完整版变位齿轮的计算方法

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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寸，不产生根切的最小变位系数以及齿顶厚S=0.4m和Sa=0时的变位系数Xsa=0.4m和Xsa=0如表1所列。Xmin
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


式中：a-----压力角，a=20°;a'――啮合角；
表1齿数z=8〜20圆柱齿轮的变位系数
ZXminXsa=0.4mXsa=
0
80.53
90.47100.42110.36120.30130.24140.18150.12160.0617018—0.0519—0.1120—0.17
0.18
0.220.270.310.350.390.430.460.500.530.560.590.62
0.560.630.700.760.820.880.930.981.031.081.131.181.23
△y=xs—y
Z2、Zi大、小齿轮的齿数



将上述三式分别除以，则得：
由上述公式可以看岀，当齿形角a一定时，Xz、yz和均只为啮合角a'的函数。在设计计算时，只要已知Xz、yz>Ayz和a'四个参数中的任一参数，即可由变位齿轮的Xz、yz>Ayz和啮合角a'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a=20°,啮合角a'=22°18',试确定总变位系数xz、中心距变动系数y及齿顶高变动系数
△y。
解：
根据a'=22°18'查表2,得：
Xz=0.01653,yz=0.01565,Ayz=0.00088由此得：
例2：已知一直齿内啮合变位齿轮副，齿数y及Ay。
乙=19,Z2=64,a=20°,啮合角a'=21°18'
解：
根据a'=21°18'查表2,得:
xz=0.00886,yz=0.00859,Ayz=0.00027由此得：

求xz、




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△W2sinaxm当a=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：
W=Wm+0.684xm
式中：W――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>Ayz和啮合角a'(a=20°
a，
19°20°
21—.-o
(分yzXzAyyzXzAyzyzXz
Ay0—0.00616—0.006010.000150.000000.000000.000000.006550.006710.00016
1606592014011011000666
6830172596582014021021000
677694017358657301303203200068970601745765630130420430007007180185566554012053053000
7117300196556544012064064000722742020
7546535011075075000734754020
8536525011085086000745766021
952651501109609600075677802210—0.00516—0.005060.000100.001060.001070.000010.007680.007890.00022
1150649601011711800177980102312496486010128129001
790814023134864770091391390018028250241447646700914915000181383702415466457009160161001
82585002516456448008171172001836862026
17445438007182183001847874027
18435428007192194002859886
0271942541800720320500287089802820—0.00415—0.004080.000070.002140.002160.000020.008820.009100.00029
21

007225227002893923030
224053980062362380029059350302339524QO/I38900524624900391694703138425Q7/I37900525726000392895903237436900526827100393997203326364359005279282003951984033
27
354
349005290293003962996034
AW=


2829

344333323339329319
004004


301312

304315

003003

974985

0.01009021

035036
30313233343536373839404142434445464748495051525354555657585960012345678910111213141516171819202122232425

「0.00313—0.003090.000040.003230.003263032990043343382922890043443492822790033553602722690033663712612590023773832512493883940022412380023994052304104172280022202180024214280030.009970.010330.00036
0040.01009046037005058038020005032070039005043083040006055095040
067041006108
006087121042007090133043007102146044
—0.00210—0.002080.000020.004320.004390.000070.011130.011580.00045
199198001443451008125171046189187454462137184047001008178177001465473008148196048
167476485009209049168001160
158157001487496009172222050147146499508009184235051001137126116
136126115
001000000
510521532
519531542
009010010
195207219
247260273
052053054
—0.00105—0.001050.000000.005430.005540.000110.012310.012860.00055095095000553565011243299056084084565577254311057000012074074576589013324058000266063063000588600013278337059053052599013290350000612060042042000610624014302363061032032636015314376000621062021021000632647015325389064
644659015337402065011010000—0.00000—0.000000.000000.006550.006710.000160.013490.014150.000660.01349
3613733853974094214334454570.014694814935055175295415535655780.01590602614626638651
0.014150.000660.020850.022380.001530.028620.031450.002834280670972521558762851604412671578891762780681104540691222811599021922904670701352969162921612084800711483109292242951624940731603251659422402985070741733399562563001665200751863541689692723035330761983681709832883050.015470.000780.022110.023830.001720.029960.033040.003085600792243981740.03010320310573237412175023337314080586081249427178036353317
083442050369319600262180
6130842754571820633853216274711830774013240862886400873014861850904183286533135011044343300881886670893265161901184503320.016800.000900.023390.025300.001910.031310.034670.00326694092352546194145483328707721735748
093095097098
365378390403
560575590605
195197200202
158172185199
499516532549
331334337340


2627282930313233343536373839404142434445464748495051525354555657585960

204213565342206226582346
240598348208
254615351210
「0.017120.018160.001050.024680.026810.002130.032670.036310.00354724830481696215648357106281736844108494711217295665360749858109507726219309372681761871110520741221322698376773885533756223336715379112785899114546772226350731381798913115559787364748384228810927117572802230377765388
9411195852333917823918228180.01835
8478608728848979099229349470.019599729849970.020090220340470590720.02085
0.019550.001200.025980.028330.002350.034050.037980.00393968848237419815396121611982122624863239433832399996124638879241446849403
6518952444604060.02010126866
024127664910246474883409039130677925248488900412053131690941251502917415067133703956253516934418
134716972256530951421081
0.020950.001360.027300.029880.002580.035440.039690.004251091387430.030032605589864281241407560192635720.04003431138141769034265586434020152143783050267600037437
144796270613054441166066146809273072444180082628
1951480972756420894478222091508361132776561064502241528491292806701234530.022380.001530.028620.031450.002830.0368404041410.00457
663
675687699762775789803099100102104416429442455620635650665


完整版变位齿轮的计算方法

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