Braking System Design questions

[pereira1]

Hi everyone.
My name is Amon Pereira. I'm studying at Mechanical Engineering At Purdue University. I'm currently attempting to develop the braking system of our first Formula Electric car. Through matlab calculations, I've narrowed down our brake setup to a few choices. However, I'm having trouble committing to a design.
I have a few questions that need to be answered before I can make a final decision on our brake system:

1)What kind of deceleration g's do formula sae car typically experience without an aero package?
Seeing the results of the deceleration event in Formula SAE Austria (you may see the results at the bottom of the post)I'm considering to design our car's braking system to brake at 1.5 g's. However, one of our new members who was part of another university team, pointed out that Formula student cars typically see a deceleration of 1.0g's in competition. I need to know this value to account for weight transfer properly. If I can't know what kind of deceleration our car will be capable of, our brake system will be designed to brake at certain range of braking g's. Using the bias bar would be one of the ways of designing for that range of deceleration.

2)Can FSAE car tires have a coefficient of friction of more than 1.4 ? Do I need tire consortium data or will a rule of thumb suffice?

3) Has anyone used Dynalight or Dynapro Calipers from Willwood in their brake setup ? If yes, did they provide too much of braking torque ?
Calculations were done using Dynalight and Dynapro calipers in all four tires. It was determined that this kind of setup would be adequate to decelerate at 1.5 g since it would not put a lot of strain on the driver. However this setup would be excessive if the tires can only handle a deceleration of 1.0g's before slipping. On top of this these calipers also cause the car to have a lot more unsprung mass.

4) How do PS1 Calipers perform in formula SAE applications ?
Matlab calculations revealed that using PS1 calipers to decelerate at 1.5 g's could put a big strain on the driver. In fact using a pedal leverage of 5, our driver would need to input about 800 N (!!) of force to lockup the wheels. We tried using smaller inlet bore diameters in order to decrease our Lockup pedal force. But we went over the recommended maximum master cylinder pressure rating while doing that.
Matlab also revealed that PS1's would be adequate enough to brake at 1.0g's.

5) What is maximum pedal force that a driver can input in the pedal box ?
Through research, it was determined that a typical driver can input about 150lbf in a panic situation. However the next question is, what would be an ideal pedal force to have the tires lockup at ?
Our guess would be to have the brake system lockup the wheels when the driver inputs about 120lbf of force (80% of the maximum pedal force). Would that be reasonable ? Are there any autocross or endurance racers who could shed some light on this ? What would be your ideal pedal lockup force ?

6) What kind of rotor thickness is appropriate for an FSAE car ?
Again I'm thinking of using 0.19 in or a 0.25 in thick rotor. However, I have no reasoning behind those numbers. What would be a good step to validate a rotor thickness decision ?

I would appreciate immensely if you could leave some your thoughts on these questions. If more information on our car or reasoning is needed, please do let me know.

Thanks for the help,

Amon Pereira
Purdue Electric Racing
Purdue University,
West Lafayette,
Indiana

Enclosure: Formula Austria Deceleration Event Results


Formula Austria Deceleration Results (retrieved from http://fsae.com/eve/forums/a/tpc/f/125607348/m/530104583)
BA RacIng:
- Top-Speed: 82,2 km/h, Stopped after 14,8m -> 1,795g
- Top-Speed: 98,9km/h, Stopped after 23,9m -> 1,609g
LU Motorsport:
- Top-Speed: 91,83km/h, Stopped after 20,4m -> 1,626g
- Top-Speed: 96,77km/h, Stopped after 24,97m -> 1,475g
Hawks Racing:
- Top-Speed: 56,7 km/h, Stopped after 7,9m -> 1,600g
- Top-Speed: 95,24km/h, Stopped after 24,36m -> 1,464g
TU Graz:
- Top-Speed: 97,297km/h, Stopped after 23,53m -> 1,582g
TU Vienna:
- Top-Speed: 93,26km/h, Stopped after 21,9m -> 1,562g
Beaver Racing:
- Top-Speed: 94,7km/h, Stopped after 23,35m -> 1,510g
Raceyard Kiel:
- Top-Speed: 60,9 km/h, Stopped after 12,4m -> 1,176g
- Top-Speed: 84,9km/h, Stopped after 19,26m -> 1,472g
Elephant Racing:
- Top-Speed: 67,16 km/h, Stopped after 12,27m.-> 1,446g
UAS Graz:
- Top Speed: 84,91km/h, Stopped after19,75m -> 1,436g
Unical Reparto Corse:
- Top-Speed: 62,93km/h, Stopped after 10,9m -> 1,429g
ETS Motorsports:
- Top-Speed: 88,64 km/h, Stopped after 21,8m -> 1,417g
TU Fast:
- Top-Speed: 82,9km/h, Stopped after 19,5m -> 1,386g
- Top Speed: 84,91km/h, Stooped after 20,95m -> 1,353g
CAT Racing:
- Top-Speed:82,5 km/h, Stopped after 19,32m -> 1,385g
Dynamics e.V.:
- Top-Speed: 92,783km/h, Stopped after 24,6m -> 1,376g
KA RacING:
- Top-Speed: 77,86km/h, Stopped after 18,0m -> 1,325g
munichHMotorspot:
- Top-Speed: 85,71km/h, Stopped after 22,2m -> 1.301g
Infinity Racing:
- Top-Speed: 72,58km/h, Stopped after 16,01m -> 1,294g
fast forest:
- Top-Speed: 77,25km/h, Stopped after 19,7m -> 1,197g

[Edward M. Kasprzak]

A few references:

https://www.formulastudent.de/academy/pats-corner/advice-details/article/how-to-make-a-correct-design-and-layout-of-your-brake-system/

https://www.formulastudent.de/academy/pats-corner/advice-details/article/steves-box-of-tricks/1/ (discussion of braking starts at the bottom of the page)

[Jay Lawrence]

Hi Amon,

Your results tell you up to ~1.8g's, so that would be your maximum design deceleration. From memory we designed for about 1.6.

