Method for modeling the behavior of a ring rolling mill

Abstract

The invention relates to a method for modeling the behavior of a ring-rolling machine (1) intended to roll a cylindrical part on the basis of settings, the ring-rolling machine comprising at least one tapered roller (3) configured to move in translation in a first direction (Y) and a mandrel (2) configured to move in translation in a second direction (X), the settings comprising a setting of the speed of increase of the outer diameter of the cylindrical part as a function of the outer diameter of the cylindrical part and a setting of the height of the cylindrical part in the first direction as a function of the thickness of the cylindrical part in the second direction.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of modeling forging methods, in particular to the field of modeling circulaire rolling methods. BACKGROUND

[0002] Currently, modeling makes it possible to design new forging sequences or to optimize existing sequences, which is an important problem in industry. A forging sequence is a set of forming operations that makes it possible to produce a defect-free blank with a desired shape from a rod section using specific tools. A reliable and realistic model of all these operations, in particular of the behavior of the tools and of the rod section, makes it possible to reduce the design time of new forging sequences, since it also reduces the number of parts that must be manufactured to validate a new sequence.

[0003] Because the control principle of a press is simple, forging methods using hydraulic presses or more generally using vertical forging machines are easily modeled globally. In particular, there is only one translational movement of the press during forging. However, these forging methods are less suitable for manufacturing ring or tube sections without welding. In order to make it possible to use the material optimally, circulaire rolling methods are used to manufacture such parts.

[0004] In the case of circulaire rolling, it is complex to model the behavior of the tools because it is necessary to take into account, in a synchronized manner, the simultaneous translational and rotational movements of the different tools. Similarly, the movements of the different tools require a plurality of simultaneous variations of the parameters of the rod section that must be controlled. It should be noted that the principle of a circulaire rolling method is generally to reduce the cross section and the height of the rod section, thereby increasing the diameter of the rod section in a controlled manner.

[0005] In order to model this type of method, it is necessary to control the displacements of all the tools that make up the circulaire rolling machine. Generally, the tool commands are given as input by the operator to the control system of the rolls and depend on the part being laminated. When the operator wishes to laminate a new part, he must determine the input data in advance, which are not only the final dimensions of the part to be obtained, but also the associated variations of these dimensions.

[0006] The rolling method can be digitally modeled by finite element calculations without taking into account the adaptive operation of the tools of the rolling machine managed by the control system. In this case, it is generally necessary to machine at least one part to check the quality of the forging sequence and to collect the captured data, in particular the tool displacement data and the data on the forces exerted on the tools during the rolling of the part, to incorporate them into the modeling of the rolling method.

[0007] However, this approach has several limitations. First, it is time consuming and induces high costs to manufacture the parts to make the model. Second, each model made is only related to a specific shape of parts coming from a specific tool, so if the blank of the cylindrical billet to be manufactured is different, the behavior of the different tools cannot be predicted. Finally, this model transformation into data is complex since it requires rework on the captures.

[0008] There is a finite element calculation model which takes into account the adaptive operation of the tools of the rolling mill managed by the control system.

[0009] Currently, there are machine servo-assisted models which integrate computer codes such as Simufact. However, the models used do not take into account the mechanical aspects of the ring rolling mill 1. Thus, the accuracy of the model predictions is low and real parts need to be forged to validate the new forging sequence. Typically, existing models can underestimate the duration of the forging method by a factor of 10 for example. Existing models can also simulate radial and axial forces F 锥 . SUMMARY

[0010] The aim of the present invention is to remedy at least partially the aforementioned drawbacks, to propose a modeling method which takes into account the behavior of all the movable tools of the ring rolling mill and the interactions of all the movable tools, thus making it possible to determine the forging sequence reliably and quickly.

