齿轮计算

齿数Z129Z244模数Mn10螺旋角β110.9816271830.1908090.19438031法向压力角αn200.3639702340.9396930.34202014齿高系数ha*1齿顶间隙系数Cn*0.25分度圆直径d1295.42784d2448.235346标准中心距a371.831594实际中心距a'350中心距变动系数Yn-2.18315940.01745329端面压力角αt20.34390160.3707825540.93762283端面啮合角αt'5.056692820.08848580.99610797总变位系数XΣ-1.5528436Xn10Xn2-1.5528436分度园弧齿厚Sn115.7079633Sn24.40418604齿顶高变动系数△Yn0.63031573齿顶高ha13.69684268ha2-11.831594齿顶圆直径da1302.82153da2424.572158基园直径db1276.999888db2420.275692基园螺旋角βb10.3290946公法线尺寸计算Z'130.5762482Z'246.3915491k13.897360924k22.93854652W1107.60697W269.6785953齿全高h16.1968427齿根园直径df1270.427842df2392.178473判断根切条件259.7214182齿顶园压力角αat123.83260960.441732581αat28.1580149顶园螺旋角βa111.2683360.980722797βa210.43238150.025775075顶园法向弧齿厚Sna113.0984198Sna210.33609720.25m2.5m0.5m5Semin判断小轮齿顶是否变尖Sna1≥(0.25～0.5)m顶园齿形曲率半径ρa1=61.1799378ρa2=30.1241608端面啮合线长度ga=60.4546047(渐开线检测长度)齿形起始点曲率半径ρc1=端面重合度εa=2.01464216纵向重合度εβ=总重合度εγ=2.8042152齿根园角半径计算根园齿间宽Tfαft12.5invαft12.77116E-05αft2#NUM!(齿根单园弧半径)Son115.708Sot116.00196442Son24.40418604Stf118.89Pft129.29565932Stf2=#NUM!Tf110.4057Rf15.772312295Tf2=#NUM!注:df1≤db1,不能计算,用下式Sbt1=19.3567184Pbt1=30.00761db1*COSαt≤df1基园齿槽宽Tb1=10.6508958△=(db1-df1)/23.286023R'=5.9583182可直接用R'=Tb1/2,此时齿根园直径变小些.df1=266.349齿根过度曲线干涉验算:被磨削齿轮齿形工作曲线最低点C,其曲率半径为ρc,与C点相对应的假想啮合齿条齿角点的运动轨迹,为一延长渐开线.其曲率半径为ρ轨.ρ轨1=24.662243ρ轨2=结论:磨出的齿根园角半径Rf大于ρ轨,不产生齿根过度曲线干涉.现代制造工程2003-2齿轮齿根部最佳过度园角的计算假定一基准点K--齿轮1齿廓上的K点与齿轮2齿廓顶点相啮合,K点的半径Rk1138.5018K点压力角αk10.300058944.78779E-08Rk点齿槽宽ek1对应的园心角β14.4061544K点的坐标Xk1=rk.sin(β/2)5.32421539Yk1=rk1.cos(β/2)-rf13.185549K2点坐标Xk2K点切线与X轴夹角Δ187.4968639Δ2当Xk＞Yk时ρ13.33102897ρ2当Xk＜Yk时ρ15.41657308ρ2ρ--齿根园角半径齿高起点半径的差值为δδ17.09107988δ2Rk1'131.410763Rk2'αk1#NUM!invαk1#NUM!αk2β1#NUM!β2Xk1#NUM!Yk1#NUM!Xk2Δ1#NUM!Δ2当Xk＞Yk时ρ1#NUM!ρ2当Xk＜Yk时ρ1#NUM!ρ2已知一对园柱齿轮中心距,速比,设计齿轮模数,齿数,及螺旋角输入已知参数a=490速比I=1.517初算模数m'=19.696509取m=10初算Z'137.42337取Z1=则有β16.4264214I=齿形渐开线检测的展开长度ρj=ρat-ρbtTanα'bt1=0.0052370.72533361.17993781渐开线检测的展开长度ρj1=60.4546047277.0036867初步设定Z'1=注:此计算方法,从K点向下,齿形为直线和与直线相切的园弧,而实际使用要求渐开线齿形还要长些,此方法还要修改.K点降低到工作齿高起点.Rk与工作与大齿轮齿廓的齿顶点相啮合的小齿轮齿廓啮合点直径计算:自小轮基园切点到大轮齿顶点在啮合线上长度齿根园减小量,对强度影响不大,即取Rf2.若齿根园不能减小,按下式计算.算出的R'偏大,而且园弧与渐开线相接不圆滑成形磨时可用.小齿轮齿廓有效起始点直径大齿轮齿廓有效起始点直径齿廓工作段开始点曲率半径ρbt1=注:对得到的数据再进行角变位设计计算,求得最佳螺旋角和变位系数.齿廓工作段开始点压力角α'bt齿顶点渐开线曲率半径ρat1=齿轮齿根的滑动系数小齿轮η1max26.3730238齿廓滑移系数应小于下列数值,节园周速Vp大齿轮η2max-4.0604476用齿条形刀具加工外啮合齿轮,齿根过渡曲线干涉验算:(公式来源于现代机械传动手册155页)小齿轮齿根Tanα't-(Z2/Z1)*(Tanαat2-Tanα't)≥Tanαt-(4*(han-Xn1)*Cosβ)/(Z1*Sin(2*αt))前项0.00523706后项0.1630986判断前项≥后项,满足大齿轮齿顶不与小齿轮齿根产生过渡曲线干涉条件.