DESCRIPTION

STATE OF THE ART

The following explanation relates to a method of estimating wear of a vehicle brake element.

SUMMARY

Vehicle brake element wear sensors have been on the market for a long time and are well-known devices.

The known types of wear sensors for vehicle brake elements can be identified by their most important operating principle, such as electrical wear sensors and mechanical wear sensors.

The operating principle of electrical wear sensors involves resistor circuits, which, when there is a decrease in the thickness of the brake element, typically a disc brake pad, they create a contact between the metal disk and a sensitive area or break the electrical circuit and send a warning signal; more than one circuit may be provided at different pad depths, so that warning signals are processed by the vehicle’s computer to calculate the remaining useful life of the brake pad.

Two main versions of the electric wear sensors are available on the market: incorporated into the brake pads, or a separate sensor mounted on the brake pad and designed to maintain friction contact with the surface of the brake rotor.

Mechanical wear indicators rely on a modified back-plate that generates noise when the amount of friction material left in the pad reaches a designated reduced thickness.

The position-sensor wear indicator measures the position of the brake mechanics and sends a warning signal to the driver when a designated position has been reached.

Mixed-operation system wear sensors are also known of and available on the market. A known type of Electronic Parking Brake (EPB) can also detect pad wear by counting the number of screw/nut turns required to engage the rear brake pads - more rotations means less pad thickness.

Innovatively, patent application IT 102021000005636 filed by this same applicant discloses a method for estimating the wear of a vehicle brake element by processing temperature signals acquired on the support bracket of that element.

In said patent application, the wear of a brake element is estimated based on the variation over time of the temperature detected over long periods of time for a series of homogeneous braking events.

There is also a need, moreover, to improve a brake element’s wear estimate by making it independent of capturing the temperature change detected over long periods for a series of homogeneous braking events.

The technical task described in the present explanation, therefore, is to overcome the current limitations of known wear sensors and to improve their performance and reliability.

The technical task according to the present explanation is accomplished by providing a vehicle brake element wear estimation method which includes at least a braking disc, a wear-able block of friction material and a back support plate of said block of friction material, at least one temperature sensor configured and positioned to sense the temperature of said back support plate, and one electronic processing unit connected to said temperature sensor, comprising the actions of:

-capturing, over time, a plurality of temperature values from said at least one temperature sensor;

-processing an estimate of the thickness of said wear-able block of friction material by processing said acquired temperature values, characterized by the fact that said estimate of the thickness of said wear-able block of friction material is performed by subsequently subtracting a plurality of wear increases from the thickness of said block, where each increase in wear is calculated between the capture points of a corresponding pair of temporally consecutive temperature values t1 and t2, where each increase in wear is calculated by calculating the amount of heat transferred to said wear-able block of friction material between said capture points.

In one embodiment, at least a first contribution to said amount of heat transferred for each increase in wear is inferred from the calculation of the temperature difference acquired between said capture points t1 and t2.

In one embodiment, at least a second contribution to said amount of heat transferred for each increase in wear is inferred from the calculation of the heat dissipated by said brake element between said capture points t1 and t2.

In one embodiment, in the calculation of said amount of heat transferred, each contribution to said amount of heat transferred is modulated with parameters that make it consistent with previously acquired experimental data.

In one embodiment, the capture of the detected temperature of said back support plate is activated at each braking activation instant t1 on said braking disc and up to a predetermined instant t2 after braking release.

In one embodiment, each increase in wear is calculated at each acquisition of said detected temperature of said back support plate.

In one embodiment, the estimate of the thickness of said wear-able block of friction material is performed in real time.

The present invention also describes a vehicle brake element including a wear-able block of friction material, a back support plate of said block of friction material, a temperature sensor configured and positioned to detect the temperature of said back support plate and an electronic processing unit configured to carry out the wear estimation method described above.

BRIEF DESCRIPTION OF DRAWINGS

Various forms of implementation are portrayed in the attached drawings for purely illustrative purposes and must not in any way be interpreted as restricting the scope of this invention.

