m4
a=(z1 +z2)=(25+125)=300mm 22 d1 =mz1 =4 25=100mm
db1 =mz1 cosa =4 5cos20°=93.97mm d =(z +2h*)m=(25+2 1.0) 4=108mm a1 1 a
一对正确安装的渐开线标准直齿圆柱齿轮(正常齿制)。已知模数m=4 mm,齿数z1=25,z2=125。求传动比i,中心距a。并用作图法求实际啮合线长和重合度e 。
d2 =mz2 =4 125=500mmdb2 =mz2 cosa =4 25cos20°=469.85mm d =(z +2h*)m=(125+2 1.0) 4=508mm a2 2 a
B1B2 = 0.002 10.5 = 0.021m = 21mm (计算值:20.388 mm) -1-
8-29
BBBB21
e = 12 = 12 = =1.78(计算值:1.73) pb pmcosa 3.14 4cos20°
设在图8-54 所示的齿轮传动中,z1=20,z2=20,z3=30。齿轮材料均为45 钢调质,HBS1=240,HBS2=260, HBS3=220。工作寿命为2500h。试确定在下述两种情况中,轮2 的许用接触疲劳应力[sH]和许用弯曲疲劳应力[sF]。(1)轮1 主动,转速为20r/min;(2)轮2 主动,转速为20r/min。
图8-45 题8-29 图解 (1)轮1主动:gH2=gF2=1(轮2的接触应力为脉动循
环,弯曲应力为对称循环)
N =60ngL =60 20 1 2500=3 106 22h
p164图8-34:YN2 =1.0p165 图8-35:ZN2 =1.25p164 表8-8: SFmin =1.25,SHmin =1.0(失效概率≤1/100)p162 图8-32(c):sFlim2
=0.7 230=161MPa(轮齿受双向弯曲应力作用) p163图8-33(c):sHlim2
=480MPa
YST = 2.0p162 式8-27:[s ]=
F2
sFlim2YST
Y =
161 2
1.0=257.6MPa
S 1.25 F min
sHlim2
Z =480
1.25=600.0MPa H2 S N2 1.0
N2
p162式8-28:[s ]=
H min(2)轮2 主动:g H2=g F2=2(轮2 的接触应力和弯曲应力均为脉动循环)
N =60ngL =60 20 2 2500=6 106 22h
p164 图8-34:YN 2 = 0.99p165 图8-35:ZN2 =1.2p164 表8-8: SFmin =1.25,SHmin =1.0(失效概率≤1/100) p162 图8-32(c):sFlim2 =230MPap163图8-33(c):sHlim2 =480MPa
YST = 2.0p162 式8-27:[s ]=
sFlim2YST
230 2Y = 0.99=364.32MPa
H2
N2
p162式8-28:[s ]=
H min
sHlim2
Z =
480
1.2=576.0MPa S 1.0
一闭式单级直齿圆柱齿轮减速器。小齿轮1 的材料为40Cr,调质处
理,齿面硬度250HBS;大齿轮2 的材料为45 钢,调质处理,齿面硬度220HBS。电机驱动,传递功率P=10kW,n1=960r/nin,单向转动,载荷平稳,工作寿命为5 年(每年工作300 天,单班制工作)。齿轮的基本参数为:m=3mm, z1=25,z2=75,b1=65mm,b2=60mm。试验算齿轮的接触疲劳强度和弯曲疲劳强度。
F2
S 1.25 F min
N2
8-30
解 1几何参数计算:
-2-
d1 =mz1 =3 25=75mmd =(z +2h*)m=(25+2 1.0) 3=81mm
a1 1 a
αa1 =cos-1(d1cosa/da1)=cos-1(75cos20°/81)=29.53° d2 =mz2 =3 75=225mm
d =(z +2h*)m=(75+2 1.0) 3=231mm a2 2 a
mαa2 =cos-1(d2 cosa/da2)=cos-1(225cos20°/231)=23.75° a= (z1 +z2)= 3
(25+75)=150mm
1
22e = [z1(tanaa1 - tana￠) + z2 (tanaa2 - tana￠)]
1
2p= [25 (tan29.53°-tan20°)+75 (tan23.75°-tan20°)]=1.71 2pu=z2 /z1 =75/25=3
n2 =z1n1/z2 =25 960/75=320r/min 2载荷计算:
p152 表8-5: KA =1.0v= pd1n1 =p ?75 960=3.77m/s
60000 60000p153 表8-6: 齿轮传动精度为9 级,但常用为6~8 级,故取齿轮传动精度为8 级p152 图8-21:Kv =1.18 b2 60
fd ===0.8 d1 75
p154 图8-24:Kb = 1.07 (软齿面,对称布置) p154 图8-25: Ka = 1.25
N =60ngL =60 960 1 (5 300 8)=6.9 108 11h N = 60n gL = 60 320 1 (5 300 8) = 2.3 108 22h
p164 图8-34:YN1 =0.88,YN2 =0.92p165 图8-35:ZN1 =0.98,ZN2
=0.94p164 表8-8: SFmin =1.25,SHmin =1.0(失效概率≤1/100) p162 图8-32(c):sFlim1 =220MPa,sFlim2 =270MPap163 图8-33(c):sHlim1 =550MPa,sHlim2 =620MPa
P 10
K = KAKvKb Ka =1.0 1.18 1.07 1.25=1.58 T =9550 =9550 =99.48Nm
1
n1 960 3许用应力计算: YST = 2.0Flim1 ST
p162式8-27:[s ]=
F mins Y
Y =
220 2
0.88=309.76MPa F1 S N1 1.25
[sF2]=
sFlim2YST 270 2
YN2 = 0.92=397.44MPa