1.齿轮相关参数计算
基本参数：齿形角 α/°齿顶高系数h a*顶缝隙系数c*
2010.25
齿形角（弧度）0.349066
1.1.标准齿轮计算
模数m/m n齿数z1齿数z2分度圆直径d1/mm分度圆直径d2/mm 8100106800848
齿顶圆d a齿根圆d f齿根高h f齿高h中心距a △h a*外啮合ha1ha2h f1h f2h1h2
0.0712148810101818
内啮合ha1ha2h f1h f2h1h2
87.430291*********.4303
基本参数：齿形角 α/°齿顶高系数h a*顶缝隙系数c*
2010.25
齿形角（弧度）0.349066
1.2.高变位齿轮计算
模数m/m n齿数z1齿数z2分度圆直径d1/mm分度圆直径d2/mm 810074800592
齿顶圆d a齿根圆d f中心距a基圆直径d b
△h a*外啮合ha1ha2h f1h f2h1h2
0.1020091246141810
内啮合ha1ha2h f1h f2h1h2
1211.183932661817.1839
基本参数：齿形角 α/°齿顶高系数h a*顶缝隙系数c*
2010.25
齿形角（弧度）0.349066invαt=0.014904
1.3.1 角变位齿轮计算
模数m/m n齿数z1齿数z2分度圆直径d1/mm分度圆直径d2/mm
12151061801272
1.3.1 已知x 滚齿法加工齿顶圆d a齿根圆d f中心距a基圆直径d b
△h a*外啮合ha1ha2h f1h f2h1h2
0.07121417.3626417.3626459926.3626426.3626
y/y n0.946887△y0.053113
内啮合ha1ha2h f1h f2h1h2
9.4545414.5454692118.4545423.5455
y/y n0.7121217△y0.712122
滚齿参数：h a、h f、h、d a、d f 。ρ=
内啮合d a2取值为
基本参数：齿形角 α/°齿顶高系数h a*顶缝隙系数c*
2010.25
齿形角（弧度）0.349066invαt=0.014904
1.3.2 角变位齿轮计算
模数m/m n齿数z1齿数z2分度圆直径d1/mm分度圆直径d2/mm 4226588260
1.3.2 已知a' 滚齿法加工齿顶圆d a齿根圆d f中心距a基圆直径d b
△h a*外啮合ha1ha2h f1h f2h1h2
0.116133 6.778479 3.2984785 1.52 1.7784798.298479 4.81848
y/y n 1.5△y0.17538
内啮合ha1ha2h f1h f2h1h2
2.610754277.6107549.6107549
y/y n1△y0.152689
滚齿参数：h a、h f、h、d a、d f 。ρ=
内啮合d a2取值为
基本参数：齿形角 α/°齿顶高系数h a*顶缝隙系数c*
2010.25
齿形角（弧度）0.349066invαt=0.014904
1.3.3角变位齿轮计算
模数m/m n齿数z1齿数z2分度圆直径d1/mm分度圆直径d2/mm 4226588260
1.3.3 插齿法加工齿顶圆d a齿根圆d f中心距a基圆直径d b
△h a*外啮合ha1ha2h f1h f2h1h2
0.116133 6.778479 3.2984785 1.52 1.7784798.298479 4.81848
y/y n 1.5△y0.17538
内啮合ha1ha2h f1h f2h1h2
2.610754277.6107549.6107549
y/y n1△y0.152689
滚齿参数：h a、h f、h、d a、d f 。ρ=
内啮合d a2取值为
基本参数：齿形角 α/°齿顶高系数h a*顶缝隙系数c*
2010.25
齿形角（弧度）0.349066invαt=0
1.4 齿轮齿条计算
模数m/m n齿数z1x1/x n1分度圆直径d1/mm ha1h f1h1
10180.4180148.522.5
ha2h f2h2
1012.522.5
1.5交错轴斜齿轮计算
模数m/m n齿数z1齿数z2轴交角Σ螺旋β1螺旋β2
102265903060
中心距a0.5235991.047198
777.01706齿数比不等于分度圆直径比
当轴交角Σ=90°时，模数m/m n齿数z1齿数z2中心距a
齿数比μ=z1/z2；102265777.0171
1.6 选择外啮合齿轮变位系数的限制条件
基本参数：齿形角 α/°齿顶高系数h a*参考手册P14-23~P14-27
201
1.用齿条型刀具加工 (不根切)
2.用插齿刀加工 (不根切)
z min取整实际齿数z x min插齿刀齿数z0
17.0972*******.122666712
4.齿顶不过薄 3.用插齿刀加工标齿 (不顶切)
d a z xα插齿刀齿数z0
25025020z max
invαinvαn s a
0.01490440.01490415.707963
一般要求s a≥0.25*m，对于表面淬火的齿轮，要求s a>0.4*m。
5.保证一定重合度，要求εa≥12.
