Ball bearing cantilever system with maximal moment of inertia

[AlphaJP7]

TL;DR Summary

Trying to design a cantilever system with a bearing that's bottom heavy but has maximum moment of inertia (able to resist acceleration on the horizontal axis) to apply to the center caps of my car in order to keep the badge straight.

Hello fellow members! First and foremost I'll start by saying I couldn't be farther from a Physics connoisseur, I barely remember high school Physics/Maths. I love to know about mechanical systems and I'm an avid DIYer though.

I'm trying to design a floating center cap system for my car's wheels. I need a weight that doesn't swing on the perpendicular axis to that of rotation (front to back and vice versa) so that the shaft (cantilever, since it can only be supported on one end is the more appropriate term I think? I'm not a native speaker) always stays in the same position despite the fact that the structure around it is on a rotating axis (the wheel of my car). There's no external fixation points that aren't rotating.

As you can see here this kind of swing is exactly what I'm trying to avoid. And most systems I see are prone to it as demonstrated by this image of what it looks like.

I think I found a solution in the form of a pendulum that's secured by 2 tension wires opposite from eachother on the same axis that the shaft rotates. Something like this. It might need another bearing around the rod though, or making the weight as heavy as possible and distancing it as far from rod/cantilever as I can to increase moment of inertia, can't quite visualize it yet, would need to build it.

The final idea I have to maximize moment of inertia whyle still being bottom heavy would be something like this I guess since, from what I've gathered, a hollow cylinder (zero thick thorus ideally) is one of the 3D shapes with the most moment of inertia. Maybe even encasing the whole thing in a viscous liquid like glycerine, the sky is the limit!

Any of you have a better/easier to implement idea? As a reddit commenter stated very accurately when I exposed the problem there is that "I'm trying to find a 500$ solution to a 5$ problem" which is true, so I thought here I'd find like-minded people when it comes to solving issues like these.

Cheers and thanks for reading!

 

[onatirec]

what would these tension wires attach to that doesn't spin? I guess you have the brake caliper on one side that you could affix it to, or the metal shroud that often surrounds it. But how would you attach it while you're mounting the wheel on?

 

[AlphaJP7]

what would these tension wires attach to that doesn't spin? I guess you have the brake caliper on one side that you could affix it to, or the metal shroud that often surrounds it. But how would you attach it while you're mounting the wheel on?

Yeah, in retrospect I don't think that idea would work because, once again, I have nothing that I can fixate to that doesn't rotate. In the scheme I drew the tension wires would attach to that black plate and that rotates just the same as the shaft due to inertia. I could use a ball bearing so as to isolate it and then use a tension wire to connect the weight to the shaft. Something like this (P.S. forgot to add the bearing inside the black bar on the sideview but he's in there xD) but I'm sure that would require some fine tuning of the center of mass of the complex object formed by the weight+bar+outer ring of the bearing.

Other than that I guess the best design I got is the cylinder then.

 

[Baluncore]

This problem always reduces to what happens when there is a failure?
Does it turn with that wheel, or does it undo the nut that holds the hub on the stub axle? Such displays are prohibited here, because of the problems involved, and the distraction to other drivers.

You need to minimise the friction of the support bearing. That requires a small diameter bearing or a single pin. Any magnetic bearing would have magnetic drag effects, and collect bits of magnetic dirt from the road environment.

Windage between the wheel and the hubcap, will tend to drag the cap with the wheel, in proportion to the square of the speed. Any pendulous weight will obey a cosine law, where it will not really settle in a stable downwards direction. The resultant sum of torques, will tend to make a gauge that will display a more stable angle ~ speed relationship while moving, but that swings when you stop.

Other possible solutions.
You might be able to project a static image, onto the cap, from the body above.

If the cap was a display, like an LED or a screen that rotates with the wheel? The picture could rotate backwards on the screen, so remain upright. Imagine a goldfish swimming in the cap, followed by a cat, or a gnome winding a handle to drive that wheel, or running on the tire, pushing on the axle.

If you had a black cap, with a line of three-colour LEDs, you could synthesise any image on the rotating wheel. That would distract other drivers, who glanced momentarily, and would see a strobe effect.

 

[AlphaJP7]

This problem always reduces to what happens when there is a failure?
Does it turn with that wheel, or does it undo the nut that holds the hub on the stub axle? Such displays are prohibited here, because of the problems involved, and the distraction to other drivers.

You need to minimise the friction of the support bearing. That requires a small diameter bearing or a single pin. Any magnetic bearing would have magnetic drag effects, and collect bits of magnetic dirt from the road environment.

Windage between the wheel and the hubcap, will tend to drag the cap with the wheel, in proportion to the square of the speed. Any pendulous weight will obey a cosine law, where it will not really settle in a stable downwards direction. The resultant sum of torques, will tend to make a gauge that will display a more stable angle ~ speed relationship while moving, but that swings when you stop.

Other possible solutions.
You might be able to project a static image, onto the cap, from the body above.

