METHOD OF BENDING AND BENDING MACHINE FOR THE EXECUTION OF A METHOD OF BENDING

A method for the bending of a tubular metal article comprising at least the following steps a) determining a bending sequence of the tubular metal article by means of a calculating unit, and b) bending the tubular metal article according to the bending sequence determined during the execution of the step a) is described. During the step a) at least the following sub-steps are performed by the calculating unit: a1) defining an initial configuration and a final configuration of the tubular metal article which differs from the initial configuration by a number N of bends, a2) determining one or more explorative bending sequences as a function of the initial configuration and the final configuration, each explorative bending sequence having a cost and a3) proposing at least one or more explorative bending sequences having minimal costs as the determined bending sequence.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application claims priority from Italian patent application no. 102021000017384 filed on Jul. 1, 2021, the entire disclosure of which is incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a method of bending a tubular metal article, in particular a metal wire or a metal tube, for obtaining a certain bent tubular article. In particular, the present invention relates to a method of bending a tubular metal with article an improved determination of the sequence of the bends.

Advantageously, the present invention also relates to a bending machine, in particular a wire bending machine or tube bending machine, for the bending of tubular metal articles.

STATE OF THE ART

Bending machines are known for the bending of metal wires or for the bending of metal tubes.

Such machines are configured to execute a series of bends for obtaining a bent wire or a bent tube, respectively.

It is also known that these machines comprise at least one bending head having one or more bending groups for carrying out the bends and an activation apparatus for carrying out relative movements between the bending head and the wire or the tube.

The activation apparatus allows to obtain a relative positioning between the wire or the tube and at least one of the bending groups so that said bending group can carry out a respective bending.

It is known that the activation apparatus may be configured to move and/or rotate the bending head and/or advance and/or rotate the wire or the tube along or about an axis.

A typical bending group comprises a turret having one or more engagement elements, each configured to contact the wire or the tube and an actuator coupled to the turret and configured to rotate and translate the turret around and along an axis for bending the wire or the tube.

Typically, each wire or tube is subjected to a bending sequence by a method that provides both information regarding the bending itself (steps of curving) and information regarding the positioning of the wire or the tube (steps of alignment to change the relative position between the bending head and the wire or the tube), to obtain the respective bent wire or the respective desired bent tube.

The bending sequence must be chosen so that the wire or the tube does not interfere with parts of the bending machine and/or with itself at any time during the execution of the bending sequence.

In order to avoid these problems, an operator must manually define the bending sequence. These operations take a significant amount of time and become more and more difficult and time-consuming as the complexity of the final bent wire or tube increases.

Furthermore, it should be considered that the definition of such operations requires not only a high level of experience of the operator, but also a high basic qualification. These aspects can be problematic in countries where there is a shortage of skilled workers. In addition, a drawback may develop in contexts in which there is a high turnover of operators.

DISCLOSURE OF INVENTION

Therefore a need is felt in the sector for a further improvement of the methods of bending and/or of the bending machines which will allow to solve at least one of the known drawbacks.

In particular, there is a need felt in the sector for a method of bending and/or a bending machine that allows a reduction in the times required for the determination of the bending sequences.

The aforesaid aims are achieved by the present invention, since it relates to a method of bending a tubular metal article as defined in the independent claim. Alternative preferred embodiments are protected in the respective dependent claims.

The aforesaid aims are also achieved by the present invention, since it relates to a machine according to claim15.

BEST MODE FOR CARRYING OUT THE INVENTION

InFIG.1,1denotes as a whole a (n) (automatic) bending machine for the bending of tubular metal articles to obtain bent tubular metal articles.

Specifically, a tubular metal article can be a metal wire or a metal tube2.

According to some non-limiting embodiments, the tubular metal articles may have circular, oval, rectangular, square, elliptical or any other shaped cross-sections.

According to some non-limiting embodiments, the tubular metal articles may be hollow or solid.

According to some non-limiting embodiments, the tubular metal article comprises at least one metal material. According to some non-limiting variations, the metal articles could also comprise at least one non-metal material such as for example a composite material or a plastic material.

Reference is made hereinafter without limitation to the example of the bending of metal tubes2for obtaining bent tubes2. However, the following description also applies to the bending of other tubular metal articles such as metal wires to obtain the respective tubular metal articles.

In addition, a bending machine1for the bending of metal tubes2is described in detail below without any limiting intent. However, the following description could also apply to bending machines1for the bending of tubular metal articles such as for example metal wires.

