EP4163031A1

EP4163031A1 - Method for controlling an axial radial rolling mill for rings with variable coefficient controllers and axial radial rolling mill for rings

Info

Publication number: EP4163031A1
Application number: EP22195674.1A
Authority: EP
Inventors: Mirco CASINI
Original assignee: Project Group Srl
Current assignee: Project Group Srl
Priority date: 2021-10-11
Filing date: 2022-09-14
Publication date: 2023-04-12
Also published as: IT202100025973A1

Abstract

A method for controlling an axial radial rolling mill (100) for rings (200), wherein the axial radial rolling mill (100) comprises: a main roller (105), a contrast roller (110), a pair of guide rollers (115), and a pair of tapered rollers (130, 135); wherein the control method provides for adjusting the rotational speed of each tapered roller (130, 135) by means of the steps of: establishing a reference value (v) of the rotational speed of the tapered roller (130, 135), applying a correction (d1, d2) to said reference value (v) to obtain a corrected value (v*, v**) of the rotational speed of the tapered roller (130, 135), actuating the tapered roller (130, 135) at a rotational speed having the corrected value (v*, v**); the correction (d1, d2) comprising at least one feedback contribution (r1, r2) provided by a controller (S120, S150) of the proportional-integrative or proportional-integrative-derivative type; the control method providing for varying at least the coefficients of the proportional part and of the integrative part of the controller (S120, S150) on the basis of the value of at least one physical parameter of the ring (200) being processed.The invention also relates to an axial radial rolling mill for rings.

Description

Technical Field

The present invention relates to a method of controlling an axial radial rolling mill of the type used for hot rolling metal rings, e.g. of steel or other particular metals, including copper, aluminium, titanium or superalloys.

State of the art

Hot rolling of metal rings is a versatile metalworking process that allows the production of rings with precise dimensions and an accurate degree of roundness.
The hot rolling process starts with a semi-finished metal piece (or blank) with a "doughnut" shape at high temperature, e.g. comprised between 900°C and 1000°C in the case of steels or even much lower, e.g. comprised between 250°C and 300°C in the case of copper or aluminium.
This semi-finished piece is then rolled radially and axially until a ring of the desired dimensions is obtained.
The rolling process is performed by a machine called an axial radial rolling mill, which essentially consists of a plurality of rollers that support and shape the ring being processed.
Specifically, the axial radial rolling mill generally comprises a main roller, which is adapted to stay in contact with an outer perimeter surface of the ring being processed, and a contrast roller, commonly known as a mandrel, adapted to stay in contact with an inner perimeter surface and to compress the ring in the radial direction against the main roller.
The axial radial rolling mill may also comprise a pair of guide or centring rollers, which are designed to stay in contact with the outer perimeter surface of the ring being processed at points that are mutually symmetrical with respect to the plane of symmetry containing the axes of rotation of the main roller and the mandrel.
These guide rollers are carried by respective support arms, commonly referred to as centring arms, each of which is adapted to oscillate about an axis of oscillation parallel to the axis of rotation of the main roller and is arranged symmetrically to the axis of oscillation of the other support arm with respect to the aforementioned plane of symmetry. In this way, the guide rollers can move according to the variation in diameter of the ring being processed, while ensuring that said ring maintains its roundness and remains in a suitable position on the rolling mill.
The axial radial rolling mill also comprises a pair of tapered rollers adapted to stay in contact, respectively, with the opposite axial ends of the ring being processed, so as to compress it axially.
These tapered rollers are both motorised and are generally driven at a reference rotational speed such that their peripheral speed is equal to the peripheral speed of the ring being processed at all points of mutual contact.
This condition can be effectively achieved and maintained as long as the vertices (at least the ideal ones) of the tapered rollers are perfectly aligned with the centre of the ring being processed.
However, as the diameter of the ring being processed increases, the tapered rollers must be gradually moved radially away from the main roller, so that, beyond certain limits, it is not possible to keep the vertices of the tapered roller in the centre of the ring being processed.
Under these conditions, it is possible to determine a reference rotational speed for which the peripheral speed of the tapered rollers is equal to that of the ring being processed at only one point of mutual contact, while at all other points a difference between the peripheral speeds will occur.
This difference in peripheral speed causes "material creep" which tends to move the ring being processed to one side or the other, causing it to lose its correct centring.
To overcome this drawback, it is known to adjust the rotational speed of tapered rollers by adding a suitable correction to the reference rotational speed, which is generally obtained from the sum of one or more corrective contributions.
Some of these corrective contributions are automatically established by the rolling mill's electronic system through feedback controllers, which are designed to equalise the thrust force exerted by the ring being processed on the guide rollers in order to keep the ring centred on the rolling mill, as well as to equalise the torque applied to the tapered rollers.
These feedback controllers are commonly proportional-integrative (PI) controllers or proportional-integrative-derivative (PID) controllers, whose dynamic response to possible system imbalances depends on a series of numerical coefficients that are assigned to the proportional, integrative and possibly the derivative part of the controller, including for example the proportional gain and integration time.
Currently, these coefficients are established during the commissioning of the axial radial rolling mill, calibrating them in order to optimise the operation of the machine under predefined "nominal" conditions.
However, the "nominal" conditions used in the calibration step cannot necessarily represent all the conditions in which the rolling mill operates as the rings being processed vary and/or as the characteristics of each ring vary during the various rolling steps.
It may therefore be the case that, for certain types of rings and/or during certain rolling phases, the dynamic response of the speed controllers of the tapered rollers is inadequate, e.g. resulting in excessively large speed fluctuations and/or excessively long damping times for these fluctuations.
The resulting effect may be that of a not entirely uniform "growth" of the ring being processed (where growth means an increase in diameter with a consequent reduction in height and/or thickness), which may then undergo fluctuations and/or undulations which, in turn, may generate shape defects, e.g. in terms of circularity, flatness and/or cylindricity.

