Part 1: Box Rail Modification & Error Budget Update
As per my earlier error budgeting, the dimensions of my box rail of length 1.2m, were as follows:
Backplate: Width= 6in, Thickness 2.5in
Spacer Plates: Width= 1in, Thickness= 1in
Keeper Plates: Width= 1.5in, Thickness= 0.5in
The backplate needed to be that thick in order to achieve the required stiffness for the rail, by increasing the second moment of area. This was a result of the short spacer plates that were only 1in thick. The dimension was set to 1in as I had originally planned to mount the actuator on the top surface of the slider. (See Brainware 7) Hence the width of the slider was made as small as possible (without failing), so that the centre of actuation was as close to the centre of friction as possible. One of the primary reasons for this was because I was not sure if is was feasible for me to drill a 0.5" holes through my 8.5" slider. However, after confirming this week that this would be possible, I changed my design to accommodate the leadscrew and nut passing through the middle of the slider. I did so by increasing the thickness of the slider (and thus thickness of spacer plate to 2in.
Next, I did away with the idea of preloading my slider by providing compliance with relatively thin keeper plates that act as cantilever springs. This was done to avoid catastrophic failure of the desk, should the keeper rails shear off. Instead, I opted for providing preload by cutting slits on the slider itself. This would be a much safe option, as even if the slider breaks, it would jam inside the box rail and thus prevent the table from cashing to the floor. In light of this, I made the keeper plates incredibly stiff by increasing their thicknesses to 1in and reducing their overhang lengths to 0.5in. This also provided me with 3in of spacing between the keeper plates which allowed for a wider mounting plate for the cantilever member. ( See Part 2)
I then increased the overall width of the box rail to 7in, to result in a better proportion (Saint Venant's Principle) of overall width to width of rail. In order to maintain the same aspect ratio (2:1) of the slider, I increased the width of the spacer plates to 1.5in.
Finally, I reduced the thickness of the backplate to 1in in order to make the rail less bulky. Doing so, decreased my overall stiffness. I counteracted this by modifying the load supporting functional requirement of my desk. My maximum applied external load is now 250N ( previously 300N) for the same allowable total deflection of 5mm.
Overall the results are summarized below along with updated error budget.
Backplate: Width= 7in, Thickness 1in
Spacer Plates: Width= 1.5in, Thickness= 2in
Keeper Plates: Width= 2in, Thickness= 1in
Applied max edge loading: 250N
Correction to moment of inertial calculation for box rail
Final Error Budget:
Part 2: Detailed Design- Structural Joints
Over the past week, I made calculations to ascertain design details such as the method of attachment of various structural elements and number of fasteners required for the attachments. These calculations were based on the extreme loading situation where a 100kg person stood on edge of my desk.
Peer review with Shien Yang and Jon was helpful in addressing some concerns along the way. One critical issue as Shien Yang pointed out, was the poor torsional stiffness of L brackets.
Summary of Designs and Calculations:
1. Cantilever Member Attachment to Linear Slider
As per my design and error budgeting thus far, the table top would be secured to a steel tube that would cantilever off the slider itself. In order to achieve this, my approach is to weld the steel tubing to a steel plate with mounting holes. The welded assembly would then be directly fastened to the slider.
The appropriate number and size of screws was determined through deterministic methods, as shown below.
Note: As the leadscrew passes through the centre of the block, caution was taken to locate mounting holes on either side of the central cavity.
2. Keeper Rail Safety Check
As mentioned earlier, a major concern was the effect of the keeper plate prying open. I made calculations to ascertain that this would not occur with my modified keeper rails. ( shorter overhang).
An important consideration while doing the calculations was not to consider the keeper plate as a cantilever anymore, given the small proportion of the overhang to the length of fixed support. Thus, pure shear deformations was the primary mode of failure.
Critical Assumption: The width of the shear surface was approximated to twice the length of the bearing contact pad. ( conservative Saint Venant's Principle)
Note: The spreadsheet computes bending stress but it is not applicable in this case.
3. Box Rail Attachment to Base Member
To secure the box rail to the horizontal ground member, I planned to use wood screws along the width of the backplate and the length of the sides, to ensure that the members are securely connected, despite extreme loads.
4. Table Top Attachment
Lastly, I looked at mounting the wooden table top to the square steel tubing. The table top is a 1m by 0.5m sheet of 0.75in thick plywood. I decided to see if it was possible to secure the table top to the cantilever tubing using bolts going through both members with a nut at the bottom. Originally the square tubing had a cross section of 1.25"x1.25". For this case, the stress required to strip the threads of the nut was also considered.
As seen above, the expected number of M8 bolt&nut pairs was initially 13! However, it was determined that the table top would split due to the bending stress. (Reasonable: 100kg person standing at the end of a 0.5m long cantilever of thickness 0.019m and width 0.5m, would surely split the board) Following this, the load was decreased to 700N: case where the plywood board does not snap first. For this case 9 bolts are needed.
By increasing the crossection dimension of the tubing to 2inx2in, and changing the size of the bolts to 3/8", only 4 bolts are required!
5. Table legs to Base Member
The number of screws required to secure the two legs to the base member was determined to be 3 using similar computational methods.
Finally, details of other connections such as the length of screws required to secure the slider to the lead screw nut were also determined. My compiled spreadsheet can be downloaded below.