Various features of the different embodiments may be combined to constitute additional embodiments, which are also part of this invention.

Figure 1 schematically shows angle 1 of a vehicle suitably equipped with the components of the method;

Figures la to If show options for the placement of the temperature sensor, which may be of the contact or non-contact type;

Figure 2 schematically illustrates a system architecture for the method with smart brake pad sensors and time-based data capture;

Figure 3 schematically illustrates a system architecture for the method with smart brake pad sensors and activation-based data capture;

Figure 4 schematically illustrates a system architecture for the method with data capture based on activation of the brake;

Figure 5 schematically illustrates a flow diagram of the algorithm;

Figure 6 schematically shows the determination of successive estimates of wear increases;

Figure 7 presents two graphs showing the relationship between the detected temperature trend and the corresponding wear estimate;

Figure 8 shows a comparison between the experimental measures actually performed and wear estimate according to the method described in this invention.

DESCRIPTION OF THE METHOD The present invention is intended to protect the wear estimate of a vehicle brake element using the sum of subsequent wear increases, as calculated by means of an estimation of the amount of heat transferred to said element, regardless of how said estimate of the amount of heat is obtained.

The purpose of the invention, therefore, is to estimate brake element wear by means of heat dynamics. The strategy of the method, according to the invention, is to estimate increases in wear over short time periods, then to add up the estimated increases to obtain the pad’s actual thickness in real time.

Different system architectures may be implemented depending on which capture strategy and auxiliary sensors are used, including but not limited to the following descriptions.

Essentially, the data capture may be:

- time-based: temperatures and data from auxiliary sensors are acquired at short time intervals;

- preferably, based on activation and time: temperatures and data from the auxiliary sensors are acquired from when the brake pedal is activated at time t1 up to a predetermined time t2 after release of the pedal and/or braking; advantageously, this solution reduces the amount of power required for the system.

Advantageously, according to the method of the present invention, all acquired measurements are used for estimating the corresponding wear increases with no need to select the analyzed events.

The estimation algorithm is compatible with any driving style: with a more aggressive driving style, the estimation of increase in wear is expected to be greater.

Measurements detected by auxiliary sensors, such as ambient temperature and other variable data, can be used to refine the heat dynamics models, thus improving the performance of the estimation algorithm. Advantageously, the wear estimate is captured in real time.

Conveniently, each comer of the vehicle can be equipped with one or two pads with sensors; advantageously, wear may be estimated for each pad or as a function of the thickness of the pads of the same comer.

Each comer of the vehicle can be equipped with pads with sensors.

The wear estimate can be captured by a central vehicle processing unit and/or by individual dedicated control units at each individual comer.

PRINCIPLE OF THE METHOD

The increase in wear Δw of the friction material between two subsequent temperature captures is proportional to the friction work Wƒr implemented by the braking.

The friction work Wƒr is proportional to the amount of heat transferred to the brake pad.

The heat transferred to the brake pad is partly dissipated as δQout and partly causes, as δQin, an increase in temperature ΔT. δQin can be estimated from temperature increment measurements ΔT, which may be supplemented with readings of other variables.

The successive estimated wear increments Δw are added together to obtain total wear w.

Schematically:

DETAILED DESCRIPTION OF THE COMPONENTS OF SOME EMBODIMENTS

The following detailed description refers to the attached drawings, which form a part thereof.

In the drawings, similar reference numbers typically identify similar components, unless otherwise dictated by the context.

The forms of illustrative implementation described in the detailed description and in the drawings are not understood to be limitative. Other embodiments may be utilized and other modifications may be made without departing from the spirit or scope of the subject matter presented herein.

Aspects of the present explanation, as described generally herein and illustrated in the figures, may be rearranged, replaced, combined, separated and designed in a wide variety of different configurations, all explicitly contemplated and present in the present invention.

In the descriptive text that follows, element 20 may be referred to as “wear-able block of friction material” or “brake pad” indiscriminately; the term “brake pad temperature” may be conventionally used as “back-plate temperature”.