6.不产生过渡曲线干涉
αinvα
200.34906590.0149044
23.2150.40517820.0237323
23.21530.40518340.0237333
23.21520.40518170.0237329
斜齿分度圆螺旋角β齿宽b
00.0000100
基圆直径d b齿顶圆压力角αa端面重合度εa
d a1d a2d f1d f2a d b1d b2
816864780828824751.7541796.85934
d a1d a2d f1d f2a d b1d b2
816833.13941678086824751.7541796.85934
αinvα
200.34906590.0149044
300.52359880.0537515
450.78539820.2146018
500.87266460.319089斜齿分度圆螺旋角β齿宽b x1/x n1
00.00001000.5
径d b齿顶圆压力角αa端面重合度εa纵向重合度εβ
d a1d a2d f1d f2a d b1d b2
824600788564696751.7541556.29803
d a1d a2d f1d f2a d b1d b2
824569.632137788604-104751.7541556.29803
αinvααinvα
20.30.354301840.0156093920.42910.35655510.0159199
22.299640.389202140.020*******.42930.35655850.0159203
22.299650.389202310.020*******.42920.35655680.0159201
斜齿分度圆螺旋角βaαt齿宽b x1/x n1
00.0000726201000.5
径d b齿顶圆压力角αa端面重合度εa纵向重合度εβ
d a1d a2d f1d f2a'd1'd2'
214.72531306.725291621254737.3626445182.817181291.9081 invα'0.02092042αt'22.299640.3892021
d a1d a2d f1d f2a'd1'd2'
198.90911242.909081621314554.5454599182.817181291.9081 invα'0.01490438αt'22.299640.3892021
13.238991276.2498266.783261
d a2取值为1276.2498
αinvααinvα
23.58610.41165510.024*******.42910.35655510.0159199
23.5860.411653360.024*******.42930.35655850.0159203
23.5860.411653340.024*******.42920.35655680.0159201
斜齿分度圆螺旋角βa(外啮合)a(内啮合)αt齿宽b
00.00001748620100
径d b齿顶圆压力角αa端面重合度εa纵向重合度εβ
d a1d a2d f1d f2a'd1'd2'
101.557266.59695784.96256.44304318091.034483268.96552 invα'0.01490438α'/αt'24.719003310.431428
d a1d a2d f1d f2a'd1'd2'
93.2215125674275.2215099092.093023272.09302
invα'0.01490438α'/αt'26.112899670.4557561
-2.49394255.34979573.597634
d a2取值为256
αinvααinvα
23.58610.41165510.024********.34906590.0149044
23.5860.411653360.024*******.42930.35655850.0159203
23.5860.411653340.024*******.42920.35655680.0159201
斜齿分度圆螺旋角βa(外啮合)a(内啮合)αt齿宽b
00.00001748620100
径d b齿顶圆压力角αa端面重合度εa纵向重合度εβ
d a1d a2d f1d f2a'd1'd2'
101.557266.59695784.96256.44304318091.034483268.96552
invα'0.01490438α'/αt'24.719003310.431428
d a1d a2d f1d f2a'd1'd2'
93.2215125674275.2215099092.093023272.09302
invα'0.01490438α'/αt'26.112899670.4557561
-2.49394255.34979573.597634
d a2取值为256
插齿法计算待定
齿宽b斜齿分度圆螺旋角β齿轮转速n齿条线速度v
10000.0000800.753982237
r/min m/s
d a1d f1d b1αa1εaεβ
208163169.14467235.59067054 1.60182680
齿距p/p n齿轮中心到齿条基准线距离H
31.415926594
旋向相同：β1+β2=Σ
旋向相反：β1-β2=±Σ
中心距最小条件 β2=34.8725978
1.4349280.96215468
参考手册P14-23~P14-27
齿刀加工 (不根切)
h a0*z min’z x min
1.315.1150032150.006739055
齿刀加工标齿 (不顶切)
10111213141516
5711162645101
纵向重合度εβ总面重合度εγ当量齿数z v1αa1αa2εaεβεγz v1z v2 22.88794222.73667 1.8556647420 1.855665100106
αa1αa2εaεβεγz v1z v2 22.88794216.97077 1.9181901090 1.91819100106
x2/x n2外啮合x1=-x2内啮合x1=x2
-0.5
总面重合度εγ当量齿数z v1
αa1αa2εaεβεγz v1z v2 24.17163622.00313 1.8229791320 1.82297910074
αa1αa2εaεβεγz v1z v2 24.17163612.42147 3.0430476910 3.04304810074
αinvα
200.349065850.01490438
300.5235987760.05375149
400.6981317010.14096793
x2/x n2x
0.51
总面重合度εγ当量齿数z v10.92707725
d b1d b2αa1αa2εaεβεγz v1 169.144671195.28938.0265016323.833869 1.4215830 1.42158315
d b1d b2αa1αa2εaεβεγz v1 169.144671195.28931.7489638220.5177731 1.1035490 1.10354915
αinvα
200.349065850.01490438
300.5235987760.05375149
400.6981317010.14096793
a'(外啮合)a'(内啮合)
18090
总面重合度εγ当量齿数z v1
d b1d b2αa1αa2εaεβεγz v1
82.692951244.320135.4865362823.58895720.63933200.63933222
xΣ= 1.67538x
/x n1=0.87x2/x n2=0.80538
1
d b1d b2αa1αa2εaεβεγz v1
82.692951244.320127.4940597817.3741176 1.9400260 1.94002622
xΣ= 1.152689x
/x n1=-0.5x2/x n2=0.652689
1
αinvα
200.349065850.01490438
300.5235987760.05375149
400.6981317010.14096793
a'(外啮合)a'(内啮合)
18090
总面重合度εγ当量齿数z v1
d b1d b2αa1αa2εaεβεγz v1
82.692951244.320135.4865362823.58895720.63933200.63933222
xΣ= 1.67538x
/x n1=0.87x2/x n2=0.80538
1
d b1d b2αa1αa2εaεβεγz v1
82.692951244.320127.4940597817.3741176 1.9400260 1.94002622
xΣ= 1.152689x
/x n1=-0.5x2/x n2=0.652689
1
εγz v1
1.601826822
17∝
z v2 106
z v2 106
z v2 65
z v2 65
z v2 65
z v2 65