锥齿轮和准双曲面齿轮几何学

1锥齿轮和准双曲面齿轮几何学注1：本文件中使用的符号、术语和定义已尽可能与其他国际标准一致。由于某些4——齿顶隙，c；m；4de28——轴交角，Σ;2；hamc1，hamc2ham1，ham2大端法向侧隙outernormalbacklashallojenrc0齿根角之和sumofdedendumanglesΣθf等尖宽齿根角之和sumofconstantslotwidthdedendumangles尖宽修正齿根角之和sumofmodifiedslotwidthdedendumangles标准收缩齿根角之和sumofstandarddepthdedendumanglesΣθfS等齿高齿根角之和sumofuniformdepthdedendumanglesΣθfU中点齿根高meandedendumhfm1，hfm2hmhmw旋转方向directionofbchamρmβ刀齿组数numberofbladegroupsz07齿数numberofteethz12冠轮齿数numberofcrowngezp中点法向弦齿厚meannormalcsmnc1，smnc2中点法向弧齿厚meannormalsmn1，smn2ac —8FaxNNFradNf“lim jenjetjmnjmtkc kd— khfp kt—n1PT1Nm9GB/TXXXXX—XXXX/ISO2350u xhm1 xsm1，xsm2 xsmn—z0 z1 zp—。。。。。。。βe1，βe2。βi1，βi2。βm1，βm2。△Σ。。。。η。。。v。ρbρlimρP0∑。∑θf。ΣθfC。ΣθfS。ΣθfM。ΣθfU。ζo。ζm。ζmp。ζR。4.1概述4.2齿轮类型4.2.1概述传动类型由齿轮的安装位置、可用空间和工况条件4.2.2直齿锥齿轮4.2.3弧齿锥齿轮特别用于高速传动时，可降低振动和噪声。弧齿锥齿轮齿面可以进行精4.2.4零度齿锥齿轮锥齿轮的机床上加工。零度锥齿轮齿面也可以进行精加工。螺旋角小于10°的锥齿轮有时也归类为零4.2.5准双曲面齿轮4.3传动比4.4轮齿旋向轮齿螺旋方向的选用原则，是在齿轮工作旋转方向时，在大小轮轴线方向上产生相互推开的关于准双曲面齿轮螺旋方向与偏置方向的选4.5齿轮初始参数），十分必要的。以下各部分内容有助于用户了解其加工中的相互为此，将几种相互关联的基本收缩类型定义如下（为齿根线通常绕节线中点倾斜，以保持中点法截面内工5.3.1.2等尖宽收缩齿根角之和公式（C.4表明刀具半径rc0对根线倾斜影响很——大的刀盘半径会增大齿根角之和。如果刀盘半径大太，所产生的收缩在齿高方向上会影响另——小的刀盘半径会减小齿根角之和。事实上，如果刀盘半径rc0＝Rm2sinβm2，齿根角之和将变为零，这将变成等高齿。如果rc0＜Rm2sinβm2，会出现齿高的反向收缩。这5.3.1.3尖宽修正(根锥倾斜)5.4齿根角修正a）端面铣削法，；ρP0；ρmβ;5.7准双曲面齿轮设计5.8最一般的齿轮传动类型5.9准双曲面齿轮几何5.9.2交叉点ΣXXXXaXXXz1,2XXXX——X—de2XX—XXXXXβm1 X— βm2X XXXXXXz0XXXX6.2确定锥齿轮和准双曲面齿轮的节u=z2/z1......................................................................................(1)=arctan...............δ2=Σ-δ1...................................................................................(3)eRe1,2=............................................mRm1,2=Re2-...............................................................................(5)βm1=βm2....................................................................................(6)be2 u=z2/z1......................................................................................(8)βΔ1=βm1...........................................................ΔΣ=Σ-90。..............................................................................(10)((sinη)δint2=arctan...........de2de2-b2sinδint22εi'=arcsin.....................K1=tanβΔ1sinεi'+cosεi'.....................................................................小轮中点半径近似值，rmn1=.......................................迭代开始mpt2(tanδint2cosmpt2(tanδint2cosΔΣ-sinΔΣ)+rmn1 ε2=arcsin........................δint1=arctan|+tanδint1=arctan|+tanΔΣcosη|.......................................................ε'2=arcsin..............................................................小轮的中点螺旋角，βm,int1(K-cosε')min(K-cosε')mint1（sinε)ΔK=sinε'2(tanβΔ1-tanβmint1)................................................................小轮中点半径增量，Δrmpt1δ=arctan|δ=arctan|+cosεtanΔΣ|(28)seca(tanβ-tanβ)(sinη)(sinε1)-tanalim++Rm1cosβm1-Rm2cosβm2 ............................................................................(22)(Δr)ε1-sinη)||.........................................ε'1=arcsin............................................................βm1βm2=βm1-..............................................................................(27)2（tanηcosΔΣ1) Rm1=..........................................大轮中点锥距，Rm2Rm2=..............................................小轮中点半径，rmpt1m1sinδ1.............................................................................(31)极限压力角，αlimalim=arctan-tanδ2R2..............................................(32)极限曲率半径，ρlim(tanβtanβ)11plimlimm1(tanβtanβ)11zp=................................................