DE102020211666A1 - Method and device for performing a screwing process using methods of artificial intelligence - Google Patents

Abstract

The invention relates to a computer-implemented method for carrying out a self-tapping process with a predetermined preload force (F), with the following steps:
- Screwing (S2) a screw (3) into a workpiece (4), in particular until a predetermined first maximum screwing torque is reached;
- Recording (S3) of the course of the screwing torque during the screwing process;
- Determining (S4, S5) an in particular second maximum screwing torque (T _max ) depending on the screwing torque curve and depending on the predetermined prestressing force (F) using at least one trained, data-based parameter model;
- Screw in (S6) the screw (3) with a screwing torque (T) that is limited to the maximum screwing torque (T _max ).

Description

technical field

The invention relates to methods for performing a mechanical screwing process and in particular to methods for performing a self-tapping process.

Technical background

In the case of self-tapping screws, a self-tapping screw is screwed into a material of a joining partner that is in particular provided with a pre-drilled hole. The self-tapping screw cuts the mating thread in the material of the joining partner when it is screwed in for the first time. As a rule, the self-tapping screw is loosened again after a first tightening, in which the screw head is pressed with the chin against the material of the joining partner, and then finally tightened with a predetermined screw torque, whereby the screw torque is limited to a maximum screw torque during the second tightening .

From the prior art, such. B. from Seneviratne, LD et al., "Theoretical modeling of self-tapping screw fastening process", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, pages 135 to 154, physical models are known to to determine the screwing torque with which a self-tapping screw may be screwed in during final tightening. However, the formulas given there are not applicable to changed conditions, such as other materials.

Disclosure of Invention

According to the invention, a method for carrying out a screwing process according to claim 1 and a device according to the independent claim are provided.

Further developments are specified in the dependent claims.

• - Einschrauben einer Schraube in ein Werkstück, insbesondere bis zum Erreichen eines vorgegebenen ersten maximalen Schraubmoments;
• - Aufzeichnen des Schraubmomentenverlaufs während des Schraubvorgangs;
• - Ermitteln eines, insbesondere zweiten, maximalen Schraubmoments abhängig von dem Schraubmomentenverlauf und abhängig von der vorgegebenen Vorspannkraft mithilfe mindestens eines trainierten datenbasierten Parametermodells;
• - Einschrauben der Schraube mit einem Schraubmoment, das auf das maximale Schraubmoment begrenzt ist.

According to a first aspect, a computer-implemented method for carrying out a screwing process, in particular a screw-forming process, with a predetermined preload force is provided, with the following steps:

• - Screwing a screw into a workpiece, in particular until a predetermined first maximum screwing torque is reached;
• - Recording of the course of the screwing torque during the screwing process;
• - Determining a, in particular second, maximum screwing torque as a function of the screwing torque curve and as a function of the predetermined prestressing force using at least one trained data-based parameter model;
• - Screw in the screw with a screwing torque that is limited to the maximum screwing torque.

In particular, screwing torque curve characteristics can be determined depending on the screwing torque curve, with the at least one data-based parameter model being trained to provide a screwing process parameter depending on the screwing torque curve characteristics, with the maximum screwing torque being determined as a function of the at least one screwing process parameter and as a function of the predetermined preload force.

In the self-tapping process, an initial tightening is a self-tapping screw that is threaded into a pilot hole in a material, with the screw tapping its own mating thread. The screw is then loosened by about a quarter to a full turn and finally tightened with a specified maximum screwing torque. The tightening torque to be applied increases sharply as soon as the chin of the screw rests on the joining partner, so that the preload force acting between the screw head and the joining partner is built up.

The preload force that acts between the screw head and the joining partner is not measured directly, since a sensor for realizing a measurement in series production is difficult or impossible to implement. A calibration of the preload force is also difficult due to manufacturing tolerances of the screws, the pilot hole and the workpiece material with constant parameters of the screwing process, since this is subject to a significant static uncertainty. However, the expected value of the axial preload force achieved is the greater, the greater the maximum screwing torque set when screwing in.