Your calipers will provide however much torque your system tells them to (this is determined by your drivers left leg, pedal ratio, master cylinders, bias, etc.)

If you are worried about the amount of force required, build some adjustability into your system (maybe have 3 different mounting points on your pedal so that you get different pedal ratios). For what it's worth, 800N is high but not too unreasonable. I drove an old F1 car last year and the instructor told me that it was designed for 700N, and it felt fantastic (albeit with big slicks, wings, higher speeds, and carbon rotors).

Rotor thickness will be a compromise between (at least) heat dissipation, available materials, and rotating mass.

Edward's links should reinforce all this as well, and from memory there's a good braking design guide amongst Claude's Optimum G stuff.

[MCoach]

1)What kind of deceleration g's do formula sae car typically experience without an aero package?
Seeing the results of the deceleration event in Formula SAE Austria (you may see the results at the bottom of the post)I'm considering to design our car's braking system to brake at 1.5 g's. However, one of our new members who was part of another university team, pointed out that Formula student cars typically see a deceleration of 1.0g's in competition. I need to know this value to account for weight transfer properly. If I can't know what kind of deceleration our car will be capable of, our brake system will be designed to brake at certain range of braking g's. Using the bias bar would be one of the ways of designing for that range of deceleration.

If a driver was decelerating at 1g on our team, I would simply ask them to brake harder. 1.5 g's is a good reference.


2)Can FSAE car tires have a coefficient of friction of more than 1.4 ? Do I need tire consortium data or will a rule of thumb suffice?

Rule of thumb is fine unless you want to really complicate things. Which you really don't need to. 1.5g reference it is.

3) Has anyone used Dynalight or Dynapro Calipers from Willwood in their brake setup ? If yes, did they provide too much of braking torque ?
Calculations were done using Dynalight and Dynapro calipers in all four tires. It was determined that this kind of setup would be adequate to decelerate at 1.5 g since it would not put a lot of strain on the driver. However this setup would be excessive if the tires can only handle a deceleration of 1.0g's before slipping. On top of this these calipers also cause the car to have a lot more unsprung mass.

We used to use the Dynalight on our cars back in like 2006. That's a beastly caliper you have there. Considering it's size, I'm guessing you want to use 13 wheels. Plenty of room for big brakes. However, I would choose something much smaller. The brakes we ran last year had a 1" diameter piston, 4 front each, and two rear each. Smooth as a baby's bottom on braking. The rear calipers we ran weighed half a pound each loaded with brand new pads.

4) How do PS1 Calipers perform in formula SAE applications ?
Matlab calculations revealed that using PS1 calipers to decelerate at 1.5 g's could put a big strain on the driver. In fact using a pedal leverage of 5, our driver would need to input about 800 N (!!) of force to lockup the wheels. We tried using smaller inlet bore diameters in order to decrease our Lockup pedal force. But we went over the recommended maximum master cylinder pressure rating while doing that.
Matlab also revealed that PS1's would be adequate enough to brake at 1.0g's.

Max line pressure is not really a hard limit....more like a suggestion. Just take that and multiply by 1.5x. There, now you have a new maximum line pressure reference. :) I think AP used to rate their motorcycle calipers to 4000 psi line pressure (2000 psi?) and have since reduced it to 1000 psi without changing the design, just looking for a larger safety factor to sell by. The PS1's are adequate to use for even an aero car. Toledo used them on all four wheels last year.

5) What is maximum pedal force that a driver can input in the pedal box ?
Through research, it was determined that a typical driver can input about 150lbf in a panic situation. However the next question is, what would be an ideal pedal force to have the tires lockup at ?
Our guess would be to have the brake system lockup the wheels when the driver inputs about 120lbf of force (80% of the maximum pedal force). Would that be reasonable ? Are there any autocross or endurance racers who could shed some light on this ? What would be your ideal pedal lockup force ?

We have a "motivational design poster" hanging in our office of mistakes and things to look out for when designing. On that poster we have written, "a frantic driver can put 250lbs into a gear lever or pedal" with 250lbs struck out and 450lbs written in it's place. I can leg press upwards of 300lbs and I'm not a very big guy. Think of what a driver weighing 220lbs and built to play football can do...because you might end up with one of those guys, we did.

I've personally designed between 75lbf - 120lbf pedal input force with some success. Maybe cite an ergonomic paper or something similar. We just did so out of keeping the drivers comfortable. I don't want to attempt to crush an elephant when using the brakes, nor trying to sneak past my parents room coming home late from a party; I want something comfortable that feels natural.



6) What kind of rotor thickness is appropriate for an FSAE car ?
Again I'm thinking of using 0.19 in or a 0.25 in thick rotor. However, I have no reasoning behind those numbers. What would be a good step to validate a rotor thickness decision ?

That rotor thickness sounds beefy as well, more suited for something like a Formula Ford. Since 2011, I've varied our iron-based rotors from 3mm (.118") to 5mm( .196") in thickness. I don't replace them until they've worn to 2.5 mm (.098") which seems to blow some peoples mind. *poof*

Want an easy way to simulate a rotor use? I've suggested this in other threads, but don't want to be bothered to dig it up. Think back to physics 1. It's all about F=ma.
F=ma
F=ma
F=ma

Good. Now, that that is clear. The force you are looking for is the force of the car decelerating (negative acceleration if you're a phys or math major, they hate that word). How do you solve that? Easy, there is one unknown. F = (mass of car {including driver!}) x (deceleration of car). You've already assumed a deceleration, 1.5Gs. Now I'm going to assume a mass, 600lbs. 1.5 x 600 lbs = 900lbs of force. That's what you're trying to stop. But, it's not just that, it's kinetic energy. Back to phys 1 again.

