WO2014064319A1 - Method for monitoring the roughness of a part in real time during a machining process - Google Patents

Abstract

The invention relates to a method for monitoring the surface roughness of a part in real time during a machining process carried out by a machine-tool. The method comprises the following steps: obtaining an incremental hybrid model representing the machining process and evaluating the incremental hybrid model in real time in order to obtain the surface roughness. This method is especially useful in micro-machining processes, where the operator cannot personally check the results of the operations, though it is also applicable to machining operations in general. The described method is simple and easy to implement, providing precise results allowing operators to make appropriate decisions during the machining process. The use of the method according to the invention allows the quality of the machined parts to be improved while reducing the total production time.

Description

 DESCRIPTION

Method to monitor in real time the roughness of a piece during a machining process

Object of the invention

 The invention is part of the field of industry, specifically in the processes of machining parts using numerical control machines (CNC).

The main object of the present invention is a method for monitoring the surface roughness of a piece in real time during the machining process of said piece.

Background of the invention

 The surface roughness of a machined part constitutes one of the most important characteristics to know the quality of the piece, constituting an evaluation of the effectiveness of the manufacturing process carried out. The procedure used for the measurement of surface roughness can become a differentiating element in terms of competitiveness, since it influences criteria such as performance and productivity of the manufacturing strategies used to form parts.

Currently, it is possible to achieve a relatively high precise measurement of the roughness of macroscale machined parts in relatively simple ways. However, this precision and simplicity is reduced as the dimensional scale at which it works is reduced, becoming critical in the microscale and nanoscale. In other words, determining the finish of small microscale parts is much more difficult, being especially problematic when the roughness requirements are between 0.3 nm and 7.0 nm. Note that the adjustment and finishing of micro parts can affect the quality and operation of assemblies at a higher level. Although there is no generalized consensus regarding the definition of nanomechanized, micromachining and macromachining terms, a widely accepted definition for these terms is their literal meaning, that is, nanomechanizing for machining dimensions between 1 and 999 nm, micromachining for dimensions between 1 and 999 μιη and macromechanized for dimensions larger than 1 mm. It should be noted that the micro and nano ranges vary depending on factors such as the machining method, the type of product, the material, among others. It should also be noted that to frame the technology used on a certain scale, it is not necessary that the piece that is manufactured has all its dimensions on that scale.

Currently, the procedures with greater roots in the industry to accurately measure the surface roughness of manufacturing are carried out post-process, that is, once the manufacturing operations are completed, thus influencing the total manufacturing time of the piece. For this, the so-called profilometers or roughness meters are normally used, which are devices equipped with a needle that touches the surface whose roughness is to be measured. High variations of the surface are measured by moving the needle (or the surface). The movements of the needle are converted into electrical signals that are then amplified, digitized and introduced to the computer to analyze the data.

In the microscale case, the probe head and the needle are small-scale versions of traditional contact profilometers. However, unlike the traditional contact method, the measurement is recorded when there is a change in the constant movement of the microsensor (damped). Currently, needles of extraordinarily small sizes are available, such as 0.125 mm in diameter and 10 mm in length. When the tip approaches the object to be measured, its micromotion is damped by the proximity to the surface of the piece. This threshold step change in the micro-movement is recorded as a measurement point. A drawback of the measurement of the roughness in parts in the microscale with profilometers is related to the positioning of the micro-piece for inspection with the profilometer. Due to the small size of the pieces, it is difficult to physically see the position of the piece to be measured under the probe head to align the movement of the needle with the piece. A pre-positioning system is needed, using supports, shims, holes or some system that allows the piece to be placed under the probe head. In short, these are complex systems.

Other post-process measurement procedures are also known, such as those described in US7630086, US6163973 and US5608527. The first of these documents describes the use of a laser emitter to detect manufacturing defects on the surface of silicon wafers, magnetic discs or transparent glass substrates, obtained by polishing operations. The other two documents employ a method of measuring surface roughness without contact whose purpose is, on the one hand, to avoid aggressive collisions of the stylus instrument with the part and, on the other, to detect imperfections in the pressing rollers in the manufacture of plates of metal, respectively.

Some methods are also known for monitoring or measuring different variables or events, such as roughness, which are carried out in-process, that is, during manufacturing operations. These methods are mainly focused on macroscale machining operations. Among these methods, we can highlight the technologies that propose the monitoring of surface roughness in-process from the measurement of variables that characterize the temporal behavior of cutting operations.

As an example, documents US6626029 and US7463994, which propose methods for measuring surface roughness in polishing, cylindrical grinding or surface machining operations, can be cited. In the case of the first document, the measurement is made from the measurement of the acoustic emission during the process of cutting and using a high frequency piezoelectric transducer. The second document uses the principle of thermo-electromotive force that is generated during the contact of electrical conductive materials.