[0011] This object is achieved by the present invention by a method for modeling the behavior of a ring-rolling machine intended to roll a cylindrical part on the basis of set values, the ring-rolling machine comprising at least one conical roller configured to move in translation along a first direction and a mandrel configured to move in translation along a second direction, the set values comprising a set value of the speed of increase of the outer diameter of the cylindrical part as a function of the outer diameter of the cylindrical part and a set value of the height of the cylindrical part along the first direction as a function of the thickness of the cylindrical part along the second direction, the method comprising the following steps: E1 - obtaining a first set of parameters of the behavior of the ring-rolling machine by a control equation relating the translation speed of the mandrel along the second direction of translation to the speed of increase of the outer diameter and to the set values; E2 - carrying out a finite element calculation of the value of the force exerted on the conical roller on the basis of the first set of parameters; E3 - comparing the calculated value of the force exerted on the conical roller with at least one threshold force allowed by the ring-rolling machine, and if the value of the force exerted on the conical roller is greater than the allowed force threshold, obtaining a second set of parameters such that the speed of increase set value is not followed, correcting the second set of parameters to obtain a third set of parameters; if the calculated value of the force exerted on the conical roller is less than the allowed force threshold, correcting the first set of parameters by taking into account the stiffness of the mandrel to obtain a third set of parameters; the third set of parameters being the characteristic of the behavior of the ring-rolling machine for the given set values.

[0012] Other features, objects and advantages of the invention will become apparent from the following description, which is purely illustrative and non-limiting and must be read in conjunction with the attached drawings, in which:

[0013] - the first set of parameters obtained by the control equation comprises the speed of displacement of the conical roller and the translation speed of the mandrel

[0014] - the control equation is given as follows:

[0015]

[0016] where s is the position of the mandrel, is the translation speed of the mandrel, is the speed of increase of the outer diameter D of the part to be rolled;

[0017] - during the comparison step E3, the at least one allowed force threshold depends on the outer diameter of the cylindrical part;

[0018] - during the correction step, the deformation of the cage of the mandrel is taken into account so that the third set of parameters is obtained by a shift of at least one parameter of the behavior of the mandrel of the ring-rolling machine, the cage of the mandrel being modeled as a spring with a stiffness constant k. BRIEF DESCRIPTION OF DRAWINGS

[0019] Other features, objects, and advantages of the application will become apparent from the following description, which is purely illustrative and non-limiting, and must be read in conjunction with the accompanying drawings, in which:

[0020] Figure 1 A toroidal piece rolling mill enabling the rolling of cylindrical pieces is schematically shown.

[0021] Figure 2a and Figure 2b The steps of a method for modeling the behavior of a toroidal piece rolling mill according to the application are schematically shown.

[0022] Figure 3 A cylindrical piece that can be obtained by a toroidal piece rolling method is schematically shown.

[0023] Figure 4 An example of input set values of a toroidal piece rolling mill is shown.

[0024] Figure 5 A system for controlling the movement of a movable tool of a toroidal piece rolling mill is schematically shown. Figure 1

[0025] Figure 6 Different paliers defined by threshold force values allowed by the conical rollers of the rolling mill are shown.

[0026] Figure 7 is a graph showing the variation of the axial force at the conical rollers calculated by a model obtained by the method according to the application, calculated by a model of the prior art, and measured experimentally.

[0027] Figure 8 is a graph showing the variation of the radial force at the mandrel calculated by a model obtained by the method according to the application, calculated by a model of the prior art, and measured experimentally.

[0028] Figure 9 is a graph showing the variation of the outer diameter of the piece during rolling calculated by a model obtained by the method according to the application, calculated by a model of the prior art, and measured experimentally.

[0029] Figure 10 is a graph showing the variation of the speed of increase of the outer diameter of the piece during rolling calculated by a model obtained by the method according to the application, calculated by a method of the prior art, and measured experimentally.

[0030] ​Only the elements necessary for understanding the application are shown. For ease of reading of the drawings, similar elements are denoted with the same reference numerals on all the drawings. DETAILED DESCRIPTION

[0031] Figure 1 The system for manufacturing a cylindrical part, referred to as a ring 5, is schematically shown in the ring rolling method shown in Figure 2a and Figure 2b The ring rolling mill 1 comprises at least one conical roller 3 which translates along a first direction Y and which rotates along a second roller direction X'. In the exemplary embodiment shown, the ring rolling mill 1 comprises an upper conical roller 3 and a lower conical roller 3'.