(Rz)v=arcsincosβm2λ=90。-βm2+v...........................................................................(36)冠轮到刀盘中心距，ρΡ0pP0=..................................................η1m2cosβm2(zp+z0)..............................................................zp齿向中点曲率半径，ρmβpmβm2cosβm2tanβm2+................................齿向中点曲率半径，ρmβpmβ0..................................................................................(40)迭代结束齿宽系数，cbe2cbe2=.......................................v=arctan...................λ=90。-βm2+v...........................................................................(43)u=................................................................小轮节锥角初次近似值，δ1appδ1app=arctan.............大轮节锥角初次近似值，δ2appδ2app=Σ-δ1app p..................................................................(47)准双曲面尺寸系数近似值，Fapp=...........................小轮中点节圆近似直径，dm1appdm1app=................................................92=arctan...........................................................(50)冠轮近似中点半径，Rmapp dm22sin92.............................................................................(51)η193=arctan.............=arctandm2cosζmapp+dpΣΣ-tan(Q32ζmapp)......................δ2=Σ-δ1................................................................................δ2imp=arctan(tanδ2''cosζmapp).............................ηp=arctan.................................................................ηapp=arctan..............ζmimp=arcsin- Ftan ucos(Σ-δ2imp)...................................................ζmpimp=arctan................................................................准双曲面尺寸系数，FF=cosβm2...............................................................+ζmpimp)dm1=.........................................04|||dm2cosζmimp+dm1|dm2cosζmimp+dm1cosΣcosηp-|δ2imp=Σ-δ1imp............................................................................(65)δ2tanδ2''impcosζmpimp)................................................................(66)05=arctanc...........η=arctantanηappsin05(68)pimpη=arctan........................................................(69)小轮轴平面内偏置角，ζmζm=arcsin(tanδ2tanη)......................................................................(70)小轮和大轮节平面内偏置角，ζmpζmp=arctan......................................................βm1=βm2+ζmp.............................................................................(72)dm12...........................................................................(73)辅助角，ξξ=arctan(tanΣcosζm)-δ2...................................................................(74)ξ=90。-δ2.............................................................tanξcosζmp).....................................................................(76)Rm1δ1........................................................大轮中点锥距，Rm2Rm2=2.................................................冠轮到刀盘中心距，ρP0pP0=.................................................互补角，φcomp 检查变量，Rmcheck 迭代结束齿宽系数，cbe2cbe2=0.5..............................u=................................................................对于随后的迭代，从准双曲面尺寸系数F开始F=1..................................................................|sinΣ|sinΣ|δ2=arctan||...................................（u)|F+cos（u)=Σ-δ2.................................................................................(87)迭代开始大轮中点节圆直径，dm2dm2e2-b2sinδ2..........................................................................(88)小轮轴平面内偏置角，ζm=arcsin(cosζmsinΣcosδ2-cosΣsinδ2).......................................................