主轴强度刚度等计算公式汇总及实例

+］≮280MPa

许用疲劳应力［σ-1］=177～213MPa二、轴的强度计算

1.轴的结构设计和受力分析轴的结构尺寸参见WYJ133-20-3

受力分析：轴伸端上轴的最大载荷为50KN转子部分的磁极重约为0.92KN轴伸处飞轮重约为1.12KN

额定转矩(扭矩)TN=1100Nm=1.1×106N㎜外解得：圆柱滚子轴承支反力：FA=22.96KN 调心滚子轴承支反力：Fc=75.0KN1)调心滚子轴承支承中点C截面 C截面弯矩 MC=3.99×106Nmm

2)轴伸端支承中点E截面弯矩, (E至受力点距离) E截面弯矩ME=1.35×106N㎜

2.轴的C截面强度校算 (截面直径)

抗弯断面系数 W=πd3/32=269.39㎝3

抗扭断面系数 WP=πd3/16=538.78㎝3弯曲应力幅σa=MC/W=14.81MPa切应力幅τm=τa=TN/(2WP)=1.02MPa对称循环弯曲应力的平均应力 σm=0正应力有效应力集中系数Kσ=2.73切应力有效应力集中系数Kτ=1.96表面质量系数β=0.91尺寸系数εσ=0.6,ε

τ

=0.68

平均应力折算系数ψτ=0.21只考虑弯矩作用时的安全系数

Sσ=σ-1/［Kσσa/(βεσ)+ψσσm］=4.32只考虑扭矩作用时的安全系数

Sτ=τ-1/［Kττa/(βετ)+ψττm］=53.70C截面安全系数 S=SσSτ/√S2σ+S2τ=4.31 >［S］=1.3～2.5即C截面是足够安全的

3.轴的E截面强度校算 (截面直径,键槽宽,高, )

320185280177

ab170

78500.921.121.122.9574.993.9926.51.35140269.39538.7814.801.02

02.731.960.910.60.680.214.3253.664.31OK120

c248

22

抗弯断面系数 W=πd3/32-bt(d-t)2/d=151.2㎝3抗扭断面系数 WP=πd3/16-bt(d-t)2/d=320.9㎝3弯曲应力幅σa=ME/W=8.931MPa切应力幅τm=τa=TN/(2WP)=1.71MPa对称循环弯曲应力的平均应力 σm=0正应力有效应力集中系数Kσ=2.73切应力有效应力集中系数Kτ=1.96表面质量系数β=0.91尺寸系数εσ=0.6,ε

τ

=0.7

平均应力折算系数ψτ=0.21只考虑弯矩作用时的安全系数

Sσ=σ-1/［Kσσa/(βεσ)+ψσσm］=4.32只考虑扭矩作用时的安全系数

Sτ=τ-1/［Kττa/(βετ)+ψττm］=53.70E截面安全系数 S=S2σSτ/√S2σ+Sτ=4.31 >［S］=1.3～2.5即E截面是足够安全的三、轴的钢度计算1.扭转变形

材料的切变模量 G=8.1×108MPa 轴受转矩作用的长度和外直径： ㎜

d1l1d2l2

扭转角: T×10+6 ,G×10+8,

5842TiliG40.47106/m0.25/m~1/mi1di2.挠度计算

各轴段的直径和长度: ㎜

d1d2d3d4d56074120120152l1l2l3l4l515.519434323各轴段弯矩: ×105N㎜

M0M1M2M3

M403.567.9217.79

28.06在B处加单位力不从1N时引起轴上各段的弯矩:N㎜

M'0M'1M'2M'

3M'408.4318.7742.17

22.57

在D处加单位力不从1N时引起轴上各段的弯矩:N㎜

168.74338.398.531.63

02.731.960.910.60.70.217.5034.637.33OK

8.114010112069.54.74E-07OK

d6140l626.5M533.68M'512.08

d7140l751.5M639.87M'

6M01'M02'

