This makes intuitive sense, and would seem to explain why low strength axles tend to bend when used over very long distances, but thinking about it in terms of pressure is not exactly the best way to go about explaining it, because the pressure on the ball need not be the same as the pressure on the axle. Furthermore, pressure is not the defining characteristic that an intake with good “compression” would need. It’s actually simply just the force on the ball that matters for that, as the normal force the intake puts on the ball is directly proportional to the frictional force that moves the ball. Spreading the force out over a larger area can help stabilize the ball by increasing the necessary torque to turn the ball; however, this is typically a quality of the intake system itself rather than the relative axle strength.
The reason low strength axles tend to bend so much is related to what you said about the distance between the supports of the axle. If you analyze the torque generated about one of the supports (which essentially will act as a pivot) you will see that a very low force can create quite a high torque on the axle because of how far away the supports are from where the force is being applied. Even then, I see a lot of people saying that low strength axles are more than strong enough for the task. In my opinion, this is not the case at all. The way the axle is going to resist bending is by creating a counter-torque to act against the one created by the force on the intake. However, the axle cannot simply generate this torque. This torque is created by the tensile strength of the steel axle. We know that steel has a very high tensile strength, but the amount of this that is turned into a counter torque is related to the sin of the angle that the axle has bent already. This means two things:
- The counter torque generated is very small. For small angles, we can approximate sin(theta) as theta, and this shows real quick that the amount of the tensile strength that is turned into a counter torque is going to be an incredibly small fraction of the tensile stress the axle is under.
- The second thing we can observe from the fact that the torque is proportional to the sin of the angle created is that when there is no bend in the axle (theta=0), there is quite literally no restoring torque created. This means that the axle must bend a little to balance the torque on it.
TLDR:
The physics of having widely spaced supports on a low strength axle is not at all in favor of low strength axles being strong enough to resist bending noticeably. You’re much better off using high strength axles that can create a high restoring torque even with low angle displacement.