KE = 1/2mv^2.
Sound familiar? It should. We want to get rid of all of that energy. But we really can't, we can only convert it to some other form of energy. We want to use the brakes to change that energy into heat using friction, just like rubbing your hands together to generate heat on a cold day in the heartland of Detroit. Let's assume there is 0% cooling, 0% losses, lumped sum mass, and 100% efficiency in our system. This reduces our brake model to two equations that equal our input and output. We already have the input, let's check out the output:

The output will be heat. How much does your rotor heat up? Glad you asked! The temperature of an object is governed by several aspects of the material itself.
Q = Cp(m)(delta T)
Q = change in enthalpy
Cp = heat capacitance of the material. This will be different for steel, cast iron, titanium, plastic, coal, a fuzzy bunny, etc.
m = mass of the material.
delta T = change in temperature.


You can use any units you like, just make sure they are consistent. So, these two equations will constitute our thermal brake model.

I'm going to make a small tweak here to our equations.

1/2mv^2 --> 1/2m(v1 - v2)^2
Now we can find the energy generated from a differential in speed, so 60mph to 30mph or whatever you're interested in.
The input to the rotor will be equal to the energy that needs to be dissipated by the car:

KE = Q

1/2mv^2 = Cp(m)(delta T)

([1/2]*m*(v1-v2)^2)/(Cp * m) = delta T


Using this, you can find what the temperature rise is over a single stop, run it several times for several straights and add cooling equations to find what it will do during a lap, and you'll see a lot of what's going on. Typically you want to keep your rotor under melting and in the range of whatever your brake pads work at.


Hope this helped. Feel free to PM me.

[pereira1]

A few references:

https://www.formulastudent.de/academy/pats-corner/advice-details/article/how-to-make-a-correct-design-and-layout-of-your-brake-system/

https://www.formulastudent.de/academy/pats-corner/advice-details/article/steves-box-of-tricks/1/ (discussion of braking starts at the bottom of the page)

Dr. Kasprzak

Thanks for the reference documents !

Regards,

Amon Pereira

[pereira1]

1)What kind of deceleration g's do formula sae car typically experience without an aero package?
Seeing the results of the deceleration event in Formula SAE Austria (you may see the results at the bottom of the post)I'm considering to design our car's braking system to brake at 1.5 g's. However, one of our new members who was part of another university team, pointed out that Formula student cars typically see a deceleration of 1.0g's in competition. I need to know this value to account for weight transfer properly. If I can't know what kind of deceleration our car will be capable of, our brake system will be designed to brake at certain range of braking g's. Using the bias bar would be one of the ways of designing for that range of deceleration.

If a driver was decelerating at 1g on our team, I would simply ask them to brake harder. 1.5 g's is a good reference.


2)Can FSAE car tires have a coefficient of friction of more than 1.4 ? Do I need tire consortium data or will a rule of thumb suffice?

Rule of thumb is fine unless you want to really complicate things. Which you really don't need to. 1.5g reference it is.

3) Has anyone used Dynalight or Dynapro Calipers from Willwood in their brake setup ? If yes, did they provide too much of braking torque ?
Calculations were done using Dynalight and Dynapro calipers in all four tires. It was determined that this kind of setup would be adequate to decelerate at 1.5 g since it would not put a lot of strain on the driver. However this setup would be excessive if the tires can only handle a deceleration of 1.0g's before slipping. On top of this these calipers also cause the car to have a lot more unsprung mass.

We used to use the Dynalight on our cars back in like 2006. That's a beastly caliper you have there. Considering it's size, I'm guessing you want to use 13 wheels. Plenty of room for big brakes. However, I would choose something much smaller. The brakes we ran last year had a 1" diameter piston, 4 front each, and two rear each. Smooth as a baby's bottom on braking. The rear calipers we ran weighed half a pound each loaded with brand new pads.

4) How do PS1 Calipers perform in formula SAE applications ?
Matlab calculations revealed that using PS1 calipers to decelerate at 1.5 g's could put a big strain on the driver. In fact using a pedal leverage of 5, our driver would need to input about 800 N (!!) of force to lockup the wheels. We tried using smaller inlet bore diameters in order to decrease our Lockup pedal force. But we went over the recommended maximum master cylinder pressure rating while doing that.
Matlab also revealed that PS1's would be adequate enough to brake at 1.0g's.

Max line pressure is not really a hard limit....more like a suggestion. Just take that and multiply by 1.5x. There, now you have a new maximum line pressure reference. :) I think AP used to rate their motorcycle calipers to 4000 psi line pressure (2000 psi?) and have since reduced it to 1000 psi without changing the design, just looking for a larger safety factor to sell by. The PS1's are adequate to use for even an aero car. Toledo used them on all four wheels last year.

5) What is maximum pedal force that a driver can input in the pedal box ?
Through research, it was determined that a typical driver can input about 150lbf in a panic situation. However the next question is, what would be an ideal pedal force to have the tires lockup at ?
Our guess would be to have the brake system lockup the wheels when the driver inputs about 120lbf of force (80% of the maximum pedal force). Would that be reasonable ? Are there any autocross or endurance racers who could shed some light on this ? What would be your ideal pedal lockup force ?

We have a "motivational design poster" hanging in our office of mistakes and things to look out for when designing. On that poster we have written, "a frantic driver can put 250lbs into a gear lever or pedal" with 250lbs struck out and 450lbs written in it's place. I can leg press upwards of 300lbs and I'm not a very big guy. Think of what a driver weighing 220lbs and built to play football can do...because you might end up with one of those guys, we did.

I've personally designed between 75lbf - 120lbf pedal input force with some success. Maybe cite an ergonomic paper or something similar. We just did so out of keeping the drivers comfortable. I don't want to attempt to crush an elephant when using the brakes, nor trying to sneak past my parents room coming home late from a party; I want something comfortable that feels natural.



6) What kind of rotor thickness is appropriate for an FSAE car ?
Again I'm thinking of using 0.19 in or a 0.25 in thick rotor. However, I have no reasoning behind those numbers. What would be a good step to validate a rotor thickness decision ?

