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本帖最后由 1561720203 于 2014-3-24 16:41 编辑
普通圆柱蜗杆传动几何尺寸计算
(轴交角90度,已知中心距)
啮合中心距: A=input(95)
蜗杆轴向模数: m=input(5)
蜗杆头数: z1=input(1)
蜗杆分度圆直径: d1=input(40)
蜗轮齿数: z2=input(30)
蜗轮分度圆直径: d2=m*z2= 150
蜗杆直径系数: q=d1/m= 8
齿数比: u=z2/z1= 30
蜗轮变位系数: x2=A/m-0.5*(q+z2)= 0
蜗杆分度圆柱导程角: r=atan(z1/q)= 7.125016
法向模数: mn=m*cos(r)= 4.961389
蜗杆轴向齿距: px1=pi*m= 15.707963
蜗杆螺旋线导程: pz1=px1*m= 78.539816
蜗杆轴向齿形角: angle=input(20)
蜗杆节圆直径: d'1=(q+2*x2)*m= 40
蜗杆节圆柱导程角: r'=atan(z1/(q+2*x2))= 0.125
渐开线蜗杆:
基圆柱导程角: rb=acos(cos(angle)*cos(r))= 21.182185
基圆直径: db1=z1*m/tan(rb)= 12.902668
法向基节: pbm=pi*m*cos(rb)= 14.646674
蜗杆齿顶高: ha1=m= 5
蜗杆齿根高: hf1=1.2*m= 6
蜗杆全齿高: h1=ha1+hf1= 11
顶隙: c1=0.2*m= 1
齿根圆角半径: pf=0.3*m= 1.5
蜗杆齿顶圆直径: da1=d1+2*ha1= 50
蜗杆齿根圆直径: df1=d1-hf1*2= 28
蜗杆齿宽: b1=2.5*m*(z2+1)^0.5= 69.597055
蜗杆螺牙分度圆轴向弦齿厚: sx1_=0.5*m*pi= 7.853982
蜗杆螺牙分度圆示向弦齿厚: sn1_=0.5*pi*m*cos(r)= 7.793332
蜗杆螺牙法向测齿高度: hcn1_=m+0.5*sn1_*tan(0.5*asin(sn1_*sin(r)^2/d1))= 5.005840
测棒直径: dm=1.67*m= 8.35
蜗杆跨棒距: md1=d1-(px1-0.5*pi*m)*cos(r)/tan(angle)+dm*(1/sin(angle)+1)= 51.351762
蜗轮分度圆螺旋角: B2=r'= 0.125
蜗轮中圆螺旋角: Bm2=r= 7.125016
蜗轮分度圆直径: d2=m*z2= 150
蜗轮中圆直径: dm2=d2+2*m*x2= 150
蜗轮齿顶高: ha2=(1+x2)*m= 5
蜗轮齿根高: hf2=(1.2-x2)*m= 6
蜗轮全齿高: h2=ha2+hf2= 11
蜗轮齿顶圆直径: da2=d2+ha2*2= 160
蜗轮齿根圆直径: df2=d2-2*hf2= 138
蜗轮外圆直径: de2=da2+m= 165
蜗轮齿宽: b2=2*m*(0.5+(q+1)^0.5)= 35
蜗轮齿宽包角: xita=2*asin(b2/d1)= 122.089951
蜗轮喉圆半径: rg2=A-0.5*da2= 15
db2=d2*cos(angle)= 140.953893
端面重合度: ea=(0.5*(da2^2-db2^2)^0.5+m*(1-x2)/sin(angle)-0.5*d2*sin(angle))/(pi*m*cos(angle))= 1.817161
蜗杆转速: n1=input(2000)
分度圆处滑动速度: vs=pi*d1*n1/(6*10000*cos(r))= 4.221388
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~有错:
蜗杆节圆柱导程角: r'=atan(z1/(q+2*x2))= 0.125
正确的结果为:
r'=atan(z1/(q+2*x2))= 7.12502
下面是宇航CAD的计算结果:
D:\普通圆柱蜗杆传动几何尺寸计算.txt
