Patent Publication Number: US-9416835-B2

Title: Method of estimating brake pad wear and vehicle having a controller that implements the method

Description:
TECHNICAL FIELD 
     The present teachings generally include a method of estimating brake pad wear and a vehicle having a controller that implements the method. 
     BACKGROUND 
     Brake pad life monitoring has been implemented on vehicles in various ways. Some vehicles have mechanical sensors that provide an audible sound when the brake pad wears sufficiently that the sensor contacts the brake rotor. Some vehicles have an electronic sensor that provides a one-time signal when brake pad wear reaches a predetermined amount of wear, and may indicate this to a vehicle operator as a percentage remaining brake pad life in a vehicle information center accessible on the dash board or steering wheel. A more advanced wear life algorithm estimates brake pad wear based on an estimated rotor temperature correlated with typical driving conditions requiring relatively low braking energy. 
     Some vehicle owners occasionally or routinely exhibit aggressive, high energy braking behavior either on public roads or during race track maneuvering. Race track operation of a vehicle requires attention to brake pad wear, as brake pads may tend to wear more quickly under the relatively high speed maneuvering. Visually inspecting brake pads during race track sessions is inconvenient, as “pit stop” time is extended. 
     SUMMARY 
     A method of estimating brake pad wear on a vehicle is accurate even under high energy braking conditions, such as under race track conditions. Brake pad wear rates change markedly under high energy braking conditions as new wear mechanisms of the brake pad are triggered. The brake pad wear rates are sensitive to vehicle dynamics under high energy braking conditions, as later weight transfer during combined braking and cornering will drive energy to the further outboard brakes. As used herein, an “outboard” component is generally further from a longitudinal center axis of the vehicle, while an “inboard” component is generally closer to the longitudinal center axis of the vehicle. An outboard direction is away from the longitudinal center axis, while an inboard direction is toward the longitudinal center axis. Factors such as aerodynamic drag, tire drag, and engine braking vary much more during high energy, race track driving conditions. Moreover, the method can optionally apply different models to determine brake pad wear dependent upon whether standard, relatively low energy or relatively high energy braking is occurring. 
     The method may include determining, via an electronic controller, required braking energy to be dissipated by a braking system of the vehicle as a fraction of total kinetic energy of the vehicle according to an energy partitioning model. A distribution of the required braking energy is then determined whereby the required braking energy is distributed to multiple vehicle braking mechanisms on the vehicle according to a vehicle dynamics model. The method may further include determining rotor temperature of each brake rotor according to a rotor temperature model that utilizes the required braking energy and the distribution of the required braking energy, and then determining brake pad wear of each brake pad according to a brake pad wear model that utilizes the rotor temperature and the distributed required braking energy. The method then includes indicating the brake pad wear via a brake pad wear indicator output device. 
     The energy partitioning model, the vehicle dynamics model, the rotor temperature model, and the brake pad wear model are representative of vehicle conditions when the rotor temperature is greater than a predetermined minimum rotor temperature, braking speed is greater than a predetermined minimum braking speed, and the required braking energy is greater than a predetermined minimum braking energy. 
     In one aspect, the method may switch between different brake pad wear models depending on various inputs such as rotor temperature. For example, the method may include determining, via an electronic controller, brake pad wear according to a first brake pad wear model when an estimated brake rotor temperature is less than or equal to a predetermined rotor temperature, and determining, via the electronic controller, brake pad wear according to a second brake pad wear model when the estimated brake rotor temperature is greater than the predetermined rotor temperature. 
     A vehicle that has a controller that implements the method includes a vehicle body operatively connected to rotatable wheels for moving the vehicle body, and a braking system configured to stop rotation of the wheels. The braking system includes respective braking mechanisms each operatively connected with a different respective one of the wheels. Each braking mechanism has a brake rotor rotatable with the wheel and a brake pad placed in contact with the brake rotor during braking of the wheel. An electronic controller has a processor that executes a stored algorithm that determines brake rotor temperature, and then determines brake pad wear according to a first brake pad wear model when the brake rotor temperature is less than or equal to a predetermined rotor temperature, and determines brake pad wear according to a second brake pad wear model when the estimated brake rotor temperature is greater than the predetermined rotor temperature. The brake pad wear is then indicated via a brake pad wear indicator output device. 