That rotor thickness sounds beefy as well, more suited for something like a Formula Ford. Since 2011, I've varied our iron-based rotors from 3mm (.118") to 5mm( .196") in thickness. I don't replace them until they've worn to 2.5 mm (.098") which seems to blow some peoples mind. *poof*

Want an easy way to simulate a rotor use? I've suggested this in other threads, but don't want to be bothered to dig it up. Think back to physics 1. It's all about F=ma.
F=ma
F=ma
F=ma

Good. Now, that that is clear. The force you are looking for is the force of the car decelerating (negative acceleration if you're a phys or math major, they hate that word). How do you solve that? Easy, there is one unknown. F = (mass of car {including driver!}) x (deceleration of car). You've already assumed a deceleration, 1.5Gs. Now I'm going to assume a mass, 600lbs. 1.5 x 600 lbs = 900lbs of force. That's what you're trying to stop. But, it's not just that, it's kinetic energy. Back to phys 1 again.

KE = 1/2mv^2.
Sound familiar? It should. We want to get rid of all of that energy. But we really can't, we can only convert it to some other form of energy. We want to use the brakes to change that energy into heat using friction, just like rubbing your hands together to generate heat on a cold day in the heartland of Detroit. Let's assume there is 0% cooling, 0% losses, lumped sum mass, and 100% efficiency in our system. This reduces our brake model to two equations that equal our input and output. We already have the input, let's check out the output:

The output will be heat. How much does your rotor heat up? Glad you asked! The temperature of an object is governed by several aspects of the material itself.
Q = Cp(m)(delta T)
Q = change in enthalpy
Cp = heat capacitance of the material. This will be different for steel, cast iron, titanium, plastic, coal, a fuzzy bunny, etc.
m = mass of the material.
delta T = change in temperature.


You can use any units you like, just make sure they are consistent. So, these two equations will constitute our thermal brake model.

I'm going to make a small tweak here to our equations.

1/2mv^2 --> 1/2m(v1 - v2)^2
Now we can find the energy generated from a differential in speed, so 60mph to 30mph or whatever you're interested in.
The input to the rotor will be equal to the energy that needs to be dissipated by the car:

KE = Q

1/2mv^2 = Cp(m)(delta T)

([1/2]*m*(v1-v2)^2)/(Cp * m) = delta T


Using this, you can find what the temperature rise is over a single stop, run it several times for several straights and add cooling equations to find what it will do during a lap, and you'll see a lot of what's going on. Typically you want to keep your rotor under melting and in the range of whatever your brake pads work at.


Hope this helped. Feel free to PM me.


Hi Mcoach,

Thanks for sharing your experience amongst us. I have a follow-up question on the maximum line pressure. Do you know the maximum line pressure for wilwood master cylinder and calipers ?
According to Wilwood representatives, Wilwood tests their product to about 1200 psi. 1500 psi is their spec for maximum pressure in the master cylinder.

I asked what happens when 1500 is reached and this is what they replied:
Question: " Does master cylinder failure occur when the pressure in cylinder reaches or exceeds 1500 psi ? Or does that happen in the 1200-1500 psi interval.

Answer from Willwood: " Wilwood calipers may not fail at 1500 psi, this is the maximum safe pressure to preserve seal life and premature damage to the bore.:

What do you think about the maximum line pressure given this information. Do you know if wilwood puts a large factor of safety in their design ?

On the topic of factor of safety, the "Brake Handbook" by Fred Puhn says that implementing a brake system factor of safety of at least 3 is vital since the brake is a very important car system. To what factor of safety should the master cylinder side of the brake system be designed to ?
My take on this, is to design the master cylinder to at least 1.5 factor of safety.

Any thoughts ?

[Francis Gagné]

Hi Mcoach,

Thanks for sharing your experience amongst us. I have a follow-up question on the maximum line pressure. Do you know the maximum line pressure for wilwood master cylinder and calipers ?
According to Wilwood representatives, Wilwood tests their product to about 1200 psi. 1500 psi is their spec for maximum pressure in the master cylinder.

I asked what happens when 1500 is reached and this is what they replied:
Question: " Does master cylinder failure occur when the pressure in cylinder reaches or exceeds 1500 psi ? Or does that happen in the 1200-1500 psi interval.

Answer from Willwood: " Wilwood calipers may not fail at 1500 psi, this is the maximum safe pressure to preserve seal life and premature damage to the bore.:

What do you think about the maximum line pressure given this information. Do you know if wilwood puts a large factor of safety in their design ?

On the topic of factor of safety, the "Brake Handbook" by Fred Puhn says that implementing a brake system factor of safety of at least 3 is vital since the brake is a very important car system. To what factor of safety should the master cylinder side of the brake system be designed to ?
My take on this, is to design the master cylinder to at least 1.5 factor of safety.

Any thoughts ?

First off, I agree with most what Mcoach said. I would bet wilwood puts a large factor of safety in their design, but you should too. It is also true that the brakes are a safety critical part of the car!

Your safety of factor depends heavily on what you are basing it on. You should have two case, a panic braking, MAXIMUM driver leg force, you system should be able to resist this load at least one time. If wilwood is confident on a max pressure of 1500 psi, then go with that. If you really need more pressure, buy them, buy spare seals, and pressure test them before going on the track! In this case, the safety factor is 1 compared to the spec, which as a safety factor of who knows.

The other case is the normal braking case (1.5gs or any other set goal). It is safer to keep at or under the 1200 psi line, since it will/should be repeated lots of time. For the operation, we used to have a 550 N leg force, which is a bit less than the driver weight. Our justification was that most people can lift themselves on one leg multiples times without fatigue.

If you are near/over the limit of your calipers or MCs in term of pressure, you should buy some spare seals, they are usually pretty cheap anyway. If you plan of using them multiple years, rebuild them each year. And always inspect the car for any leaks before (and after) going on the track. (You should anyway, whatever pressure you have, you just need to be more rigorous)

Don't forget that not just pressure influence the resistance and wear of your seals. Factors that the FoS englobes : age, wear, type/quality of fluid, temperature! (brakes get hot), outside humidity. We used to have AP CP4226 in the rear, we used the same brakes for 3 years, pretty much in the same pressure design range, one afternoon we blown the seal and had little balls of fire inside the wheel! We did not had the seal on hand so we lost some valuable track time waiting for those to ship! We rebuild them, and used them another 2 years after without issue.