Fig. 1 provides a schematic illustration of a comer 1 of a vehicle equipped with a braking element according to the present invention.

At least a braking element of the vehicle, consisting of a wear-able block of friction material 20, a back support plate 40 and a temperature sensor 100 configured and positioned to capture the temperature of the back support plate 40.

The temperature sensor 100 is typically a contact temperature sensor integrated into the back support plate 40 or a non-contact temperature sensor.

The temperature sensor 100 may be configured and positioned to sense the temperature of the surface of the back support plate 40 or the average temperature of the back support plate 40. Some of the possible positions of the temperature sensor 100 are shown in Figures 1 to If.

For example, the temperature sensor 100, if of the contact type, may be positioned flush or overhanging a surface of the back support plate 40 adjacent to the wear-able block of friction material 20 (Figs. 1, la) or flush or overhanging on a surface of the back support plate 40 opposite the wear-able block of friction material 2 (Fig. lb), or may be integrated within the back support plate 40 (Fig. 1c). The temperature sensor 100, on the other hand, if of the contact type, may be positioned on the side of the surface of the back support plate 40 adjacent to the wear-able block of friction material 20 (Figs. Id) or on the side of a surface of the back support plate 40 opposite the wearable block of friction material 2 (Fig. le), or lateral to the back support plate 40 (Fig. If).

The temperature sensor 100 may be a separate component or may be silk-screened directly on the metal back support plate; different patterns may be made by combining different types of sensors; multiple temperature sensors may be used in the same embodiment to obtain distributed temperature monitoring.

The braking element may be a braking pad that cooperates with a disc 10, as shown by way of example in Figure 1, or a jaw that cooperates with a drum, not shown in the Figures.

As shown schematically in Figure 1, the comer 1 of the vehicle is provided with a brake pad made up of an optional back layer 30 between the wear-able block of friction material 20 and the back support plate 40.

Advantageously, the temperature sensor 100 may be incorporated in the brake pad external to the disc 10 or on the brake pad internal to the disc 10, and, advantageously, in the external braking pad and the internal braking pad.

An electronic processing unit (EPU) 200 is connected to the temperature sensor 100.

Suitably and advantageously, the electronic processing unit (EPU) 200 is connected to and receives input signals from a plurality of auxiliary sensors, typically one or more accelerometers 401, one or more ambient temperature detectors 403, one or more motion detectors 404 provided on board the vehicle.

Furthermore, at least one or more smart force sensors 402 embedded in the brake pad and a switch on the brake pedal 405 may be provided and connected to the electronic processing unit

200. Conveniently, an algorithm 300 according to the invention of the present method oversees the data collection, processing and output of the electronic processing unit (EPU) 200 in relation to the estimation of the thickness 600 of the wear-able block of friction material 20.

The method of estimating wear in a vehicle brake element according to the present invention, therefore, involves the temperature sensors 100 acquiring the temperature detected for the back support plate 40, generating the temperature signals and transmitting the temperature signals to the electronic processing unit 200, which provides an estimate of the thickness of the wear-able block of friction material 20 by duly processing the temperature signals using the algorithm 300. Advantageously, seasonal adjustment is performed using the measured ambient temperature to increase the performance and resolution of the algorithm.

Advantageously, the wear of the brake pad 20 can be estimated in real time.

Advantageously, the comer of the vehicle 1 may be equipped with one or two temperature sensors 100, wherein the wear of the brake pad 20 may be estimated for each brake pad 20 or as an average value of the brake pads 20 of that comer of the vehicle 1.

Advantageously, each comer of the vehicle 1 may be equipped with temperature sensors 100.

Advantageously, the calculation of the wear of the brake pad 20 may be performed by one central electronic processing unit 200 or by individual electronic processing units 200, each dedicated to a different comer of the vehicle 1.

