Brake System Design and Optimization: Longitudinal Tyre Forces
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Longitudinal Tyre Forces
09.38
| 00:00 | - Tyres are possibly the most complex part of nearly every racecar and as such, we'll only touch on some introductory aspects in this course. |
| 00:09 | Tyres are however the only means a braking system has to transfer the braking torque of the discs to the road surface. |
| 00:18 | The force the tyres apply to the road surface during braking is what we normally refer to as longitudinal force. |
| 00:25 | Since they are largely aligned with the north/south longitudinal axis of the car. |
| 00:31 | This is what's referred to as a frictional force which essentially resists the relative motion of the tyre and the road surface. |
| 00:40 | The coefficient of friction and therefore the longitudinal force we get from the tyre is a function of many parameters. |
| 00:47 | Some of the basic ones relevant to our discussion are vertical load, slip ratio, slip angle, camber angle, inflation pressure, temperature, and vehicle speed. |
| 00:58 | Of these, the slip ratio is the one we have direct control over with the brake pedal. |
| 01:05 | It's the most dominant parameter when it comes to a tyre producing longitudinal forces. |
| 01:10 | When a tyre is loaded longitudinally, it generates a slip ratio. |
| 01:14 | One way to help visualise a slip ratio is to think about a tyre winding up, being twisted between the rim and the road. |
| 01:24 | We have a non zero slip ratio when the forwards speed of the vehicle doesn't match the rotational speed of the tyre. |
| 01:32 | In the case of braking, the wheel is rotating slower than it should for a given vehicle speed if it were free rolling. |
| 01:38 | This difference is taken up by distortion in the tyre, both within the construction and the tread to road interface as the tread surface expands and contracts as it meets and leaves the road surface. |
| 01:51 | When a tyre is free rolling, the slip ratio is equal to zero. |
| 01:55 | During braking this slip ratio is defined as negative. |
| 01:59 | This is most often expressed as a ratio or a percentage. |
| 02:04 | For example, if the slip ratio is -0.1, this means that the tyre is rotating 10% slower than if it were free rolling. |
| 02:14 | It's important to make the point that despite the confusion name, a slip ratio does not necessarily imply that the surface of the tyre is slipping or skidding against the road. |
| 02:24 | This slip is being taken up by tyre deformation rather than the surface of the tyre potentially slipping or skidding on the track surface. |
| 02:32 | To help illustrate generalised slip ratio behaviour, here's a typical plot of slip ratio vs longitudinal tyre force with slip ratio on the horizontal axis and longitudinal force on the vertical axis. |
| 02:47 | A slip ratio of zero indicates the tyre is free rolling. |
| 02:51 | Starting from a free rolling condition and moving to the left, we can see that initially as the magnitude of the slip ratio increases, the longitudinal force also increases quickly. |
| 03:04 | Then, as the slip ratio continues to increase the increase in force reduces until it peaks and the longitudinal force begins to drop off. |
| 03:14 | There are three distinct areas that we can break this plot down into highlighted here. |
| 03:20 | The first is the linear range where the force increases linearly with slip ratio. |
| 03:26 | The second is the transitional range and the third is the frictional range. |
| 03:31 | Because we can build braking force so quickly due to the nature of hydraulic brakes, we tend to move through the linear region quite quickly. |
| 03:39 | We get the peak longitudinal force within the transitional range and this is the area we're aiming for. |
| 03:46 | At least in the initial braking when the car is travelling in a straight line. |
| 03:50 | The frictional range is where we're using too much brake pressure which means we have too much slip ratio, causing the maximum longitudinal force we can create with the tyre to decline. |
| 04:03 | This part of the plot is called the frictional area as this is the point where more and more of the tyre's contact patch is beginning to slip against the road surface because the construction and tread of the tyre is not able to deform any further. |
| 04:17 | If the slip ratio continues to increase, the entire contact patch will start to slip against the road surface. |
| 04:25 | At this point, the tyre is considered locked and the longitudinal force will drop off quickly. |
| 04:31 | This plot is for a specific tyre at a specific vertical load, slip angle, camber, inflation pressure and speed. |
| 04:39 | As such, the exact slip ratio to aim for is different for every car and tyre combination as well as each part of the circuit. |
