变位齿轮的计算方法.doc

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zxminxsa0.4mxsa08910111213141516171819200.530.470

2、.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

3、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：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2118。求x、y及y。解：根据2118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，

4、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）192021yzxzyzyzxzyzyzxzyz01234567890.006166065965865765665565465365260.006015925825735635545445355255150.000150140140130130120120110110110.000000110210320420530640750850960.00000011021

5、0320430530640750860960.000000000000000000000000000000000.006556666776897007117227347457560.006716836947067187307427547667780.00016017017017018019020020021022101112131415161718190.005165064964864764664564454354250.005064964864774674574484384284180.000100100100090090090080070070070.0010611712813914916

6、01711821922030.001071181291391501611721831942050.000010010010010010010010010020020.007687797908028138258368478598700.007898018148258378508628748868980.00022023023024024025026027027028202122232425262728290.004154053953843743643543443333230.004083983893793693593493393293190.000070070060050050050050050

7、040040.002142252362462572682792903013120.002162272382492602712822933043150.000020020020030030030030030030030.008828939059169289399519629749850.009109239359479599729849960.010090210.00029030030031032033033034035036303132333435363738390.003133032922822722612512412302200.0030929928927926925924923822821

8、80.000040040040030030020020020020020.003233343443553663773883994104210.003263383493603713833944054174280030040050050050060060060070070.009970.010090200320430550670870901020.010330460580700830951081211331460.00036037038039040040041042043044404142434445464748490.002101991891781681581471371261160.00208

9、1981871771671571461361261150.000020010010010010010010010000000.004324434544654764874995105215320.004394514624734854965085195315420.000070080080080090090090090100100.011131251371481601721841952072190.011581711841962092222352472602730.00045046047048049050051052053054505152535455565758590.0010509508407

10、40630530420320210110.001050950840740630520420320210100.000000000000000000000000000000000.005435535655765885996106216326440.005545655775896006126246366476590.000110110120130130130140150150150.012312432542662782903023143253370.012862993113243373503633763894020.00055056057058059060061062064065600.000000.000000.000000.006550.006710.000160.013490.014150.0006601234567890.013493613733853974094214334454570.014154284414544674804945075205330.000660670680690700710730740750760.020850971101221351481601731861980.0223825226728129631032533935436