One way to ensure a certain minimum preload force of the screw connection is conventionally a generous dimensioning of the screwing torque used when finally tightening the screw, so that even the smallest preload forces within the framework of statistical uncertainty are still above the required minimum preload force. If the desired If the minimum preload force is in a range that is close to the load limit of the screw, such an approach is only possible if the variance of the set preload force is correspondingly small. Therefore, the self-tapping screws used in manufacturing processes are usually designed in such a way that the minimum preload force to be set is far enough away from the load limit. As a result, in many cases the screws used are designed too large or a larger number of screws, each of which absorbs a lower preload force, is used, which has a negative effect on the product weight and product costs.

The at least one screwing process parameter can define a predefined physical screwing model that is designed to output the maximum screwing torque as a function of the predefined preload force. The above method thus provides for the use of a physical screwing model to determine a maximum screwing torque for the second tightening in particular, which is parameterized using one or more data-based, probabilistic parameter models, which can be configured, for example, as regression models, in particular as Gaussian process models is. For this purpose, a screwing torque curve is first recorded during one or more preceding screwing phases, which are carried out before the final tightening of the screw in a second tightening phase in particular, which shows the course of the applied torque over a rotation angle of the screw or over a screwing-in time, in particular up to the end of the first tightening.

Features of the screwing torque curve are extracted and one or more screwing model parameters for the physical screwing model are determined from the one or more probabilistic parameter models. The screw model parameters determined in this way are used in the physical screw model in order to calculate the necessary maximum screw torque for the second tightening, given a desired preload force.

The use of the data-based, probabilistic parameter model enables the evaluation of numerous measurement series of tightening torques during one or more preceding tightening phases in order to determine the tightening model parameters that can be used for the second tightening phase with the help of suitable physical models that can be used in the preceding tightening phases.

• - Einschrauben einer Vielzahl von Schrauben in ein Werkstück, insbesondere bis zum Erreichen eines vorgegebenen ersten maximalen Schraubmoments;
• - Aufzeichnen der Schraubmomentenverläufe;
• - Ermitteln von mindestens einem Schraubmodellparameter mithilfe von mindestens einem weiteren physikalischen Schraubmodell, das durch den mindestens einen Schraubmodellparameter definiert ist, für jeden der

Schraubmomentenverläufe, insbesondere durch Anfitten oder eine Ausgleichsrechnung, um einen jeweiligen Trainingsdatensatz zu erhalten, der den Schraubmomentenverlauf dem mindestens einen ermittelten Schraubmodellparameter zuordnet;

• - Trainieren des mindestens einen datenbasierten Parametermodells abhängig von den jeweiligen Trainingsdatensätzen.

According to a further aspect, a computer-implemented method for training at least one data-based parameter model for providing at least one screw model parameter for a physical screw model is provided, the physical screw model specifying a relationship between a preload force and a screw torque depending on the at least one screw model parameter, with the following steps:

• - Screwing a plurality of screws into a workpiece, in particular until a predetermined first maximum screwing torque is reached;
• - Recording of the screw torque curves;
• - determining at least one screw model parameter using at least one further physical screw model, which is defined by the at least one screw model parameter, for each of the

Screwing torque curves, in particular by fitting or a compensation calculation, in order to obtain a respective training data record which assigns the screwing torque curve to the at least one determined screwing model parameter;

• - Training the at least one data-based parameter model depending on the respective training data sets.

Furthermore, the at least one data-based parameter model can be trained in order to assign features of the course of the screwing torque to a parameter of the screwing model, with the features of the course of the screwing torque being determined as a function of the course of the screwing torque.

To train the data-based parameter models, the screwing model parameters are determined from the course of the screwing torque in each of the preceding screwing phases by adapting the physical screwing model applicable in the respective screwing phase to the screwing torque curve by fitting or compensating calculations. Subsequently, characteristics of the course of the screwing torque in the previous screwing phases are extracted, which can be, for example, absolute values of the screwing torque at one or more specific points in time or angles of rotation, gradients of the screwing torque at one or more specific points in time or angles of rotation and integral values of the screwing torque in specific time windows or angles of rotation . The training takes place for a parameter model based on training data sets, each of which includes the characteristics of a screwing torque curve and the or one of the associated screwing model parameters. A separate parameter model can be trained for several screw model parameters.