With particular reference toFIGS.1and2, the bending machine1comprises at least:a control unit configured to control the operation of the bending machine1itself;a bending head3, in particular operatively connected to the control unit and, configured to bend the tubes2, in particular at a bending station; andan activation apparatus, in particular operatively connected to the control unit and configured to control and/or execute a relative movement between the bending head3and the tube2.

In greater detail, the bending head3comprises one or more bending groups4, in the specific case shown two, each bending group4being configured to selectively bend the tube2. In other words, each bending group4is configured to bend the tube2.

In further detail, each bending group4may comprise at least:a respective turret5, in particular movably inserted into a respective housing seat of the bending head3;one or more engagement elements6integral with the respective turret5; anda first actuation device (known per se and not shown), in particular operatively connected to the control unit and coupled to the respective turret5and configured to actuate an angular movement and/or a translation of the turret5.

Furthermore, the control unit is configured to control each first actuation device so as to determine the bending operations by means of the angular movement and/or the translation of the turret5and consequently the relative displacements of the engagement elements6.

In this specific case, each first actuation device comprises at least one (electric) motor to determine and/or activate the angular movement of the respective turret5and/or a linear actuator, for example a pneumatic actuator, to determine the translation of the respective turret5.

In greater detail and with reference toFIG.5, the activation apparatus may be configured to move and/or rotate the tube2along and around a first axis A, respectively. Furthermore, the activation apparatus may be configured to rotate the bending head3around a second axis B.

In further detail, the activation apparatus can be provided with one or more second actuation devices configured to move the tube2along the and/or to rotate the tube2about the first axis A.

Alternatively or additionally, the activation apparatus can be provided with one or more third actuation devices configured to at least rotate the bending head3about the second axis B.

According to the non-limiting embodiment shown, the activation apparatus comprises a first group of advancement wheels7arranged one after the other and a second group of advancement wheels8arranged one after the other. In particular, each advancement wheel7faces a respective advancement wheel8so that the advancement wheels7and the advancement wheels8act on opposite sides on the tube2.

In particular, the first group and the second group are arranged upstream of the bending head3.

Further, the bending machine1, in particular the bending head3, could comprise a cutting unit configured to cut the tube2.

With particular reference toFIG.1, the bending machine1may further comprise a storage device9containing the (not bent) tube2. In particular, the activation apparatus can be configured to advance the tube2from the storage device9towards the bending head3.

In greater detail, the storage device9is configured to contain the tube2in the form of a roll.

In further detail, the storage device9comprises a support10carrying the tube2in the form of a roll, in particular the support10is designed to allow the unwinding of the tube2arranged in the form of a roll.

With particular reference toFIG.1, the bending machine1may further comprise a human-machine interface11configured to allow an operator to transmit instructions to the bending machine1, in particular to the control unit, and/or to receive information from the bending machine1.

Advantageously, the bending machine1comprises a calculating unit12, in particular operatively connected to the control unit, configured to determine a bending sequence of the tube2to obtain the bent tube2′. In particular, the calculating unit12can be arranged locally and/or remotely.

In use, the bending machine1bends the tube2for obtaining a (determined) bent tube2′.

In particular, the shape (configuration) of the bent tube2′ is defined before the method of bending is activated. More specifically, the control unit contains information relating to the bent tube2′.

In particular, the bent tube2′ is distinguished from the tube2by a number N of bends.

In greater detail, the bending machine1bends the tube2according to a determined bending sequence; in particular, the determined bending sequence comprises N bends.

The determination of the bending sequence of the tube2is made prior to the execution of the bending sequence by the bending machine1.

In greater detail during the execution of the method of bending, the following steps are performed:a) determining the bending sequence of the tubular metal article2by means of the calculating unit12; andb) bending the tube2according to the bending sequence determined during the execution of the step a).

More specifically, the bending sequence defines a plurality of steps of execution (a plurality of bends), in particular N steps of execution, which are executed one after the other, and each step of execution has a respective step of alignment and a respective step of curving which, in particular, is executed following the execution of the respective step of alignment.

During each step of alignment a relative position between the tube2and the bending head3, in particular of the one or more bending groups4, is modified and during each step of curving the bending head3, in particular at least one of the bending groups4, even more particularly at least one of the turrets5(by means of at least one engagement element6), performs a local bending of the tube2.