If the cap was a display, like an LED or a screen that rotates with the wheel? The picture could rotate backwards on the screen, so remain upright. Imagine a goldfish swimming in the cap, followed by a cat, or a gnome winding a handle to drive that wheel, or running on the tire, pushing on the axle.

If you had a black cap, with a line of three-colour LEDs, you could synthesise any image on the rotating wheel. That would distract other drivers, who glanced momentarily, and would see a strobe effect.

Do you mean distracting other drivers as in they will be looking at my center caps? That's like blaming the girl wearing the skirt for being harrassed. THEY should be focused on the road. If that's not what you meant and the problem really is the steady badges then we really need to find a way to get the symbols upfront and back rotating, cause that's clearly THE major motor vehicle accident determinant everyone's been missing. We cracked the code!

If it has the power to undo the stub axle nut by sorcery, since I'm specifically making a system that is not connected to it by anything then I'll make sure to get an exorcist to make the bad spirits settle.

I'll also be sure to run a FMEA to make sure my rear axle won't blow off because of the 2 center caps on each end. Good heavens, they might even spontaneously combust in an underground garage that's filled to the brim with LPG cars with leaky tanks. You've saved many lives here.

Thanks for the constructive comment and critics though, my physics knowledge improved immensely and solutions are aplenty. I really like the gnome idea. How tall are you? If you're looking for a part-time job you won't believe the slot that just opened.

 

[Baluncore]

THEY should be focused on the road.

Accidents also happen because male drivers look at female joggers, and female drivers look at male cyclists, but mostly at other women, who they see as a threat. Any distraction is an accident waiting to happen, we try to control those that we can, by keeping things standard.

If it has the power to undo the stub axle nut by sorcery, since I'm specifically making a system that is not connected to it by anything then I'll make sure to get an exorcist to make the bad spirits settle.

I am covering the obvious solution for the case of there being a stub axle, because it has been tried several times, and will always fail.

 

[AlphaJP7]

Accidents also happen because male drivers look at female joggers, and female drivers look at male cyclists, but mostly at other women, who they see as a threat. Any distraction is an accident waiting to happen, we try to control those that we can, by keeping things standard.


I am covering the obvious solution for the case of there being a stub axle, because it has been tried several times, and will always fail.

Alright, at least now you give me a serious answer. You shall reap what you sow. Thusly, I will say that I do see your point but I don't consider it a meaningful offense to road safety. Not anymore than the joggers and we aren't telling pretty ladies not to go for a stroll all for the benefit of road safety. So the "minimize distractions" has to have a healthy dose of common sense applied to it so as not to degenerate to lanes encased by concrete on all sides. You're incurring risk just by stepping outside your house, being agoraphobic stranded at home doesn't seem a healthy logical following.

Regarding the stub axle, I can assure you my first thought was "I'm not messing with that". Either way my E46 has a cover over it as you can see on the right (with more detail here). So that oughta protect it a little. Still not messing with it.
It's been tried before many times? I'm curious as how you got that metric, didn't think many people were doing this kind of mod anyway.

I'm looking into gimbal systems now as a possible solution. Not sure if a weight on bearings still effectively straightens the shaft though. Adressing your first comment once more, I do have lots of tiny NSK bearings and they shall play a part in the solution. Was partially joking about the FMEA part too, I'm not implementing anything before trialing a lot, worst cause scenarios, etc...

 

[Baluncore]

Thusly, I will say that I do see your point but I don't consider it a meaningful offense to road safety.

You are free to have your opinion, but I have no choice, the regulations prohibit fixed signage on hubcaps. Every little bit of free safety counts. It is an unnecessary cost and complication, with negative downsides. Any modification from standard, brings with it the liability for a litigious attack by someone who feels they were distracted by your modification. Right or wrong, that is a cost to the user. Where is the common sense in that choice?

It's been tried before many times? I'm curious as how you got that metric, didn't think many people were doing this kind of mod anyway.

One taxi company thought it was a clever idea, so covered its fleet with hub advertisements. It was clever, but not intelligent. I am old enough to have seen it tried twice in my state, and then it became a prohibited vehicle modification.
There was then a fad for aftermarket, freewheeling, ballasted hubcaps, just a few years ago, they were all gone within about 3 months. Maybe you still have them, as a kitsch modification.

 

[AlphaJP7]

You are free to have your opinion, but I have no choice, the regulations prohibit fixed signage on hubcaps. Every little bit of free safety counts. It is an unnecessary cost and complication, with negative downsides. Any modification from standard, brings with it the liability for a litigious attack by someone who feels they were distracted by your modification. Right or wrong, that is a cost to the user. Where is the common sense in that choice?


One taxi company thought it was a clever idea, so covered its fleet with hub advertisements. It was clever, but not intelligent. I am old enough to have seen it tried twice in my state, and then it became a prohibited vehicle modification.
There was then a fad for aftermarket, freewheeling, ballasted hubcaps, just a few years ago, they were all gone within about 3 months. Maybe you still have them, as a kitsch modification.