As an additional input variable for the data-based parameter model, the respective screwing process phase, from which the screwing torque characteristics were extracted, can be taken into account, such as an attachment phase in which the screw tip is inserted into the hole and the screw thread is not yet engaged, a screwing-in phase in which the screw thread engages in the inner wall of the bore and cuts an internal thread, and a first tightening phase, in which the screw head sits on the joining partner and exerts a pretensioning force on the joining partner, an unscrewing phase, during which the screw is unscrewed again, a second screwing-in phase and a second tightening phase . For this purpose, the course of the screwing torque is divided over time in order to be able to assign the areas of the screwing torque curve to the corresponding screwing process phase.

In this way, a tailor-made process control can be carried out in a multi-stage screwing process, even with different configurations of the screw and the joining partner.

However, the above method is not limited to the two-stage screwing process, but can also be applied to screwing processes with only one tightening phase.

character list

• 1 eine schematische Darstellung eines Furchschraubsystems zum Einschrauben einer selbstfurchenden Schraube in ein Werkstück;
• 2 ein Diagramm zur Darstellung des Verlaufs eines Schraubmoments während verschiedener Schraubphasen des Schraubvorgangs in das Werkstück;
• 3 ein Flussdiagramm zur Veranschaulichung eines Verfahrens zum Durchführen eines Furchschraubprozesses in dem Schraubsystems der 1; und
• 4 ein Flussdiagramm zur Veranschaulichung eines Verfahrens zum Trainieren des mindestens einen Parametermodells zur Ermittlung von Schraubprozessparametern für das physikalische Schraubmodell.

Embodiments are explained in more detail below with reference to the accompanying drawings. Show it:

• 1 a schematic representation of a tapping screw system for screwing a self-tapping screw into a workpiece;
• 2 a diagram showing the course of a screwing torque during different screwing phases of the screwing process into the workpiece;
• 3 a flowchart to illustrate a method for performing a tapping screwing process in the screwing system 1 ; and
• 4 a flowchart to illustrate a method for training the at least one parameter model for determining screwing process parameters for the physical screwing model.

Description of Embodiments

1 shows a schematic representation of a screwing system 1 as part of a manufacturing system for a product. The screwing system 1 has a screwing device 2 which, in a manner known per se, is capable of gripping a screw 3 and screwing it into a workpiece 4 by applying a screwing torque. For this purpose, the workpiece 4 is preferably pre-drilled with a bore 5, the diameter of which is smaller than the diameter of the threaded part of the screw 3. In particular, the diameter of the pre-bore can be larger than the screw diameter without the thread flank, but smaller than the screw diameter including the thread flank.

The screw 3 is usually screwed in according to a so-called self-tapping screwing process, which is carried out by a control unit 6 in that the screwing device 2 is controlled in a corresponding manner.

The self-tapping process takes place in several screwing phases, which are shown in the diagram in Fig 2 are shown. The screwing process shown here as an example takes place in two stages with a first tightening and a second, final tightening. However, the method can also be used without restriction for single-stage screwing processes. are shown in 2 the curves of the screw torque T and the preload force F over time.

The screwing phases include: an application phase e, in which the screw tip 33 is inserted into the bore 5 and the screw thread 34 is not yet fully engaged, a screwing-in phase a, in which the screw thread 34 engages the inner wall of the bore 5 and cuts an internal thread, a first tightening phase t, in which the screw 3 is tightened with a predetermined (first) maximum screwing torque, so that the screw head 31 rests with its chin 32 on the workpiece 4 and exerts a pretensioning force, a reverse rotation phase r, during which the screw 3 turns again is unscrewed a quarter to a full turn, a second screwing-in phase a* and a second tightening phase t*, in which the screw 3 is tightened with a predetermined maximum screwing torque.

It can be seen that in the first tightening phase the pretensioning force increases as soon as the chin 32 of the screw head 31 rests on the workpiece 4 . At the same time, the screwing torque T to be applied increases sharply and is limited by a predetermined maximum screwing torque T for the first tightening. In the reverse phase, the screw 3 is turned back, the preload force F is reduced to zero again and the screwing torque T used becomes negative.

