Mass Centroid Axis Revisited

[gruder]

I am new to this Forum & have been reading a thread called "How to locate the mass centroid axis" which i found was a closed thread so i had to start again.

warpspeed:
The answer to your question is quite simple as the mass axis is drawn through the front & rear CG heights & a few simple tests will reveal these positions.

willeng:
The emphasis on things you wrote although very basic in nature is not BS like mentioned, your on the right track, it is of great value to follow up on this further. Could you send me an Email please as i would like to converse with you about something that was written.
I have many articles that may interest you.

I noted that many are not convinced of this Mass Centroid Axis or have the wrong idea about it & are unaware of the total benefits & handling characteristics that can be achieved by altering this.
If the Roll axis & the Mass axis are drawn next to one another the slope between the two will determine the cars natural abillity to handle.

Eg:
If we have an upward sloping mass axis at the front, the car it will tend to understeer more due to greater weight transfer at that end of the car. Front engined/Front wheel drive cars exhibit this trait.
This is & always will be a major design key for all race cars & infact all cars.

There are many characteristics both good & bad that can be built into a car by using the mass centroid axis as a "key" design element.

Mr Smith was smarter than many recognised, all of his information is relevant in one form of racing or another even by todays standards. Todays standards in F1 for instance are all about aero with near zero suspension travel but in Smiths day it was all about true raw handling capabillity & balls.
Not sure about you guy's but i would have liked to have seen what good old Mr Smith could have down with the aero downforce available to us today---scary i would think!!

I have also been reading some threads that mention the "force based roll centres. This is an interesting subject but more on that a little later if anyone is interested??

H Gruder

 

[Aday]

There is no such thing as a mass centroidal axis. What Carroll Smith was trying to describe is the principal axis for vehicle roll inertia - this is the reference axis that minimizes roll inertia. The concept that Carroll Smith describes in "Tune to Win" is incorrect in several respects:
1. The principal axis is not found by simply connecting the front and rear center of gravity.
2. The orientation of the principal axis has NO effect on load transfer.
3. The connection between the front and rear RC is NOT the axis about which the sprung mass rolls. Several SAE papers have been written dispelling this myth.

Please don't misinterpret my remarks as disparraging Mr. Smith. I am a Formula SAE alumni now working as a vehicle dynamics analyst. I spoke to him several times when he was head design judge at FSAE, and had the utmost respect for his knowledge and success.

 

[GregLocock]

I'm told CS acknowledged that the theory in that book was wrong.

"drawn through the front & rear CG heights " There is no such thing as front and rear cg heights. A solid body can have only one cg location.

Just for grins I'll run a handling analysis on steady state and step steer, with two different sets of principal axes for the body inertia.

To make it fair, I'll let you set the parameters for the test. So I need a radius for the constant radius test, and a speed and steeer step size (at the road wheel) for the step steer test.

To make it fun, you have to tell me what the results should look like, before I run the tests.

I'll post the baseline model when I get home tonight.









Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[GregLocock]

Actually, I'll run swept steer, not constant radius.

here's the base model, it is a very neutral large sedan.

PARSFILE
* CarSimEd 3D vehicle.
* Generated by AutoSim 2.81 (PPC Dev) on January 20, 2000.
* Copyright 1996-2000. Mechanical Simulation Corporation.
* All rights reserved.

TITLE StepSteer110kph_Sedan

* Input File: C:\CARSIMED.451\RUNS_3D\680.PAR
* Run was made 17:35 on Jun. 26, 2006
FORMAT BINARY

IPRINT 1 , number of time steps between output printing (counts)
STARTT 0 , simulation start time (s)
STEP 0.001 , simulation time step (s)
STOPT 20 , simulation stop time (s)

