Lestat
28-10-2007, 18:02:58
En el Tema del S3 hubo una discu muy buena que tube con un we y ademas hay cierta incertidumbre al respecto asi que les pondre como calcular los frenos para que sepan realmente como funcionan y como mejorarlos, o en dado caso que mejorar.
How's your bias? - The math behind the art of braking
Maybe one of the most controversial discussions in the Audi/VW enthusiast circles today. Why is it such a concern? What does it do to braking performance? The answers are simple, but can be difficult to completely understand.
First by design most original factory brake systems do not split the brake force 50/50 between the front and rear axles. This is because under braking the front tires offer increased traction as weight is transferred forward. This additional traction can be utilized by increasing the brake force applied to the front axle vs. the rear. The outcome is a bias split that is more in the order of 70 front/30 rear resulting in shorter and more controlled stops.
Let’s now examine the bias of the stock brake system, ECS Big Brake Kits, and the bias of other big brake kits on the market. To start we will need to make some general assumptions about the environment in which the brake kits will operate under.
What these calculations assume:
* Pressure provided by the system is equal at all 4 corners. Most modern vehicles today rely on the function of the ABS system to balance brake bias. ABS systems do not alter brake bias until they are activated. The brake performance of vehicles equipped with active brake bias control valves or other automated brake bias systems which control hydraulic pressure cannot be modeled here.
* μ the coefficient of friction of all pads is equal. This is true in most cases as most people run the same pad material on all 4 corners.
* μ is constant at all applied pressures. Brake pad compounds do not necessarily perform in a linear fashion. A doubling of pressure does not inevitably double the created friction force
We will need to borrow a few simple rules from physics regarding torque, leverage and friction. First we will look at the actual brake system and describe how brake force is essentially calculated.
Brake Torque:
AP – Caliper Piston Surface Area - This is the total active piston area of the caliper.
μ –Coefficient of Friction - μ (pronounced mu) is the average coefficient of friction of the pad. μ varies with temperature. As μ approaches zero you scream “brake fade!” Typical pads range from .5 - .7
PS –Hydraulic Pressure of the System - This is the pressure of the brake fluid coming from the master cylinder. The harder you press on the brake pedal the higher this pressure will be.
RE - Effective Radius of clamping Force - (Described in next section below)
For comparative purposes we will be ignoring μ and PS. We can make this assumption because we are mainly interested in comparing front/rear brake bias as a factor of piston sizing and rotor diameters. Realistically we would also want to investigate rotor temperatures and its affect on μ as the brakes are used.
http://ecstuning.com/stage/images/product/brakes/ECS-Stage4/WheelTorque-220x53.gif
Effective Radius of Clamping Force:
RE -The Effective Radius of Clamping Force - Torque is defined as τ = r•F, the product of force(F) applied by the distance(r) from the rotational center. In the case of a brake rotor, force is applied to an area of the rotor ranging from the inner radius (RA) to the outer radius (RB). Assuming the pad provides and equal amount of radial coverage over this area we can calculate the average effective radius (RE) with the equation listed to the right.
An alternate method adopted by some is to assume that the pad sweep area is 1” across and that the force applied lies centered across this area. However we feel that the method shown to the right is more accurate.
http://ecstuning.com/stage/images/product/brakes/ECS-Stage4/EffectiveRadius-Calc-150x73.gif
Collecting the data, doing the math:
Accurate measurements are critical for the precise modeling of a calipers performance under braking conditions. Piston diameters are measured, their surface areas calculated and then entered into the equations above. Combined with the effective sweep radius of the rotor we are able to determine the overall brake torque created for a given unit of hydraulic pressure. We then can compare the torque capability each caliper and rotor system equally. Comparing these results with those calculated for the stock brake system we can evaluate the differences in brake bias and look for excessive changes that could negatively impact braking performance and safety.
http://ecstuning.com/stage/images/product/brakes/ECS-Stage4/MeasurePiston-250x176.jpg
Mis conclusiones, lo mas facil es o mejorar la friccion en las pastillas o aumentar el diametro de los Discos para tener mas area de contacto, en este caso lo mas viable y barato es mejorar las pastillas.
Ojo: Chequen que en la ecuacion no importa si los discos son ventilados o hiperventilados (ranurados o perforados). Obviamente mientras mas ventilacion tengan mejor frenaran pero para esta ecuacion se toma un sistema ideal, con esos datos constantes, asi que aunque nos diga que un disco frenara mejor que otro no siempre es el caso si uno es ventilado (el que menos frena segun la ecuacion) y el otro no (el que mas frena) siempre frenara mas constante el ventilado, y las primeras vueltas frenara mejor el solido hasta que se caliente.