     The method reduces the frequency of brake inspections during track sessions as the controller-provided brake pad wear estimate or remaining life estimate can be relied on to accurately estimate brake pad wear under high energy braking conditions. This enables any visual inspections of the brake pads to be scheduled in a more discriminating manner (i.e., in better correlation to a need for pad replacement), and to be of shorter duration. As a quick inspection of only the highly visible outboard portion of the brake pad can be carried out to check correlation with the controller-provided estimate, and a time-consuming, full brake corner teardown is likely unnecessary. Moreover, the accuracy of everyday pad life prognostics is improved by the incorporation of the high energy model and “switching” logic between the standard brake pad wear model and the race track brake pad wear model to account for more extreme driving even on public roads. An accurate predictive algorithm avoids the need for expensive capacitance based transducers that can provide a physical measurement of brake pad wear, and improves upon the discreet (discontinuous) pad wear life predictions provided by electronic wear sensors. 
     The above features and advantages and other features and advantages of the present teachings are readily apparent from the following detailed description of the best modes for carrying out the present teachings when taken in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic illustration of a vehicle. 
         FIG. 2  is a schematic block diagram of a system for estimating brake pad wear on the vehicle of  FIG. 1 . 
         FIG. 3  is a schematic illustration of a switching model included in the system of  FIG. 2 . 
         FIG. 4  is a schematic illustration of a brake pad with indicators correlated with predetermined amounts of wear. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to the drawings, wherein like reference numbers refer to like components throughout the views,  FIG. 1  shows a vehicle  10  that has a vehicle body  12  that is operatively connected to rotatable wheels  14 A,  14 B,  14 C,  14 D for moving the vehicle body  12  when propelled by an engine E via a transmission T. In one non-limiting example, the vehicle  10  is a front wheel-drive vehicle. Differential D 1  operatively connects the front wheels  14 A,  14 B, and a differential D 2  operatively connects the rear wheels  14 C,  14 D via half shafts as is known. Tires  15  are shown mounted on the wheels  14 A,  14 B,  14 C,  14 D. The vehicle  10  includes a braking system  16  that is configured to stop rotation of the wheels  14 A,  14 B,  14 C,  14 D. The braking system  16  includes a fluid pressure source BP in communication with respective braking mechanism  18 A,  18 B,  18 C,  18 D operatively connected with each respective wheel  14 A,  14 B,  14 C,  14 D. The braking mechanisms  18 A,  18 B,  18 C,  18 D each have a brake rotor  20  rotatable with the respective wheel  14 A,  14 B,  14 C,  14 D, and respective brake pads  22  placed in contact with opposite sides of the brake rotor  20  during braking. 
     An electronic controller C has a processor  24  that executes a stored algorithm  26  for determining brake pad wear and, accordingly, predicts remaining life of the brake pads  22 , by accurately modeling wear even when the vehicle  10  is operated under relatively extreme driving, such as relatively high energy braking conditions. Additionally, the algorithm  26  determines whether predetermined high energy braking conditions exist, and automatically switches to a high energy brake pad wear model, referred to herein as a race track model, from a standard brake pad wear model that is more accurate under more typical driving with associated lower energy braking conditions. 
     Referring to  FIG. 2 , a system  30  for estimating brake pad wear on the vehicle  10  includes various vehicle sensors  32 , and includes the controller C that receives input signals from the sensors  32  so that the processor  24  can carry out the stored algorithm  26 , represented as various modules each modeling aspects of the vehicle operation based on the sensor inputs, to produce a wear signal in a brake pad wear indicator output device  35 , such as an operator display device or an audio signal. Although only four sensors  32  are depicted, many more sensors may be included in the system  30 . The sensors  32  may include wheel speed sensors, brake pressure sensors, and other sensors and the input from the sensors  32  may include brake pressure, wheel speeds, vehicle speed, longitudinal acceleration, dynamic brake proportioning, brake apply. Various systems  34  may provide input signals, including vehicle systems and offboard systems, such as telematics systems, global positioning systems, map information. Based on the input from the sensors  32  and systems  34 , the controller C can estimate or calculate vehicle mass, road grade, amount of engine braking, braking energy, rolling resistance, appropriate rotor cooling coefficients, lateral and longitudinal acceleration, and other vehicle operating characteristics as described herein. 
