1、变位齿轮的计算方法1 变位齿轮的功用及变位系数变位齿轮具有以下功用:(1)避免根切;(2)提高齿面的接触强度和弯曲强度;(3)提高齿面的抗胶合和耐磨损能力;(4)修复旧齿轮;(5)配凑中心距。对于齿数 z820 的直齿圆柱齿轮,当顶圆直径 da=mz+2m+2xm时,不产生根切的最小变位系数xmin,以及齿顶厚 Sa0.4m 和 Sa0 时的变位系数 xsa0.4m 和 xsa0 如表 1所列。2 变位齿轮的简易计算将变位齿轮无侧隙啮合方程式作如下变换:总变位系数中心距变动系数齿顶高变动系数表 1 齿数 z820 圆柱齿轮的变位系数z xmin xsa0.4m xsa0891011121314
2、1516171819200.530.470.420.360.300.240.180.120.0600.050.110.170.180.220.270.310.350.390.430.460.500.530.560.590.620.560.630.700.760.820.880.930.981.031.081.131.181.23或 yx y式中:压力角,20;啮合角;z 2、z 1大、小齿轮的齿数。将上述三式分别除以 ,则得:由上述公式可以看出,当齿形角 一定时,x z、y z和 y z均只为啮合角 的函数。在设计计算时,只要已知 xz、y z、y z和 四个参数中的任一参数,即可由变位齿轮的
3、 xz、y z、y z和啮合角的数值表(表 2)中,查出其他三个参数,再进行下列计算。一般齿轮手册上均列有此数值表。式中正号用于外啮合,负号用于内啮合。3 计算实例例 1:已知一对外啮合变位直齿轮,齿数 z118,z 232,压力角 20,啮合角 2218,试确定总变位系数 x 、中心距变动系数 y及齿顶高变动系数 y。解:根据 2218查表 2,得:x z0.01653,y z0.01565,y z0.00088由此得:例 2:已知一直齿内啮合变位齿轮副,齿数 z119,z 264,20,啮合角 2118。求x 、y 及 y。解:根据 2118查表 2,得:x z0.00886,y z0.0
4、0859,y z0.00027。由此得:其他几何尺寸计算按常规计算进行。此外,变位齿轮的公法线长度的变动量 W2sinxm,当 20时,公法线长度变动量W0.684xm,式中 x为变位系数,应计及正、负号。因此,变位齿轮的公法线长度为:WkW k*m0.684xm式中:W k*某齿数齿轮跨测 k齿时,模数 m1 的公法线长度。表 2 变位齿轮的 yz、x z、y z和啮合角 (20)19 20 21(分) yz xz yz yz xz yz yz xz yz01234567890.006166065965865765665565465365260.00601592582573563554544
5、5355255150.000150140140130130120120110110110.000000110210320420530640750850960.000000110210320430530640750860960.000000000000000000000000000000000.006556666776897007117227347457560.006716836947067187307427547667780.00016017017017018019020020021022101112131415161718190.0051650649648647646645644543542
6、50.005064964864774674574484384284180.000100100100090090090080070070070.001061171281391491601711821922030.001071181291391501611721831942050.000010010010010010010010010020020.007687797908028138258368478598700.007898018148258378508628748868980.00022023023024024025026027027028202122232425262728290.00415
7、4053953843743643543443333230.004083983893793693593493393293190.000070070060050050050050050040040.002142252362462572682792903013120.002162272382492602712822933043150.000020020020030030030030030030030.008828939059169289399519629749850.009109239359479599729849960.010090210.00029030030031032033033034035
8、03630313233343536370.003133032922822722612512410.003092992892792692592490.000040040040030030020020020.003233343443553663773883990.003263383493603713833944050030040050050050060060060.009970.010090200320430550670870.010330460580700830951081210.0003603703803904004004104238392302202382282180020024104214
9、17428007007090102133146043044404142434445464748490.002101991891781681581471371261160.002081981871771671571461361261150.000020010010010010010010010000000.004324434544654764874995105215320.004394514624734854965085195315420.000070080080080090090090090100100.011131251371481601721841952072190.01158171184
10、1962092222352472602730.00045046047048049050051052053054505152535455565758590.001050950840740630530420320210110.001050950840740630520420320210100.000000000000000000000000000000000.005435535655765885996106216326440.005545655775896006126246366476590.000110110120130130130140150150150.0123124325426627829
11、03023143253370.012862993113243373503633763894020.0005505605705805906006106206406560 0.00000 0.00000 0.00000 0.00655 0.00671 0.00016 0.01349 0.01415 0.0006601234567890.013493613733853974094214334454570.014154284414544674804945075205330.000660670680690700710730740750760.0208509711012213514816017318619
12、80.022382522672812963103253393543680.001531551571591611621651661681700.028628768899029169299429569699830.031451601761922082242402562722880.00283285278290292295298300303305101112131415161718190.014694814935055175295415535655780.015475605735866006136276406536670.000780790800810830840860870880890.02211
13、2242372492622752883013133260.023833984124274424574714865015160.001721741751781801821831851881900.029960.030100230360500630770901041180.033043203373533693854014184344500.00308310314317319321324328330332202122232425262728290.015906026146266386516636756876990.016806947077217357487627757898030.000900920
14、930950970980991001021040.023393523653783904034164294424550.025305465605755906056206356506650.001911941951972002022042062082100.031311451581721851992132262402540.034674834995165325495655825986150.00326328331334337340342346348351303132333435360.017127247367497617737850.018168308448588718858990.0010510
15、61081091101121140.024684814945075205335460.026816967117267417567720.002132152172192212232260.032672812953093223363500.036316486656816987157310.00354357360372376379381373839798810822913927941115117119559572585787802818228230233364377391748765782384388391404142434445464748490.0183584786087288489790992
16、29349470.019559689829960.020100240390530670810.001201211221241261271301311331340.025986116246386516646776907037160.028338488638798959109259419569720.002352372392412442462482512532560.034054194334464604744885025165300.037988158328498668839009179349510.0039339639940340640941241541842150515253545556575
17、8590.019599729849970.020090220340470590720.020951091241381521661801952092240.001361381401411431441461481501520.027307437567697837968098228368490.029880.030030190340500660820971131290.002582602632652672702732752772800.035445585725866006136286426566700.039699860.040030200370540720891061230.0042542843143443744144444745045360 0.02085 0.02238 0.00153 0.02862 0.03145 0.00283 0.03684 0404141 0.00457