牵引计算(2023完美版)

专业综合实践设计题目：SS4型电力机车牵引计算学院：电气学院班级：姓名：学号：指导教师：【摘要】根据列车牵引计算的基本理论，严格按照《列车牵引计算规程》，利用手工计算和计算机编程绘图两种方式完成了列车计算坡道、牵引重量、列车换算制动率、运行时间和运行速度的计算，以及运行合力曲线图、运行速度和时间曲线图的绘制。其中计算机绘图计算部分中的绘图程序均用Matlab完成，列车运行时间和运行距离的计算程序均应用手工计算。【关键字】列车牵引制动计算1、引言随着教学改革的深入和培养铁道电气化应用人才的需要，在电力机车专业学习计划中，为了增强我们对电力机车进一步的了解，以及加强以往学习模式的改革和创新，《电力机车牵引计算》被广泛应用和推广。“牵引计算”涉及到课程的理论内容需要大量的力学知识，如牵引力的形成与计算、制动力的形成与计算、列车阻力的形成与计算、列车运行速度和时间的计算等，整合了过去的理论力学和列车牵引计算。这次课程设计使我们加强了对《电力机车牵引计算》的理论认识，熟悉了电力机车的计算标准，严格按照《列车牵引计算规程》。此次课程设计不仅注重联系实际，而且注重培养学生的能力。设计题目2.1课程设计目的在学习机车车辆基本理论的基础上，通过这一环节巩固和实践所学的主干专业课程。2.2课程设计要求认真分析课程设计的题目、具体任务，以及所给出的设计条件、根据所学理论计算和确定列车牵引质量、运行速度、运行时间、绘制合力曲线等。2.3课程设计题目描述1、已知条件SS4型电力机车牵引特性曲线：SS4型电力机车电阻制动特性曲线：SS4型电力机车牵引计算主要数据：2、列车阻力计算，给出列车阻力计算公式。所谓列车阻力，是指列车运行时作用在列车上阻止列车运行并且不能用人力操控的外力，用大写W表示，单位为N或KN。作用在电力机车和车辆上的阻力分别为机车阻力和车辆阻力。显然W=+(KN)按照引起列车阻力的原因，列车阻力可分为两大类：（1）基本阻力——列车在任何情况下运行都存在的阻力。用代表阻力的字母右下角加角标“0”来表示，如分别表示列车，电力机车，车辆的基本阻力。（2）附加阻力——列车在某些特殊情况下运行时除基本阻力外所增加的阻力，如坡道阻力等。试验表明，作业在机车车辆上的阻力都与其重量成正比，所以牵引计算中常用单位重量的阻力，称为单位阻力，以小写字母w表示，单位为N或KN，因此有机车单位阻力：(N/KN)车辆单位阻力：(N/KN)列车单位阻力：(N/KN)发生的阻力，分为起动阻力Rs，运行阻力Rr，坡道阻力Rg，曲线阻力Rc和隧道阻力Rt。（1）起动阻力所谓起动阻力是由车轴和轴承直接接触导致的摩擦阻力引起的，车辆或者列车在平坦直线的道路上起动所受到的阻力。（2.5）在这里，Rs：出发阻力（N），rs：出发阻力（N/t），W：列车质量（t）。起动阻力的值根据轴承的种类有所不同，每吨29N左右，受到轴承构造和气温等的影响，在起动后速度到1km/h后急剧减少。0~3km/h是出发阻力的领域，之后进入走行阻力领域。这些关系如下图所示:图2.5起动阻力和运行阻力（2）运行阻力所谓运行阻力是指列车在平坦直线轨道上行走时受到的阻力，如后面所描述的那样，可用公式(2.6)表示。构成因素包括：和速度无关的轴承部分的摩擦阻力（公式(2.6)a项）；和速度成正比的车轮和钢轨之间的摩擦阻力（公式(2.6)的b项）；和速度的平方成正比的空气阻力（公式(2.6)的c项）。其中a项，b项和列车质量成正比。另外，随着速度加快，c项的空气阻力变大，空气阻力分为列车前方受到的前面阻力，由于列车后部的空气变得稀薄而形成的后部阻力，编组车辆间的涡流形成的车间阻力和由车辆侧面与空气摩擦形成的侧面阻力，根据车辆的形状，断面积，连结辆数和接触面的状态而变化。由于运行阻力的因素特别复杂且相互关联，所以根据走行试验的结果一般如以下公式所示，各数值根据不同车辆而定。运行阻力一般分为隧道外阻力和隧道内阻力。（2.6）这里，Rt：走行阻力(N)，v：走行速度(km/h),a,b,c：常数，W：列车质量(t).（3）坡道阻力坡道阻力是列车或车辆在斜坡上的时候，因重力的分力形成的往斜坡下方拉的作用力，以上坡度为正，下坡度为负。图2.6坡道阻力图2.3中，因为△ABC和△abc是三个角相等的相似三角形，对应边的长度相等，所以.(2.7)通常用BC/AC表示坡度，即tanθ，因为铁路线路的坡度角度θ非常小，所以如果AB=BC，则（θ=2°，即34.9‰以内可视为同一值）。另外，铁路路线中用10/1000这样的千分率表示BC/AC的坡度，表示为10‰。设坡度为g/1000,动轮上质量为W（t），坡度阻力Rg（N）如以下公式所示，每吨的坡道阻力可用千分率表示为坡度值。（2.8）3、 牵引计算基本原理，简要给出编程用到的牵引计算公式。（1）列车总牵引力：所有动车的轮周牵引力之和。（2）制动力：所有参与制动的轮周制动力之和。（3）牵引电机转矩τ（N∙m）和转速n（rpm），列车速度v（km/h）和车轮在踏面上的总轮周牵引力Fp（kN），与总轮周制动力Fb(kN)有如下的关系：（2.1）（2.2）（2.3）D：车轮直径（m），G：齿轮传动比，N：牵引电动机台数，：齿轮的传动效率。