In greater detail, after the execution of each step of curving, the tube2presents a (new) intermediate configuration.

In even greater detail, prior to the execution of the first step of curving, the tube2presents a (substantially) linear configuration (the tube2extends along a longitudinal axis, in particular parallel, even more particularly coaxial, to the first axis A). After executing the last step of curving, the tube2corresponds to the bent tube2′.

In still further detail, during each step of curving, the respective bending of the tube2is obtained by activating the respective bending group4, in particular of the respective turret5, and a first (free) portion13of the tube2relative to a second portion14of the tube2is bent (seeFIG.2), e.g. this second portion14being held stationary during the execution of the respective step of bending. In particular, during each step of curving an angle defined between the first portion13and the second portion14is obtained. Even more particularly, at least the specific shape of the first portion13varies from one step of curving to the other and/or the defined angles may vary between steps of curving.

Furthermore, during each step of curving at least one of the first actuation devices activates the respective bending group4, in particular the respective turret5to execute the respective bending of the tube2.

Preferably, during the execution of each step of curving, the tube2is tightened, i.e. the tube2can neither translate along the nor can it rotate about the first axis A.

More specifically, during the step of alignment, the correct positioning of the tube2relative to a specific bending group4is obtained so that it can perform the correct bending, i.e. so that it can perform the correct step of curving.

In further detail, during each step of alignment, the second actuation devices move the tube2along the and/or rotate the tube2about the first axis A and/or one or more third actuation devices at least rotate the bending head3about the second axis B.

Furthermore, during the method and before the execution of the step a) and step b), an initialization step is performed during which the shape of the bent tube2′ is defined.

More specifically, during the initialisation step, the shape of the bent tube2′ is inserted and/or read and/or retrieved by the control unit. In particular, the shape of the bent tube2′ is provided digitally and describes the three-dimensional configuration of the bent tube2′.

In further detail, the shape of the bent tube2′ may be provided to the control unit by one or more software systems which in turn may be based on Computer-Aided Design (CAD) and/or Computer-Aided Manufacturing (CAM) software and/or distributed computer systems for monitoring and supervision (also known as SCADA).

Preferably, a step of cutting can also be performed during the method, during which the bent tube2or the tube2′ is cut. In particular, the step of cutting can be performed before, during or after the execution of the bending sequence.

Preferably, one or more repetition steps are executed during which the step b) is repeated with a new tube2based on the bending sequence determined during the execution of the step a) (and without step a) being performed again). In this way, mass production is achieved.

In greater detail and with reference toFIGS.2to5, at least the following sub-steps are executed by the calculating unit12during the step a):a1) defining an initial configuration20and a final configuration21of the tube2(see, for example,FIG.4), where the final configuration21differs from the initial configuration by a number N of bends;a2) determining one or more explorative bending sequences22as a function of the initial configuration20and the final configuration21, each explorative bending sequence22having a cost which is a function of the bending costs in terms of energy and/or time; anda3) proposing at least one or more explorative bending sequences22having minimal costs, particularly compared to other possible bending sequences, as the determined bending sequence.

In particular, the calculating unit12receives information relating to the shape of the bent tube2′ from the control unit.

FIGS.3and4show an example for determining at least one bending sequence according to the step a). In the example, the tube2′ differs from the initial tube2in the presence of N=3 bends (bends numbered 1, 2 and 3). In theory, the final configuration can be obtained starting from the initial configuration by following six different paths (see paths a) to f)).

In greater detail, during the step a2) one or more paths (in theory six paths a) to f)) from the initial configuration20to the final configuration21are defined. Each path presents a plurality of possible intermediate configurations of the tube2.

In further detail, each intermediate configuration is connected to a subsequent intermediate configuration by means of a bend (i.e. by the implementation of a respective step of execution).

Furthermore, during the step a2), the respective associated cost for each of the one or more paths is determined, which associated cost is dependent on the cost of the respective bends, i.e. the cost of the respective steps of execution.

Preferably, the respective bends of the one or more paths corresponding to the minimum associated costs, define the one or more explorative bending sequences22to be proposed during the step a3).

In addition, during the step a) the intermediate configurations that are not available are excluded, e.g. because they would contact a portion of the bending machine1.

For example, in the specific case shown inFIG.3, during the step a) it is determined that the paths d) and f) involve minimal costs, while the paths a), b), c) and e) are less preferable, in particular to be excluded.