     It should be appreciated that the electronic controller C may be configured as a single or distributed control device that is electrically connected to or otherwise placed in hard-wired or wireless communication with the engine E, the transmission T, the braking system  16 , and various vehicle components, including sensors, for transmitting and receiving electrical signals for proper execution of the algorithm  26 . 
     The electronic controller C includes one or more control modules, with one or more processors  24  and tangible, non-transitory memory, e.g., read-only memory (ROM), whether optical, magnetic, flash, or otherwise. The electronic controller C may also include sufficient amounts of random access memory (RAM), electrically-erasable programmable read-only memory (EEPROM), and the like, as well as a high-speed clock, analog-to-digital (A/D) and digital-to-analog (D/A) circuitry, and input/output circuitry and devices (I/O), as well as appropriate signal conditioning and buffer circuitry. 
     The electronic controller C can be a host machine or distributed system, e.g., a computer such as a digital computer or microcomputer, acting as a vehicle control module, and/or as a proportional-integral-derivative (PID) controller device having a processor, and, as the memory, tangible, non-transitory computer-readable memory such as read-only memory (ROM) or flash memory. Therefore, the controller C can include all software, hardware, memory, algorithms, connections, sensors, etc., necessary to monitor the vehicle  10  and control the system  30 . As such, one or more control methods executed by the controller C can be embodied as software or firmware associated with the controller C. It is to be appreciated that the controller C can also include any device capable of analyzing data from various sensors, comparing data, and making decisions required to monitor brake pad wear and alert the vehicle operator of brake pad life. Moreover, the electronic controller C can be configured in different embodiments to include a brake controller, a powertrain controller, and other controllers onboard or offboard the vehicle  10 . 
     The algorithm  26  begins by determining rotor temperature according to a standard rotor temperature model  36 . The standard rotor temperature model  36  utilizes a calculation of braking energy  38  and a first set of cooling coefficients  40  for a thermal temperature model of the brake pads  22 . The calculated braking energy  38  and cooling coefficients  40  are appropriate (i.e., substantially accurate) for vehicle operating conditions with relatively low energy braking, typical of standard driving conditions, as further described herein. Accordingly, the first rotor temperature model  36  utilizes a calculated braking energy  38  and an equation for heat transfer from each rotor  20  that utilizes cooling coefficients  40  selected to correlate with the standard driving conditions. 
     The cooling rate of the rotors  20  when they are not in use helps determine the brake pad temperature, and is dependent on the mass of the rotor  20 , vehicle design, vehicle speed, wheel speed, ambient temperature, altitude, etc. As the vehicle  10  moves, the air flowing around each rotor  20  will determine how fast it is cooled from the previous braking event. The cooling coefficients  40  used in the lumped capacitance model of temperature decay (Equation 1) are selected to be correlated with relatively standard driving conditions with rotor temperature below a predetermined rotor temperature, vehicle speed below a predetermined vehicle speed, and braking energy below a predetermined braking energy. As further discussed herein, lower cooling coefficients are used when such driving conditions are not met (i.e., under high energy driving conditions for which a race track rotor temperature model is used to estimate rotor temperature). 
     The lumped capacitance model for brake rotor cooling is as follows: 
                         ⅆ   T       ⅆ   t       =       -     b   ⁡     (     T   -     T   a       )         +     D   ⁡     (   1   )           ;           (   1   )               D   =       P   d     pVc             (   2   )               
where P d  is brake residual drag, ρ is the density of the rotor material, V is the volume of the rotor material, and c is the specific heat capacity of the rotor material. The term b is the “cooling coefficient” and is equal to:
 
