Inertia force calculation during braking with ABS

[marellasunny]

When all the 4 wheels are braking,it seems logical to write the longitudinal acceleration like this-
$$m_{vehicle}.a_x = Sum of F_B $$
Where
F_B are the brake forces at the 4 wheels.
Now,what would the equation look like when ABS is working?

Some of the wheels would be braking while others would be accelerating(1.is that correct?)
Or,is it case in ABS that all the wheels are braking all the time?
I've read that the principle of the ABS is based on limiting the brake pressure.

 

[Damo ET]

I'm not sure how you would work the formula, but the principal of ABS it to prevent the wheels from locking up or under/stopping rotating. A rotating tyre has more traction than a sliding tyre, which is why it requires releasing the brake peddle (after locking up a tyre) to get that tyre rotating again (on cars without ABS). So the ABS modulates the brake peddle force applied to each set of brakes to prevent each tyre from excessively slowing compared to the others. Damo

 

[Raj]

In Normal case , ABS only controls the wheel which is in Unstable state (Locking State). The control of ABS is by giving brake pressure increase and decrease depending on the Stability condition of the wheel. So, This will make the wheel velocity from dropping immediately and reducing the slip. So, In this case, the Deceleration of the wheel is decreased slowly compared to without ABS case trying to match it with the actual vehicle characteristics. It will be a matter of seconds for which ABS operates.so, For longer time, You can use the Acceleration of vehicle same as acceleration of the wheel if you don't have the information of the wheel deceleration when in ABS.

I recommend you to take the torque equations into consideration instead of forces as you can have Engine torque(Driving Torque) , Braking torque , Inertail torque components and other componets like rolling resistance , Aerodynamic drag etc into consideration.

Please correct if what i suggested is wrong

 

[jack action]

It is still the same equation because you use the sum of each tire braking force. For more precision, the «equivalent mass» of the vehicle should be used in the equation and that will vary slightly with rotational difference in speed for each wheel.

To estimate the maximum total braking force, it is easy to average those to some value for quick estimate (which should be very similar to the non-ABS case with no sliding).

Some of the wheels would be braking while others would be accelerating(1.is that correct?)

Why would a wheel accelerate if you press the brake pedal and not the accelerator? It will either brake or roll freely. At very low speed, if you have an automatic transmission with a torque converter, some power can be transmitted to the wheel, but in most cases there will be enough engine braking to contribute to the deceleration of the vehicle.

I've read that the principle of the ABS is based on limiting the brake pressure.

Correct.

 

[marellasunny]

Thanku all.