Vertical mounted master cylinder

Hello! I' m Lee from South Korea.

Actually, I'm in charge of brake system for 2015 FSAE. I have several questions about vertical mounted master cylinder.

In last competition, I saw that many teams installed vertical mounted master cylinder for Pedal system.

My team will also use bearing mounted master cylinder which is 77 series one from Tilton engineering to reduce overall length of pedal box.

But, I wonder how I can get pedal ratio.

When using vertical mounted master cylinder, balance bar should be installed upward. From that, I got 3.29 of pedal ratio. I think it's not enough for braking force.

Could you guys give me an advice of pedal ratio for vertical mounted master cylinder? I calculated 3.7 by looking over the following thesis.

http://dspace.mit.edu/bitstream/hand.../191801934.pdf

I wonder that those calculating method is right or not.

Thanks.

No one can answer that question without knowing your master and caliper bores and rotor diameter.
What is your calculated pedal force per g of braking? If you can show the math that comes to that answer it will be much easier for others to help double check your work.

Thank you for your reply.

I calculated pedal force per 1.5g of braking. I got 1.5g of data by installing G sensors in last-year car for 2014 FSAE.

Here are several math things with picture to get pedal ratio.

Attachment 379Attachment 380Attachment 381Attachment 382

From those equations, I got 3.29 of pedal ratio.

My team's car need 2871N of front braking force and 1248.6N of rear braking force for 1.5g braking.

But, 3.29 of pedal ratio is not enough for us to generate braking force from Driver's foot.

Based on 3.29 of pedal ratio with 60kgf pedal effort from driver's foot, it generates only 2111N of front braking force and 962N of rear braking force.

It seems to increase pedal ratio. But, I want to know I did right things to get pedal ratio as picture that I attached.

How do you guys derive pedal ratio? It's first time to design pedal system with using vertical mounted master cylinder for me.

Could you give me an advice?

Front and rear Master cylinder bore = 0.015875m
Front rotor diameter = 0.187m
Rear rotor diameter = 0.177m
Tire diameter = 0.450m
Caliper diameter = 0.0254m

Thanks

Lee (Shawn...),

I started reading the MIT thesis you referenced, but after seeing ~half-a-dozen errors in as many pages I stopped.

One of your diagrams has the length C varying from 162.88 mm to 135.048 mm. Really? Do you really think that you need, or can even measure, this length to an accuracy of microns!!!???

Your reliance on the MIT thesis indicates that your teachers know nothing about car braking systems.

Your ignorance of practical tolerances indicates that your teachers know nothing about real-world Engineering.

I strongly suggest that you approach whoever is responsible at your school, and ASK FOR YOUR MONEY BACK!
~o0o~

Meanwhile, if you put in the effort of posting ALL your calculations on this thread, then maybe someone here might be bothered checking them.

Z

(PS. BTW, I would aim for a Pedal-Ratio = ~2 (maximum of ~3).)

Sure the 77 series has a stroke of 1.1 inches, but I doubt that you will use all of it, especially with one inch single piston calipers. I would estimate - purely internet speculation here - that the mc stroke is more on the order of half inch or so. Thirty+ degrees of brake pedal rotation seems a bit high to me. I imagine, to a certain extent brake pedal travel is a matter of personal preference, and personally, I like it to be very little - more like 10ish. I also got c final as 134.3376 - rounded off to the nearest 10 thou millimeter.

Thank you for your reply.

Yes, 162.88 mm to 135.048 mm means pull stroke of Tilton's 77 series master cylinder.

This is just an assumption of pull stroke.

Z,

As a former brake system designer I have a few comments against your post. Our brake pedal travels .2" linear inches to achieve full lock of front and rear tires. Most of this travel comes from the fact that we have a very large pedal ratio to balance our system against the physically small components. This doesn't seem to have any adverse effects and one particular driver on a car swap day from another school had described the brake pedal feel of our car as "a pair of angel titties". Very easy to modulate input force, moves like a brick wall.

A vague suggestion of pedal ratio (mechanical gain) of 2 - 3 (most road vehicles use a mechanical gain of ~3 - 5) isn't very helpful as this neglects the hydraulic gain from the system. 2 - 3 might be suitable with tiny master cylinders that would most certainly be at the limit of their fluid displacement capacity to move the caliper pistons. Sure it's nice for minimizing the stress in the pedal, but short sighted in the rest of the system design.

Lee, pedal ratios on FSAE cars can vary wildly and tend towards the high side due to the minuscule components and high grip that must be overcome. Don't be surprised if you end up needing some ratio like 9:1 to accomplish your goals. On the flip side, aiming for Z's suggested pedal ratio of 2:1 requires fairly large brake system components that add more weight to the car than just reinforcing the brake pedal a little more. Also, the costs will be much higher to buy these larger components if that is a concern for you.

