合力曲线公开课获奖课件

第四章

合力曲线、运动方程及时分解算1第1页本章重要内容合力曲线图绘制列车运动方程列车速度时分计算(分析法)列车速度时分曲线绘制(图解法)线路纵断面化简2第2页1合力曲线图绘制及应用合力可表达为：牵引运行时C=F-W0＝f1(v)惰行时C=-W0＝f2(v)制动运行时C＝-(W0+B)＝f3(v)作用在列车上合力(N)与列车所受重力(kN)之比称为单位合力，以小写字母c来表达，即:(N/kN)3第3页一、单位合力曲线图绘制把列车在不一样样运行工况单位合力与运行速度变化关系绘成曲线c=f(v)。绘制列车单位合力曲线图，应先编制列车在平直道上单位合力曲线计算表，即列表计算出列车在不一样样速度下相对于牵引、惰行、制动等三种工况时所受到单位合力。4第4页1)关系式牵引运行单位合力(N/kN)惰行时单位合力

(N/kN)常用制动单位合力

(N/kN)5第5页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引123456789惰行10制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制6第6页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.823456789惰行10制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制7第7页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23456789惰行10制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制8第8页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.818456789惰行10制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制9第9页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.87656789惰行10制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制10第10页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.8765w0"=0.92+0.0048v+0.000125v2(N/kN)0.9810.9811.0661.1771.3121.331.3581.4371.4731.5241.6071.6581.8692.1046789惰行10制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制11第11页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.8765w0"=0.92+0.0048v+0.000125v2(N/kN)0.9810.9811.0661.1771.3121.331.3581.4371.4731.5241.6071.6581.8692.1046W0"

=

G·w0"·g×10-3(kN)28.8628.8631.3734.6238.6139.1439.9542.2843.3444.8447.3048.7954.9961.92789惰行10制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制12第12页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.8765w0"=0.92+0.0048v+0.000125v2(N/kN)0.9810.9811.0661.1771.3121.331.3581.4371.4731.5241.6071.6581.8692.1046W0"

=

G·w0"·g×10-3(kN)28.8628.8631.3734.6238.6139.1439.9542.2843.3444.8447.3048.7954.9961.927W0=

W0´+W0"

(kN)32.2132.2135.1138.8343.3843.9844.9147.5548.7550.4653.2554.9461.9669.8089惰行10制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制13第13页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.8765w0"=0.92+0.0048v+0.000125v2(N/kN)0.9810.9811.0661.1771.3121.331.3581.4371.4731.5241.6071.6581.8692.1046W0"

=

G·w0"·g×10-3(kN)28.8628.8631.3734.6238.6139.1439.9542.2843.3444.8447.3048.7954.9961.927W0=

W0´+W0"

(kN)32.2132.2135.1138.8343.3843.9844.9147.5548.7550.4653.2554.9461.9669.808C=Fy-W0(kN)341.5341.5313.6296.6283.9282.7226.2197.9186.7171.7148.9128.772.234.49惰行10制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制14第14页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.8765w0"=0.92+0.0048v+0.000125v2(N/kN)0.9810.9811.0661.1771.3121.331.3581.4371.4731.5241.6071.6581.8692.1046W0"

=

G·w0"·g×10-3(kN)28.8628.8631.3734.6238.6139.1439.9542.2843.3444.8447.3048.7954.9961.927W0=

W0´+W0"

(kN)32.2132.2135.1138.8343.3843.9844.9147.5548.7550.4653.2554.9461.9669.808C=Fy-W0(kN)341.5341.5313.6296.6283.9282.7226.2197.9186.7171.7148.9128.772.234.49c=C×103/[(∑P+G)·g](N/kN)11.0911.0910.199.6359.229.187.346.426.065.574.834.172.341.11惰行10制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制15第15页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.8765w0"=0.92+0.0048v+0.000125v2(N/kN)0.9810.9811.0661.1771.3121.331.3581.4371.4731.5241.6071.6581.8692.1046W0"

=

G·w0"·g×10-3(kN)28.8628.8631.3734.6238.6139.1439.9542.2843.3444.8447.3048.7954.9961.927W0=

W0´+W0"