[0032] The ring rolling mill comprises a driving cylinder 4 which rotates around an axis which is tangential to the first direction Y, substantially vertical. The rotation speed of the driving cylinder 4 is controlled by a control unit 10 schematically shown in Figure 5

[0033] The mill 1 comprises another cylindrical tool, referred to as a mandrel 2, which also rotates around an axis along the first direction Y. The mandrel 2 can translate along a second direction X which is substantially orthogonal to the first direction Y. The translation and rotation movements of the mandrel 2 are controlled by the control unit 10.

[0034] Figure 3 An example of a cylindrical ring 5 which can be obtained by rolling a bar-like section with the ring rolling mill 1 is shown. To form a ring 5 having a height a along the first direction Y and a thickness e and an outer diameter D along the second direction X, an operator can arrange the ring 5 under the at least one conical roller 3 and between the mandrel 2 and the driving cylinder 4.

[0035] The rotation movement of the conical roller 3 is performed simultaneously with the translation movement of the conical roller 3 so as to enable varying the height a of the ring 5. In a related manner, the rotation movement of the driving cylinder 4 and of the mandrel 2 is performed simultaneously with the translation movement of the mandrel 2 so as to enable varying the thickness e of the ring.

[0036] At the same time, the set of tool movements varies the outer diameter or external diameter D of the ring 5.

[0037] To obtain a ring 5 having desired dimensions, it is suggested to input to the control unit 10, also referred to as control system 10, of the ring rolling mill 1 input setting values. The input setting values comprise at least the desired dimensions of the cylindrical ring 5 to be rolled. Preferably, the input setting values also comprise a variation law of the dimensions of the ring 5.

[0038] ​In an exemplary embodiment, the set value comprises a speed of increase of the outer diameter of the cylindrical ring 5 as a function of the outer diameter D .

[0039] The set value can comprise a set value of the height a(e) of the cylindrical ring 5 along the first direction Y as a function of the thickness e of the ring 5 along the second direction X. An example of such an input set value is illustrated in Figure 4 .

[0040] Based on the set values input to the control unit 10, the control unit 10 can control the translational and rotational movements of the movable tools 2, 3, 4 of the rolling mill 1, as schematically illustrated in Figure 5 . Each forging sequence is associated with specific set values. In particular, once the desired outer diameter D 目标 , the ring rolling method is stopped.

[0041] The first step El of the method for modeling the behavior of the ring rolling mill 1 is to determine a control equation that enables to associate the input set values with at least one movement of the movable tools 2, 3 of the rolling mill 1. The control equation enables to obtain a first set of behavior characteristic parameters of the ring rolling mill 1.

[0042] Preferably, this is the problem of determining a control equation that enables to associate the input set values with all the movements of the movable tools 2, 3 of the rolling mill 1.

[0043] In an exemplary embodiment, this is the problem of associating the speed of increase of the outer diameter D of the ring 5 to be rolled with the speed of increase of the thickness e of the ring 5 to a specific forging sequence. The speed of increase of the thickness e is directly associated with the translational movement of the mandrel 2 along the second direction X, and thus with the translational speed of the mandrel .

[0044] Preferably, the relationship between the speed of increase of the outer diameter D and the speed of increase of the thickness e also depends on other parameters of the ring 5, i.e. the height a of the ring, the outer diameter D of the ring and the thickness e of the ring.

[0045] To determine the control equation that describes the different movements of the rolling mill 1, it is possible to study the principle of the servo-assisted circuit of the rolling mill 1, which enables to manage all the displacements of the movable tools 2, 3, 4 based on the set values input by the operator.

[0046] In the exemplary embodiment, the control equation has been determined to reproduce the behavior of a part of the rolling mill 1 and the main set values input by the operator into the control unit 10 of the rolling mill 1, the control equation being given as follows:

[0047]

[0048] where s is the position of the mandrel, the position of the mandrel being directly related to the thickness e of the ring, is the translation speed of the mandrel, the translation speed of the mandrel being directly related to the speed of increase of the thickness e of the ring , h is the position of the conical roller, and is the displacement speed of the conical roller.