I would also say that referencing the recommended pedal input force from the National Highway Transportation Safety Administration (NHTSA) was key for me to understanding how much is too much and too little for the drivers to handle. 60kgf sounds rather high to me. Maybe half of that would be more manageable? Try testing it out with your drivers and a scale to see what they can easily modulate.

MCoach,

"one particular driver on a car swap day from another school had described the brake pedal feel of our car as "a pair of angel titties"."

you mean the wife swap day

Yes, certainly. Wife Swap Day.

Hello shawnBaek89,

The methodology of designing braking system starts from your car vehicle dynamics, after you calculates your braking forces on each tire you will need to develop the hydraulic system that fits your calculation on a wide range. there are several parameters on the braking system starts from the pedal ratio - bias(front - rear) MC bore sizes calipers bore and rotor, to make your life easier try to fix some parameters and change the others then do some iterations and check your outputs . you may build a system that gives you the braking forces you need with a pedal ratio = 5 and driver force = 400 and so on . build a matlab code for your iterations and vary your inputs, creat a new methodology to chose the fit system to your car.

And a word to say i did read mit paper that shawnBaek89 mentioned and there are some errors.

Thank you for all of you guys kind reply.

To Ahmad rezq,

What is the error of MIT paper? Is there any wrong about calculation of pedal ratio from MIT?

MCoach,

Quote:

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Originally Posted by MCoach

... one particular driver ... described the brake pedal feel of our car as "a pair of angel titties".

---

This has me baffled.

I am guessing that he meant the feel of BOTH pedals, accelerator and brake? In which case "angel titties" is probably a good optimisation goal, though hard to put numbers to.

But ... if you described your girlfriend thus, then might she not get very upset that you are suggesting that she has one that is very firm, pert, and upwards pointing, while the other is soft, squishy, and sagging down to the floor? :)
~o0o~

Back to brakes.

Quote:

---

"Very easy to modulate input force, moves like a brick wall."

---

I AGREE with this as a major design goal. Namely, a rock-hard brake pedal with minimal movement.

This contrasts with many newbie Brake-Guys, such as the OP, who seem to think that "the ideal" is to use almost all of the Master-Cylinder's stroke. So they aim for a pedal travel of several inches. <- WRONG!!! (Are you paying attention, Lee?)
~o0o~

BUT!!!

Quote:

---

"A vague suggestion of pedal ratio (mechanical gain) of 2 - 3...
... isn't very helpful as this neglects the hydraulic gain from the system ...
... might be suitable with tiny master cylinders ...
... short sighted in the rest of the system design ...
... requires fairly large brake system components ...
... more weight ...
... costs will be much higher ..."

---

All above comments are WRONG!

In fact, the reason I only mentioned the pedal ratio was to see who would repeat the above false arguments. It is a common mistake.

I reckon the main reason that most FSAEers automatically assume that the pedal ratio must be around 5 is that the pedal is one of the very few brake-system parts that the students actually make (disc is the other). And ... "since everyone else uses a pedal ratio = ~5, we should too..."!

Very disappointing that so few students think for themselves...
~o0o~

So, here are a few brief suggestions on how to get rock-hard brake pedals (much easier than "rock-hard abs" :)).

Obviously, the aim is to minimise unnecessary freeplay, and flex of stressed components.

Freeplay at the pads is mainly controlled by the piston seals, so not much you can do there. But reducing "pad knock-back" from warped discs or sloppy wheel-bearings helps. Freeplay at the pedal includes the small but necessary stroke needed to uncover the MC's "refill hole". This stroke is multiplied directly by the pedal ratio. So lesser pedal ratio = lesser MC freeplay = better.

Flex is reduced by lowering structural stresses. For given size components, this is easiest done by lowering the forces acting on them. Now consider these components and the forces acting on them, starting at the wheel-end first.

1. THE CALIPER - A greater normal force Fn between pads and disc means more squashing of the pads, more spreading of the caliper, and hence more flex. Less normal force Fn = less flex of pads and caliper = better. For a given required deceleration force at the wheelprint, Fn is mainly determined by Radius.wheel/Radius.disc, and by the "Mu" of the pads.

So reduce R.w/R.d as much as possible, perhaps easiest by starting with small radius wheels and tyres. Then choose the highest Mu pads that are available, economical, durable enough, and have the right "feel". There is NOT a great deal to be gained in this area if you are using off-the-shelf parts.

2. THE HYDRAULICS - Greater hydraulic pressure means more squashing of the brake-fluid, more expanding of the brake-lines and other wetted components, and hence more flex. Less hydraulic pressure = less flex = better.

So aim to get the required Fn pad-disc force with a lesser (but still practical!) hydraulic pressure. This simply means CHOOSING CALIPERS WITH LARGE PISTON AREA! More details below. (Interestingly, another recent thread has the OP worrying that his pressures are too low, because they are lower than everyone else's!!!)

