Has anyone strengthened the rear arm using Gaz Coilovers?

[GeoffBob]

Crap, I've just spotted a mistake in my model. My tyres are glued to the road, almost as if the car were on rails When the car runs over an obstacle, launching both the sprung mass and unsprung mass upwards, the tyre is pulling them back down (in tension) since the tyre can't let go of the road. This explains why there is roughly as much load in tension as in compression. This is of course utter bollox. In reality the tyre should let go of the road and launch itself along with the rest of the car.

It's a small matter to correct. I'll post more results when its sorted. Kindly consider this a work in progress.

[GeoffBob]

Right, all fixed. The tyre now lets go of the road while falling into a hole or launching over a ”ayump”a.

Quite informative results as well. See below the displacement of the sprung mass (blue), un-sprung mass (green), tyre (red) and pot-hole (black) as the wheel falls into a 100mm deep x 1m wide bowl shaped hole while travelling at 50 km/h. Please note that I’ve widened the hole over the previous example to make clearer the effect of ”afalling”a into the hole.

Note how the tyre (in red) breaks contact with the road (in black) as the wheel drives over the edge. Note then how the un-sprung mass and outer surface of the tyre (which are closely connected through the tyre wall) fall into the hole as a) gravity pulls the whole lot down and b) the spring kicks out against the damper. Note then how the tyre collides with the opposite side of the hole, at which point the outside surface of the tyre (red) is forced to follow the contour of the hole (black) while the tyre compresses between the un-sprung mass (green) and the road.

More interestingly, note how the tyre and un-sprung mass launch themselves out of the hole and ascend ~64mm into the air. All through this event the sprung mass (in blue), upon which the occupant rides, remains reasonably disconnected from the jarring motions of the un-sprung mass by virtue of the forgiving suspension components, falling and rising by just over 20mm, despite having driven over a 100mm deep pot-hole. The tyre (red) once again conforms to the track (black) after the wheel lands, with visible compression and rebound of the un-sprung mass (green) against the tyre.

EDIT: please click on the graphs to make bigger if unclear.



See below the total suspension load (blue), damper load (green) and spring load (red) as the wheel interacts with this atypical suburban landmark at 50 km/h. Note how the total suspension load progressively declines towards and passes zero as the tyre falls into the hole, having lost contact with the road surface. Compared to the earlier presented graphs the total load upon the suspension components in tension peaks at -100kg. I rather suspect that this is within the limits of two M6 bolts. Note, however, as the load climbs to a peak value of +775kg in compression after the tyre reconnects with the hole approximately 1m of travel into its suburban journey. Quite interesting is that, despite the tyre breaking contact with the road as it emerges from the hole, the total load continues to rise as the tyre and un-sprung mass launch themselves out of the hole, but the sprung mass continues to fall.



Anyone see any errors please let me know and I’ll modify the model accordingly.

Oh, and in conclusion it now appears that the bolt in question is indeed sufficiently strong. The question now is what sort of track incident (short of mounting the pit-wall) would cause it to fail. Any suggestions anyone? I’ll happily pop them in the model.

[Demlotcrew]

Ive been thinking about this thread, one of the things that came to me was that all the calculations are assuming the car is riding on its rims, no one has taken the tyre in to account which for simplicity we can assume acts like a 500nm spring.

Not at all Andrew, the "un-sprung mass" (although not the most accurate description in this case) in the model is riding on a tyre.

As above:

The un-sprung mass (rim, tyre, hub, disc, calliper etc.) is set to 25kg, with 210kg of sprung mass connected to the un-sprung mass through the spring and damper. The un-sprung mass is isolated from the road through the tyre, which effectively forms an air-spring with spring constant of roughly 500N/mm. The actual tyre spring constant will, of course, depend upon the pressure at which it is operated and the stiffness of the tyre wall.

Missed that point!

[GeoffBob]

No worries Andrew.

Since no one else has volunteered a scenario, I'll volunteer one myself.

Consider what would occur if you mounted (in your car that is) a 120mm high x 1m long bump at 50 km/h. Would you expect your suspension to survive? Chances are actually quite good provided nothing bottoms out. If you run out of damper travel or your springs bind, then it's unlikely to be a happy outcome.

Here's what the model says will happen when the spring travel is limited to a very forgiving 100mm in compression. This was achieved by defining the spring as non-linear in the model. The spring was given a linear spring constant of 80N/mm in the uncompressed position, but was set to become markedly stiffer as it approached full compression, effectively mimicking the action of a bump-stop.

