A pair of mating steel spur gears with a 0.75-in face width transmits a load of 40 lbf. For estimating the contact stresses, make the simplifying assumption that the teeth profiles can be treated as cylindrical with instantaneous radii at the contact point of interest of 0.47 in and 0.62 in,

Question

A pair of mating steel spur gears with a 0.75-in face width transmits a load of 40 lbf. For estimating the contact stresses, make the simplifying assumption that the teeth profiles can be treated as cylindrical with instantaneous radii at the contact point of interest of 0.47 in and 0.62 in, respectively. Estimate the maximum contact pressure and the maximum shear stress experienced by either gear.

Accepted Answer

[latex]v=0.292, E=30 Mpsi , l=0.75 ext { in, } d_{1}=2(0.47)=0.94 ext { in, } d_{2}=2(0.62)=1.24 ext { in. }[/latex]

Eq. (3-73):

[latex]b=\left(\frac{2(40)}{\pi(0.75)} \frac{2\left(1-0.292^{2} ight) /\left[30\left(10^{6} ight) ight]}{1 / 0.94+1 / 1.24} ight)^{1 / 2}=1.052\left(10^{-3} ight) ext { in }[/latex]

Eq. (3-74):

[latex]p_{\max }=\frac{2 F}{\pi b l}==\frac{2(40)}{\pi(1.052)\left(10^{-3} ight)(0.75)}=32275 psi =32.3 kpsi[/latex]

From Fig. 3-39,

[latex] au_{\max }=0.3 p_{\max }=0.3(32275)=9682.5 psi =9.68 kpsi[/latex]

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Eq. (3-73): [latex]b=\sqrt{\frac{2 F}{\pi l} \frac{\left(1-v_{1}^{2} ight) / E_{1}+\left(1-v_{2}^{2} ight) / E_{2}}{1 / d_{1}+1 / d_{2}}}[/latex]

Eq. (3-74): [latex]p_{\max }=\frac{2 F}{\pi b l}[/latex]

Question 3.139: A pair of mating steel spur gears with a 0.75-in face width ...

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