(90)小轮和大轮节平面内偏置角，ζmpζmp=arcsin...........................................................mmn=...........................................βm1=βm2+ζmp 准双曲面齿轮尺寸系数，F dm1=F......................................................Rm1δ1...........................................................大轮中点锥距，Rm2Rm2=2n辅助角，sm9m=δ2tanζm)A3(βm2-v)A4+9m)cosβm2A5=sinζmpcos9mcosvA7cos(βm2+9m)-中间变量，RmintRmint-Rm1<0.0001Rm1δ2迭代结束f“limxhm1kdkhfpkcxsmnktjmn，jmt2，jen，jet2(1)xhm1ham)|1(x)cham1(x)khapkdkd2kd(1)khfpkc)xsmnxsmntd|kc+|(tananD+tananC)-|ktdm1m1sinδ1..........................................................................(11大轮中点节圆直径，dm2dm2m2sinδ2 轴夹角与90°的差值，△Σ:ΔΣ=Σ-90。 小轮轴平面内偏置角，ζmζm=arcsindm2+.....................小轮和大轮节平面内偏置角，ζmpζmp=arcsin....................................................apm2sinζmp...........................................................................(115)mmn=.................................alim=-arctantaδ2R............................................(117)anD=adD+falimalim anC=adC-falimalim aeD=anD-alim aeC=anC+alim 大轮大端锥距，Re2Re2+cbe2b2..........................................................................(122)Ri2e2-b2.............................................................................(123)砂轮大端节圆直径，de2de2 di2 大端端面模数，met2met2 计算点到大轮大端的齿宽，be2e2-Rm2 大轮交叉点沿轴线到中点的距离，tzm2tzm2m12-0.5cosζmtzm2m12-0.5cosζmtanΔΣ|dm2+m12|2cosδ1（cosδ1) mmam1,2fm1,2 （138）小轮交叉点沿轴线到中点的距离，tzm1tzm1=cosζmcosΔΣ-tzm2sinΔΣ...........................................................(130)tz1,2=Rm1,2cosδ1,2-tzm1,2 hmw=2hmw=2mmnkhap大轮中点齿顶高，ham2mn(khap-xhm1)大轮中点齿根高，hfm2mn(khfp+xhm1)小轮中点齿顶高，ham1mn(khap+xhm1) 小轮中点齿根高，hfm1mn(khfp-xhm1)mn(khfp-khap)........................................................................(137)mn(khap+kδa2=δ+θa2..........................................=δ-θf2.............................................................................(141)δ=δ=arcsin(sinΔΣsinδ+cosΔΣcosδcosζ) f2zR2f2Rsinθ-hcosθ小轮根锥切平面内偏置角，ζRζR=arcsinRm2R-sδf2-QR......................................小轮顶锥切平面内偏置角，ζ0-ssδa2-Q0...................δa1=arcsin(sinΔΣsinδf2+cosΔΣcosδf2cosζR) θa1=δa1-δ1...................................................................θf1=δ-δf1...........................................................................（149)大轮顶锥顶点越过交叉点的距离，tzF2tzF2=tz2-tzF2=tz2-m2a2am2a2大轮根锥顶点越过交叉点的距离，tzR2tzR2z2+............................小轮顶锥顶点越过交叉点的距离，tZF1asinζRcosδ-tasinζRcosδ-tsinδ-c小轮根锥顶点越过交叉点的距离，tzR1tzR17.5确定小轮齿宽b1....................................................................................................................................从计算点到前冠的小轮齿宽，b1A....................................................................................................................................小轮齿宽，b1bb2 计算点到大端的小轮齿宽，be1 bb-be1 λ,=arctan.....................小轮齿宽，breri1=..................................(1)mwsinζRΔgxe=cosδa1+Δbx1-(hfm2-c)sinδ1.....................................................cosθa1................................................Δgxi=(1-cbe2)breri1cosδa1+Δbx1+(hfm2-ccosθa1................................................计算点到大端的小轮齿宽，be1am1sinδ1cosθe1cosδa1a1 Δgxi-ham1sinδ1cosδ1-tanθa1sinδ1 11p1mnmp bb+be1...............................1(1+tan2ζmp) 计算点到大端的小轮齿宽，be1 b-be1..............................................................................(169)1-bp1)/2.......................................................................... 计算点到大端的小轮齿宽，be1－bi1 Re21=....................Ri21=....................v=arcsin(z0mmn/2rc0)...............