錐齒輪承載能力計(jì)算方法 第20部分：膠合承載能力計(jì)算 閃溫法

1錐齒輪承載能力計(jì)算方法第20部分：膠合承載能力計(jì)算閃溫法使用者需要注意：當(dāng)公式用于較大的中點(diǎn)平均螺旋角(βm1+βm2)/2>45°、較大的有效壓力角αe>30°和/或較大齒寬b＞13mmn時(shí)，根據(jù)ISO10300計(jì)算的結(jié)根據(jù)經(jīng)驗(yàn)和理論研究[7]，本文件描述了錐齒輪和準(zhǔn)雙曲面齒輪膠合承載能力計(jì)算的一種方法——本文件中的公式旨在建立統(tǒng)一的可接受的鋼制直齒錐齒輪、斜齒錐齒輪、弧齒錐齒輪、零度齒錐齒輪和準(zhǔn)雙曲面齒輪的抗膠合能力的計(jì)算方法。這些公式也同樣適用于漸縮齒和等高齒。在下文中，本文件發(fā)布時(shí)，錐齒輪和準(zhǔn)雙曲面齒輪的抗膠合本文件中的公式基于當(dāng)量圓柱齒輪和限定的錐齒輪（它的當(dāng)量圓柱齒輪的端面重合度εvα<2）。下列文件中的內(nèi)容通過文中的規(guī)范性引用而構(gòu)成本文件必不可少的條款。其中，注日期的引用文件，僅該日期對應(yīng)的版本適用于本文件；不注日期的引用文件，其最新版本（包括所有的修改單）適ISO10300-1錐齒輪承載能力計(jì)算方法第1部分：概述和通用影響系數(shù)（Calculationofloadcapacityofbevelgears—Part1:Introductionandgeneralinfluencefofloadcapacityofbevelgears—Part2:Calculationofsurfacedurability(pitting)]（Gears—FZGtestprocedures—Part1:FZGtest capacityofoils）ISO17485錐齒輪精度制（BevelISO23509錐齒輪和準(zhǔn)雙曲面齒輪幾何學(xué)（Bevelandhypo注：GB/T43146—2023錐齒輪和準(zhǔn)雙曲面齒輪幾何學(xué)（ISO2A*Y計(jì)算接觸點(diǎn)Y處的局部載荷分擔(dān)系數(shù)XLS的相關(guān)區(qū)域aarefB—BMN/(ms0.5K)μmCeffμm--XT>1.0時(shí)的許用溫度函數(shù)的變化率K-K-D-E'N/mm2e-FnNFvmtNfm,Yfr,Yft,YG-gvagYμmμmi-KHβ,Y-LY-MY-PVZPpHN/mm23p*Y-SS,Y-sx,Y-Nms--N/mmXCA-XE-XL-XLS,Y-XQ-XS-XT-XWrelT-XY-x1,2,Yy1,2,YZEzY-εf--εvf--4Ns/m2Ns/m2℃℃℃℃℃℃℃θOil,ref℃λλMλz,Y-μY-ρMkg/m3ρrel,Cρrel,YρtN/mm2N/mm2°012DCTY5.1概述5.2局部幾何參數(shù)5小輪齒頂方向的gY被定義為正值，小輪齒根方向的gY被定義為負(fù)值。端面嚙合線gY(A)=?gva2 gY(E)=gva1 =·······················gva——當(dāng)量圓柱齒輪齒頂嚙合線長度；dv——當(dāng)量圓柱齒輪的分度圓直徑；dva——當(dāng)量圓柱齒輪的齒頂圓直徑；dvb——當(dāng)量圓柱齒輪的基圓直徑。兩邊界點(diǎn)之間的端面嚙合線長度可以根據(jù)使用者的需要細(xì)分為i個(gè)區(qū)段。為了避免下列公式的計(jì)算結(jié)果為無窮大，不在齒頂和齒根邊界點(diǎn)處對中點(diǎn)螺旋角為零(βm=0）的錐齒輪進(jìn)行計(jì)算。排除中點(diǎn)螺旋角為零(βm=0）的錐齒輪的齒頂和齒根邊界點(diǎn)，使用輔助變量ks，使用公式（4）計(jì)算端面嚙6(x1,Y;y1,Y)——接觸線起始點(diǎn)坐標(biāo)(x2,Y;y2,Y)——接觸線終點(diǎn)fm,Y——接觸點(diǎn)Y處的中點(diǎn)接觸線的嚙合坐標(biāo)ft,Y——接觸點(diǎn)Y處的齒頂接觸線的嚙合坐標(biāo)fr,Y——接觸點(diǎn)Y處的齒根接觸線的嚙合坐標(biāo)βvB——基圓處的螺旋角gvα——當(dāng)量圓柱齒輪端面方向的嚙合線可以使用公式（5公式（7）來計(jì)算嚙合區(qū)域齒頂ft,Y、中點(diǎn)fm,Y和齒根fr,Y處的接觸線長度/距離?！究梢允褂霉剑?公式（7）來計(jì)算ft,Y、fm,Y和fr,Y】fm,Y=(gva2?gvα/2+gY).cosβvb ft,Y=fm,Y+pvet.cosβvb fr,Y=fm,Y?pvet.cosβvb βvb——基圓處的螺旋角；pvet——端面基圓齒距。