There are also technologies that use closed-loop control strategies to control surface roughness in real time or introduce control actions to achieve improvement. Document US7792604 develops a technology that introduces control actions in the machine position control system, softening the changes in the speed of advancement that lead to an improvement in surface roughness. Similarly, document US4926309 describes an adaptive controller for adjusting surface roughness, during mass production of parts, from its estimation using a mathematical model, which uses as input the speed of advance of the machine and surface roughness Measurement of the last piece manufactured. Similarly, document US3829750 describes a similar procedure applied to grinding processes from the measurement of process variables, such as torque, temperature and vibrations. Make an adjustment of the speed of advance using stochastic optimization strategies of a figure of merit, as is the case of the material starting cup and its relation to the desired surface roughness.

Other technologies implement optimization algorithms for the adjustment or selection of the set of machining parameters in manufacturing processes. Among them, document US5903474, which claims a method to achieve the optimal selection of machining parameters in turning operations from tool wear and applying multi-objective optimization strategies, can be highlighted.

Also of special interest is document US6671571, also focused on issues of finishing but in this dimensional case, and that develops a procedure that automatically introduces compensations in the program of the piece that is manufactured from the measurement that is made of its geometric dimensions once the machining operations are completed. With a view also to the control of the dimensional finish, document US4974165 describes a real time control system of the movement of the cutting tool in turning operations to obtain a suitable machining profile through the continuous measurement of the real diameter of the piece swivel

In short, although there are currently several procedures that aim to monitor the roughness of a piece in real time during the machining process, none of them get completely satisfactory results.

Description of the invention

 The inventors of the present application have developed a method of monitoring surface roughness in real time relatively simple and easy to implement, and that provides precise results that allow the operator to make the most appropriate decisions during the machining process itself. The use of the process of the invention allows both to improve the quality of the machined parts and to reduce the total time spent, thus improving the net productivity of the process. It is an especially useful method in micro-machining processes, where the operator cannot verify the results of the operations by himself, although it is applicable to any general machining process. For this reason, in the present application the term "machining" also encompasses "micro-machining."

The method of the invention to monitor in real time the roughness of a piece during a machining process, where said process is carried out by a machine equipped with a machining tool, basically comprises the following steps: obtaining a representative incremental hybrid model of the machining process; and evaluate the incremental hybrid model in real time to obtain surface roughness. Next, each of these steps is described in more detail: Obtaining an incremental hybrid model

In this first step, an incremental hybrid model representative of the machining process is obtained that allows surface roughness to be obtained from data of the feed per tooth and the vibration of the machine on the Z axis. The feed per tooth is defined as the distance that each tooth of the tool advances in relation to the piece for each turn it makes. This information is obtained from the speed of advance of the machine, its speed of rotation and the geometric information of the tool, which are normally available internally in the machine, specifically in its controller. On the other hand, the vibration of the machine on the Z axis is measured using an accelerometer installed in the clamp or clamping mechanism of the piece.

The incremental hybrid model is formed by a function that is obtained from the superposition of a global model and a local model. The global model provides a first general approximation that allows roughness to be obtained from the quadratic value of the feed rate per tooth and the mean quadratic vibration on the Z axis, and is formed by a polynomial of two inputs of order m. The local model, meanwhile, allows us to approximate more precisely those areas of the global model that do not adequately represent the behavior of the machining process, and is obtained using the Fuzzy k-Neighbors Neighbors approach with a number of neighbors k and a blur coefficient p.

This model is adjusted based on a set of data that includes the quadratic value of the feed per tooth, the average quadratic value of the vibration on the Z axis and the surface roughness obtained from a piece previously machined by the machine. In principle, any number of samples can be used as long as they are sufficient to adequately characterize the process behavior, although in a preferred embodiment of the invention at least 20 samples are used. Thus, in a preferred embodiment of the invention the incremental hybrid model is obtained by implementing the following steps:

Obtain a set of data of quadratic mean vibration on the Z axis, advance by quadratic tooth and surface roughness from a piece machined by the machine.

 Adjust, from this data set, the global model using a least squares algorithm.

 Adjust, based on this data set, local models of surface roughness by applying the Fuzzy k-Nearest Neighbors (F-kNN) technique and using a Euclidean standard for the calculation of proximity between neighbors.

 Form the incremental hybrid model from the superposition of the global model and the local model.

The data used (advance by quadratic tooth and quadratic mean vibration on the Z axis) vary between very different ranges. As a consequence, global and local models work in extreme conditions that could lead to the discarding of some of the input variables, losing information that could be relevant. To avoid this, in a preferred embodiment of the invention a normalization of the mean quadratic vibration in the Z axis and the advance by quadratic tooth is carried out prior to the adjustment of the global and local models. Preferably, the mean quadratic vibration on the Z axis is normalized in relation to its maximum value within the data set, and the feed per quadratic tooth is normalized relative to the radius of the tool.