In addition, the Applicant has found it advantageous, particularly in terms of calculation time, to define the bent tube2′ as the initial configuration20and the non-bent tube2as the final configuration21. In other words, it is advantageous to determine the one or more bending sequences using the calculating unit12by starting from the bent tube2′ and defining one or more bending sequences that enable to obtain the non-bent tube2and having minimal costs compared to other possible bending sequences.

According to such an embodiment, the bending sequence to be carried out during the step b) corresponds to the reverse order of that determined during the step a), in particular during the sub-step a2).

With reference to the example inFIGS.3and4, during the step a), the calculating unit12determined two explorative bending sequences with minimal costs, in particular the bending sequences 0-2-3-1 (path d)) or 0-3-2-1 (path f)). The other possible bending sequences (paths a), b), c) and e)) involve higher costs that make these bending sequences undesirable or impossible. Then, during the step b), the tube2is bent according to the bending sequence 1-3-2 or 1-2-3, in particular according to that bending sequence that is chosen by the operator.

The execution of the step a), in particular of the sub-step a2), is explained in greater detail with reference toFIG.5.FIG.4specifically exemplifies the path 0-2-1-3 (path e)) which, however, ultimately turns out to have higher costs than the paths 0-2-3-1 and 0-3-2-1. It can be seen that the bent tube2′ differs from its subsequent intermediate configuration in the bend2, which in turn differs from the subsequent intermediate configuration in the bend1, which in turn differs from its subsequent intermediate configuration (i.e. the tube2) in the bend3. Therefore, the cost of the respective explorative bending sequence22is determined by the cost of the sequence of the bends2,1and3.

Advantageously, during the step a), a sub-step a4) (simulation) is also performed during which a three-dimensional simulation is executed, by the calculating unit12, following the bending sequence and/or one or more explorative bending sequences in order to verify the feasibility of the bending sequence and/or one or more explorative bending sequences. In particular, during the sub-step a4), in order to verify the feasibility of the bending sequence and/or one or more explorative bending sequences, it is simulated for the bending sequence and/or for one or more explorative bending sequences whether the tube2(even partially bent) or the tube2′ could interfere with, in particular beat against, one or more portions (parts) of the bending machine1.

In particular, during the step b) only those explorative bending sequences22are considered which should not create a risk that the tube2, the partially bent tube2or the bent tube2′ may interfere with the portions of the bending machine1. However, in order to exclude any risk, it is advantageous to perform step a4).

In greater detail, during the step a4) a three-dimensional model of the bending machine1as a whole or partially and of the tube2is simulated and the steps of execution, in particular the respective steps of alignment and the respective steps of curving are simulated, during which the intermediate configurations of the tube2and (eventually) the bent tube2′ are obtained. In the event that, during the step a4), the simulation of the execution determines that the implementation of at least one of the steps of execution (of the bends) would result in a contact of the tube2with a portion of the bending machine1, the respective explorative bending sequence22is discarded and is not proposed during the step a3).

According to some embodiments, a step a5) of signaling is also performed during which a plurality of explorative bending sequences proposed during the sub-step a3) are displayed by means of the human-machine interface11. Preferably, an operator selects by means of the human-machine interface11one of the explorative bending sequences22as the bending sequence to be used during the step a). This can be advantageous as the operator, in his choice, can consider additional aspects that are not strictly connected to the operation of the bending machine1itself. These aspects may be one or more of the following:process steps to be carried out in the plant in which the bending machine1is present that follow the finalization of the bends of the tube2′ such as the removal of the tube2′ from the bending machine1;the wish for the bending head3or the bending heads3to be in a certain configuration following the completion of the step a);the specific arrangement of the bending machine1in the factory.

In greater detail, during the step a2) the cost of each bending (of each step of execution) is determined at least as a function of the energy necessary and/or the time necessary during the respective step of alignment.

Preferentially, the cost of each bending is determined solely in dependence on the respective step of alignment, in particular a respective alignment cost E associated with each step of alignment (in other words, the alignment cost E is the energetic and/or time cost for executing the respective steps of alignment of the various explorative bending sequences). In other words, the cost of each bending is not determined in dependence on the respective step of curving, in particular the cost of each bending is not determined as a function of the energy needed and/or the time necessary for executing the respective step of curving.

