Twin Special Rear Hub Nut

[TC2000]

Gavin, the load path is correct, but what is the only connection between the hub carrier and the drive shaft? The wheel bearing. so it does transmit the axial load, not?

Only in case you have the twin link suspension, otherwise the hub carrier is free to move sideways.

[GavinT]

Gavin, the load path is correct, but what is the only connection between the hub carrier and the drive shaft? The wheel bearing. so it does transmit the axial load, not?

No, not really, but perhaps a better visualisation is this.
Squat down behind the car again as per Reply #13.

Look at the suspension and mentally remove both bearings from the hub carrier.
What happens?

It should be seen that (aside from the axle assembly going wonky) the load paths still work and the suspension also works.

Now, reinstall the bearings.
The bearings permit axle rotation, of course, and the outer captured bearing stops the hub carrier from moving about. It should be seen that the bearings accept radial loads, but don't see axial loads.

Make sense?

[BDA]

Gavin, I see what you say. But not completely, or? The lower control arm is leaning onto the hub carrier and gearbox.

I'm not quite sure what you mean by "leaning onto the hub carrier and gearbox".

Perhaps it's easier to consider the rear suspension in plan view, thus:

The front trailing arm and the lower link form the two legs of the lower wishbone.
The front trailing arm and the half shaft form the two legs of the upper wishbone.

As a result, the wheel movement is dictated by the two outer pivots of those two logical wishbones - one being the outer bush of the lower link and the other being the outer U-joint on the half shaft.
Kinda have to use the imagination to visualise how these wishbones come about because it's not as obvious as in the front suspension.

Now, squat down behind the car and view the suspension from there.
Imagine the load paths as the car sits on its wheels. It should be seen that the wheels are putting the half shafts in compression by pivoting on the lower link outer bush. The lower link is thus, in tension.

I hope that makes sense, but does it address the question?

This is a fairly simple situation but it's been an age since I've dont this sort of analysis I could easily be wrong but I came  up with a different analysis than you. Check me on this:

First I want to make sure we're all talking about the same thing. In my analysis, we are interested in the outside rear wheel in a turn. I suspect that the forces on the inside wheel are pretty insignificant and in any case, the situation would be just be reversed in terms of the directions of the forces, not magnitude.

The force goes through the tire contact patch at the bottom of the tire which has to be reacted by the two links (the lower link and the half shaft). This is going to make the upright try to pivot on the outside lower link which puts compression forces on the lower link and tension on the upper link or half shaft since it has to counteract the moment (torque if you will) from the contact patch to the outer lower link pivot.

If I'm correct, it makes me reassess what I used to think about loads on the tranny. I used to think the tranny took really heavy loads, especially in compression, but my analysis implies that the heavier loads are in tension and relatively less in comparison to the loads on the lower link. The tranny would experience compression from forces on the inside tire but those should be much less than the outside tire.

Did I goof?

[GavinT]

I reckon you're right, BDA.

But my version examines the static position where the load on the contact patch is essentially vertical.
You're demonstrating that a lateral force on the contact patch changes the forces applied to the links.
Aren't we both right, but just considering different dynamics?

Good point about loads on the tranny.
To that end, it's also interesting that we've all seen Europas driven around with bent lower links (done it myself, but shhhh).
If the compression loads were hight on that piddly 1 inch diameter 'nothing special' steel tube, you'd think we'd have seen some catastrophic failures . . but we haven't.

It'll take someone smarter than me (not hard) to quantify all the relative dynamic loads involved.
I'd be interested to hear if someone's done that.

[BDA]

Keep in mind here that I in no way claim to be a suspension dynamicist (is that a thing?).

I would think that vertical loads would impinge on the shock mounts and the stub axle. The lower link and the half shaft are jointed at both ends so they provide no resistance. The amount of loads on the stub axle would be determined by the amount of damping produced by the shock and the resistance from the spring. I’m somewhat less confident of this because it implies that when the car is at rest, there is no stress on the stub axle due to the weight of the car (which seems wrong). I think that’s actually correct but I wouldn’t be surprised if I was missing something.

If I am on the right track with this stuff, I think that getting an idea of the loads involved is not that difficult. To simplify (and overstate) them, we can assume that the outside tire takes the entire weight of the back of the car in a turn. If the car is generating 1g, then the force on the contact patch is equal to the weight of the rear of the car.

My simplification turns this into a pretty simple statics problem (and frankly, even at that, I’d have get out my old statics book, if I could find it, to try to put any numbers to this - that’s how much I’ve forgotten!) and it is certainly a lot more complicated than that but I THINK my simplification gives an idea of the loads we’re dealing with - excluding shock loads, some small multiples (< 1.5) of the weight of the rear of the car.

Since the lower link is jointed at both ends, theoretically it shouldn’t have any bending loads and a round steel tube as is used on the lower link should be plenty strong enough to deal with the compressive loads we’re talking about but in the real world, they can bend. My inclination is to suspect some violence imparted to it. It could bend from yielding in compression but I think that’s probably highly unlikely unless you hit a curb or something. However, I have twin link rear and one of my upper links is bent! For it to be hit by anything, that thing would have to find its way past the lower link and the half shaft, neither of which show any damage, or something would have to hit the top of my wheel and a hit that hard would definitely damage my wheel! So far, I have no explanation.

DISCLAIMER: The fact that I am so far unable to understand how my upper link got bent could put all my analysis into question!    I would love to see an article on suspension stresses! If anyone knows of one, please post a link!

