# What Is the Maximum Speed of a Hollow Shaft Given Specific Shear Stress Limits?

• josh16
In summary, the conversation discusses the use of a hollow shaft with an internal diameter of 72 mm and wall thickness of 24 mm to transmit a power of 90 kW. The question is posed about the maximum speed of shaft rotation if the shear stress must not exceed 150 MPa. The solution is found to be 22.66 rad/s, but the calculation for the external diameter is not clear. The use of an equation to find the OD is suggested and the OP is asked about their understanding of the terms 'internal diameter' and 'wall thickness'.
josh16

## Homework Statement

A hollow shaft has an internal diameter of 72 mm and wall thickness of 24mm is to be used to transmit a power of 90 kW.

what would be the maximum speed of shaft rotation if the shear stress must not exceed 150 MPa ??

## Homework Equations

http://www.amesweb.info/Torsion/CalculationStepsForTorsionalStress.aspx

## The Attempt at a Solution

I got 22.66 rad/s. I am getting stuck at finding the external diameter

Last edited by a moderator:
The OP states the ID of the shaft is 72 mm and the wall thickness is 24 mm. It's not clear why you are stuck calculating the OD of the shaft.

is there an equation to find the OD

Yes there is. Do you know what the terms 'internal diameter' and 'wall thickness' mean? How did you work the problem in the OP without doing this calculation first?

of shaft.

I would approach this problem by first understanding the physical principles involved in hollow shaft rotation and the factors that affect its maximum speed. I would start by researching the equations and principles of torsion and shear stress, as these are the key factors in determining the maximum speed of rotation for a hollow shaft.

Next, I would use the given information about the internal diameter, wall thickness, and power transmission to calculate the maximum shear stress using the equation for torsional stress. This would give me a value of 150 MPa as the maximum shear stress.

To find the external diameter of the shaft, I would use the equation for torsional stress again, but this time solving for the external diameter. This would involve rearranging the equation and plugging in the known values for the internal diameter, wall thickness, and maximum shear stress. This would give me the required external diameter of the shaft.

Finally, I would use the equation for maximum speed of rotation, which takes into account the maximum shear stress and the external diameter, to calculate the maximum speed of rotation for the given power transmission. This would give me the final answer of 22.66 rad/s.

In conclusion, as a scientist, I would approach this problem by understanding the underlying principles and equations involved, and using them to systematically solve for the required variables. By doing so, I can ensure the accuracy and reliability of my solution.

## 1. What is hollow shaft rotation?

Hollow shaft rotation is a type of rotational motion in which the axis of rotation passes through the center of a hollow cylindrical object. This allows for the transfer of torque and rotation from one end of the shaft to the other.

## 2. How is hollow shaft rotation different from solid shaft rotation?

The main difference between hollow shaft rotation and solid shaft rotation is the presence of a hollow core in the former. This allows for a lighter and more efficient design, as well as the potential for additional functions such as fluid or electrical transfer through the shaft.

## 3. What are the advantages of using hollow shaft rotation?

Hollow shaft rotation offers several advantages, including weight reduction, increased efficiency, and the potential for additional functions. It also allows for the use of smaller and more compact motors or other rotational devices.

## 4. How is hollow shaft rotation used in practical applications?

Hollow shaft rotation is commonly used in various industries such as automotive, aerospace, and manufacturing. It is often used in high-speed applications where weight and efficiency are crucial, such as in turbines and electric motors.

## 5. What are some common materials used for hollow shaft rotation?

Hollow shafts can be made from a variety of materials, including metals such as steel, aluminum, and titanium, as well as composite materials like carbon fiber. The choice of material depends on the specific application and required properties such as strength, weight, and corrosion resistance.

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