and 397 µ are reverse indicators, reverse processing is required. Here 398 η is a positive indicator and needs to be processed in a positive 399 way. The calculation formula of positive standardization of 400 data is shown in formula (6).  where Zij is the data after the normalization of the i-th sample 410 where d j is the information utility value of each index.
where F(R a ) is the comprehensive evaluation index. Since all 446 evaluation indexes are standardized as positive, the larger the 447 value of F(R a ), it means that under this roughness condition, 448 the contact resistance and friction coefficient are smaller, and 449 the current carrying efficiency and current collection stability 450 are better, that is, the overall current collection condition of 451 pantograph-catenary system is better. Therefore, within the 452 experimental range, the R a value that maximizes F(R a ) is the 453 optimal roughness value.  According to the calculation method of derivative in math-461 ematics (the calculation formula is shown in formula (11)), 462 the roughness parameter R a = 5.86 µm, F(R a ) reaches 463 the maximum value, that is, the pantograph-catenary current 464 collection condition is the best at this time.