变位齿轮的简易计算.doc

变位齿轮的简易计算变位齿轮的应用越来越普遍，但有的仍利用无侧隙啮合方程式进行计算，相当麻烦，且容易出差错。今推荐用表格法进行计算，简捷、方便、不易出差错。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zxminxsa0.4mxsa08910111213141516171819200.530.470.420.360.300.240.180.120.0600.050.110.170.180.220.270.310.350.390.430.460.500.530.560.590.620.560.630.700.760.820.880.930.981.031.081.131.181.23或 yxy式中：压力角，20°；啮合角；z2、z1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，xz、yz和yz均只为啮合角的函数。在设计计算时，只要已知xz、yz、yz和四个参数中的任一参数，即可由变位齿轮的xz、yz、yz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，z232，压力角20°，啮合角22°18，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22°18查表2，得：xz0.01653，yz0.01565，yz0.00088由此得：例2：已知一直齿内啮合变位齿轮副，齿数z119，z264，20°，啮合角21°18。求x、y及y。解：根据21°18查表2，得：xz0.00886，yz0.00859，yz0.00027。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：WkWk*m0.684xm式中：Wk*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、xz、yz和啮合角（20°）（分）19°20°21°yzxzyzyzxzyzyzxzyz01234567890.006166065965865765665565465365260.006015925825735635545445355255150.000150140140130130120120110110110.000000110210320420530640750850960.000000110210320430530640750860960.000000000000000000000000000000000.006556666776897007117227347457560.006716836947067187307427547667780.00016017017017018019020020021022101112131415161718190.005165064964864764664564454354250.005064964864774674574484384284180.000100100100090090090080070070070.001061171281391491601711821922030.001071181291391501611721831942050.000010010010010010010010010020020.007687797908028138258368478598700.007898018148258378508628748868980.00022023023024024025026027027028202122232425262728290.004154053953843743643543443333230.004083983893793693593493393293190.000070070060050050050050050040040.002142252362462572682792903013120.002162272382492602712822933043150.000020020020030030030030030030030.008828939059169289399519629749850.009109239359479599729849960.010090210.00029030030031032033033034035036303132333435363738390.003133032922822722612512412302200.003092992892792692592492382282180.000040040040030030020020020020020.003233343443553663773883994104210.003263383493603713833944054174280030040050050050060060060070070.009970.010090200320430550670870901020.010330460580700830951081211331460.00036037038039040040041042043044404142434445464748490.002101991891781681581471371261160.002081981871771671571461361261150.000020010010010010010010010000000.004324434544654764874995105215320.004394514624734854965085195315420.000070080080080090090090090100100.011131251371481601721841952072190.011581711841962092222352472602730.00045046047048049050051052053054505152535455565758590.001050950840740630530420320210110.001050950840740630520420320210100.000000000000000000000000000000000.005435535655765885996106216326440.005545655775896006126246366476590.000110110120130130130140150150150.012312432542662782903023143253370.012862993113243373503633763894020.00055056057058059060061062064065600.000000.000000.000000.006550.006710.000160.013490.014150.0006601234567890.013493613733853974094214334454570.014154284414544674804945075205330.000660670680690700710730740750760.020850971101221351481601731861980.022382522672812963103253393543680.001531551571591611621651661681700.028628768899029169299429569699830.031451601761922082242402562722880.00283285278290292295298300303305101112131415161718190.014694814935055175295415535655780.015475605735866006136276406536670.000780790800810830840860870880890.022112242372492622752883013133260.023833984124274424574714865015160.001721741751781801821831851881900.029960.030100230360500630770901041180.033043203373533693854014184344500.00308310314317319321324328330332202122232425262728290.015906026146266386516636756876990.016806947077217357487627757898030.000900920930950970980991001021040.023393523653783904034164294424550.025305465605755906056206356506650.001911941951972002022042062082100.031311451581721851992132262402540.034674834995165325495655825986150.00326328331334337340342346348351303132333435363738390.017127247367497617737857988108220.018168308448588718858999139279410.001051061081091101121141151171190.024684814945075205335465595725850.026816967117267417567727878028180.002132152172192212232262282302330.032672812953093223363503643773910.036316486656816987157317487657820.00354357360372376379381384388391404142434445464748490.018358478608728848979099229349470.019559689829960.020100240390530670810.001201211221241261271301311331340.025986116246386516646776907037160.028338488638798959109259419569720.002352372392412442462482512532560.034054194334464604744885025165300.037988158328498668839009179349510.00393396399403406409412415418421505152535455565758590.019599729849970.020090220340470590720.020951091241381521661801952092240.001361381401411431441461481501520.027307437567697837968098228368490.029880.030030190340500660820971131290.002582602632652672702732752772800.035445585725866006136286426566700.039699860.040030200370540720891061230.00425428431434437441444447450453600.020850.022380.001530.028620.031450.002830.0368404041410.00457