Once the incremental hybrid model is obtained, it is possible to adjust the order m of the polynomial of the global model, the number of neighbors k of the local model and the blur coefficient p of the local model based on a simulated tempering algorithm, thus improving the accuracy of the surface roughness values obtained.

In short, these steps are carried out for each machine that you want to characterize by means of the procedure described, being the The last result is a function of two inputs (feed per quadratic tooth and mean quadratic vibration on the Z axis) and one output (surface roughness). b) Evaluate the incremental hybrid model

Once the incremental hybrid model of the machine in question has been adjusted according to the previous data, it is only necessary to enter feed data per quadratic tooth and quadratic mean vibration in the Z axis obtained in real time during a micromachining process to obtain the roughness Superficial instant at that time.

Preferably, the evaluation of the incremental hybrid model in turn comprises the following steps:

Acquire the feed per tooth and the vibration on the Z axis during a time window whose duration is proportional to the period of rotation of the tool, preferably 10 times said period of rotation.

 Calculate the mean quadratic value of the vibration on the Z axis during said time window and normalize it in relation to the maximum value of the vibration within the same data window.

 Normalize the feed per square tooth relative to the radius of the tool.

 Enter the normalized values of feed per quadratic tooth and average quadratic vibration on the Z axis in the incremental hybrid model to obtain instantaneous surface roughness.

In a preferred embodiment of the invention, before starting the data acquisition, the effective start of the machining is detected taking into account the moment in which the tool contacts the part, preferably depending on the conductivity of the machine-tool-part assembly ( in the case of electrically conductive materials). This operation prevents errors related to the start of taking measurements before the machining process has actually begun.

In another preferred embodiment of the invention, the acquired vibration data on the Z axis is filtered to eliminate the harmonics of frequencies below the rotation frequency of the tool. This filtering can be accomplished in different ways, but in a preferred embodiment of the invention a-high pass digital filter with infinite impulse response (IIR) Butterworth 6 ^or order and whose cutoff frequency is used is equal to half of the tool's rotation frequency.

Normally, this method will be coded as a computer program and implemented, in its simplest version, by means of a computer connected to the machine, to obtain the feed per tooth, and to a vibration sensor that allows to obtain the vibration in the axis Z. Accordingly, the invention also extends to computer programs, particularly computer programs arranged on or within a carrier, adapted to carry out the invention. The program may have the form of source code, object code, an intermediate source of code and object code, for example, in partially compiled form, or in any other form suitable for use in the implementation of the process of the invention.

The carrier can be any entity or device capable of supporting the program. For example, the carrier could include a storage medium, such as a ROM, a CD ROM, a semiconductor ROM, a magnetic recording medium, a flexible disk or a hard disk.

In addition, the carrier can be a transmissible carrier, for example, an electrical or optical signal that could be transported through electrical or optical cable, by radio or by any other means. When the program is incorporated into a signal that can be carried directly by a cable or other device or medium, the carrier may be constituted by said cable or other device or medium.

As a variant, the carrier could be an integrated circuit in which the program is included, the integrated circuit being adapted to execute, or to be used in the execution of the corresponding processes.

Brief description of the figures

 Fig. 1 shows the acquisition and processing system used to acquire the data necessary to carry out the process of the invention.

Fig. 2 shows the behavior of the real roughness compared to the estimated one considering the training data corresponding to a micromachining process.

Fig. 3 shows the behavior of the real roughness compared to that estimated during microfiber operations (validation in process).

Fig. 4 shows the behavior of the error in process during the microfusing operations of Fig. 3.

Preferred Embodiment of the Invention

 An embodiment of the invention will be described in greater detail below, explaining the process carried out to choose the variables and algorithms used in the invention. In this specific example, the calculation of the hybrid model has been applied to a micromachining process.

Choice of variables representative of the micromachining process

The surface roughness and specifically the Ra is one of the most used industrial indicators to evaluate the surface quality of a machined part. Ra is defined: R

The roughness is normally expressed in microns, or in our case in nanometers, and Ra is defined as the arithmetic mean of the absolute values of the points with distance and, with respect to the midline of the measured roughness profile.

However, in the literature it is not clear which are the variables that have the greatest influence on surface roughness, at least in the microscale. Therefore, an experimental study of the different variables involved in the machining process has been carried out to determine which of them are the most suitable to predict the roughness of the piece in real time. The consequences of the study carried out allow us to conclude that variations in surface roughness with cutting speed have different behaviors for different values of feed per tooth.

