主轴强度刚度等计算公式汇总及实例

320185280177abc17078248500.921.121.122.9574.993.9926.51.35140269.39538.7814.801.0202.731.960.910.60.680.214.3253.664.31OK12022C截面弯矩MC=3.99×106Nmm解得：圆柱滚子轴承支反力：FA=22.96KN调心滚子轴承支反力：Fc=75.0KN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1)调心滚子轴承支承中点C截面一、选材某种型号电机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弯曲疲劳极限τ-1≮185MPb许用静应力［σ+］≮280MPa许用疲劳应力［σ-1］=177～213MPa二、轴的强度计算40CrHB284～322抗拉强度σb≮700MPb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屈服点σb≮500MPb弯曲疲劳极限σ-1≮320MPb2.轴的C截面强度校算(截面直径)抗弯断面系数W=πd3/32=269.39㎝3E截面弯矩ME=1.35×106N㎜2)轴伸端支承中点E截面弯矩,(E至受力点距离)Sσ=σ-1/［Kσσa/(βεσ)+ψσσm］=4.32只考虑扭矩作用时的安全系数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=0.6,3.轴的E截面强度校算(截面直径,键槽宽,高,)Sτ=τ-1/［Kττa/(βετ)+ψττm］=53.70ετ=0.68C截面安全系数S=SσSτ/√Sσ2+Sτ2=4.31［S］=1.3～2.5即C截面是足够安全的平均应力折算系数ψτ=0.21只考虑弯矩作用时的安全系数168.74338.398.531.6302.731.960.910.60.70.217.5034.637.33OK8.1d1140l1101d2120l269.54.74E-07OKd1d2d3d4d5d6d76074120120152140140l1l2l3l4l5l6l715.51943432326.551.5M0M1M2M3M4M5M603.567.9217.7928.0633.6839.87M0'M1'M2'M3'M4'M5'M6'08.4318.7742.1722.5712.082.挠度计算各轴段的直径和长度:㎜各轴段弯矩:×105N㎜在B处加单位力不从1N时引起轴上各段的弯矩:N㎜在D处加单位力不从1N时引起轴上各段的弯矩:N㎜［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：㎜扭转角:T×10+6,G×10+8,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=SσSτ/√Sσ2+Sτ2=4.31Sσ=σ-1/［Kσσa/(βεσ)+ψσσm］=4.32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,ετ=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26415840.4710/0.25/~1/iiiiTlmmmGdM00'M01'M02'M03'M04'M05'M06'07.1115.8335.5655.2965.84782M'1+M'22M'2+M'1B处挠度4.2M'1+M'28.4335.6479.71106.9057.2124.165.2M'2+M'116.8745.98103.1187.3046.7312.087.Ii*1056.3614.72101.79101.79262.03188.578.(li/Ii)1052.44E-051.29E-054.22E-064.22E-068.78E-071.41E-069.M1×(4.)(8.)0.00E+001.64E+022.67E+028.03E+021.41E+021.14E+0210.M2×(5.)(8.)1.46E+024.70E+027.75E+021.03E+031.38E+026.77E+0111.=9.+10.1.46E+026.34E+021.04E+031.84E+032.79E+021.82E+0212.=Σ114.12E+0313.y=Σ11/6E0.0032703750.034结论OK4.2M'01+M'027.1130.0567.22126.41176.42209.685.2M'02+M'0114.2238.7786.95146.14186.97221.847.Ii*1056.3614.72101.79101.79262.03188.578.(li/Ii)1052.44E-051.29E-054.22E-064.22E-068.78E-071.41E-069.M1×(4.)(8.)0.00E+001.38E+022.25E+029.50E+024.34E+029.92E+0210.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OKM10'M11'M12'M13'M14'M15'M16'0.091176470.2029411760.4558823530.7088240.84411761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D处挠度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㎜C截面偏转角'6016''''11222110.00330.034(2)(2)6liiiBiiiBiIMMydlmmymmEIlyMMMMMMEI'61016''''111122121110.00330.034(2)(2)6liiicciiicciIMMydlmmymmEIlyMMMMMMEI4.2M'11+M'120.090.390.861.622.262.695.2M'12+M'110.180.501.111.872.402.847.Ii*1056.3614.72101.79101.79262.03188.578.(li/Ii)1052.44E-051.29E-054.22E-064.22E-068.78E-071.41E-069.M1×(4.)(8.)0.00E+001.77E+002.88E+001.22E+015.57E+001.27E+0110.M2×(5.)(8.)1.58E+005.08E+008.38E+002.22E+017.09E+001.59E+0111.=9.+10.1.58E+006.85E+001.13E+013.44E+011.27E+012.87E+0112.=Σ119.54E+0113.θC=Σ11/6E7.57078E-05rad0.05结论OKWYJ133WYJ103键规格22×1432×18h＇67l＇3948d120120〔σp〕8080T11232001612800TN11000002200000OKNO四、轴的临界转速（本电机转速低，可以不验算临界转速）静联接键盘秘能伟递的力矩T=1/2h＇l＇d〔σp〕Mpa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77.58转子中点至左端面d8120l826.5M7M813.550B3A0D610.5441180.4558821AM07'M08'0.45882426.50210000188574108.433824182.5053.00131.0026.50188.57101.792.73E-062.60E-061.99E+031.87E+024.85E+020.00E+002.47E+031.87E+021