冠轮到刀盘中心距，ρP0RR2+r-2Rm2rc0sin(βm2-v).........................................................i21（i21（pbsinΨi21) (R-pcosΨ)(2Rrsinβ-R2+R2)pb1+sinδ2.........................................................................辅助角，ve21辅助角，vi21-rc（2Ri21pP0)................................................................大端螺旋角，βe21βe21 β=arctan|i21b(Rβ=arctan|i21b大端螺旋角，βe21βe21=arcsin|m2c0m2m2 i21（2Ri21rc0).......................................................i21（2Ri21rc0).......................................................端面滚切法和端面铣削法：节锥大端偏移角，ζep21节锥小端偏移角，ζip21ip21（Ri21)........................................................................大端螺旋角，βe1βe1+ζep21........................................................................(R(R-pcosΨ)(R-pcosΨ)(2Rrsinβ-R2+R2)(2Rrsinβ-R2+R2)βi1+ζip21...........................................................................(188)辅助角，φe2=arccos...............（2Ri2pP0).................................................................大端螺旋角，βe2βe2 βi2 大端螺旋角，βe2βe2=arcsin|m2c0m2m2 βi2=arcsin|m2c0m2m2 大端齿顶高，haehae1,2am1,2e1,2tanθa1,2...................................................................fm1,2e1,2tanθf1,2............................................................................................................................................hai1,2am1,2-bi1,2tanθa1,2...................................................................小端齿根高，hfihfi1,2fm1,2-bi1,2tanθf1,2..............................................................................................................................................C+CnC)/2....................................小轮齿厚修正系数，xsm1x=x-j1Rm2cosβm2sm1smnen4mmncos“nRe2cosβe2........................................................采用大端端面侧隙jet2计算x=x-jRm2cosβm2sm1smnet24mmnRe2 采用中点法向侧隙jmn计算xsm1=xsmn-jmn.................................................................采用中点端面侧隙jmt2计算cosβm2....................................................................xsm1smn-cosβm2....................................................................4mmn小轮中点法向弧齿厚，4mmnsmn1mnπ+2mmn(xsm1+xhm1tanCn)........................................大轮齿厚修正系数，xsm2采用大端法向侧隙jen计算xsm2=-xsmn-jen1Rm2cosβm2.......................................................4mmncosCnRe2cosβe2采用大端端面侧隙jet2计算Rm2Rm2cosβm2xsm2=-xsmn-jet2................................................................4mmnRe2采用中点法向侧隙jmn计算xsmxsm2=-xsmn-jmn................................................................采用中点端面侧隙jmt2计算xsm2=-xsmn-jmt2大轮中点法向弧齿厚，smn2cosβm24mmn...................................................................(21smn2mnπ+2mmn(xsm2-xhm1tanan)........................................................(211)smt1,2=smn1,2/cosβm1,2......................................................................(212)dm1,2(1-sin2βm1,2cos2an)cosδ1,2.........................................................smnc1,2=dmn1,2sin(smn1,2/dmn1,2)...............................................................(214)「(s)]+0.5dmn1,2cosδ1,21-cos..........................................Re1e1............................................................................(216)Ri1m1-bi1............................................................................(217)de1=2Re1sinδ1................................................di1=2Ri1sinδ1............................................................aedae1,2=de1,2+2hae1,2cos dfe1,2=de1,2-2hfe1,2cosδ1,2 dai1,2=di1,2+2hai1,2cosδ1,2 dfi1,2=di1,2-2hfi1,2cosδ1,2 e1,2cosδ1,2-hae1,2sinδ1,2 前冠到交叉点的距离，txi1,2txi1,2=tzm1,2-bi1,2cosδ1,2-hai1,2sinδ1,2 t1cosδa1a1f1zR1zF1f1 zF1xo1sin(θ+θ)-(t1cosδa1a1f1zR1zF1f1 Ri1<Re...........................................................Rx2检查点的大轮螺旋角，βx2βx2x2Qx2...................