如果fm,Y、ft,Y或fr,Y的絕對值大于fmax，接觸線在嚙合區(qū)之外。因此，將接觸線長度lb,Y[見公式（13）]和lb0,Y[見公式（14）]的長度設(shè)置為零。否則，使用公式（8）~接觸線末端的坐標(biāo)（x1,2,Y；y1,7x1,Y x2,Y=bv,eff v,eff·······················(11)(bv,eff(bv,eff) 應(yīng)使用fm,Y、ft,Y和fr,Y計(jì)算三條接觸線的x1,2,Y和y1,2,Y。應(yīng)使用公式（13）~公式（15）計(jì)算接觸線長度lb,lb,Y=lb0,Y(1?Clb,Y) lb0,Y——理論接觸線長度；2,)2·········································(15)bv——當(dāng)量齒輪齒寬；fmax——至中點(diǎn)接觸線的最大距離。5.2.3局部等效曲率半徑ρrel,YYpYρrel——垂直接觸線的局部等效曲率半徑；tanαvettanαvet.\dvb1/2dvb2/25.2.4局部載荷分擔(dān)系數(shù)XLS,Y i···················A=τ.p.lb,Y·······································································(19)AY*——計(jì)算接觸點(diǎn)Y處局部載荷分擔(dān)系數(shù)（XLS,80·············································(20)(x1,Y;y1,Y)——接觸線起始點(diǎn)坐標(biāo)gvα——當(dāng)量圓柱齒輪端面方向的嚙合線長度gY——Y在節(jié)點(diǎn)P處的坐標(biāo)MY——嚙合線中心用于（計(jì)算）接觸應(yīng)力的局部螺旋線載荷分布系數(shù)KHβ,Y，應(yīng)使用公式（21）~公式（23）來計(jì)算。Ya ····················Y=·····························KHβ——螺旋線載荷分布系數(shù)。應(yīng)使用公式（24）和公式（25）計(jì)算局部修正接觸應(yīng)力σH,mod,Y。4································σH,Y=.ZE.XLS,Y······································σH,Y——局部接觸應(yīng)力；9ZE——彈性系數(shù)。el,Y.··································································································沿齒長方向的齒面速度（wt1,2swt1,2s=vmt1,2.sinβm1,2·····································································(28)βm——中點(diǎn)螺旋角。接觸點(diǎn)Y處，齒廓方向的局部齒面速度（wt1,2h,Y.cos·······································2h,Y=vmt2.cos······································αnD,C——驅(qū)動齒面/從動齒面的展局部齒面速度（wt1,2,Y=··············································垂直接觸線的局部齒面速度（wt1,2vert,Yβ βB——接觸線的傾斜角；ωwt1,2,Y——接觸點(diǎn)Y處齒長和齒廓方向齒面速度t1,2,Y=arctan··········································①wt1,2,Y=90 接觸點(diǎn)Y處的速度之和（vΣ,Y····················································vΣst1s2s vΣh,Y=wt1h,Y+wt2h,Y vΣh,Y——齒廓方向的速度之和。接觸點(diǎn)Y處垂直于接觸線的速度之和（vΣvert,YvEvert,Y=wt1vert,Y+wt2vert,Y 接觸點(diǎn)Y處滑動速度（vg,Yvgs=vmt1.cosβm1.(tanβm1?tanβm2) =2.vmt1,gY.············································vgh,Y——接觸點(diǎn)Y處齒廓方向的滑動速度。