列车的总牵引功率P（kW）是速度和轮周牵引力的乘积，如公式（2.4）所示：（2.4）（1）牵引制动特性曲线：图2.1牵引与制动特性曲线（2）线路条件：表1线路坡度数据编号起点里程终点里程坡度(‰)坡长(m)限速(km/h)201.6016004031.62.175.15704042.173.0248508053.023.75.168073.74.14-4.8440104.145.035890115.035.561.6530135.566.901340156.97.69-3.6790177.698.94-2.41250198.949.550610229.5510.39-2.58402310.3911.36-3.89702511.3612.34-0.79802612.3412.950.66102812.9513.95-2.910003013.9514.7908403114.7915.7-0.69103415.717-0.31300371718-1.11000401819.71.117004319.721.5-318004421.522.7-0.112004722.723.650.39505023.6525.70.120505125.726.7-0.510005326.727.9-0.512005527.928.9-0.710005628.931-12100573132.25-1.212506032.2533.93-0.516806133.9334.7-2.27706334.735.9-1.812006435.937-0.81100673737.9909906937.9938.65-16607238.6540.10.714507340.140.55-1.54507440.5541.55-0.210007741.5543.2016508043.244.51.513008444.545.850.713508745.854701150914748.750.51750409548.7550.701950402.4课程设计的具体任务（1）计算牵引质量、校验并确定区段牵引质量；计算列车换算制动率等。（2）编制合力表，绘制合力曲线。（3）化简线路纵断面的运行时间及制动距离等。（4）绘制列车运行速度线和列车运行时间线。（5）编制点算程序计算，并计算及绘图，编程语言不限。3、总体设计速度控制策略3.1选定计算坡道，计算牵引重量（含校验）3.1.1限制坡道的确定根据本题所给线路情况，在该牵引区段内坡度为8.5‰，长度为2600m的坡度，是是牵引重量受限制的坡道（限制坡道内）。3.1.2牵引重量的计算用均衡速度法计算牵引重量：列车在任何一个区间运行，总会遇到一些长短不等、坡度不一的坡道。在所有的坡道内，总有一个是最难通过的，而列车的最大牵引重量往往是被这个最难通过的上坡道限制的。如果该坡道具备计算坡道的特征，就可以用均衡速度法计算牵引重量选定计算坡道为8.5‰且对于SS4型电力机车有=100Km/h，=127KN则：=1.02+0.0035v+0.000320=1.02+0.0035*100+0.000320*5.60(N/KN)=1.82+0.0100*v+0.000145*=1.61+0.0040*100+0.000187*3.88(N/KN)又因为=8.5‰，P=863.28KN所以牵引重量为G===8247.323（KN）由计算牵引重量可将客车按以下方式编组：机车牵引客车质量4800t。3.1.3牵引重量校验由于牵引重量已假设为，现只需对其进行校验。按起动地段的破多么验算牵引重量：根据提意及电力机车牵引的滚动轴承货物列车演算公式易得===16278.81（KN）显然大于G，所以按限制坡道计算出来的牵引重量在车站能够可靠启动。3.2计算列车制动率标记重55t装有GK型制动机的客车车辆，盘形制动装置，中磨合成闸片（装有踏面制动单元）每辆车换算闸瓦压力重车为250KNSS4型电力机车每台换算闸瓦压力为280KN。=16*250+280=4280（KN）则列车换算制动率为：===0.4513.3编制合力表，绘制合力曲线3.3.1合力计算表在绘制列车单位合力曲线图时，要先编制单位合力曲线图。在已知电力机车类型，数量及编挂情况，牵引重量，以及列车换算制动率的机车上，易得列车在牵引，惰性，制动三种工况下所受到的单位合力，如表3.1所示：表3.1SS4型电力机车合力计算表计算条件：ss4型电力机车，P=184t，QUOTE=0.2，QUOTE=70km/h运行工况栏数速度（km*QUOTE）项目0102028.73036.74041.2475057.46070牵引1F（kN）541.5541.5505.3486.1474.2363.0224.6204.0149.12QUOTE=0.6F（kN）324.9324.9303.2291.5284.55217.8134.8122.489.534QUOTE=2.27+0.00156QUOTE（N/kN)2.432.432.893.553.674.374.774.925.586.177.417.899.915QUOTE=PQUOTE(kN)17.1617.1620.4125.0725.9230.8733.6934.7539.4143.5852.3355.7370.006C=QUOTE-QUOTE=（2）-（5)(kN)307.75307.75282.76265.75250.86183.0582.4566.6719.507C=QUOTE43.5743.5740.0337.6235.5225.9211.679.442.76惰行8QUOTE=QUOTE2.432.432.892.923.674.374.775.586.177.899.91常用制动9QUOTE=0.358+QUOTE0.3580.3370.3200.3070.2960.2860.2780.271510b=1000QUOTE(N/kN)71.667.46461.459.257.255.654.311c=QUOTE+0.5b(N/kN)38.2336.1334.8934.3734.3734.7735.6937.06电阻制动12QUOTE(kN)0167.8333.5482.7376.7482.7374.7321.813QUOTE=QUOTE(kN)023.7647.2268.3453.3368.3453.0545.5614c=QUOTE+0.9QUOTE(kN)2.4323.8145.3864.4352.3761.5147.7450.913.3.2合力曲线根据合力计算表中的数据，运用Matlab编程绘制合力曲线如图3.1至3.5。