(kN)32.2132.2135.1138.8343.3843.9844.9147.5548.7550.4653.2554.9461.9669.808C=Fy-W0(kN)341.5341.5313.6296.6283.9282.7226.2197.9186.7171.7148.9128.772.234.49c=C×103/[(∑P+G)·g](N/kN)11.0911.0910.199.6359.229.187.346.426.065.574.834.172.341.11惰行10c=-W0×103/[(∑P+G)·g]=-w0(N/kN)-1.05-1.05-1.14-1.26-1.41-1.43-1.46-1.54-1.58-1.64-1.73-1.78-2.01-2.27制动111213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制16第16页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.8765w0"=0.92+0.0048v+0.000125v2(N/kN)0.9810.9811.0661.1771.3121.331.3581.4371.4731.5241.6071.6581.8692.1046W0"

=

G·w0"·g×10-3(kN)28.8628.8631.3734.6238.6139.1439.9542.2843.3444.8447.3048.7954.9961.927W0=

W0´+W0"

(kN)32.2132.2135.1138.8343.3843.9844.9147.5548.7550.4653.2554.9461.9669.808C=Fy-W0(kN)341.5341.5313.6296.6283.9282.7226.2197.9186.7171.7148.9128.772.234.49c=C×103/[(∑P+G)·g](N/kN)11.0911.0910.199.6359.229.187.346.426.065.574.834.172.341.11惰行10c=-W0×103/[(∑P+G)·g]=-w0(N/kN)-1.05-1.05-1.14-1.26-1.41-1.43-1.46-1.54-1.58-1.64-1.73-1.78-2.01-2.27制动110.3770.2230.1820.1630.1530.1520.1500.1470.1460.1440.1420.1410.1370.1341213SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制17第17页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.8765w0"=0.92+0.0048v+0.000125v2(N/kN)0.9810.9811.0661.1771.3121.331.3581.4371.4731.5241.6071.6581.8692.1046W0"

=

G·w0"·g×10-3(kN)28.8628.8631.3734.6238.6139.1439.9542.2843.3444.8447.3048.7954.9961.927W0=

W0´+W0"

(kN)32.2132.2135.1138.8343.3843.9844.9147.5548.7550.4653.2554.9461.9669.808C=Fy-W0(kN)341.5341.5313.6296.6283.9282.7226.2197.9186.7171.7148.9128.772.234.49c=C×103/[(∑P+G)·g](N/kN)11.0911.0910.199.6359.229.187.346.426.065.574.834.172.341.11惰行10c=-W0×103/[(∑P+G)·g]=-w0(N/kN)-1.05-1.05-1.14-1.26-1.41-1.43-1.46-1.54-1.58-1.64-1.73-1.78-2.01-2.27制动110.3770.2230.1820.1630.1530.1520.1500.1470.1460.1440.1420.1410.1370.13412b=1000φh·

θh(N/kN)105.6062.3751.0045.7542.7342.4542.0641.1240.7740.3239.7139.3938.3737.5813SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制18第18页工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.8765w0"=0.92+0.0048v+0.000125v2(N/kN)0.9810.9811.0661.1771.3121.331.3581.4371.4731.5241.6071.6581.8692.1046W0"

=

G·w0"·g×10-3(kN)28.8628.8631.3734.6238.6139.1439.9542.2843.3444.8447.3048.7954.9961.927W0=

W0´+W0"

(kN)32.2132.2135.1138.8343.3843.9844.9147.5548.7550.4653.2554.9461.9669.808C=Fy-W0(kN)341.5341.5313.6296.6283.9282.7226.2197.9186.7171.7148.9128.772.234.49c=C×103/[(∑P+G)·g](N/kN)11.0911.0910.199.6359.229.187.346.426.065.574.834.172.341.11惰行10c=-W0×103/[(∑P+G)·g]=-w0(N/kN)-1.05-1.05-1.14-1.26-1.41-1.43-1.46-1.54-1.58-1.64-1.73-1.78-2.01-2.27制动110.3770.2230.1820.1630.1530.1520.1500.1470.1460.1440.1420.1410.1370.13412b=1000φh·