SYSTEM ARCHITECTURES

The following description illustrates three different but not limitative system architectures, each of which can be implemented based on the chosen data acquisition strategy and auxiliary sensors; each architecture can be used with any one of the algorithm strategies.

Time-based data capture architecture.

Figure 2 schematically shows a system architecture of the time-based data acquisition method. All sensor data acquisitions are performed at time points defined by the electronic processing unit 200.

Typically, the interval between data collection time points is between 1 second and 60 seconds, preferably 30 seconds.

Different sensors may be sampled at different sampling rates.

The architecture includes at least temperature sensor 100, accelerometers 401, ambient temperature sensors 403, smart force sensors 402 of the pad, motion sensors 404, and an electronic processing unit 200 with the algorithm 300.

Smart force sensors 402 include at least one shear force sensor and/or a pressure force sensor.

Accelerometers 401, force sensors 402, and motion sensors 404 may or may not be used for the wear estimation.

Accelerometers 401, force sensors 402, and motion sensors 404 may be used to quantify dissipative terms or provide alternative methods for calculating braking force work.

Ambient temperature sensors 403 are used for seasonal adjustments of the data collected by temperature sensors 100.

The accelerometers 401 are connected to the electronic processing unit 200, wherein the accelerometer 401 acquires vehicle acceleration as defined by the electronic processing unit 200 and generates a vehicle acceleration signal that is transmitted to the electronic processing unit 200.

The smart plate force sensors 402 are connected to the electronic processing unit 200, wherein the smart pad force sensors 402 acquire at least one force as defined by the electronic processing unit 200 and generate a force signal that is transmitted to the electronic processing unit 200. The vehicle motion sensor 404 is connected to the electronic processing unit 200, wherein the vehicle motion sensor 404 acquires vehicle movement as defined by the electronic processing unit 200 and generates a motion signal that is transmitted to the electronic processing unit 200.

The collected data is processed by the electronic processing unit 200 through the algorithm 300; the signals of accelerometers 401, the smart force sensors of the pad 402, and the vehicle motion sensors 404 are processed to offset and adjust the wear estimate and/or to select and/or to detect a significant event, i.e. a significant braking event.

Finally, an estimate of wear increase 500 of the brake pad 20 is provided.

Activation-based data acquisition architecture: first example.

Figure 3 schematically shows a system architecture for the method with smart brake pad sensors and activation-based data capture.

In an activation-based data acquisition strategy, the temperature data acquisition (of the pad and/or braking system and/or environment) is performed only when a significant event occurs, i.e. a significant braking event.

The architecture includes at least temperature sensor 100, accelerometers 401, ambient temperature sensors 403, smart force sensors of the pad 402, motion sensors 404, a unit for acquisition strategy 201 and an electronic processing unit 200 with the algorithm 300.

A unit for acquisition strategy 201 can be used for selecting significant braking events from among all braking events detected by the accelerometers 401 and the smart force sensors of the pad 402.

Accelerometers 401 and/or force sensors 402 may or may not be used for the wear estimation.

Accelerometers 401 and/or force sensors 402 and/or and motion sensors 404 and/or ambient temperature sensors 403 may be used to quantify dissipative terms or provide alternative methods for calculating braking force work. Ambient temperature sensors 403 are used for making seasonal adjustments to the data collected by temperature sensors 100; other known instruments that can detect environmental changes may be used for seasonal adaptation purposes.

The collected data is processed by the electronic processing unit 200 through the algorithm 300 and an estimate of the wear increase 500 of the brake pad 20 is provided.

Activation-based data acquisition architecture: second example.

Figure 4 schematically shows a system architecture for the method in which the brake pads are equipped with smart force sensors and where the data capture is based on activation.

The architecture includes at least the temperature sensor 100, accelerometers 401, ambient temperature sensors 403, a brake pedal switch or a vehicle information network 405, motion sensors 404, a unit for acquisition strategy 201, and an electronic processing unit 200 with the algorithm 300.

In a data-acquisition strategy based on activation, the data acquisition from the temperature sensors 100 and the data acquisition from ambient temperature sensors 403 are performed only when a significant braking event occurs.