                   hA   pVc           (   3   )               
where h is the convective heat transfer coefficient and A is the working area (exposed to convective cooling airflow). Cooling coefficients are measured in vehicle tests by recording the cooling rate of the brake rotors and fitting the lumped capacitance model to the recorded data. Cooling coefficients vary approximately linearly with vehicle speed. Cooling coefficients may be measured at discrete speeds, and may then a linear model may be fit to the data to determine cooling coefficients at any speed. Typical cooling coefficient values will vary by brake rotor design and vehicle environment. An example cooling coefficient versus vehicle speed relationship could be:
 
 b= 0.00033 V+ 0.0033  (4)
 
where V is the vehicle forward velocity in kilometers per hour.
 
     The calculated braking energy  38  used in the rotor temperature model  36  is an estimate of the braking energy dissipation in the braking mechanisms  18 A,  18 B,  18 C,  18 D. This calculation uses various inputs, such as stopping distance, stopping time, brake pad temperature, etc. The master cylinder pressure of the braking system  16 , the weight distribution in the vehicle  10  and the dynamic brake proportioning for the proportional brake pressure at each wheel  14 A- 14 D can be used to determine the brake pressure. The dynamic brake proportioning is based on where the weight in the vehicle  10  is distributed, and is a known calculation. Vehicle mass can be estimated based on engine torque, and is a process well known to those skilled in the art. The mass of the vehicle  10  may change as a result of the number of passengers, load in the trunk, fuel capacity, etc. Further, those skilled in the art understand various ways to estimate the road grade in combination with the estimation of the vehicle mas. 
     The processor  24  can calculate the braking energy  38  for use in the standard rotor temperature model  36  by Equation (5) below. The braking energy  38  is the work done by the braking mechanisms  18 A- 18 D to decelerate the vehicle  10 , and is the total work minus the rolling resistance, the aerodynamic drag, the engine braking and the road grade. The brake work can be used to calculate the power dissipated by the braking mechanisms  18 A,  18 B,  18 C,  18 D, where power equals work per unit of time. The power can be calculated at predetermined time intervals during the braking event, for example, every 10 milliseconds. 
                     Braking   ⁢           ⁢   Energy     =         1   2     ⁢     M   ⁡     (       V   1   2     -     V   F   2       )         -     E     Rolling   ⁢           ⁢   Resistance       -     E   Grade     -     E   Engine               (   5   )               
In Equation (5), M is the mass of the vehicle; E Rolling Resistance  is the energy required to roll the vehicle  10  on a flat grade, which is a known value; E Grade  is the energy required to roll the vehicle  10  as a result of the grade of the road, which is also a known value; E Engine  is the braking provided by the engine E itself, and is also a known value; V 1  is the velocity of the vehicle  10  at the beginning of the braking event; and V F  is the velocity of the vehicle  10  at the end of the braking event. In an alternate embodiment, vehicle  10  deceleration can be used instead of the vehicle speed V, and can be provided by a longitudinal acceleration sensor.
 
     The total braking power dissipated by each brake pad  22  during the braking event can also be estimated as the product of braking force and vehicle velocity. Braking force can be calculated as:
 
Braking Force=pressure×area×μ  (6)
 
Where μ is the friction coefficient of the brake pad  22 , which is a function of the pad temperature, and area is the surface area of the brake pad  22 . Alternately, the braking power can be calculated as:
 
                     Braking   ⁢           ⁢   Energy     =       (     Torque     Rolling   ⁢           ⁢   Radius       )     ×   Velocity             (   7   )               
The torque is calculated for both the front and the rear of the vehicle  10  and is a function of the brake pressure and the dynamic brake proportioning. The Rolling Radius is the rolling radius of the wheel  14 A,  14 B,  14 C, or  14 D, and velocity is the vehicle velocity.
 
