Brake Pedal Questions

[Ahmad Rezq]

Hello everyone,
I'am Ahmad Rezq from CURT (Cairo University Racing Team).
I'am working on the brake pedal of our new car and i have some questions
Please excuse my English :D :D

1 - Pedal Geometry

321322323
I uploaded to you the geometry of the pedal and my target is to see the pedal ratio change with pedal travel
a is the total pedal length, theta is the pedal angle, d is the distance between the pedal pivot the bias bar mount , c is the length of both the master cylinder rod the balance bar end , also i set a fixed point which is on the mounted point of the master cylinder to the pedal box and i draw b with an angle of fai, and then epsi angle is as illustrated.
i used pedal ratio 6 and i calculated an initial position with pedal angle = 80 deg , and i have the value of
the length c and also the value of d so i got the initial value of b,epsi and fai . then i built a matlab code which iterated the change of this geometry with the change of the pedal angle theta. my pedal ratio is the change of the pedal arc which is delta theta * a divided by the change of length c. and i attached to you 2 graphs , first one is the change of pedal ratio with pedal travel , the second is the relation between MC travel and Pedal travel. Are these calculations right ?

2 - Pedal length
my second question is about the pedal length , I know that it depends on ergonomics , and I selected 24 CM pedal. any suggestions?

3 - Pedal Travel
I'am confused a little bit about calculating the pedal travel which locks the wheels. i got an equation from brake design and safety which i used to calculate the pedal travel.
pedal_travel(cm)=0.9*car_weight(N)*deceleration(g)/f_driver.
And due to some calculations i got maximum travel = 5 cm

thanks,

[MCoach]

Ahmad,

The first part looks good as long as long as it works well with the rest of your system. The pedal ratio shouldn't really be your main concern, but more related to your overall gain between the pedal and the input force to the tire at the contact patch. I referenced the National Highway Traffic Safety Administration (NHTSA) here in the states for subjective "optimal" values that were evaluated. There are some documents around on there website that are very, very useful for brake design in regard to driver feel and response. Are you also designing the rest of the brakes system as well?

Link: http://www.nhtsa.gov/NCSA

I've tried several different pedal lengths and overall they are mostly related to driver foot positioning and ankle angle of the driver. There isn't a big difference unless it gets uncomfortable.

The pedal travel calc may be a good reference for road cars and assuming their compliances but I don't think it would correlate very well in the racing world.
First thing to calculate for pedal travel is the fluid that must be displaced to push the pistons until they touch the rotors. With proper in-line valves, this can be made close to 0 and without can be a large component of your pedal travel without force even being applied to the tire! Pedal travel is also a component of your pedal ratio. Closer to 1:1 means the pedal travels less far to displace the same fluid from the master cylinder but also increases the force necessary to use it. Increasing the master cylinder bore also decreases your pedal travel. Most of all, look out for "wubby" things; these are things I would describe as visibly not stiff and can be anything that deflects and isn't as stiff as I want it to be. In the world of engineering, everything is a spring.

Unfortunately, the pedal travel calc is not very easy to do without a lot of information so I just base it on the (master cylinder total displaced area)/(caliper total area) and the compliance estimation of both. The higher quality the components, typically the lower the pedal travel. So, for reference full lock up for my values currently are about .2" of pedal travel locks the wheels. Don't take this as gospel though, because the values that I used to use based on the old design that was handed to me was ~2.125" of pedal travel to lock the tires.

I hope this points you in the right direction.

[Ahmad Rezq]

MCoach,

In the first thank you for your comment, I'am also making the all braking system of 2015 car. I finished the system calculations or you can say the design methodology in order to select the proper components size ( Masters - Calipers - bias ..).

I checked your link and it seems helpful, and for the pedal length actually my top target is trying to reduce pedal weight as possible, so far I reached to 200 gm with Aluminum pedal 24 cm long and when i simulated it i got Factor of safety = 3 with max displacement = 1.5 mm . and it seems acceptable for me.