In addition, in general an increase in cutting speed leads to a reduction in roughness. This occurs primarily for the following reasons:

- The surface roughness mechanism at low cutting speeds includes not only geometric considerations, but also the effects of minimum chip thickness, elastic recovery, and drag action.

 - Increasing the rate of wear at low speeds will lead to a non-uniform tension on the tool and a rapid spread of wear, which will significantly affect the surface characteristics.

 - The effect of the microstructure of the workpiece, when the thickness of the chip is in the order or less than the average grain size.

- The rate of increase in surface tension due to the effect of size and the flow effect of plastic (similar to drag) that depends on the tool-piece combination.

Experimental observations revealed that the interaction of cutting speed and chip loading (feed per tooth) is a fundamental criterion for deciding the roughness of micro-channels in micro-milling operations. Experimental observations also showed that the levels of feed per tooth and the interaction of the cutting speed and chip loading are crucial factors in the micro-milling operation. The drastic variation of the specific cutting pressure and the cutting forces at lower feed per tooth clearly indicates the effect of the minimum chip thickness on the micro-machining. Therefore, one of the variables chosen for the estimation of surface roughness in this invention has been the feed per tooth, a signal that can be obtained from internal machine signals.

However, only one variable is insufficient to make a good prediction of surface roughness in real time. It is necessary to use another variable that is able to systematically capture in real time the influence of aspects such as run-out, tool geometry and the effect of size with a view to more realistic capture of the elimination mechanism of material in the micro-scale and its influence on the roughness.

Of all the variables analyzed, the one that offers the best signal-to-noise ratio and whose cost of the sensor is cheaper is the vibration signal from an accelerometer. Certainly it is a relatively non-invasive sensor to the process, robust and whose cost and signal processing is not as expensive with acoustic emission sensors nor as invasive as force sensors.

Ultimately, in the present invention the variables used to model and characterize the surface finish are the advance by quadratic tooth and the quadratic mean vibration in the Z axis of the machine.

Experiments performed More than 200 experiments were carried out with the objective of studying and analyzing the behavior of the variables in microtaladrado and microfresado processes. As an example, we can mention the experiments carried out in Tungsten (WCu), using 0.2 mm, 0.5 mm, 1 mm and 1.8 mm diameter drills and drills, which allow studying a very wide area and potentially very important from the commercial point of view and the efficiency of micromachining processes. A range of turning speeds between 8000 rpm and 45000 rpm was analyzed, and surface finishes were measured from 70nm to 500nm.

Selection of the representative model of the micromachining process At present there have been great advances in the techniques and methods for modeling complex and large-scale systems. Only through a model or similar representation can a system be understood, evaluated, controlled and optimized effectively. The task of modeling a process is to obtain a representation of its behavior through mathematical representations (differential equations, integral equations, etc.). The complexity and non-linearity of some processes make the task of modeling through classic techniques a difficult and expensive task.

In general, one of the main drawbacks when selecting a model for a system is that you need to know the structure of the model (parametric model) before making any approximation. Unfortunately, in most real problems, the definition of the structure or functional form of the model is not a problem that can be easily solved and, any decision in this respect could very subjectively influence the nature of the problem. For this reason, non-parametric or free model techniques have been developed, which are based on the use of a simple generic model that is iteratively adjusted.

Among the different free model methods ■ spare parts and literature, the incremental models proposed by Pedrycz, where the axis of the model design exploits the principle of incrementality. Following this principle, any model must begin with its most generic form and the simplest form one could imagine. However, it is not necessary to stop the design in this step, since if necessary, the model is iteratively refined (adjusted) by invoking some more refined (and localized) technique to model some particular regions of the space of entry. The present invention is based on this principle, proposing the development of an incremental hybrid model. The basic or global model has to be as simple as possible, so linear regression techniques are presented as a viable solution, because they are easy to develop. After building the basic model, additional hybrid models need to be refined with an incremental counterpart such as the fuzzy k-Nearest Neighbors fuzzy clustering algorithm.

In short, to model the micromachining process the present invention employs a non-parametric technique called incremental hybrid model, which was developed by W. Pedrycz and K.C. Kwak in "The development of incremental models". IEEE Transactions on Fuzzy Systems, 2007. 15 (3): p. 507-518. This technique uses a basic or global model that captures the general behavior of the system and overlays a local model that captures its local behavior. Additionally, in order to smooth the transitions between the global model and the local model, a local smoothing strategy based on the fuzzy clustering algorithm described by S. B. Roh, T.C. Ahn and W. Pedrycz in "The refinement of models with the aid of the fuzzy k-nearest neighbors approach". IEEE Transactions on Instrumentation and Measurement, 2010. 59 (3): p. 604-615.

