锥齿轮承载能力计算方法 第32部分：锥齿轮和准双曲面齿轮的ISO评价体系 胶合承载能力算例

4锥齿轮承载能力计算方法第32部分：锥齿轮和准双曲面齿轮的ISO评价体系胶合承载能力算例和/或较大的齿宽（b>13mmn）时，ISO10设计。如果本文件描述的内容只涉及以上一种或多种（而非全部）形式，会有特本文件中的公式基于当量圆柱齿轮，仅限于当量圆柱齿轮端面重合度εvα<2的锥齿轮。计算结果在），ofloadcapacityofbevelgears—Part20:Calculationofscuffingloadcapacity—Flashtemperaturemethod）注：GB/Z10062.20—XXXX锥齿轮承载能力的计算方法第20部分：胶合承载能计算闪温法（ISO/TS5A.1初始数据节锥参数的初始数据如表A.1所示，齿廓参数的输入数Σ90°√√√a√√√z1,2√√√dm2 √ de2大轮大端节圆直径√—√√√√βm135°√——βm235° √√刀盘半径√√√z0——√√20°20°fαlim0xhm1—chamkhap kdkhfp—kcxsmn—kt jet22.1342°6.4934°ρa01ρa02spr1D,Cspr2D,C表A.3和表A.4列出了与几何及工况有关的参6dm1,2ζmp0°ham1,24.836mm/ζR0°hfm1,22.394mm/Re1,2工作齿/非工作齿有效压力角20°/20°Rm1,2工作齿面/非工作齿面切齿压力角20°/20°70.253°αlim极限压力角0°δa1,226.240°/72.387°δf1,263.760°khfp基本冠轮齿根高系数xsm1,2小轮/大轮齿厚修正系数ζm小轮轴向平面偏置角0.000°met24.536mmsmn1,2b2eff低小轮和大轮装配条件T1KA小轮和大轮的材料数据（表面渗碳硬化钢）Eν7ρMλMRzRaRzfptθOilθOil,Refρ15当量圆柱齿轮的计算结果列于表A.5，应力、速度和摩擦系数列计算结果如表A.7所示，允许的啮合温度如表A.8所示。安全系数的计算结果可88−−dv2sinαvetgY(E)=gva1注：在以下的所有公式中，gY是关于Y的函数gY=gY(Y)0.085mm1.397mm2.709mm4.021mm5.334mm6.646mm7.958mm9.27mm离fm,Y=(gva2−gvα/2+gY).co99tanY+tanβvb21.59mm21.59mm21.59mm21.59mm21.59mm2.593mm4.643mm6.694mm8.744mm(−x1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff (y2,Y=−x2,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff x1,Y21,Y−y2,Y215.25mm15.25mmllbm,Y离ft,Y=fm,Y+pvet.cosβvb5.064mm6.17mm7.275mm8.38mm9.485mm10.59mmtany+tanβvb9.938mm16.09mm18.14mm(y1,Y1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff 0.417mm1.729mm3.041mm4.353mm5.665mm(−x2,Ytanβvb+fYcosβvb+tanβvb|fY(22, bv,eff Clb,Y2,|)(2,|)(2,bv,efffYfmax00008.964mm6.53mm4.095mm1.661mmlbt,Y8.428mm6.186mm3.92mm1.615mm离fr,Y=fm,Y−pvet.cosβvbtany+tanβvb7.551mm9.601mmfYcosβvbfYcosβvb+tanβvb|(fYsinβvb+,|−2(gvα−bv,efftany)tany+tanβvb(y1,Y1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff ((y2,Y=−x2,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb(bv,eff))|2,|0.895mm2.207mm00000.060.07lb0r,Y=x1,Y2−y2,Y24.095mm6.53mm8.964mmlbr,Ylb,Y)3.92mm6.186mm8.428mm数0000数1数0000=τ.pY.lbt,Y1A,Y=τ.p,Y.lbm,Y8.295mmA,Y=τ.pY.lbr,Y4.874mm7.021mm9.207mm0.650.7917.02mm1Hβ00wt1,2s=vmt1,2.sinβm1,2(|sinαnD,C(ddv1/2,1.61m/s度(|sinαnD,C(ddv2/2,2.33m/swwt1,Ywt1h,Y41.31°25.21°.sin1.78m/swt2vert,Y2,Y.sin2,Y)vΣh,Y1.83m/s1.94m/s3.24m/svgsmt1.cosβm1.(tanβm1−tanβm2)0.011m/s0.187m/s0.362m/s0.537m/s0.712m/s0.887m/s1.062m/s1.238m/s0.120.221712.67N/mm2916.008N/mm21635.31N/mm2PL.R0.25.XL22−D−DLde2」XCA=1.0其中B>5ηθ.Pθα38数6.