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1、 Chapter 3 Torsion 从动轮从动轮主动轮主动轮从动轮从动轮 /kWeN mr min9 549PMne2e1e3e0 xMeMT eeMexnnMeMexMex /kwer min9 549pMnmN6366mN5 .4774mN159154e3e2e1e MMMM 0023e2e TMMMx mN95493e2e2 MMTmN5 .47742e1 MTxMe2Me3T2Me21T133Me4Me1Me3Me2Me2mN5 .47742e1 MTmN63664e3 MTmN9549max T0101r dxxMeMedx ABDC () dd2AAA rrArrT 22 rT
2、0 yF. 00 xzFMzyxd)dd( l lr TO lrrT 22 G )1(2 EG 变形几何关系变形几何关系物理关系物理关系静力关系静力关系 观察变形观察变形 提出假设提出假设变形的分布规律变形的分布规律应力的分布规律应力的分布规律建立公式建立公式deformationgeometricrelation Distribution regularity of deformationDistribution regularity of stressEstablish the formulaExamine the deformationthen propose the hypothesi
3、s physicalrelationstaticrelationabb12dtand GGxEGTTADGDG ) G xGGdd abATTDbdD12GG TAA d TAxGA dddTAxGA ddd2 p2dIAA pddGITx PIT max tmaxppmaxmaxWTITIT maxpt IW dO)d(2d A32d2d42032pdAIdA 162/32/34maxptdddIW dODdd32)1(44p DI)1(1643t DW其中其中Dd M1M2ABCllMe1Me2ABCll1Me2CT12Me2CMe1BT2 4kNm2kNm+_T maxtmaxmaxWT
4、 M1M2ABCllMPa5 .34)1(1643max DT maxtmaxmax WTtmax WTmaxt TW tmax WT ABCMeAMeBMeC22 14 +_MPa84.6416/ )12. 0(102216/33311t11max1 dTWTMPa3 .7116/ )1 . 0(101416/333222t2max2 dTWT2max1max ll(a)(b)2t2max1t1maxWTWT dd2D22t1tWTWT 16)1(16432312t1t DdWW()3341211616 dD194. 18 . 0113412 dD512. 0)8 . 01(194. 1)1
5、(4)(4222122221222212 dDddDAA (pddGITx xGITllddp pTlGI () prad mTlGI max ()maxmaxprad mTGI D+Me2Me3Me1180)2(pepe GIaMGIaMMPa7 .69tmaxmax WT mkN292e M33. 2180)23(pepe GIaMGIaMCBBACA D+Me2Me3Me 图示为某组合机床主轴箱第4轴示意图,轴上有,三个齿轮,动力由5轴经齿轮输送到四轴,再由齿轮和带动1,2和3轴,1和2轴同时钻孔,共消耗功率0.756KW,3轴扩孔,消耗功率2.98KW,若4轴转速183.5r/min,
6、材料为45钢,G=80GPa,取 , 试设计轴的直径. MPa40 mo/5 . 1,Dd MeMe .20 934 dDDD34ptmm1006. 22/ DIWMPa1 .96tmaxmax WT().4454p17 83 10 mm32DI ./ maxmaxp1801 81mTGImkN98. 1e MTDd MeMeMPa1 .9616/3maxmax dT 22mm17494 dA实实222mm5774)7176( 空空A329. 0174957712 AACMeabABlACBMeMeAMeB00eee MMMMBAxCMeabABlCMeabABlBCAC 1ppACT aM
7、aGIGI e eA APeP2GIbMGIbTBBC baMMABee 0eee MMMBAlMaMlMbMBA/ee ACBMeMeAMeBMeMelABe0 xabMMMMBA ppabABaabbM lM lG IG IMeMeMelABMaMbppaaabbbG IMMG IpppaaaaabbG IMG IG IpppbbbaabbG IMG IG IMbMaMeBA MeMelAB(a )PRdF(a)RdPPQT(b)FSTFPF2SFDTFF 在靠近轴线的内侧点处,总应力达到最大:) 12(884332max21maxDddFDdFDdF3max8dFD33max88)615
8、. 04414(dFDkdFDccc ccckdDc615. 04414, max (a)RdPPQT(b)FSTFPF2p2T lGI 2FDT Dnl 2344F D nGd Ol ll ll lFW21 432421GdnDFF l l4343648GdnFRGdnFD l lnRGdnDGdc3434648 令令cF l l得得N2510)105 .59(64)1014)(1080)(1055(643439334 nRGdFl l5 . 81014)105 .59(2233 dRdDcMPa325Pa10325)1014(1025 .592510(817. 186333max dFDk
9、 .bhT3tIhb max max tmaxWT tGITl max 2thbW 3t31 hI 2t31 hW h/b1.01.21.52.02.53.04.06.08.010.00.2080.2190.2310.2460.2560.2670.2820.2990.3070.3130.3330.1410.1660.1960.2290.2490.2630.2810.2990.3070.3130.3331.0000.9300.8580.7960.7670.7530.7450.7430.7430.7430.743mkN4 MT229. 0246. 0 4833tm1028605. 01 . 022
10、9. 0 hbI 3622tm106 .6105. 01 . 0246. 0 hbW MPa65106 .6140006tmax WT/m1rad/m01745. 0102861080400089t GIT 22)d( dsT minmax2T dd21s ba maxmin22 MPaTTab -9-95000500042.542.52 55075102 5507510附录:I.1 静矩和形心静矩也称为一次矩AzydASAyzdAS形心AydAyAAzdAzAyASzzASy组合图形的静矩和形心niiizyAS1niiiyzAS1niiniiiAyAy11niiniiiAzAz11I.2 惯性矩和惯性半径AzdAyI2AydAzI2惯性矩又称二次矩惯性半径:AIiyyAIizz极惯性矩ApdAI2yzApIIdAyxI)(22 长方形 实心圆 空心圆123bhIy几种常见截面的计算公式123hbIz644DIIzy324DIp64)(44dDIIzy32)(44dDIpI.3 惯性积AyzyzdAI坐标系的两个坐标轴中只要有一个为图形的对称轴,则图形对这一坐标系的惯性积等于零。I.4 平行移轴公式AaIIycy2AbIIzcz2abAIIyCzCyz习题讲解1、画出扭矩图应力分布图