This month’s challenge ties into the Mathcad for Mechanical Engineers Webinar. Your challenge, should you choose to accept it, is to create a worksheet that calculates the stresses on a key in a keyway for a crankshaft and flywheel.
The Scenario
A key is a mechanical component used to transfer power between a rotating shaft and a machine component (in the image below, a flywheel). The torque is 150 Newton-meters.
The shaft diameter where the flywheel is attached has a diameter of 50mm. The key length is 50mm with a breadth (width) of 12.5 mm and total height of 10 mm. The size of the chamfers on the key is 1 mm, but you can ignore them for the stress calculations if you wish.
The Challenge
Your task is to calculate the following:
- Calculate the torque that can be transmitted by the reduced shaft diameter (the diameter not including the keyway).
- Calculate the shear stress and compressive stress on the key and shaft.
- (Optional) Using the technique presented by Dr. Heffernan in this video, include a simple image of the shaft and key with a transparent background. The image does not have to be to scale. The transparent background is the important part.
- (Optional) Create a Chart Component or X-Y Plot of the shear stress as function of the breadth / width of the key. (Or for more intuitive communication, plot the ratio of shear stress relative to the yield strength in shear as a function of the key . (Assume that the material fails in shear at half the nominal yield strength.)
- (Optional) Use Combo Boxes, Tables, Matrices, or other methods to turn this into a “working” worksheet, where users can select different materials, design factors, torque cycles, or other factors of your choosing.
Assumptions
- The components are made of steel (assume a yield strength of 250 MPa).
- Assume that the depth of the keyface between the key and shaft is half the height, but if you want to use the more complicated calculation involving the shaft radius and chamfer size, feel free to do so.
- For the design factor, assume a fixed / close fit keyway.
- For the application factor, assume a uniform load and a uniform power source (in other words, a factor of 1).
- For the fatigue life factor, assume 10 million unidirectional torque cycles.
As always, you should create a worksheet that stands on its own. Judging is based not just on your answers but how you communicate this information to someone picking up the worksheet for the first time. Aesthetics matter.
References
https://calculator.academy/shaft-torque-calculator/ for a shaft torque calculator
https://www.engineersedge.com/mechanics_machines/cylindrical_shaft_moment_of_inertia_13119.htm for moments of inertia
http://steeljis.com/roymech/keyways/key_strength.php (This page has everything you need for the shear stress and compressive stress, but could benefit from Mathcad’s real math notation.)
https://calcdevice.com/torsion-of-shaft-with-keyway-id211.html
https://www.engineersedge.com/calculators/shaft_keyway_shear_and_yield_strength_15867.htm
Find the Mathcad Community Challenge Guidelines here!
Dave;
Just an observation-- the sides of the keyway (that react the compressive stress) are slightly less than your calculation:
The shaft perimeter falls away as the width increases. It would be informative to plot compressive stress in the sidewall as a function of key width, Might find an optimum dimension for width/height.
Your example is a good exercise in basic engineering, but it could be a great example of why Mathcad is such a useful tool for engineering design.
The garbage variables are not necessary. If you just need one single value as return value from a combo box, simply assign it a normal variable, not a vector.
You may either see this behaviour as inconsistent (as you expected that is should be assigned a 1x1 matrix - which throws an error) or you may see it as a piece of convenience 😉
