工程力学圆轴扭转

1、Nanjing University of TechnologyNanjing University of TechnologynMeMeTMeMeMxTeTMeTM Me e9549N mPMne7024N mr / minPMn马力 mBmCmAmD50PS15PS20PS=300rpmABCDPPPPn50702470241170N m300AAPmn1570247024351N m3002070247024468N m300BBCDDPmmnPmnmCmCmBTmB1351 N mT2702 N mTmD3468N mmmmmABCD1170351468N mN mN mmDmCmBm

2、A123mDT(N m)TTT123351702468 N mN mN m 四轮有无更好的四轮有无更好的排列方式？排列方式？mDmCmBmA11223 ABCDABCDtt， xdd xGGddt TAxGAxGAAAAddddddd2tPAIA d2PGITxdd PPITGITGt PPITGITGt PDPITIT2maxmaxtmaxppIWPWTmaxttmaxtmax最大剪应力最大剪应力出现在哪？出现在哪？ PWTmaxmaxt maxmaxmaxmaxxWxTxIxxTxPPtt=d / D24220d2d32DpADIA 3max216pppIIDWD44242242d2d13

3、232DpAdDdDIA 34max1216pppIIDWDdDtAApTI100000150043210544.(.) 6366.MPamaxpTWt10000041610534.(.) 8488.MPattminmax.10204244MPaTDTD132341616108(.)DD214311081192.由TDTD113434161161t()() 由得DDDD1222214105241052(.)(.)得TTDD1133/222828 .3P1=14kW, P2= P3= P1/2=7 kWn1=n2= 120r/min360r/minr/min12361203113zznn3Mx1

4、=T1=1114 N.mMx2=T2=557 N.mMx3=T3=185.7 N.m 16.54MPaPa1070111416E9-31P1maxWMxt .69MPa22Pa105055716H9-32P2maxWMxt .98MPa12Pa1053718516C9-33P3max.WMxt max pTWtt t (0.50.60)t (0.8 1)t60954995492291.76N m250Pmn由mDD34346161229176161084010().(.)得D 791 . mm63.3mmd 2902 2.50.94490DtD 34344(1)90(1 0.944 )2940

5、01616PDWmm3max91.5 1051MPa29400 10PTWt 60MPatmax51MPatmax316TDt实33616 1.5 10m53mm51 10D实2222290850.3153ADdAD空实实TdT.)Dd11022 .AADd空实2212410540783(.). PddT xxGIx pddBBABAAT xxGIx dPTlGI1ni iiPiT lGI pddT xxxGIx(1)pTlGImax(2)pTWt( )( )12得：maxppIGlWt618080100059010296. 233.mld2得ld2223004030

6、tmax G272180. 009425.MPamaxpmWt009425100041663.118.N m2ACB1m2m3mABlACl1231592N m955N m637N mmmmABABBAPTlG IACACCAPTlG I34129955300107010(8010 )3234129637500107010(8010 )3231.52 10 rad31.69 10 rad41.7 10 radCBCABAACB1m2m3mABlACl 在线弹性、小变形条件下，分别求出在在线弹性、小变形条件下，分别求出在m1和和m3单单独作用下，独作用下，C截面相对截面相对B截面的扭转角，然后叠

7、加。截面的扭转角，然后叠加。1231592N m955N m637N mmmmACB1m2m3mABlACl31()ABACABCBPPmllm lG IG I33412412991592300 10637(300500) 1070107010(80 10 )(80 10 )323241.7 10 rad mmmAB0ABACCBmaG Im bG IApBp0Am bmlBm aml maxmaxpmaxddT xxGIx PTGI pTGI 1.51.5rad/m2m2180 44p132DdID， 44p1 5rad/m1218032DTGIG.4429-350mm1.5 80.4 10

8、100mm 101100mm2 180 329.688103 N.m9.688 kN.m 。 tmaxt11.01.21.52.02.53.04.06.08.010.00.208 0.219 0.231 0.246 0.258 0.267 0.282 0.299 0.307 0.313 0.3330.141 0.166 0.196 0.229 0.249 0.263 0.281 0.299 0.307 0.313 0.3331.000 0.9300.858 0.796 0.767 0.753 0.745 0.743 0.743 0.743 0.743m ax21m ax/3Th bTGh bt

9、t t短 边 最 大 剪 应 力=1/3max22331313TTh bhTTGh bGht1002.2245hbh/b=2.0时，=0.246, =0.796h/b=2.5时， =0.258, =0.767h/b=2.0 =0.2462.50.258 =?h/b=2.22时时2.22 2.00.246 (0.258 0.246)0.2512.5 2.02.222.00.796(0.7960.707)0.7832.52.03max2293 1059.02MPa0.251 100 4510Thbt1max0.783 59.0246.21MPattA2245004dmmA=10045=45002mmd=75.7mm3max393 1035.2275.71016PTPaMPaWt 必须是圆轴，否则横截面将不再保持平面必须是圆轴，否则横