四、设计计算题10—52 设计一直齿圆柱齿轮传动[1],原用材料的许用接触应力为[σH]1=700MPa,[σH]2 =600MPa,求得中心距a=100mm;现改用[σH]1=600MPa,[σH]2=400MPa的材料,若齿宽和其它条件不变,为保证接触疲劳强度不变,试计算改用材料后的中心距a′。_(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)_解:_(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)_ 即_(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)_10—53 一直齿圆柱齿轮传动,已知zl=20,z2=60,m=4mm,B1=45mm,B2=40mm,齿轮材料为锻钢,许用接触应力[σH]1=500MPa,[σH]2=430MPa,许用弯曲应力[σF]1=340MPa,[σF]2=280MPa,弯曲载荷系数K=1.85,接触载荷系数K=1.40,求大齿轮所允许的输出转矩T2 (不计功率损失)。_(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)_解:1、计算弯曲强度允许的输出转矩_(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)_2、计算接触强度允许的输出转矩_(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)_大齿轮所允许的输出转矩T2=168938Nmm。10一54有一对闭式软齿面直齿圆柱齿轮传动,已知小齿轮齿数z1=20,传动比i=3,模数 m=4mm,齿宽 b = 80 mm,齿面接触应力σH = 400MPa,大齿轮齿根弯曲应力 σF2 = 50 MPa。现可忽略载荷系数K对强度的影响,试求:(1)小齿轮的齿根弯曲应力σF1;(2)当其他条件不变,而 b =40mm时的齿面接触应力σ′H和齿根弯曲应力σ′F1、σ′F2;(3)当传动比i及其他条件不变,而 z1= 40,m = 2 mm时的齿面接触应力σ″H和齿根弯曲应力σ″F1、σ″F2。_(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)_解:(1)_(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)_(2)_(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)_(3) (因为d1不变)_(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)__(n)=sqrt (dfrac {xF)(b{a)_(1)}}cdot dfrac (upm 1)(u)cdot (z)_(n)(z)_(k)=sqrt (dfrac {2k{T)_(1)}(bd{x)^2}}cdot dfrac (u+1)(u)cdot (z)_(n)(z)_10—57 设计铣床中一对直齿圆柱齿轮传动,已知功率P1=7.5kW,小齿轮主动,转速n1=1450r/min,齿数z1=26,z2=54,双向传动,工作寿命Lh=12000h。小齿轮对轴承非对称布置,轴的刚性较大,工作中受轻微冲击,7级制造精度。