αp,θ.E,EEh,Y=1.95.103.Prel,Y.G0.73.U0.09μmμmμmμmμmμmμmμmμmμmμmh0,Y=h0,,Y.Cth,Y.1.05.e−0.16.Rz0.03µmXL=1.0矿物油1)ε其中ε=2.01vΣvert,Y.XL.CRS11BM1BM1BMBM2PM2.cM2.λM2θθfl,Y.σH,mod,Y.g,Y.2BM1wt,vert1,Y+BM2wt,vert,2Y 8Prel,Y.σH,mod,Y,XEXQ.Kr1TXW具有平均奥氏体含量的钢1WrelTX=XWWrelTWTXWT1度θS,DIN+1.4.XL.XWrelT.T183(100)0.02.||(v40,XT=0.45.||.||.|expXT=0.45.||.||.|exp|其中aref=91.5mm(θOil,ref,(1.0,(dm1+dm2,(XT−1).CTh其中CTh=0;XT>1.0θS,YC,YK或θS,YKC,YC,YKS,min7.08.37.24.83.63.02.52.12.5Σ√90°√√a√√√√√ √ de2√—√√√√βm1—50°——βm2√ √√√√√z0√ √√20°20°fαlim1xhm1—khap—kdkhfp—kc—kt1°fαlim4°xhm1khapkhfpζmp11.390°ζR10.319°2.508mm/4.092mmRe1,2工作齿面/非工作齿面有效压力角20°/20°Rm1,2工作齿面/非工作齿面切齿压力角22.253°21.288°/68.323°−2.253°小轮/大轮顶锥角25.232°/69.323°20.303°/64.324°khfp基本冠轮齿根高系素xsm1,2ζm10.603°smn1,2b2eff低T1KAEνρM440J/(kgK)（按照GB/Z10062.20—XXXX的表5）λMRzRaRzfptθOil,Refρ15当量圆柱齿轮的计算结果列于表B.5，应力、速度和计算结果如表B.7所示，允许的啮合温度如表B.8所示。安全系−−dv2sinαvetgY(A)=−gva2gY(E)=gva1点gY(Y)=(gY(A)+ksgvα)+Y.注：在以下所有的公式中，gY是一个关于Y的函数gY=gY(Y)-2.96mm0.17mm1.214mm2.257mm3.301mm4.344mm5.388mm6.431mm离fm,Y=(gva2−gvα/2+gY).cosβvb2.57mm3.667mm4.764mm5.86mm6.957mm8.053mm9.15mm12.44mm(y1,Y1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff -4.77mm-4.68mm(y2,Y=−x2,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb(v,eff)2,4.68mm4.77mmx1,Y2−y2,Y2lb,Y)离ft,Y=fm,Y+pvet.cosβvb4.644mm5.432mm6.219mm7.006mm7.794mm8.581mm9.368mm11.73mm(y1,Y1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff 0.552mm1.595mm2.639mm3.682mm4.726mm(−x2,Ytanβvb+fYcosβvb+tanβvb|fY(22, bv,eff lb0t,Yx1,Y−x2,Y2−y2,Y2lbt,Ylb,Y)8.786mm7.454mm6.115mm4.767mm3.408mm2.033mm离fr,Y=fm,Y−pvet.cosβvb-9.368mm-8.581mm-7.794mm-7.006mm-6.219mm-5.432mm-4.644mm-3.857mmtany+tanβvb2.681mm3.778mm4.874mm5.971mm7.067mm8.164mm9.261mm12.55mm(y1,Y1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff (+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff 0.492mm1.535mm2.579mm3.622mm4.241mm4.331mmlb0r,Y=x1,Y−x2,Y2−y2,Y23.554mm5.007mm6.461mm7.914mm9.368mmlbr,Ylb,Y)3.408mm4.767mm6.115mm7.454mm8.786mm数数111数=π.pY.lbt,YA,Y=π.p,Y.lbm,YA,Y=π.pY.lbr,Y1.030.910.85接触点Y处的垂直于啮合线22.73mm1Hβ22,+y2,Y)2(|(bv,eff2y1,Y+y2,Y)2(|(bv,eff2y1,Ygvα2va22数00wt1,2s.sinβm1,2度(|sinαnD,C(ddv1/2,0.67m/s度0.62m/s1.83m/s9.568°14.61°20.97°22.46°23.95°21.83°.sinwt2vert,Y2,Y.sin2,Y)1.66m/s和2.68m/s2.87m/svgs=vmt1.cosβm1.