Question

A 6 in. solid steel shaft have been mounted into an electric motor using a flanged bolt coupling. If the motor has a capacity of 300 hp at 500 rpm, (a) determine how many ¼” diameter bolt (8700 psi maximum shear stress) is needed on a 9 inches bolt circle diameter flanged bolt coupling. (b) If a pulley having a 2 in. hub length will be attached to the shaft using a square key (25200 psi maximum shear stress), determine the dimension of the key.

Answer 1

a) We need 8 bolts on the flanged bolt coupling.

b)In this case, the dimension of the key is approximately 0.014 inches.

Step-by-step explanation:

(a) To determine the number of ¼" diameter bolts needed on the flanged bolt coupling, we first need to calculate the maximum shear force on each bolt.

The maximum shear force is given by the formula:

Maximum Shear Force = (Maximum Shear Stress) x (Cross-sectional Area of Bolt)

Since we are given the maximum shear stress of 8700 psi and the diameter of the bolt is ¼", we can calculate the cross-sectional area of the bolt using the formula for the area of a circle:

Area of Bolt = π/4 x (Bolt Diameter)^2

Substituting the values, we get:

Area of Bolt = π/4 x (0.25)^2 = 0.04909 square inches

Now, we can calculate the maximum shear force:

Maximum Shear Force = (8700 psi) x (0.04909 square inches)

= 426.0183 pounds

Next, we calculate the total maximum shear force on all the bolts by dividing the motor capacity (300 hp) by the angular velocity (500 rpm) and multiplying by a conversion factor of 5252:

Total Maximum Shear Force = (300 hp) x (5252) / (500 rpm)

= 3153.6 pounds

Finally, we divide the total maximum shear force by the maximum shear force on each bolt to determine the number of bolts needed:

Number of Bolts = Total Maximum Shear Force / Maximum Shear Force per Bolt

= 3153.6 pounds / 426.0183 pounds ≈ 7.4 bolts

Since we cannot have a fraction of a bolt, we would need to round up to the nearest whole number.

Therefore, we need 8 bolts on the flanged bolt coupling.

(b) To determine the dimension of the square key, we can use the formula for the maximum shear stress:

Maximum Shear Stress = Force / (Length x Width)

The maximum shear stress is given as 25200 psi, and we need to find the width of the square key. Rearranging the formula, we get:

Width = Force / (Maximum Shear Stress x Length)

Substituting the values, we have:

Width = (3153.6 pounds) / (25200 psi x 9 inches) ≈ 0.014 inches

Therefore, the dimension of the square key is approximately 0.014 inches.