Car model (Lagrangian)

[delacf]

Hi, folks. I'm doing this problem (obtaining Eqs. Moving through the Lagrangian) and I think I found a typo in the book: Reza Jazar, Vehicle Dynamics. However,I have checked if misprints appeared in recent editions of the book... ... And nothing.



Here, the typo. In the potential energy function:


What do you think ? Is it correct ? I don´t think so

Thank you very much

[DaveW]

For what's worth, I think you are correct, but I don't think that is the only typo. What happened to kRf & kRr?

[delacf]

Thank you very much, Dave. Yes, he only considered front anti-roll bar.

I will continue writing on this topic. I will write the equations of motion and other... ...I think maybe this will help for someone.

Regards

[delacf]

This is the Lagragian of the system:



Regards

[Pierce89]

Ahh this thread reminds me of the good old days.

[MadMatt]

Never heard of that book but what they wrote is clearly wrong. I would do as you've done, inverting b1 and b2. I might have this in one of my courses but I don't have access to them at the moment. Nevertheless I am sure your correction is right.

[DaveW]

This is the Lagragian of the system...

Just to spice things up a little, and to make the model more useful, you might think about adding an inerter to each corner suspension element, and then to isolate each using a series spring, representing "installation" compliance. A third suspension element at each axle, reacting heave & pitch (only), might also be useful....

[delacf]

Yes, DaveW. That is my intention: Inerter, Roll damper, third spring-damper...

[Cold Fussion]

How do you find the book? I'm interested in learning more about vehicle dynamics, especially now that I'm apart of an fsae team.

[DaveW]

Yes, DaveW. That is my intention: Inerter, Roll damper, third spring-damper...

This might help, perhaps, courtesy of F1T's "tex" operator:

If is the force carried by a suspension module, is the inertial displacement of the hub and is the local inertial displacement of the sprung mass, then the transfer function of the suspension module is:



which is a first order lead filter with representing the spring rate, and representing the damping coefficient, is , is the angular frequency.

If an inerter of mass is placed in parallel with the damper, the transfer function becomes:



which is a second order lead filter. Alternatively, if the inerter is removed and a spring of value placed in series with the suspension module, the transfer function becomes:



which is a first order "all pass" filter. If an inerter is now added to the above, the transfer function becomes:



which is a second order "all pass" filter. Note that is no longer representative of the displacement of the damper in either of the last two cases...

[delacf]

Thank you very much for your time, DaveW. It's very interesting. I'll work about it

If is the force carried by a suspension module, is the inertial displacement of the hub and is the local inertial displacement of the sprung mass, then the transfer function of the suspension module is:



which is a first order lead filter with representing the spring rate, and representing the damping coefficient, is , is the angular frequency.

If an inerter of mass is placed in parallel with the damper, the transfer function becomes:



which is a second order lead filter.

I thought the inerter connected both sides of the vehicle ( at least I think it is the most widely used scheme), DaveW. am I wrong ?

Regards

[DaveW]

I thought the inerter connected both sides of the vehicle ( at least I think it is the most widely used scheme), DaveW. am I wrong ?

No & Yes.... A 3rd mounted inerter is the most common arrangement in F1, but I believe the first car helped by inerters to a series championship (to be fair, not F1) used them on all four corners (it had no provision for 3rd inerters).

In any event, I included both options - case 3 (without) and case 4 (with). For a 3rd element it is necessary to re-define .

For me, the inclusion of "installation" compliance is important particularly because it couples with inerters, which can then have a major effect on hub mode control (reducing both the natural frequency and damping ratio).

[delacf]

I think I could write the rayleigh function due to roll-damper as:



It's very similar to anti-roll bar.

And I have a question too... How can I define the contact patch load transfer function ??? What is its definition ???

I thought it was well:



... But this transfer function have more zeros than poles...

Regards