@Mcoach, AP Racing might have not change the casing, but they might have change the seals (Cheaper? more temperature resistant?) that could have affected the rated pressure. Or they changed the quality of the bore machining, which impacts the sealing and wear capability also. Or maybe they had problems with user at high pressure and safeguard themselves even though they really can withstand repeated high pressure, but IMO we can't assume that.

[Charles Kaneb]

Make sure that your secondary systems are up to the forces your driver can produce. Every action has an equal and opposite reaction.

One of my karting friends complained about excessive braking force required. It turns out that the bushing at the bottom of the pedal had seized. She broke the seat trying to get the kart stopped...

A scared man can apply 500# of force to a pedal with one leg and half a ton with two. That's 2000 N. The rules say your pedal has to stand up to at least 1800 N

[MCoach]

1500psi is on the high end of what we've seen for normal braking. Are you exceeding that on normal braking calcs or the panic braking calcs?

We've assumed a tire mu, but I curious what you are using for a brake pad mu?
It's nearly impossible to come up with that value unless you have a reference temperature-pad mu curve, or you can estimate an operating value.
I'm also curious what pad material and rotor size you've chosen. It'll tell me a lot about the rest of the system. If your hydraulic (MC:Caliper) and mechanical (pedal ratio) ratios are really low, there may be an error in your calcs.

Seals are a big thing, bore integrity is another one, but I feel more comfortable pushing the safety factor on parts that I know are replaceable. The caliper housing itself will take literally thousands of psi, but the seals and pistons may be the weak point. Good thing those parts are replaceable.

[MCoach]

Double post. Derp.

Here is the temperature-mu curve I was talking about:
http://www.wilwood.com/BrakePads/BrakePadsApp.aspx

It's easy enough to pick an 'operating temperature' at say 600F or 800F or whatever to pull a 'static' mu value for calcs.
If you are feeling adventurous and MATLAB adept, you can redraw the whole curve and use it to find the balance of your car through various states of braking. It can give an idea of how close to ideal braking you want to get without running into front/rear brake lock up reversal. Honestly, I don't bother with that and just get it in the range of +/- 5% balance of git'er'done. After that, the driver and set up makes a big enough difference to void anything closer to 'perfect'.

It makes it difficult to aim for ideal when one driver is 100lbs and the next is 250lbs. Throw a brake bias knob at them and they'll figure it out on their own when they get in the car.

[Francis Gagné]

MCoach,

The only issue with this caliper design, is that the only pad available for the PS-1 is Sintered Metallic (SM), which the temperature-mu curve falls under the TBD category. The only information available is :


Formulation for Power Sports and Industrial applications. High friction
excellent cold torque response, medium temperature range

And then they say :


Medium friction compound with very little change in friction throughout its temperature range
Good wear and friction properties with a moderate tempearature range.

It seems it is "High" and "Medium" friction at the same time? Anyway, at least it seems the mu is pretty constant with temperature, which should simplify things not having the data. Then the only question will be by how much your pedal force / ratio is off in your design.

It is a design pad for steel rotors, so I would guess it more in the upper temperature range compared to the pads designed for aluminum. They say Medium temperature range, so probably 500F to 1000F. In this range, their Medium-high friction pads fall into the .55 to 0.65 CoF. But all those pads are Race Only, the SM is street use ok. The guess would be somewhere in between 0.45 and 0.55 CoF. But this is all pure speculation! So in all the cases, the design should work to lock up the wheels with the lowest Mu at your highest «operating» driver force.

If you absolutely want data for the pads, you will need to machine other pads to fit the caliper, bit of an hassle for nothing I think.

Make sure that your brake balance adjustement range at your operating conditions covers your incertitude range on the pads CoF, and then test, and retest!

[MCoach]

Bastards. That data would be useful!

We used to run the purple pads coupled with our infamous aluminum brake rotors. There isn't any data for those but our mu estimate was .47. Yeah, that could be a slight problem. Maybe someone on here who's run the Wilwood PS-1 can chime in for us.

In relation to the bias bar comment, what type of master cylinders do you run? What I've done recently is use the push type bearing supported master cylinders that allow me to design variable pedal ratios into it's mounting bracket. I can estimate a range of the overall gain I'm aiming for and then dial it in that way.

[Owen Thomas]

About the PS-1 pads; I have an email from a rep at Willwood stating "The Sintered Metallic pad has a 0.60 CF at 200 degrees Fahrenheit" after asking about friction properties. I took this to assume that they have some pretty good bite at low temps, but are susceptible to fade when they're worked hard. Similar to typical "road car" pads, which is not surprising given that they are labeled as industrial and not race pads.

Regarding caliper/mc pressure, all the components will be rated and tested at a higher pressure than stated on the spec sheet (safety, quality, etc). But, the component in question (calipers especially) were DESIGNED to operate within a pressure range. If you run a caliper rated for 800 psi at 1200, it might not fail right away or ever, but how much unwanted flex do you think might show up and give you a spongy pedal anyways? I'd be willing to bet it is significant.

[MCoach]

Owen, are you a user of the PS-1 calipers? Any concerns about using them relating to OP?

[pereira1]

1500psi is on the high end of what we've seen for normal braking. Are you exceeding that on normal braking calcs or the panic braking calcs?

We've assumed a tire mu, but I curious what you are using for a brake pad mu?
It's nearly impossible to come up with that value unless you have a reference temperature-pad mu curve, or you can estimate an operating value.
I'm also curious what pad material and rotor size you've chosen. It'll tell me a lot about the rest of the system. If your hydraulic (MC:Caliper) and mechanical (pedal ratio) ratios are really low, there may be an error in your calcs.

Seals are a big thing, bore integrity is another one, but I feel more comfortable pushing the safety factor on parts that I know are replaceable. The caliper housing itself will take literally thousands of psi, but the seals and pistons may be the weak point. Good thing those parts are replaceable.