Disclosure of the invention

In the light of the foregoing, an object of the present invention is to solve or at least to mitigate the aforementioned drawbacks of the prior art, in the context of a simple, rational and relatively low cost solution.
These and other objects are achieved thanks to the features of the invention as set forth in the independent claims. The dependent claims outline preferred and/or particularly advantageous aspects of the invention but not strictly necessary for implementing it.
In particular, one embodiment of the invention makes available a method of controlling an axial radial rolling mill for rings,

wherein the axial radial rolling mill comprises:
- a main roller adapted to stay in contact with an outer perimeter surface of the ring being processed,
- a contrast roller having an axis of rotation coplanar to the axis of rotation of the main roller and adapted to stay in contact with an inner perimeter surface of the ring being processed,
- a pair of guide rollers having axes of rotation parallel to the axis of rotation of the main roller and adapted to stay in contact with the outer perimeter surface of the ring being processed, and
- a pair of tapered rollers having coplanar axes of rotation on said plane of symmetry, which are respectively designed to stay in contact with the opposite axial ends of the ring being processed,
wherein the control method provides for adjusting the rotational speed of each tapered roller by means of the steps of:
- establishing a reference value of the rotational speed of the tapered roller,
- applying (e.g. adding) a correction to said reference value in order to obtain a corrected value of the rotational speed of the tapered roller,
- actuating the tapered roller at a rotational speed having the corrected value, and
wherein the correction comprises - or is obtained as a function of (e.g. from the sum of)
- a feedback contribution provided by a proportional-integrative (PI) or proportional-integrative-derivative (PID) controller.