* PARAMETER VALUES

ASW_MAX 360 , Maximum allowed steering wheel angle (in driver model) (deg)
CSFY(1) -0.0003 , Front suspension compliance: d(steer)/d(Fy) (deg/N)
CSFY(2) 0 , Rear suspension compliance: d(steer)/d(Fy) (deg/N)
CSMZ(1) 0.004 , Front suspension compliance: d(steer)/d(Mz) (deg/N/m)
CSMZ(2) 0 , Rear suspension compliance: d(steer)/d(Mz) (deg/N/m)
CSMZF 0.003 , Steering system compliance: d(steer)/d(Mzl + Mzr)/2) (deg/N/m)
CTFX(1) 0.0004 , Front suspension compliance: d(toe)/d(Fx) (deg/N)
CTFX(2) 0 , Rear suspension compliance: d(toe)/d(Fx) (deg/N)
DS(1) 2 , Front damper rate, at shock absorber (N-s/mm)
DS(2) 2 , Rear damper rate, at shock absorber (N-s/mm)
HCG 550 , Nominal height of entire vehicle C.G. (mm)
HRC(1) 50 , Nominal height of front axle roll center (mm)
HRC(2) 120 , Nominal height of rear axle roll center (mm)
HWC(1) 307 , Undeflected height of front wheel center (mm)
HWC(2) 307 , Undeflected height of rear wheel center (mm)
IW(1) 1.1 , Spin moment of inertia of front wheel (kg-m2)
IW(2) 1.1 , Spin moment of inertia of rear wheel (kg-m2)
IXX 400 , Moment of inertia of entire vehicle (kg-m2)
IXZ 0 , Product of inertia of entire vehicle (kg-m2)
IYY 2704 , Moment of inertia of entire vehicle (kg-m2)
IZZ 3136 , Moment of inertia of entire vehicle (kg-m2)
KAUX(1) 800 , Front auxiliary stiffness, including anti-sway bar (N-m/deg)
KAUX(2) 600 , Rear auxiliary stiffness, including anti-sway bar (N-m/deg)
KFX(1) 100000 , Front tire longitudinal stiffness (N)
KFX(2) 100000 , Rear tire longitudinal stiffness (N)
KFYCAM(1) -60 , Front tire camber stiffness (N/deg)
KFYCAM(2) -60 , Rear tire camber stiffness (N/deg)
KS(1) 30 , Front suspension spring stiffness (at spring) (N/mm)
KS(2) 45 , Rear suspension spring stiffness (at spring) (N/mm)
KT(1) 210 , Front tire vertical stiffness (N/mm)
KT(2) 210 , Rear tire vertical stiffness (N/mm)
LCGT 1200 , CALC - Distance from F axle to total vehicle CG (mm)
LRELAX(1) 600 , Front tire relaxation length (mm)
LRELAX(2) 600 , Rear tire relaxation length (mm)
LTK(1) 1550 , Front axle track width (mm)
LTK(2) 1550 , Rear axle track width (mm)
LWB 2700 , Wheelbase (mm)
MF 1000 , Vehicle mass supported by front axle (2 wheels) (kg)
MR 800 , Vehicle mass supported by rear axle (2 wheels) (kg)
MT 1800 , CALC - Total vehicle mass (kg)
MU 1 , Tire/ground friction coefficient (-)
MUS(1) 100 , Front axle unsprung mass (2 wheels) (kg)
MUS(2) 80 , Rear axle unsprung mass (2 wheels) (kg)
RAP(1) -0.05 , Wheelbase change per unit jounce at front axle (-)
RAP(2) 0 , Wheelbase change per unit jounce at rear axle (-)
RCAM(1) -0.04 , Wheel camber change per unit jounce at front axle (deg/mm)
RCAM(2) -0.06 , Wheel camber change per unit jounce at rear axle (deg/mm)
RDAMP(1) 0.8 , Front ratio of jounce at wheel to damper stroke (-)
RDAMP(2) 0.9 , Rear ratio of jounce at wheel to damper stroke (-)
RMF 0.555556 , CALC - Ratio: proportion of load on front axle (-)
RMR 0.444444 , CALC - Ratio: proportion of load on rear axle (-)
RMYBK(1) 200 , Front wheel ratio of brake torque to pedal input (N-m/MPa)
RMYBK(2) 70 , Rear wheel ratio of brake torque to pedal input (N-m/MPa)
RMYTH(1) 0 , Front wheel ratio of drive torque to throttle input (N-m)
RMYTH(2) 1000 , Rear wheel ratio of drive torque to throttle input (N-m)
ROLL_STOP 45 , Roll angle for stopping the simulation (deg)
RSPRNG(1) 0.8 , Front ratio of suspension jounce to spring compression (-)
RSPRNG(2) 0.7 , Rear ratio of suspension jounce to spring compression (-)
RSW 16 , Steering gear ratio (-)
RTIME 0.05 , CALC -- Computational efficiency (sec/sim. sec) (-)
RTOE(1) 0 , Wheel toe change per unit jounce at front axle (deg/mm)
RTOE(2) 0 , Wheel toe change per unit jounce at rear axle (deg/mm)
SPEED 110 , Vehicle forward speed (kph)
SPEED_ON_OFF 1 , Speed control switch (0.0 -> off, 1.0 -> on) (-)
STARTS 182.844 , Starting station number (beginning of simulation) (m)
STOPS 10000 , Stopping station number (stop simulation when this is reached) (m)
TDLAG 0 , Lag time used by driver model (s)
TPREV 1 , Preview time used by driver model (s)
VLOW_ALPHA(1) 5 , Front low-speed threshold for modified tire relaxation equations (kph)
VLOW_ALPHA(2) 5 , Rear low-speed threshold for modified tire relaxation equations (kph)
VLOW_KAPPA(1) 2 , Front low-speed threshold for modified longitudinal slip equations (kph)
VLOW_KAPPA(2) 2 , Rear low-speed threshold for modified longitudinal slip equations (kph)
VLOW_SPINA(1) 2 , Front low-speed threshold for modified wheel spin equations (kph)
VLOW_SPINA(2) 2 , Rear low-speed threshold for modified wheel spin equations (kph)
V_STOP -1 , Low-speed limit for stopping the simulation (kph)
XDESIGN 182.844 , NIL (-)
YDESIGN 436.717 , NIL (-)