The two-stage process of tightening the screw 3 in this exemplary embodiment serves to be able to more precisely determine the screw model parameters for determining the screw torque to be applied for a defined preload force, so that the preload force between the workpiece 3 and the screw head 31 can be set more precisely.

wobei jede Schraubphase i des Schraubprozesses e, a, t, r, a*, t* durch einen Startwinkel und einen Endwinkel definiert ist. In der Rückdrehphase r ist der Endwinkel kleiner als der Startwinkel, da die Schraube 3 hier in entgegengesetzter Richtung gedreht wird. Man erkennt, dass die zugrundeliegenden Schraubmodelle zwar unterschiedlich sind, jedoch durch identische Parameter v₁,...,v_n, k₁, ..., k_r die Vorspannkraft F und den Drehwinkel ϕ definiert sind. Während die Schraubprozessparameter v₁, ..., v_n Modellparameter sind, die für jeden Schraubprozess veränderlich sein können, wie beispielsweise der Durchmesser der Vorbohrung 5 oder auch die notwendige Energie, um die Schraube 3 ausgehend von einem Drehwinkel 41 bis zum einem Drehwinkel 42 zu drehen, stellen die Modellparameter k₁, ..., k_r Parameter dar, welche sich innerhalb einer Serie von Verschraubungen nicht ändern und deren Werte daher für eine Serie nur einmalig bestimmt werden müssen. Beispielsweise können die Modellparameter k₁, ..., k_r relevante Materialeigenschaften der Schraube 3 und/oder des Werkstücks umfassen.The individual process phases of the screwing process follow different functions, with the overall screwing torque T being defined as $$\begin{array}{l}T\left(\varphi ,f,{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">v</figure-callout>}}_1,...,v_n,{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">k</figure-callout>}}_1,...k,i\right)=\\ \{\begin{array}{l}{T}_e\left(\varphi ,f,{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">v</figure-callout>}}_1,...,v_n,{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">k</figure-callout>}}_1,...k\right),i=1:\text{attachment}\hfill \\ T_a\left(\varphi ,f,{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">v</figure-callout>}}_1,...,v_n,{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">k</figure-callout>}}_1,...k\right),i=2:\text{first screwing}\hfill \\ T_t\left(\varphi ,f,{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">v</figure-callout>}}_1,...,v_n,{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">k</figure-callout>}}_1,...k\right),i=3:\text{first dressing}\hfill \\ T_{\mathrm{right}}\left(\varphi ,f,{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">v</figure-callout>}}_1,...,v_n,{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">k</figure-callout>}}_1,...k\right),i=4:\text{R}\ddot{\text{and}}\text{turn back}\hfill \\ T_{a*}\left(\varphi ,f,{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">v</figure-callout>}}_1,...,v_n,{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">k</figure-callout>}}_1,...k\right),i=5:\text{second screwing}\hfill \\ T_{t*}\left(\varphi ,f,{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">v</figure-callout>}}_1,...,v_n,{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">k</figure-callout>}}_1,...k\right),i=6:\text{second dressing}\hfill \end{array}\end{array}$$

where each screwing phase i of the screwing process e, a, t, r, a*, t* is defined by a start angle and an end angle. In the reverse turning phase r, the end angle is smaller than the starting angle, since the screw 3 is turned in the opposite direction here. It can be seen that the underlying screw models are different, but the preload force F and the angle of rotation ϕ are defined by identical parameters v ₁ ,...,v _n , k ₁ ,..., k _r . While the screwing process parameters v ₁ , ..., v _n are model parameters that can be changed for each screwing process, such as the diameter of the pilot hole 5 or the energy required to turn the screw 3 starting from a rotation angle 41 to a rotation angle 42 to rotate, the model parameters k ₁ , ..., k _r represent parameters which do not change within a series of screw connections and whose values therefore only have to be determined once for a series. For example, the model parameters k ₁ , . . . , k _r can include relevant material properties of the screw 3 and/or the workpiece.