[0049] This non-linear control equation makes it possible to obtain, from the input set values, a first translation speed of the mandrel with a theoretical thickness s as illustrated in Figure 4 .

[0050] It is also possible to associate the speed of increase of the outer diameter D of the ring 5 to be rolled with the speed of increase of the height a of the ring 5 along the first direction Y .

[0051] Preferably, the relationship between the speed of increase of the outer diameter D and the speed of increase of the position h also depends on other parameters of the ring 5, namely the height a of the ring, the outer diameter D of the ring and the thickness e of the ring.

[0052] The control equation for obtaining the first set of behavior characteristic parameters of the ring rolling mill 1 can be integrated into the finite element calculation code. In the exemplary embodiment, the control equation can be integrated into the Forge calculation code by the editor of the Transvalor calculation code.

[0053] The finite element calculation code makes it possible to model the rolling method and in particular to calculate the force F 锥 exerted by the conical roller 3 on the ring 5 during the rolling method as a function of the first set of parameters.

[0054] To improve the control model obtained previously, it is possible to take into account the mechanical characteristics of the ring rolling mill 1. In particular, it is possible to incorporate into the modeling a first mechanical model representing the limitation of the force on the conical roller 3 and a second mechanical model converting the elasticity of the mandrel 2.

[0055] It is also necessary to manage the interaction of the two mechanical models with the model of the servo-assisted loop of the ring-rolling machine. Finally, it is necessary to form assumptions consistent with the ring-rolling method to make the models interact with each other. This makes it possible to obtain a final control model representative of the actual situation.

[0056] Force limitation incorporated into the tapered roller 3

[0057] In order to avoid damaging the roller 1, the force F applied on the tapered roller 3 锥 must not exceed a threshold value F 阈 . In an example embodiment, the threshold value F 阈 depends on the outer diameter D of the ring 5 being rolled. For example, the threshold value F 阈 (D) can depend on the position along the second direction X of the point of the outer boundary of the ring 5 having a diameter D which is in contact with the surface of the tapered roller 3.

[0058] Figure 6 An example embodiment is shown in which four force threshold values F 阈 (D) = {N1, N2, N3, N4} are defined, defining four force limitation levels associated with three different threshold values of the outer diameter D. The force threshold values depend on the type of rolling machine 1. For example, it is possible to have N1 = 50 tons, N2 = 100 tons, N3 = 150 tons, N4 = 200 tons. D 最大 corresponds to the maximum outer diameter that can be rolled. D 最大 is preferably less than the axial dimension of the tapered roller 3 along the second direction X.

[0059] In order to manage the interaction of the first mechanical model with the model of the servo-assisted loop of the ring-rolling machine 1 having a control equation, two different cases can be defined.

[0060] Preferably, when the radial force F 锥 of the tapered roller 3 exceeds the threshold value F 阈 , the first mechanical model is involved.

[0061] This modeling method comprises a step E3 of comparing the calculated value of the force F 锥 applied on the tapered roller 3 with the threshold value F 阈 of the force allowed by the rolling machine 1.

[0062] If the value of the force F 锥 applied on the tapered roller is greater than the allowed threshold value F 阈 , a second set of parameters corresponding to a first set of correction parameters is obtained.

[0063] During the force limitation, the control equation, for example one of the previously presented control equations, is no longer applied. A constant force is applied by the conical roller 3 to the ring 5. The first set of parameters will therefore modify the displacement of the conical roller 3 to ensure the maximum force allowed. Since the force applied to the first mechanical model is reduced with respect to the theoretical force calculated by the finite element calculation code, this will result in a reduction of the increasing speed of the outer diameter D .

[0064] In the exemplary embodiment, the second set of parameters is calculated by the control equation only as a function of the input set value h(s) of the height of the ring 5 along the first direction Y as a function of the thickness s of the ring 5 along the second direction X, so that the increasing speed of the set value is not followed.

[0065] The model described makes it possible to take into account more reliably the behavior of the ring rolling machine 1 in the transition zone, in which the force F 锥 applied by the conical roller 3 of the model is too great to be allowed by the tool.