=······················································6.3接觸點(diǎn)Y處的相對潤滑油膜厚度(λz,Y）·······················································h0,Y=h,Y.Cth,Y.1.05.e?0.16.Rz h0,Y——接觸點(diǎn)Y處的潤滑油膜厚度；=···················································LYλ——油的規(guī)定熱傳導(dǎo)率系數(shù)（對于礦物油：λ=0.133W/(mK)···················································Rz——平均表面粗糙度[見公式（54）]。ηθ=10?6.vθ.pθ····················································(48)loglog(vθ+0.7)=A.log(θ+273)+B A=················B=loglog(v+0.7)?A.log(313)·························································(51)ρθ——溫度為θ時(shí)的潤滑油密度。pθ=pLp」如果不知道ρ15的值（數(shù)據(jù)使用公式（53）能近似計(jì)算礦物油的密度。p15=43.37.log(v40)+805.5 Rz=0.5.(Rz1+Rz2) Rz——平均表面粗糙度。根據(jù)Ertl/Grubin[5],[6]，在接觸點(diǎn)Y處潤滑油h,Y=1.95.103.prel,Y.G0.73.U.G=106.αp,θ.E αp,θ——壓力-黏度系數(shù)。如果特定潤滑油在溫度為θ時(shí)的壓力-黏度系數(shù)(αp,θ)的值未知，公式（57）能近似計(jì)算（見參, α38=2.657.10?8.η8.1348 α38=1.466.10?8.η8.0507 α38=1.392.10?8.η8.1572 應(yīng)使用公式（63）~公式（67）計(jì)算接觸點(diǎn)Y處的局部摩μσsx,Y.λ Cλ,Y——接觸點(diǎn)Y處的潤滑油膜厚度系數(shù)； XL7接觸點(diǎn)Y處的局部接觸溫度(θC,Y）應(yīng)計(jì)算接觸點(diǎn)Y處的局部接觸溫度(θC,Y即本體溫度(θM在穩(wěn)定運(yùn)行條件下為常數(shù)）和接觸點(diǎn)Y處沿嚙合線的局部閃溫(θfl,Y）之和，見公式（68）。接觸點(diǎn)Y處的局部接觸溫度(θC,Y）+θfl,Y·····················································(68)θM——本體溫度；齒輪的功率損耗是通過測量或綜合分析來確定，根據(jù)相似設(shè)計(jì)經(jīng)驗(yàn)進(jìn)在評估功率損耗時(shí)，如果沒有合適的可供使用的測量結(jié)果或?qū)嶋H經(jīng)驗(yàn)，宜使用下述簡化公式進(jìn)行.T.XL······························(69)XL——潤滑劑系數(shù)；arel——相對準(zhǔn)雙曲面齒輪偏置距。齒輪副的本體溫度(θM）能由7.3.2和7.3.3中規(guī)齒輪副的本體溫度(θM）是通過測量或綜合分析來確定，根據(jù)相似設(shè)計(jì)經(jīng)驗(yàn)進(jìn)行確認(rèn)。根據(jù)Otto[10]和KleinlZ對PVZP進(jìn)行修正，能使用公式(70)~公式(73)計(jì)算出本體溫度(θM）。+7400.0.72.········································θOil——油溫；··············································XCA——齒頂修緣系數(shù)（見7.3.4XS——潤滑方式系數(shù)。對于噴油潤滑，潤滑方式系數(shù)（XSXS=1.2 對于浸油潤滑，潤滑方式系數(shù)（XS0.8<XS=0.8.?D<3.7·············································ed——浸入深度；D——旋轉(zhuǎn)方向系數(shù)，把齒輪副的驅(qū)動方向?qū)Ρ倔w溫度的影響考慮在內(nèi)。Klein所做的實(shí)驗(yàn)研究--7.3.4齒頂修緣系數(shù)（XCA）嚙合輪齒的彈性變形導(dǎo)致齒頂在高滑動區(qū)域產(chǎn)生過載。