内啮合角变位圆柱齿轮计算

名称外齿轮内齿圈模数m小齿轮Z1大齿轮Z2分度圆压力角α齿顶高系数ha＊顶隙系数c＊变位中心距a'插齿刀齿数Z02插齿刀变位系数X02插齿刀齿顶高系数ha02＊未变位中心距a中心距变动系数y啮合角α’(度)22.00022°00′00″总变位系数XΣ变位系数的分配x1,x2-0.00600.2911插内齿轮时的啮合角α02'插内齿轮时的中心距a02分度圆直径d42.000105.00080.259齿根圆直径df38.232109.555齿顶圆直径da44.955102.832全齿高h3.3613.361齿顶高ha1.4771.084齿根高hf1.8842.277齿顶压力角αa(度)28.606916.3614插齿刀的齿顶压力角αa02(度)端面重合度εα轴向重合度εβ按已知条件计算校验重合度及插齿时的顶切和啮合时的干涉14.6480.50328.58371.8603εβ=00.0149040.007192830.28330.020054内啮合角变位圆柱齿轮传动几何尺寸计算1.50028.00031.50031.92570.00020.001.0015.788094920.2550.01.2500.2971总重合度εγ0.7798020.6764460.9618210.277216正火调质钢小齿轮齿厚合格淬火钢小齿轮齿厚合格固定弦齿厚Sc^2.0747871.7998731.0999010.760487跨测齿数/槽数k4810.72461523.121374-0.0041040.19914216.08076634.980774精度等级77单个齿距极限偏差±fpt#REF!#REF!5个齿距累积极限偏差±fpk#REF!#REF!齿距累积总偏差Fp#REF!#REF!齿廓总偏差Fα#REF!#REF!齿廓形状偏差ffα#REF!#REF!齿廓倾斜极限偏差±fHα#REF!#REF!螺旋线总偏差Fβ#REF!#REF!螺旋线形状偏差ffβ#REF!#REF!螺旋线倾斜极限偏差±fHβ#REF!#REF!公差输出(单位μm)测量尺寸计算（选一种）不会产生重叠干涉校验重叠干涉校验小齿轮齿顶厚度1.860338校验内齿轮加工时是否产生范成顶切避免小齿轮齿根干涉的条件(小齿轮滚刀加工)不会产生内齿轮齿根干涉会产生小齿轮齿根干涉0.046089不会产生展成顶切校验插内齿时是否产生径向切入顶切避免内齿轮齿根干涉的条件查表2.2-14跨k齿的公法线长度Wk固定弦齿高hc^0.0125320.0040370.008024切向综合总偏差Fi'#REF!#REF!一齿切向综合偏差fi'#REF!#REF!径向综合总偏差Fi#REF!#REF!一齿径向综合偏差fi#REF!#REF!径向跳动公差Fr#REF!#REF!d1=mz1d2=mz2da02=m*(Z02+2*ha02＊+2*X02)df1=d1-2*(ha＊+c＊-x1)*mdf2=da02+2*a02da1=df2-2a'-2*(c＊)*mda2=df1+2a'+2*(c＊)*mh1=(da1-df1)/2h2=(df2-da2)/2ha1=(da1-d1)/2ha2=(d2-da2)/2hf1=(d1-df1)/2hf2=(df2-d2)/2cosαa1=d1*cosα/da1cosαa2=d2*cosα/da2cosαa02=m*Z02*cosα/da02cosα’=(m/2/α’)(Z2-Z1)cosαinvα'=tanα'-α'(弧度)a'εα=1/2π(Z1（tanαa1-tanα’)-Z2(tanαa2-tanα’))εβ=0invα=tanα-α(弧度)y=(a'-a)/mha＊内啮合角变位圆柱齿轮传动几何尺寸计算代号mZ1Z02ha02＊X02Z2αα02'c＊a=1/2(d2-d1)=1/2*m*(Z2-Z1)XΣ=X2-X1=(Z2-Z1)/（2*tanα）*（invα'-invα)按变位系数选择原则适当分配，而后再行验算invα02'=invα+2*(X2-X02)/(Z2-Z02)*tanαa020.714285714-0.03832591232.8974035532.239700013.5816408343.93093388Sa1大于0.25m(调质钢)/大于0.4m(淬火钢)1.113029862Sc1=(π/2+2X1tanα)*m*cosα²Sc2=(π/2-2X2tanα)*m*cosα²hc1=(da1-d1)/2-(Sc1*tanα)/2hc2=(d2-da2)/2-(Sc2tanα)/2+Δh2k1=(α/180°)*z1+0.5k2=(α/180°)*z2+0.5Wk1*=cosα(π(k1-0.5)+z1*invα)Wk2*=cosα(π(k2-0.5)+z2*invα)ΔWk1*=2*X1*sinαΔWk2*=2*X2*sinαWk1=(Wk1*)*m+(ΔWk1*)*mWk2=(Wk2*)*m+(ΔWk2*)*m齿宽b尺寸如下20Sa1=da1*((π+4*X1*tanα)/2/Z1+invα-invαa1）Z02tanαa02+(Z2-Z02)tanα02’≥Z1tanαa1+(Z2-Z1)tanα’Z2tanαa2-(Z2-Z1)tanα’≥Z1tanα-4*（ha＊-x1）/sin2αinvαa1=tanαa1-αa1(弧度)（Z02/Z2)≥（1-（tanαa2/tanα02')cosδ1=(ra2²-ra1²-a'²)/（2*ra1*a'）(右边为δ1结果，单位弧度)cosδ2=(ra2²-ra1²+a'²)/（2*ra2*a'）(右边为δ2结果，单位弧度)Z1(δ1+invαa1)-Z2(δ2+invαa2)+invα’(Z2-Z1)≥0εγ=εαδα2=（π/2Z2）-（2X2tanα/Z2）-invα+invαa2Δh2=(da2*(1-cosδα2)）/2invαa2=tanαa2-αa2(弧度)渐开线反函数ainvαA10.007192827渐开线值A20.275671358中间值(3*A1)^(1/3)-3*A1/7.9A30.282873556正切函数TAN(A2)A40.080017449平方值(A3)^2A50.275554239(弧度)中间值(A1+A2-A3)/A4+A2A615.78809492角度值ainv(α)引用方法渐开线值渐开线反函数0.0071928315.78809492df2近似计算109.6233801