The physical screw model T _t* is to be used for the second tightening in order to set the specified preload force F without being able to measure the preload force on the production line. The maximum screwing torque T _max required for this is calculated with the screwing model and the screw 3 is then tightened accordingly until this screwing torque T (in Nm) is reached with the screw rotation stopped.

In principle, the method can also be used for a single-stage screwing process in which only the screwing phases e, a, t are considered. The tightening phase represents the final tightening of the screw. The required screw model parameters are recorded through the observations in the attachment phase and in the screwing-in phase and are used to determine the screwing torque T to be applied in the (first) final tightening phase.

In the flow chart of 3 a process is shown which can be implemented in the screwing system 1 as software or hardware. The method provides for screwing a screw into a workpiece so that the screw head 31 presses onto the workpiece 4 with a defined preload force F (in N).

In step S1, a desired prestressing force F is indicated accordingly.

The screwing-in process is then started in step S2. For this purpose, the screw 3 is rotated at a predetermined speed or a predetermined speed profile and placed on the pilot hole 5 with a defined, predetermined press-on force. In the engagement phase e, the thread of the screw 3 is not yet fully engaged in the pilot hole 5 and is looking for an engagement point in order to cut into the material of the workpiece 4 . Subsequently, the screw 3 is screwed in during the screwing-in phase a. The thread of the screw 3 cuts into the wall of the pilot hole 5 and thus forms a screw thread.

The subsequent first tightening phase t relates to the phase from when the screw head is placed on the workpiece and lasts until a first predetermined maximum screw torque T _max is reached. The first predetermined maximum screwing torque T _max corresponds to a maximum screwing torque that is selected with a safety margin to a screwing torque at which tearing off of the screw head is likely or certain. In addition, the first specified maximum screwing torque should be greater than a second specified maximum screwing torque T _max for the subsequent second tightening, so that thread cutting cannot occur again during the second tightening.

The course of the screwing torque T is recorded during the screwing process.

In step S3, the screwing torque profiles for one or more of the screwing phases e, a, t are used to determine screwing torque profile features that determine, for example, absolute values of the screwing torque at one or more specific points in time, gradients of the screwing torque at one or more specific points in time, and integral values of the screwing torque th time windows during the screwing phases e, a, t determined.

In step S4, at least one screw model parameter v ₁ , . . . , v _n is now determined from the screw torque characteristics using at least one data-based parameter model. The screw model parameters correspond to parameters of a physical screw model and represent variables that can vary during the screwing process, such as the diameter of the pilot hole or the energy required to turn the screw from a rotation angle ϕ1 to a rotation angle ϕ2.

Once the corresponding screwing model parameters have been determined, the screw 3 is screwed in further in step S5 in the reverse rotation phase r and a second screwing-in phase a*.

To set the maximum screwing torque T _max for the second tightening, the physical screwing model T _{t *} for the second tightening is determined using the at least one screwing model parameter v ₁ , . . . , v _n previously determined from the data-based parameter model.

The screw 3 is then tightened in step S6 in the second tightening phase with the corresponding maximum screw torque T _max for the second tightening.

wobei p der Gewindesteigung, µ₁ einem Reibungskoeffizienten zwischen Schraube und Bohrung, D_s größter Durchmesser der Schraube, D_h Durchmesser der Bohrung, µ₂ einem Reibungskoeffizienten zwischen Schraubenkopf und Werkstück, D_sh dem Durchmesser des Schraubenkopfes, D_n dem Durchmesser der Schraube ohne Gewinde entsprechen. Diese Größen entsprechen den Schraubmodellparametern v₁, ..., v_n.The screw model can, for example, correspond to a model from the document mentioned at the outset, as follows $$T=f\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\pi }+\frac{{\mu }_1}{cOs\beta }\left(\frac{D_s+D_H}{4}\right)+{\mu }_2\left(\frac{D_n+D_{sH}}{4}\right)\right)$$

where p is the thread pitch, µ ₁ is the coefficient of friction between the screw and the hole, D _s is the largest diameter of the screw, D _h is the diameter of the hole, µ ₂ is the coefficient of friction between the screw head and the workpiece, D _sh is the diameter of the screw head, D _n is the diameter of the screw without match thread. These quantities correspond to the screw model parameters v ₁ , ..., v _n .

