EP1308223A2 - Simulating method of a 3-roll-bending process - Google Patents

Abstract

The method of simulation of three roller bending of a light alloy motor vehicle chassis beam involves using a computer program with the parameters of the beam used for passage of the beam through the three roller bending press. The parameters include the beam cross section deformation and the bending radius or clamping condition. A finite difference model is used incorporating the bending movement curves for the beam.

Description

The invention relates to a method for simulating the bending of a bending body, in particular a profile with a three-roll bending process in which the bending body at least once or several times an arrangement of three in the conveying direction successively arranged rollers is guided, of which the two outer rollers on one side of the bending body and the other roller on the opposite side of the bending body are arranged, the rollers rest on the surface of the bending body and the middle roller by one Distance Z is fed in the direction of the bending body, so that on the bending body a moment M acts, the simulation method as a computer program is designed to calculate parameters of the bending body according to serves the passage of the bending body through the roller assembly.

Bent aluminum extrusions are of great importance for lightweight structures of vehicle construction, profile system technology as well as the construction and furniture industry. As a flexible forming process, 3-roll profile bending is good for small batch sizes can be used.

Each profile geometry requires radial because of the process inherent in bending and transverse shape changes the planning of your own rolling strategy, so for example a definition of the roller geometry, possibly an implementation of support media in hollow profiles and a definition of the machine control data.

In order to simplify this planning, it is desirable to press the 3-roll profile to be computer-aided in the simplest possible way.

The detection of the elastic and plastic deformations caused by bending mechanics FEM analyzes require a high profile with complex cross sections Discretisation. The workpiece length to be cross-linked in 3-roll profile bending is until a steady state of deformation is reached at least 1.5 times the roller gap. The resulting high number of Elements leads in process modeling with shear force introduction via roller contact for profiles of the type examined with currently common computers at computing times > 100h, so this approach for process planning is out of the question.

Against this background is the creation of a simulation process, which on modern computers in a manageable computing time of, for example, only a few Can realize minutes, the object of the invention.

The invention solves this problem by the subject matter of claim 1.

• der Biegekörper wird in Ersatz des realen Kontinuums als Modell aus einem einlaufenden und einem auslaufenden Biegebalken beschrieben,
• für den einlaufenden und den auslaufenden Biegebalken werden die Biegelinien mit Hilfe eines Finite-Differenzen-Modelles unter Berücksichtigung des querschnittsspezifischen Momenten-Krümmungsgesetzes für den einlaufenden und den auslaufenden Biegebalken ermittelt.

The simulation procedure then has at least the following steps:

• the bending body is described as a model of an incoming and an outgoing bending beam in replacement of the real continuum,
• for the incoming and outgoing bending beams, the bending lines are determined with the help of a finite difference model taking into account the cross-section-specific moment curvature law for the incoming and outgoing bending beams.

With the invention in particular a hybrid method from FEM and analytical Process simulation for process planning optimized for computing time.

The cross-sectional geometries of extruded profiles are often highly complex. critical for the first, FEM-supported process design with a given bending radius and material is the cross-sectional deformation to be expected for the specific tool. This planning phase defines the process limits with optimal, profile-supporting Tool design.

A second planning step based on an analytical approach takes into account springback, friction-transferable performance and Roller distance, the roller advance z and the number of roller passes n firmly.

In particular, the hybrid method from FEM and analytical process simulation allowed the tool-specific prediction of the cross-sectional deformations, the Springback of cross section and bending radius as well as the stress condition. Using the FEM results, the Roll position and the number of roll passes to achieve the bending radius established.

The basic idea is to differentiate between the incoming and the outgoing bar. The incoming beam is deformed while on the outgoing one Beam no longer acts a deformation force, this beam relaxes, i.e., it springs back somewhat against the direction of deformation.

At the coupling point of the incoming and the outgoing beam there is a constant profile cross-sectional area to assume, although the cross-sectional geometry deformed.

Preferably, for the incoming and outgoing bending beams Bending lines are calculated iteratively as an initial value problem and with continuum conditions aligned at the cross point of the two bars.