07.1115.83

材料的弹性模量 E=2.1×105MPa截面的惯性矩 I=πd4/64,单位㎜4轴中间转子支架支承点B处挠度M00'

M03'

35.56M04'55.29M05'65.84

M06'

78

yBi166li0MiMi'dl0.0033mmy0.034mmEIi2M'1+M'22M'2+M'1

yBi1liM1(2M'1M'2)M2(2M2'M1')6EII8.4316.87

6.362.44E-050.00E+001.46E+021.46E+02

35.6445.9814.721.29E-051.64E+024.70E+026.34E+024.12E+030.003270375

OK

30.0538.7714.721.29E-051.38E+02

79.71103.11101.79

106.9087.30101.79

57.2146.73262.03

24.1612.08188.57

B处挠度4. 2M'1+M'25. 2M'2+M'17. Ii*1058. (li/Ii)1059.M1×(4.)(8.)10.M2×(5.)(8.)11.=9.+10.12.=Σ1113.y=Σ11/6E

结论 D处挠度4. 2M'01+M'025. 2M'02+M'017. Ii*1058. (li/Ii)1059.M1×(4.)(8.)

4.22E-064.22E-062.67E+028.03E+027.75E+021.03E+031.04E+031.84E+03

8.78E-071.41E-061.41E+021.14E+021.38E+026.77E+012.79E+021.82E+02

0.034

7.1114.226.362.44E-050.00E+00

67.2286.95101.79

126.41146.14101.79

176.42186.97262.03

209.68221.84188.57

4.22E-064.22E-062.25E+029.50E+02

8.78E-071.41E-064.34E+029.92E+02

10.M2×(5.)(8.)1.23E+023.96E+026.53E+021.73E+035.53E+021.24E+0311.=9.+10.1.23E+025.34E+028.78E+022.68E+039.87E+022.24E+0312.=Σ111.01E+0413.y=Σ11/6E0.0080154660.034

结论OK

3.轴上调心滚子轴承支承中点C截面的偏转角计算

在C截面处加单位力矩1N㎜时引起轴上各段的弯矩: N㎜

M11'M12'M13'M14'M15'M16'M10'

0.091176470.2029411760.4558823530.7088240.84411761'6liMMi1icycdl0.0033mmy0.034mm0EIi1iC截面偏转角6l''''cyciM(2MM)M(2MM1111221211)i16EII4. 2M'11+M'125. 2M'12+M'117. Ii*1058. (li/Ii)1059.M1×(4.)(8.)

0.090.186.362.44E-050.00E+00

0.390.5014.721.29E-051.77E+00

0.861.11101.79

1.621.87101.79

2.262.40262.03

2.692.84188.57

4.22E-064.22E-062.88E+001.22E+01

8.78E-071.41E-065.57E+001.27E+017.09E+001.59E+011.27E+012.87E+01

0.05

10.M2×(5.)(8.)1.58E+005.08E+008.38E+002.22E+0111.=9.+10.1.58E+006.85E+001.13E+013.44E+0112.=Σ119.54E+0113.θC=Σ11/6E7.57078E-05rad

结论OK

四、轴的临界转速（本电机转速低，可以不验算临界转速）

五、键的强度计算

假设压力在键的接触长度内均匀分布，则根据挤压强度或耐磨性的条件性计算，求得联接所能传递的转矩

静联接 键盘秘能伟递的力矩 T= 1/2 h＇l＇d〔σp〕Mpa

WYJ133WYJ103

键规格22×1432×18h＇67l＇3948d120120〔σp〕8080T11232001612800TN11000002200000

OKNO

转子中点至左端面

77.5

8

d8120l826.5

M713.55B 31M80A0D6

0.5441180.455882

1A

M07'26.5

M08'

0

0.45882421000018857410

8.433824

182.50131.00188.57

2.73E-061.99E+034.85E+022.47E+031

53.0026.50101.79

2.60E-061.87E+020.00E+001.87E+02