The attachment phase e usually corresponds to three turns during which the thread in the area of the conical inlet of the screw 3 comes into engagement. The screwing-in phase a then begins. The individual screwing phases e, a, t can be identified from the course of the screwing torque. The transition between the attachment phase e and the screwing phase a can be determined by an increase in the screwing torque with a gradient above a predetermined first screwing torque gradient threshold value. The transition from the screwing-in phase a to the first tightening phase t can be determined by a corresponding further increase in the screwing torque to be applied with a gradient above a predetermined second screwing-torque gradient threshold value.

mit der Varianz ${\sigma }^2\left(x_{N+1}\right)=c-k^T{C}_N^{-1}k$

ausgegeben. Hier bedeutet C_N die Kovarianzmatrix, welche gegeben ist durch C(x_n, x_m) = k(x_n,x_m) + β^-1δ_nm, wobei x_n bzw. x_m Kombinationen von Merkmalen sind, die bereits in das Parametermodell aufgenommen wurden. Die Größe β stellt die Präzision (Kehrwert der Varianz) der Normalverteilung dar, welche für die Reproduzierbarkeit von Experimenten bei gleichem Satz von Merkmalen steht. δ_nm ist das Kronecker-Symbol.The parameter model is a data-based, probabilistic model, in particular a regression model, such as B. a Gaussian process model or the like. The expected value μ of the Gaussian process is used for the _prediction of one of the screwing model parameters _{v 1} , $\mu \left(x_{N+1}\right)=k^T{C}_N^{-1}t$

with the variance ${\sigma }^2\left(x_{N+1}\right)=c-k^T{C}_N^{-1}k$

issued. Here, C _N means the covariance matrix, which is given by C(x _n , x _m ) = k(x _n ,x _m ) + β ^-1 δ _nm , where x _n and x _m are combinations of features already mentioned in the parameter model were included. The quantity β represents the precision (reciprocal of the variance) of the normal distribution, which stands for the reproducibility of experiments with the same set of characteristics. δ _nm is the Kronecker symbol.

mit den wählbaren Hyperparametern Θ₀ und Θ₁. Θ₁ ist entscheidend für den Einfluss des Abstandes zwischen den Funktionswerten bei den Merkmalssätzen x_n und x_m, weil die Funktion für große Werte von Θ₁ gegen null geht.The scalar c is usually given by c = k(x _N+1 , x _N+1 ) + β ^-1 . The vector t contains the respective results for the individual feature sets x _i . The vector k contains the values of the kernel function, which encodes the information to what extent the result of the combination of the features _xn still has an influence on the result of the features _xm . Large values stand for a high influence. If the value is 0, there is no influence. To predict the expected value µ and the variance σ in the above formula, k is calculated from all feature sets x _i (i=1 ... N) and the feature set x _N+1 to be examined. An exponential kernel can preferably be used for the kernel function to be used in the specific case $$k\left(x_n,x_m\right)={\mathrm{<figure-callout\; id="0"\; label="\theta "\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_0\text{ex}\left(-{\mathrm{<figure-callout\; id="1"\; label="\theta "\; filenames="DE102020211666A1\_0006.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_1\Vert x_n-x_m\Vert \right)$$

with the selectable hyperparameters Θ ₀ and Θ ₁ . Θ ₁ is crucial to the influence of the distance between the function values in the feature sets x _n and x _m , because the function tends to zero for large values of Θ ₁ .

The expected value E(v _N+1 )=µ(x _N+1 ) and the variance can be derived from this model for each bolt torque curve and the bolt torque characteristics x _N+1 determined from it for a corresponding bolt model parameter v ₁ , ..., v _n Determine Var(v _N+1 ) = σ ² (x _N+1 ).

The training of the parametric model can be carried out according to a method as illustrated by the flow chart of FIG 4 is shown to be carried out.

For this purpose, in step S11 screwing torque profiles are determined from the screwing torque profiles preceding the second tightening phase, in particular the engagement phase e, the first screwing-in phase a and the first tightening phase t.