A unit for acquisition strategy 201 can be used for selecting significant braking events from among all braking events detected by the accelerometers 401 and the brake pedal switch 405.

In an activation-based data acquisition strategy, the temperature data acquisition (from the pad and/or the braking system and/or the environment) is performed only when a significant event occurs, i.e. a significant braking event.

Accelerometers 401 and/or motion sensors 404 may or may not be used for the wear estimation. Accelerometers 401 and/or the brake pedal switch and/or the vehicle information network 405 may be used to quantify dissipative terms or provide alternative methods for calculating braking force work. Accelerometers 401 and/or motion sensors 404 and/or ambient temperature sensors 403 may be used for the selection of significant braking events.

Ambient temperature sensors 403 are used for making seasonal adjustments to the data collected by temperature sensors 100; other known instruments that can detect environmental changes may be used for seasonal adaptation purposes.

The collected data is processed by the electronic processing unit 200 through the algorithm 300 and an estimate of the wear increase 500 of the brake pad 20 is provided.

ALGORITHM DIAGRAM

The collected signals are processed for possible spikes and measurement errors to reduce their impact on wear estimation.

The increase in the temperature ΔT of the brake pad between two subsequent time points t1 and t2 is calculated.

The amount of heat dissipated δQout is calculated, preferably but not exclusively, as a function of each piece of data detected and processed by the available sensors.

Other phenomena that may contribute to the dynamics of the heat are considered, preferably but not exclusively and depending on what sensors are available.

The temperature increase ΔT, the dissipated heat δQout, and any other phenomena considered are processed and combined to generate an estimate of the amount of heat transferred to the brake pad δQin.

The estimate of the amount of heat transferred to the brake pad δQin is converted into the estimate of the increase in wear Δw of the friction material.

The new increase in wear Δw is subtracted from the known and/or previously calculated pad thickness to obtain its actual thickness in real time. Figure 5 schematically illustrates the flow diagram of the algorithm 300 in the electronic processing unit 200.

The data captured by the temperature sensor 100 is processed by signal process section 310; the ambient temperature signals transmitted by ambient temperature sensors 403 are processed by signal process section 311, the signals captured by auxiliary sensors 401, 402, 404 and 405 are processed by signal process section 312.

The temperature signal thus processed by section 310 is transferred to the calculation sections 320, which estimate the increase in temperature ΔT; the signals processed by the process sections 310, 311 and 312 flow both into calculation section 321, which determines the amount of heat dissipated δQout, and into calculation section 322, which manages and processes the data detected for boundary phenomena.

The data processed by calculation sections 320, 321 and 322 flow into the complex calculation section 330, which determines the estimation of the amount of heat transferred to the brake pad δQin, and sequentially the increase in wear Δw 500 of the friction material.

The thickness estimate 600 is then calculated and provided in real time by subtracting the wear increase Δw 500 from the known thickness of the pad.

IMPLEMENTATION STRATEGIES

Here are some implementation schemes - exemplary but not exhaustive - of the wear estimation method for a vehicle brake element according to the present invention.

Implementation, general case 1

This first scheme may be considered the most typical and general scheme: this scheme includes all others (whether described here or not) as more specific cases. The presence of auxiliary sensors is considered, even if they are not essential: their measurements, when available, are processed by the algorithm 300 and used to estimate heat dissipation and to consider other boundary phenomena.

We define Δw as the estimate of the calculated wear increase for the difference ΔT of the temperature T between the two acquisitions after the next two time points t1 and t2, w old as the wear estimate previously calculated at t1; the new wear estimate w new is the sum of w old and Δw .