θh(N/kN)105.6062.3751.0045.7542.7342.4542.0641.1240.7740.3239.7139.3938.3737.5813c=-(0.5b+w0)(N/kN)-53.8-32.2-26.6-24.1-22.8-22.7-22.5-22.1-22.0-21.8-21.6-21.5-21.2-21.1SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦合力曲线计算措施及绘制19第19页合力曲线图20第20页二、单位合力曲线图应用1)考虑加算坡道影响措施：将速度坐标轴ov向上(ij为正时)或向下(ij为负时)平移ij值(由于wj＝ij)。速度坐标轴平移后，曲线上各点单位合力c值即发生了对应增减。21第21页合力曲线图22第22页2)确定列车在各坡道上均衡速度定义：列车上合力c=0速度称为均衡速度。曲线图23第23页合力曲线图24第24页3)判断列车运动状态由单位合力曲线图分析列车在某种工况和速度时运动状态：加速、减速或匀速。(1)根据合力值判断。(2)根据均衡速度判断。在牵引或惰行工况时，不管什么坡道，列车速度总是趋向于该工况均衡速度。常用制动工况均衡速度v均是很不稳定。25第25页合力曲线图26第26页三、常用制动限速常用制动均衡速度实质上是因制动而受限制最高容许速度，它也是一种制动限速，称为常用制动限速。紧急制动限速：按计算制动距离原则计算紧急停车所容许最高速度。27第27页2列车运动方程根据动能定律：系统动能微分等于作用于该系统合力微功，可以导出列车运动微分方程式。根据动能增量和合力功相等。计算公式：Ek＝mv2/2+∑Iω2/2Wf＝C·S＝C·V·t⊿Ek＝⊿Wf28第28页列车运动方程由动能动量定理可得：dv/dt=120c(km／h2)或dv/dt=2c(km／(h·min))或dv/dt=c/30(km／(h·s))29第29页列车运动方程又：(h)

对上式两边积分，便得到求解列车运行时分方程：(h)考虑到(km)对上式积分，即得到求解列车运行距离方程：(km)30第30页在实际计算时，一般采用简化措施：把列车速度范围划分为若干个速度间隔，并假定在每个速度间隔内单位合力为常数，等于该速度间隔内平均速度所对应单位合力cp。列车运动方程31第31页列车运动方程因此(h)

列车在每个速度间隔内运行时间(h)32第32页同理，(km)因而列车在每个速度间隔内运行距离⊿S为：(km)(m)列车运动方程33第33页3列车速度时分曲线计算(分析法)例：SS1型电力机车牵引G=3000t重货品列车，在如图所示区间运行，计算通过甲乙车站时运行时分。0500810005900012006800甲乙34第34页SS1型电力机车单位合力计算表P=138t,G=3000t,θh=0.28,滚动轴承重车,v0=80km/h,中磷闸瓦工况栏号项目\速度01020304041.24347.95052.957.4607080牵引1∑F(kN)415.2415.2387.4372.7363.6363.0301.2272.7261.6246.9224.6204.0149.1115.82Fy=0.9F(kN)373.7373.7348.7335.4327.2326.7271.1245.4235.4222.2202.1183.6134.2104.23w0´=2.25+0.0190v+0.000320v2(N/kN)2.4722.4722.7583.1083.5223.5763.6593.8944.0004.1514.3954.5425.1485.8184W0´=

∑(P·w0´)·g×10-3(kN)3.3473.3473.7344.2084.7684.8414.9535.2725.4155.6195.956.1496.9697.8765w0"=0.92+0.0048v+0.000125v2(N/kN)0.9810.9811.0661.1771.3121.331.3581.4371.4731.5241.6071.6581.8692.1046W0"

=

G·w0"·g×10-3(kN)28.8628.8631.3734.6238.6139.1439.9542.2843.3444.8447.3048.7954.9961.927W0=

W0´+W0"

(kN)32.2132.2135.1138.8343.3843.9844.9147.5548.7550.4653.2554.9461.9669.808C=∑F-W0(kN)341.5341.5313.6296.6283.9282.7226.2197.9186.7171.7148.9128.772.234.49c=C×103/[(∑P+G)·g](N/kN)11.0911.0910.199.6359.229.187.346.426.065.574.834.172.341.11惰行10c=-W0×103/[(∑P+G)·g]=-w0(N/kN)-1.05-1.05-1.14-1.26-1.41-1.43-1.46-1.54-1.58-1.64-1.73-1.78-2.01-2.27制动110.3770.2230.1820.1630.1530.1520.1500.1470.1460.1440.1420.1410.1370.13412b=1000φh·

θh(N/kN)105.6062.3751.0045.7542.7342.4542.0641.1240.7740.3239.7139.3938.3737.5813c=-(0.5b+w0)(N/kN)-53.8-32.2-26.6-24.1-22.8-22.7-22.5-22.1-22.0-21.8-21.6-21.5-21.2-21.135第35页合力曲线图36第36页分析法注意事项速度间隔一般取10整数倍，速度转折点要选用；对应不一样样坡度要移动合力曲线横轴；注意限速，超过限速要改用其他工况；变坡点要试凑；试凑误