變位齒輪的計(jì)算方法

1、變位齒輪的計(jì)算方法1變位齒輪的功用及變位系數(shù)變位齒輪具有以下功用：（1）避免根切；(2)提高齒面的接觸強(qiáng)度和彎曲強(qiáng)度；(3)提高齒面的抗膠合和耐磨損能力；(4)修復(fù)舊齒輪；(5)配湊中心距。對(duì)于齒數(shù)z820的直齒圓柱齒輪，當(dāng)頂圓直徑da=mz+2m+2xm時(shí)，不產(chǎn)生根切的最小變位系數(shù)xmin，以及齒頂厚Sa0.4m和Sa0時(shí)的變位系數(shù)xsa0.4m和xsa0如表1所列。2變位齒輪的簡(jiǎn)易計(jì)算將變位齒輪無(wú)側(cè)隙嚙合方程式作如下變換：總變位系數(shù)中心距變動(dòng)系數(shù)齒頂高變動(dòng)系數(shù)表1齒數(shù)z820圓柱齒輪的變位系數(shù)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：壓力角，20°；嚙合角；z2、z1大、小齒輪的齒數(shù)。將上述三式分別除以，則得：由上述公式可以看出，當(dāng)齒形角一定時(shí)，xz、yz和yz均只為嚙合角的函數(shù)。在設(shè)計(jì)計(jì)算時(shí)，只要已知xz、yz、yz和四個(gè)參數(shù)中的任一參數(shù)，即可由變位齒輪的xz、yz、yz和嚙合角的數(shù)值表(表2)中，查出其他三個(gè)參

3、數(shù)，再進(jìn)行下列計(jì)算。一般齒輪手冊(cè)上均列有此數(shù)值表。式中正號(hào)用于外嚙合，負(fù)號(hào)用于內(nèi)嚙合。3計(jì)算實(shí)例例1：已知一對(duì)外嚙合變位直齒輪，齒數(shù)z118，z232，壓力角20°，嚙合角22°18，試確定總變位系數(shù)x、中心距變動(dòng)系數(shù)y及齒頂高變動(dòng)系數(shù)y。解：根據(jù)22°18查表2，得：xz0.01653，yz0.01565，yz0.00088由此得：例2：已知一直齒內(nèi)嚙合變位齒輪副，齒數(shù)z119，z264，20°，嚙合角21°18。求x、y及y。解：根據(jù)21°18查表2，得：xz0.00886，yz0.00859，yz0.00027。由此得：其他幾何

4、尺寸計(jì)算按常規(guī)計(jì)算進(jìn)行。此外，變位齒輪的公法線長(zhǎng)度的變動(dòng)量W2sinxm，當(dāng)20°時(shí)，公法線長(zhǎng)度變動(dòng)量W0.684xm，式中x為變位系數(shù)，應(yīng)計(jì)及正、負(fù)號(hào)。因此，變位齒輪的公法線長(zhǎng)度為：WkWk*m0.684xm式中：Wk*某齒數(shù)齒輪跨測(cè)k齒時(shí)，模數(shù)m1的公法線長(zhǎng)度。表 2變位齒輪的yz、xz、yz和嚙合角（20°）（分）19°20°21°yzxzyzyzxzyzyzxzyz01234567890.006166065965865765665565465365260.006015925825735635545445355255150.0001501

5、40140130130120120110110110.000000110210320420530640750850960.000000110210320430530640750860960.000000000000000000000000000000000.006556666776897007117227347457560.006716836947067187307427547667780.00016017017017018019020020021022101112131415161718190.005165064964864764664564454354250.005064964864774

6、674574484384284180.000100100100090090090080070070070.001061171281391491601711821922030.001071181291391501611721831942050.000010010010010010010010010020020.007687797908028138258368478598700.007898018148258378508628748868980.00022023023024024025026027027028202122232425262728290.00415405395384374364354

7、3443333230.004083983893793693593493393293190.000070070060050050050050050040040.002142252362462572682792903013120.002162272382492602712822933043150.000020020020030030030030030030030.008828939059169289399519629749850.009109239359479599729849960.010090210.00029030030031032033033034035036303132333435363

8、738390.003133032922822722612512412302200.003092992892792692592492382282180.000040040040030030020020020020020.003233343443553663773883994104210.003263383493603713833944054174280030040050050050060060060070070.009970.010090200320430550670870901020.010330460580700830951081211331460.000360370380390400400

9、41042043044404142434445464748490.002101991891781681581471371261160.002081981871771671571461361261150.000020010010010010010010010000000.004324434544654764874995105215320.004394514624734854965085195315420.000070080080080090090090090100100.011131251371481601721841952072190.01158171184196209222235247260

10、2730.00045046047048049050051052053054505152535455565758590.001050950840740630530420320210110.001050950840740630520420320210100.000000000000000000000000000000000.005435535655765885996106216326440.005545655775896006126246366476590.000110110120130130130140150150150.012312432542662782903023143253370.012

11、862993113243373503633763894020.00055056057058059060061062064065600.000000.000000.000000.006550.006710.000160.013490.014150.0006601234567890.013493613733853974094214334454570.014154284414544674804945075205330.000660670680690700710730740750760.020850971101221351481601731861980.022382522672812963103253

12、393543680.001531551571591611621651661681700.028628768899029169299429569699830.031451601761922082242402562722880.00283285278290292295298300303305101112131415161718190.014694814935055175295415535655780.015475605735866006136276406536670.000780790800810830840860870880890.02211224237249262275288301313326

13、0.023833984124274424574714865015160.001721741751781801821831851881900.029960.030100230360500630770901041180.033043203373533693854014184344500.00308310314317319321324328330332202122232425262728290.015906026146266386516636756876990.016806947077217357487627757898030.000900920930950970980991001021040.02

14、3393523653783904034164294424550.025305465605755906056206356506650.001911941951972002022042062082100.031311451581721851992132262402540.034674834995165325495655825986150.00326328331334337340342346348351303132333435363738390.017127247367497617737857988108220.018168308448588718858999139279410.0010510610

15、81091101121141151171190.024684814945075205335465595725850.026816967117267417567727878028180.002132152172192212232262282302330.032672812953093223363503643773910.036316486656816987157317487657820.00354357360372376379381384388391404142434445464748490.018358478608728848979099229349470.019559689829960.02

16、0100240390530670810.001201211221241261271301311331340.025986116246386516646776907037160.028338488638798959109259419569720.002352372392412442462482512532560.034054194334464604744885025165300.037988158328498668839009179349510.00393396399403406409412415418421505152535455565758590.019599729849970.020090220340470590720.020951091241381521661801952092240.001361381401411431441461481501520.027307437567697837