Global model

When prior knowledge of the system to be modeled is not available, the use of generic models such as linear regressions or second-order polynomials are, in general, good options for representing the overall behavior of the system. In In our particular case, the global model of the system to be modeled is obtained by adjusting a polynomial of degree m using the least squares algorithm. The output of the global model would therefore have the following expression: B ( ^x i) = f _B ( ^x iAXi)) (b)

X,. . . t

being the i-th entry point and (x ' _t ) the output value of the

X

point ' .

The procedure for obtaining the global model consists in calculating and storing the parameters of the function to be adjusted (in our case the polynomial). The evaluation of the algorithm at an objective point that consists in evaluating the function at that point with the parameters obtained during training, that is, the values of advance per quadratic tooth and quadratic mean vibration in the Z axis obtained in the described experiments.

Local model

 The procedure chosen to obtain the local model in incremental hybrid modeling is the Fuzzy k-Nearest Neighbors (F-kNN) approach. F-kNN is the fuzzy version of kNN, which consists of averaging the value of the points closest to the target point. The kNN algorithm therefore assumes that nearby points have a similar value. To calculate the proximity the Euclidean norm will be used, although using the normalization that will be described later, we will see that it is equivalent to using another norm.

The learning of F-kNN is lazy, so in this phase we only need to store the known data (entry points and values). When evaluating, from an objective point q, we obtain the following set:

N = {d _t D} where D is the set of entry points for the algorithm and one of the closest neighbors to q.

The similarity between the points of N and q is calculated as follows:

where ⁿ i is the i.-e. if .mo neighbor of the target point q, and p is blur coefficient.

We can now calculate the value of the objective point q using average of the objective values of the points of the set weighted by the similarity S:

Incremental Hybrid Model

The incremental model is responsible for meshing the two models described above.

The basic model training consists of performing the training of the basic and incremental models. So be

^• _f ° ( ^x ) the function that evaluates the basic model. Then we can calculate the prediction error of the basic model as follows: s (x) = t (x) -y _B (x)

These errors constitute the set D, input of the local model where the neighbors of q are calculated using (f), and are memorized in their training. The evaluation of a point q by the incremental model is obtained by adding to the output of the basic model the compensatory term calculated by the local model following equation (g), that is:

 In the present invention we work with data (roughness, advance by quadratic tooth and quadratic average vibration on the Z axis) whose values vary in very different ranges. This makes both the global and local algorithm work in extreme conditions in which they can discard some of the input variables and only give weight to the one with a wider domain. For example, in the local model, the selection of neighbors will discard the variables with short ranges, since they have little influence on the norm.

To avoid this problem, the data can be normalized. Yes

X- denoted by the variable j of the entry point i, we can obtain the normalized points as follows:

n

where

mean of the jth variable, is its standard deviation and n is the number of entry points. Next, all the steps of the algorithm for the incremental model collection are summarized First, the part is performed of the training of the model from the objective data, to later evaluate the model obtained with the new data to consider.

Training :

 1. Obtaining training parameters:

 to. Parameters of the basic global model (the order of polynomial m).

 b. Parameters of the local model (k and p, although not necessary during training). C. Input data and output values (y) ·

2. Normalization of y 'by (h).

3. Training of the global model:

 to. Calculation of the polynomial coefficients.

4. Calculation of errors using equation (g)

5. Training of the local model using the errors:

 to. Memorization of the input data and corresponding errors

Evaluation :

 1. Obtaining the evaluation points

 2. Normalization of the evaluation points with (h), but with μ and or of the training

 3. Evaluation of the basic model at each evaluation point

 4. Evaluation of the local model at each evaluation point with (g)

5. Evaluation of the incremental model at each evaluation point with (f)

 6. Data normalization using the inverse of (h)

Optimization of the hybrid model parameters based on the simulated tempering algorithm Finally, the simulated tempering algorithm can be used to optimize the parameters of the hybrid model obtained in the previous steps. Simulated tempering (SA) is a meta-heuristic search method for solving global optimization problems that simulates the physical process of material tempering, which consists of heating these materials and then slow cooling them down. increase the size of its crystals and reduce its defects, and thereby minimize the energy of the entire system.

The method was proposed independently by S. Kirkpatrick, CD Gelatt and MP Vecchi, of the "IBM Thomas J. Watson Research Center", in 1983 and by Vlado Cerny, of the Institute of Physics and Biophysics of the University of Comenius (Bratislava) , in 1985. The algorithm is an adaptation of the Metropolis-Hastings algorithm, which is a Monte Cario type method for generating state samples of a thermodynamic system.