图3.1牵引运行合力曲线图图3.2惰性运行合力曲线图图3.3常用制动合力曲线图图3.4电阻制动合力图图3.5合力曲线图以上各工况合力曲线绘制，是通过所给数据点拟合出的关于速度的高阶函数，这种方法简单易行，且计算准确，避免了认为绘图带来的较大误差。各工况单独绘制时，图形比较直观，当几种工况绘制在一张坐标纸上时由于比例缩小，显得略有畸变，但不会影响计算精度。3.4线路纵断面化简（运行时间、制动距离等）为使区间内坡道数目减少，试凑工作量降低，需在满足一定化简要求下对线路进行化简。之后再利用合力曲线和线路化简纵断面进行运行时间的解算。制动距离：已知制动初速=80km/h，=0km/h。换算摩擦系数按平均速度50km/h计算=0.443电力机车单位基本阻力按SS4型机车计算=1.02+0.0035*50+0.000320*=1.995（N/kN）客车车辆单位基本阻力公式计算=0.92+0.0048v+0.000125=2.81（N/kN）则==2.73（N/kN）（1）加算坡度千分数紧急制动时有效制动距离=79.68m空走距离=3.5（S）=60.326m制动距离=79.68+60.326=140.006m（2）加算坡度千分数紧急制动时有效制动距离=131.35m空走距离=1.9（S）=42.256m制动距离=131.35+42.256=173.606m（3）加算坡度千分数紧急制动时有效制动距离=157.91m空走距离=2.86（S）=70.76m制动距离=157.91+70.76=228.67m（4）加算坡度千分数紧急制动时有效制动距离=214.760m空走距离=4.06（S）=112.868m制动距离=214.760+112.868=327.628m（5）加算坡度千分数紧急制动时有效制动距离=220.44m空走距离=4.46（S）=123.988m制动距离=220.44+123.998=344.438m（6）加算坡度千分数紧急制动时有效制动距离=207.287m空走距离=3.5（S）=97.3m制动距离=207.287=344.438m加算坡度千分数‰028.5-7-120紧急制动距离（m）140174713281243053.5计算及绘制列车运行速度和运行时间线第一坡段ij=0,L=1600m牵引工况V:010km/hv=5km/h对应r=7.93N/KNS010km/h=4.17(10-0)/7.93=53mt==0.63minV:1020km/hv=15km/h对应r=6.96N/KNS1020km/h=4.17(20-10)/6.96=180m=233mt==0.72min=1.35minV:2030km/hv=25km/h对应r=6.33N/KNS2030km/h=4.17(30-20)/6.33=329m=562mt==0.79min=2.14minV:3036km/hv=33km/h对应r=6.08N/KNS3630km/h=4.17(36-30)/6.08=272m=834mt==0.49min=2.63minV:3640km/hv=38km/h对应r=6.05N/KNS3640km/h=4.17(40-36)/6.05=210m=1044mt==0.33min=2.96min此时速度已经达到40km/h，但是还没走完这个区段，然后惰行V:4038km/hv=39km/h对应r=-1.36N/KNS4038km/h=4.17(40-38)/1.36=478m=1522mt==0.74min=3.7min此时快要出坡须试凑牵引工况V:3839km/hv=38.5km/h对应r=6.06N/KNS4850km/h=4.17(50-48)/6.06=70m=1592mt==0.08mint=3.78min相差8米，在误差范围内，可以接受，进入下一坡段第二坡段ij=5.1,L=570m,惰行工况V:3925km/hv=32km/h对应r=-1.26-5.1=-6.36N/KNS3925km/h=4.17(39-25)/6.36=587m=2179mt==1.10min=4.88min偏差9米，在可接受范围之内第三坡段ij=4,L=850m牵引工况V:2532km/hv=28.5km/h对应r=7.43-4=3.43N/KNS2532km/h=4.17(32-25)/3.43=485m=2664mt==1.02min=5.9minV:3235km/hv=33.5km/h对应r=6.06-4=2.06N/KNS3235km/h=4.17(35-32)/2.06=407m=3071mt==0.73min=6.63min偏差在可接受的范围内，拼凑成功第四坡段ij=5.1,L=680m,牵引工况V:3537km/hv=36km/h对应r=6.05-5.1=0.95N/KNS3537km/h=4.17(37-35)/0.95=632m=3703mt==1.05min=7.68min第五坡段ij=-4.8,L=440m牵引工况V:3743km/hv=40km/h对应r=5.83+4.8=10.63N/KNS3743km/h=4.17(43-37)/10.63=188m==3891mt==0.28min=7.96minV:4349km/hv=46km/h对应r=5.69+4.8=10.49N/KNS4349km/h=4.17(49-43)/10.49=219m==4110mt==0.29min=8.25min偏差在可接受的范围内，拼凑成功。