渐开线花键计算公式

渐开线花键计算公式

30°平齿根花键计算书第1页

模数 m = 3

齿数 z = 15

标准压力角αD = 30°

配合代号：H7/h7

分度圆直径D = m×z = 45

基圆直径Db = m×z×cos(αD) = 38.9711

周节p = π×m = 9.42477796076937

内花键大径Dei = m×(z+1.5) = 49.5

外花键作用齿厚上偏差 esv = 0

(根据<<机械传动设计手册>>1463页表9-1-49或由公差代号计算)

外花键渐开线起始圆直径最大值：

DFemax = 2×((0.5Db)^2+(0.5Dsin(αD)-(hs-0.5esv/tan(αD))/sin(αD))^2)^0.5 = 41.8669

(其中hs = 0.6m = 1.8)

内花键小径 Dii = DFemax+2CF) = 42.47

(其中CF = 0.1m = .3)

内花键基本齿槽宽E = 0.5πm = 4.71238898

外花键基本齿厚S = 0.5πm = 4.71238898

内花键：

内花键总公差T+λ = 40i*+160i** = 179

其中i* = 0.45(D)^(1/3) + 0.001D (D = (30×50)^0.5 = 38.7298334620742)

i** = 0.45(E)^(1/3) + 0.001E (E = (3×6)^0.5 = 4.24264068711928)

周节累积公差 Fp = 7.1(L)^0.5 + 18 = .078

其中分度圆周长之半L = πmz/2 = 70.6858347057703

齿形公差ff = 6.3ψf + 40 = .062

其中公差因数ψf = m + 0.0125D = 3.48412291827593

齿向公差Fβ = 2.0×(g)^0.5 + 10 = .023

其中花键长度 g = 40

综合公差λ= 0.6((Fp)^2 + (ff)^2 + (Fβ)^2)^0.5 = .061

作用齿槽宽最小值Evmin = 0.5πm = 4.712

实际齿槽宽最大值Emax = Evmin + (T+λ) = 4.891

实际齿槽宽最小值Emin = Evmin + λ =4.773

作用齿槽宽最大值 Evmax = Emax - λ = 4.83

外花键：

外花键大径Dee = m×(z + 1) = 48

外花键小径Die = m×(z - 1.5) = 40.5

外花键总公差T+λ = 40i*+160i** = 179

其中i* = 0.45(D)^(1/3) + 0.001D (D = (30×50)^0.5 = 38.7298334620742)

i** = 0.45(E)^(1/3) + 0.001E (E = (3×6)^0.5 = 4.24264068711928)

周节累积公差 Fp = 7.1(L)^0.5 + 18 = .078

其中分度圆周长之半L = πmz/2 = 70.6858347057703

齿形公差ff = 6.3ψf + 40 = .062

其中公差因数ψf = m + 0.0125D = 3.48412291827593

齿向公差Fβ = 2.0×(g)^0.5 + 10 = .023

其中花键长度 g = 40

综合公差λ= 0.6((Fp)^2 + (ff)^2 + (Fβ)^2)^0.5 = .061

作用齿厚最小值Svmin = Smin + λ = 4.594

实际齿厚最大值 Smax = Svmax - λ = 4.651

实际齿厚最小值 Smin = Svmax - (T+λ) =4.533

作用齿厚最大值 Svmax = S + esv = 4.712

30°平齿根花键计算书第 2 页

量棒直径 DRi = DRe = 5.04

内花键量棒中心圆上的压力角invαi = Emax/D + invαD - DRi/Db

= 4.891/45 + inv(αD) - 5.04/38.9711

= .108688888888889+5.37514935913267E-02-.129326603560074

= 3.31224454025424E-02

αi = 25.7996333°

内花键棒间距最大值MRimax = Db × cos(90/z)/cosαi - DRi = 37.3

内花键棒间距最小值 MRimin = MRimax - Ki×T = 37.07

其中Ki = cosαD × cos(90/z)/sinαi T = (T+λ)-λ

外花键量棒中心圆上的压力角invαe = DRe/Db + invαD + Smin/D - π/z

= 5.04/38.9711 + inv(αD) + 4.533/45 - π/15

= .129326603560074+5.37514935913267E-02+.100733333333333-.209439510239319 = 7.43805866859188E-02

αe = 33.1259646°

外花键跨棒

距最大值MRemin = Db × cos(90/z)/cosαe + DRe = 50.74 外花键跨棒距最小值MRemax = MRemin + Ke×T = 50.557其中Ke = cosαD × cos(90/z)/sinαe T = (T+λ)-λ

挤压强度计算

计算挤压应力σc = 1000T/(ψ×z×h×l×r) = 27.1 MPa

其中传递转矩T = 30000×P/π/n = 658.5722 N×m

系数ψ取 0.75

齿数 z = 15

花键工作高度h = 0.8×m = 2.4

花键工作长度 l = 40

花键平均半径 r = D/2 = 22.5