As before, the road surface is in black, with the displacement of the sprung mass, un-sprung mass and tyre in blue, green and red respectively. Note how, after striking the bump the tyre compresses (green line drops below the black). As would be expected the sprung mass is progressively lifted upwards and launched into the air, achieving a total height of just over 300mm. Just over the crest of the bump the tyre breaks contact with the road. Note how the tyre and un-sprung mass flap up and down while in flight (as the spring and damper interact). The wheel "lands" roughly 7m after first impacting the bump, after which (as expected) the sprung mass lurches into the ground. Anything less than 100mm of ground clearance and the underside of the car will bottom out on the road. Assuming it has sufficient ground clearance the car launches back up into the air again after 9.3m of travel, plaintively flapping its little wheel as it again flies through the air, touching down again at ~14m.



See the forces involved below. Note how severe the force is when the spring is compressed to its maximum as the tyre first strikes the bump. After that the forces barely exceed 1.5 ton. While both you and your car would most certainly feel this bump, its questionable (imo) as to whether the load on the suspension (due to the initial impact with the bump) would be sustained for long enough to do much physical damage. Think of it as being like a hammer blow peaking at 70kN of force. Hmmm? I honestly think the cars suspension components and mounts might actually survive this one. I'm not sure baout my back though.



Of course what the model doesn’t predict (since it only models a single wheel) is how the car would pitch itself forward in-flight due to a forwards located COG.

Anyone feel like taking on a sleeping policeman at 30mph to prove me right or wrong? Be sure to take a camera with.

[Demlotcrew]

Well my mum E46 touring didn't fare well with a sleeper in france at 50km/h and thats stock! And what about bump stops?

I dont think the rear would be too badly damaged?

[GeoffBob]

Well my mum E46 touring didn't fare well with a sleeper in france at 50km/h and thats stock! And what about bump stops?

I dont think the rear would be too badly damaged?

The model only considers one wheel Andrew, so for the whole car to jump as indicated all four wheels would have to mount the bump at the same time . That's obviously not very realistic, but still, it's a starting point. The model is effectively of a 235kg monocycle, which is fine for predicting the behaviour of one wheel over an object provided the object doesn’t result in a shift in the cars weight distribution (between that wheel and the other three), which, let’s face it, is going to happen if the object in the road is big enough.

The next step is to model four wheels (each the same as the above monocycle) connected by a frame with distributed mass. Then I can model how a whole car would interacted with a pot-hole or bump. It will then be possible to run the front wheels over a bump, causing the front to launch upwards, followed by the rear wheels, sending the rear after the front. If the rear is lighter than the front (typically the case) the rear will take off faster than the front, causing the nose to pitch downwards ”“ not a nice way to land ”“ causing serious damage to the front suspension. This is more than likely what happened to your mum’s E46.

By making the spring nonlinear I have effectively included a bump-stop with the spring, so the model already includes a bump-stop.

[redcar]

Does it take into account an antiroll bar?

[GeoffBob]

Does it take into account an antiroll bar?

Now that is a most excellent question.

At present is does not since I am currently only modelling one wheel (in order to predict the forces on that wheels suspension components) and the assumption is that the other three wheels around it are behaving exactly the same. Hence, an ARB would have no effect since an ARB exerts a force in proportion to the difference in height between two adjacent wheels (and all wheels are at the same height since they are all traversing the same object at the same time).

I would, however, be sure to include an ARB when I have four wheels up and running. The great thing is that (from a maths point of view) it is really easy to inlcude an ARB. With a "four wheeler" model it will be possible to see the effect on all four wheels when only one wheel, say, strikes an object or falls in a hole.

[redcar]

Does it take into account an antiroll bar?

Now that is a most excellent question.

At present is does not since I am currently only modelling one wheel (in order to predict the forces on that wheels suspension components) and the assumption is that the other three wheels around it are behaving exactly the same. Hence, an ARB would have no effect since an ARB exerts a force in proportion to the difference in height between two adjacent wheels (and all wheels are at the same height since they are all traversing the same object at the same time).

I would, however, be sure to include an ARB when I have four wheels up and running. The great thing is that (from a maths point of view) it is really easy to inlcude an ARB. With a "four wheeler" model it will be possible to see the effect on all four wheels when only one wheel, say, strikes an object or falls in a hole.

Interesting. May i ask, are you a physics/maths expert? You're amazing at all these calculations.

[GeoffBob]

[redcar]

[GeoffBob]

[I do always find your posts and graphs very interesting, especially the ones involving brake master cylinders and pedal boxes etc. in some of Theo's threads.

Ta

I usually investigate these little problems for my own benefit (to learn something), but it makes it all the more worthwhile if there is someone out there who has a common interest.