DE102017122073B4 - Process and control of a bending machine - Google Patents

Abstract

Method for controlling a bending machine, wherein the bending machine for bending a metal sheet has at least three rollers that can be positioned relative to one another and the position of the rollers is determined by means of an iterative finite element method and taking into account the stress-strain properties of a material of the metal sheet based on the elastic deformation and the plastic deformation in the Lüders region and plastic deformation in the region of uniform strain, whereby the finite element modeling takes gravity into account.

Description

The invention relates to a control method and a corresponding control for controlling a bending machine

The bending of large metal sheets into shaped parts, which are then inserted into a larger assembly, is typically carried out with sheet metal bending machines, which are fed a metal sheet from one side and which force the metal sheet into a desired shape as precisely as possible. On the one hand, the effect of the force and the parameters of the sheet metal determine the degree of deformation.

Typically, but not necessarily, a metal sheet that is fed in essentially has the temperature of its surroundings, ie the process of sheet metal bending is cold forming. Even if the embodiments of the invention described below are based on such a cold metal sheet, the method described and the corresponding control should not be restricted thereto. The method described can also be used for a heated or hot sheet.

Different presses, for example press brakes, as well as embossing machines and so-called roll bending machines are known for bending sheet metal. Although the method described here and the control are described below using a so-called round bending machine, the invention should not be limited to this, but can be used for all bending methods in which a metal sheet, also called metal plate, has to be equipped with a comparatively large radius, whereby a metal sheet can be bent to several different radii.

The round bending machines described here work according to the known method of roll rounding and have at least three rolls. The sheet metal to be bent is clamped between two rollers, at least one of which is motor-driven, so that a sheet metal clamped between the rollers can be moved by rotating the rollers. To bend the sheet metal, a bending force is exerted on the sheet metal by means of a further roller. Depending on the geometric arrangement of the rollers and the properties of the sheet metal, the sheet metal can be moved between the rollers of the bending machine by means of the at least one driven roller in such a way that the sheet metal is bent over its length. The smallest possible bending radius is limited by the diameter of the roller arranged in the bending direction.

The degree of deformation during a bending process depends on a large number of parameters. On the one hand, the geometry of the rollers relative to each other during the bending process and the geometric dimensions of the roller arranged in the bending direction determine the smallest possible diameter during bending.

On the other hand, the geometric dimensions and the material properties of the sheet metal to be bent during the bending process have a considerable influence on the deformation.

Modern bending machines, in particular machines for bending large sheet metal, which require considerable force to bend and are intended to achieve the most precise bending result possible, can have a so-called CNC control (computerized numerical control), i.e. a computer-aided numerical control. This can typically control the rollers and arrangement of the rollers and/or determine the necessary settings of the bending machine for a desired bending result and then adjust the machine accordingly. A typical problem when bending large sheets of metal is the deviation of the deformation actually achieved from the desired deformation. Such deviations can be caused by the fact that the actual material properties of the metal sheet, for example the flexural strength and/or the limit between elastic and plastic deformation, deviate from those on which the calculation of the settings of the bending machine was based.

The EP 1 308 223 A2 discloses a method for simulating the bending of a bending body, in particular a profile, using a three-roller bending method.

Furthermore, the DE 21 2016 000 100 U1 an NC plate bending machine with two rolls operated at different speeds and variable curvature. Based on this, the task is to eliminate the previously mentioned problems. This object is achieved with a method having the features of claim 1 or a control having the features of claim 6 .

The method described below and the corresponding control are based on determining the necessary settings of the bending machine for bending a metal sheet as precisely as possible on the basis of available input parameters. The method and a bending machine set up for carrying out the method are described below and with reference to the figures.

• 1 eine schematische Darstellung der Walzen einer Biegemaschine;
• 2 ein Flussdiagramm einer Ermittlung der Maschinenparameter;
• 3 einen schematischen Verlauf einer Biegelinie zwischen zwei Walzen,
• 4 ein Ablaufdiagramm.

while showing

• 1 a schematic representation of the rolls of a bending machine;
• 2 a flow chart of a determination of the machine parameters;
• 3 a schematic course of a bending line between two rolls,
• 4 a flowchart.

1 shows a schematic section through the rolls of a bending machine. The bending machine 1 has at least one top roll 2 , one bottom roll 3 and at least one first side roll 4 . The bending machine can optionally have a second side roller 9 .