[0066] Figure 7 A comparison is shown between the axial force F 锥 calculated by the proposed modeling method, the axial force calculated by the model of the prior art which does not take this mechanical model into account, and the force measurements of the experiment. It can be observed that the proposed modeling method describes the axial force on the conical roller 3 more reliably.

[0067] During the rolling method, the calculated diameter D of the ring 5 will increase to a diameter value at which the force changes. If the calculated value of the force applied on the conical roller 3 is less than the new allowed force threshold, the set of parameters is calculated according to the control equation under normal operation.

[0068] During step E3 of the proposed modeling method, the first set of parameters or, where applicable, the second set of parameters are corrected to obtain a third set of corrected parameters, which makes it possible to translate the dynamics of all the movable tools of the ring rolling machine 1, in particular the mandrel 2. The third set of parameters is therefore the characteristic of the behavior of the ring rolling machine 1 for a given set value.

[0069] The stiffness of the mandrel 2 is taken into account

[0070] In order to improve the modeling method, the third set of parameters can be calculated to take into account the stiffness of the mandrel 2. The control equation determined during the first step E1 uses the theoretical position of the mandrel 2.

[0071] In the exemplary embodiment, the mandrel 2 can be housed in a cage which is elastically deformed during the rolling process, the consequence of which is to disturb the position of the mandrel 2. It has been empirically observed that the actual thickness e of the ring 5 is generally greater than the theoretical thickness e. It has been found that the control unit 10 of the ring rolling machine 1 does not take into account the deformation of the cage of the mandrel 2 being controlled during the rolling process.

[0072] The elastic deformation of the mandrel cage 2 can simply be modeled as the deformation of a spring attached between the mandrel 2 and the actuator 21, which enables the mandrel 2 to move in translation along the second direction X.

[0073] It can be considered that the cage of the mandrel 2 behaves as a spring with a stiffness k, which exerts a force on the ring 5 radially according to the position of the mandrel 2 along the axis in the second direction X. In this exemplary embodiment, the values of the third set of parameters are obtained by adding a positive or negative offset.

[0074] The offset to be applied as a correction can depend on the radial force calculated by the finite element calculation code.

[0075] In particular, in the example in which the set of parameters comprises the speed of increase of the thickness s of the ring 5 (the speed of increase of the thickness of the ring directly depending on the translational movement of the mandrel 2), it is meaningful to add this second mechanical model since the stiffness of the mandrel 2 is taken into account, which enables the theoretical stroke of the mandrel to be changed, the theoretical stroke of the mandrel being in particular affected by the virtual deformation of the cage.

[0076] Preferably, this second mechanical model can be integrated in the Forge calculation code by Transvalor.

[0077] Figure 8 A comparison is shown between the radial force calculated by the proposed modeling method, the radial force calculated by the model of the prior art which does not take into account this second mechanical model, and the force measurements of the experiment. It can be found that the proposed modeling method more reliably accounts for the radial force on the mandrel 2.

[0078] The described method for modeling the behavior of the ring rolling machine 1 thus makes it possible to obtain a complete model which provides the behavior of the ring rolling device.

[0079] In order to more fully illustrate the contribution of the developed model, it is possible to compare the results modeled using the servo-assisted model of the rolling machine of the prior art with the results modeled using the newly described model, which takes into account the two mechanical models representative of the mechanical characteristics of the mandrel 2 and of the tapered roller 3.

[0080] Figure 9 and Figure 10Comparison between the variations of the outer diameter D of the ring 5 calculated by the model of the prior art, calculated by the described model and obtained by experimental measurements and the speed of increase of the outer diameter of the ring 5 Comparison between the variations of the outer diameter D of the ring 5 calculated by the model of the prior art, calculated by the described model and obtained by experimental measurements and the speed of increase of the outer diameter of the ring 5

[0081] It can be seen that the described modeling method makes it possible to obtain a new model that more faithfully follows the real variations of the parameters. Thus, for the set values corresponding to a new forging sequence, it is possible to provide all the parameters that characterize the variations of the rolled part and the behavior of the rolling mill 1.