普通圆柱蜗杆传动几何尺寸计算
(轴交角90度,已知中心距)
啮合中心距:A=95 = [ 95 ]
蜗杆轴向模数:M=5 = [ 5 ]
蜗杆头数:Z1=1 = [ 1 ]
蜗杆分度圆直径:D1=40 = [ 40 ]
蜗轮齿数:Z2=30 = [ 30 ]
蜗轮分度圆直径:D2=M*Z2 = [ 150 ]
蜗杆直径系数:Q=D1/M = [ 8.0 ]
齿数比:U=Z2/Z1 = [ 30.0 ]
蜗轮变位系数:X2=A/M-0.5*(Q+Z2) = [ 0.0 ]
蜗杆分度圆柱导程角:R=ATAN(Z1/Q) = [ 7.12502 ]
法向模数:MN=M*COS(R) = [ 4.96139 ]
蜗杆轴向齿距:PX1=PI*M = [ 15.708 ]
蜗杆螺旋线导程:PZ1=PX1*M = [ 78.5398 ]
蜗杆轴向齿形角:ANGLE=20 = [ 20 ]
蜗杆节圆直径:D_1=(Q+2*X2)*M = [ 40.0 ]
蜗杆节圆柱导程角:R'=ATAN(Z1/(Q+2*X2)) = [ 7.12502 ]
渐开线蜗杆:
基圆柱导程角:RB=ACOS(COS(ANGLE)*COS(R)) = [ 21.1822 ]
基圆直径:DB1=Z1*M/TANG(RB) = [ 12.9027 ]
法向基节:PBM=PI*M*COS(RB) = [ 14.6467 ]
蜗杆齿顶高:HA1=M = [ 5 ]
蜗杆齿根高:HF1=1.2*M = [ 6.0 ]
蜗杆全齿高:H1=HA1+HF1 = [ 11.0 ]
顶隙:C1=0.2*M = [ 1.0 ]
齿根圆角半径:PF=0.3*M = [ 1.5 ]
蜗杆齿顶圆直径:DA1=D1+2*HA1 = [ 50 ]
蜗杆齿根圆直径:DF1=D1-HF1*2 = [ 28.0 ]
蜗杆齿宽:B1=2.5*M*(Z2+1)^0.5 = [ 69.5971 ]
蜗杆螺牙分度圆轴向弦齿厚:SX1=0.5*M*PAI = [ 7.85398 ]
蜗杆螺牙分度圆示向弦齿厚:SN1=0.5*PAI*M*COS(R) = [ 7.79333 ]
蜗杆螺牙法向测齿高度:HCN1=M+0.5*SN1*TANG(0.5*ASIN(SN1*SIN(R)^2/D1)) = [ 5.00584 ]
测棒直径:DM=1.67*M = [ 8.35 ]
蜗杆跨棒距:MD1=D1-(PX1-0.5*PAI*M)*COS(R)/TANG(ANGLE)+DM*(1/SIN(ANGLE)+1)
= [ 51.3518 ]
蜗轮分度圆螺旋角:B2=R1 = [ 7.12502 ]
蜗轮中圆螺旋角:BM2=R = [ 7.12502 ]
蜗轮分度圆直径:D2=M*Z2 = [ 150 ]
蜗轮中圆直径:DM2=D2+2*M*X2 = [ 150.0 ]
蜗轮齿顶高:HA2=(1+X2)*M = [ 5.0 ]
蜗轮齿根高:HF2=(1.2-X2)*M = [ 6.0 ]
蜗轮全齿高:H2=HA2+HF2 = [ 11.0 ]
蜗轮齿顶圆直径:DA2=D2+HA2*2 = [ 160.0 ]
蜗轮齿根圆直径:DF2=D2-2*HF2 = [ 138.0 ]
蜗轮外圆直径:DE2=DA2+M = [ 165.0 ]
蜗轮齿宽:B2=2*M*(0.5+(Q+1)^0.5) = [ 35.0 ]
蜗轮齿宽包角:XITA=2*ASIN(B2/D1) = [ 122.09 ]
蜗轮喉圆半径:RG2=A-0.5*DA2 = [ 15.0 ]
DB2=D2*COS(ANGLE) = [ 140.954 ]
端面重合度:EA=(0.5*(DA2^2-DB2^2)^0.5+M*(1-X2)/SIN(ANGLE)-0.5*D2*SIN(ANGLE))/(PAI*M*CO
S(ANGLE)) = [ 1.81716 ]
蜗杆转速:N1=2000 = [ 2000 ]
分度圆处滑动速度:VS=PAI*D1*N1/(6*10000*COS(R)) = [ 4.22139 ]
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