This is advantageous as it facilitates and shortens the calculations of the calculating unit12. In this context, it should be considered that the same steps of curving are to be carried out for each possible bending sequence (in a different order between the various bending sequences). Furthermore, the differences between the possible bending sequences lie in the step of alignment that varies between the bending sequences. Therefore, the relevant cost for determining whether explorative bending sequence22entails a minimal cost than another explorative bending sequence22is (substantially) only determined by the steps of alignment.

With reference to the example inFIGS.3and4, while the respective steps of curving1,2and3are substantially independent of the sequence itself, the costs resulting from the respective steps of alignment are different. In the case of the bending sequence 0-2-3-1, a first step of alignment must be executed in order to be able to execute the respective step of curving2, followed by a second step of alignment in order to execute the respective step of curving3and finally a third step of alignment in order to execute the respective step of curving1.

In the case of the bending sequence 0-3-2-1, a first, second and third steps of alignment must be executed in order to execute the respective steps of curving3,2and finally1.

The same reasoning applies to the bending sequences (a), b), c) and e)) ofFIGS.3and4, which are considered disadvantageous from a cost point of view as they are too costly compared to the other cases.

Analogous to the movements to be considered during the step a), the calculating unit12considers for determining the cost of each step of alignment:i) a linear movement Δx of the tube2along the first axis A;ii) a rotation40of the tube2about the first axis A; andiii) a rotation40of the bending head3about the second axis B.

Then, the calculating unit12determines the alignment cost E of each step of alignment in dependence on the respective Δx, the respective Δθ and/or the respective42. In particular, the alignment cost E of each step of alignment is determined in proportion to the respective Δx, the respective Δθ and/or the respective42.

In greater detail, the calculating unit12determines the alignment cost E of each step of alignment according to the following formula:E=w1*|Δx/Δxmax|+w2*|Δθ/Δθmax|+w3*|ΔΩ/ΔΩmax|, wherein w1, w2and w3are respective weighting factors and Δxmax, Δθmaxand ΔΩmaxare respective maximum values.

It should be noted that the relationship with the respective maximum values takes into account the different ranges and the different units. Therefore, the relationship with the respective maximum values scales the respective values and defines an a-dimensional cost.

Furthermore, each movement i), ii) and iii) may be more or less fast and/or may consume less or more energy compared to the other movements i), ii) and iii). This aspect is considered through the choice of the weighting factors. Preferably, the sum of the weighting factors w1, w2and w3is equal to 1 (w1+w2+w3=1).

Advantageously, during the step a2) the one or more paths corresponding to the minimum associated costs are determined by the calculating unit12by means of a graph search algorithm.

Preferably, the graph search algorithm is an A* algorithm. In particular, the A* algorithm identifies a path configuration20the final from the initial towards by each intermediate configuration21classifying configuration by means of an estimate of the best path that passes through that intermediate configuration.

In particular, by using an A* algorithm, the most promising paths can be determined without the need to calculate all possible paths.

In addition, during the execution of the graph search algorithm, intermediate configurations that are not available are excluded, e.g. because they would contact a portion of the bending machine1.

In greater detail, during the step a2), one or more paths are explored by means of the execution of the following sub-steps (of A* algorithm):a2i) setting the initial configuration20as a start configuration;a2ii) determining the cost F from the start configuration to a subsequent intermediate configuration in proportion to the sum G of the bending cost (of the respective steps of alignment) from the initial configuration20to the subsequent intermediate configuration and a (sub-) estimate of the cost H of the bends (of the respective steps of alignment) of the remaining path from the subsequent intermediate configuration to the final configuration21(in other words F=G+H);a2iii) repeating the sub-step a2ii) for one or more of the other subsequent intermediate configurations;a2iv) choosing the one or more subsequent intermediate configurations with the minimal cost;a2v) for each chosen subsequent intermediate configuration setting the subsequent intermediate configuration as the new start configuration and repeating the sub-steps a2ii) to a2v) until arriving at the subsequent intermediate configuration defined by the final configuration21.

In greater detail, the cost F is determined on the one hand from a cost G calculated as a function of the steps of execution, in particular the respective steps of alignment and/or the alignment costs from the initial configuration20to the subsequent intermediate configuration and on the other hand by an estimate of the cost H still necessary to arrive from the subsequent intermediate configuration to the final configuration21.

In further detail, the respective cost G is calculated as a function of the respective Δx, the respective Δθ and/or the respective ΔΩ. In addition, the respective cost H is estimated as a function of the number of bends N and the number of bends already executed; in other words, the respective cost H depends on the number of bends still required to arrive from the respective subsequent intermediate configuration to the final configuration21.

