chip updates: some chassis calculations [updates]
Yes, so we've already built the robot but since I've started working on documentation it's probably a good idea to run some basic calculations to verify the sanity that this frame isn't in ridiculous amounts of danger of yielding and things like that. So we set up a Fusion simulation.
"This paragraph is essentially a justification of why little to no math was done on the frame components. When we were initially building chip, being a project for fun, we didn't have much of a choice in design/build materials and etc. We had a few bars and motors and they got put together to create the frame. We likely should have completed more calculations to determine if the frame design would be sufficient before building it, but after testing the frame has held up to all the situations chip has been put through so we are confident the frame works for the Operational Design Domain of chip. We will produce extensive calculations for the next version, and for the legs and later parts of the design. (we're sorry!)
It is worth nothing, however, the maximum force any individual leg can carry is 250N (if we estimate platform weight as 500N) and that generates a max torque (as we will see in the leg design) of < 50N in both in the direction of motor torque, and in the plane perpendicular to the motor torque. The magnitudes of these forces and torques are not worrying for a 6061-T6 aluminum frame like the one constructed.
We did do some testing on one of the Double-H frames to see if they could width-stand the bending force individually. We applied 250N loads directly vertically to diagonal motor mounts and fixed the two other motor mounts. We defined a bonded contact set between all the individual pieces and ran the simulation. The results are shown in the diagram to the right. We understand a bonded contact set is unreasonable considering the discussion we're about to have on system flex, but we are including this as the loads this frame is seeing are higher than they will ever be on the frame because of the high load estimate of the static simulation. The frame should never see these kinds of loads under our operation conditions as we're assuming all the vertical force of one leg is being supported by only half of the frame and none of the gearboxes. In addition is the fact that we've fixed the un-loaded corners which is completely unreasonable. But if the frame can survive this loading, it can survive the loading we are putting it under.
As to the numbers we are seeing in the results themselves. We used 6061-T6 cold-formed as opposed to hot-formed because Vex Pro does not specify which of the two they used in their manufacturing and cold-formed has a lower Young's Modulus that hot-formed 6061 according to Fusion 360's database. The minimum safety factor we are seeing in image four is 1.49 which is not idea but is still larger than 1.0 meaning even under impossible conditions the frame will not yield. The deflection map looks concerning with almost 1cm of deflection under these loads, but again, the simulation isn't remotely accurate to the real life loading of this frame.
Finally, in this section, we want to talk about system flex. There are possible locations for flex in this system that we think will not be of concern, again, due to the loads the system actually experiences. The locations identified as at risk for flexing are the attachment between the Double-H frames and the motors, and the attachments between the bars of the Double-H frames. These locations are places where flex could occur. Because of the loads in play, the flex should not be large enough to cause yielding or fatigue in the material. But further physical testing will help us solidify this estimate.
It is important to make the point that while limited mechanical calculations have been done on the chassis, at no point has testing of the platform under any conditions revealed any cases of concern around the frame area itself. There have been other causes for concern we will point out later. "