For the area entering the rollers (index e) and the different bending moment curvature laws from the area running out of the rolls (index a) stated.

The bar bending lines are also preferably described with the parameter t as flat curves in vector, parameterized form: r = r (t); r = (X; Y).

The following continuum conditions are particularly advantageously assumed in the coupling point of the incoming and the outgoing bar: a) Tangent equality r _e = r _a ;
d r _e / dt = d r _a / dt; b) Equal moment M _e = M _a c) Consolidation equality K _e M = K _a M.

The cross section specific moment curvature laws - curvature K = K (M) with M: = bending moment acting on the bending body - are for the incoming and the outgoing area, for example, experimentally or - particularly advantageous - determined numerically.

A finite element analysis, for example, in which a shear force-free analysis is suitable, is suitable for this purpose Bending process is calculated.

The incoming bending beam is expedient during the first pass through the roller arrangement described as a straight line and the outgoing bending beam as a circular arc. In contrast, in further runs the incoming and / or the outgoing Bending beam described as a circular arc.

Advantageous embodiments can be found in the subclaims.

Figur 1a-d

den Ablauf eines 3-Walzen-Profilbiegens anhand von Darstellungen aufeinanderfolgender Bearbeitungsschritte bei einem Durchlauf der Walzenanordnung sowie eine Darstellung des gebogenen Profils;

Figur 2

eine schematische Veranschaulichung des Ablaufes eines erfindungsgemäßen Simulationsverfahrens;

Figur 3

ein Diagramm eines beispielhaft errechneten, querschnittsspezifischen Momentenkrümmungsgesetzes;

Figur 4

eine graphische Veranschaulichung eines Finite-Differenzen-Modelles;

Figur 5

ein Diagramm, welches Meßergebnisse von Biegevorgängen verdeutlicht, zu denen zuvor eine Simulation errechnet wurde;

Figur 6

ein Diagramm, welches den Einfluß eines Stützmediums auf den Biegevorgang veranschaulicht;

Figur 7

eine weitere Veranschaulichung eines 3-Walzen-Profilbiegen s; und

Figur 8

eine beispielhafte Folge von Zustellschritten bei einem 3-Walzen-Profilbiegen,

Figur 9

eine Veranschaulichung des Biegezustandes erster Iteration.

The invention is described in more detail below using an exemplary embodiment with reference to the figures. It shows:

Figure 1a-d

the sequence of a 3-roll profile bending on the basis of representations of successive processing steps in one pass through the roll arrangement and a representation of the bent profile;

Figure 2

a schematic illustration of the sequence of a simulation method according to the invention;

Figure 3

a diagram of an example calculated, cross-section-specific moment curvature law;

Figure 4

a graphical illustration of a finite difference model;

Figure 5

a diagram which illustrates measurement results of bending processes for which a simulation was previously calculated;

Figure 6

a diagram illustrating the influence of a support medium on the bending process;

Figure 7

a further illustration of a 3-roll profile bending; and

Figure 8

an exemplary sequence of infeed steps for a 3-roll profile bending,

Figure 9

an illustration of the bending state of the first iteration.

Fig. 1 illustrates a 3-roll profile bending with here three cylindrical rolls of the same diameter 1, 2, 3. Two of the rollers 1, 3 are arranged such that their axes lie in a plane parallel to the profile. The middle roller 2 is on the other hand, arranged on the side of the profile opposite the rollers 1 and 3.

In the starting position of Fig. 1 a, the outer periphery of each of the rollers touches the profile.

Then the middle roller becomes perpendicular to the profile extension by a path "z" delivered in the direction of the profile (Fig. 1b). The resulting bending moment leads to a deformation of the profile. When the profile is fed through the roller arrangement it receives the geometry of Fig. 1c.

The sequence of steps 1a-c is referred to below as a "delivery step".

Generally, it is necessary to do several consecutive bending operations 1 a-c, that is to say a plurality of infeed steps Z1, Z2, Z3,..., Zn (not shown here) so as not to damage the profile.

So it is particularly desirable to maintain the profile cross section, what can optionally be supported by support media 5 in grooves 6 of the profile (see Fig. 2).

