Calculate Shaft Radius for Coupling System, 100rpm Rotate

[neyganesh]

Pls help me calculate the shaft radius of a coupling system that's goin to rotate an prespex cylindrical at 100 rpm by a motor... the dia of cylinder is 6 in and its width is 1 in. the material to be rotated is 10 gm s of sand... bulk density if the sand is 3000 kg per m^3...

 

[Astronuc]

Is this a homework problem? Is seems somewhat ill defined, particularly with respect to constraints, e.g. power, stress, materials, . . . .

What is the orientation of the cylinder - horizontal or vertical? That will make difference regarding the distribution of the sand. Is the sand to be tumbled, as in a tumbler/blender.

For starters calculate the volume of the cylinder and the volume of sand.

 

[ravenprp]

To calculate the shaft radius for the coupling system, we first need to determine the torque required to rotate the prespex cylinder at 100 rpm. This can be calculated using the formula:

Torque (T) = Moment of Inertia (I) x Angular Acceleration (α)

Since the cylinder is rotating at a constant speed, the angular acceleration (α) is equal to zero. Therefore, the torque required is simply the moment of inertia (I) of the cylinder.

The moment of inertia of a solid cylinder is given by the formula:

I = 1/2 x Mass x Radius^2

In this case, the mass of the cylinder is 10 grams, or 0.01 kg. The radius of the cylinder is given as 3 inches, or 0.0762 meters. Therefore, the moment of inertia is:

I = 1/2 x 0.01 kg x (0.0762 m)^2 = 2.91 x 10^-5 kgm^2

Now, we can calculate the torque required:

T = 2.91 x 10^-5 kgm^2 x 0 rad/s^2 = 0.00 Nm

Next, we need to consider the weight of the sand being rotated. The force required to rotate the sand can be calculated using the formula:

Force = Mass x Acceleration

The mass of the sand is 10 grams, or 0.01 kg. The acceleration is equal to the gravitational acceleration, which is 9.8 m/s^2. Therefore, the force required to rotate the sand is:

Force = 0.01 kg x 9.8 m/s^2 = 0.098 N

Now, we can calculate the total torque required:

Total Torque = Torque to rotate the cylinder + Torque to rotate the sand

Total Torque = 0.00 Nm + 0.098 N x 0.0762 m = 0.00746 Nm

Finally, we can use the formula for torque to calculate the shaft radius:

T = Fr x Radius

Where Fr is the force required and Radius is the radius of the shaft. Rearranging the formula, we get:

Radius = T / Fr

Substituting the values, we get:

Radius = 0.00746 Nm / 0.098 N = 0.0762 m

Therefore,