第六坡段ij=5,L=890m牵引工况V:4950km/hv=49.5km/h对应r=5.59-5=0.59N/KNS4950km/h=4.17(50-49)/0.59=700m=4810mt==0.85min=9.10min转为惰性工况V:5047km/hv=48.5km/h对应r=-1.52-5=-6.52N/KNS5047km/h=4.17(50-47)/6.52=186m=4996mt==0.23min=9.33min误差34m可以接受试凑成功进入下一坡段第七坡段ij=1.6,L=530m牵引工况V:4751km/hv=49km/h对应r=5.57-1.6=3.97N/KNS7270km/h=4.17(51-47)/3.97=520m=5516mt==0.50min=9.83min误差较小，试凑成功，进入下一坡段第八坡段ij=0,L=1340m牵引工况V:5161km/hv=56km/h对应r=4.30N/KNS5161km/h=4.17(61-51)/4.30=1086m=6602mt==1.16min=10.99minV:6163km/hv=62km/h对应r=3.71N/KNS6163km/h=4.17(63-61)/3.71=279m=6880mt==0.27min=11.26min误差20m，试凑成功，进入下一坡段第九坡段ij=-3.6,L=790m惰行工况V:6365km/hv=64km/h对应r=-1.83+3.6=1.77N/KNS6365km/h=4.17(65-63)/1.77=603m=7483mt==0.56min=11.82min由惰行转为牵引工况V:6567km/hv=66km/h对应r=3.33+3.6=6.93N/KNS6567km/h=4.17(67-65)/6.93=159m=7642mt==0.14min=11.96min误差48m，试凑成功，进入下一坡段第十坡段ij=-2.4,L=1250m惰行工况V:6768km/hv=67.5km/h对应r=-1.92+2.4=0.48N/KNS6768km/h=4.17(68-67)/0.48=1173m=8815mt==1.04min=13.00min由惰行转为牵引工况V:6870km/hv=69km/h对应r=3.04+2.4=5.44N/KNS6870km/h=4.17(70-68)/5.44=211m=9026mt==0.18min=13.18min误差86m，试凑成功，进入下一坡段第十一坡段ij=0,L=610m牵引工况V:7073km/hv=71.5km/h对应r=2.75N/KNS7370km/h=4.17(73-70)/2.75=650m=9676mt==0.55min=13.73min第十二坡段ij=-2.5,L=840m牵引工况V:7379km/hv=76km/h对应r=2.09+2.5=4.59N/KNS7379km/h=4.17(79-73)/4.59=829m=10505mt==0.65min=14.38min第十三坡段ij=-3.8,L=970m制动工况V:7969km/hv=74km/h对应r=-28.28+3.8=-24.48N/KNS7969km/h=4.17(79-69)/24.48=252m=10757mt==0.20min=14.58min转换为惰行工况V:6971km/hv=70km/h对应r=-1.97+3.8=1.83N/KNS6971km/h=4.17(69-71)/1.83=638m=11395mt==0.55min=15.13min误差35m，试凑成功，进入下一坡段第十四坡段ij=-0.7,L=980m惰行工况V:7169km/hv=70km/h对应r=-1.96+0.7=-1.26N/KNS7169km/h=4.17(71-69)/1.26=927m=12322mt==0.79min=15.92min误差18m，试凑成功，进入下一坡段第十五坡段ij=0.6,L=610m牵引工况V:6971km/hv=70km/h对应r=2.86-0.6=2.26N/KNS6971km/h=4.17(71-69)/2.26=517m=12839mt==0.44min=16.36min制动工况V:7166km/hv=68.5km/h对应r=-29.26-0.6=-29.86N/KNS7166km/h=4.17(71-66)/29.86=96m=12935mt==0.08min=16.44min误差15m，试凑成功，进入下一坡段第十六坡段ij=-2.9,L=1000m惰行工况V:6668km/hv=67km/h对应r=-1.86+2.9=1.04N/KNS6668km/h=4.17(68-66