According to the invention, the control method provides for varying (i.e. adjusting) at least the coefficients of the proportional part and of the integrative part of said controller on the basis of at least one physical parameter of the ring being processed.
For example, the control method may provide for acquiring (e.g. measuring, calculating or receiving as input in any other way) the value of said at least one physical parameter and, subsequently, using said value to determine (e.g. calculate, establish or derive in any other way) the values of the coefficients supplied to the controller.
Thanks to this solution, it is advantageously possible to configure, for each ring being processed, rotational speed controllers for the tapered rollers with the most appropriate dynamic response to obtain a substantially uniform "growth" of the ring, thus reducing the occurrence of shape defects and obtaining, for example, better circularity, flatness and/or cylindricity of the finished ring.
According to an aspect of the invention, the coefficients of the proportional part and the integrative part that are varied (or adjusted) may be the proportional gain and the integration time.
These are in fact the coefficients of the proportional and integrative parts that are most commonly used in PI or PID type controllers.
However, it is not excluded that, in other embodiments, each of these coefficients may be replaced by an equivalent coefficient, i.e. obtained as a function of the first two.
For example, in some PI or PID-type controllers, the integration time could be replaced by the integrative gain, which is equal to the ratio of the proportional gain and the integration time.
According to another aspect of the invention, said at least one physical parameter of the ring being processed (based on which the controller coefficients are varied) may be chosen from the group consisting of weight of the ring being processed, volume of the ring being processed, thickness of the ring being processed (also called "section" or "wall"), height of the ring being processed, diameter of the ring being processed.
It should be noted here that "thickness" means the radial dimension of the ring wall, i.e. the dimension measured along a direction orthogonal to the ring axis, while "height" means the axial dimension of said wall, i.e. the dimension measured along a direction parallel to the ring axis.
The parameters mentioned above have the greatest impact on the rolling process, so variations in these parameters generally require a different dynamic response from the speed controllers of the tapered rollers of the rolling mill.
In particular, the parameter normally having the greatest impact is the weight of the ring being processed (or equivalently its volume), which, in the context of the present invention, represents the preferred parameter on the basis of which the control method will be able to vary the coefficients of the proportional and integrative part of the controller.
It is however possible, and sometimes preferable, for the control method to vary the coefficients of the proportional and integrative part of the controller on the basis of two or more of the parameters listed above, e.g. on the basis of weight (or volume) and thickness and/or one or more of the remaining parameters.
Another aspect of the invention provides that each of the variable coefficients of the controller (i.e. at least those of the proportional and integrative parts) is provided by a correlation matrix (or table) in which a plurality of values of the variable coefficient are stored and individually correlated to a corresponding value of said at least one physical parameter of the ring being processed.
With this solution, the computational load required to implement the control method can be advantageously reduced.
In this context, the correlation matrix can be determined empirically.
For example, the correlation matrix can be determined (or constructed) by carrying out a multiplicity of empirical tests, each time using rings with different characteristics and, during each test, empirically establishing which coefficients of the proportional and integrative part of each controller allow a stable setting of the correction to be applied to the rotational speed of the tapered rollers (e.g. that it does not oscillate or that it has oscillations that tend to dampen rapidly) reducing error as much as possible.
In particular, empirical tests can be carried out with rings of different weights (i.e. volume) and repeated, for each ring, at different stages of its "growth" in the rolling process (generally corresponding to different cross-sections, diameters and heights).
Using the coefficients thus determined, it is then possible to populate matrices (or tables) which, for each value of the ring's physical parameters (e.g. weight, volume, cross-section, etc.), associate a corresponding value of the coefficients of each controller.
Alternatively, each of the variable coefficients of the controller may be calculated by means of a mathematical function relating one or more of the above physical parameters of the ring being processed to the variable coefficient of the controller.
In this way, it is generally possible to obtain controller coefficients that are more accurate and precisely matched to the characteristics of the ring being processed.
The mathematical function can also be obtained empirically, e.g. by interpolating the values of the coefficients obtained from the empirical tests outlined above.
However, it is not excluded that, in other embodiments, the mathematical function can be obtained on a theoretical basis.
According to a preferred aspect of the invention, the variation of the coefficients of the proportional part and the integrative part of the controller is performed repeatedly during the rolling of the ring being processed.
In other words, it is preferable that, during the rolling process of a ring, the coefficients of each controller vary continuously as the physical parameters of said ring (e.g. cross-section, diameter and height) change.
This ensures that the dynamic response of the controllers is always the most appropriate at any time during the rolling of the ring being processed.
However, it is not excluded that, in other embodiments, the variable coefficients of each controller can be varied (adjusted) as part of a preliminary setting step that is carried out before ring rolling begins and then kept constant.
This solution could be implemented, for example, if the variable coefficients of the controller are only varied on the basis of the weight (or volume) of the ring being processed, as these parameters remain essentially constant throughout the entire rolling process. According to a different aspect of the invention, the feedback contribution of at least one of the tapered rollers (e.g. of a first of said tapered rollers) may be obtained by the steps of:

measuring the force applied by the ring being processed on each guide roller,
calculating a difference between the measured forces,
using said difference as an input of the controller which outputs said feedback contribution.