根據(jù)公式（74齒頂修緣系數(shù)（XCA）考曲面齒輪；假設(shè)計(jì)算出的齒輪在載荷最大時(shí)顯示最佳的鼓形修XCA=1+0.06+0.18.εvmax+0.02+0.69ax···························εv1,2=······················································XCA=1.0 fl,YYH,2mod,YBM1wt,vert1,Y+BM2wt,vert2,Y1000.EXQθfl,YYH,2mod,YBM1wt,vert1,Y+BM2wt,vert2,Y1000.EXQB=·················································(78)BM1,2——熱接觸系數(shù)；XE——跑合系數(shù)（見Michaelis[9]）對于跑合齒面的XE；XE=1.0························································(79)對于非跑合齒面的XE；XQ=Xarel··················································對于(εf/εa)≤1.0X=XQ(arel=0)=1.0 對于1.0<(εf/εa)≤2.0對于(εf/εa)>2.0X=XQ(arel=0)=0.6 ················································································································λM——熱傳導(dǎo)系數(shù)。3鋼8.1標(biāo)準(zhǔn)膠合試驗(yàn)的極限溫度(θS,DIN）錐齒輪和準(zhǔn)雙曲面齒輪的潤滑油通常按照APIGL-4或APIGL-5的分類來規(guī)定。由于沒有APIθS,DIN=80+0.23.XL.T1T+1.4.XL.XWrelT.T183.(|100)|0.02 (v40,θS,DIN=90+0.3.XL.T1T+3.2.XL.XWrelT.T183 θS,DIN=90+0.3.XL.T1T+6.4.XL.XWrelT.T183 θS,DIN=90+0.2.XL.T1TH+2.75.XL.XWrelT.T13 T1T——FZG試驗(yàn)加載階段的小輪轉(zhuǎn)矩（見表6T1TH——準(zhǔn)雙曲面齒輪膠合試驗(yàn)中加載階段的小輪轉(zhuǎn)矩（根據(jù)Klein[7]X=······················································XWrelT——相對材料結(jié)構(gòu)系數(shù)；對于標(biāo)準(zhǔn)試驗(yàn)[見公式（87）~公式（90）]XWT=1 XW——結(jié)構(gòu)系數(shù)（見表7）。123456789NmXW——低于平均值——高于平均值8.2考慮接觸溫度影響的許用溫度(θSC）對于XT≤1.0θSC=θS,DIN+(XT?1).CTn··············································(93)對于XT>1.0θSC=θS,DIN+(XT?1).CTh··············································(94)CTn CTh XT0.8···································aref＝91.5mm θOil,ref=90oC θOil,ref——參考油溫；試驗(yàn)[13]表明，使用含有添加劑的潤滑油潤滑的齒輪的許用膠合溫度(θS,Y）會受到接觸暴露時(shí)間對于tC,Y≥tKθS,Y θ=θ+C.(t?t) θSC——長時(shí)間接觸時(shí)的許用溫度，單位為攝氏度(°CCS——許用膠合溫度的變化率，單位為開爾文每微秒tK——曲線拐點(diǎn)處的接觸暴露時(shí)間，單位為微秒(μs）。t=max(t,t)················································(102)添加抗膠合添加劑的油品可使用以下值：CS=19接觸點(diǎn)Y處的局部安全系數(shù)（SS,Y）SS,YSS,min——最小膠合安全系數(shù)。[1]ISO6336-2,Calculationofloadcapacityofspurandhelicalgears—Part[2]ISO/TS6336-22:2018,Calculationofloadcapacityofspurandhelicalgears