Basically, in each iteration the algorithm generates a point randomly and calculates the distance between the new point and the previous one through a probability distribution with a scale proportional to the temperature. The algorithm accepts all new points that reduce the desired objective, but also accepts points that increase it with a certain probability. By accepting the points that increase the objective, the algorithm avoids getting caught in local minimums, and allows a greater exploration of the search space for more possible solutions. The algorithm, according to its progress, selects a tempering schedule to systematically decrease the temperature. With the decrease in temperature, the algorithm reduces the search space until it converges to a minimum.

The simulated tempering method consists mainly of three relationships:

ST ( ^X ): Probability density of the state space of ^ n X = [x ¹ i =!, ..., £>

parameters', referring to T _r as the temperature. h ( ^v AE) ^and : From the variation of the energy, obtained as the difference between the current value and the previous one, calculate the probability of acceptance of a new cost function.

T (^ k) ': Planning of the "tempering temperature" T in k steps of tempering time.

The probability of acceptance is based on the opportunity of a

 F

new state with "energy", relative to the previous state with

"energy", e- T l -AE / T

liAE) -E .. T -E T AE / T

e ^{k + 1} + e ^k l + e - ^E k + \ ^{~ E} k

The above equation is nothing more than the Boltzmann distribution, the difference in energy between the consecutive states and the energy value at each instant, is determined by the cost function to be minimized.

Considering the set of states x, with an energy e (x ^J ), a set of probability distributions .li.dad ^r p (x) 'and the distribution of energy by state d (e (x)) _r the algorithm also can be described from total energy E ■

E = p (x) d (e (x)) i From a reference state ^x , the maximum entropy value SS of the system can be obtained as,

The use of Lagrange multipliers to limit energy to the average value ¹ T, leads to the most likely distribution of Gibbs G (x) 'normalized:

where ^ 7 is the function of participation, n

 Hamiltonian used as an ener function

For the distributions of the states (m), introduced above, and probabilities of acceptance of the type as defined in (14), the equilibrium principle of the detailed balance sheet is maintained. For example, given the distributions of consecutive states G (x ^K ) and G (x ^K , _^ ^{+ í} ), applying the first term of acceptance,

AE) = h (E _l , are equal

G (x _k ) h (AE (x)) = G (x _{k + l} )

The above is sufficient to establish that all system states can be sampled. However, tempering planning disrupts the balance every time the temperature changes, and in this way, at best, this should be done carefully and gradually.

An important aspect in the simulated tempering algorithm is the selection of the range of the parameters to be searched. In practice, the calculation of continuous systems requires discretization, so we can assume that the workspace can be discretized without much loss of information. There are also certain restrictions required when used cost functions with integral values. In several applications, techniques are often used to reduce the initial space as the search progresses. For example, for many physical systems it is possible to choose as a probability density function of the state space of the parameters, the following Boltzmann distribution: g (A _X ) = (2nT) - ^{D / 2} e- ^ ^{/ (2T} >; Ax = Xr

(P) taking Ax in pra.cti ■ ■ ca as desvi aci ■ ó.n between two consecutive states and being adema, s ^± T, a measure of fluctuations in the distribution # dimensional space one of x. From

& ⁽ ^ * _{r is} γ _1Ξί shown that it is sufficient to obtain a global minimum of energy ^{v 7} if you select to vary in the form:

' ^U (q) being the initial temperature and large enough is chosen. Usually, temperature planning is also usually done exponentially, that is:

T {k) = T _Q e ^{a ~}

 T (k + \) to T (k)

where ci is a reduction constant whose values are adjusted between 0.8 and 0.99. On the other hand, for a rapid variation of temperature ¹ , it is also frequently used

T (k) = T _Q / k

^W (s)

In practical applications of the algorithm, from the calculation of the energy change Δ £ ^"and from acceptance probability h (^ AE) ' as defined in (p), criteria they used Acceptance-rejection of the current state ^Λ , using the Metropolis algorithm. According to this criterion, the probability of acceptance is

 D

compare with a number between 0 and 1, generated randomly by a uniform distribution, thus preventing premature convergence towards a local minimum and continuing the search for the global minimum.

The simulated tempering algorithm is executed iteratively, generating new states that minimize energy - System ^C

(objective function), its execution will end up taking into account several different conditions: a) The energy level

It is less than or equal to a certain preset limit value.

b) it has reached the level of tolerance for variation preconceived or ■ _Λ-nd and Energi-A- ^{J L} F- ^1.

 c) A maximum number of predetermined iterations is reached. d) The maximum allowed execution time of the algorithm has been exceeded.

