Suspension suspense

[ScottAndrews]

Did you mean, “UP from the ground, “ and not down from the body?

I probably described that poorly...The wheel doesn't move at all. Both wheels are on the ground.

In a corner with no ARB. the roll force of the body increases the downward force on the outer wheel and reduces the downward force on the inner wheel. I think we can agree on this.

With an ARB, the force on the inside wheel from the bar is up, toward the body, compressing the spring, but gravity applies a force to the body and the wheel down toward the ground (the wheel does not lift off the ground). The force to do that comes from the outside wheel. Since the bar has to compress the inner wheel spring, and the weight of the car doesn't change, the force on the outer wheel is reduced..

Seems our disconnect is really a matter of perspective...

The ARB reduces the downward force (the weight) one outside wheel, and increases the force onthe inside wheel. It does this by unloading the outer spring and transferring the load to the inner spring. Remember, the wheels never leave the ground, so this is all about increasing or decreasing the forces, not about lifting a wheel...

Another way to visualize this is this:
Consider an perfectly stiff roll bar. If the outer wheel force is increased in a corner, then that force will try to compress the spring. When it does that the (infinitely stiff) ARB compresses the inside wheel spring by the SAME AMOUNT. If the inside spring is compressed the same as the outside spring, then there is NO BODY ROLL. Since the car is now level and both springs are compressed the same, the load on each spring is the same. So load has been transferred by the bar from the outside wheel to the inside wheel.

The result is that the outer spring is compressed only half as much as it would otherwise be without the bar, and the inside spring is compressed twice as much (since it is compressed from what would have otherwise been an extended position).

 

[ScottAndrews]

Arde;
Looking way back at your original post, the question of shocks vs springs remains...

With classical dynamics the system would be a damped harmonic oscillator, where friction damped the motion of the system. Here is a link to the math for that. Pretty simple if you are familiar with differential equations.

Oscillator damped by a constant-magnitude friction force

Although a simple spring/mass system damped by a friction force of constant magnitude shares many of the characteristics of the simple and damped harmonic oscil

pubs.aip.org

This model would apply to cars from the 20's and 30's that had friction shocks. The damping of the oscillations is linear.

Today, however, with hydraulic shocks the damping force is related to the velocity of the suspension movement. That will change the above differential equation by making the friction term speed dependent instead of constant. In this model the damping effect is exponential, meaning it has much greater effect for large fast motions than it does for smaller slower motions.

This is an interesting article on this. Scroll down to the viscous damped article.

https://www.sciencedirect.com/topics/physics-and-astronomy/viscous-damping

 

[Arde]

Very clear Scott, at the risk of getting pedantic I have one more dilemma to understand. According to your analysis and one more expert write-up, it would appear like the car sinks more during cornering that in straight driving, and the rigid sway bar keeps the car horizontal but at a lower to the ground position. That would be the result of the sway bar pushing down on the inside suspension side. I think that is a red herring. While that pushing down is accurate, the inside chassis gets a raising force due to the lateral force applied to the CG as much as the outside gets a lowering force. The springs operate identically to extension as they do to compression, therefore that raising force from the inside is transferred to the outside and there should be no net dropping of the car height. IMHO the only vertical force is gravity, so it would be very strange if the car lowered its height by the application of just a lateral force, but what do I know...

 

[ScottAndrews]

Very clear Scott, at the risk of getting pedantic I have one more dilemma to understand. According to your analysis and one more expert write-up, it would appear like the car sinks more during cornering that in straight driving, and the rigid sway bar keeps the car horizontal but at a lower to the ground position. That would be the result of the sway bar pushing down on the inside suspension side. I think that is a red herring. While that pushing down is accurate, the inside chassis gets a raising force due to the lateral force applied to the CG as much as the outside gets a lowering force. The springs operate identically to extension as they do to compression, therefore that raising force from the inside is transferred to the outside and there should be no net dropping of the car height. IMHO the only vertical force is gravity, so it would be very strange if the car lowered its height by the application of just a lateral force, but what do I know...

I think that's an interesting observation. I have not experienced my car significantly lowering in hard corners, so you are probably right. I think this may be a result of something I mentioned in terms of limitations of the super simple model I used. Specifically, as the body rolls, the CG moves with it, and so you no longer have nice right triangles for the math. In addition, the lower arms are not usually perfectly horizontal, so the lateral force will try to move the pivot point for the lower arm out, which will act as a lever to raise the car around the tire contact point.

So it may well be that the sway bar acts to reverse the roll, but other effects act to raise the car.

I'll do some research and see if I can find a detailed article on this. As I said earlier, it would be cool to develop a Matlab model and do some simulations.