The bottom roller 3 and the top roller 2 can be positioned relative to one another in such a way that they clamp a metal sheet. At least one of the two rollers 2, 3 is motor-driven so that it can rotate a metal sheet 5 clamped between the upper and lower rollers. In the figure, the direction of rotation of the motor-driven top roller 2 is illustrated by the arrow 6 . In an alternative embodiment, the bottom roller 3 can be motor-driven, or both rollers can be motor-driven. The sheet metal 5 clamped between the upper and lower rolls can accordingly be moved in the feed direction, see arrow 7, or counter to the feed direction with a corresponding rotation of the rolls.

The sheet metal 5 to be bent can be clamped by exerting a contact pressure with which the sheet metal is clamped between the lower roller 3 and the upper roller 2; illustrated by the pressure cylinder 8. The contact pressure causes increased friction of the sheet to be bent between the upper and lower rollers, so that the sheet can be moved in a conventional manner and depending on this pressure and the coefficient of friction between the sheet and the driven roller(s). .

To bend the sheet metal using a bending roller machine, the sheet metal is guided between the rollers so that the force for forming can be applied to the sheet metal. As described above, the movement can be brought about in that the upper and/or lower roller or these in interaction with other rollers clamp the metal sheet and move it with a corresponding drive of the rollers. In one embodiment (not shown), the sheet metal can also be clamped between three or more rollers, of which at least one is driven, so that the sheet metal can be moved over it. In a further embodiment not shown here, none of the rollers is motor-driven. In this case, the metal sheet is moved between the rollers by another device, not shown here.

The force for bending the sheet is applied to the sheet 5 by at least three rollers. The at least three rollers are positioned relative to each other geometrically and taking into account the properties of the metal sheet in such a way that the metal sheet can only be moved by the rollers when the metal sheet is deformed. Typically, the rollers 2, 3, 4 and optionally 9 can be positioned relative to each other in their respective positions, for example, can be moved and/or adjusted by means of a motor drive, so that the relative position of the rollers can be adapted to the requirements of a bend. For a bending process, the at least three rollers are to be positioned relative to one another in such a way that they bring about the desired bending of the sheet metal, taking into account the properties of the sheet metal.

1 12 shows a metal sheet 10 which is fed to the bending machine 1 in the direction of the arrow 7 . In this embodiment, the sheet metal is clamped between the top roll 2 and the bottom roll 3 . The top roller 2 is motor-driven, see arrow 6, and accordingly moves the metal sheet 10 onto the side roller 4. This can be positioned relative to the top and bottom rolls and placed in such a way that the metal sheet rests against them when moving in the direction of side roll 4, the side roller exerts a force on the metal sheet and bends it so that the metal sheet is only deformed in the direction of side roller 4 can be moved. In other words, the movement of the rollers 2, 3 and 4 bends the metal sheet. Since the sheet metal 10 is bent here on the outlet side of the bending machine 1, i.e. on the side of the top and bottom rolls on which the sheet metal leaves the bending machine, but not on the inlet or feed side, this is in 1 bending shown is a so-called outlet-side bending.

The bending of the sheet also depends essentially on the geometric arrangement of the rolls relative to one another, in particular on the positioning of the side roll 4 relative to the position of the top and bottom rolls. It can be seen that the bending radius increases as the distance between the side roll and the top and bottom rolls increases.

Furthermore, it is known that the plastic deformation of a sheet depends not only on the geometric arrangement of the rolls, but also on the geometric dimensions of the sheet and the material properties of the sheet. Consequently, these factors are important in determining the Settings of the bending machine must be taken into account if the intended bending of the sheet metal is to be achieved as precisely as possible during a bending process.

The method of determining the settings of the machine is performed by a controller that typically includes a digital signal processor. This runs a program which determines the settings of the bending machine based on the properties of a bending machine 1 to be controlled and the properties of the metal sheet to be bent. Optionally, the controller can control the bending machine directly, so that the bending machine is adjusted according to the determined settings.

The material properties of a sheet metal to be bent can be described by a so-called stress-strain curve of the material. This is essential for a sheet metal bending process and should be taken into account when determining the settings of the bending machine.

When determining the settings for the bending machine, the elastic and plastic behavior of the material of the sheet metal to be bent are taken into account, among other things. An essential property is the flow behavior of a metal of the sheet metal to be bent. 2 shows a stress-strain curve for a known aluminum alloy and a steel S235, in which the stress is plotted against the strain. The curve for the aluminum alloy 21 initially shows a linear increase and a smooth transition to a more gently increasing area.

In contrast, the stress-strain curve for the steel 22 shows a linear increase typical for steel up to a first point 22a, the upper yield point, from which the curve has a significantly lower or no more slope up to a second point 22b, the Has the start of hardening and ends with fracture.