In the specific case described in this document, the simulated tempering algorithm begins its execution with initial values of the parameters of the hybrid mcremental model

,

M _ñ . . . . . .

where ^υ is the initial order of the model, the initial number of neighbors is K ^υ and Pn ^υ is the i.ni.ci.al value of the blur coefficient and the MAE behavior index (mean absolute error) is evaluated as a function objective or "system energy", using the expressions (t) and (u):

As a next step in the execution of the algorithm, iteratively the current ^HIM modeling parameters are disturbed

HIM

to generate another ^NEW and the MAE index is reassessed. The acceptance or rejection criteria is based on the Metropolis algorithm. The simulated tempering algorithm simulates, iteratively, the metal tempering process as you search for a solution. A random disturbance is generated on the design variables m, k, p which, in turn, generates a change in the objective function, that is, the MAE behavior index. These disturbances depend on a temperature index, T and a temperature reduction rate (OÍ = [0.5,0.99]). In the work of DY Sun and PM Lin in "The solution of time optimal control problems by simulated annealing," Journal of Chemical Engineering of Japan, vol. 39, pp. 753-766, 2006, a detailed description of this temperature control parameter can be found.

The temperature index decreases at each iteration of the algorithm, thus reducing the size of the disturbance as the search progresses. Each set of model parameters obtained by this method is replaced in the equations of the incremental hybrid model and the accuracy of the model is evaluated with each of the training data. The MAE performance index is evaluated by comparing the simulated responses with the desired responses.

If the performance index is lower than the previous performance index, then the new parameters take the place of the previous parameters. Otherwise, the new parameters of the model are not immediately discarded, but are subject to a probability evaluation process where the probability P of the cost of the new parameters, meters (MAE ^and _mw ^r ) is calculated with relation to the best previous cost ( ^riULV ), using the Boltzmann equation: (MAE _PREV -MAE _NEW )

P = e ^T (v)

The probability P is then compared with a threshold value n (which is a value between 0 and 1 generated by a uniform distribution). If P> n, then the new model parameters are accepted as

MAE _NFW MAE _PRFV

yes < ^rnc 'and are rejected if P <n. This mechanism prevents premature convergence to a local minimum and allows to approach the global minimum. After this stage, the temperature index is reduced by means of a tempering planning using the reduction constant OÍ = [0.5.0.99].

This whole process is repeated until the MAE performance index has reached a minimum acceptable level or until the temperature value has reached a value too low to disturb the parameters. The main objective is to obtain an optimal modeling of the parameters that serve to achieve a fast and precise model through the minimization of the mean absolute error (MAE) as an index of performance. The optimal adjustment of the modeling parameters is done offline using the simulated tempering method, obtaining an incremental hybrid model capable of representing with very good precision the actual behavior of the process.

In short, the process of the invention has two clearly differentiated phases: first, training of a representative model of the micromachining process; and secondly, roughness evaluation based on the model obtained in the previous phase. The training phase of the model is only carried out once for each specific machine, and the hybrid model obtained can then be used to assess the roughness in real time during the machining of a part as many times as necessary.

Fig. 1 shows the experimental setup used for the data acquisition and processing. The vibration sensor (2) installed in the clamp or clamping mechanism of the part to measure the vibration of the machine tool (1) on the Z axis is observed. The analog signal of the sensor (3) is acquired by acquisition cards (4) and is processed by a real time acquisition and processing program embedded in a high performance computing device (5). The data acquired and processed are made available on a local network (6), and can be accessed through a remote web client (7). The information necessary for the calculation of the advance per tooth, such as the speed of advance of the machine, the speed of rotation and the geometric information of the tool, is also made available in the local network (6) through a server of real time data (8) of the numerical control 1 (CNC) of the machine (10). Both computing devices are interconnected through the fieldbus (9).

Table 1 shows the set of 21 experimentally obtained data that have been used in this example to carry out the adjustment of the described incremental hybrid model. This table shows not only the feed data per tooth, vibration on the Z axis and surface roughness, but also a large number of auxiliary data:

PosY: Position on the Y axis of the tool tip, relative to the origin of the part [mm].

PosX: Position on the X axis of the tool tip, relative to the origin of the part [mm]. f: Feed rate [mm / min].

n: Speed of rotation [1 / min].

fz: Feed per tooth [um] .r: Tool radius [mm].

 Accel rms: Mean quadratic value of the vibrations in the data range [g].

 Accel max: Maximum value of the vibrations in the data range [g].

Ra: Average absolute surface roughness in the interval [nm]. Rq: Mean quadratic surface roughness in the interval [nm].

 Rv: Maximum depth of the surface valley in the interval [nm].

Rp: Maximum height of the surface peak in the interval [nm].

Samples / Interval: otal samples in the interval for roughness measurement.