Which regulations, if you mind? Litigious attack? This sounds very American, no offense because I deeply respect the country. Here in Europe there are no such regulations if you mean in the legal sense. And even then, these things don't end up in court. Or else BMW and Rolls Royce wouldn't sell their own kit. I'm just trying to slightly improve on the idea since the original one's don't fight my older model and I have to make'em myself.
Thanks for the history lesson with the taxi thing though, very interesting and it clearly shows why that implementation was awful.

P.S.: Found the solution through a patent of all things. The Rolls Royce system is far superior to the one implemented on BMWs (they're owned by the same group but that price gap gotta be justified ain't it!)

 

[jack action]

I'm trying to design a floating center cap system for my car's wheels. I need a weight that doesn't swing on the perpendicular axis to that of rotation

Or else BMW and Rolls Royce wouldn't sell their own kit. I'm just trying to slightly improve on the idea [...]

[...]

P.S.: Found the solution through a patent of all things. The Rolls Royce system is far superior to the one implemented on BMWs

So you want to improve the design that engineers of the most high-end companies have worked on?

The only possibility is pretty much connecting it to the axle somehow:

​

The only drawback is that you have to make a hole in your hub dust cover, which I don't find very smart. One should consider making a seal for this hole.

 

[AlphaJP7]

So you want to improve the design that engineers of the most high-end companies have worked on?

The only possibility is pretty much connecting it to the axle somehow:

​

The only drawback is that you have to make a hole in your hub dust cover, which I don't find very smart. One should consider making a seal for this hole.

Yeah, connecting it to the axle is out of question, I think I've got enough tools now to design a decent system. A shame I can't find any diagram for the Rolls Royce caps in particular. This is the one I'll end up going for.

P.S.: Quite the preposterous proposition that I could improve on them, that was for sure not well put. I meant that, for example, the BMW design is inferior to the Rolls one and I don't believe it's a matter of lack of expertise on the engineering team from the former. So improving meant "aproximate it more to the higher end".

 

[Tom.G]

A shame I can't find any diagram for the Rolls Royce caps in particular.

Get a copy of the patent from the Patent Office -- at least here in the States, the patent office has most patents available on-line for free download.

[EDIT] Google has a Patent page for US patents; but I find it difficult to use [/EDIT]

Cheers,
Tom

 

[Baluncore]

I do not think the badge needs to remain upright while travelling, but it needs to right itself when the vehicle stops. That would allow a weighted badge to be used, neutrally buoyant, in a sealed capsule. The capsule would have a clear window on the outside, with an opaque background. If the fluid was silicone oil, the badge would rotate while travelling, then quickly settle upright when stopped. There would be no need for a seal or bearings, just a central locator pin behind the badge, to keep the badge away from resting on the peripheral wall.

 

[AlphaJP7]

Get a copy of the patent from the Patent Office -- at least here in the States, the patent office has most patents available on-line for free download.

[EDIT] Google has a Patent page for US patents; but I find it difficult to use [/EDIT]

Cheers,
Tom

Thanks for the input! I've tried searching for Rolls Royce patents for the center cap system unsuccessfully. Maybe they haven't patented it. I've gotten a pretty good gyst of how it works though.

 

[AlphaJP7]

I do not think the badge needs to remain upright while travelling, but it needs to right itself when the vehicle stops. That would allow a weighted badge to be used, neutrally buoyant, in a sealed capsule. The capsule would have a clear window on the outside, with an opaque background. If the fluid was silicone oil, the badge would rotate while travelling, then quickly settle upright when stopped. There would be no need for a seal or bearings, just a central locator pin behind the badge, to keep the badge away from resting on the peripheral wall.

That's actually a very cool idea. I was messing around with the idea of using a high cps liquid (in this case glycerine) in some way. Just an hypothetical question, how do these kind of fluids react to passing through a thin-holed wire mesh. I would imagine there would be some resistance, isn't that how some shock absorbers work?

 

[Baluncore]

You need to ask a less hypothetical, more specific question.

I was considering something like one half of a borosilicate glass Petri dish, backed by a 3D printed insert, that locks in as the hubcap. UV and chemical stability are important.

An air bubble, that hides behind the outer ring, should allow for thermal expansion of the fluid. Any fluid will limit freewheeling of the badge. Silicone oil is clear and comes in different grades. Glycerine is thicker than needed and may change chemically over time.

 

[AlphaJP7]

You need to ask a less hypothetical, more specific question.

I was considering something like one half of a borosilicate glass Petri dish, backed by a 3D printed insert, that locks in as the hubcap. UV and chemical stability are important.

An air bubble, that hides behind the outer ring, should allow for thermal expansion of the fluid. Any fluid will limit freewheeling of the badge. Silicone oil is clear and comes in different grades. Glycerine is thicker than needed and may change chemically over time.

Alright, I thought glycerine was fairly stable, but indeed there are many flavours of silicon oil with different viscosity and it's just a matter of experimenting. I have no "hands-on" feel for the viscosity required to prevent freewheeling.

I was asking because I'm aso conceptualizing a design like this, and since disc bidirectional rotary dampers are fairly expensive I wondered if putting a mesh somewhere in the liquid would act the same way to counter the rotation of the weighted symbol on acceleration. I know this is beyond engineering but I like the challenge.