The area of linear increase up to point 22a reflects Hooke's law, according to which stress and strain are proportional to one another and the material deforms elastically rather than plastically.

The essentially plateau-shaped course of the stress-strain curve from the upper yield point 22a ends with the so-called Lüders strain 22b. In this area of almost constant stress, only the elongation of the material increases, i.e. the material is stretched plastically. This material behavior is also referred to as so-called Lüders strain. The nominal stress remains approximately constant in the area of the (lower) yield point and is independent of the upper yield point. This type of plastic and thus permanent deformation typically occurs due to a local stress increase.

From the second point, 22b, i.e. the end of Lüders elongation, the range of uniform elongation begins, i.e. the stress-strain curve changes its slope. Typically, the stress increases and the material hardens until the stress reaches its maximum value, the tensile strength, at which point the stress can appear to decrease again, actually increasing due to the decreasing cross section (neckdown). The range of uniform elongation ends with the elongation at break.

In one embodiment, the stress-strain curve of the sheet metal to be bent is described by at least parameters, namely in particular by the flow stress (yield stress), the coefficient of elasticity (E modulus or tensile or elongation modulus), the tensile strength or breaking strength (tensile strength) and the end of Lüders extension, referred to in the literature as Lueders extension, the density and [??].

An operator of the machine can enter this into the control by means of a graphic user interface of a computer. The values to be entered are known, for example, from a test report for the (sheet metal) material. In an alternative embodiment, the material parameters can be taken from a database in which the information for the various materials is stored.

und wobei σ die Spannung, E den Elastizitätsmodul und ε die Dehnung bezeichnet.When determining the settings for bending a metal sheet using a bending machine, on the one hand the elastic deformation is taken into account in a known manner according to Hook's law, where applies $$\sigma =E\ast \in$$

and where σ is the stress, E is the modulus of elasticity, and ε is the strain.

wobei trueStress die auf den tatsächlichen Querschnitt (Einschnürung) bezogene Spannung ist, trueStrain die tatsächliche Dehnung, K ein Festigkeitskoeffizient und n ein Verfestigungsexponent (strain hardening exponent) ist. Dabei gilt für den Zusammenhang zwischen der tatsächlichen Dehnung (trueStrain) und der nominellen Dehnung ε $$trueStrain=\text{ln}\left(1+\in \right)$$

The calculation of the plastic deformation is based on the actual stress (true stress) and actual strain (true strain), since the assumption of constant cross-sections is subject to errors for large deformations. The plastic deformation is therefore determined according to $$t\mathrm{right}\mathrm{and}eSt\mathrm{right}ess=K\ast t\mathrm{right}\mathrm{and}eSt\mathrm{right}ai{n}^n$$

where trueStress is the stress related to the actual cross section (neckdown), trueStrain is the actual strain, K is a strength coefficient, and n is a strain hardening exponent. The following applies to the relationship between the actual strain (trueStrain) and the nominal strain ε $$t\mathrm{right}\mathrm{and}eSt\mathrm{right}ain=\text{ln}\left(1+\in \right)$$

The same applies to the relationship between the actual stress (trueStress) and the nominal stress σ $$t\mathrm{right}\mathrm{and}eSt\mathrm{right}ess=\sigma \ast \left(1+\in \right)$$

To determine the settings of the bending machine, the calculations are based on the stress-strain curve, with the area of the Lüders strain and the area of uniform strain being used as a basis for the plastic deformation of the sheet metal. In other words, the calculations are based on the stress-strain curve in two sections, namely for deformations to the left of the Lüders point and to the right of the Lüders point 22b, so that the Lüders effect and the uniform strain are taken into account.

wobei der linke Term (mit n1 und K1) in der Klammer den ersten Abschnitt, also vor dem Lüderspunkt 22b, beschreibt und der rechte Term den zweiten Abschnitt, also rechts des Lüderspunkts 22b beschreibt.Accordingly, the stress σ is determined as the maximum over the two sections $$\sigma =\text{Max}(\text{log}{\left(1.0+\in \right)}^{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102017122073B4\_0010.png"\; state="\{\{state\}\}">n</figure-callout>}1}\ast \frac{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="DE102017122073B4\_0010.png"\; state="\{\{state\}\}">K</figure-callout>}1}{1+\in },\text{log}{\left(1.0+\in \right)}^{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DE102017122073B4\_0010.png"\; state="\{\{state\}\}">n</figure-callout>}2}\ast \frac{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102017122073B4\_0010.png"\; state="\{\{state\}\}">K</figure-callout>}2}{1+\in })$$

where the left-hand term (with n1 and K1) in the brackets describes the first section, i.e. in front of the Lüders point 22b, and the right-hand term describes the second section, i.e. to the right of the Lüders point 22b.