MCoach,

I did make a mistake in my calc. My equations were in fact over predicting the torque the brake system would have to provide in order to have the car brake at 1.5 g's. With the mistake corrected, the line pressures are just as you said earlier not close to the 1200 psi limits.
I wish I had seen this mistake much earlier this semester.

I was using a brake pad mu of 0.6.

[MCoach]

Excellent. Glad you found that.
I'm currently chasing a similar thing on my end. Trying to figure out why my calcs predict some value and it takes 3/4 of that to actually lock up the tires....
The hunt continues.

0.6 seems reasonable considering the input from Owen.

[Jay Lawrence]

MCoach, just taking a stab in the dark but have you tried to physically lock the tyres from high speed with gradual brake application? Typically the lockup test is done with a very quickly applied stab, and I imagine this would be quite different from the tyres perspective than a gradual application (someone can probably explain why a lot better than I can. In fact I hope someone does; would certainly explain why the correct braking technique works better). Other possible causes could be the interaction between pad and rotor, especially if you have drilled/grooved rotors and non-tapered pads, but once again I'm just guessing.

[Francis Gagné]

@Jay

The difference in needed locking force between a very fast or slower brake application reside in part in the dynamic behavior on the tire. Look at this paper: http://soliton.ae.gatech.edu/labs/ptsiotra/Papers/vsd02.pdf they model the tire longitudinally considering the tire relaxation and then make a ABS model with it. I do believe that FSAE tires exhibits similar behavior, excepts that the relaxation length would be shorter, I have no data on this whatsoever.

My simplified interpretation is that, when applying the brake as a dirac, the slip ratio will augment rapidly since the tire forces are smaller than in its steady state behavior. By the time the tire reaches it's steady force, the slip ratio is already higher than the peak slip ratio of the tire. Therefore, the needed torque to overgo the peak is lower. There will also be temperature related effects of both your tire and your brake rotor/pad that will affect there CoF, in this case I have no data on this, so I have no idea how much of role it plays in this.

Interesting to note that in the LuGre model (which seems to have a good correlation with dynamic experimentation from what I have read), the peak friction diminishes with speed. The faster to go, the less brake torque you need to lock. It is also another reason why the acceleration event is won in the first few meters!


@Mcoach

How did you measured your locking force?

[MCoach]

Yeah, we were finally getting data from that a few weeks ago. Rotors have a smooth surface, no slots or holes. Max decel testing from ~60mph with some runs of gradual lock up. Everything seems to line up except line pressure. My guess is underestimating efficiency of the system. We used to use really, really poor MCs. I apply an efficiency factor (F_w, Force_wasted) for compliance in the system because it used to be that big of a deal. The other culprit could be underestimating the brake pad friction. There could also be a bubble in the line where I my sensor is located...

We're running more testing this week, so I won't have time to chase it for a bit. Need to look over the data as we go to keep up.

[Jay Lawrence]

Francis,

Thanks very much for that, I was thinking along those lines also. The other thing I considered was that perhaps a step input into the system would cause the dampers to operate in a possibly less controlled zone (somewhere between high speed damping and low speed damping) thus reducing contact patch control.

[Owen Thomas]

Owen, are you a user of the PS-1 calipers? Any concerns about using them relating to OP?

Yes, I switched us to the PS-1's on the rear this year. They are currently on a shelf waiting to be put onto the 2014 car, however, so they are untested. I am not worried about over pressure because the system is designed to lock the tires at ~600 psi. Reading through this thread made me realize that I forgot to include efficiency in my numbers, but still not worried.

Sorry it took so long to get back to this, hope the information helps.

[EPMPaul]

6) What kind of rotor thickness is appropriate for an FSAE car ?
Again I'm thinking of using 0.19 in or a 0.25 in thick rotor. However, I have no reasoning behind those numbers. What would be a good step to validate a rotor thickness decision ?


The best reference I've found for sizing rotors is Rudolf Limpert's Brake Design and safety(there,s a copy at your uni's library). The third chapter on thermal design give some hand/Excel Calcs which should enable you to size your rotors fairly quickly(like one afternoon). The way I did it was to use OptimumLap to get an idea of how many braking zones there are and how long a braking event lasts for a given circuit(I used Lincoln),as well as the time between braking events. There's then a scenario of repeated braking in the thermal design chapter for solid rotors(close enough in our case). There's also some correlations for convection coefficient providing you don't actively cool your rotors(which I haven't seen yet in FSAE).

The combination of the above factors yields a temp graph that looks something like the photo. While it's probably not the nicest way to size rotors it will give you an idea of what kind of thermal mass you'll need to not boil the crap out of your brake fluid. Also, note that the ups and downs of the braking- cooling cycle aren't presented.

In my case they're probably still a little oversized. One cute thing this chart shows though is that the proper amount of thermal mass for endurance might not be the right amount of thermal mass for endurance(yes i know tech wise it doesn't work and the difference in inertia is probably negligible enough but hey just saying).

in the chart I show it takes something like 70 braking events(~5 laps) to get the entire setup up to temperature(so you'll need more brake pressure to brake during the autocross event than at the end of the endurance). One thing that can also be peculiar is that front and rear pads don't necessarily have similar temperature characteristics (depending on whether you use similar compounds front and rear.)which should make for some strange bias effects(One more reason to have adjustable bias providing your drivers sort of know where to go with it).

One last thing. Last year we ran our car mostly in a parking lot on a fairly low course speed with a short intervals between brake events. This resulted in some rather hot brakes(think 800°C in peak as per our thermal paint). So something to keep in mind when designing is where you test also. Not the case for everybody but from a brakes point of view, comp isn't necessarily the worst case scenario. Our rotors didn't go over 300°C at Lincoln last year. so yeah pretty violent difference


Concerning the relaxation length of the tires, you don't seem to have access to TTC data. If you did I think BillCobb posted and example code for fitting relaxation length by siumulating the test using an already existing model and recreating the testing cycle. you can then use a correlation factor between a given relaxation length and your fit to find the "real" relaxation length. Keep in mind this is for the TTC conditions so just at one speed. Might vary with speed though I seem to remember a mention of it in the historical part of RCVD. Personnaly I have other fish to fry but if you want to bust it is possible using TTC data. As for overall levels of grip the data from austria is probably a better guide than the TTC data for your purposes seeing as there are some fairly large differences in grip between reality and TTC(a good 30-35% as per the orginal TTC paper).