For each new pad temperature acquisition Tnew and ambient temperature acquisition Tamb:

- the ΔT is calculated as the difference between Tnew at time point t2 and the previous Told at time point t1 ;

- the amount of heat dissipated δQout ^(α) (T, Tamb, ....) is calculated, where (α) is a set of parameters to be fine-tuned by comparing them with the detected experimental parameters and the points represent any further measurement detectable by the auxiliary sensors;

- the amount of heat transferred δQin is calculated based on a plurality of contributions, typically a first contribution from a calculation of the temperature difference ΔT acquired between acquisition points t1 and t2, a second contribution δQout from the calculation of the amount of heat dissipated, and to the extent possible, other contributions from other boundary phenomena: where (β) is another set of modulation parameters that make it consistent with previously acquired experimental data;

- the wear increase 500 is calculated as Δw = γ . δQin;

- the wear value w is updated as w new = w old + Δw ;

- the thickness 600 of the pad is updated by subtracting the value of the wear increase 500 from the known and/or calculated thickness; - the parameters in α, β, γ are processed to maximize correspondence with the detected experimental data.

Implementation, specific case 2

This second scheme may be considered a specific instance of the general scheme described above.

In this case, the only effects that contribute to the heat transfer estimate δQin are a first contribution from a calculation of the temperature difference ΔT acquired between acquisition points t1 and t2 and a second contribution δQout from the calculation of the amount of heat dissipated; the presence of auxiliary sensors is considered but is not necessary.

For each pad temperature acquisition Tnew and ambient temperature acquisition Tamb:

- ΔT is calculated as the difference between Tnew and the previous Told,'

- the amount of heat dissipated δQout ^(α) (T, Tamb, ....) is calculated, where (α) is a set of parameters to be fine-tuned by comparing them with the detected experimental parameters and the points represent any further measurement detectable by the auxiliary sensors;

- the amount of heat transferred is calculated δQin = ( β ₁ ΔT + δQout) +, which identifies the amount ( β ₁ ΔT + δQout) when it is positive, or otherwise set to zero, where ( β1) is a set of modulation parameters consistent with previously acquired experimental data;

- the increase in wear is calculated as Δw = γ . δQin;

- the wear value w is updated as w new = w old + Δw ;

- the thickness 600 of the pad is updated by subtracting the value of the wear increase 500 from the known and/or calculated thickness;

- the parameters in α, β1, γ are processed to maximize correspondence with the detected experimental data.

Implementation, specific case 3 This third scheme may be considered a specific instance of the general scheme described above. In this case, it is assumed that the pad temperature detector is the only sensor available and that only the first contribution from a calculation of the temperature difference ΔT acquired between the acquisition points t1 and t2 contributes fully to the amount of heat transferred to the brake pad δQin, without any dissipation.

For each pad temperature acquisition Tnew:

- ΔT is calculated as the difference between Tnew and the previous Told;

- the amount of heat transferred δQin = ( β ₁ ΔT)+ is calculated, where ( β1) is a set of modulation parameters consistent with previously acquired experimental data;

- the increase in wear is calculated as Δw = γ . δQin;

- the wear value w is updated as w new = w old + Δw ;

- the thickness 600 of the pad is updated by subtracting the value of the wear increase 500 from the known and/or calculated thickness;

- the parameters in β1, γ are processed to maximize correspondence with the detected experimental data.

FROM DISCRETE TIME TO CONTINUOUS TIME WEAR MODEL

As mentioned, the wear increment of the friction material between two successive temperature acquisitions is proportional to the frictional work performed by braking.

The frictional work is proportional to the quantity of heat δQin transferred to the brake pad.

The heat δQ _in transferred to the brake pad is partially dissipated and partially causes an increase in the temperature of the brake pad.

It is possible to estimate δQ _in by measuring the temperature of the brake pad, possibly supplemented by the reading of other variables.

In the discussion that follows: D = initial thickness of the brake pad

A = area of the brake pad that conies into contact with the brake disc i = i- ^th acquisition of the temperature measurement acquired at time t _i , where i = 1, 2, 3, . N x _i = thickness corresponding to the i- ^th acquisition of temperature measurement. x _i-1 = thickness corresponding to the i-1- ^th acquisition of temperature measurement.

