30° 平齿根花键计算书

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 = 0.3)
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 = 0.078
其中分度圆周长之半L = πmz/2 = 70.6858347057703
字串8
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 = 0.023
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
字串6
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-.20943951023 9319 字串4
= 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
根据联接情况：静联接
使用、制造条件：中等
热处理工艺：齿面未经热处理
许用挤压应力 [σc] = 60--100 MPa 挤压强度满足要求σc < [σc]。