【分享】ZA与ZN蜗杆蜗轮的几何计算差异

mrmrw · 发表于 2014-4-3 08:38

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MITCalc软件的帮助界面上，给出了ZA和ZN两种蜗杆蜗轮传动副的几何计算公式，这套公式和国内的有点差异，在这里贴出，供蜗轮蜗杆设计者参考。
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源文件的网址：http://www.mitcalc.com/doc/gear4/help/en/gear4.htm
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Formulas (geometry calculation)

The formulas given in this article are used in geometry calculation.

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1- Centre-line section (mx,ax,sx,ex) , 2-Normal section (mn,an,sn,en), 3-Worm frontal section

Worm basic profile parameters: m (DP for calculation in inches),a,ha*,c*,rf* Module and pressure angle in the centre-line section are selected for spiral gearing ZA, while module and pressure angle in the normal section are selected for common gearing ZN,ZI,ZK,ZH.

Worm and worm gear parameters: z1, z2, x1=0, x2=x

Transmission ratio
i=z1 / z2
Pitch diameter
ZA: d1=mx • z1 / tan(g) = q • mx; d2=mx • z2
ZN: d1=mn • z1 / tan(g) = q • mn; d2=mn • z2
Rolling diameter
ZA: dw1=d1+2 • x • mx; dw2=d2
ZN: dw1=d1+2 • x • mn; dw2=d2
Equivalent diameter: dwe2=2 • a - d2
Mean diameter: DIN (10): dm1=2 • a - dm2; (11) dm1=q • mx
Tip diameter
ZA: da1=d1 + 2 • ha* • mx; da2=d2 + 2 • (ha* + x) • mx; dae2 = da2 + 2 • v • mx
ZN: da1=d1 + 2 • ha* • mn; da2=d2 + 2 • (ha* + x) • mn; dae2 = da2 + 2 • v • mn
Root diameter
ZA: df1=d1 - 2 • (ha* + c*) • mx; df2=d2 - 2 • (ha* + c* - x) • mx
ZN: df1=d1 - 2 • (ha* + c*) • mn; df2=d2 - 2 • (ha* + c* - x) • mn
Addendum
ZA: ha1=ha* • mx; ha2=(ha* + x) • mx
ZN: ha1=ha* • mn; ha2=(ha* + x) • mn
Dedendum
ZA: hf1=(ha* + c*) • mx; hf2=(ha* + c* - x) • mx
ZN: hf1=(ha* + c*) • mn; hf2=(ha* + c* - x) • mn
Pitch angle
ZA: tan(g)=mx • z1 / d1 = z1 / q
ZN: tan(g)=mx • z1 / d1 = z1 / q
Tooth thickness; Tooth space thickness
ZA: sx1=ex1=0.5 • p • mx; sn1=en1=0.5 • p • mx • cos(g);
sx2=0.5 • p • mx + 2 • x • mx • tan(ax); ex2=0.5 • p • mx - 2 • x • mx • tan(ax); sn2=sx2 • cos(g); en2=ex2 • cos(g)
ZN: sn1=en1=0.5 • p • mn; sx1=ex1=0.5 • p • mn / cos(g)
sn2=0.5 • p • mn + 2 • x • mn • tan(an); en2=0.5 • p • mn - 2 • x • mn • tan(an); sx2=sn2 / cos(g); ex2=en2 / cos(g)
Worm face width
ČSN(ZA): [z1<4] L=(11 + 0.06 • z2) • mx; [z1>=4] L=(11 + 0.09 • z2) • mx
ČSN(ZN): [z1<4] L=(11 + 0.06 • z2) • mn; [z1>=4] L=(11 + 0.09 • z2) • mn
DIN (40): L=((de2 / 2)^2 -(a - da1 / 2)^2)^0.5
Worm gear face width
ČSN: [z1<4] b2=0.75 • (1 + 2 / q) • d1; [z1>=4] b2=0.67 • (1 + 2 / q) • d1
DIN: b2<=b2max=2*((dm1/2)^2-(a-de2/2)^2)^0.5
Centre-line distance
ČSN(ZA): a=0.5 • (d1 + d2) + x • mx; a=0.5 • mx • (q + z2 + 2 • x)
ČSN(ZN): a=0.5 • (d1 + d2) + x • mn; a=0.5 • mx • (q + z2 / cos(g) + 2 • x)
DIN: a=(dm1 + dm2) / 2; a = (dwe1 + d2) / 2

cxw770 · 发表于 2014-4-28 07:27

看来这两种总体差不多啊

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