For the pedal travel i will try to do much with the brake system volume analysis,


Unfortunately, the pedal travel calc is not very easy to do without a lot of information so I just base it on the (master cylinder total displaced area)/(caliper total area) and the compliance estimation of both. The higher quality the components, typically the lower the pedal travel. So, for reference full lock up for my values currently are about .2" of pedal travel locks the wheels. Don't take this as gospel though, because the values that I used to use based on the old design that was handed to me was ~2.125" of pedal travel to lock the tires.

i would like to know , what was the driver force that locks the tires for that system ( 2.125" of pedal travel )

[Jay Lawrence]

Ahmad,

Your graphs indicate pedal travel of up to 20cm!!!!!!!!!!! I would suggest something closer to 20mm.
I would also not stress too much about the mass of the components if this is your first time designing a brake system. You have stated a displacement of 1.5mm and that you are using Aluminium (assuming 6061 or similar). Remember that fatigue is a pretty critical factor for aluminium components, and the brake pedal is subject to some pretty serious fatigue style loading. Australian standards talk about a factor of something like 0.4 for yield when fatigue is considered (i.e. allowable stress = 0.4 x yield). There are other references available for this. Also don't underestimate the force that can be placed on the pedals (not sure if there's a rules mandated design load or not but I'd put something like 1000N on it).

Apart from that, ask drivers how much force they'd like to see on the brake pedal (you can design a practical experiment to determine this).

[MCoach]

Good catch on that Jay, I thought the pedal had said 20mm...

We have a paper hanging up in the design area with some design "rules". One of which says to not underestimate a scared driver. A scared driver can put 200lbs (200 is crossed out and replaced with 400lbs written in in pen) on a pedal, steering wheel or gearshift leaver.

This came about after a brake pedal was designed to the old rule and we had a failure. Aluminum did happen to be involved.

[Ahmad Rezq]

Jay Lawrence & MCoach .
I wanna explain that the 20 cm is end condition i added to my graph no more . and it's not the pedal travel to lock my wheel . due to my calculations i got 5 cm to lock my wheels

for the pedal my maximum stresses is 200 Mpa and iam using AL7075 , and according to Australian standards the pedal will fail due to fatigue. so i must reduce the stresses.

[Jay Lawrence]

Ahmad,

You don't have to comply with Australian Standards. I gave it to you as a reference for further research into fatigue loading, and I used the words 'something like 0.4' because I can't remember for sure. In fact the 0.4 may even have been from Mechanical Engineering Design by Shigley. You should have someone at your uni who can guide you better on fatigue analysis.

Your pedal travel still sounds a bit high (though not unreasonable), especially if you haven't taken into account various factors including line bulge, compliance, and calliper spreading. There are ergonomic studies that suggest that people can modulate pressure a lot better than they can modulate distance. This means that you want to minimise your pedal travel distance. This will also help with reaction/application times.

[Ahmad Rezq]

Jay Lawrence
0.4 Not definite number i know but it's some safe one , i will do more search or maybe the best way is to use the fatigue analysis , but for my point of view i think FSAE brake pedal the fatigue is not critical problem , please anyone correct me if I'am wrong ?

for the pedal travel yes 5 cm is not acceptable distance for me i will make volume analysis calculation for the system try to calculate accurate number.

[,4lex S.]

Fatigue may not be critical IF you specify a large enough ultimate load. It also depends a lot on the geometry of the part and how it has to be configured to take the load.

I recommend you take a look at the article below, which has a good outline of driver control robustness. (I recommend reading most of Pat's Corner on the FSG website)

https://www.formulastudent.de/academy/pats-corner/advice-details/article/steves-box-of-tricks/

[Bemo]

The rules already give you the number for the max. force applied to the brake pedal. They say that it has to withstand an applied force of 2000N. At least in Germany and Austria a scrutineer will sit in your car and push the brake pedal as hard as he/she can to check, if it is stiff enough. Even if nothing brakes but there is to much visible deflection during that test you will have to stiffen the whole thing.

The pedal travel is something I'd say which should just be as low as possible. The pedal should have a hard pressure point and the braking torque should be controled by the pedal force. This means you should choose a pedal force at which you want the wheels to lock, not a pedal travel. The force you choose for that is up to you. Try to do some measurements with your drivers in the driving position to determine a proper pedal force.