Answer to Question #238584 in Mechanical Engineering for Maps

Question

A 20° full depth spur pinion is required to transmit 1.8 kW at a speed of 1540 rpm. If the pinion has 21 teeth and is manufactured from a heavy duty 817M40 steel; Select a suitable gear from the limited choice given in Tables 6.7 -6.10, specify the:

1.1 module and face width based on the Lewis formula. (9)

1.2 the gear module and the face width if the power transmitted is doubled (3)

1.3 the gear module and the face width if the speed is doubled and the power is still 1.8 kW? (3)

Hint: In all the above, show all your calculation steps (Start with m =1) in all cases.

Answer 1

Solution

From the law of conservation of momentum

$m_1 V_{1i} + m_2. V_{2i} = m_1V_1 + m_2V_2$

where vii- velocities before collision are v1i=5 m/s Particles of $m_1=10 kg$

we have

$V_{2i}$

$V_i$

$V_2$

from here:

$v_1=\frac{v_{1i}(m_1-m_2)}{m_1+m_2}+\frac{v_{2i}(2)(m_2)}{m_1+m_2}=\frac{5(10-5)}{10+5}+\frac{3\times2\times5}{10+5}=3.66m/s$

$v_2=\frac{v_{1i}(2)(m_1)}{m_1+m_2}+\frac{v_{2i}(m_2-m_1)}{m_1+m_2}=\frac{5\times2\times10}{10+5}+\frac{3(5-10)}{10+5}+=5.66m/s$

$v_1=3.66m/s$

$v_2=5.66m/s$