大齿轮齿根Tanα't-(Z1/Z2)*(Tanαat1-Tanα't)≥Tanαt-(4*(han-Xn2)*Cosβ)/(Z2*Sin(2*αt))前项-0.1443359后项0.02134267判断前项≥后项,满足小齿轮齿顶不与大齿轮齿根产生过渡曲线干涉条件.输入已知参数W1=107.60697-0.055W2=69.6785953W1s=107.551967-0.085W2s=69.5935953W1x=107.521967W2x=69.5535953Xn1s=-0.0080407Xn2s=-1.56527Xn1x=-0.0124264Xn2x=-1.571117615.6494316S0n2s=4.31372959S0n1x15.6175063S0n2s=4.2711624815.9423373S0t2s=4.39446835S0t1x15.9098144S0t2x=4.35110453节园直径d'1278.082192d'2421.91780819.3123031S't2s=10.6696926S't1x19.2816898S't2x=10.6288749节园周节P'30.124861130.12486110.214296420.1428653最大法向侧隙Jbnmax0.210003最小法向侧隙Jbnmin0.14000302Ts=0.04W2s=-0.301667W2x=-0.34167按经验公式计算jbnmin=(2/3)(0.06+0.0005ai+0.03mn)0.356667按JIS标准规定(5,6级精度齿轮侧隙)W1=power(d1,1/3)+0.65m13.1601469W2=power(d2,1/3)+0.65m14.1530644齿轮付最小侧隙Jtmin=jtmin1+jtmin2273.1321126υ＞30m/s341.415141Jtmax=jtmax1+jtmax2860.36615475级精度时764.769915输入已知invαK0.01964548第一项22.2972106第二项0.45023513第三项0.00876795第四项0.00010206齿轮付推荐的最小侧隙jbnmin分园端面弧齿厚S0t1s分园法向弧齿厚S0n1s节园齿厚上下偏差S't1s已知渐开线函数,求其对应的角度(近似计算)外啮合角变位齿轮齿侧间隙计算(前面要输入齿轮计算参数)求出对应公法线上下偏差的变位系数最大端面齿侧间隙Jwtmax最小端面齿侧间隙Jwtminαk=21.8556414°量棒(球)直径dM16.817.2817.32取dM(输入)2.57-0.0290201invαMt2-0.0394601查渐开线函数表αMt129.5355241查渐开线函数表αMt222.1597475cosαMt10.87005022cosαMt20.9261358偶数齿时M1320.942298M2456.364887奇数齿时M1320.475378M2456.07574-0.0292219invαMt2s=-0.0396656-0.029332invαMt2x=-0.0397624查表输入αMt1s=29.3227368查表输入αMt2s=查表输入αMt1x=29.2257197上偏差M1s-M1=查表输入αMt2x=偶数齿时M1s=320.275964-0.66633388偶数齿时M2s=M1x=319.974536下偏差M1x-M1=M2x=奇数齿时M1s=319.810021-0.96776246奇数齿时M2s=M1x=319.509035M2x=上偏差M1s-M1=-0.6653566上偏差M2s-M2=下偏差M1x-M1=-0.9663432下偏差M2x-M2=invαMt1-0.0290201输入数据:输入功率P=22KW转速n1=8系数Aa=480K=1.6u=6.16667ψd=许用接触应力σHP=1500系数Am=12.5中心距a≥675.456893许用弯曲应力σFP=≥188.2639577齿轮双向受力时齿宽系数ψa0.20.250.30.350.4ψd10.716670.895833331.0751.2541671.43333333载荷变动较大时取0.2～0.4.当a=85d1=41b=a*ψa=21.2529.7534量棒(球)跨距M计算ψd1在齿轮非对称配置,结构刚性较大,硬齿面,载荷变动较小时取0.3～0.6.对应公法线下偏差的invαMt1x=量棒中心所在园压力角invαMt1斜齿园柱齿轮强度初步设计主动齿轮分度园直径d1按弯曲强度确定模数mn≥(采用公式)invαMt=Sn/(d*cosβ)+invαt+dm/(db*cosβb)-π/ZM值的上下偏差计算对应公法线上偏差的invαMt1s=齿轮参数2210111°20.34390163500Xn2=0.4776250.8Rz3.2177774.375NC1=4.53576746C2=4.87905242B=0.39694197A=83.7712499Kv=1.02248508园整取1.1右边有祥细计算KHβ=1.25KFβ=1.33a.小齿轮单对齿啮合系数ZB=1(εβ＞1)输入参数顶园直径da1=302.82基园db1=顶园直径da2=424.57基园db2=端面重合度εα2.014642157纵向εβM1=#NUM!M2=ZB=#NUM!ZD=5.0292374920.7045325152538.912103中等冲击σH2=2538.9121031550Mpa0.958467164ZNT2=1(磨光齿轮Ra＜0.8,Rz＜4μm)否则取等于22.齿间载荷分配系数KHa,KFa=25.接触强度寿命系数ZNT1=26.润滑油膜影响系数ZL*ZV*ZR=10.基园螺旋角βb=斜齿园柱齿轮强度校核计算12.齿宽b=14.齿距极限偏差fpt1=16.分度园直径d1=11.实际中心距a'=9.端面压力角αt=13.法向变位系数Xn1=15.齿面粗糙度(Ra)20.齿向载荷分布系数21.齿面接触