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Closing the Design Loop
Measuring Repeatability, Stiffness and Performance of my Desk
Testing My Desk
After successfully building my desk, it was time to close the design loop by measuring repeatability and stiffness of the desk. These measurements were then compared to theoretical values calculated during the design phase. I first performed a repeatability test for the table top. My goal was to estimate the repeatability of the table at the topmost and bottom most positions. I hot glue gunned a laser pointer to the tip of the table and traversed the table up and down, between the lowest and highest positions, and recorded the position of the laser pointer on the wall. By measuring the spread in pointer position and knowing the distance between the table tip and the wall, I was able to compute the angular error in position and thus the geometric error of the table top at these two extreme operating points.
The video above covers the procedure I followed.
Laser Pointer and markings on wall
Results of Repeatability Test
The total travel of the table top was measured to be 20". This is exactly what I wanted and listed in my FRDPAARC table. From the measured spreads in vertical and horizontal direction at both the topmost and bottom most points, I was able to compute the repeatability at these respective operating points. ( Refer to spreadsheet below of measurements)
Summary of Results:
1. Angular repeatability at highest point: 0.067deg (580 microns of variation in table top position)
2. Angular repeatability at lowest point: 0.043deg (370 microns of variation in table top position)
As observed, the variations were slightly different at the two points. I expected this to be the case. During the build week, the humidity in the shop significantly increased due to the heavy rains in Cambridge. This humidity change caused the beech hardwood to expand irregularly along the structure. As a result, the inner faces of the box rail were no longer parallel and caused the slider to get suck at certain locations. To overcome this, I selectively sanded those regions (on one side of the rail) where the slider would get stuck. While this process allowed the slider to travel inside the box rail, it caused variation in the bearing clearance along the rail. Hence, the desk has different repeatability characteristics at different height locations.
How does this compare to my intended design? Originally, I apportioned 1.15mm to geometric errors for the bearing (max deflection of table top due to clearance in bearing). I designed to achieve this with an 8.5" slider with a radial clearance of 0.25mm on each side. While I did originally achieve this clearance in the construction of my rail, the sanding of the rail, caused the clearance to significantly increase.
From the measurement of deflection at the tip of my table top (extreme position along width), I was able to back calculate my clearance.
At the topmost position, the deflection at the tip was measured to be 3.4mm. This corresponds to a radial clearance of 0.73mm (Total clearance of 1.47mm) .
Learning outcome: Precision manufacturing with wood is challenging especially with hardwood in environments where humidity is subjected to change.
Next, I measured the stiffness of my desk at the topmost position, by loading the structure at the tip and measuring the deflection. I used 10lb & 20lb weights for this test.
The observed deflections for the respective weights are listed below.
How does this compare to the error budget deflection?
By substituting the 20 lb loading at the topmost position, the error budget suggests that the deflection should be 0.75mm at the tip. Thus, the theoretical stiffness for the table is 118N/mm.
Finally, I measured the "performance" of my desk which I characterise as the lifting ability of the desk. I added weights at the tip of my table top and tried to actuate the desk upwards. The tiny NEMA 17 (0.45Nm) was easily able to lift up the table top with a 10lb weight added. However when I added 20lbs of weight, the motor was unable to lift this table top.
How does this compare to expected performance?
When sizing the leadscrew, I determined that I would be able to lift up 200N using the NEMA 17 (obtained for free).
NEMA 17 specs
How does this compare to expected performance?
When sizing the leadscrew, I determined that I would be able to lift up 200N using the NEMA 17 (obtained for free). The total weight I lifted during my test = weight of steel tube + weight of table top + 10lb= 120N
In addition to the loading, the motor has to overcome frictional force of the slider against the rail. The frictional force = force on bearing * friction coefficient. This amounts to 39N. The total load lifted by the motor thus equals 159N. As this is less than 200N, the motor is able to lift it.
When a 20lb load is added, the total load to lift becomes 233N. As this is greater than 200N, the motor is unable to lift it.
All the results from my testing can be viewed in the spreadsheet that can be downloaded below. The design loop was successfully closed.
Designing and building this desk has been nothing short of extreme fulfilment. The deterministic design process has totally changed the way I approach design and engineering problems. PHYSICS WORKS. The FUNdaMENTALS was an invaluable resource to learn about precision machine design. I am confident I will continue to broaden my understanding on machine design and build on the takeaways from this class. There were times during the design of the desk where I thought I should skip the analysis and just go with my gut feeling. Especially when designing the connections of all the members. But I'm glad I decided to rely on physics and properly size each and every component in my desk. Relying on physics not only ensures reliability and repeatability, but also allows for minimal design. There is no chance of over engineering something. This has huge cost saving benefits! The designs also look much cleaner! (No hackathoning parts together to make something work). I consider this desk to be a "production ready" design and not a "proof of concept" project. This class has helped me realise how to take a concept and turn in into a robust design that is ready for commercialization. I am excited more than ever about machine/product design! I have learnt so much from this course and would like to sincerely thank Professor Slocum for the invaluable opportunity to learn under his tutelage.
Possible causes of difference in theoretical & actual stiffness:
A few reasons come to mind to explain the difference.
1. The table top is mounted on a steel tube (2.5"x2.5"x1/8"). The length of the tube is 400mm (this was the length I obtained for free) in real life while the length of the table is 500mm. Thus there is a 100mm long section of the tabletop that is not supported by the steep tube. While testing, I placed the 20lb weights over this unsupported region. As I did not model this difference in the error budget, the deflection in the error budget is for a steel tube of length 400mm. Thus, the lower stiffness of the overhanging wooden table top caused more deflection than predicted.
2. Other sources of extra deflection could be from using dissimilar woods in the construction of the base elements. I used softwood (pine) for the legs which is salvaged from a wooden crate and I joined two slabs of maple and beech resp. to make the base. The lower actual stiffnesses of these members could have decreased the stiffness of the overall structure.
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