(完整版)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z 8 20 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Sa 0.4m 和 Sa 0时的变位系数xsa 0.4m 和 xsa 0 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：总变位系数齿顶高变动系数1 齿数 z 8 20 圆柱齿轮的变位系数zxminxsa0.4m xsa 080.530.180.5

2、690.470.220.63100.420.270.70110.360.310.76120.300.350.82130.240.390.88140.180.430.93150.120.460.98160.060.501.031700.531.0818 0.050.561.1319 0.110.591.1820 0.170.621.23yx 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由上述公式可以看出，当齿形角 一定时，xz、yz和 y z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

3、、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z1 18， z2 32，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：xz 0.01653 ， yz 0.01565 ，y z 0.00088由此得：例2：x 、已知一直齿内啮合变位齿轮副，齿数z1 19， z2 64，20°，啮合角 21° 18。求y 及 y

4、。解：根据 21 ° 18查表2，得：xz 0.00886 ， yz 0.00859 ，y z 0.00027 。由此得：其他几何尺寸计算按常规计算进行。W此外，变位齿轮的公法线长度的变动量 W 2sin 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：*Wk Wk m 0.684xm式中：Wk*某齿数齿轮跨测k 齿时，模数m 1 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 °yzxzy zyzxzy zyzxzy z

5、0 0.00616 0.006010.000150.000000.000000.000000.006550.006710.00016160659201401101100066668301725965820140210210006776940173586573013032032000689706017457656301304204300070071801855665540120530530007117300196556544012064064000722742020754653501107507500073475402085365250110850860007457660219526515011

6、09609600075677802210 0.00516 0.00506 0.000100.001060.001070.000010.007680.007890.000221150649601011711800177980102312496486010128129001790814023134864770091391390018028250241447646700914915000181383702415466457009160161001825850025164564480081711720018368620261744543800718218300184787402718435428007

7、1921940028598860271942541800720320500287089802820 0.00415 0.004080.000070.002140.002160.000020.008820.009100.00029210072252270028939230302240539800623623800290593503023395389005246249003916947031243843790052572600039289590322537436900526827100393997203326364359005279282003951984033273543490052902930

8、03962996034283443390043013040039740.0100903529333329004312315003985021036323319300.00313 0.003090.000040.003230.003260030.009970.010330.00036313032990043343380040.01009046037322922890043443490050200580383328227900335536000503207003934272269003366371005043083040352612590023773830060550950403625124900

9、238839400606710804137241238002399405006087121042382302280024104170070901330433922021800242142800710214604440 0.00210 0.00208 0.000020.004320.004390.000070.011130.011580.00045411991980014434510081251710464218918700145446200813718404743178177001465473008148196048441681670014764850091602090494515815700

10、14874960091722220504614714600149950800918423505147137136001510519009195247052481261260005215310102072600534911611500053254201021927305450 0.00105 0.00105 0.000000.005430.005540.000110.012310.012860.000555109509500055356501124329905652084084000565577012254311057530740740005765890132663240585406306300

11、0588600013278337059550530520005996120132903500605604204200061062401430236306157032032000621636015314376062580210210006326470153253890645901101000064465901533740206560 0.00000 0.00000 0.000000.006550.006710.000160.013490.014150.0006600.013490.014150.000660.020850.022380.001530.028620.031450.002831361

12、42806709725215587616028523734410681102671578891762783385454069122281159902192290439746707013529616191620829254094800711483101629292242956421494073160325165942240298743350707417333916695625630084455200751863541689692723039457533076198368170983288305100.014690.015470.000780.022110.023830.001720.029960

13、.033040.00308114815600792243981740.030103203101249357308023741217502333731413505586081249427178036353317145176000832624421800503693191552961308427545718206338532116541627086288471183077401324175536400873014861850904183281856565308831350118810443433019578667089326516190118450332200.015900.016800.0009

14、00.023390.025300.001910.031310.034670.0032621602694092352546194145483328226147070933655601951584993312362672109537857519717251633424638735097390590200185532337256517480984036052021995493402666376209941662020421356534227675775100429635206226582346286877891024426502082405983482969980310445566521025461

15、5351300.017120.018160.001050.024680.026810.002130.032670.036310.00354317248301064816962152816483573273684410849471121729566536033749858109507726219309681372347618711105207412213226983763577388511253375622333671537936785899114546772226350731381377989131155597872283647483843881092711757280223037776538

16、839822941119585818233391782391400.018350.019550.001200.025980.028330.002350.034050.037980.00393418479681216118482374198153964286098212262486323943383239943872996124638879241446849403448840.020101266518952444608664064589702412766491024647488340946909039130677925248488900412479220531316909412515029174154893406713370395625351693441849947081134716972256530951421500.019590.020950.001360.027300.029880.002580.035440.039690.00425519721091387430.03003260558986428529841241407560192635720.04003431539971381