Design
In the Space Systems Lab (SSL) we are developing an Optics testbed, on which we are spinning a masked image and developing image processing techniques to verify whether a rotating strip mirror telescope can achieve the same resolution as a circular telescope. The testing requires that we mount an image onto a motor on the testbed, which must be accurately aligned with two telescopes. I think a 2D Elastically Averaged Coupling (EAC) would be a great way to achieve this. The high stiffness will reduce the chances of “flapping” during image rotation and the good repeatability will ensure the alignment of the image. I chose the 2D coupling with slots design because: it is the lightest design to attach to the motor; it requires no redesign of the motor hub; it is 2D so reduces the cantilever over the motor shaft and it is quick and easy to manufacture, which will be good for making multiple for varying test images.
Find links to my full write-up and results, part drawings, my solid model and the equations / code used for my predictons here:
The design is shown in Figure 1.
Find links to my full write-up and results, part drawings, my solid model and the equations / code used for my predictons here:
The design is shown in Figure 1.
Figure 1: CAD model of Elastically Averaged coupling, drawn in SolidWorks.
Manufacturing
I manufactured both pieces of my Elastically Averaged Coupling (the top piece with the slots and the bottom piece to hold the dowel pins) by cut from acrylic using a laser cutter. I press fit the dowel pins into my acrylic so that I could ensure that they were mounted very close to vertical. I also cut the laser mounts from acrylic with the laser cutter. The parts and final assembly are shown in Figure 2.
Figure 2: (a) Laser cut slot part with laser holder mounted in countersunk holes and with T-slots. (b) Dowel pin holder having been laser cut and having snugly fit the dowel pins with a hand drill to ream out the undersized hole. (c) Full assembly of the EAC module.
Testing
I confirmed my performance predictions via testing. I mounted a laser pen on top of my coupling with two laser cut parts with V-grooves. I measured the stiffness by mounting the base part of my Elastically Averaged Coupling to an optical bench using ¼”-20 screws. I used the tab on the end of the slot part of the EAC to apply a moment. I then measured the deflection of the laser beam on the wall 7.5 meters away to calculate stiffness. I was also able to break my coupling at one point from applying too much load (approximately 100 Newtons). This was the torsional limit of the coupling because the thinnest pieces of acrylic in between the slots snapped. I measured the accuracy of the coupling on the mill using an edge finder and a center finder to measure the position of a slot / hole cut into the top part of the EAC. The test setups I used is shown in Figure 3. I also tried to measure the x, y and z repeatability using a dial indicator; however, the deflections were smaller than the resolution of the instrument, so I was unsuccessful in obtaining any results for this.
Figure 3: (a) The test setup used to apply a load to the EAC and measure the deflection of the laser beam to calculate the stiffness of the coupling. (b) Accuracy was found with an edge finder and a center finder on the mill with the slot and hole cut into the parts.
Results and Analysis
Along with the predictions I made using my design / equations code, I also ran an Finite Element Analysis (FEA), shown in Figure 4, to validate my calculations. SolidWorks predicted that the angular stiffness of my EAC was 5992 Nm/rad. Since this is pretty close to my predicted value of 5920 Nm/rad, I assumed that my calculations were correct.
Figure 4: Finite Element Analysis was carried out on the slot part of the EAC to verify if the predicted stiffness results made sense.
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 is attached at the end of my full write-up document.
Table 1: Summary of predictions and testing results and how they compare for my Elastically Averaged Coupling.
Conclusions
My Elastically Averaged Coupling performed on the order of magnitude that I expected in terms of accuracy and stiffness; however, overall it was a little worse than I had predicted. This was likely due to wear in the coupling that had occurred while I was playing with it before testing. The values for the radial / vertical repeatability could not be measured with the available equipment because the results were smaller than the resolution of the measuring device. As future work, it would be possible to measure the radial stiffness of the module with a dial indicator and a spring scale.