检查点的大轮螺旋角，βx2βx2小轮检查点在节面中的偏移角，ζxp2xp2（Rx2)ζ=arcsinxp2（Rx2)βx1=βx2+ζxp2...........................................................................(233)dx1x1sinδ1...........................................................................(234)对应的大轮检查点处节圆直径，dx2dx2x2sinδ2..........................................................................(235)检查点的中点法向模数，mxnmxn=cosβx2........................................................小轮检查点处的有效直径，dEx1 对应的锥距，REx1REx1=2..............................................znx1检查点的极限压力角，“limxalimx=-arctantaδ21s............................................(240)工作齿面检查点的有效压力角，“eDxaeDx=anD-alimx 非工作齿面检查点的有效压力角，“eCxaeCx=anC+alimx 如果aeCx<aeDx：aeminx=aeCx.............................................................................(243)如果aeCx>aeDx：aeminx=aeDx.............................................................................(244)确定小轮计算点的最小轮廓偏移系数，xhmminx1：检查点处的检查工具补偿，khapxkhapx=khap+.................................小轮检查点处的最小变位系数，xhx1xhx1=1.1khapx-znx1mxaeminx 小轮计算点处的最小变位系数，xhmminx1xhmminx1=xhx1+.............................................................(247)如果xhm1>xhmminx1，则在检查点不发生根切。大轮待检查点的锥距，Rx2Ri2<Re.................................................检查点的大轮螺旋角，βx2βx2x2x2............................................................检查点的大轮螺旋角，βx2βx2检查点的中点法向模数，mxndx2x2sinδ2..........................................................................mxn=cosβx2.......................................................................... z2........................................................(1-sin2βx2cos2an)cosβx2cosδ2如果anC<anD:aeminx=anC..............................................................................(255)anC>anD:aeminx=anD..............................................................................(256)确定小轮计算点处的最小变位系数，xhmminx1：由于xhm2=﹣xhm1因此需要进行此检查以避免大检查点处的检查工具补偿，khapxkhapx=khap+...............................小轮计算点处的最小变位系数，xhmmaxx1xhmmaxx1=-1.1khapx-(znx2mxnsin2aeminx2mmn)......................................................如果xhm1>xhmmaxx1，则应避免在检查点发生根切。），A.2公式集的结构hap、齿根高系数khfp、齿厚修正系数xsmn和齿廓偏移系数Xhm。而AGMA标准使用可用数据类型I表示，也可用数据类型IIA.3节锥参数A.4弧齿锥齿轮和准双曲面齿轮尺寸基本数据的确定7.2节中确定了进一步计算所需的部分数值。对于准双曲面齿轮而言计算点处齿高的确定根锥角和顶锥角的确定大端和小端螺旋角的确定在前锥（Ri1）和背锥（Re1）处计算小轮的螺旋角。为了得到小轮螺旋角，首先需要确定相关边界齿厚是根据外端法向侧隙jen、计算点法向侧隙计算出修正系数xsm1和xsm2。通常情况下，在计算理论齿厚时侧隙应设为零。A.5根切检查刀盘上的刀尖运动就相当于产形轮的一个齿,产形轮的旋转轴与铣齿机的摇台轴线重合，被加工齿确，因此用平面产形轮近似估计根切量是一个很好的解决通常，由于齿向滑移的影响，偏置距不应大于大轮大端节圆直径的25%，对于重载应用场合，偏设计人员应根据齿轮在预期寿命下的功率与转T=.............................................................（B.1）P——功率（kW给出了准双曲面齿轮小轮的节圆直径初值dedeplm1=de1..........................................................（B.2）de1——小轮的大端节圆直径，从图B.2或B.3中取较大者（mma——小轮偏置距（mm）；u——传动比。δint1=arctan....................................................（B.3）Σ——轴交角。δint2=Σ-δint1...........................................................（B.4）Reint2=2t1.........................................................（B.5）de2=2Reint2sinδint2........................................................（B.6）图B.3选取或由式（B.2）计算得到小轮大端节圆直径。从这两个尺寸中选 ——GB/TXXXXX—XXXX/ISO2350GB/TXXXXX—XXXX/ISO2350传动比，u小轮齿数，z11.0~1.51.5~1.751.75~2.02.0~2.52.5~3.03.0~3.53.5~4.04.0~4.54.5~5.05.0~6.06.0~7.57.5~1099987655|2-||2-|（Re)2|1-|为选取合适的螺旋角，首先应根据式（B.7）和（B.8）计算纵向重合度(b)................................(b)....................................................