3. THE PEDAL - Greater pedal ratio means greater stresses in the pedal structure, and in the MC-push/pullrod(s), and in the many connecting joints including the bias-bar, and in all the surrounding structure out to the MC(s) mounts, and hence more flex. Less pedal ratio = less stresses everywhere for a given amount of structure = less flex = better.

So, summing up, if the OP chose calipers with, say, 1.5" diameter pistons, and ALL ELSE AS BEFORE, then he would have less than half the hydraulic pressure, so roughly half the flex there (it is not quite linear). Furthermore, for the same foot-force on the brake pedal and the same MC(s), he would only need half the pedal ratio, which gives roughly ONE-QUARTER the flex there (the relationship is roughly quadratic).

Note that the calipers would NOT need to have any more mass because the spreading force on them is unchanged, so structurally they can remain the same. They just have bigger "holes" in them. However, the brake pedal and associated structure around it (ie. including the MC mounts, etc.) would be much simpler, lighter, stiffer, ... = better.
~o0o~

Finally,

Quote:

---

"Our brake pedal travels .2" linear inches to achieve full lock of front and rear tires. Most of this travel comes from the fact that we have a very large pedal ratio ..."

---

"0.2 linear inches" is GOOD ENOUGH, IMO. It seems that the rest of the system must be well-detailed.

However, if you want an even rock-harder brake pedal, then you can use smaller bore MC(s) fitted at a lower pedal ratio. Given that your foot pedal only travels ~5 mm, and the MC thus moves much less (ie. /PR), you should not have any problems with "... fluid displacement capacity to move the caliper pistons."

Or you can go all the way and try bigger caliper pistons (or more of them), and an even smaller pedal ratio.
~o0o~

Bottom line, just because everyone else does something stupid, does not mean that you should too.

Z

I think your stress analysis of the system adequate, and yes my style is loose and fast, but that' fine by me.

I think I will take your advise on suspension topics on this topic, aiming for what is an acceptable amount of compliance and movement rather than "optimizing" the system.
My goals (when working this system) were pushing the limits on minimizing mass without giving up the "angel titties" feeling. I got quite a chuckle of out of it, but he certainly was not describing the gas pedal. So in our case, a high pedal ratio, high stresses, high temperatures, and tiny calipers are the compromise for a weight and cost efficient system that provides a system that reacts with respect to the drivers (exceeded!!!) expectations.

Main thing here is packaging. I don't think we'd be able to fit a caliper with 1.5" pistons in our system. Hell, I spec'd 0.070" clearance between the caliper and wheel shell and we were only working with 1" piston caliper. So it's not like I was not trying to get what I could out of the system. We're using the smallest master cylinders that we can so there is not an easy change in this design. To a driver, anything under .25" seems to be irrelevant, they just don't notice.

Cheers.

Thank you for all of you guys comments.

It would be really great help for me to design the awesome brake system!

From a Human Machine Interface perspective, there's a reason that newer combat aircraft use control columns (centre-sticks) that function only on force input.. they deflect only enough to allow strain gages to function. The human body can control things much more accurately when moving things in 3-d space is removed from the equation. Most driving instructors tell you to concentrate on flexing only the larger muscles in your thigh to modulate braking force.

One would think this should also apply to throttle control, but I haven't seen anyone try that yet.

Packaging sure would be a lot easier with a brake and/or throttle by wire system fed from a pressure sensitive pad bonded to the inner skin of the front bulkhead....

Quote:

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Originally Posted by shawnBaek89

It would be really great help for me to design the awesome brake system!

---

Some more suggestions for "Brake-Guys" to think about.

1. To repeat above point, a "rock-hard" brake pedal with good "feel" is a good goal to aim for. MCoach's ~5 mm of movement of the brake pedal qualifies as rock-hard. It is generally easier to achieve this rock-hard-edness with a low pedal ratio, and lowish hydraulic pressures.
~~~o0o~~~

2. Where to put the MCs?

The general big-picture rule for packaging components of these cars is "Everything heavy to be low down and close to the CG". This reduces CG-height and Yaw-inertia for better all-round performance. (This rule also applies when packing the family wagon for holidays. :))

The common location of MCs in front of the pedals puts them far away from the CG. This is NOT TOO BAD, because the MCs are quite light.

BUT (!!!) this also pushes the HEAVY front-bulkhead and IA about a foot (0.3 metres) forwards of where it could be. It also makes the chassis heavier by an extra 0.3 metres of unnecessary and heavy structure.

So, why not put the MCs and bias-bar parts, say, hmmm...,
... under the driver's left knee?

Plenty of room there. Just use a pull-rod (or two) coming back from the left side of the brake pedal, at a pedal ratio of about ~2.

End result is that the chassis can be shorter, lighter, stiffer, and with much lower yaw inertia. And (!) bias-bar adjustment can be done by the driver, whilst driving, with his left hand on a small knurled knob on the end of the bias-bar. Too easy! (I have seen a Team spend almost a year trying to design an electric servo-motor controlled bias adjuster, before they eventually gave up because too hard...)
~~~o0o~~~

3. Question: Why is almost (*) every bias-bar ever made mounted HORIZONTALLY?
Answer: "Because that is how everyone else has done it before, so we have to do the same!". Grooooaaannnn... :(

A conventional brake pedal and single MC is a planar linkage lying in a vertical (side-view) plane. So, as a planar linkage, all its joints can be simple revolutes.