)/1.04=1074m=14009mt==0.96min=17.40min误差59m，试凑成功，进入下一坡段第十七坡段ij=0,L=840m牵引工况V:6872km/hv=70km/h对应r=2.86N/KNS6872km/h=4.17(72-68)/2.86=817m=14826mt==0.70min=18.10min误差36m，试凑成功，进入下一坡段第十八坡段ij=-0.6,L=910m惰行工况V:7270km/hv=71km/h对应r=-1.96+0.6=-1.36N/KNS7270km/h=4.17(72-70)/1.36=871m=15697mt==0.74min=18.84min误差3m，试凑成功，进入下一坡段第十九坡段ij=-0.3,L=1300m惰行工况V:7066km/hv=68km/h对应r=-1.97+0.3=-1.67N/KNS7066km/h=4.17(70-66)/1.67=1359m=17056mt==1.20min=20.04min误差56m，试凑成功，进入下一坡段第二十坡段ij=-1.1,L=1000m牵引工况V:6673km/hv=69.5km/h对应r=2.91+1.1=4.01N/KNS6673km/h=4.17(73-66)/4.01=1012m=18068mt==0.87min=20.91min误差68m，试凑成功，进入下一坡段第二十一坡段ij=1.1,L=1700m惰行工况V:7367km/hv=70km/h对应r=-1.99-1.1=-3.09N/KNS7367km/h=4.17(73-67)/3.09=1134m=19202mt==0.97min=21.88min转为牵引工况V:6769km/hv=68km/h对应r=3.09-1.1=1.99N/KNS6769km/h=4.17(69-67)/1.99=570m=19772mt==0.50min=22.38min误差72m，试凑成功，进入下一坡段第二十二坡段ij=-3,L=1800m惰行工况V:6972km/hv=70.5km/h对应r=-1.98+3=1.02N/KNS6972km/h=4.17(72-69)/1.02=1729m=21501mt==1.47min=23.85min误差1m，试凑成功，进入下一坡段第二十三坡段ij=-0.1,L=1200m惰行工况V:7268km/hv=70km/h对应r=-1.99+0.1=-1.89N/KNS7268km/h=4.17(72-68)/1.89=1236m=22737mt==1.06min=24.91min误差37m，试凑成功，进入下一坡段第二十四坡段ij=0.3,L=950m牵引工况V:6872km/hv=70km/h对应r=2.86-0.3=2.56N/KNS6872km/h=4.17(72-68)/2.56=912m=23649mt==0.78min=25.69min误差1m，试凑成功，进入下一坡段第二十五坡段ij=0.1,L=2050m惰行工况V:7266km/hv=69km/h对应r=-1.94-0.1=-2.04N/KNS7266km/h=4.17(72-66)/2.04=1693m=25342mt==1.47min=27.16min转入牵引工况V:6668km/hv=67km/h对应r=3.16-0.1=3.06N/KNS6668km/h=4.17(68-66)/3.06=365m=25707mt==0.33min=27.49min误差7m，试凑成功，进入下一坡段第二十六坡段ij=-0.5,L=1000m第二十七坡段ij=-0.5,L=1200m第二十八坡段ij=-0.7,L=1000m分析该纵断面，26号、27号、28号坡道坡度性质相同，可以考虑将其进行化简根据化简公式，易得*3200=0.5*1000+0.5*1200+0.7*1000=0.56由检查公式进行验算第二十六坡段，通过验算第二十七坡段，通过验算第二十八坡段，通过验算所以这三段坡段可用一个ij=-0.56,L=3200m的等效坡段代替牵引工况V:6878km/hv=73km/h对应r=2.51+0.56=3.07N/KNS6878km/h=4.17(78-68)/3.07=1983m=27690mt==1.63min=29.12min转为惰行工况V:7875km/hv=76.5km/h对应r=-2.13+0.56=-1.57N/KNS7875km/h=4.17(78-75)/1.57=1219m=28909mt==0.96min=30.08min误差9m，试凑成功，进入下一坡段第二十九坡段ij=-1,L=2100m第三十坡段ij=-1.2,L=1250m第三十一坡段ij=-0.5,L=1680m第三十二坡段ij=-2.2,L=770m第三十三坡段ij=-1.8,L=1200m第三十四坡段ij=-0.8,L=1100m分析该纵断面，29号、30号、31号、32号、33号、34号坡道坡度性质相同，可以考虑将其进行化简根据化简公式代入数据，可得=-1.13，由检查公式进行验算第二十九坡段，通过验算第三十坡段，通过验算第三十一坡段，通过验算第三十二坡段，通过验算第三十三坡段，通过验算第三十四坡段，通过验算所以这六段坡段可用一个ij=-1.13,L=8100m的等效坡段代替惰行工况V:7565km/hv=70km/h对应r=-1.97+1.13=-0.84N/KNS7565km/h=4.17(75-65)/0.84=6950m=35