(tanβm1−tanβm2)0.023m/s0.163m/s0.304m/s0.444m/s0.585m/s0.725m/s0.866m/s1.03m/s0.381068.47N/mm21369.83N/mm2885.645N/mm2554.287N/mm2((6,(gva,max,σH,mod,Y=σH,Y+|.eσH,mod,Y=σH,Y+|.e+0.25|.max(σH,Y).|Y761.749N/mm2P+1.993.10−5.Ra0.25.XL22−D−DLde2」XCA=1.0for（因此？）B>5([a.b]V,1.2XCAlog(313/373)ηθ.Pθα386.αp,θ.E,0.000221390.000200640.00016702=1.95.103.Prel,Y.G0.73.U0.09μmμmμmμmμmμmμmμmμmμmμm0.99990.99990.99990.9999h0,Y=h,Y.Cth,Y.1.05.e−0.16.RzXXL=1.0formineraloil（未翻译？）1)ε其中ε=2.01.XL.CRS1XE=1.01BM2PMPM2.cM2.λM2θC,Yr1TXW具有平均奥氏体含量的钢1WrelTX=XWWrelTWTXWT1度(XT−1).CTh其中CTh=0forXT>1.0θS,YtKC,Y算例3是一个准双曲面齿轮组，其几何参数根据ISO23509规定的方法2据如表C.1所示，齿廓参数的输入数据如表CΣ√√90°√a√√√√√ de2√√—√√√√βm1—√——βm2√ 21.009°√√√√z0√—√20°20°fαlim1xhm1—khap—kdkhfp—kc—ktjet20°0°ρa01ρa02表C.3和表C.4列出了与几何及工况有关的ζmp23.969°ζR21.647°Re1,2工作齿面/非工作齿面有效压力角20°/20°Rm1.2工作齿面非工作齿面切齿压力角24.132°63.212°-4.132°63.212°63.212°khfp基本冠轮齿根高因素xsm1,2ζm21.647°smn1,2b2eff低T1KAEνρMλMRzRa0.5µm/0.5µmRzfptθOil,Refρ15计算结果如表C.7所示，允许的啮合温度−−dv2sinαvetgY(A)=−gva2gY(E)=gva1点注：在下面的公式中gY是关于Y的函数，gY=gY(Y)fm,Y=(gva2−gvα/2+gY).cosβvb=fYcos=fYcosβvb+tanβvb|(fYstanY+tanβvb((b,eff)1v,efftanY+tanβvbfYcosβvb+tanβvb|(fYsinβvb+,|−2(gvα−bv,efftanY)(y1,Y1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff 0.559mm2.186mm(−x2,Ytanβvb+fYcosβvb+tanβvb|fY(22, bv,eff 1.069mm2.697mm4.325mm5.953mm6.869mm7.187mm7.504mm7.822mm8.139mmx1,Y2−y2,Y2lb,Y)ft,Y=fm,Y+pvet.cosβvb6.297mm7.696mm9.094mm13.29mm=fYcos=fYcosβvb+tanβvb|(fYstanY+tanβvb8.899mm(y1,Y1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb(v,eff)2,6.26mm(−x2,Ytanβvb+fYcosβvb+tanβvb|fY(22, bv,eff 0000lbt,Ylb,Y)fr,Y=fm,Y−pvet.cosβvb-13.29mm-9.094mm-7.696mm-6.297mm-4.899mmtany+tanβvb2.288mm4.488mm6.687mm8.887mm((b,eff)12,Ytany+tanβvbv,efffYcosβvb+tanβvb|(fYsinβvb+,|−2(gvα−bv,efftany)(y1,Y1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff (−x2,Ytanβvb+fYcosβvb+tanβvb|fY(22, bv,eff -6.26mm0.251mm0000lb0r,Y=x1,Y222.664mm5.224mm7.784mmlbr,Ylb,Y)2.569mm4.972mm7.339mm9.685mm000010000=π.pY.lbt,YA,Y=π.p,Y.lbm,Y9.594mm9.594mm7.302mmA,Y=π.pY.lbr,Y0.591mm2.007mm3.941mm6.148mm8.446mm9.875mm1Hβlbm,Y数00wt1,2s.sinβm1,2度(|sinαnD,C(ddv1/2,度(|sinαnD,C(ddv2/2,2.02m/st1h,.sin6.39m/swt2vert,Y2,Y.sin2,Y)vΣh,Y4.14m/s6.99m/s和vgsmt1.cosβm1.(tanβm1−tanβm2)vgh,Y=2.vmt1.gY0.569m/s1.386m/s2.204m/s3.021m/s3.838m/s4.656m/s5.473m/s6.51m/s7.59m/s1292.3405N/mm21595.052N/mm21669.754N/mm21650.7234N/mm21651.948N/mm21632.9453N/mm21578.668N/mm21560.7383N/mm21508.893N/mm21491.5251N/mm21388.571N/mm21372.7248N/mm21199.146N/mm21185.5644N/mm2 P+1.993.10−5L.R0.25.XL22XS=1.2喷射润滑XCA=1.0forB>5([a.b]V,1.2XCALP」log(313/373)ηθ6.Pθα38αp,θ6.