     After an estimated rotor temperature is provided using the standard rotor temperature model  36 , the algorithm  26  then proceeds to a switching model  42 , which determines whether the first brake pad wear model (i.e., the standard brake pad wear model  58 ) or a second brake pad wear model (i.e., a high-energy braking brake pad wear model, referred to as the race track brake pad wear model  82 ) will be utilized. The switching model  42  makes the determination based at least partially on an estimated rotor temperature  44 , braking speed  46 , and calculated braking energy  38 . The estimated rotor temperature  44  is initially from the standard rotor temperature model  36  from Equation (1) above, or may be from the race track rotor temperature model  80  after the algorithm  26  proceeds through that estimation. Braking speed is the same as wheel speed, and can be obtained from wheel sensors, or calculated based on sensor signals from an engine speed sensor, or a transmission output speed sensor. The calculated braking energy  38  can be as described in Equation (5) above. 
     More specifically, referring to  FIG. 3 , the switching model  42  considers the estimated rotor temperature  44 , an estimated braking speed  46 , and braking energy  38 . The switching model  42  will only proceed to estimate rotor temperature according to the race track temperature model  80  under certain conditions. First, the race track temperature model  80  will be used when a predetermined minimum rotor temperature RT MIN  or a predetermined minimum braking speed BS MIN  are determined to be exceeded a predetermined number of times within a predetermined time period. In block  50  of the switching model  42 , the estimated rotor temperature  44  is compared to the predetermined minimum rotor temperature X. If the estimated rotor temperature  44  is greater than the predetermined minimum rotor temperature X, then the switching model  42  proceeds to an event counter  52  and adds one event to the tally of events tracked by the event counter  52 . If the estimated rotor temperature is less than or equal to the predetermined minimum rotor temperature X, then the count of the event counter  52  is not increased, and the switching model  42  proceeds to block  54  to determine whether a vehicle operator has selected the race track mode (i.e., the race track brake pad wear model  82 ) such as by depressing an operator input button  55 , shown in  FIG. 1 , providing an audible command, or otherwise provided a signal indicating a selection of the race track mode. If it is determined that the race track mode has been selected, then the switching model  42  proceeds to block  56 , as described further with respect to  FIG. 2 . Otherwise, the switching model  42  proceeds to block  58  to determine brake pad wear according to the standard brake pad wear model  58 , discussed further herein, unless it is determined in block  54  that the vehicle operator has selected the race track brake pad wear model  82 . The standard brake pad wear model  58  is also referred to herein as a first brake pad wear model or an alternative brake pad wear model, and the race track brake pad wear model  82  is also referred to herein as a second brake pad wear model or a high energy brake pad wear model. 
     Similarly, in block  60  of the switching model  42 , the braking speed  46  is compared to the predetermined minimum braking speed Y. If the braking speed  46  is greater than the predetermined minimum braking speed Y, then the switching model  42  proceeds to the event counter  52  and adds one event to the tally of events tracked by the event counter  52 . If the braking speed  60  is less than or equal to the predetermined minimum braking speed Y, then the count of the event counter  52  is not increased, and the switching model  42  proceeds to block  54  to determine whether a vehicle operator has selected the race track mode and, if so, then the switching model  42  proceeds to block  56 , as described further with respect to  FIG. 2 . Otherwise, the switching model  42  proceeds to block  58  to determine brake pad wear according to the standard brake pad wear model  58 . 
     If the switching model  42  proceeds to block  52  and adds an event to the counter, the switching model  42  then proceeds to block  62  to determine whether the frequency of increasing the count of the event counter in  52  is greater than a predetermined threshold frequency. The frequency of increasing the count is an indicator of the frequency of aggressive braking by the operator of the vehicle  10 , as evidenced by the relatively high rotor temperature  44  and the relatively high braking speed  46  determinations of blocks  50  and  60 . If the threshold frequency is exceeded, then modeling brake pad wear according to the race track brake pad wear model  82  is appropriate, and the switching model  42  proceeds to block  56  of  FIG. 2 . Otherwise, the switching model  42  proceeds to the standard brake pad wear model  58 , unless it is determined in block  54  that the vehicle operator has selected the race track brake pad wear model, in which case the switching model  42  moves to block  56 . 
     The switching model  42  also evaluates braking energy  38  as a separate potential indicator of the appropriateness of the race track brake pad wear model  82  or the standard brake pad wear model  58 . In block  64 , the switching model  42  determines whether braking energy  38  exceeds a predetermined minimum braking energy. If, so, the switching model  42  proceeds to block  66  to determine how long the braking energy  38  remains greater than the predetermined minimum braking energy Z. If it is determined in block  68  that the predetermined minimum braking energy Z is exceeded for longer than a predetermined minimum period of time, then the switching model  42  proceeds to block  56  of  FIG. 3  to determine brake pad wear according to the race track brake pad wear model  82 . Otherwise, the switching model  42  determines brake pad wear according to the standard brake pad wear model  58 , unless it is determined in block  54  that the vehicle operator has selected the race track brake pad wear model. 
     Referring again to  FIG. 2 , if the switching model  42  has proceeded to the standard brake pad wear model  58 , then brake pad wear is determined according to a mathematical relationship of brake pad wear to rotor temperature that is most accurate in relatively low braking energy operating conditions (i.e., during a normal operating mode, not during driving on a race track or with other similar high energy driving maneuvers). Under the standard brake pad wear model  58 , the algorithm  26  inputs the applied braking force into a physical thermal model for first order dynamics to determine an estimate of the rotor temperature. Brake pad dynamometer tests can be used to obtain the brake pad friction coefficient as a function of rotor temperature and the amount of wear expected at each pad temperature. 
     Under the standard brake pad wear model  58 , the force required to stop the vehicle can be estimated as:
 
Force=mass×acceleration  (8)
 
