Solved: In straight-bevel gearing, there are some analogs

Chapter 15, Problem 15-7

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In straight-bevel gearing, there are some analogs to Eqs. (14–44) and (14–45) pp. 766 and 767, respectively. If we have a pinion core with a hardness of \(\left(H_B\right)_{11}\) and we try equal power ratings, the transmitted load \(W^t\) can be made equal in all four cases. It is possible to find these relations:

                                               

(a) For carburized case-hardened gear steel with core AGMA bending strength \(\left(s_{a t}\right)_G\) and pinion core strength \(\left(s_{a t}\right)_P\), show that the relationship is

\(\left(s_{a t}\right)_G=\left(s_{a t}\right) P \frac{J_p}{J_G} m_G^{-0.0323}\)

This allows \(\left(H_B\right)_{21}\) to be related to \(\left(H_B\right)_{11}\).

(b) Show that the AGMA contact strength of the gear case \(\left(s_{a c}\right)_G\) can be related to the AGMA core bending strength of the pinion core \(\left(s_{a t}\right)_P\) by

\(\left(s_{a c}\right)_G=\frac{C_p}{\left(C_L\right)_G C_H} \sqrt{\frac{S_H^2}{S_F} \frac{\left(s_{a t}\right)_P\left(K_L\right)_P K_x J_P K_T C_s C_{x c}}{N_P I K_s}}\)

If factors of safety are applied to the transmitted load \(W_t\), then \(S_H=\sqrt{S_F}\) and \(S_H^2 / S_F\) is unity. The result allows \(\left(H_B\right)_{22}\) to be related to \(\left(H_B\right)_{11}\).

(c) Show that the AGMA contact strength of the gear \(\left(s_{a c}\right)_G\) is related to the contact strength of the pinion \(\left(s_{a c}\right)_P\) by

\(\left(s_{a c}\right)_P=\left(s_{a c}\right)_G m_G^{0.0602} C_H\)