A conventional brake pedal with a horizontal bias-bar is a 3-D linkage. That is, for everything to work properly, more "flexibility" is required in the joints than can be had from a few simple revolutes (ie. more DoFs needed). So, usually some Ball-Joints are used. But the BJs in typical bias-bar linkages can have excessive friction, which adversely effects the biasing of "brake balance". So suppliers of "real racer's brake stuff" keep the same overall layout of horizontal bias-bar, but they then replace the BJs with more expensive and complicated "crossed needle-bearing trunions" (ie. joints that look like UJs) to reduce friction.

BUT (!!!), making the simple conceptual change of mounting the bias-bar VERTICALLY, with the two MCs mounted one-above-the-other, allows the whole linkage to be planar again. Now only a few, simple, low-friction, needle-bearing revolutes (or even simpler "knife-edge revolutes"!) are needed to eliminate the friction problems.

I can imagine some very simple such arrangements mounted under the driver's left knee, near the cockpit left wall. Simpler, stiffer, lighter, less friction, easier to make, so cheaper, etc., etc...

Z

(* PS. The earliest Citroen ID/DSs, introduced ~1955, had AUTOMATIC (load sensitive) F/R brake-balance adjustment via a bias-bar that was mounted in the same plane as the brake pedal. I know of NO other use of such "common sense" (= "the least common of all the senses..."). Later Citroens used an even simpler, but equally effective, system.)

Z,

There is a rule requiring the brake components to above the chassis lower surface (T7.1.7), which combined with the template rules, makes that solution very difficult. Especially for those with low mount steering.

I believe the common interpretation is that an additional "guard" does not count as part of the "chassis" if it is lower than the mandated leg bay lower tube.

Pete

Still I believe there is room left where the rack mounts (or thereabout). I believe Tokai university (Japan) used a similar system to what Z describes back in 2007 (?). BTW that car was really "out-of-the-box" thinking...

You can build such systems you want if you know how to compromise with the other systems if you wanna build back master cylinder have a cup of tea with the steering guy also the ergonomics guy chassis and set your design. don't make it individually and send the design to the chassis guy you will find pieces of rocks falling from the sky on your head ask you to edit your design. backing to the backward master cylinder mount.
if you want to build this system keep in your mind these things
1 - a back masters mount will save some chassis weight.
2 - if your rack is at the bottom you must know the space you have to place your masters
3 - think of the evacuation of the car as the driver will have a long travel passing the masters the rack and the steering column
Regards

Pete,

With a vertical bias-bar the total width of this braking system would only be about 30 mm. I can imagine this mounted against the left wall of the cockpit, just under a typical gear-shifter linkage (which takes up similar width). Plenty of room for the footbox template to pass.

I have in mind an "L-shaped" adjustable pedal tray. This has a lateral RHS at the front to carry the bottom pivots of the two pedals, a longitudinal RHS coming back along the left side of the cockpit floor, and a smallish diagonal brace to triangulate the L. The whole thing can slide fore-aft in some simple rails, and is anchored by a single pin at its left-rear corner, very close to the bottom-left-side of the FRH. The MCs and bias-bar are also mounted near here, so very easy access for anyone, including the driver whilst driving.
~~~o0o~~~

Harry,

Tokyo Denki at OZ-2013 had its MCs/bias-bar mounted roughly centrally and just rearward of the R&P (from memory). All this, including R&P, was under a "false floor" so the driver could walk over it, but above the bottom chassis rails. IIRC they had a horizontal bias-bar. The pull-rod coming back from the brake pedal ran close to the centreline of the car.

My guess is that they came to this idea from their quest for the "lightest, most agile" car. Hence shorter chassis, etc., as per my previous post.
~~~o0o~~~

Ahmad,

Yes indeed, the Chassis-Guy and Brake-Guy MUST TALK TO EACH OTHER! :)

In fact, this is all easiest done in one person's head. So, traditionally a single Chief-Engineer sorted out all these big-picture issues (eg. "Yes! I can make the chassis lighter and stiffer by ... redesigning the brakes!"), while the Minions did the detail design. Later on, the most hard-working and talented Minions would become CEs.

Z

Z,
Strongly Agree.