KHN1ζHlim10.9×600
[?H]1 = = = 540 MPa
S1
KHN2ζHlim20.93×550
[?H]2 = = = 511.5 MPa
S1
取[?H]1和[?H]2中的较小者作为该齿轮副的接触疲劳许用应力，即
[?H] = [?H]2 = 511.5 MPa
2）试算小齿轮分度圆直径
3
d ≥ 1t
?2KTZZZZ
Ht1u±1?HEεβ
×× u?[ζ ]ψdH?
?2
? ??
32×1.3×25.88×10005.06+1?2.44×189.8×0.664×0.985?2 = ××??
15.06511.5?? = 30.459 mm
（2）调整小齿轮分度圆直径 1）计算实际载荷系数前的数据准备 ①圆周速度v
πd1tn1π×30.459×631.11v = = = 1.01 m/s
60×100060×1000
②齿宽b
b = φdd1t = 1×30.459 = 30.459 mm
2）计算实际载荷系数KH ①由表查得使用系数KA = 1.25。
②根据v = 1.01 m/s、8级精度，由图查得动载系数KV = 1.08。 ③齿轮的圆周力
Ft1 = 2T1/d1t = 2×1000×25.88/30.459 = 1699.334 N
KAFt1/b = 1.25×1699.334/30.459 = 69.74 N/mm < 100 N/mm
查表得齿间载荷分配系数KH? = 1.4。
④由表用插值法查得8级精度、小齿轮相对支承非对称布置时，KH? = 1.339。 则载荷系数为：
KH = KAKVKH?KH? = 1.25×1.08×1.4×1.339 = 2.531
3）可得按实际载荷系数算的的分度圆直径
d1 = d1t
及相应的齿轮模数
mn = d1cos?/z1 = 38.033×cos14°/24 = 1.538 mm
模数取为标准值m = 2 mm。 3.几何尺寸计算 （1）计算中心距
a =
3
KH32.531 = 30.459×1.3 = 38.033 mm KHt
(z1+z2)mn
2cosβ
=
(24+121)×2
2×cos14°
= 149.434 mm
中心距圆整为a = 150 mm。 （2）按圆整后的中心距修正螺旋角
? = arccos
(z1+z2)mn
2a
= arccos
(24+121)×2
2×150
= 14.843°
即：? = 14°50′35″
（3）计算大、小齿轮的分度圆直径
z1mn24×2d1 = = = 49.655 mm
cosβcos14.843°
z2mn121×2d2 = = = 250.345 mm
cosβcos14.843°
（4）计算齿轮宽度
b = ?d×d1 = 1×49.655 = 49.655 mm
取b2 = 50 mm、b1 = 55 mm。 4.校核齿根弯曲疲劳强度 （1）齿根弯曲疲劳强度条件
2KFT1YFaYSaYεYβcos2β?F = ≤ [?F]
32φdmnz1
1）确定公式中各参数值 ①计算当量齿数
ZV1 = Z1/cos3? = 24/cos314.843° = 26.569 ZV2 = Z2/cos3? = 121/cos314.843 = 133.955
°
②计算弯曲疲劳强度的重合度系数Y??基圆螺旋角：
?b = arctan(tan?cos?t) = arctan(tan14.843°×cos20.561°) = 13.936° 当量齿轮重合度：
??v = ??/cos2?b = 1.663/cos213.936°= 1.765
轴面重合度：
?? = φdz1tan?/π = 1×24×tan14.843°/π = 2.025
重合度系数：
Y? = 0.25+0.75/??v = 0.25+0.75/1.765 = 0.675
③计算弯曲疲劳强度的螺旋角系数Y??
β14.843
Y? = 1-??120 = 1-2.025×120 = 0.75
④由当量齿数，查图得齿形系数和应力修正系数
YFa1 = 2.58 YFa2 = 2.16 YSa1 = 1.62 YSa2 = 1.83
⑤计算实际载荷系数KF
由表查得齿间载荷分配系数KF? = 1.4
根据KH? = 1.339，结合b/h = 11.11查图得KF??????????则载荷系数为
KF = KAKvKF?KF? = 1.25×1.08×1.4×1.309 = 2.474
⑥计算齿根弯曲疲劳许用应力[?F]
查得小齿轮和大齿轮的弯曲疲劳极限分别为?Flim1 = 500 MPa、?Flim2 = 380 MPa。 由图查取弯曲疲劳寿命系数KFN1 = 0.85、KFN2 = 0.89 取安全系数S=1.4，得
KFN1ζFlim10.85×500
[?F]1 = = = 303.57 MPa
S1.4
KFN2ζFlim20.89×380
[?F]2 = = = 241.57 MPa
S1.4
2）齿根弯曲疲劳强度校核
22KFT1YFaYSaYεYβcosβ?F1 =
32φdmnz1
2×1000×2.474×25.88×2.58×1.62×0.675×0.75cos214.843°=
321×2×24= 54.946 MPa ≤ [?F]1
22KFT1YFaYSaYεYβcosβ?F2 =
32φdmnz1
2×1000×2.474×25.88×2.16×1.83×0.675×0.75cos214.843°=
321×2×24= 51.964 MPa ≤ [?F]2 齿根弯曲疲劳强度满足要求。 5.主要设计结论
齿数z1 = 24、z2 = 121，模数m = 2 mm，压力角? = 20°，螺旋角? = 14.843°= 14°50′35″，中心距a = 150 mm，齿宽b1 = 55 mm、b2 = 50 mm。 6.齿轮参数总结和计算
代号名称 模数m 齿数z 螺旋角β 齿宽b 分度圆直径d 齿顶高系数ha 顶隙系数c 齿顶高ha 齿根高hf 全齿高h 齿顶圆直径da 计算公式 m×ha m×(ha+c) ha+hf d+2×ha 高速级小齿轮 2mm 24 左14°50′35″ 55mm 49.655mm 1.0 0.25 2mm 2.5mm 4.5mm 53.655mm 高速级大齿轮 2mm 121 右14°50′35″ 50mm 250.345mm 1.0 0.25 2mm 2.5mm 4.5mm 254.345mm