859mt==5.95min=36.03min转为牵引工况V:6573km/hv=69km/h对应r=2.98+1.13=4.11N/KNS6573km/h=4.17(73-65)/4.11=1120m=36979mt==0.97min=37.00min误差21m，试凑成功，进入下一坡段第三十五坡段ij=0,L=990m惰行工况V:7371km/hv=72km/h对应r=-2.01N/KNS7371km/h=4.17(73-71)/2.01=597m=37576mt==0.50min=37.50min牵引工况V:7173km/hv=72km/h对应r=2.69N/KNS7173km/h=4.17(73-71)/2.69=446m=38022mt==0.37min=37.87min误差32m，试凑成功，进入下一坡段第三十六坡段ij=-1,L=660m惰行工况V:7372km/hv=72.5km/h对应r=-2.01+1=-1.01N/KNS7372km/h=4.17(73-72)/1.01=599m=38621mt==0.50min=37.37min误差29m，试凑成功，进入下一坡段第三十七坡段ij=0.7,L=1450m惰行工况V:7265km/hv=68.5km/h对应r=-1.95-0.7=-2.65N/KNS7265km/h=4.17(72-65)/2.65=1509m=40130mt==1.32min=38.69min误差30m，试凑成功，进入下一坡段第三十八坡段ij=-1.5,L=450m制动工况V:6561km/hv=63km/h对应r=-30.26+1.5=-28.76N/KNS6561km/h=4.17(65-61)/28.76=73m=40203mt==0.07min=38.76min转为牵引工况V:6165km/hv=63km/h对应r=3.66+1.5=5.16N/KNS6165km/h=4.17(65-61)/5.16=407m=40610mt==0.39min=39.15min误差60m，试凑成功，进入下一坡段第三十九坡段ij=-0.2,L=1000m惰行工况V:6562km/hv=63.5km/h对应r=-1.82+0.2=-1.62N/KNS6562km/h=4.17(65-62)/1.62=981m=41591mt==0.93min=40.08min误差41m，试凑成功，进入下一坡段第四十坡段ij=0,L=1650m惰行工况V:6257km/hv=59.5km/h对应r=-1.73N/KNS6257km/h=4.17(62-57)/1.73=1434m=43025mt==1.45min=41.53min转为制动工况V:5747km/hv=52km/h对应r=-32.34N/KNS5747km/h=4.17(57-47)/32.34=134m=43159mt==0.15min=41.68min误差41m，试凑成功，进入下一坡段第四十一坡段ij=1.5,L=1300m第四十二坡段ij=0.7,L=1350m分析该纵断面，41号、42号坡道坡度性质相同，可以考虑将其进行化简根据化简公式代入数据，可得=1.09，由检查公式进行验算第四十一坡段，通过验算第四十二坡段，通过验算所以这两段坡段可用一个ij=1.09,L=2650m的等效坡段代替惰行工况V:4737km/hv=42km/h对应r=-1.4-1.09=2.49N/KNS4737km/h=4.17(47-347)/2.49=1407m=44566mt==2.01min=43.69min惰行工况V:3727km/hv=32km/h对应r=-1.26-1.09=2.35N/KNS3727km/h=4.17(37-27)/2.49=1136m=45702mt==2.13min=45.82min惰行工况V:2725km/hv=32km/h对应r=-1.18-1.09=2.27N/KNS2725km/h=4.17(27-25)/2.49=191m=45893mt==0.44min=46.26min误差43m，试凑成功，进入下一坡段第四十三坡段ij=0,L=1150m惰行工况V:2518km/hv=21.5km/h对应r=-1.13N/KNS2518km/h=4.17(25-18)/1.13=1111m=47004mt==3.10min=49.36min误差4m，试凑成功，进入下一坡段第四十四坡段ij=0.5,L=1750m惰行工况V:188km/hv=13km/h对应r=-1.05-0.5=-1.55N/KNS188km/h=4.17(18-8)/1.55=699m=47703mt==3.23min=52.59min牵引工况V:818km/hv=13km/h对应r=7.08-0.5=6.58N/KNS818km/h=4.17(18-8)/6.58=165m=47868mt==0.76min=53.35min牵引工况V:1822km/hv=20km/h对应r=6.51-0.5=6.01N/KNS1822km/h=4.17(18-22)/6.01=111m=47979mt==0.33min=53.68min惰行工况V:2214km/hv=18km/h对应r=-1.09-0.5=-1.59N/KNS2214km/h=4.17(22-14)/1.59=755m=48734mt==2.52min=56.20min误差16m，试凑成功，进入下一坡段第四十五坡段ij=0,L=1950m惰行工况V:146