Closing the Loop: Stiffness Test

Adjustable Standing Desk: Static Stiffness Test 1 (Bottom of travel) from Shien Yang Lee on Vimeo.

Adjustable Standing Desk: Static Stiffness Test 2 (Top of travel) from Shien Yang Lee on Vimeo.

The first test I did to close the loop on my design process is a static load test to determine the stiffness of my desk. I took differential measurements at the very edge of my desktop with a dial indicator while adding and removing dead weights (10 lbs. nominal). In addition to the two large weights you see me placing and removing in the videos, there is also a small 2.5-lb. plate that I kept on the edge of the desk throughout the test (out of shot). This is intended as a small preload to take up any geometric errors (i.e. slop) and give me a good structural stiffness reading.

I carried out two stiffness tests with the desktop at the two extremes of its travel. The results of my stiffness tests are summarized in this spreadsheet. In summary, my error budget overestimated the stiffness at both positions (by 57% at the bottom of the travel and 34% at the top of the travel). I think there are a number of reasons for this:

  • My coarse estimates for contact stiffnesses (both linear and rotational) at bearings and joints were significantly overoptimistic. One issue with designing structures in wood is that these numbers are not well-documented in the literature. The anisotropicity of wood also makes it much more complicated to calculate these values analytically. In future, I am likely to resort to quick first-order FE simulations to get better estimates for these contact stiffnesses early in the design process.
  • The aggregate material properties I used are likely to have significant uncertainty due to natural variation in biological materials. But I think this is a minor contributor to error in this instance because the clear beech I used is probably quite uniform.
  • In my error budget, I treated most members as pure Euler beams for simplicity. In hindsight, this probably contributed significantly to the prediction error for deflections due to flexing of my boxways/columns, since they have such heavy cross-sections. The fact that there is a much bigger deviation from predictions when the desktop is at the bottom of its range of motion (57% vs. 34%) supports this hypothesis — shear deformations become more influential as the beam spans shorten.

Despite the significant deviation from predicted stiffness values, going through the error budgeting process and using first-order analytical models in the design process has put me in the ballpark of where I need to be. Had I relied on “intuition” or the famed “hackathon approach” to size components, I would have made a few members significantly smaller… Even considering possible modelling errors, deterministic models are invaluable in quickly getting into the neighborhood of the optimal solution.

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