Brake System Design and Optimization: Proportioning Valve, Pedal Feel and Master Cylinders
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Proportioning Valve, Pedal Feel and Master Cylinders
13.15
| 00:00 | - In the previous module, we sized our brake discs and callipers and chose suitable pads which allowed us to calculate the hydraulic pressure required to achieve our braking requirements. |
| 00:10 | From here, we can now start moving back towards the pedal and rounding out our calculations. |
| 00:16 | At this point, if we plan on using a proportioning valve, we need to factor it into the calculation. |
| 00:22 | We always want to use an adjustable proportioning valve to make use of the tunability. |
| 00:28 | Whether this is a screw type or lever type doesn't change the effect on the calculations. |
| 00:33 | We just figured out that in the higher G braking event when the most load is transferred to the front tyres, we require 663 psi of rear brake line pressure. |
| 00:45 | This is the condition that requires the most amount of front bias. |
| 00:49 | Every other condition, be it from less pedal application or less grip, will need more rearward bias. |
| 00:56 | Let's look at this plot from Tilton where each line represents a different setting of the proportioning valve. |
| 01:02 | We can see that that proportioning valve regulates the pressure to the rear brakes above a certain pressure, meaning that the change in output pressure is reduced relative to the input pressure. |
| 01:15 | Before the knee point of each line, the change in input pressure to output pressure is equal so the slope is 1:1. |
| 01:23 | After the knee point, the slope is always 3:1 so if the input pressure is increased by 3psi, the output pressure only increases by 1psi. |
| 01:34 | Essentially this means if the proportioning valve was set to position 3, to allow for adjustment either way, to achieve an output pressure of 663psi, we actually need to be generating around 1000psi or 6900kPa of input pressure. |
| 01:54 | If our system is correct, it should be fairly close but we may need to use a small adjustment either way to dial it in. |
| 02:02 | Using pressure sensors in the brake lines can give us a lot better understanding of what's really going on. |
| 02:09 | The issue with proportioning valves, other than the extra weight and cost is that they require a small amount of extra volume displacement that results in a slightly softer pedal feel. |
| 02:20 | Their use in pure motorsport applications is often argued either way, since the brakes are most commonly used at full power, even if the time on the brakes varies. |
| 02:30 | But the benefit in lower power stops is clear. |
| 02:34 | We'll continue these calculations assuming the inclusion of a proportioning valve and we'll say that for our target, 74% bias at 1.2G deceleration we now require 6900 kPa of rear brake line pressure. |
| 02:51 | We'll also be able to adjust the proportioning valve if the setup of the vehicle changes significantly and requires more rear bias. |
| 02:59 | For example, adding rear downforce. |
| 03:01 | The next step is a bit of a juggling act and requires an iterative approach to calculate a suitable setup since the pedal effort, pedal ratio and master cylinder sizing all need to be considered together. |
| 03:15 | Most pedal boxes, both factory and motorsport style, allow for about 100mm or more of brake travel but that doesn't mean we would ever want to use that. |
| 03:25 | We actually want to leave at least 50 - 60mm of space between the brake pedal and the firewall or whatever is limiting the movement to make sure that we never run out of pedal travel before achieving the maximum braking pressure. |
| 03:41 | Motorsport pedal boxes generally offer adjustable pedal ratios that can range from as low as 3.5:1 up to 6:1, sometimes even higher. |
| 03:52 | And around 40mm of brake pedal travel is fairly standard in motorsport applications to allow for heel and toe downshifting and a firm pedal with good feedback. |
| 04:02 | Although the pedal positions are usually adjustable and will depend on the driver's preference, we'll target around 40mm of travel. |
| 04:10 | While some drivers prefer a firmer pedal and some require a lighter pedal, 50kg or 110 pounds of force is a reasonable maximum pedal pressure for an average adult. |
| 04:23 | At least one that should be behind the wheel of a racecar anyway. |
| 04:26 | Let's also start with a pedal ratio of 5:1 to allow for some adjustment either way and of course we want to design around the bias bar in the central location so the pedal force is split evenly to each master cylinder, allowing for a full range of bias adjustment in each direction when required. |
| 04:45 | A brake booster would also have an effect here by multiplying the pedal input just like what's achieved with the pedal ratio however not as consistently so for our example we'll assume we're not using a brake booster. |
| 04:57 | With a 50kg pedal effort, 5:1 pedal ratio and the bias bar central, 125kg or 1230 newtons is transferred into each master cylinder. |
| 05:10 | Dividing this force by the required pressure will therefore give us our required master cylinder area. |
| 05:17 | So along with the area of a circle formula, we can find that to achieve 5257kPa in the front circuit, we require a 17.2mm diameter master cylinder. |
| 05:30 | Which is very close to the common 11/16th inch size. |
| 05:35 | And likewise, to achieve 6900kPa in the rear circuit, we require a 15mm master cylinder which is essentially 3/5ths of an inch. |
| 05:47 | 11/16ths is on the smaller end of the spectrum of common master cylinder sizes and 3/5ths is actually a bit too small but we'll come back to this after discussing pedal travel. |
| 05:58 | The majority of the pedal travel and therefore master cylinder travel will actually be free play as the calliper pistons move to take up the pads and engage the brakes. |
| 06:09 | It's fair to assume that under normal operation, there should be about 0.5mm or so of total piston travel to take up the pads. |
| 06:18 | That's 0.5mm of movement from one pad to the other or 0.25mm for each pad. |
