变位齿轮的计算方法

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x min以及齿顶厚 Sa0.4m 和 Sa 0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 z 8 20 圆柱齿轮的变位系数zxminxsa 0.4m xsa 080.

2、530.180.5690.470.220.63100.420.270.70110.360.310.76120.300.350.82130.240.390.88140.180.430.93150.120.460.98160.060.501.031700.531.0818 0.050.561.1319 0.110.591.1820 0.170.621.23y x y式中：压力角， 20°； 啮合角； z 2、 z 1 大、小齿轮的齿数，则得：将上述三式分别除以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

3、 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：x z 0.01653 ， y z 0.01565 ，yz 0.00088 由此得：例 2： 已知一直齿内啮合变位齿轮副，齿数 y 及 y。解：根据 21°1

4、8查表 2，得：z119，z264， 20°，啮合角 21°18求 x 、x z 0.00886 ， y z 0.00859 ，yz 0.00027 由此得：W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W2sin xm，当 20°时，公法线长度变动量0.684xm ，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* m 0.684xm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&#

5、176;yzxzyzyzxzyzyzxzyz0 0.00616 0.006010.000150.000000.000000.000000.006550.006710.0001616065920140110110006666830172596582014021021000677694017358657301303203200068970601745765630130420430007007180185566554012053053000711730019655654401206406400072274202075465350110750750007347540208536525011085086

6、000745766021952651501109609600075677802210 0.00516 0.00506 0.000100.001060.001070.000010.007680.007890.00022115064960101171180017798010231249648601012812900179081402313486477009139139001802825024144764670091491500018138370241546645700916016100182585002516456448008171172001836862026174454380071821830

7、01847874027184354280071921940028598860271942541800720320500287089802820 0.00415 0.004080.000070.002140.002160.000020.008820.009100.0002921007225227002893923030224053980062362380029059350302339538900524624900391694703124384379005257260003928959032253743690052682710039399720332636435900527928200395198

8、403327354349005290293003962996034283443390043013040039740.0100903529333329004312315003985021036323319300.00313 0.003090.000040.003230.003260030.009970.010330.00036313032990043343380040.0100904603732292289004344349005020058038332822790033553600050320700393427226900336637100504308304035261259002377383

9、0060550950403625124900238839400606710804137241238002399405006087121042382302280024104170070901330433922021800242142800710214604440 0.00210 0.00208 0.000020.004320.004390.000070.011130.011580.0004541199198001443451008125171046421891870014544620081371840474317817700146547300814819604844168167001476485

10、009160209049451581570014874960091722220504614714600149950800918423505147137136001510519009195247052481261260005215310102072600534911611500053254201021927305450 0.00105 0.00105 0.000000.005430.005540.000110.012310.012860.00055510950950005535650112432990565208408400056557701225431105753074074000576589

11、01326632405854063063000588600013278337059550530520005996120132903500605604204200061062401430236306157032032000621636015314376062580210210006326470153253890645901101000064465901533740206560 0.00000 0.00000 0.000000.006550.006710.000160.013490.014150.0006600.013490.014150.000660.020850.022380.001530.0

12、28620.031450.00283136142806709725215587616028523734410681102671578891762783385454069122281159902192290439746707013529616191620829254094800711483101629292242956421494073160325165942240298743350707417333916695625630084455200751863541689692723039457533076198368170983288305100.014690.015470.000780.02211

13、0.023830.001720.029960.033040.00308114815600792243981740.030103203101249357308023741217502333731413505586081249427178036353317145176000832624421800503693191552961308427545718206338532116541627086288471183077401324175536400873014861850904183281856565308831350118810443433019578667089326516190118450332

14、200.015900.016800.000900.023390.025300.001910.031310.034670.003262160269409235254619414548332822614707093365560195158499331236267210953785751971725163342463873509739059020018553233725651748098403605202199549340266637620994166202042135653422767577510042963520622658234628687789102442650208240598348296

15、99803104455665210254615351300.017120.018160.001050.024680.026810.002130.032670.036310.0035431724830106481696215281648357327368441084947112172956653603374985810950772621930968137234761871110520741221322698376357738851125337562233367153793678589911454677222635073138137798913115559787228364748384388109

16、2711757280223037776538839822941119585818233391782391400.018350.019550.001200.025980.028330.002350.034050.037980.00393418479681216118482374198153964286098212262486323943383239943872996124638879241446849403448840.020101266518952444608664064589702412766491024647488340946909039130677925248488900412479220531316909412515029174154893406713370395625351693441849947081134716972256530951421500.019590.020950.001360.027300.029880.002580.035440.039690.00425519721091387430.03003260558986428529841241407560192635720.0400343153997138