EBD ( Electronic Brake Force Distribution ) and Optimum Brake Force Distribution - Part 1

 Review of Weight Transfer

When we apply the braking force, weight transfer happens to the front. Therefore, front vertical force gets heavier, and rear vertical force gets lighter.

Brake force is the horizontal force proportional to the vertical reaction force. The proportional constant is tire friction coefficient μ.

The role of rear brake is very important for vehicle stability. Rear brake force should always not only keep its quantity not to provoke wheel locking but also keep its maximum quantity just below the force level causing the rear wheel locked up. That is the way to use the brake system with the maximum efficiency. 

Optimum Brake force distribution – Normalized Force

The picture above shows an optimum brake force distribution curve. Vertical axis represents normalized braking force of rear wheel Fnr, and horizontal axis represents the normalized braking force of front wheel Fnf. 

Here, the normalized force means its value is dimensionless. The two normalized forces are obtained by the corresponding brake force divided by the vehicle weight mg for the front and the rear respectively.

The reason why normalized forces are used in brake design curve is that we can design the optimum brake force distribution curve without consideration of vehicle weight. I will show you that in the brake force distribution part 2.

Optimum Brake force distribution – How to read it

The picture above explains how to read optimum brake force distribution curve. Black curve describes the optimum brake force distribution on which friction coefficients are all the same at all wheels.

The red lines with 45 degrees counterclockwise show the constant deceleration on which every point has the same deceleration value.

For example, on the line of 0.6g, every point has the same deceleration 0.6g. The same way goes in 0.5g line and 0.4g line. Therefore, every point on the line ⓐ-ⓕ has the same 0.6g, every point on the line ⓑ-ⓔ has the same 0.5g and every point on the line ⓒ-ⓓ has the same 0.4g.

ⓐⓐⓕⓑⓒⓓⓔⓖⓗⓘ

The meaning of Point ⓐ,ⓑ,ⓒ is that the rear brakes take charge of all the brake forces when front brakes fail or the front tire friction coefficient is completely zero.

Likewise, the meaning of Point ⓓ,ⓔ,ⓕ is that the front brakes take charge of all the brake forces when rear brakes fail or the rear tire friction coefficient is completely zero.

Brake force distribution – Proportioning Valve

In the picture above, black line describes the optimum brake force distribution and red lines represent the constant deceleration lines. 

Blue Line shows the characteristic curve of proportioning valve which is employed to prevent the rear wheel locking. Normally, it has two straight lines and has safety gap from the optimum brake force distribution  curve. Of course, there is proportioning valve with 3 straight lines.

The green area shows the lost rear brake forces because of proportioning valve. Proportioning valve can help the vehicle avoid wheel locking but leave the drawback of green area to be removed for brake efficiency.

Proportioning valve was widely used before EBD

When we use the proportioning valve, the rear brake forces are always lower than the optimum brake distribution curve. Therefore, we end up with the problems of small braking force at the rear wheels as follows

1. Unduly onerous burden on the front wheels
2. Requiring higher brake pedal pressure at the given deceleration.
3. Accelerating front tire and brake pad wear compared with rear ones
4. Need for bigger brake system in the front wheels compared with rear ones.

EBD can overcome the the problems listed above.

 

Brake force distribution –  EBD

EBD Stands for Electronic Brake Force Distribution.

Yellow curve describes the brake force distribution lines employed by EBD. It looks like saw shape. 

EBD makes the brake system to use the maximum rear brake forces to the full which is more than that described by the optimum brake force distribution curve.

EBD continuously measures the ratio(Rs) of rear to front wheel slip

let's look into EBD control logic from pointⓐ to pointⓒ.

  ⓐ In the braking, brake force is increasing to the point ⓐ. When Rs gets bigger than predefined                 value, EBD closes the corresponding rear brake valve not to raise that rear brake force further.                 Now, the point ⓐ moves horizontally to the point ⓑ.

  ⓑ When the driver increases the force on the brake pedal and front brake slip increases, EBD open             the corresponding valve to raise that rear brake force further. Now, the point ⓑ moves vertically             to the point ⓒ.

  ⓒ Again, When Rs gets bigger than predefined value, EBD closes the corresponding rear brake valve         not to raise that rear brake force further. Now the point  moves horizontally to the right side.

  EBD repeats the steps above many times

In this way, EBD help the vehicle use maximum rear brake forces.

You can find the same explanation in the reference book(Brakes, Brake Control and Driver Assistance Systems by Konrad Reif)

Advantages of EBD

• No need for proportioning valve
• Difference of wear between the front and the rear one can be significantly reduced for tire and brake pad
• EBD keeps brake efficiency for whole of vehicle life time.
• EBD provides optimum handling stability for all driving conditions including uphill, downhill, cornering, any kind of payload, any kind of powertrain status.
• Stopping distance with EBD can be shorter at the same pedal force
• Small additional cost is enough for EBD installation on your existing ABS.
• Front brake size(capacity) can be reduced.