     The front/rear brake proportioning information and the cornering information available from the controller C can be used to determine the power distribution on each axis and corner. The vehicle mass estimation is available from the controller C, and is also used in these equations. From the braking energy or the braking power, the brake pad temperature can be determined as a proportional value, and from the brake pad temperature, the brake pad wear can be determined as a proportional value, typically from a look-up table in the processor  24 . Those skilled in the art would readily understand how to provide a look-up table that was populated based on the relationship between the braking energy and the brake pad temperature and the brake pad temperature and the brake pad wear based on the calculations discussed above and the properties of the brake pad  22 . Each time the algorithm  26  calculates the wear of the brake pad  22 , it is added to the previous calculations of wear over time, and can then be extrapolated from the vehicle mileage to determine the remaining mileage for each brake pad  22 . 
     Alternatively, if the switching model  42  proceeds to block  56  as discussed with respect to  FIG. 3 , then the algorithm  26  estimates brake pad wear according to the race track brake pad wear model  82 . The estimation begins in block  56  in which a required braking energy to be dissipated by the vehicle braking system  16  is determined as a fraction of the total vehicle kinetic energy according to an energy partitioning model, also referred to as a brake system/road load energy partition model  56 . In other words, the vehicle energy to be braked is partitioned between the braking system  16  and other systems that can dissipate the energy. Brake system/road load energy partition model  56  models aerodynamic drag, tire losses, and powertrain braking losses based on vehicle speed, lateral acceleration, and gear selection. Various vehicle operating conditions are considered, such as the transmission gear ratio  70 , vehicle speed  72 , and the braking energy  38 . As discussed herein, the transmission gear ratio  70  correlates with the amount of energy that can be dissipated by engine braking. The vehicle speed  72  is used to determine the amount of energy dissipated by aerodynamic drag on the vehicle  10 . First, the aerodynamic force on the vehicle  10  is determined as follows: 
                     Aero   ⁢           ⁢   Force     =       1   2     ⁢     C   d     ×   p   ×   A   ×     V   2               (   9   )               
where C d  is the aerodynamic drag coefficient, ρ is air density, A is the vehicle cross sectional area, and V is vehicle velocity. The aerodynamic drag coefficient C d , air density ρ, and vehicle cross sectional area A may be constants stored in the processor  24 . Alternatively, air density ρ can be varied according to a sensed air temperature.
 
     The powertrain force is then determined according to the formula:
 
Powertrain Force=Gear Trans ×Gear Axle ×Torque Engine,Motoring   ×R   tire   (10)
 
where Gear Trans  is the transmission gear ratio, determined from a lookup table of gear ratios according to the current gear ratio  70 ; Gear Axle  is the drive axle ratio, also determined from a stored lookup table; Torque Engine,Motoring  is the engine motoring torque, determined from a stored lookup table of engine speed and throttle position; and R tire  is the radius of each tire  15 .
 
     Next, the tire force is determined according to the formula:
 
Tire Force= K ( V )×Slip Angle  (11)
 
where K is an empirically-determined coefficient relating tire losses to vehicle slip angle and vehicle speed; and Slip Angle is the vehicle overall slip angle, as may be indicated by a signal from a chassis controls portion of the processor  24 .
 
     With these values determined, the processor  24  can then calculate the portion of vehicle kinetic energy to be dissipated by the braking system  16  according to the ratio: 
                     Braking   Fraction     =               Total   ⁢           ⁢   Decel   ⁢           ⁢   Force     -     Aero   ⁢           ⁢   Force     -                 Powertrain   ⁢           ⁢   Force     -     Tire   ⁢           ⁢   Force               Total   ⁢           ⁢   Decel   ⁢             ⁢             ⁢   Force               (   12   )               
where Total Decel Force is the force according to Equation (8).
 
     Following block  56 , the algorithm  24  proceeds to block  74 , in which vehicle dynamics are modeled according to the high energy vehicle operating parameters of the race track mode, and the required braking energy is then distributed to the braking mechanisms  18 A,  18 B,  18 C,  18 D at the wheels  14 A,  14 B,  14 C,  14 D according to the modeled vehicle dynamics. First, the change in the front-rear weight distribution of the vehicle  10  in the race track mode, ΔW, is calculated according to the formula: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     W 
                   
                   = 
                   
                     
                       Weight 
                       Total 
                     
                     × 
                     
                       A 
                       X 
                     
                     × 
                     
                       CG 
                       WB 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     where CG is the center of gravity height; WB is the wheelbase height, and A X  is the fore-aft vehicle acceleration (i.e., longitudinal acceleration  78 ). 
     The front-rear weight distribution in the vehicle  10  is then calculated as follows:
 
 W   front   =W   front,static   +ΔW   (14)
 
 W   rear   =W   rear,static   −ΔW   (15)
 
where W Front,Static  is the static weight over the front axle, and W Rear,Static  is the static weight on the rear axle.
 