[0082] In particular, this makes it possible to optimize the rolling operation without the need to manufacture real parts. Thus, it is possible to reduce the design cost of the forging sequence.

[0083] Finally, thanks to the proposed modeling method, it is possible to provide the duration of the rolling method, which is considered unknown and depends on the part to be rolled. In particular, this makes it possible to know whether there is a risk of cold forging the part. This control method also makes it possible to limit the risk of producing a scrap part.

Claims

1. A method for modeling the behavior of a ring rolling mill (1) intended to roll a cylindrical part based on set values, the ring rolling mill comprising at least one tapered roller (3) configured to move in translation along a first direction (Y) and a mandrel (2) configured to move in translation along a second direction (X), the set values comprising a set value of the speed of increase of the outer diameter of the cylindrical part as a function of the outer diameter of the cylindrical part and a set value of the height of the cylindrical part along the first direction as a function of the thickness of the cylindrical part along the second direction, the method comprising the steps of: El - obtaining a first set of behavior characteristic parameters of the ring rolling mill (1) by a control equation relating the speed of translation of the mandrel (2) along the second direction of translation to the speed of increase of the outer diameter and the set values as functions; E2 - performing a finite element calculation of the value of the force exerted on the tapered roller (3) based on the first set of behavior characteristic parameters; E3 - comparing the calculated value of the force exerted on the tapered roller (3) with at least one threshold force allowed by the ring rolling mill (1), and if the value of the force exerted on the tapered roller is greater than the allowed threshold force, E4 - obtaining a second set of parameters such that the speed of increase set value is not followed, E5 - correcting the second set of parameters to obtain a third set of parameters; if the calculated value of the force exerted on the tapered roller is less than the allowed threshold force, E6 - correcting the first set of behavior characteristic parameters by taking into account the stiffness of the mandrel to obtain a third set of parameters; the third set of parameters being the behavior characteristic of the ring rolling mill for the given set values, wherein the second set of parameters is calculated by the control equation only as a function of the input set value of the height of the cylindrical part along the first direction as a function of the thickness of the cylindrical part along the second direction, such that the speed of increase set value is not followed, wherein during the correction step, the deformation of the cage of the mandrel is taken into account, such that the third set of parameters is obtained by a shift of at least one behavior characteristic parameter of the mandrel of the ring rolling mill, the cage of the mandrel being modeled as a spring with a stiffness constant k. the control equation being given as follows: wherein: - D is the outer diameter of the cylindrical part, - h is the height of the cylindrical part along the first direction, - H is the height of the mandrel along the first direction, - X is the translation speed of the mandrel along the second direction, - Y is the translation speed of the tapered roller along the first direction, - k is the stiffness constant of the cage of the mandrel, - D0 is the initial outer diameter of the cylindrical part, - h0 is the initial height of the cylindrical part along the first direction, - H0 is the initial height of the mandrel along the first direction, - D1 is the final outer diameter of the cylindrical part, - h1 is the final height of the cylindrical part along the first direction, - H1 is the final height of the mandrel along the first direction, - D2 is the outer diameter of the cylindrical part at the end of the calculation, - h2 is the height of the cylindrical part along the first direction at the end of the calculation, - H2 is the height of the mandrel along the first direction at the end of the calculation, - D3 is the outer diameter of the cylindrical part at the end of the calculation, - h3 is the height of the cylindrical part along the first direction at the end of the calculation, - H3 is the height of the mandrel along the first direction at the end of the calculation, - D4 is the outer diameter of the cylindrical part at the end of the calculation, - h4 is the height of the cylindrical part along the first direction at the end of the calculation, - H4 is the height of the mandrel along the first direction at the end of the calculation, - D5 is the outer diameter of the cylindrical part at the end of the calculation, - h5 is the height of the cylindrical part along the first direction at the end of the calculation, - H5 is the height of the mandrel along the first direction at the end of the calculation, - D6 is the outer diameter of the cylindrical part at the end of the calculation, - h6 is the height of the cylindrical part along the first direction at the end of the calculation, - H6 is the height of the mandrel along the first direction at the end of the calculation, - D7 is the outer