Design
For my rotational motion module, I decided to make a spindle. Find links to my full write-up and results, part drawings, my solid model and the equations / code used for my predictons here:
My spindle design is shown in Figure 1 - a cross sectional view of the spindle is shown to highlight how the bearings were arranged in their housings.
- Full write-up with results
- Part drawings
- Solid model
- Bill of materials (BOM)
- Design spreadsheet for predictions
My spindle design is shown in Figure 1 - a cross sectional view of the spindle is shown to highlight how the bearings were arranged in their housings.
The important design features in my spindle are:
Fixed end supports radial and angular loads:
Floating end supports radial loads:
Overall:
Fixed end supports radial and angular loads:
- Two deep groove bearings (back to back alignment)
- Sliding fit between shaft and inner race
- Interference fit between housing and outer race (radial preload)
- Lock nut (with diameter small enough such that it only axially preloads the inner race) to axially preload the bearing against the wider part of the shaft
- Wave washer for knowledge of preload
- Shim with inner diameter larger than that of the inner race and outer diameter approximately the same as the outer races such that it separates the outer races when a preload is applied
Floating end supports radial loads:
- One deep groove bearing
- Sliding fit between shaft and inner race
- Interference fit between housing and outer race (radial preload)
Overall:
- Bearing sets are spaced at least three times of the thickness of the bearing (St. Venant)
Manufacturing
Figure 2 shows the final model of the spindle that I built. I initially waterjet the housings and then used a reamer to make the holes in the housing an interference fit with the bearing. Having evaluated the tolerances of the reamers,, it seemed that the 1.125” reamer would be too large to provide the recommended 0.002” of interference required for an effective interference fit for the bearing. I therefore decided to use a 28.5 mm metric reamer: this gave me an interference fit of between 0.001” and 0.003” depending on what side of the tolerance bounds the reamer fell.
I found Koyo deep groove open ball bearings in the machine shop: care was taken to ensure that no dirt got inside them and high pressure air was used to clean them before they were fit into the housings. I used a shim between the two bearings on the outer race and a wave washer and lock nut to preload the inner races.
I used a lathe to turn down the ends of the aluminium rod I had found and neck it right before the end of the external thread, which I put in using a die. The diameter of the rod was turned down to 0.498” because this would provide an appropriate sliding fit between the inner race and the rod.
The L-bracket mounts on the bearing were machined on the mill and then cut to size with a bandsaw. An end mill was used to clear out a large hole to ensure there was no unnecessary friction on the face of the bearing as it turned and holes to mount the housings to the L-bracket and the L-bracket to the optical bench were drilled with a program on the mill.
I found Koyo deep groove open ball bearings in the machine shop: care was taken to ensure that no dirt got inside them and high pressure air was used to clean them before they were fit into the housings. I used a shim between the two bearings on the outer race and a wave washer and lock nut to preload the inner races.
I used a lathe to turn down the ends of the aluminium rod I had found and neck it right before the end of the external thread, which I put in using a die. The diameter of the rod was turned down to 0.498” because this would provide an appropriate sliding fit between the inner race and the rod.
The L-bracket mounts on the bearing were machined on the mill and then cut to size with a bandsaw. An end mill was used to clear out a large hole to ensure there was no unnecessary friction on the face of the bearing as it turned and holes to mount the housings to the L-bracket and the L-bracket to the optical bench were drilled with a program on the mill.
Testing
For testing a dial indicator was used to evaluate the deflection of the shaft and a spring scale was used to apply a force for stiffness analysis.
To measure radial total indicator runout, I set the dial indicator up at various positions along the shaft and recorded the maximum dial indicator reading achieved when the shaft was rotated. At the position of maximum runout, I spun the shaft several times and recorded the dial indicator reading at various intervals. To measure radial repeatability, I marked the shaft and rotated it back to that spot many times and recorded the dial indicator reading each time. To measure the axial accuracy and repeatability, I carried out the same procedure as for the radial parameters but moved the dial indicator to the end of the shaft such that the pointer was located at the center of the circular face and parallel with the shaft.
The radial stiffness was measured by applying a force at the center of stiffness of the shaft and the deflection was measured at that point with a dial indicator. The angular stiffness was measured by attaching a small keychain laser pointer aligned with the center of the spindle to the end of the shaft with adhesive and applying a force to the shaft and observing any movement in the laser point on a sheet of paper 8 meters away.
The test setups are shown in Figure 3.
To measure radial total indicator runout, I set the dial indicator up at various positions along the shaft and recorded the maximum dial indicator reading achieved when the shaft was rotated. At the position of maximum runout, I spun the shaft several times and recorded the dial indicator reading at various intervals. To measure radial repeatability, I marked the shaft and rotated it back to that spot many times and recorded the dial indicator reading each time. To measure the axial accuracy and repeatability, I carried out the same procedure as for the radial parameters but moved the dial indicator to the end of the shaft such that the pointer was located at the center of the circular face and parallel with the shaft.
The radial stiffness was measured by applying a force at the center of stiffness of the shaft and the deflection was measured at that point with a dial indicator. The angular stiffness was measured by attaching a small keychain laser pointer aligned with the center of the spindle to the end of the shaft with adhesive and applying a force to the shaft and observing any movement in the laser point on a sheet of paper 8 meters away.
The test setups are shown in Figure 3.

Figure 3: Test setups for analyzing rotational motion module. (a) The dial indicator setup for measuring total radial indicator runout and radial repeatability. (b) The dial indicator setup for measuring axial accuracy and repeatability. (c) The setup of the dial indicator and the spring scale for measuring stiffness.
Results and Analysis
Table 1 gives a breakdown of the measured results from testing and the predictions I made using the analysis and equations in my design spreadsheet. An appendix for the actual testing results can be found at the end of my full write-up document.
Conclusions
For the stiffnesses of my model, my predictions held up pretty well in testing. My predictions for stiffness were likely very good on account of the stiff ball bearings that I used and the known properties of the shaft. The accuracy and repeatability tests showed that in real life my spindle was much better than my predictions, likely because I used conservative estimates, assuming that all dimensions fell at the worst end of the tolerance range. Overall, I am happy with my module - it feels smooth and the predictions matched up in a way that was easy to explain.