As fir friction coefficient of the pads. The number vary pretty wildly. For the AP Racing pads it looks like 0.39 throughout the temp range from what I remember. We're changing to ISR on the front his year and we contacted a pad manufacturer and he sent some data with a peak at like 0.55. try changing those values in your excel sheet and you'll see it gives some pretty wild results. The 0.55 was for a competition pad whereas the 0.39 is for a more conservative semi street type of application.

http://www.ferodoracing.com/it/motorcycle/array_cooling.htm

This should give oyu an idea of just how much your compound can fuck your calcs up. Also wear isn't much of an issue in FSAE but it is highly temperature dependant. So not an absolute like the table shows. We don't run enough to make a large difference but if your sticky pads disappear in two endurances because you're cookin em, life might get expensive.

Another interesting thing with that chart is that peak friction coefficient occurs at something like 400°C. Dependant on the manufacturer it varies but mostly it hangs around 3-400°C in Iron rotor /compounds. Another thing I discovered recently like literrally 2 weeks ago(from SBS; they have some really nice tech specs btw) is that your coefficient of friction is also dependant on rubbing speed and pad pressure. this varies by about 5-10% so leaving yourself some margin for error is probably a good idea.

That's it for me. I've probably missed a couple points but whatever. and gone on a little too much on others but it might fill in a couple of the blanks that are left here and there

[MCoach]

The point about pad friction compound is very valid. A large part of why I considered an adjustable pedal ratio in the first place. Switching to the ISR calipers, we didn't know what we were getting into. I didn't know it would be .37 or .6 or anything anywhere in between. The only thing I was aware of is that people were reporting is that they were super sweet, lightweight, a bit on the expensive side, radial mount, and wore out the pads quickly. Fortunately, I made an accurate guess and we settled in the sweet spot of driver force input. The pad wear problem, we never actually ran into. It may have been the conservative rotor design, or the operating temperature, but we just changed our first set of pads. We went through 5 sets of tires before we changed our first set of pads. And the rears still looked brand new! The fronts seemed to have a slight inclination to them, little bit of tapering, but ultimately worn out.

It may be because we were operating at a higher range than most teams, but again, I cannot validate our success with pad wear this year, yet. I can say that we run rotors that are thinner than the ones used by ETS. ETS had teething problems last year testing their rotors. They shattered 8 sets I believe I was told, but again, it's just one of those things to look out for.

I'd go on to claim that most of the brake systems used in FSAE are oversized for their application.

[angel_aso]

Back to the topic of rotor temperature evolution, I made a little model of our own rotors to see how the temperature would vary during the endurance event.

First I collected the speed and brake line pressure data collected by the sensors in a past event. This information helped me to know: Initial speed, final speed, braking time and time between braking applications. I wrote down this information for every single stop of an arbitrary lap. I also had the temperature of each rotor collected by the sensors.

For the model, I built in Matlab a little programm using finite differences and assuming one-dimensional heat transfer (perpendicular to the rotor). The boundary conditions were q=0 on the simmetry axis and a constant flux+convection at the surface during braking time. During the time between stops, only convection.

For the energy into the rotors the following formulas were used:
Front:
E = 1/2*m*(vi^2-vf^2)*brake bias*1/2*fraction into pad
q = E/(braking_time*Total area of front rotor) ---> The area includes both sides
Rear:
E = 1/2*m*(vi^2-vf^2)*(1-brake bias)*1/2*fraction into pad
q = E/(braking_time*Total area of rear rotor) ---> The area includes both sides

The results of the simulation are shown in the image attached.

The problem is that this data doesn't correlate with the data gathered by the temperature sensors of the car, which show maximum temperatures of around 250ºC for the front rotors and 120ºC for the rear rotors. I have used a heat transfer coefficient (h) of around 100 plus an equivalent h for ratiation that depends on temperature.

Does someone know which temperaures are common for the endurance event? And for EPMPaul, which imput values did you use for your model (cooling time between stops, inital speed...)?

Using an alternative simple lumped system model, as described in Rudolf Limpert's book, I obtained the results of the second image.

162163

[Goost]

angel_aso,

It looks to me like q has units Watts/m^2, was this intentional?
Not quite following; what does 'fraction into pad' mean? is it (1-fraction_into_tires)? how did you find the value?

I'm not sure about the 'constant convection' assumption. shouldn't the equation be

q_dot = h*A*(T_rotor-T_ambient)*dt (1)

it's nonlinear in time so you can't assume a constant convection.

A friend of mine wrote a paper on this a few years ago (SAE 2006-01-1975), I should probably just refer you to that.

if I recall, that h value of 100 (if the units are Watts/(m^2*C)) is decent (bit high maybe); I think you will find experimentally it will vary with both time and rotor temperature too...

It's one of these issues where, to make your data match, you might end up needing a complex definition of the simple value for 'h' because you used a simple definition of a complex system to reduce it to that single constant.

Hope it helps, heat transfer is, I admit, not my forte.

[Buckingham]

Keep in mind that the section of rotor under the pad, the section just leaving the pad and the section of rotor just entering the pad will be different temperatures during braking. This might change what you consider your Maximum temperature to be. Make sure your model matches your measurement.

[angel_aso]

Goost,

the units are intentionally in W/m^2, so for example, the convective heat flux is: q(W/m^2) = h(W/m^2*K)*(T_rotor - T_surface)
As for the heat transfer coefficient, I know that I could include a more realistic vaule that varies with speed and temperature, but since the constant value I used is quite high as you said, I would obtain an even higher temperatures in the simulation.
With the "fraction to the pad" coefficient I wanted to take into account that when the heat is generated by the friction between rotor and pad, part of the heat is absorved by the pad. There are some formulas for estimating it in Rudolf Limpert's book "Brake design and Safety".
As for the heat that goes into the tire, I did not include it for the moment. Does someone know how could this be included and if its effect is significant?