     The left-right weight distribution is then determined as follows: 
                       Δ   ⁢           ⁢     W   F         A   Y       =           W   S       t   F       ⁡     [           h   2     ⁢     K     F   ⁢           ⁢   ′             K   F     +     K   R     -       W   s     ⁢     h   2           +         l   -     a   s       l     ⁢     Z   RF         ]       +         W   uF       t   F       ⁢     z   WR                 (   16   )                   Δ   ⁢           ⁢     W   R         A   Y       =           W   S       t   R       ⁡     [           h   2     ⁢     K     R   ⁢           ⁢   ′             K   F     +     K   R     -       W   s     ⁢     h   2           +         a   s     l     ⁢     Z   RR         ]       +         W   uR       t   R       ⁢     z   WR                 (   17   )               
where ΔW F , ΔW R  is the change in lateral distribution of weight between the left and right of the vehicle  10 ; A Y  is the lateral acceleration (i.e., lateral acceleration  76 ); W S  is the sprung weight at height h S  and perpendicular distance h 2  from the Neutral Roll Axis; W uF  and W uR  are the front and rear unsprung weights at heights z WS  and z WR , respectively; K F , K R  are the front and rear suspension roll rates, respectively; a s  is the distance between the front roll center and the sprung mass center of gravity; and
 
     
       
         
           
             
               
                 
                   
                     K 
                     
                       F 
                       ⁢ 
                       
                           
                       
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                         ( 
                         
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                             a 
                             S 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         
                           
                             W 
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                             h 
                             2 
                           
                         
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   
                     K 
                     
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                       K 
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                     - 
                     
                       
                         
                           a 
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                           W 
                           S 
                         
                         ⁢ 
                         
                           h 
                           2 
                         
                       
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   19 
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     The vehicle dynamics model of block  74  then determines whether the square root of the sum of the lateral acceleration squared and the longitudinal acceleration squared is greater than a predetermined traction threshold. That is, block  74  determines whether the following is true:
 
√{square root over ( A   Y     2     +A   X     2   )}&gt;Traction_Threshold  (20)
 
The parameter Traction_Threshold equates loosely with the “traction circle” limit for the vehicle&#39;s tires, and will be set at a level above which exceeding the traction available at one or more wheel locations becomes likely. A typical value would be 0.7, and it would be tunable in vehicle development.
 
If not, braking energy is distributed according to the standard brake pad wear model of block  58 , i.e., according to the following:
 
                       Braking   ⁢           ⁢   Energy   ⁢           ⁢   Fraction   ⁢           ⁢   Front     =         A     piston   ,   front       ⁢     R     effective   ,   front       ⁢     μ   front         (               A     piston   ,   front       ⁢     R     effective   ,   front       ⁢     μ   front       +                 A     piston   ,   rear       ⁢     R     effective   ,   rear       ⁢     μ   rear             )         ;           (   21   )               
and
 
Braking Energy Fraction Rear=(1−Braking Energy Fraction Front)  (22)
 
     However, if the square root of the sum of the lateral acceleration squared and the longitudinal acceleration squared is greater than the predetermined traction threshold, then the braking energy is distributed according to available vertical force at each wheel  14 A,  14 B,  14 C,  14 D. For example, for a combined braking and right-hand turn, where Traction_Threshold is exceeded in Equation 20 above, block  74  calculates:
 
 W   left   _   front   =W   front   +ΔW   F , as the weight at wheel 14 A;   (23)
 
 W   right   _   front   =W   front   −ΔW   F , as the weight at wheel 14 B;   (24)
 
 W   left   _   rear   =W   rear   +ΔW   R , as the weight at wheel 14 C;   (25)
 
and
 
 W   left   _   rear   =W   rear   −ΔW   R , as the weight at wheel 14 D.   (26)
 
     The braking energy computed from the energy portioning model of block  56  is apportioned to each brake corner according to the fraction of the total vehicle mass. For example, if: 
                   W     left   ⁢   _   ⁢   front         W   S       =     40   ⁢   %       ,         
then 40% of the total braking energy is routed into the left front brake corner.
 
