Sizing Shaft Key for Machine Element Design Problem

In summary, for your Design of Machine Elements class, you need to design a copper square tapered key to connect a 400mm-diameter shaft to a flywheel and jaw mechanism without exceeding a torque of 700kN m. This can be done by determining the maximum torque the key can withstand using equations for shear and bearing stress, and then calculating the dimensions and allowable stresses for the key. You should also consider other factors to ensure the design is safe and reliable.
  • #1
Shawnzyoo
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For my Design of Machine Elements class this problem is being posed.
This is exactly as the problem is stated.

The torque on the 400mm -diameter shaft connecting the flywheel with the jaw mechanism should never go above 700kN m. Dimension a copper square tapered key so that the shaft is not damaged.

So really just trying to find the length/width/height of the key.
I know that the the only stresses on the key are shear and bearing stress.
Tau(design)=2T/dwl
Sigma(design)=4T/dlh
Copper Sy=69e6 Pa Su=220e6 Pa

I am not too sure on where to begin with this (I have started it and went no-where).
Does anyone have any insight on where to go with this problem?? By the way I am not looking for an answer just general guidance.
Any suggestions?
Thank You.
 
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  • #2
The first step is to determine the maximum torque that the key can withstand. You can do this by using the equations you have provided (Tau(design)=2T/dwl and Sigma(design)=4T/dlh). This will give you a maximum torque that the key can support. Once you have determined the maximum torque, you can then calculate the dimensions of the key. For example, if you want a square key, you can use the equation dlh = 2T/Tau(design) to calculate the length, width and height of the key. You can then use the equations Su = 4T/dlh and Sy = 2T/dwl to calculate the allowable shear and bearing stresses for the key. Once you have calculated the dimensions and allowable stresses for the key, you can then compare these values to the yield strength of copper (Sy = 69MPa and Su = 220MPa) to determine if the key is suitable for your application. Finally, you may want to consider other factors such as the size of the key slot in the shaft and the material properties of the key to ensure that the design is safe and reliable.
 
  • #3


I would approach this problem by first understanding the concept of key design and its purpose in connecting the flywheel to the jaw mechanism. A key is a small, wedge-shaped component that is used to transmit torque and prevent relative motion between two rotating elements. In this case, the key is made of copper which has a shear yield strength of 69e6 Pa and an ultimate tensile strength of 220e6 Pa.

Next, I would review the equations for calculating the shear and bearing stresses on the key. It is important to note that the key is subjected to both shear and bearing stresses, and both of these stresses must be taken into consideration for proper key design. The equations provided in the problem statement can be used to determine the design values for these stresses.

Once the design values for shear and bearing stresses have been determined, I would then use the material properties of copper to calculate the required dimensions of the key. This would involve using the equations for shear stress and bearing stress, along with the known values for torque and dimensions of the shaft, to solve for the length, width, and height of the key.

It is also important to consider factors such as safety factors and tolerances in the design process. These can impact the final dimensions of the key and should be taken into account.

In summary, the key design for this machine element problem involves understanding the purpose of the key, calculating the design values for shear and bearing stresses, and using material properties and equations to determine the required dimensions. It is important to carefully consider all relevant factors and to double check calculations for accuracy.
 

What is a sizing shaft key?

A sizing shaft key is a mechanical component used to connect rotating machine elements such as gears, pulleys, and couplings to a shaft. It serves as a torque transmitting element and prevents slippage between the shaft and the connected element.

Why is it important to correctly size a shaft key?

Correctly sizing a shaft key is crucial to ensure the efficient and safe operation of a machine. An undersized key can result in slippage and damage to the machine, while an oversized key can cause stress concentration and premature failure of the key or shaft.

What factors should be considered when sizing a shaft key?

When sizing a shaft key, factors such as the torque and power transmitted, shaft diameter, keyway dimensions, and material properties should be taken into account. The key should also be able to withstand any shock or impact loads that may occur during operation.

How do you determine the size of a shaft key?

The size of a shaft key is determined by using equations and tables provided in engineering handbooks. The equations take into consideration the factors mentioned above and provide a recommended key size for the given application.

What are the consequences of an incorrectly sized shaft key?

An incorrectly sized shaft key can lead to various consequences, including reduced efficiency and performance of the machine, increased wear and tear, and potential failure of the key or shaft. It can also result in costly repairs and downtime for the machine.

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