Part 1: Machine Updates
Concept 1: Single Rail L Desk
Over the past week, I decided to delve deeper into the "L Desk" concept. I decided not to pursue the scissor linkage design over concerns of safety.
Using my design spreadsheet, I was able to evaluate the stiffness of the design and size several crucial component such as bearing and structural members. This was extremely valuable in validating whether the design would meet stiffness requirements assigned in week 4 while avoiding resonant frequencies that are detrimental to humans.
Below are the expressions derived for making first order estimations of stiffness of the design. From suggestion during the peer review session, I corrected the angular deflection for the member under torsion (member 3). I was reminded that the expression I derived was for a beam fixed at one end, but in reality, the member is fixed at both ends. Hence, I made the correction by halving the length of the beam. I later realized that I would need to half the moment applied to member 4 as there are two units of member 4 that would divide the external moment between them.
With these corrections, I updated my previous design spreadsheet to predict the stiffness of the structure. From previous analysis, I knew that the table top would need to mounted on a tapered member, in order to miminize deflection. Hence, the new spreadsheet assumes the member to be tapered. For the deflection calculation of this member, I incorporated Professor Slocum's Beam_Tapered_Thickness spreadsheet into mine. I assigned t_b to be the length of the slider which was determined from error apportionment.
The results from the spreadsheet are as follows:
As evident, I was unable to lower my Total Vertical Displacement to the desired value, without using unreasonable geometries for the members. The largest contributor to the displacement was the torsional member (member 3). The angular displacement due to torsion is given by
The polar moment of area was calculated for a circular cross-section. Given the small value of shear modulus for Birch plywood (620MPa), the deflection was fairly large even for a member diameter of 6 inches. At this point, it only made sense to switch the material of this member to something stronger, such as Aluminum.
I switched to Aluminum for members 3 and 4 and optimized geometries to achieve the desired stiffness.
Thus, I was able to achieve the required stiffness while avoiding sensitive frequencies!!
Summary of dimensions and materials of members:
Member 2 (Rail): Birch Plywood, 6in x 6in cross-section
Member 3 (Torsional member): Aluminum, 0.7m long, 4in x 2in cross section
Member 4 (Legs): Aluminum, 0.5m long, 3in x 2in cross section
My Spreadsheet can be downloaded by clicking on the icon below.
Ergonomics & Manufacturing:
The dimensions of the desk were determined with ergonomic considerations in mind. The width of the desk is 1m while the length is 0.5m. I measured the desired heights of the table top for use while sitting and standing to be 0.76m and 1.2m respectively. While this range is customised to my physique, I am sure it will be comfortable for use by a wide range of people.
Manufacturing the box rail and the slider will be the most challenging aspect of the desk, given the relative precision needed for these components. The rest of the structure is fairly simple in terms of geometry. Careful consideration will need to be placed while determining joining methods for the various structural members. Using fasteners like bolts and nuts might be best since disassembly is needed before I can ship the desk back home to Singapore. With combinations of wood and metal elements, the stiffness of the joints will be tricky to compute.
Part 2: Bearing Backlash Reduction
To reduce backlash in the slider, we can preload the slider-rail system. For my design, I decided to add the preload springs to the slider as opposed to the rail, as shown in the picture below.
Buna-N is the choice for the soft spring while a hard/slippery plastic will be used as the stiff spring. Given that the surface irregularity along the inner surface of the rail can be upto 0.1mm, the preload deflection of the Buna-N spring will be around 1mm. This is to ensure that the sudden change in spring expansion/compression does not cause significant vibrations. (from higher change in energy of spring system)
The thickness of the stiff plastic will be 1mm while the Buna-N layer will be 2mm thick.
Part 3: Seek & Geek
For this week's Seek & Geek, I inspected this salt dispensing wheel barrow.
As evident in the video, the axle connecting the two wheels is used to drive a turbine-like dispenser that scatters salt, tangential to the direction of rotation. A lever at the handle, allows the operator to open and close an opening at the bottom of the salt bucket. When opened, the salt is dispersed in all direction, as the operator walks the wheelbarrow. A transmission system (shown below), converts the axle's rotation, to rotation about an axis that is perpendicualr to the axle.
I then speculated on the type of gears used in the transmission. Given the geometry of the housing, my first guess would be a pair of bevel gears, with the larger gear mounted to the axle.
I then estimated the gear ratio by comparing the number of revolutions of the dispenser to the number of rotations of the wheel. I noted that for every full rotation of the wheel, the dispenser makes 4 full revolutions. Hence the system is geared down 4:1.
Given that the average human walks at average speed of 5km/hr or 1.4m/s and that the wheels were approximately 10 inches in diameter, the average angular velocity of the axle is approximately 10rad/s. From the gearing, the angular velocity of the dispenser is thus 40rad/s. If the length of the blade on the dispenser is about 3 inches (75mm), the average exit velocity of a globule of salt is 3m/s! This can scatter the salt grains over a wide area!