When simulating 3-beam profile bending, a cross-section-specific one is created first Torque curvature law determined (e.g. experimental or numerical).

The specified profile radius must also be observed.

As can be seen from FIG. 2, the infeed data n (number of roll passes) and Z (infeed path of the roll in the direction of the bending body during the nth rolling process) are calculated in the simulation, a hybrid model being used from a finite element method Determination of the moment curvature law is used: M = f (K);

Then with a finite difference calculation K n = f (Z n , K n-1 ); determined with R = 1 / K, so that: Z n = f (R n , R n-1 ) is applied (see also Fig. 4).

3 illustrates an example of a cross-section-specific one determined in this way Torque curvature law for that indicated in cross section in Fig. 1 or 3 Profile.

The selected computing time-optimized model is based on the assumption of shear force-free Bending in which the profile-supporting effect of the rollers through implementation levels and the fixing of knots is depicted. The method allows even with very complex profile geometries and the use of internal support media small number of elements; the computing times are in the range less minutes. The examinations with MS-AutoForge are carried out with elastic-plastic Substance law and the material data for AIMgSi0.5 performed. The friction is implemented in the model using Coulomb's law. Isoparametric 8-node elements with a trilinear approach were used.

The simulation result is e.g. Cross-sectional deformations, springback of Cross section and bending radius as well as the stress condition and the forming capacity to disposal. 6 shows the calculated cross-sectional deformations after unloading of the curved profile. As expected, they are transverse to the bending axis Profile grooves are at high risk of deformation. Variant calculations for different Bending radii show that the profile has exceeded the tolerance from 550 mm. By Inserting polyoximetylene support strips can deform the endangered Cross-sectional areas are kept within the tolerance. The analysis of the radial Springback allows the geometry and material-specific determination precorrected radius data, which are used as target values for the control data generation of the Serve machine.

The model is based on a geometric approach to describe the roll gap ratios for predefined roll spacings and geometries. The material is assumed to be rigid-plastic. Deformations occur only in the middle profile area in a sufficiently large bending moment relative to the roll distance. Fig. 8 shows the geometric situation for the first roll pass, in which the incoming profile is described by a straight line and the outgoing profile by a circular arc. For the following runs, incoming and outgoing profile areas are each described by circular equations, which is confirmed by experimental investigations and comparative, shear-loaded FEM analyzes. The result of the calculation given the target radius and any number n of roll passes are the infeeds z ⁿ and the resulting bending radii R ⁿ . The elastic springback of the bending profile is recorded by the described FEM-assisted pre-correction of the bending radii. The criterion for the smallest possible number of passes is the transferability of the calculated forming performance through friction.

As already stated, the finite difference model used describes the Bending process of the 2-beam model based on the assumption of a beam reduction Lines and assuming a section-wise row bend. This is simple Way the determination of the bending lines for certain load conditions and boundary conditions possible.

The model limits are the contact points of the outer rollers.

It allows the determination of the bending lines for certain load conditions and Boundary conditions. The model limits are the contact points of the outer rollers. The first bar describes the part of the workpiece entering the mill stand up to the moment maximum, the second the expiring. Both bars are subject previously with FEM (or alternatively with another method, e.g. empirically with bending test) determined cross-section and material-specific torque curvature law M = f (K). The law is through a nonlinear range marked for load and a linear range for relief.

• Tangentengleichheit
• Momentengleichheit
• Verfestigungsgleichheit (keine Verformung mehr möglich), d.h. gleicher Punkt im Momenten-Krümmungsgesetz.

The incoming beam experiences an elastic-plastic deformation as the bending moment increases. The outgoing part is relieved and deformed only elastically (like a leaf spring). The coupling conditions between the bars in point 1 are

• tangent equality
• moment equality
• Consolidation equality (no more deformation possible), ie same point in the moment curvature law.

Given the Vorbiegeradius R _n-1 and the desired outlet radius R _n is iteratively via a FD approach for the delivery of _{n is} determined which satisfies the three coupling conditions. To math. Description of the bending lines, when calculating and displaying the results, the curvature K = 1 / R with K = 0 is used for straight profiles instead of the radius.

