SLARCK.xls

Short-Long-Arm Roll Centre Kinematics

Greg Locock

December 2002

Important Note: to make this spreadsheet run you MUST switch iteration on, >Tools>Options>Calculation. You may need to fiddle with the parameters in that options box, I set max iterations to 10000 and max change to 0.000001 and it seems to work fine. I have only used it in Excel 97, it should be upwards compatible. Note that this setting is reset by the first spreadsheet you open in a session, just to make things interesting.


Introduction

This program works out the roll centre locations for a suspension using short long arm (SLA) layout. It uses the geometric method, ie establishes the IC of each pair of arms, then uses the intersection of the line joining each IC to its contact patch to give the roll centre. A crude measure of the roll centre height is given, which assumes that the roll centre is central, laterally. (Hah)

There are two separate working pages, Design, where the suspension is set up at its design height, and then Bump where the suspension can be rolled or bumped, by specifying a rotation for each of the lower arms. This allows examination of the motion of the roll centre as the vehicle corners and/or bounces. Change data in the blue boxes, important results are shown in the orange boxes. Do not type in the white boxes, you'll be sorry.

Lower control arm rotations are specified in radians, clockwise, from the design position. For roll thetaR=thetaL, for jounce thetaR=-thetaL, approximately. If you set them both to 0 you should be back at design.

Incidentally if this all seems a bit hard, well, go and buy Milliken and Milliken "Race Car Vehicle Dynamics". You may also want to check out Dilbert's thoughts on engineers and user interfaces.


Graphics

The geometry of the suspension is crudely displayed in the chart 'geom', and the graphical method used to find the roll centre is shown in 'pic'. The latter was useful while debugging the program, I'm not sure it really tells you much.


Geometric Roll Centre vs Force Based Roll Centre

The SAE currently specifies a force based method to find the roll centre. During a manouevre it moves in a different way to the geometric roll centre. This spreadsheet was primarily written to allow me to investigate those differences.


Rolling Radius

You can change the rolling radius in the bump worksheet. If you know your roll and jounce wheel rates, and the tyre rate, then you can adjust the RR (and hence the contact patch location) to compensate for tyre deflection. I haven't seen this in the literature, there may be a good reason not to do it.


MacPherson Strut

With a bit of thought you can probably use this program to find the roll centres of a MacP setup, at least at design.


Example

The geometry included is roughly similar to, but completely different from, that used in a large production sedan, which has a live rear axle. The behaviour of the real geometry is quite different to this one in certain respects. In particular I have set this up so that at 5 degrees of roll the roll centre has moved right over to the outboard contact patch. This is, to say the least, an odd thing to do, but it may lead to better control as the inner wheel lifts off. The pay-off is that the track change in bounce and roll is excessive. This is partly due to the high camber gain.

Rolling radius of tyre	300	mm		
static camber		0	deg		
						Y	Z
centre of wheel					-770.0	550.0
hence contact patch				-770.0	250.0
						-726.9	526.2
Lower control arm to body			-350.0	460.0
Lower control arm to spindle			-750.0	484.2
Upper control arm to body			-460.6	755.0
Upper control arm to spindle			-575.6	800.8



Frustrated?

Try using Goal Seek or the Solver to get a particular solution. Good Luck. They are both in the Tools menu although you may need to load the Solver in from the tool pack, which you do from the Add-Ins command from the same menu. I've left a couple of the Solver blocks in the worksheets. Using Solver is a matter of persistence, it successfully found the geometry in the example, but it takes a bit of fiddling to get there.


Enhancements

I have no current intention of improving this thing, it did the job I needed it for. If you want a general purpose suspension geometry analysis program then go and get the excellent susprog3d, find it using google. The zipped demo is a 2.6 Mb download, and is worth every byte. 


Errors

If you find any mistakes (apart from those discussed later) then let me know, if you like. greglocock@yahoo.com.au (1)I have had a crash that could not be resolved with undo, where the entire spreadsheet became infested with error messages. This is a problem that occurs when one of the iterative loops gets corrupted with non numerics. Save often. (2)There is also an error with large UCA angles, as they go over-centre. Set both sides to maximum jounce, then check whether the rightmost columns on 'Bump' are all zeroes. These are the difference between the left and right hand hardpoints, and should be zero for a symmetrical suspension in pure jounce. (3)The orientation of the stub axles is incorrect, it should be perpendicular to the tyre centreline, not the spindle. This is just a visual error, it has no effect on the accuracy.


Disclaimer & blurb

The spreadsheet, SLARCK.xls, is supplied as is. All results should be checked independently before being used in a real design. If you use this spreadsheet as the basis for further work please acknowledge me. If you forward the spreadsheet on to anyone please also include this text file. If you send me a note I'll try and let you know if there are any changes to the spreadsheet. Note that there are some 'shortcuts' in the calculations, if you put in a very strange geometry the answers may be significantly in error. 

(c) Greg Locock              Titanic Enterprises           December 2002      