How's your bias? - The math behind the art of braking
Maybe one of the most controversial discussions in the Audi/VW enthusiast circles today. Why is it such a concern? What does it do to braking performance? The answers are simple, but can be difficult to completely understand.
First by design most original factory brake systems do not split the brake force 50/50 between the front and rear axles. This is because under braking the front tires offer increased traction as weight is transferred forward. This additional traction can be utilized by increasing the brake force applied to the front axle vs. the rear. The outcome is a bias split that is more in the order of 70 front/30 rear resulting in shorter and more controlled stops.
Let’s now examine the bias of the stock brake system, ECS Big Brake Kits, and the bias of other big brake kits on the market. To start we will need to make some general assumptions about the environment in which the brake kits will operate under.
What these calculations assume:
* Pressure provided by the system is equal at all 4 corners. Most modern vehicles today rely on the function of the ABS system to balance brake bias. ABS systems do not alter brake bias until they are activated. The brake performance of vehicles equipped with active brake bias control valves or other automated brake bias systems which control hydraulic pressure cannot be modeled here.
* μ the coefficient of friction of all pads is equal. This is true in most cases as most people run the same pad material on all 4 corners.
* μ is constant at all applied pressures. Brake pad compounds do not necessarily perform in a linear fashion. A doubling of pressure does not inevitably double the created friction force
We will need to borrow a few simple rules from physics regarding torque, leverage and friction. First we will look at the actual brake system and describe how brake force is essentially calculated.
Brake Torque:
AP – Caliper Piston Surface Area - This is the total active piston area of the caliper.
μ –Coefficient of Friction - μ (pronounced mu) is the average coefficient of friction of the pad. μ varies with temperature. As μ approaches zero you scream “brake fade!” Typical pads range from .5 - .7
PS –Hydraulic Pressure of the System - This is the pressure of the brake fluid coming from the master cylinder. The harder you press on the brake pedal the higher this pressure will be.
RE - Effective Radius of clamping Force - (Described in next section below)
For comparative purposes we will be ignoring μ and PS. We can make this assumption because we are mainly interested in comparing front/rear brake bias as a factor of piston sizing and rotor diameters. Realistically we would also want to investigate rotor temperatures and its affect on μ as the brakes are used.
http://ecstuning.com/stage/images/product/brakes/ECS-Stage4/WheelTorque-220x53.gif
Effective Radius of Clamping Force:
RE -The Effective Radius of Clamping Force - Torque is defined as τ = r•F, the product of force(F) applied by the distance(r) from the rotational center. In the case of a brake rotor, force is applied to an area of the rotor ranging from the inner radius (RA) to the outer radius (RB). Assuming the pad provides and equal amount of radial coverage over this area we can calculate the average effective radius (RE) with the equation listed to the right.
An alternate method adopted by some is to assume that the pad sweep area is 1” across and that the force applied lies centered across this area. However we feel that the method shown to the right is more accurate.
http://ecstuning.com/stage/images/product/brakes/ECS-Stage4/EffectiveRadius-Calc-150x73.gif
Collecting the data, doing the math:
Accurate measurements are critical for the precise modeling of a calipers performance under braking conditions. Piston diameters are measured, their surface areas calculated and then entered into the equations above. Combined with the effective sweep radius of the rotor we are able to determine the overall brake torque created for a given unit of hydraulic pressure. We then can compare the torque capability each caliper and rotor system equally. Comparing these results with those calculated for the stock brake system we can evaluate the differences in brake bias and look for excessive changes that could negatively impact braking performance and safety.
http://ecstuning.com/stage/images/product/brakes/ECS-Stage4/MeasurePiston-250x176.jpg
Mis conclusiones, lo mas facil es o mejorar la friccion en las pastillas o aumentar el diametro de los Discos para tener mas area de contacto, en este caso lo mas viable y barato es mejorar las pastillas.
Ojo: Chequen que en la ecuacion no importa si los discos son ventilados o hiperventilados (ranurados o perforados). Obviamente mientras mas ventilacion tengan mejor frenaran pero para esta ecuacion se toma un sistema ideal, con esos datos constantes, asi que aunque nos diga que un disco frenara mejor que otro no siempre es el caso si uno es ventilado (el que menos frena segun la ecuacion) y el otro no (el que mas frena) siempre frenara mas constante el ventilado, y las primeras vueltas frenara mejor el solido hasta que se caliente.