Equivalent stiffness

[delacf]

My intention is to calculate how to vary the equivalent stiffness of a spring when it makes an angle with the horizontal.





Regards,

delacf

[Ciro Pabón]

Good question. As I see it, yes, for every displacement x of the tyre in the vertical direction (I would call that y, but it's the same thing), the spring will be compressed a distance equal to . This is valid for small displacements, because the angle with the horizontal will vary if you move the tyre too much in the vertical direction.

As for the forces, a vertical force Fx (also I would like to call it Fy, but...) will provide you with a force .

The force Fx is composed of a force Fr, in the direction of the spring, plus a force Fy that is pulling the lower arm.

Like this:



You can also think that the force Fx is making the suspension to rotate around the point where the spring is attached to the chassis, but this torque equal to "Fx * horizontal distance to chassis attachment point", that is trying to rotate the wheel in the counterclockwise direction is compensated by a torque equal to "Fy * vertical distance to chassis attachement point", which goes clockwise.

I'd say that an explanation to the stiffer suspension would be that you're changing movement in the vertical direction for a force that is trying to "rip" the wheel out of the car (or better, pulling the lower arm). The smaller is , the larger the "ripping force".

... or so I think, but I know structures, not mechanical engineering, so all this is original "research".

[delacf]

Sorry. I was wrong.

if we set the spring angle, we would have:



This will leave an equivalent stiffness:



Where



Gracias Ciro

Regards,

delacf

[delacf]

Hi, I plotted the curve:





We see the following:

It is quite linear in the range 0.6-1.2 radians (69-34 degrees)

The maximum stiffness occurs when the spring is vertical.

When the wheel is raised, the spring angle to the horizontal decreases -> It reduces the stiffness. "We went down the curve"

Regards,

delacf

[Belatti]

So now you know, if you want to keep a rather linear motion ratio you will put the spring at 45°

What would you do if you want a progressive motion ratio?

[Ciro Pabón]

A spring with an axis that is a segment of a circle, of course.

It worked in Piccard's batyscaphe (no, not that Piccard, the original one).

[Belatti]

shhhhhh

[delacf]

Damn. I'm doing my enrollment in an English school. I do not know if I understand correctly, Bellatti.

I'm learning. We try to reach solutions. What do you mean by progressive motion ratio?

I'll shoot. We have:



Then:





X [radians]

Regards,

delacf

[Ciro Pabón]

shhhhhh

Don't worry, I won't tell anyone outside the Internet.

By progressive, I think, Belatti means that it has to become stiffer with large displacements. Man, these guys at TC know how to cheat...

Thinking about it, there I go with a crazy idea: you could invert the spring (the lower arm would become the upper arm, and the spring would go from the bottom of the chassis to the top of the wheel at 135 degrees) so, when the wheel bumps, the suspension would go through an arc making the spring more vertical. You could increase somehow the progression by using short arms. The spring would have to work in tension. This would be a very strange cheat (probably it is not practical, even TC officers would notice that and the camber would go to hell, but in a good way, perhaps with an upper arm longer than the lower one). Mmmmm... I don't think so, erase that. Somebody would have thought of that, if it could work.

Belatti speaks a foreign dialect remotely related to Spanish, delacf: he's from Argentina; his ancestors used to speak Spanish, but their descendants don't speak it anymore, so you better stick to English, unless you want to decipher what ""dejá nomás, que algún chabón chamuye al cuete y sacudile tu firulete" means.

[Caito]

shhhhhh

Belatti speaks a foreign dialect remotely related to Spanish, delacf: he's from Argentina; his ancestors used to speak Spanish, but their descendants don't speak it anymore, so you better stick to English, unless you want to decipher what ""dejá nomás, que algún chabón chamuye al cuete y sacudile tu firulete" means.

xD.



I found(susp software) that it's not only a matter of angle as It may seem. It's also a matter of the arc it's travelling. Although it's a circle(the path that the wishbone is doing) you may start lower from the horizontal. When the wheel goes up, it goes "away" from the center. So you think you may gain in turn of angle, but you lose because the point is going away so one benefit is countered by the other.

Moving the points you can have it flat(constant) or almost any way you wish, it's really cool to play with that.

Regardless of the initial angle of the spring, you can have any of the configurations.

Bye bye!

[Belatti]

Ciro, we dont cheat at TC, for that you have to have the blessing of the TC "big brother" and of course, pay tribute. We prefer the use of lateral thinking while interpreting the rulebook. In that case if the big brother finds us, remaining quiet and being polite is enough to escape large punishments. Sorry, the "shhhhhh" was in order to let delac think a bit and make his statement, so we can them help him on that base

and you are, as usual, correct, we south americans do not speak spanish, but hopefully we understand it

Caito left good stuff to think about. After that, forget about the bi-dimentional thing and remember the circle traced by the lower wishbone may have a component thats not in the "X-Y" plane.

[Ciro Pabón]

Sure, there is no cheating in racing. Just interpretations of rules. We all are interpreting gentlemen, including me.... For example, some days I can interpret you out of the track with a small push of the bumper.

So, how do you make progressive springs? Interpret that for me, please.

And yes, yo te manyo, chabón (in English: I can interpret you, mate... or so I think. Lunfardo is hard to interprete).

[delacf]

The spring stiffness decreases linearly. Without thinking: a simple solution(but I do not think that is the most elegant): We could use springs with coils not equally spaced. Have to think about how to do this by varying the susp geometry.

Regards,

delacf

[Belatti]

you can use any spring you want to achieve the progression you want, by combination or not

to do it geometrically as you wish, just play a little bit till you find the progression in the motion ratio

[delacf]

Other matters:

If we derive the equivalent stiffness, we have:



If we plot this we know at what points the slope is steeper.




If we consider only the “speed” with which changes the stiffness, does not look good an angle approximately 45 degrees. I would try it at an angle of at least 60 degrees. Obviously we have to consider many other aspects.