How to design a shaft pdf

Pins however, are the better component to use if you want a failure to occur if you expect there is a change that torque levels could become too high. The reason why is because set screws and press fits can mar up the surface of the shaft, causing issues later when you try to fix the assembly.

To calculate a stress due to a moment caused by bending the following equation would be used. Note the stress due to a moment is a normal stress. To calculate the shear stress due to bending, also known as transverse shear , the following equation would be used.

Notice for the above example there are 3 different stresses that can be determined. This a normal stress due to an axial force. Refer to the image below. Now that all four different types of stress have been discussed the next step is to find the maximum normal and maximum shear stress resulting from multi directional loads.

The first method that could be used is the principle stress and maximum shear stress. Refer to the equations below. It is important to note that stress can vary across the cross-section of the shaft depending on the applied stress. Finally, the final type of stress that could occur on a shaft is a stress concentration. A stress concentration is when the stress is amplified due to a change in the geometry. This can occur on a shaft that has a change in diameter, has a key way, or a slot for a retaining ring.

The table below provides a list of stress concentrations for some specific example. To use the values in the table above you would multiply the nominal stress in area that is effected by the stress concentration by the stress concentration value.

As you can see stress concentrations can make you expected stress grow exponentially, depending upon how abrupt the change is. Above I talked about how to find the stresses due to static loading. However, since the shaft will be rotating along with its components this actually a dynamic problem. This means that the axial, bending, and torsional stress could have alternating a midrange components.

This could eventually fatigue the part over time causing it to fail even if the static analysis says that the shaft will not reach the materials yield stress. For example, think about what happens when you bend a paper clip back and forth.

It will eventually break. The same thing can happen to a shaft after certain amount of cycles, normally ranging in the thousands to millions. This is why over time you generally have to replace components in your car, even if the part looks like it is still good.

To solve for the mid-range and alternating stresses the following equations would be used. For this problem the torque is constant which means it does not alternate due to the wheel rotating. Because of this the resulting shear stress from the torque will only be treated as midrange shear stress with no alternating stress. The lb weight will always being push up on the wheel. However, since the shaft is rotating, and the lb weight is not follow the rotation, the stress fields due to bending will rotate as the shaft rotates.

This will result in an alternating normal bending stress and an alternating transverse shear stress on the shaft. Both will have a maximum and minimum stress and a midrange stress that will need to be found by using the equations above. Next, we can use the distortion energy failure theory to find the resulting von Mises mid-range stress and the alternating stress by using the following equations. The following article discusses in detail on how to find all of the values needed to find the endurance limit for the equation above.

Finally, once you know what the endurance limit is, and what you know what the Von Mises stresses are, you can solve for the safety factor. There are different methods that can be used to solve for the safety factor, and each will produce a slightly different answer.

A fourth criteria that can used is the ASME-elliptic criteria which is represented by the equation below. To meet the above criteria n must be greater than or equal to 1 if it is less than 1 then the part is predicted to fail.

Conservative designers will use the modified-Goodman criteria. Either way though the part must pass the Langer Static criteria otherwise the part is predicted to fail statically.

Finally, the endurance limit can used to predict the fatigue stress in relation to a certain number of cycles by using the following equations. When analyzing shafts you do not need to analyze every point of a shaft, and from the above two sections you can see that this would be daunting task to do.

Instead you should only focus on a few critical locations. This first area that you should focus on is the outer surface of the shaft where the moment of the shaft is the greatest. For a shaft that is support like a cantilevered beam the moment will be at its greatest where the beam is supported. For a shaft that is supported on both ends you will need to create a moment diagram to find out where the greatest moment is.

You will also want to focus on areas where torque in present. As mentioned above, a single torque will be constant between the component that is transmitting the torque and the component that the torque is being transmitted to.

There could however be situations where there are multiple torques interacting on a shaft. This could cause some torques to cancel each other out and other torques to be added together. Again, to determine where the maximum torque would be on a shaft you will need to create a free body diagram.

Also, you should focus on areas of the shaft that have high stress concentrations that could amplify what might considered an insignificant stress into a stress that could cause failure. When there is a bending moment there is a shear stress as well as a normal stress due to the moment.

Generally, the shear stress caused by a moment is insignificant in comparison to normal stress caused by the moment. Due to this fact you may not even need to consider that shear stress in your analysis. The one case where you would want to consider it is when the bending moment is on a short stubby beam, which in those cases the shear stress could be significant when compared to the normal stress due to a bending moment.

Also, remember if you are analyzing the shear stress due to the bending moment the maximum shear stress will be present at the centroid of the shaft, while it will be negligible on the surface of the shaft.

This is the reverse for the normal stress due to bending as well as the shear stress due to torsion. Download Download PDF. Translate PDF. Determine the diameter of the shaft using maximum principal stress and maximum shear stress theories of failure and assuming a factor of safety of 2. The allowable tensile stress for the shaft material is MPa and the allowable shear stress is 85 MPa.

Taking torsion and bending factors as 1. Also find out the dimensions for a hollow shaft with outside diameter limited to 30 mm. Compare the weights of the two shafts. It rotates at r. The belt tensions are also shown in the figure. Additionally, he has interested in Product Design, Animation, and Project design.

He also likes to write articles related to the mechanical engineering field and tries to motivate other mechanical engineering students by his innovative project ideas, design, models and videos. Just wondering what were you referring to?

Just trying to understand. Your notes are very helpful. Really appreciate the work, time and effort you put in. We should consider torsional rigidity as well as lateral rigidity. Your email address will not be published. Save my name and email in this browser for the next time I comment. This site uses Akismet to reduce spam. Learn how your comment data is processed. Introduction to Pressure Vessels Vessels, tanks, and pipelines that carry, store, or receive fluids are called pressure vessels.

A pressure vessel is defined as a container with a pressure Knuckle Joint A knuckle joint is used to connect two rods which are under the action of tensile loads. However, if the joint is guided, the rods may support a compressive load. A knuckle joint