Bearing Preload System Build and Test

Material Sourcing

This week, I built and tested a bearing preload system for my linear motion axis. As described in my post on the design for this system, the preload is provided by a compliant elastomeric layer in an oversized slider that is compressed by the side rails. Since I only need a small piece of material, I was reluctant to incur the cost of ordering some well-documented engineering elastomer. I took a walk in Blick’s instead in search of cheap materials.

I eventually found some relatively flexible carving blocks intended for making printing blocks of rubber stamps that looked like they might work. They had traditional linoleum pads as well as a softer rubber blocks marketed as being easier to carve. The latter is what I went with as my first-order analysis suggested that excessive preload for the required deformation would be a significant challenge, especially considering my relatively anemic motor.

Build

Using the dimensions calculated by my spreadsheet, I made up a new wooden slider core on the table saw and found a scrap piece of 0.25″ aluminum sheet to use as the bearing pad. On initial dry fitting, I found the slider almost impossible to force into the boxway — probably a result of the very approximate modulus value I used for the undocumented rubber compound. To compensate for this, I took the wooden portion of the slider down very slightly using a belt sander, using a guide to keep the sides square. I also gave the aluminum plate a good brush with some grey Scotchbrite to expose a fresh, smooth bearing surface.

Test

I repeated the “along axis” repeatability test I did on the original motion axis a few weeks ago to try to characterize the effect of adding preload on performance. For a description of the test procedure, see my previous post. I found that the preloaded linear motion axis repeated to within 6 mm measured 2.9 m away. This translates to a total (side to side) angular error of 0.12 degrees, which is more than 50% better than the non-preloaded design. I believe the residual error can be attributed to slight movements of the entire system resulting from motor acceleration (The linear motion axis was just placed on a table without clamping), as well as imperfect alignment relative to the wall (essentially an Abbe offset).

Actuated Linear Motion Axis

I ordered a cheap leadscrew assembly intended for low-cost 3D printers from Amazon. The leadscrew came with a brass flanged lead nut, a pair of ball bearings mounted in zinc blocks, and a flexible coupling that fits the NEMA 17 motor output shaft. The leadscrew has a diameter of 8 mm, a pitch of 2 mm, and 4 starts. This means it has an overall lead of 8 mm/rev.

A quick note about running leadscrews directly in bearing bores: conventional engineering wisdom states that it is a bad idea to run threaded rods in bearings because of small load-bearing area results in high stresses. This is still true for leadscrews, but the trapezoidal threadform retains the major diameter across the width of its lands, making it less problematic to run them in bearing bores compared to “standard” fastener threadforms which are triangular and taper to an acute angle.

Repeatability Testing

Actuated Linear Motion Axis Test from Shien Yang Lee on Vimeo.

I tested the repeatability of the actuated linear motion axis in two ways.

Repeatability along motion axis

First, I repeated the “straightness” test I carried out last week for the linear axis without the actuator.After running the carriage back and forth between its extreme positions 8 times, I got a group of laser projection points with the maximum spread of 15 mm at a distance of 2.9 m. This translates to a side-to-side angular error of 0.3°, which is a ~75% improvement from the 1.29° measured on the non-actuated axis. I think there are two factors contributing to this improvement.

First, the motor and leadscrew is able to repeat axial position better than I could by hand. This places the carriage closer to the same locations when each measurement is taken. This theory is supported by the observation that points measured at each position (X0 vs. X100) all lay within 5 mm of each other (angular uncertainty of <0.1°). This suggests that most of the error measured comes from global straightness and parallelism errors in the box way instead of local “wiggling” of the slider.

Second, the leadscrew provides a degree of preload to take up part of the radial clearance. I drilled the slider for the lead nut using a portable drill and did not make the hole perfectly square to the faces of the slider. This slight misalignment places the simply-supported leadscrew (I left it floating in the bearing on the non-driven side) under bending, causing it to act as a preload spring. However, as we learned in class, this is not a good preload configuration since the system’s stiffness varies according to the square of carriage’s distance from one end.

Repeatability orthogonal to motion axis

My second repeatability test was aimed at measuring the precision with which the actuator can move the carriage to a specified position. I attached my laser pointer to the carriage orthogonally, such that it projected a beam perpendicular to the direction of motion. For the adjustable standing desk, this is the sensitive direction.

I recorded the position of the projected beam across the 100 mm-long travel of the carriage on 10-mm intervals. The repeatability at each position was within 1 mm. Note that we are now measuring axial displacement instead of angular error, so using a laser pointer conferred no resolution advantage.

More interestingly, I observed the effects of backlash in this test. I moved the carriage to each position in the following sequence:

0 > 100 > 10 > 90 > 20 > 80 > 30 > 70 > 60 > 40 > 50

Each reversal in direction caused the distance traveled to be short by approximately 1 mm. This is consistent with the perceptible backlash in the low-quality lead nut.

Linear Motion Axis Fabrication and Testing

Fabrication

I fabricated my linear motion axis (boxway) from scrap plywood and a plywood-oriented strand board laminate scrounged from around campus. As mentioned in my previous post, I wanted to keep the slider cross-sectional dimensions to a minimum of 1″ x 1″ in order to accommodate the flange nut when I incorporate the lead screw. Unfortunately, the only sufficiently thick material I could find was the plywood-oriented strand board laminate. This forced me to use the porous and irregular surface of cut oriented strand board as bearing surfaces instead of a smoother material. To compensate for the surface asperities and higher coefficient of friction associated with this material, I increased the radial clearance from my design value of 0.005″ to 0.01″.