| 04:47 | However, for modern tyres, the shape of this plot and general behaviour is always the same and it's helpful to keep in mind as we continue to discuss braking in this course. |
| 04:58 | Another important concept we need to understand is vertical load sensitivity. |
| 05:03 | This is where the coefficient of friction that the tyres have during braking changes based on the vertical load applied to them. |
| 05:11 | If we simplify down the longitudinal tyre forces and look at them in terms of coefficient of friction, as we increase the vertical load, we decrease the coefficient of friction which is what we see here on this plot. |
| 05:25 | This is an important point to keep in mind and refer back to. |
| 05:29 | When we're braking we're transferring vertical load from the rear tyres to the front tyres. |
| 05:33 | This means the front tyres now have a lower coefficient of friction than they did before we started braking. |
| 05:41 | The actual longitudinal force the tyres can produce is greater than what they were capable of before we transferred the load, simply because now they have more vertical load acting on them. |
| 05:53 | It's just that we have a lower coefficient of friction on the front tyres than we had before, doubling the vertical load, doesn't double the longitudinal grip. |
| 06:03 | The implication here is that the longitudinal load transfer decreases the overall braking capability of the car. |
| 06:10 | The coefficient of friction of the front tyres has decreased and the coefficient of friction of the rear tyres has increased. |
| 06:18 | At this point, I want to make a note on tyre width and more specifically the tyre contact patch. |
| 06:25 | As friction force between the tyre and road is equal to the normal force at the tyre, multiplied by mu being the coefficient of friction, we can see that increasing the contact area doesn't increase the frictional force since area doesn't factor into the friction equation. |
| 06:43 | This does however reduce the pressure at the interface between the two surfaces. |
| 06:48 | As the force is being divided over a larger surface area. |
| 06:53 | This has its own benefits such as decreasing heat generation and wear. |
| 06:57 | However there is a special consideration with rubber, as we just discussed the coefficient of friction changes with the normal force but more specifically, normal pressure at the interface. |
| 07:10 | So while the contact patch area doesn't directly appear in the friction equation, it actually factors into the coefficient of friction which of course is part of the friction equation, meaning the contact patch does have an affect on the grip available. |
| 07:25 | But having a wide tyre, doesn't necessarily mean a bigger contact patch, assuming the tyres have the same inflation pressure. |
| 07:32 | Often, with a wider tyre of the same diameter, the contact patch will be wider but also shorter in the longitudinal direction. |
| 07:41 | Additionally, the contact patch deforms and changes shape with different loads and the width and length of the contact patch can have different impacts on the longitudinal forces. |
| 07:52 | With all of this in mind, it becomes increasingly difficult to understand exactly how the load sensitivity affects the frictional forces produced by a tyre. |
| 08:02 | This is a non linear relationship and completely different for every tyre but we could expect a change in coefficient of friction of around 0.1 for about every 400 kg of tyre load. |
| 08:15 | For a road racing vehicle, the load transfer and resulting tyre loads and generally in the range where this has a relatively insignificant impact on the grip available at each axle, especially considering the variable nature of braking. |
| 08:30 | Keep this in mind as later in the course, we'll be making some assumptions around this information that will help us complete some practical design work. |
| 08:39 | In professional environments and top tier motorsports, the engineers will have access to tyre data to help but naturally this is outside the scope of this course. |
| 08:49 | In this module, we've discussed some of the basic mechanisms on how tyres produce longitudinal force. |
| 08:56 | The amount of longitudinal force a tyre can produce during braking is dependent on many parameters but is primarily influenced by slip ratio. |
| 09:05 | For each set of conditions, there is an optimal slip ratio for a tyre to produce maximum longitudinal force. |
| 09:13 | Otherwise known as braking force. |
| 09:15 | The brake pedal force used by the driver is the primary parameter that determines the slip ratio experienced by the tyres. |
| 09:23 | We also learned that the coefficient of friction a tyre can produce in braking is sensitive to vertical load. |
| 09:31 | The lower the vertical load, the higher the coefficient of friction. |