diameter of the cylindrical part at the end of the calculation, - h7 is the height of the cylindrical part along the first direction at the end of the calculation, - H7 is the height of the mandrel along the first direction at the end of the calculation, - D8 is the outer diameter of the cylindrical part at the end of the calculation, - h8 is the height of the cylindrical part along the first direction at the end of the calculation, - H8 is the height of the mandrel along the first direction at the end of the calculation, - D9 is the outer diameter of the cylindrical part at the end of the calculation, - h9 is the height of the cylindrical part along the first direction at the end of the calculation, - H9 is the height of the mandrel along the first direction at the end of the calculation, - D10 is the outer diameter of the cylindrical part at the end of the calculation, - h10 is the height of the cylindrical part along the first direction at the end of the calculation, - H10 is the height of the mandrel along the first direction at the end of the calculation, - D11 is the outer diameter of the cylindrical part at the end of the calculation, - h11 is the height of the cylindrical part along the first direction at the end of the calculation, - H11 is the height of the mandrel along the first direction at the end of the calculation, - D12 is the outer diameter of the cylindrical part at the end of the calculation, - h12 is the height of the cylindrical part along the first direction at the end of the calculation, - H12 is the height of the mandrel along the first direction at the end of the calculation, - D13 is the outer diameter of the cylindrical part at the end of the calculation, - h13 is the height of the cylindrical part along the first direction at the end of the calculation, - H13 is the height of the mandrel along the first direction at the end of the calculation, - D14 is the outer diameter of the cylindrical part at the end of the calculation, - h14 is the height of the cylindrical part along the first direction at the end of the calculation, - H14 is the height of the mandrel along the first direction at the end of the calculation, - D15 is the outer diameter of the cylindrical part at the end of the calculation, - h15 is the height of the cylindrical part along the first direction at the end of the calculation, - H15 is the height of the mandrel along the first direction at the end of the calculation, - D16 is the outer diameter of the cylindrical part at the end of the calculation, - h16 is the height of the cylindrical part along the first direction at the end of the calculation, - H16 is the height of the mandrel along the first direction at the end of the calculation, - D17 is the outer diameter of the cylindrical part at the end of the calculation, - h17 is the height of the cylindrical part along the first direction at the end of the calculation, - H17 is the height of the mandrel along the first direction at the end of the calculation, - D18 is the outer diameter of the cylindrical part at the end of the calculation, - h18 is the height of the cylindrical part along the first direction at the end of the calculation, - H18 is the height of the mandrel along the first direction at the end of the calculation, - D19 is the outer diameter of the cylindrical part at the end of the calculation, - h19 is the height of the cylindrical part along the first direction at the end of the calculation, - H19 is the height of the mandrel along the first direction at the end of the calculation, - D20 is the outer diameter of the cylindrical part at the end of the calculation, - h20 is the height of the cylindrical part along the first direction at the end of the calculation, - H20 is the height of the mandrel along the first direction at the end of the calculation, - D21 is the outer diameter of the cylindrical part at the end of the calculation, - h21 is the height of the cylindrical part along the first direction at the end of the calculation, - H21 is the height of the mandrel along the first direction at the end of the calculation, - D22 is the outer diameter of the cylindrical part at the end of the calculation, - h22 is the height of the cylindrical part along the first direction at the end of the calculation, - H22 is the height of the mandrel along the first direction at the end of the calculation, - D23 is the outer diameter of the cylindrical part at the end of the calculation, - h23 is the height of the cylindrical part along the first direction at the end of the calculation, - H23 is the height of the mandrel along the first direction at the end of the calculation, - D24 is the outer diameter of the cylindrical part at the end of the calculation, - h24 is the height of the cylindrical part along ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ wherein said first set of behavior characteristic parameters, obtained by said control equation, comprises a displacement speed of said conical roller and a translation speed of said mandrel , ​ ​ 2. The method of claim 1, wherein, ​ where s is the position of the mandrel, is the translation speed of the mandrel, is the increasing speed of the outer diameter D of the cylindrical part (5) to be rolled, h is the position of the conical roller, and is the displacement speed of the conical roller.

3. The method of claim 1 or 2, wherein, ​

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