km/hv=10km/h对应r=-1.02N/KNS146km/h=4.17(14-6)/1.02=654m=49388mt==3.92min=60.12min转为牵引工况V:614km/hv=10km/h对应r=7.16N/KNS614km/h=4.17(14-6)/7.16=93m=49481mt==0.56min=60.68min转为牵引工况V:1420km/hv=17km/h对应r=6.79N/KNS1420km/h=4.17(20-14)/6.79=125m=49606mt==0.44min=61.12min惰行工况V:2023km/hv=19km/h对应r=-1.10N/KNS2023km/h=4.17(20-18)/1.1=288m=49894mt==0.91min=62.03min制动工况V:188km/hv=13km/h对应r=-42.64N/KNS188km/h=4.17(18-8)/42.64=25m=49919mt==0.91min=62.94min惰行工况V:87km/hv=7.5km/h对应r=-1.01N/KNS87km/h=4.17(8-7)/1.01=62m=49981mt==0.50min=63.44min制动工况V:70km/hv=3.5km/h对应r=-53.14N/KNS70km/h=4.17(7-0)/53.14=4m=49985mt==0.07min=63.51min误差15m，试凑成功，以上运算可以模拟列车到站时速度为0.牵引合力（N/KN）机车总牵引力（N）每段的平均速度（km/h）牵引总功率(kW)行车里程（m）运行时间（min）000007.93387721.80725538.5025126.50.636.96340295.5584151417.898161431.356.33309492.9432252149.25655397.52.146.08297269.6832332724.9720966982.636.05295802.892383122.363869392.960039012833.76.06296291.822438.53168.67643415573.78003201885.54.887.43363275.287228.52875.9293572421.55.906.06296291.822433.52757.1600142867.56.636.05295802.892362958.0289233877.685.83285046.4232403167.1824837977.965.69278201.3976463554.7956364000.58.255.59273312.093649.53758.04128744609.100048.5049039.335.57272334.2328493706.77150252569.834.3210240.072563270.40112605910.993.71181393.1784623123.9936286741.511.26006407181.511.823.33162813.8232662984.9202327562.511.960067.508228.513.003.04148634.8416692848.8344648920.513.182.75134455.8671.52670.442775935113.732.09102186.4536762157.26957610090.514.38007401063114.58007001107615.130070011858.515.922.86139834.0944702718.9962812580.516.360068.501288716.44006701347217.402.86139834.0944702718.9962814417.518.100071015261.518.840068016376.520.042.91142278.746469.52746.7702431756220.91007001863521.883.09151079.4936682853.7237681948722.380070.5020636.523.85007002211924.912.86139834.0944702718.996282319325.690069024495.527.163.16154502.0064672875.45400825524.527.492.51122721.5304732488.51992226698.529.120076.5028299.530.08007003238436.032.98145701.2592692792.6074683641937.000072037277.537.502.69131522.2776722630.4455523779937.870072.5038321.537.370068.5039375.538.690063040166.538.763.66178948.5264633131.59921240406.539.150063.5041100.540.080059.504230841.53005204309241.680042043862.543.69003204513445.820026045797.546.260021.5046448.549.360013047353.552.597.08346162.7232131250.03205647