After cutting the component pieces to size with the table saw, I glued up the assembly using copier paper (thickness = 0.0035″) as shims to achieve the necessary clearances. For example, a 3-layer stack of paper brings me within 0.0005″ of my design clearances. A mistake I made during this step was neglecting to account for the thickness of the glue layer, this ended up causing my boxway to have excessive radial clearance, increasing error motions.

Testing

Boxway Test from Shien Yang Lee on Vimeo.

I tested the geometric error in my linear motion axis using a laser pointer. I moved the slider between extreme positions on the axis of travel, while applying slight moments to take up the angular “backlash” caused by radial clearance. The position of the projected beam on a surface 4845 mm away was recorded between each adjustment.

Boxway testing: recorded beam positions and analysis

The maximum lateral displacement of the laser beam was 109 mm, which corresponds to an angular error of 1.29°. This is the total side-to-side rotation, which we expect to be twice that predicted by our deterministic geometric error analysis utilizing radial clearances. For my boxway with 0.01″ of radial clearance, I predicted a sine error of 48.5 mm when measured 4845 mm away. The actual value is slightly higher than expected, which I attribute to the mistake I made in not accounting for thicknesses of adhesive layers as well as imperfect clamping during the glue up.

 

Update: Kinematic Coupling

This week, I got a chance to get on the CNC router in the Makerworkshop to build the three-groove coupling with magnetic preload that I had designed and mocked up with soft materials.

The fabrication process went smoothly and I was very satisfied with the product. The “snap” provided by the magnets used for preload is particularly satisfying. I often find myself toying with this coupling, and can see myself keeping this around as a conversation piece for a long time to come.

Testing

Magnetic Kinematic Coupling Test from Shien Yang Lee on Vimeo.

As before, I tested the angular repeatability of this coupling using my trusty laser pointer. One issue I ran into was the difficulty of rigidly fixturing a disc-shaped object in my apartment where I had minimal tools. I ended up attaching the bottom disc (with the grooves) to my desk using three strips of gaffer tape spaced 60° apart, taking advantage of the tape’s flexibility to place the disc under quasi-exact constraint. This is possible because the tape is virtually incapable of applying any lateral or compressive forces due to its flexibility.

Over 8 cycles, I obtained a group of points all lying within 2 mm of each other on a wall 2.9 m away. This suggests an angular error of only 0.04° — a 15-fold improvement over the melon-and-cardboard mock-up! I think at least part of this error can be attributed to the imperfect fixturing — impact loads when the balls engage the grooves may have caused the fixed disc to move slightly. The actual angular error is probably even lower!

Three-Groove Kinematic Coupling Fabrication

My original plan was to machine my coupling from plywood and glue in steel contact elements. Unfortunately, the CNC router in the Makerworkshop is down for repairs. Inspired by Prof. Slocum’s demonstration using bagels and fruits, I decided to make a version of my design using soft materials. I thought this would be sufficient to help me build intuition. I had already acquired all the materials and generated toolpaths for the original plywood and steel design, so I plan to also produce that once the machine is back up. A performance comparison between my soft materials mockup and the final version would be interesting.

Melon Coupling Fabrication

I had a perfectly ripe honeydew melon I was looking forward to eat, and decided to borrow a small part of it to build my mockup. I cut the melon into 2 circular discs and punched holes in one of them, placing each hole on a vertex of an equilateral triangle. I then “transferred punch” those holes onto the other disc using a chopstick, thereby laying out the positions of the matching vee grooves. Cutting the vee grooves was a good chance for me to practice my knife skills.

I had hoped to glue the bearing balls to the melon disc over the holes. I had even whipped up a batch of starch-based glue to try this (gelatinizing cornstarch is a popular cooking technique in Chinese cuisine!). Unfortunately, the moist surface of the melon didn’t take well to adhesives, and I had to fall back on making the top half of the coupling from cardboard, to which I glued the steel balls.

Repeatability Testing

Melon Kinematic Coupling Repeatability Test from Shien Yang Lee on Vimeo (CC-BY-SA 4.0)

I tested the cardboard-melon coupling for angular repeatability using a laser pointer projecting onto a wall 59-inches away. The maximum spread over 5 engage-disengage cycles was 5/8″. Converting this sine error to an angular error using simple trigonometry, we find that the coupling is repeatable to within 0.607°. Extremely impressive for a coupling made out of ripe (so soft!) melon and cardboard with minimal measuring. I think this demonstrates how robust the concept of exact constraint design is against fabrication and material inconsistencies.

Melon coupling repeatability test calculation

Machined Plywood + Steel Coupling

Update: See the fabrication and testing of my revised (non-melon) kinematic coupling here.

Planar Exact Constraint Toy Fabrication

I intend to make this toy out of plywood and wooden dowel pins. A combination of the Makerworkshop being closed for the week and the desire to get some peer review feedback before building the final version led me to fabricate a works-like prototype from cardboard.

Planar Exact Constraint Toy Mock-up (Photo by Shien Yang Lee, CC-BY-SA 4.0)

One potential issue that this mock-up highlighted to me was the undesirable out-of-plane tipping caused by the additional weight of the fixtured object moving the system’s center of mass forward. In this configuration, the object is essentially held on by friction against the pins, which is non-ideal. The magnitude of this effect will be smaller in the final version since the fixtured object will have a much smaller mass relative to the plywood board. I think I will be able to correct this tipping in the final version by calculating the moment contributions of the board and the fixtured object, and offsetting the screw eye attachment point backwards.