$$K1=\sigma yield\ast \frac{1+\left(\frac{\sigma yield}{E}\right)}{Log{\left(1+\left(\frac{\sigma yield}{E}\right)\right)}^{n1}}$$

$$n2=\frac{\text{Log}\left(\frac{\sigma tensile\ast \left(1+\epsilon tensile\right)}{\sigma distinct\ast \left(1+\epsilon distinct\right)}\right)}{Log\left(\frac{Log\left(1+\epsilon tensile\right)}{Log\left(1+\epsilon distinct\right)}\right)}$$

$$K2=\left(\frac{\sigma yield}{E}\right)\ast \frac{1+\epsilon distinct}{Log{\left(1+\epsilon distinct\right)}^{n2}}$$

wobei E der Elastizitätsmodul, σyield die Streckgrenze/Fließspannung, σdistinct die Spannung am Lüderspunkt 22b ist, εdistinct die Dehnung am Lüderspunkt 22b ist, σtensile die Bruchspannung, und εtensile die Dehnung beim Bruch bezeichnet.The parameters n1 and K1 as well as n2 and K2 describe the parameters of the plastic deformation and can be determined based on the theoretical stress and strain values according to the following equations $$n$$$$1=\frac{\text{log}\left(\frac{\sigma \mathrm{i.e}istinct\ast \left(1+e\mathrm{i.e}istinct\right)}{\sigma yiel\mathrm{i.e}\ast \left(1+\left(\frac{\sigma yiel\mathrm{i.e}}{E}\right)\right)}\right)}{LOG\left(\frac{LOG\left(1+e\mathrm{i.e}istinct\right)}{LOG\left(1+\left(\frac{\sigma yiel\mathrm{i.e}}{E}\right)\right)}\right)}$$

$$\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="DE102017122073B4\_0010.png"\; state="\{\{state\}\}">K</figure-callout>}1=\sigma yiel\mathrm{i.e}\ast \frac{1+\left(\frac{\sigma yiel\mathrm{i.e}}{E}\right)}{LOG{\left(1+\left(\frac{\sigma yiel\mathrm{i.e}}{E}\right)\right)}^{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102017122073B4\_0010.png"\; state="\{\{state\}\}">n</figure-callout>}1}}$$

$$\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DE102017122073B4\_0010.png"\; state="\{\{state\}\}">n</figure-callout>}2=\frac{\text{log}\left(\frac{\sigma tensile\ast \left(1+etensile\right)}{\sigma \mathrm{i.e}istinct\ast \left(1+e\mathrm{i.e}istinct\right)}\right)}{LOG\left(\frac{LOG\left(1+etensile\right)}{LOG\left(1+e\mathrm{i.e}istinct\right)}\right)}$$

$$\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102017122073B4\_0010.png"\; state="\{\{state\}\}">K</figure-callout>}2=\left(\frac{\sigma yiel\mathrm{i.e}}{E}\right)\ast \frac{1+e\mathrm{i.e}istinct}{LOG{\left(1+e\mathrm{i.e}istinct\right)}^{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DE102017122073B4\_0010.png"\; state="\{\{state\}\}">n</figure-callout>}2}}$$

where E is the modulus of elasticity, σyield is the yield point/yield stress, σdistinct is the stress at Lüders point 22b, εdistinct is the strain at Lüders point 22b, σtensile is the stress at break, and εtensile is the strain at break.

Furthermore, the springback of the sheet metal is taken into account when determining the settings of the bending machine, whereby a conventional bi-linear elasto-plastic model is used as a basis for the springback, with which a corresponding bending moment can be determined depending on the material and geometric properties. This takes into account how far the sheet metal has to be bent beyond the desired bending radius so that the desired bending radius is reached after the sheet metal springs back.

For the determination, i.e. the calculation, of the settings of the bending machine, a bending moment of the sheet metal is finally determined, which runs through an imaginary center line of the sheet metal, with the calculation of the bending moment based on the described non-linear elastoplastic model with a numerical calculation over several iterations is carried out.

