Thermal Modeling

2011 July 21
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Special thanks to Waleed Rahhal, Chief Technologist (and Owner) of Fiber Concepts. Waleed is an applied mathematician who analyzes all sorts of components under stress and thermal changes for high tech companies and the aerospace industry. He is also married to my wife’s cousin! Waleed was kind enough to undertake analysis on the roaster bowl. The following work is entirely his.

I’ve been wanting to know how the roaster bowl will expand in size when heated. This knowledge is extremely important to make sure that the fixed components and the rotating components maintain a proper gap throughout the entire temperature range. If we make the gap too small at room temperature, the bowl could rub or even seize at high temperatures. However, we want the smallest gap possible to prevent coffee beans (or coffee bean fragments) from entering the gap.

Waleed first did a hand calculation to determine how the bowl would expand. He used the geometry of the bowl and the material characteristics (for 455 steel), along with the temperature range to do the calculation.

The results show that the radius of the bowl will grow by 0.048″ in going from 70°F to 500°F and that the height of the bowl will increase by 0.024″. Waleed then used finite element analysis to confirm his results and give a better graphical presentation of expansion.

Waleed also added the effects of 35lbs. of green coffee to the model. The results were identical to the hand calculation radially (0.048″).

The finite element model’s results were identical vertically at 0.024″. Waleed also modeled various kinds of stresses in the bowl as it is heated and spins.

This is a graphical representation of the radial stresses on the bowl spinning at 100RPM at full load and at 500°F. We are still reviewing the various stresses in the bowl, but it appears that none of them represent a serious problem.

The modeling of thermal expansion has given us excellent data. We can now use this information to begin designing the fixed components for the roaster.

 

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One Response
  1. July 21, 2011

    Holy cow… this whole process is really making me wish I liked coffee! This is seriously one of the most interesting and informative blogs I read, and I read a lot of blogs. Thank you so much for sharing this process with us in such a fun way.

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