The iteration process preferably proceeds as follows (FIG. 9):

First, the roll diameter and center points (infeed) and the pre-bending radius are defined and an initial contact angle α _{1 is} specified.

The following first procedure is then carried out:

Procedure 1:

1. Specification of an initial force F _e1 in beam e

Last: Biegemomentverlauf infolge F_e1

Biegewiderstand: K = f(M) aus Momenten-Krümmungsgesetz (nichtlinearer Bereich)

2. Calculation of the bending line using a finite difference method (FD). Boundary conditions:

Load: bending moment curve due to F _e1

Bending resistance: K = f (M) from the moment curvature law (non-linear range)

3. Calculation of distance s _e1 bending line roller

4. Iteration to establish contact by varying F _e1 → F _en Goal: s _en <contact tolerance,
Calculation of the max. Bending moment M _e on contact

This is followed by the following second procedure:

Procedure 2:

1. Specification of an initial force F _a1 in beams a pre-curved with procedure 1

Last: Biegemomentverlauf infolge F_a2

Biegewiderstand: K = f(M) aus Momenten-Krümmungsgesetz (linearer Bereich des vorgekrümmten Balkens)

2. Calculation of the bending line using the finite difference method (FD). Boundary conditions:

Load: bending moment curve due to F _a2

Bending resistance: K = f (M) from the moment curvature law (linear area of the pre-curved beam)

3. Calculate distance S _a1 bending line roller

4. iteration to establish contact by varying F _a1 → F _at target: s _an <contact tolerance,
Calculation of the max. Bending moment M _a on contact
Here M _e ≠ M _a , please note
ie not all coupling conditions are fulfilled in this phase.

The following third procedure is then carried out (procedure 3):

Iteration for torque adjustment by varying the contact angle from α ₁ → α _n and repeating procedures 1 and 2.
Goal: M _a = M _e , calculation of the bending line for a given pre-bending radius, roll diameter and infeed

Procedures 1-3 are carried out automatically for different deliveries and result in the form of a characteristic curve of the outlet curvature as Function of delivery.

1. Generierung der Steuerdaten und Einstellung der Walzmaschine

2. Walzen auf Basis dieser Daten

3. On-line-Erfassung der Istkrümmung über vorhandene Krümmungssensoren

4. Berechnung der zur Korrektur evtl. Krümmungsabweichungen notwendigen Steuerdaten und Korrektur der Einstellung der Walzmaschine, d.h. generierung von Steuerdaten und Einstellung der Walzmaschine mit Hilfe der Ergebnisse eines Finite-Differenzen-Modelles, sodann Rückkehr zu Schritt "2".

With the procedures that can be programmed in PASCAL, for example, computing times in the seconds range can be achieved with modern PCs. The method for generating control data is therefore even real-time capable and can be used for the control of roll bending processes to maintain the rolling radius under the influence of disturbance variables. Process control using the new method is carried out in 4 steps:

1. Generation of control data and setting of the rolling machine

2. Rolling based on this data

3. On-line detection of the actual curvature via existing curvature sensors

4. Calculation of the control data necessary to correct any curvature deviations and correction of the setting of the rolling machine, ie generation of control data and setting of the rolling machine using the results of a finite difference model, then return to step "2".

Claims (21)