αp,θ.E,=1.95.103.Prel,Y.G0.73.U0.090.9998h0,Y.Cth,Y.1.05.e−0.16.Rz0.02XL=1.0矿物油1)ε其中ε=2.0Cλ,Y1σH,mod,Y.XL.CRS0.071数XE=1.01253K436Kθr1TXW平均奥氏体含量的钢1WrelTX=XWWrelTWTXWT1θS,DIN+1.4.XL.XWrelT.T183(100)0.02.||(v40,XT=0.45.||.||.|expXT=0.45.||.||.|exp|其中a=91.5mm(θOil,ref,(1.0,(dm1+dm2,refθTh其中CTh=0；当XT>1.0tC,YtC1,Y,tC2,Y)415.99µs462.89µsθKKSS,Y=θS,Y−θOil≥SS,minθC,Y−θOilΣ√√√90°a√√√√√ √ de2√√—400mm√√√βm1—√——βm2√ √30°√√√z0√—√519°20°fαlim0xhm1—khap1kd—khfpkc xsmn—jet20°0°ρa01ρa02表D.3和表D.4列出了与几何及工况ζmp12.922°4.852mmζR12.265°6.368mm/Re1,2工作齿面/非工作齿面有效压力角19.269°Rm1,2工作齿面/非工作齿面切齿压力角19°/21°71.360°-1.731°71.360°71.360°khfp基本冠轮齿根高因素xsm1,2ζm12.265°smn1,2b2eff低T1KAEνρM440J/(kgK)（按照GB/Z10062.20—XXXX的表5）λMRzRaRzfptθOil,Refρ15当量圆柱齿轮的计算结果列于表D.5，应力、速度和摩计算结果如表D.7所示，允许的啮合温度如表D.8所示。−−dv2sinαvetgY(A)=−gva2gY(E)=gva1点注：以下公式中gY是关于Y的函数，gY=gY(Y)离fm,Y=(gva2−gvα/2+gY).cosβvb=fYcos=fYcosβvb+tanβvb|(fYstanY+tanβvb5.026mm8.293mm11.56mm21.36mm(−x1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff -10.92mm-8.933mm-6.423mm-3.913mm(y2,Y=−x2,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff 6.423mm8.933mm10.92mmlb0m,Yx1,Y22−Clb,Y)36.27mm36.24mm36.23mm36.24mm36.27mm离ft,Y=fm,Y+pvet.cosβvb9.473mm11.56mm17.82mm24.08mm=fYcos=fYcosβvb+tanβvb|(fYsinβvb+,|+2(gvαtanY+tanβvbfYcosβvbfYcosβvb+tanβvb|(fYsinβvb+,|−2(gvα−bv,efftanY)tanY+tanβvb26.39mm(−x1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb(2,2.462mm4.972mm7.482mm9.992mm(y2,Y=−x2,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff 00lb0t,Yx1,Y2−y2,Y27.855mm3.925mm7.522mm3.805mm离fr,Y=fm,Y−pvet.cosβvb-24.08mm-17.82mm-11.56mm-9.473mm-7.386mm1,Ytany+tanβvb 9.797mmfYcosβvbfYcosβvb+tanβvb|(fYsinβvb+,|−2(gvα−bv,efftany)tany+tanβvb(−x1,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff (y2,Y=−x2,Ytanβvb+fYcosβvb+tanβvb|fYsinβvb+(22, bv,eff 0.048mm2.558mm5.068mm7.579mm000.07Ib0r,Y=x1,Y21,Y−y2,Y27.855mmIbr,Y=Ib0r,Y(1−Clb,Y)7.522mm数0.560.2200数1数000.56=π.pY.Ibt,Y（和上面一样看不出l还是I）计算承载分担系数XLS的相A,Y=π.p,Y.Ibm,Y（和上面一样看不出l还是I）28.37mm28.37mm计算承载分担系数XLS的相A,Y=π.pY.Ibr,Y（和上面一样看不出l还是I）2.399mm4.917mm 14.83mm1.16接触点Y处的垂直于啮合线1K−1Hβ（和上面一样看不出l还是I）00wt1,2s.sinβm1,2度(|sinαnD,C(ddv1/2,0.78m/s度(|sinαnD,C(ddv2/2,2.94m/s3.36m/s2.01m/s1.99m/s.sin2.18m/swt2vert,Y2,Y.sin2,Y)1.44m/s2.19m/s5.09m/s和2.77m/s0.12m/s0.34m/