Δ w _i = x _i - x _i-1 = -Δ x _i = wear increment between acquisition i and acquisition i-1 ΔT _i = positive variation of temperature between acquisition i and acquisition i-1

(ΔT _i ) ⁺ = max (0, ΔT _i ) δQ _in,i = heat transferred to the brake pad between acquisition i and acquisition i-1 γ = constant, experimentally determined β = set of modulation parameters

In general, it is true that:

The increments are then summed up to calculate the thickness after n time steps:

In one of the possible implementations of the wear model, we have that: where

C _p = specific heat of brake pad p = density of brake pad

The formula to calculate the wear increment according to the wear model adopted is: where γ is a parameter calculated with a statistical method that encompasses all the constants. The aforementioned wear model considers temperature and wear increments at discrete time intervals and allows for the calculation of the estimated current thickness of the wearable block by subtracting from the initial thickness wear increments, estimated on the basis of the thermal energy exchanged by the brake pad at a discrete time interval.

This discrete-time wear model is congruent with the fact that the acquisition of temperature signals and other signals (ambient temperature, force, etc.) take place through sampling.

Physically, however, these wear increments in fact take place with a continuous flow over time, and advantageously, the invention also provides a new wear model that takes this into account. The continuous-time wear model arises as a limit of the discrete-time wear model for acquisition intervals that tend toward zero and is formulated as a differential equation that connects the infinitesimal wear increment to the various quantities available to the model (positive increase in temperature, thickness, etc.).

Let us therefore now consider the case when temperature and wear increments are taken over infinitesimally short times dt.

In this case infinitesimal increments Δ x _i and T _i are substituted by the time derivatives dx(t)/dt and dT(t)/dt.

The general case is:

In the simplest example above, the differential equation looks like the following. dx(t)/dt = - γx(t) (dT(t)/dt) ⁺ where (dT(t)/dt) ⁺ = max (0, dT(t)/dt)

The solution of this differential equation may be performed numerically in most cases (with Euler discretization, or by higher order methods), or analytically, for particular choices of the function If solved numerically by the Euler method, this differential equation brings back to the discrete time wear model.

In particular cases the differential equation can be solved analytically.

For example, for the simple example above where the differential equation is dx(t)/dt = - γx(t) (dT(t)/dt) ⁺ there is the following explicit solution: x(t) = De ^a where

Note that since the acquisition of temperatures always happens discretely, the [integral] above needs to be calculated from discrete values.

Advantageously, then, the invention provides a modeling of the relationship between the infinitesimal wear increments and the other quantities available in terms of a differential equation.

Advantageously in this new formulation, sometimes the wear calculation can be made even without directly summing the infinitesimal wear increments.

Advantageously, as stated, unlike the wear model that considers temperature and wear increments at discrete time intervals, the wear model that considers temperature and wear increments at infinitesimal time intervals allows for the calculation of the estimate of wear without the need to know the value of the wear increments.

EXPERIMENTAL RESULTS

The graphs in Figure 8 show the results of a specific implementation, general case 1, as described above. The algorithm was developed with long-term tests where two vehicles were driven until the pads were completely consumed while repeating various physical measures of partial wear, as represented by the circles on the graphs; the solid line represents what was returned by the algorithm, which was subsequently fine-tuned on the same data.

The margins of error represented by the RMSE (root mean square error) for the first vehicle is 0.29mm and for the second vehicle is 0.42mm; the MAE (mean absolute error) for the first vehicle is 0.56mm and for the second vehicle is 0.81mm.

In effect, it was found that the method according to the invention is particularly advantageous for providing a reliable and safe real-time estimate of wear in a vehicle brake element.

Changes and variations to the all the above are possible, naturally; the method for estimating wear in a vehicle brake element, conceived in this way, is subject to numerous modifications and variations, all within the scope of the inventive concept, as depicted in the claims; furthermore, all details can be replaced with other technically-equivalent elements.

In practice, any kind of materials and systems may be used, according to the needs and the state of the art.