To do this, the thickness of the sheet metal is divided into a large number of elements, with the large number in turn depending on the material properties and the absolute thickness. Typically, empirical values are used for this, so that the computational effort is kept within limits. In one embodiment, the sheet thickness can preferably be modeled with more than 40 layers, particularly preferably with 20 and with at least three layers of the same thickness. The calculation of the bending moment is based on the stress-strain curve. The assumed strain of a layer follows the assumptions of the Euler-Bernoulli beam theory. For each layer, the corresponding stress is calculated, so that based on the stresses of the elements, the result for the sheet bending moment can be calculated as the sum of the individual moments of all layers.

To determine the springback of the sheet metal, a non-linear stress distribution in the sheet metal is assumed due to an elasto-plastic stress distribution with the same resulting moment. The springback can now be calculated based on this model according to the elastoplastic model.

Based on this calculation model, a bending line of the sheet metal is determined, which 3 is shown schematically, with the calculation model taking into account non-linear geometric and non-linear material properties as well as non-linear effects at the contact points of the sheet metal with the rolls of the bending machine. 3 shows a top roll 2 and a side roll 3 arranged on the outlet side, between which a metal sheet 5 is guided, which is shown here schematically as a bending line. The bending line, which represents the metal sheet here, is divided into a number of adjacent segments K1, K2. The contact points of the segments are tangential to the rolls 2, 3 and the side roll 3 exerts a force F on the metal sheet, represented here by the bending line.

The calculation of the settings for the bending machine based on the model described above is performed using a finite element calculation method. Each element K1, K2 ... etc. of the sheet metal is defined by its radius and the geometric length, with the radius of an element depending on the bending moment, which in turn depends on the contact points.

Based on the calculation model described above, a non-linear system of equations results for the calculation of the machine parameters, which is solved using an iterative method.

Pre-calculated values of bending and springback for a material and sheet thickness can be used to speed up the calculations.

4 shows a flowchart for solving the system of equations by means of the controller, with the respective iteration steps being implemented as an executable computer program which runs on a digital signal processor.

Following the start of the program 401, the starting values for iteration steps to be carried out subsequently are calculated. Based on rough estimates, suitable starting values are calculated in order to be able to converge on meaningful and conclusive results.

After the calculation of the starting values, the loop over the multiple iteration steps begins in step 403. In the subsequent method steps 404 to 405, focal points to the left and right of the bending point are determined to take gravity into account. Subsequently, bending lines are determined between the top roll and a bottom roll, step 406, and between the top roll and the side roll, step 407. In step 408, a force balance is calculated and then, step 409, and a corresponding Jacobian matrix is created. Based on this, in step 410 new function values are calculated for solving the system of equations. Then, in step 411, it is checked whether the calculated function values differ sufficiently little from the previously calculated set of function values. If necessary, 413 the iteration method converges and sufficient accuracy is achieved so that the parameters of the side roll position of the bending machine can be transferred to the bending machine based on the calculated values. In addition, the rotational position of the top roll (top roll TR) must be determined, step 414. The iteration over the calculation steps thus ends in 413.

In the event that the calculated function values of the system of equations to be solved were not determined with sufficient accuracy in a loop run, step 412, a bending radius at the bending point is determined in step 416 and the loop over the calculation steps 403 to 411 is run through again until the check of the calculated function values in step 411 shows that these differ sufficiently little from the previously determined set of function values.

Reference List

1

bending machine

2

top roller

3

bottom roller

4

First side roller

5

sheet

6

Arrow for the direction of rotation of the top roller

7

Arrow feed movement sheet metal

8th

Pressure cylinder contact pressure bottom roller

9

Second side roller

10

sheet

21

Stress-strain curve aluminium

22

Stress-strain curve steel

22a

Stretch limit

22b

Lüder stretch

401-416

calculation steps

Claims (6)

Method for controlling a bending machine, wherein the bending machine for bending a metal sheet has at least three rollers that can be positioned relative to one another and the position of the rollers is determined by means of an iterative finite element method and taking into account the stress-strain properties of a material of the metal sheet based on the elastic deformation and the plastic deformation in the Lüders region and plastic deformation in the region of uniform strain, whereby the finite element modeling takes gravity into account. procedure after claim 1 , whereby the stress required for an elongation is determined as the maximum of a stress in the Lüders area and in the area of uniform elongation. procedure after claim 2 , where a stress is determined based on Young's modulus, yield point, stress and strain at the Lüders point, and stress and strain at break. A method according to any one of the preceding claims, further based on the elastic deformation of the sheet metal. A method according to any one of the preceding claims, wherein the finite element modeling of the sheet metal comprises segmentation into a plurality of layers and into a plurality of segments. Controller for controlling a bending machine with at least three rollers that can be positioned relative to one another and a digital signal processor for carrying out a method according to claim 1 is set up.

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