785.553.356.51318293.6904201768.2982847923.553.680018048356.556.20001004906160.127.16350074.166410972.4282449434.560.686.79331983.7416171567.70100249543.561.12001904975062.030013049906.562.94007.504995063.44003.504998363.51运行时间和速度曲线4、算表的Matlab程序4.1合力曲线程序lcclearP=863G=8633V0=100h=0.451V=[0,10,20,30,40,50,60,75,84,90,100]V1=[0,10,20,30,40,50,60,75,84,90,100]F=[230.0,221.7,213.6,205.3,197.1,188.9,180.7,168.3,160.9,156.0,127.0]F1=0.9*FW01=1.02+0.0035*V+0.000426*V.^2W02=1.82+0.01*V+0.000145*V.^2W0=(P*W01+G*W02)/1000R=F1-W0r1=1000*R/(P+G)r2=1000*W0/(P+G)k=0.356.*(3.6.*V1+100)./(14.*V1+100)+0.0007.*(110-V0)b=1000*h*kr3=r2+0.5*bBd=[0,136,136,136,136,136,136,136,122,108.2,98]bd=0.9*1000*Bd/(P+G)w0=[0.0017,0.0019,0.0020,0.0022,0.0024,0.0026,0.0029,0.0032,0.0036,0.0040,0.0044]r4=w0+bdV4=[0,10,20,30,40,50,60,75,84,90,100]plot(V,r1,V,-r2,V,-r3,V4,-r4)gridon运行结果：P=863，G=8633，V0=80，h=0.4510V=01020304050607580V1=01020304050607580F=230.0000221.7000213.6000205.3000197.1000188.9000180.7000168.3000160.9000156.0000127.0000F1=207.0000199.5300192.2400184.7700177.3900170.0100162.6300

151.4700144.8100140.4000114.3000W01=1.02001.09761.26041.50841.84162.26002.76363.67884.31994.78565.6300W02=1.82001.93452.07802.25052.45202.68252.94203.38563.68313.89454.2700W0=16.592317.647819.027120.730322.757425.108427.783332.402935.524437.751241.7216R=190.4077181.8822173.2129164.0397154.6326144.9016134.8467119.0671109.2856102.648872.5784r1=20.051419.153618.240617.274616.284015.259214.200412.538711.508610.80977.6430r2=1.74731.85842.00372.18312.39652.64412.92583.41233.74103.97554.3936k=0.36300.20870.16810.14940.13860.13160.12670.12150.11930.11800.1162b=163.713094.138775.829767.379462.514159.351657.131154.814153.790053.212752.3942r3=83.603848.927839.918635.872833.653632.319931.491430.819330.636030.581830.5907Bd=0136.0000136.0000136.0000136.0000136.0000136.0000136.0000122.0000108.200098.0000bd=012.889612.889612.889612.889612.889612.889612.889611.562810.25489.2881w0=0.00170.00190.00200.00220.00240.00260.00290.00320.00360.00400.0044r4=0.001712.891512.891612.891812.892012.892212.892512.892811.566410.25889.2925V4=01020304050607580901004.2牵引运行合力曲线程序：（matlab）clcclearr1=[20.5,19.15,18.24,17.27,16.28,15.26,14.20,12.71,11.66,10.81,7.64]V=[0,10,20,30,40,50,60,70,80,90,100]plot(V,r1)gridon运行结果:r1=20.5000191.500018.240017.270016.280015.2