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Table 1: Experimental data used for the development of the incremental hybrid model Using this data set as the starting data, the incremental hybrid model corresponding to the machine used in this example is adjusted as follows:

Model Order:

 Number of neighbors:

 Blur coefficient

The model has as its output the average absolute surface roughness

( ^R a), expressed in nanometers (nm) and as inputs the quadratic value of the feed per tooth () normalized in relation to the radius of the tool (F), both expressed in nanometers (nm), and the mean square vibration in the Z axis ( ^rms ) normalized in relation to its maximum value (A " ^IUA ) during a temporary window

Mathematically, it can be represented as:

V ^r A _{max j} ^

 Finally, Figs. 2-4 graphically show the results of the estimation of the surface roughness of some processes using the model obtained. Specifically, Fig. 2 shows the estimated surface roughness values when the own data from Table 1 used to calculate it is entered into the model obtained. Obviously, the result is that the actual and estimated values coincide, so the error is 0%.

Fig. 3 shows an example of prediction of surface roughness with new data corresponding to a microfressing process. The estimated roughness values and actual roughness values, which were subsequently measured with a profilometer, have been represented. As can be seen visually, the monitoring method used follows quite precisely the real roughness behavior in most cases. To check it, Fig. 4 illustrates the error behavior in the roughness estimate corresponding to Fig. 3, observing that the absolute average error among all the tests performed is 10.9%.

Claims

1.- Procedure to monitor in real time the roughness of a piece during a machining process, where the procedure is carried out by a machine equipped with a head to which a machining tool is coupled, characterized in that it comprises the following steps: Obtain an incremental hybrid model of the machining process from a set of data for the velocity per quadratic tooth, the mean quadratic vibration on the Z axis and the surface roughness obtained from a piece machined by the machine, being the incremental hybrid model formed by the superposition of a global model and a local model, where the global model is formed by a polynomial of two inputs of order m and the local model is obtained using the Fuzzy k-Nearest Neighbors approach with a number of neighbors k and a blur coefficient p; and evaluate said incremental hybrid model by introducing feed rate data per quadratic tooth and quadratic mean vibration on the Z axis obtained in real time during a machining process to obtain instantaneous surface roughness at that time.

2. Method according to claim 1, wherein the set of data of quadratic mean vibration on the Z axis, feed rate per quadratic tooth and surface roughness used to form the incremental hybrid model is formed by at least 20 samples.

3. - Method according to any of claims 1-2, wherein the step of obtaining the incremental hybrid model comprises:

- obtain a set of data of quadratic mean vibration on the Z axis, feed rate per quadratic tooth and surface roughness from a piece machined by the machine; adjust, from said data set, the global model using a least squares algorithm; adjust, based on this data set, local models of surface roughness by applying the Fuzzy k-Nearest Neighbors (F-kNN) technique and using a Euclidean standard for the calculation of proximity between neighbors; and form the incremental hybrid model from the superposition of the global model and the local model.

4. Method according to claim 3, further comprising the step of normalizing the average quadratic vibration in the z axis and the advance by quadratic tooth prior to the adjustment of the global model and the local model.

5. Method according to claim 4, wherein the vibration in the Z axis is normalized in relation to its maximum value within the data set, and the feed per tooth is normalized in relation to the diameter of the tool.

6. Method according to any of claims 3-5, which further comprises the step of adjusting the order m of the polynomial of the global model, the number of neighbors k of the local model and the blur coefficient p of the local model in base to a simulated tempering algorithm.

7. - Method according to any of the preceding claims, wherein the step of evaluation of the incremental hybrid model comprises: a) acquiring the advance by quadratic tooth and the vibration in the Z axis during a time window whose duration is proportional to the period of tool rotation;

b) calculate the mean quadratic value of the vibration on the Z axis and normalize in relation to its maximum value during said time window; c) normalize the feed per square tooth relative to the tool radius;

 d) Enter the normalized values of mean quadratic vibration on the z axis and feed per quadratic tooth in the incremental hybrid model to obtain instantaneous surface roughness.

8. Method according to claim 7, wherein the time window has a duration corresponding to 10 times the period of rotation of the tool.

9. Method according to any of claims 7-8, which also comprises, before starting the data acquisition, the step of detecting the effective start of the machining taking into account the moment in which the tool contacts the part.

10. Method according to claim 9, wherein the detection of the moment in which the tool contacts the part is determined based on the conductivity of the machine-tool-part assembly.

11. Method according to any of claims 7-10, which further comprises a step of filtering the acquired vibration data on the Z axis.

12. Method according to claim 11, wherein the filtering is carried out by a digital filter of infinite impulse response (IIR) of Butterworth high-pass of 6 ^or order whose cutoff frequency is equal to half of the tool rotation frequency.

13. Computer program comprising program instructions to make a computer carry out the procedure according to any of claims 1 to 12.

14. Computer program according to claim 13, incorporated in storage media.

15. Computer program according to claim 13, supported on a carrier signal.