* Brake input vs. time
BRKIN_TABLE
0, 0
10, 0
ENDTABLE


* Cornering stiffness vs. load (30 pts max)
IAXLE 1 , Table ID number
KFYA_TABLE
0, 0
500, 131.1
1000, 213
2000, 346
3000, 459.6
4000, 562.1
5000, 657.1
6000, 746.6
8000, 913.2
10000, 1067.5
12000, 1212.9
ENDTABLE

IAXLE 2 , Table ID number
KFYA_TABLE
0, 0
500, 131.1
1000, 213
2000, 346
3000, 459.6
4000, 562.1
5000, 657.1
6000, 746.6
8000, 913.2
10000, 1067.5
12000, 1212.9
ENDTABLE


* Steering wheel input vs. time. Column 1 = time (sec). Column 2 =
* steering wheel angle (deg).
STEERSW_TABLE
0, 0
0.1, 30
3, 30
ENDTABLE


* Throttle input vs. time
THROTTLE_TABLE
0, 0
2, 0
ENDTABLE


* Pneumatic trail vs. load (30 pts max)
IAXLE 1 , Table ID number
TRAIL_TABLE
0, 12
2000, 15
4000, 23
6000, 36
8000, 52
ENDTABLE

IAXLE 2 , Table ID number
TRAIL_TABLE
0, 12
2000, 15
4000, 23
6000, 36
8000, 52
ENDTABLE

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[hemipanter]

I wonder what the theory about "force based roll centres" is? I tried to look a few treads back but didnt find very much about the subject.
It sounds like Rc location should be dependent on load.

