A CI bevel gear pair, having pitch circle diameters of 80 mm and 100 mm, is used for transmitting 3 kW power at a pinion speed of 1200 r.p.m The tooth system is $14 1/2^0$ composite. If the static strength of pinion and gear is 56MPa, determine:

i) the module ii) the face width and iii) the surface hardness

Assume velocity factor accounts for dynamic load.

Mumbai University > Mechanical Engineering > Sem 7 > Machine Design 2

Marks: 14M

Year: Dec 2016

Given

PCD (d_1) = 80

PCD (d_2) = 100

P = 3000 W

N = 1200

$\alpha = 14.5^0$

$[\sigma_b] = 56MPa$

Solution:

$d_1 = m_tz_1$

where

No. of teeth on pinion = z_1

Assuming $\sum = 90^0$

$\delta_1 = tan^{-1} \bigg[\frac{sin \sum}{i + cos \sum}\bigg] = 38.659 \hspace{2cm} i = 1.25$

$\delta_2 = 90 - \delta_1 = 51.3401$

No. of teeth on virtual pinion $Z_{v1} = \frac{2}{sin^2 \alpha}$

$Z_{v1} = \frac{2}{sin^2 14.5}\\ Z_{v1} = 31.9029$

$Z_1 = Z_{v1} cos \delta_1\\ z_1 = 24.912\\ Z_1 \approx 25\\ Z_2 = iz_1\\ Z_2 = 31.25\\ Z_2 \approx 32$

PCD $(d_1) = M_tZ_1\\ M_t = \frac{80}{25}\\ M_t = 3.2$

$M_t = 1.26 M_{av}\\ M_{av} = 2.539 mm$

$\psi = \bigg[ \frac{5}{sin \delta_1} = 8\\ b = \psi M_{av} = 20.312\\ b \approx 21 mm$

Induced surface hardness

$\sigma_c = \frac{0.72}{(R - 0.5b)} \sqrt{\frac{\sqrt{(i + 1)^3}}{ib}E[M_t]}$

where R = 3b = 63 mm

$bc = 475.693 n/mm^2$