With particular reference toFIG.6, number1′ denotes a second embodiment of a bending machine according to the present invention. The bending machine1′ is similar to the bending machine1and for this reason it is described below only limited to the differences with respect to the bending machine1itself, indicating parts that are equal or equivalent to parts already described with the same reference numbers.

In particular, the bending machine1′ differs from the bending machine1in that it comprises two bending heads3that are spaced apart from each other, in particular along the first axis A.

In particular, the bending machine1′ is configured to bend a tube2having two free portions13. In addition, each bending head3is configured to bend a respective free portion13.

In particular, each bending head3comprises a single bending group4.

In further detail, each bending head3is movable along the first axis A and a third axis C, the third axis C being perpendicular to the first axis A and the second axis B.

In addition, the bending machine1′ comprises a gripping device24interposed between the bending heads3, in particular the gripping device24is centred relative to the bending heads3.

More specifically, the gripping device24is configured to retain the tube2during the operations of the bending heads3. Preferably, the gripping device24is also configured to rotate the tube2about the first axis A. In particular, the gripping device24defines a second actuation device.

In further detail, during each step of alignment the following movements are executed:i) a linear movement Δx of the tube2along the first axis A;ii) a rotation40of the tube2about the first axis A;iv) a linear movement Δz of the bending head3along the third axis C; andv) a linear movement Δxaof the bending head3along the first axis A.

Then, during the execution of the step a) the calculating unit12determines the alignment cost E of each step of alignment as a function of the respective Δx, the respective Δθ, the respective Δxaand/or the respective Δz.

In greater detail, the calculating unit12determines the alignment cost E of each step of alignment according to the following formula:

In addition, the limits Δxmaxand Δzmaxcan be defined as the extremes of the attainable rectangular area of each bending head1, Δθmaxcan be defined as equal to 2π and Δxa,maxcan be defined as the length of the tube2before executing the bending sequence. The weighting factors w1, w2, w4and w5can be scaled based on the time and/or energy necessary for executing a step of alignment, and be normalised so that w1+w2+w4+w5=1, in particular 1 denotes a unit cost for executing the step of alignment in terms of energy and/or time.

In further detail, the respective cost G is calculated as a function of the respective values Δx, Δθ, Δxa, and Δz.

With particular reference toFIG.7, number1″ denotes a third embodiment of a bending machine according to the present invention. The bending machine1″ is similar to the bending machine1′ and for this reason it is described below only limited to the differences with respect to the bending machine1′ itself, indicating parts that are equal or equivalent to parts already described with the same reference numbers.

In particular, the bending machine1″ differs from the bending machine1′ in that each bending head3comprises two bending groups4.

During each step of alignment the following movements are executed:i) a linear movement Δx of the tube2along the first axis A;ii) a rotation40of the tube2about the first axis A;iii) a rotation40of the bending head3about the second axis B; andv) a linear movement Δxaof the bending head3along the first axis A.

Then, during the execution of the step a) the calculating unit12determines the alignment cost E of each step of alignment as a function of the respective Δx, the respective Δθ, the respective Δxaand/or the respective42.

In greater detail, the calculating unit12determines the alignment cost E of each step of alignment according to the following formula:

The weighting factors w1, w2, w3and w4can be scaled based on the time and/or energy necessary for executing a step of alignment, and be normalised so that w1+w2+w3+w4=1, in particular 1 denotes a unit cost for executing the step of alignment in terms of energy and/or time.

In further detail, the respective cost G is calculated as a function of the respective values Δx, Δθ, ΔΩ and Δxa.

From an examination of the characteristics of the bending machines1,1′ and1″ and/or the method according to the present invention, the advantages it allows to be obtained are evident.

In particular, it is possible to determine a bending sequence to be used that avoids interfering with portions of the bending machines1,1′ and1″ at any time during the execution of the bending sequence, in a fast and reliable manner.

A further advantage is that the bending machines1,1′ and1″ can also be operated by less trained operators.

Another advantage can be seen in the possibility that an operator can choose a bending sequence to be used from a choice proposed by the calculating unit12. In this way, the operator can choose the bending sequence also in dependence on factors that are not strictly dependent on the bending machines1,1′ and1″.

Finally, it is clear that modifications and variations may be made to the bending machine1,1′ or1′ and the method of bending described and shown here which do not depart from the scope of protection defined by the claims.