Process for simulating the bending of a bending body, in particular a profile, using a three-roll bending process, in which the bending body is guided at least once or several times an arrangement of three rollers (1, 2, 3) arranged one behind the other in the conveying direction, of which the two outer rollers are arranged on one side of the bending body and the further roller on the opposite side of the bending body / is wherein the rollers rest on the surface of the bending body and the middle roller is advanced by a distance Z in the direction of the bending body, so that a moment M acts on the bending body; the simulation method being designed as a computer program which is used to calculate parameters of the bending body after the bending body has passed through the roller arrangement, in particular the bending radius R and / or the cross-sectional deformation, and / or the resilience of the cross-section and bending radius and / or the stress state and / or the forming performance, has at least the following steps: a) the bending body is described as a model of an incoming and an outgoing bending beam to replace the real continuum, b) for the incoming and outgoing bending beams, the bending lines are determined with the help of a finite difference model, taking into account the cross-section-specific moment curvature law for the incoming and outgoing bending beams. A method according to claim 1, characterized in that for the incoming and the outgoing bending beam, the bending lines are iteratively calculated as an initial value problem and are compared with continuum conditions in the coupling point of the two beams. Method according to claim 1 or 2, characterized in that different bending moment curvature laws are applied for the area (index e) entering the rolls and the area (index a) leaving the rolls. Method according to one of the preceding claims, characterized in that the beam bending lines are described with the parameter t as flat curves in vector, parameterized form: r = r (t); r = (X; Y). Method according to one of the preceding claims, characterized in that the following continuum conditions are assumed in the coupling point of the incoming and the outgoing bar: d) Tangent equality r _e = r _a ;
d r _e / dt = d r _a / dt; e) Equal moments M _e = M _a f) consolidation equality K _e M = K _a M. Method according to one of the preceding claims, characterized in that the cross-section-specific moment curvature laws: curvature K = K (M) with M: = bending moment acting on the bending body for the incoming and outgoing area are determined experimentally. Method according to one of the preceding claims, characterized in that the cross-section-specific torque curvature laws K = K (M) for the incoming and the outgoing area are determined numerically. Method according to one of the preceding claims, characterized in that the cross-section-specific torque curvature laws K = K (M) for the incoming and the outgoing area are determined numerically by a finite element analysis. Method according to one of the preceding claims, characterized in that a bending process free of lateral forces is calculated in the finite element analysis. Method according to one of the preceding claims, characterized in that the incoming bending beam is described as a straight line and the outgoing bending beam as a circular arc during the first pass through the roller arrangement. Method according to one of the preceding claims, characterized in that the incoming and / or the outgoing bending beam in the second and all further roll passes is described as a circular arc. Method according to one of the preceding claims, characterized in that the finite difference model is calculated on the assumption that pure bending occurs in sections. Method according to one of the preceding claims, characterized in that the roll infeed z and the number of roll passes n are calculated taking into account the springback, the friction-transferable power and the roll spacing. Method according to one of the preceding claims, characterized in that the simulation determines the roll position and the number of roll passes in order to achieve the bending radius. Method according to one of the preceding claims, characterized in that the iteration process runs through the following procedures one or more times in succession: Procedure 1: 1.1 Specification of an initial force F _e1 in beams e 1.2 Calculation of the bending line using a finite difference method (FD); Boundary conditions: Load: bending moment curve due to F _e1 Bending resistance: K = f (M) from the moment curvature law (non-linear range) 1.3 Calculation of distance s _e1 bending line roller 1.4 Iteration to establish contact by varying F _e1 → F _en Aim: s _en <contact tolerance, calculation of the max. Bending moment M _e on contact, then procedure 2: 2.1 Specifying an initial force F _a1 in
with Procedure 1 pre-curved beams a 2.2 Calculation of the bending line using the finite difference method (FD); Boundary conditions: Load: bending moment curve due to F _a2 Bending resistance: K = f (M) from the moment curvature law (linear area of the pre-curved beam) 2.3 Calculation of distance s _a1 bending line roller 2.4 Iteration to establish contact by varying F _a1 → F _at destination: s _an <contact tolerance, calculation of the max. Bending moment M _a on contact, then procedure 3: 3. iteration for torque adjustment by varying the contact angle from α ₁ → α _n and repeating procedures 1 and 2; Goal: M _a = M _e , calculation of the bending line for a given pre-bending radius; Roll diameter and infeed. Method for simulating the bending of a bending body, in particular for simulating the bending of a profile using a three-roll bending method according to one of the preceding claims, characterized in that the method is used in real time to control a roll bending process. A method according to claim 16, characterized in that the real-time process control runs through the following steps: Generation of control data and setting of a rolling machine, Rolling on the basis of this data, Online recording of the actual curvature via existing curvature sensors, and Calculation of the curvature deviations necessary for the correction Control data and correction of the setting of the rolling machine, i.e. Generation of control data and setting of the rolling machine with the help the results of a finite difference model, then return to step "2".

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