[GavinT]

Hmmm . . the load on the stub axle at rest must be whatever constitutes the corner weight - gravity, resisted by the spring.
One way would be to weigh the corner. Alternatively, it could be calculated if we know the spring rate, the spring free length and the geometry of the spring pivot points relative to the stub axle and the chassis .

I reckon if the car is generating 1g lateral force and we assume the rear of the car weighs 900 pounds and the inside wheel is essentially unloaded, then all of that 900 pounds is lateral force at the contact patch.
Add to that the preexisting mass via gravity on the outside corner also acting on the contact patch.

But can that be right?

[BDA]

It’s obviously a much more complicated situation than we’ve been describing but I think our simplification helps us get some sense of the magnitude of the forces. After all, we’re looking at it statically and this is a very dynamic situation. Cornering forces act through th CG of the car causing the car to lean transferring weight to the outside wheels, changing the suspension geometry and the angle of the tires to the road… And maybe the best thing I said is that, save for shock loads, we’re talking about small multiples of the static weight weight at the wheel (plus the weight transferred to that wheel). But I feel pretty safe in saying that since F= ma where m is the mass of the car and a is the acceleration (e.g. cornering Gs, vertical gravity, etc.). Since the mass of the car doesn’t change and our cars probably don’t generate more than about 1g, the tire would resist at most the weight felt at each wheel. (earlier I suggested 1.5g as a generous max)

Sorry for the brain fart. Your obviously correct that the weight of the car goes through the axles! Jeez! No excuse, I just went stupid!!

A while ago, I did find a course on vehicle dynamics on YouTube (https://www.youtube.com/watch?v=LZ82iANWBL0&list=PLbMVogVj5nJTW50jj9_gvJmdwFWHaqR5J). IIRC, I got through the first four or five classes and realized that I really needed to take notes and I hadn’t and I didn’t want to start over so I filed it away. Being a college class (in India, I believe), it is very general so he discussed things like pulling trailers up hill which didn’t interest me at all but I probably couldn’t ignore those classes without missing information I needed later. Maybe I’ll take it up again with pencil and paper this time and find the rest of my mistakes in these posts! The suspension design videos I’ve found seem to be about geometry rather than force/stress analysis.

[kram350kram]

Maybe someone can explain how the "control arms" (driveshaft and lower link) when in either tension or compression, depending upon loading, seem dependent upon well maintained engine and transmission mounts? Seems to me when the links are loaded, side forces are transferred to and thru the transmission, then to the mounts and then to the frame? If this is the case worn or lose mounts would have to have a detrimental effect on handling. Even with new mounts, this design and associated movements cannot be optimum for handling? Can't really get a visual on this, what am I missing?

[TurboFource]

Kram,
I believe you are correct any movement of engine and tranny mounts affects the suspension/handling.

I plan to minimize this with stiffer mounts.

[BDA]

I've already pretty much gotten to the end of my force/stress analysis of the suspension but you raise a good point. One of the knocks on the Europa rear suspension is that engine torque and other forces that cause displacements in the engine and tranny move the inner suspension pivot points. Obviously, the thicker the rubber mount, the more movement it can allow. I wouldn't think most people would appreciate solid motor mounts on a street car.

Analysis of the effect of the movement of the inner pivots which would include how much the mounts deflect would be welcome but I haven't seen it. On a 1600 cc motor I suspect the biggest problem from the deflection in the pivots would be due to turning forces. For your 289, kram350kram, you would have more to worry about. You my want to work up some way of mounting the lower links to a frame bulkhead or something similar. Or just live with it.

I probably should mention that when I got my NG3 kit from Richard (now Lotus Supplies), the tranny mount bushings are pretty thin and should provide minimal movement at the rear or the tranny. That should help the situation a fair amount because it should also limit any movement by the motor. Since I have spherical rod ends on my lower and one end of my upper links (the other end of the upper link is solid and pivots in one plane only so it shouldn't be a problem), I shouldn't get any deflection from cornering loads. But my point is that there probably ways to minimize the movement of your engine/tranny unit without resorting to solid mounts.

[EuropaTC]

If this is the case worn or lose mounts would have to have a detrimental effect on handling. Even with new mounts, this design and associated movements cannot be optimum for handling? Can't really get a visual on this, what am I missing?

You're not missing anything, that's exactly right. One of the areas my chassis was failing was in the area around where the engine mounts meet the frame and I'm convinced that it was a combination of corrosion & fatigue from the pattern of damage, Lotus stiffened that area up for a reason.

I even think it was commented on by the designers in the series about making the Elise, something about "the suspension is hung from the engine/gearbox, that's not acceptable today so we're going for a subframe"

Brian

[TurboFource]

BDA,
Can you post pics of your mounts?

[kram350kram]

Here are the motor and trans mounts. All are vertically loaded under compression as opposed to being in shear like in the stock mounts. This should minimize any side to side movement. Comments.

[TurboFource]

Seems to me there is a lot of rubber in the mounts and still potential for movement even though they are in compression ….. (but I am no engineer)….are they urethane?

What does the tranny mount look like?

[kram350kram]

Not urethane but hard rubber. Same engine mounts used on the Ford 289 high performance Cobra and GT350 Mustang engines. The rear trans mount and frame cradle is shown in the last two pictures. Trans mount is for to a 4x4 Dodge 2500, hard rubber too.