Vehicle stiffness

I would like to preface this with acknowledging that I am by no means an expert.

I am currently co-oping with a group at an un-named company. My group is tasked with providing empirical evidence proving the relationship between vehicle stiffness. Ask anyone that’s been around motorsports and they will tell you that stiffer=better. While some objective testing performed upholds this trend, it just isn’t that simple. I am going to break down some key concepts, then dive into theory. Unfortunately, I can’t publish any of the data I gathered, it is all classified as confidential.


The 4 big points of discussion/interest.

Global vehicle stiffness: This is how much the entire vehicle twists under load. The measurement is (usually) performed on a bare tub, no glass doors, trim or suspension. This is called a body in prime (BIP) The BIP is then placed on a testing rig with the Front end rigidly affixed at the strut mounts. The one side of the rear of the vehicle is constrained in the vertical axis while the rest are left open to movement. The other corner is then loaded. Precise measurements are taken at hundreds of points throughout the vehicle. The overall stiffness is then calculated. The standard unit is Knm/rad (kilo-newton meter per radian)

Local stiffness: This refers to the stiffness of the front and rear halves of the vehicle. It can be measured in a similar manner to global stiffness.

Point stiffness: This refers to how rigid specific points of interest are. A few examples are steering rack mounts, LCA mounts and subframe mounts. This is usually measured in terms of deflection in each axis, they are usually less than 2 mm, but can be greater under extreme load cases.

Global Mode: this is essentially the natural frequency of the BIP. At first I couldn’t picture how this could have any effect on steering/handling but it is apparently one of the key players. The method of measurement is quite barbaric. We can either simulate it in CAD (not very accurate and incredibly time consuming) or we can whack the BIP with a big ass hammer and record the frequency it vibrates at. We can also use this method to measure the stiffness of local points as frequency and stiffness are directly related.

How do these change the way my car drives?

All of the stiffness metrics have effects on turn in crispness, midcorner response as well as caster/camber/toe curves and overall handling characteristics. Intuition tells us that if we want a stiff chassis, we add bracing. Whether if it is in the form of strut tower braces, subframe connectors or roll cages. While marginal gains have been observed when these changes have been applied, there seems to be a point of diminishing returns (for those of us that are familiar with them, think of a tire slip angle vs lateral acceleration graph). I believe that this is due to the relationship between the 3 stiffness metrics. You cannot increase one disproportionately to the others without changing the path the mechanical energy transmitted at the tire. i.e. if you increase the global stiffness to a relative infinity by burning in a cage, the local stiffness will no longer be sufficient in preventing large deformations. I personally believe that this issue can easily be overcome with bolt on bracing. The real head scratcher is point stiffness, we really can’t change that easily after the vehicle leaves the factory, at least not in a way that we can quickly reverse for testing the theory. (we can add a lower tie bar to the front subframe). Even if you have a chassis that is infinitely stiff, it can’t make up for weak point stiffness, just like it doesn’t matter if you have a 10” dick if you cant get hard. In fact, I think that it can make the issue worse. When there is a point that is weak compared to the rest of the structure, the loads will then be concentrated at that point instead of being distributed evenly throughout the load path.

What should I do for chassis strengthening on my car? As I am typing this I am sitting in a lab testing a 2011 Focus (euro diesel hatchback) with various bars and braces for stiffness metrics. If you guys want some more info on it or predictions of the results just let me know. Unfortunately, I won’t be around when the results are processed. The places that we have concentrated on adding stiffness to are: Rear shock towers, mid chassis brace, front LCA mounting points (corksport makes a tie bar), the “horseshoe brace” right behind the sub frame and some strut tower to cowl bracing. The horseshoe, mid-chassis and rear bracing acts as effective way to sure up the global torsion, in fact the rear shock tower brace is one of the largest players. Prior testing shows that local stiffness has a greater effect on vehicle attributes than the others, barring global mode which has been optimized by the manufacturer and is very difficult to change without lots of CAD/FEA. The points I would recommend adding braces to are as follows in order of priority: LCA tie bar, rear shock tower brace, horseshoe brace, and mid chassis bracing.

I can update and add info/graphs as if you guys want, I dont know what you want to see tho.

 

I can only speak for myself...

I would be interested in graphs on these areas you suggest. I'm not an engineer but you don't need to be to see a delta with the proper unit of measurement, of which you've already provided.

Also, by "horseshoe brace" do you mean one of these blue ones in the pic? I ask because these are supplemental and not replacements.

 

The Horseshoe brace is the rear factory brace in that picture. That supplemental bracing looks to be tying it into the subframe and the whole shebang into the body.

 

Attached is an excel sheet with some of the deformations on a 2011 ish focus hatchback, it’s a euro diesel hatchback. The rear deformations are only the right half of the vehicle; I couldn’t position the cameras to capture all of the points in one shot.

I omitted the X axis deformations, as they are very noisy and not relevant. The positive Z axis is up and down in the vehicle with the y axis being left to right, the passenger side being the positive direction. The first two smaller lists are the deformations for the rear. The vehicle was loaded on a kinematics and compliance machine to apply force in the y axis. We can also simulate steady state loading (sustained speed on a skid pad for example) but I chose to use the lateral load case as it is easier to notice trends.

“config 1” is a stock representation and config 4 has a rear strut tower brace installed. Don’t you worry about config 2-3, there’s some black magic involved that I can’t disclose.


Summary:

The deformations are labeled as “Ry AVG and Rz AVG”, the x,y and z are merely the starting coordinates You can ignore them. The “rrfy” is the force input for the right rear wheel, you can ignore that too, it is just there for error checking my huge sheets with over 200 runs. The ry std and ry noise are the standard deviations and noise levels for each point. For this purpose, it can be ignored as well.

The deformations in the rear are reasonably low, the trailing arm to body mounts and the LCA to subframe mount are the big-movers at ~0.5mm. When the rear shock tower brace was added, these points deformed ~0.2mm less. Feel free to do some math yourself, I was going to add a calculation tab but it may have made things more confusing.


As for the front end, The front LCA mounting point at the subframe shows as a major weak point. The steering gear mount also show a fair amount of deformation. I’ll let you guys look through it for yourselves and answer any questions you may have.