What I found myself is that Rc is pretty much located in the centre of the car (not talking height)while the forcelines is carrying load according to weight transfer-tiregrip. Then depending on forceline angle in a specific rollangle situation we got different jacking situations.

Goran Malmberg

 

[GregLocock]

Goran, I suggest you do a google search on the forums, using "force based roll centres" as a search term.

The SAE definition is (not very helpful):

9.4.28 ROLL CENTER : The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll. (See Note 16.)

9.4.29 ROLL AXIS : The line joining the front and rear roll centers.

9.4.30 SUSPENSION ROLL STIFFNESS : The rate of change in the restoring couple exerted by the suspension of a pair of wheels on the sprung mass of the vehicle with respect to change in suspension roll angle.

9.4.31 VEHICLE ROLL STIFFNESS : Sum of the separate suspension roll stiffnesses.

9.4.32 ROLL STIFFNESS DISTRIBUTION : The distribution of the vehicle roll stiffness between front and rear suspension expressed as percentage of the vehicle roll stiffness.

16. The roll center defined in 9.4.28 constitutes an idealized concept and does not necessarily represent a true instantaneous center of rotation of the sprung mass.

There are a few ways of measuring it. I like the the rig test that looks at the change in vertical load on the tires as the contact patch is pushed sideways, as that is talking about load transfer in a very direct fashion. When you do that in practice you find that anyone who thinks they know where their RCH is to an accuracy of better than 25 mm has either got very low friction ball joints or a very large sample size.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[rpmag]

Greg, just when I think I am getting somewhere with understanding very basic suspension you go and post something and I need to go have a sit down in a quite darkened room!
Can you (briefly) run through some of the data and indicate which is the more significant aspects WRT this topic?

 

[GregLocock]

Which topic? Mass centroids (basic dynamics textbook), load transfer or roll centres?

On the latter if you zip back through the archives here you'll find that 4 years ago I was not very interested in them. I've modified my views since then, but still regard geometry based roll centres (GRC) with a huge pinch of salt. FBRC, as measured above, seems to me to be measuring something useful.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[rpmag]

Sorry for the delay. No, my reply was WRT the data listed. I have just put the next magazine in the printers, so I have some brain space for 1-2 weeks. I will get milliken out and read up on the mass centroid.
We have discussed GRC and FBRC in the past, I will not cover that ground again. I will start collecting the link data from the car list as described in a previous thread.

 

[Aday]

Be carefull about reading up on Roll Centers and "mass centroids" in Milliken. My recollection is that the description given in RCVD is in error! The only correct discussion of RC's I have seen in print are in SAE papers and Mark Ortiz's articles in Racecar Engineering.

 

[rpmag]

thank you I will keep that in mind

 

[Knap]

http://racingteam.manchester.ac.uk/...r.pdf#search="weight transfer rc suspension "

The chassis roll centre is the point in the vertical plane at which transverse forces can be applied to the
sprung mass without kinematics roll occurring. The body therefore rolls about this point.
Body roll occurs as a consequence of the relative position of the suspended mass COG versus the roll
centre.
The distance between the RC and sprung mass COG is critical. A higher RC is effectively a stiffer anti-
roll bar. It follows that the lower the roll centre, the more roll that occurs in a corner. The moment of
inertia varies with the SQUARE of the distance between them. The lower this inertia, the higher the
response but the less the stability (this applies exactly as it did in yaw in previous conversation). When
there is less roll, the energy must go somewhere and this is primarily the wishbones but also the tyres
through lateral fluctuations. Because it is difficult to heat FS tyres up it may be better to have a higher
RC (even though this reduces stability in weight shift) because the bottom of the wheel moves outward
rather than the top of the wheel inward in bump causing this warming effect. If the RC was placed higher
we would require more compliant tyres in roll, particularly in the side walls. Another advantage would be
the quicker response in tight cornering.
A cause of understeer may be less chassis roll on the front of the car than on the rear. This results in not
enough weight being shifted from the front inside wheel to the outside wheel and so less grip being
generated. If the front grip is not larger than the rear then no yaw moment will be produced. Lowering
the front roll centre to persuade more roll can solve this problem.

