A 4140 steel shaft, heat-treated to a minimum yield strength of 100 ksi, has a diameter of 1 7/16 in. The shaft rotates at 600 r
pm and transmits 40 hp through a gear. The hub upon which the gear is seated is 1.5 in wide. You have in stock 1137 OQT 1300 carbon steel that you are considering using as a key to seat the gear hub. What dimensions will the key need to be? Is this material appropriate for the application? If not, select a more appropriate material.
2 answers:
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Answer:
22.90 × 10⁸ kg
Explanation:
Given:
Diameter, d = 0.02 m
ωₙ = 0.95 rad/sec
Time period, T = 0.35 sec
Now, we know
T=
where, L is the length of the steel cable
g is the acceleration due to gravity
0.35=
or
L = 0.0304 m
Now,
The stiffness, K is given as:
K =
Where, A is the area
E is the elastic modulus of the steel = 2 × 10¹¹ N/m²
or
K =
or
K = 20.66 × 10⁸ N
Also,
Natural frequency, ωₙ =
or
mass, m =
or
mass, m =
mass, m = 22.90 × 10⁸ kg