| 06:26 | Once the pads are in contact with the disc, the piston travel should be fairly minimal to build up our brake pressure and apply the required clamping force. |
| 06:35 | Excessive pedal travel here can be the result of too much compliance in the system from a lack of stiffness or the need to bleed the brakes. |
| 06:44 | Since our front calliper piston area is 2510mm² and the rear is 1377mm², for the pistons to travel 0.5mm, the volume of fluid displaced in each front calliper is 1255mm³ and 688.5mm³ in each rear calliper. |
| 07:10 | With 2 callipers in each circuit, the means the front master cylinder needs to displace 2510mm³ and the rear 1377mm³. |
| 07:23 | An 11/16th master cylinder has a bore area of 239mm² and a 3/5ths would equate to a 182.41mm². |
| 07:36 | Dividing the volume displacement requirements by this area, we can find that the front master cylinder needs to travel about 10.5mm and the rear cylinder about 7.5. |
| 07:49 | If our pedal ratio was 5:1, the central push rod will move the mean or average of these two distances so 9mm, and this would equate to about 45mm of pedal travel which isn't too bad. |
| 08:03 | But if we add a small amount of travel for compliance in the system, as well as the proportioning valve, then it's a bit more than we'd ideally want. |
| 08:11 | Another thing to note here is that the front master cylinder needs to travel 3mm further to engage the brakes so the push rod needs to be adjusted 3mm further out for that master cylinder when attaching it to the bias bar. |
| 08:26 | The resulting tilt of the bias bar will be small enough that the bias migration when the brakes are applied will be insignificant. |
| 08:35 | We have a few options here to fix our issues. |
| 08:38 | One would be starting with a more aggressive pad compound like the N05S which you can see brings the coefficient of friction up to 0.5. |
| 08:47 | Lowering the pressure requirement for the same braking torque. |
| 08:51 | Meaning our master cylinders can be larger and therefore the pedal travel is reduced to about 41mm. |
| 08:59 | Bigger discs would also have a similar effect but we're already at the maximum size that we can fit under our current wheels. |
| 09:06 | With an increase in pedal ratio, larger master cylinders can also be used to generate the same brake line pressure for the same pedal effort. |
| 09:14 | However the decrease in master cylinder travel will be offset by the increase in pedal travel from an increase in pedal ratio. |
| 09:23 | So the resulting pedal travel is essentially unchanged. |
| 09:27 | This is why it's best to design to a particular pedal ratio and then use it as a tuning tool after the system is specced. |
| 09:35 | Increasing the pedal ratio to give a longer, lighter pedal or descreasing it to give a shorter, firmer pedal. |
| 09:42 | Increasing the master cylinder sizes to 7/8ths for the front and 11/16ths for the rear reduces the pedal travel to about 31mm at the compromise of an increase in pedal effort to about 65kg to achieve the same brake pressure. |
| 09:59 | This is on the high side but if we maintain these master cylinder sizes, we can increase the pedal ratio to 6.5:1 and achieve the same brake pressure with about 50kg of pedal effort and 40mm of pedal travel. |
| 10:14 | These changes to the master cylinder sizes approximately maintain our bias but if the mass is done on the hydraulic leverage ratio we'd see a small change which would correspond to a small change in the clamping force and therefore bias. |
| 10:30 | This is always going to be the case as the exact master cylinder size we need is more than likely not available. |
| 10:37 | Therefore the bias bar will need to be adjusted slightly to compensate, although less than what would be required for different track conditions so it's really not a concern. |
| 10:47 | At least we've targeted a central position so we'd still have a lot of adjustment in either way. |
| 10:53 | The final thing to note for the system design is that the total master cylinder stroke is significantly more than the travel we use with the system bled. |
| 11:02 | We need the pedal to contact the floor or a hard stop before the master cylinder reaches its maximum travel to avoid damaging the master cylinder. |
| 11:12 | For example, if we had 100mm of pedal travel, and a pedal ratio of 5:1, we're going to need our master cylinder to have more than 20mm of travel. |
| 11:23 | Also worth mentioning is that 100mm of pedal travel would allow us to still engage the brakes with about 0.5mm of knock back on each pad which is where the pads and therefore the calliper pistons are knocked back away from the disc due to the disc not running perfectly straight. |
| 11:42 | This is something we need to keep in mind for maintenance and brake package stiffness if it becomes an issue in testing but we'll leave it there for now and come back to the subject in more detail soon. |
| 11:54 | Before wrapping up, it's important to understand that aero downforce loads, tyre load sensitivity and contact patch considerations are included in this process for higher level applications and for the upper tiers of motorsport, these can play an important role. |
| 12:10 | We did discuss both of these factors throughout the course and while including aero loads isn't too much more difficult, calculations around tyres require a much deeper understanding which is outside the scope of this course. |
| 12:24 | With that covered, let's summarise what we've learned before checking out our calculator tool in the next module. |
| 12:30 | Once we have our base pressure requirements defined, we need to factor in the proportioning valve assuming we're using one, as this has a further impact on our pressure requirements. |
| 12:40 | From there, it's back to the pedal end where we size the master cylinder to achieve our hydraulic pressure from our target pedal effort, all while considering the volume of fluid displaced and therefore the master cylinder and pedal travel. |
| 12:55 | It can take a few iterations of changing the master cylinder sizes and pedal ratio to achieve our desired pedal effort and travel but if we can't seem to get what we want, then we may need to reconsider our choice of callipers, discs and pistons or alternatively, the performance we're targeting might be unrealistic. |