In step S12, the screwing torque curves are fitted in each screwing phase to the physical model on which the respective screwing phase is based, in order to determine at least part of the screwing model parameters v ₁ , . . . , v _n that are required for the physical model of the second tightening phase.

• In Schritt S13 werden jedem der Schraubmomentenverläufe Schraubmomentenverlaufsmerkmale zugeordnet. Die Schraubmomentenverlaufsmerkmale können Gradienten, Integralen, Absolutwerten jeweils an ausgewählten Winkelabschnitten entsprechen.

In this way, the tightening torque curves can be assigned to physical models for the various tightening phases, such as:

• In step S13, each of the screwing torque profiles are assigned screwing torque profile features. The characteristics of the screw torque course can correspond to gradients, integrals, absolute values, each at selected angle sections.

In step S14, a separate parameter model is trained for each of the determined screwing model parameters in order to assign the assigned screwing torque characteristics of a screwing process to the respective screwing model parameters.

In this way, the parameter model can be trained based on the characteristics of the course of the screwing torque and based on the screwing model parameters that result from the underlying physical models for the individual screwing phases.

Claims (10)

Computer-implemented method for carrying out a screwing process, in particular a self-tapping screwing process, with a predetermined prestressing force (F), with the following steps: - screwing (S2) a screw (3) into a workpiece (4), in particular until a predetermined first maximum screwing torque is reached; - Recording (S3) of the course of the screwing torque during the screwing process; - Determining (S4, S5) an in particular second maximum screwing torque (Tmax) depending on the screwing torque curve and depending on the predetermined prestressing force (F) using at least one trained, data-based parameter model; - Screw in (S6) the screw (3) with a screwing torque (T) that is limited to the maximum screwing torque (T _max ). procedure after claim 1 , where screwing torque curve characteristics are determined depending on the screwing torque curve, the at least one data-based parameter model being trained to provide a screwing process parameter depending on the screwing torque curve characteristics, the maximum screwing torque (T _max ) depending on the at least one screwing process parameter and depending on the specified preload force (F ) is to be determined. procedure after claim 2 , whereby one or more of the following variables are determined from the course of the screwing torque as features of the course of the screwing torque: Absolute values of the screwing torque at one or more specific points in time or angles of rotation, gradients of the screwing torque at one or more specific points in time or angles of rotation and integral values of the screwing torque in specific time windows or specific angles of rotation. Procedure according to one of Claims 1 until 3 , wherein the at least one data-based parameter model comprises a regression model, in particular a Gaussian process model. Procedure according to one of Claims 1 until 4 , wherein the at least one screwing process parameter defines a predetermined physical screwing model that is designed to output the maximum screwing torque (T _max ) as a function of the predetermined preload force (F). Computer-implemented method for training at least one data-based parameter model for providing at least one screw model parameter for a physical screw model, wherein the physical screw model specifies a relationship between a preload force and a screw torque depending on the at least one screw model parameter, with the following steps: - screwing a plurality of screws into one Workpiece, in particular until a predetermined first maximum screwing torque is reached; - Recording (S11) of the screw torque curves; - Determination (S12) of at least one screw model parameter using at least one further physical screw model, which is defined by the at least one screw model parameter, for each of the screw torque curves, in particular by fitting or a compensation calculation, to a respective training data to obtain a data set that assigns the screwing torque curve to the at least one determined screwing model parameter; - Training (S14) of the at least one data-based parameter model depending on the respective training data sets; - Using the at least one data-based parameter model in a screwing process. procedure after claim 6 , wherein the at least one data-based parameter model is trained in order to assign screwing torque curve features to a screwing model parameter, the screwing torque curve features being determined as a function of the screwing torque curve. Device for carrying out a method according to one of the preceding claims. Computer program product, comprising instructions which, when the program is executed by a computer, cause the latter to carry out the steps of the method according to one of Claims 1 until 7 to execute. A machine-readable storage medium comprising instructions which, when executed by a computer, cause the computer to perform the steps of the method of any one of Claims 1 until 7 to execute.

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