[Goost]

angel_aso,

sounds like you're on the right path.

~~~~

As far as energy into the tires (as heat), I would think it is small compared to the braking component.
Easy enough to test if you have any tire data:
'Power flux' for the tire is just Fx*Vsx (N*m/s) with Fx - Longitudinal Force, Vsx - Longitudinal Slip Velocity.

Also, drag from the steered tires (a Fx created from Fy*sin(steer_angel)) may be contribute significantly to the braking force in some situations. That would also be less energy into the rotors and more into the tires.

[Z]

As far as energy into the tires (as heat), I would think it is small compared to the braking component.
Easy enough to test if you have any tire data:
'Power flux' for the tire is just Fx*Vsx (N*m/s) with Fx - Longitudinal Force, Vsx - Longitudinal Slip Velocity.

Also, drag from the steered tires (a Fx created from Fy*sin(steer_angel)) may be contribute significantly to the braking force in some situations. That would also be less energy into the rotors and more into the tires.

Goost,

I would say that "energy into the tyres" is quite large, and, in fact, can far exceed "energy into the brakes". However, you do have the right approach to calculating it, namely scalar product of force and velocity vectors.

Tyres get hot in corners mainly due to "slip-angle drag". Since slip-angle can be 0.1 radians or more (~6+ degrees), it follows that the heat flux into the tyres is about 10+% of cornering force x velocity (ie. a lot, and easy to calc.).

Similarly, during braking with, say, 20% longitudinal-slip-ratio (quite typical of hard braking), then 20% of kinetic-energy-turned-into-heat goes into the tyres and road surface, and 80% into the brakes. If you completely lock-up the brakes (ie. no slip between pad and rotor), then ALL the heat energy goes into the tyre and road surface, and none into the brakes...

Z

[Goost]

Z,

"small"
"large"

By now I should know better than to use subjective words on this forum.

"quite typical of hard braking"

But you should too.

~~~

While your reasoning and drawings are nearly impeccable, you rarely if ever provide real data for justification.
In this case, I think the estimate of 20% slip is nearly double the actual amount during peak braking.
I have attached a longitudinal force vs slip curve from real data (only the tractive force is available for budgetary reasons, let us assume the curve is symmetric). Fx is normalized obviously.

What do you think? is 20% still a fair guess? It may be, I'm just curious how you arrive at that number. where are your data?
In other data (I cannot present) from another series, a 5 or 6% slip ratio is more nearly the peak.

Your comment about wheel lock-up is a clever concept, have never quite thought of it like that, very interesting.

~~~

do you have any comments or insight on angel_aso's equations? that's actually the topic of concern in here.
His measured temps were (both) about 27% lower than the simulated ones.
We could attribute that to a lot of things, but until we nail down some real numbers for use in his simulation it's not going to improve his model's accuracy nor clarity.

[Z]

Z,

"small"
"large"

By now I should know better than to use subjective words on this forum.


Goost,

My quantitative interpretation of a "small" effect is that it is one, that if ignored in a calculation, still leaves the calculation within whatever error margin you expect.

By contrast, anything with a "large" effect makes a real mess of your numbers whenever you ignore it. Much as the Matlab generation love to quote numbers to five significant digits (or 8?, or 12?), most engineering calcs of the above type are doing well to be accurate in the first digit (ie. within 10%). If you ignore a "large" effect, then even that first digit will be way off.

IMO good engineers spend as much time considering how big their errors are, as they spend actually calculating the numbers.

(Edit: Of course, the modern fix for bad calculations is simply to include a "global grip factor", or some such, that can be tweaked AFTER you know the correct result, so that the calculated result now looks remarkably accurate!)
~~~o0o~~~


... you rarely if ever provide real data for justification.
In this case, I think the estimate of 20% slip is nearly double the actual amount during peak braking.
I have attached a longitudinal force vs slip curve from real data...
My "real data" comes from my "real life". :)

In this case, my real data is the screaching noise my tyres frequently make when I stomp on the brakes of my NON-ABS equipped car. Stupid young person (or maybe really old person!) pulling out of a side street, or dog running out onto road, etc.

How many FSAE cars have ABS? Without ABS, or a really skillful driver, what chance is there of the longitudinal-slip remaining at its "optimum" value of, let's say, 10.846234%? Or, for that matter, anywhere near that peak?

Bottom line here, anytime the brakes are close to lock-up, the tyres will be absorbing more energy than the brakes.
~~~~~o0o~~~~~


do you have any comments or insight on angel_aso's equations? that's actually the topic of concern in here.
His measured temps were (both) about 27% lower than the simulated ones.
We could attribute that to a lot of things, but until we nail down some real numbers for use in his simulation it's not going to improve his model's accuracy nor clarity.

The 27% error is what happens when "large" effects are treated as if they are "small" (ie. negligible).

More details of angel_aso's equations would help here, but it seems that he (she?) is assuming that the only way that the car's kinetic energy is dissipated is via the brakes.

As noted before, longitudinal-slip "heat-into-the-tyres/road" is a "large" factor.

And slip-angle drag is also significant (and not only during cornering, but also in a straight line if the car has significant toe-in or toe-out).

Smaller, but still worth including, is tyre-rolling-drag (higher for racing tyres than road tyres, but very roughly 1% of Fz).

And, of course, engine-braking drag.

And, of course, the everpresent AERO-DRAG.

And, in the spirit of the Second Law of Thermodynamics, you should expect that any other so far unaccounted factors will also have the same sign as those above, so they make life a little easier for the brakes by helping to slow the car down...

And then there is the whole business of that "h" coefficient.....

Z

[stevenholland]

I write a custom matlab gui to help me solve these variables. Might be a good reference for your own design. I posted the software on my blog at
http://engineerforbeer.wordpress.com/2013/12/30/custom-fsae-brake-software/ . It starts with an input force by the driver, iterates to solve at what force brake lock is initiated. Then it plots all this over your bias bar adjustable range.