     Following block  74 , the algorithm  24  proceeds to block  80  to determine rotor temperature according to a lookup table of stored experimental data relating braking energy to rotor temperature, such as from testing on a vehicle dynamometer. The look-up table is determined the same as according to block  36 , but with: (i) braking energy apportioned to the wheels  14 A- 14 D according to the above formulas to more accurately determine rotor temperature at each wheel  14 A- 14 D under the high energy, race track mode vehicle operating conditions, and (ii) reduced cooling coefficients b in equation (1) the lumped capacitance model for brake rotor cooling. The reduced cooling coefficients in the second (higher temperature) driving mode (i.e., the race track driving mode) are due to changes in brake rotor material thermal properties (increase in specific heat capacity in particular) and convective cooling behavior. Example measurements show a 6% reduction in high temperature brake cooling coefficients (starting temperature above 600 degrees Celsius) versus lower temperature brake cooling coefficients (starting temperature around 400 degrees Celsius). 
     Next, the algorithm  26  relates rotor temperature determined according to the race track rotor temperature model  80  to brake pad wear in the race track brake pad wear model  82 . The estimated rotor temperature determined for a particular time step of the algorithm  26  according to the race track rotor temperature model  80  and the braking energy from the vehicle dynamics model  74  at each wheel  14 A- 14 D during that time step are inputs to the race track brake pad wear model  82 . The inputs are related to experimental testing data stored in a look-up table or to a fitted equation of volumetric wear per unit of braking energy input, which may be in cubic millimeters per Kilojoule versus temperature in degrees Celsius. The correlation provides an estimated volumetric wear of the brake pad  22  during that time step. Linear wear can then be tracked according to the race track brake pad wear model  82  that also accounts for the properties of the brake pad  22 . More specifically, linear wear of a respective one of the brake pads  22  is calculated as: 
                     Wear   linear     =         ∑     t   =   0     t     ⁢           ⁢     Wear   timestep         Area   Pad               (   27   )                 FIG. 4  shows a brake pad  22  with an initial thickness th and a direction of linear wear from an upper surface  90  to a lower surface  92  that is secured to the brake rotor  20 . Each time the algorithm  24  calculates the wear of each brake pad  22 , whether under the standard brake pad wear model  58  or the race track brake pad wear model  82 , the wear is added to previous calculations of wear over time, and the remaining mileage for each brake pad  22  can be extrapolated from vehicle mileage and the initial thickness of the brake pad  22 .
 
     In  FIG. 4 , the brake pad  22  is shown with two physical wear sensors  94 A,  94 B each of which is operatively connected to the controller C. The physical wear sensors  94 A,  94 B are in the form of wires embedded at different predetermined depths in the brake pad  22 . Other types of brake sensors could instead be used, such as an indirect sensor or sensing mechanism to infer the brake pad thickness. Suitable examples include brake fluid level sensors or measuring the displacement of the brake calipers, such as in an electro-mechanical or brake-by-wire system. When the brake pad  22  linear wear reaches the depth D 1  of the first physical wear sensor  94 A, the physical wear sensor  94 A will cause a signal  86 A to the controller C, either by breaking or by making contact with the rotor  20 . Similarly, when the brake pad  22  linear wear reaches the depth D 2  of the second physical wear sensor  94 B, the second physical wear sensor  94 B will cause a signal  86 B to be sent to the controller C. These signals from the sensors  94 A,  94 B are indicative of specific, actual brake pad thicknesses and can be used to gradually ramp out any differences between the estimation of the brake pad thickness from the brake pad wear models  58  or  82 , and the actual thickness over the remaining pad thickness and life. 
     Accordingly, after estimating brake pad wear according to the standard brake pad wear model  58  or according to the race track brake pad wear model  82 , the algorithm  24  proceeds to the wear correction model  84 . If a signal from the first physical wear sensor  94 A has not yet been received, then no correction to the estimated brake pad wear is made. The algorithm  24  then proceeds to box  94  under which a brake pad wear signal or indication is produced and provided to the vehicle operator via the brake pad wear indicator output device  35  of  FIG. 1 , indicating the amount of estimated brake pad wear or the amount of remaining brake pad life, which is correlated with the remaining brake pad thickness determined from the estimated brake pad wear. 
     If the wear correction model  84  has received a physical wear sensor signal  86 A from the first physical wear sensor  94 A, the estimated brake pad wear is compared to the predetermined brake pad wear (i.e., wear of linear thickness D 1 ). If a significant difference exists between the estimate and the actual thickness, as determined when the sensor signal  86 A or  86 B is received, then this difference is used to adjust (i.e., correct) the estimated brake pad wear so that when the pad  22  is near the replacement period, or near the depth D 2  of the next physical wear sensor  94 B, the total system accuracy will be as high as possible. This will involve increasing or decreasing the estimate of the pad life remaining at a rate different from that observed so that the end of the life of the pad  22  will be accurately determined. 
     The algorithm  26  then proceeds to block  94  to provide an indication of brake pad wear or of remaining brake pad life to the vehicle operator. The algorithm  26  then proceeds to block  36 , and then to the switching model  42  and, after a predetermined time period, again determines whether vehicle operating conditions indicate that the standard brake pad wear model  58  or the race track brake pad wear model  82  should be applied. As the algorithm  24  repeats, when the controller C subsequently receives a physical wear sensor signal  86 A from the second physical wear sensor  94 B, the wear correction model  84  again adjusts the estimated brake pad wear models  58 ,  82 . 
     While the best modes for carrying out the many aspects of the present teachings have been described in detail, those familiar with the art to which these teachings relate will recognize various alternative aspects for practicing the present teachings that are within the scope of the appended claims.