3D Kinematics
The 3D instant roll axis of the front and rear suspended mass may not align. They must align through the
suspension travel (not just in static) otherwise the chassis will be twisted. So, deal with the cause (and
align them) or the effect (build a very stiff chassis). As well as this, it is normally assumed that the front
and rear COG heights are the same when in fact they can be very different.
The method is to divide the car into 10 ‘slices’, each slice having a COG, stiffness and damping. Build a
jig to measure the car (and use 10 linear potentiometers). Measure damping and the natural frequency
of each section by releasing the chassis from a displacement.

 

[GregLocock]

"The chassis roll centre is the point in the vertical plane at which transverse forces can be applied to the
sprung mass without kinematics roll occurring. "

OK

"The body therefore rolls about this point."

Wrong.

"The distance between the RC and sprung mass COG is critical. A higher RC is effectively a stiffer anti-
roll bar. It follows that the lower the roll centre, the more roll that occurs in a corner. The moment of
inertia varies with the SQUARE of the distance between them."

Wrong. The moment of inertia is not related to the roll centre height at all.

I really hope Claude didn't write either of those two statements.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Aday]

I'll have to agree with Greg here....The chassis does not roll about the Roll axis. MBD simulations quickly dispell this myth. A few good SAE papers have also be written on this topic.

The MOI of the sprung mass about the axis connecting the front and rear RC would only be relevant if the vehicle actually rolled about the roll axis, but it does not.

 

[crashbox455]

so if the roll center doesn't indicate anything in the way of where the car rolls,


then why does it exist as a data point? what does it indicate?

 

[GregLocock]

Read the definition.

9.4.28 ROLL CENTER : The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll. (See Note 16.)

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[GregLocock]

In other words, a high roll centre means that more of the load transfer is transmitted via the linkages, whereas in a low roll centre more of the load transfer is transmitted via the springs. This is very useful as the two routes have different time constants.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[hemipanter]

The geometry of the A-arms does not produce a "bearing" for the chassis to roll around. What the A-arms does produce is a forceline that has an angle which pretty exact govern the "anti effect". The weight transfer is CGH*W*G/Tw, just take away the "anti" and the roll number is what is left. As this "roll number" represent a roll motion is obvious, the question is where its axis of centre is? As there is no centre effect bearing present, something else must govern the pattern of roll motion.

With my physical models I have found that I can locate a mechanical roll centre within a pretty large area of the chassis body and still be able to roll the car. We could say that the car sort of like a square board with a spring at each corner. If we take 100p away from one side and put 100p down at the other side, the board will roll about its middle point.

If the roll centre is lowered 4 inch to ground level at one end of the car and raised 4 inch at the other end, the geometric weight transfer will be altered. What happen is that one end will take all the geometric weight transfer then, while the elastic component stays the same and the chassis will no longer be rolling horizontally as we got a sloped roll axis.

This way we can say thet there IS a roll centre even if not a fixed velded in bearing.

Goran Malmberg

 

[GregLocock]

Ben's pointed out that the following statement can be rewritten, and then makes sense.

"The distance between the RC and sprung mass COG is critical. A higher RC is effectively a stiffer anti-
roll bar. It follows that the lower the roll centre, the more roll that occurs in a corner. The moment of
inertia varies with the SQUARE of the distance between them."

Should read

"The distance between the RC and sprung mass COG is critical. A higher RC is effectively a stiffer anti-
roll bar. It follows that the lower the roll centre, the more roll that occurs in a corner. The chnage in moment of
inertia about a given roll axis varies with the SQUARE of the distance between the roll axis and the cg of the body."

Which apparently is what CR was getting at. And that's fine.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.