（B.7）|||||ZReεβ=KZtanβm-tan3βmRe...........................................（B.8）Re——外锥距（mm）；met——端面模数（mm）；b——齿宽（mm）；βm——中点螺旋角。对于准双曲面齿轮副，可使用公式（B.9）计算小轮螺z1de2βm1=25+5+90a..................................................（z1de2βm1——小轮中点螺旋角；GB/TXXXXX—XXXX/ISO2350GB/TXXXXX—XXXX/ISO2350加端面重合度、减小轴向力和分离力、增加根据应用的需求，可以选择更大或更小的名义压力角。较小的有效压力角会增大根切的风险。角。啮合条件完全平衡时，极限压力角的影响系数应取fαlim=1。工作齿））角至少取25°。为了平衡非工作面和工作齿面的啮合条件，极限压力角影响系数应取fαlim=1。为了使用标和25°适用于重型传动场合。GB/TXXXXX—XXXX/ISO235098769876如果沿着整个齿长方向的顶隙都是恒定值的话，在中点齿宽处进行计算。通常，顶隙系数kc取值GB/TXXXXX—XXXX/ISO2350在加工met2=1.27或更小模数的小模数齿轮切的中点齿顶高系数。对于表C.2，应计算当量η=asin(sinζmcosδ2)······························································(C.9876GB/TXXXXX—XXXX/ISO2350图C.1齿厚系数ktGB/TXXXXX—XXXX/ISO2350C.5.1齿根角之和，∑θfΣθfs（Rm2)（Rm2)ΣθfC=Re2taosβm1-Rm2βm2………………(C.4)θθf20GB/TXXXXX—XXXX/ISO2350θf2θf2GB/TXXXXX—XXXX/ISO2350Fmt2Fmt1小轮轴向力，Fax1,DGB/TXXXXX—XXXX/ISO2350（cosβm1大轮轴向力，Fax2,D=tananDsinδ2-tanβm2cosδ2Fmt2·························（cosβm2)小轮轴向力，Fax1,CFax1,C=tananCsinδ1-tanβm1cosδ1Fmt1·····························（cosβm1大轮轴向力，Fax2,C cosβm2=|tananC()|Fmt2···································)对于工作齿面的载荷小轮径向力，Frad1,DFrad1,D大轮径向力，Frad2,D(=|tananD(cosδ1) -tanβm1sinδ1|cosδ1)cosβm1)Frad2,D=tananDcosδ2+tanβm2sinδ2Fmt2...............................................（D.8）（cosβm2)对于非工作齿面的载荷小轮径向力，Frad1,CFrad1，CF大轮径向力，Frad2,C cosβm1=|tananC()|Fmt1............................................)Frad2,C=tananCcosδ2-tanβm2sinδ2Fmt2......................（D.10）（cosβm2)GB/TXXXXX—XXXX/ISO235负号(-)表示径向力的方向指向正在啮合的齿轮，此时的GB/TXXXXX—XXXX/ISO2350表E.1标准刀盘半径rc0和刀齿组数z0z0z0z0175277353577555965595553 3 3 ———————————————————————GB/TXXXXX—XXXX/ISO2350∑90°×××a×××z1,2××× ×—de2×—××××βm1—×——βm235° ×××××z0 ××20°20°fαlim0xhm1 kdkhfp kcxsmn ktjen2.1342°6.4934°GB/TXXXXX—XXXX/ISO2350khfpxsmnu==2.786..............................................δ=Σδ=70.253。........................eRe1,2==93.973mm...................................mRm1,2=Re2=81.273mm..................................................................(Fβm1=β35。..................................................................be2cbe2dm1=54.918mm.....................................dm2=152.987mm........................................GB/TXXXXX—XXXX/ISO235ΔΣ=Σ-90。=0。...................................................................小轮轴平面偏置角，ζmap=Rm2sinζmp=0.000mm mnmmn==3.213mm..................极限压力角，αlimalim=-arctantaδ2R=0。.......................................(F.14)工作齿面切齿压力角，αnDanD=adD+f“limalim=20。 anC=adC-f“limalim=20。..................................................................(F.16)工作面有效压力角，αeDaeD=anD-alim=20。.....................................................................(F.17)非工作面有效压力角，αeC Re2 Ri2 大轮的大端面齿顶圆直径，de2de2 GB/TXXXXX—XXXX/ISO235di2 met2 m2-Ri2=12.700mm.................................................................(F.25)沿大轮轴线交叉点沿轴线到中点的距离，tzm2tzm2m1sinδ2-0.5cosζmtanΔΣdm2+dm1cosδ2=27.459mm..................................(F.26)2cosδ1沿小轮轴线交叉点沿轴线到中点的距离，tzm1tzm1=cosζmcosΔΣ-tzm2sinΔΣ=76.493mm...............................................(F.27)沿轴线节锥顶点越过交叉点的距离，tz1,2tz1m1cosδ1-tzm1=0mm................................................................(F.28)tz2m2cosδ2-tzm2=0mm................................................................(F.29)=2mmnkhap=6.427mm.................................................................(F.30)khap-xhm1)=1.591mm..........................................................khfp=5.639mm...........................mnkhap=4.836mm.................................小轮的中点齿根高高，hfm1khfp-xhm1)=2.39