Thanks to this solution, the control method automatically tends to adjust the rotational speed of the tapered rollers so as to equalise the forces applied by the ring being processed on the guide rollers and thus keep it centred on the rolling mill.
According to another aspect of the invention, the feedback contribution of at least one of the tapered rollers (e.g. of a second of said tapered rollers) may be obtained by the steps of:

measuring the torque applied to each tapered roller,
calculating a difference between the measured torques,
using said difference as an input of the controller which outputs said feedback contribution.

Thanks to this solution, the control method automatically tends to adjust the rotational speed of the tapered rollers so as to equalise the torque applied thereto, thus preventing the ring being processed from warping or tilting.
Another embodiment of the invention makes available an axial radial rolling mill for rings, comprising:

a main roller adapted to stay in contact with an outer perimeter surface of a ring being processed,
a contrast roller having an axis of rotation coplanar to the axis of rotation of the main roller and adapted to stay in contact with an inner perimeter surface of the ring being processed,
a pair of guide rollers having axes of rotation parallel to the axis of rotation of the main roller and adapted to stay in contact with the outer perimeter surface of the ring being processed,
a pair of tapered rollers having coplanar axes of rotation on said plane of symmetry, which are respectively adapted to stay in contact with the opposite axial ends of the ring being processed, and
an electronic processing unit configured to perform the control method outlined above.

Finally, the invention also makes available software comprising a computer code which, when executed by a computer, enables the computer to execute the control method described above.
These embodiments of the invention achieve essentially the same advantages as mentioned above, in particular that of making the speed regulation of tapered rollers faster and more effective, reducing the occurrence of defects in the ring being processed.

Brief description of the drawings

Further features and advantages of the invention will be more apparent after reading the following description provided by way of non-limiting example, with the aid of the figures illustrated in the accompanying drawings.

Figure 1 is a perspective view of the essential mechanical components of an axial radial rolling mill.
Figure 2 is a plan view of the axial radial rolling mill of figure 1, with the addition of the support arms for the guide rollers and their actuators.
Figure 3 is a block diagram of a control method of the axial radial rolling mill of figures 1 and 2.

Detailed description

Figures 1 and 2 schematically illustrate an axial radial rolling mill 100 for hot-rolling metal rings, e.g. of steel or other special metals, including copper, aluminium, titanium or super alloys.
The rolling mill 100 first comprises a main roller 105, preferably cylindrical in shape, which is adapted to rotate on itself about its central axis A.
The main roller 105 may have a cylindrical shape or possibly a shaped profile to allow the production of rings with circular, flanged, spherical or variously shaped profiles.
Preferably, the axis of rotation A of the main roller 105 is oriented vertically, but it is not excluded that, in other embodiments, it may be oriented horizontally.
The main roller 105 is preferably motorised, i.e. it is connected to at least one motor adapted to place it in rotation.
The rolling mill 100 also includes a contrast roller 110, usually called a mandrel or pin, which is adapted to rotate about its central axis B.
Similarly to the main roller 105, the contrast roller can also be cylindrical in shape (e.g. smaller in diameter than the main roller 105) or have a shaped profile to allow the production of rings with circular, flanged, spherical or variously shaped profiles.
The axis of rotation B of the contrast roller 110 is coplanar and substantially parallel to the axis of rotation A of the main roller 105, so that the two rollers are mutually flanked.
The term "substantially" means that the axis of rotation B of the contrast roller 110 may not only be perfectly parallel to the axis of rotation A of the main roller 105, but may also be inclined by a few degrees with respect to the latter (e.g. between 0° and 5° in either direction).
Often, this inclination is adjustable and settable by means of appropriate actuators, e.g. electric or hydraulic, which are managed by the control system of the rolling mill 100. The contrast roller 110 is preferably an idler roller, i.e. it is free to rotate about its own axis of rotation B without being associated with any drive motor.
The contrast roller 110 can be combined with actuator members (not shown) to make it translate in a direction orthogonal and coplanar to both axes of rotation A and B, so that the mutual distance between the contrast roller 110 and the main roller 105 can be varied.
The roller 100 also comprises a pair of guide rollers 115, preferably cylindrical in shape, each of which is adapted to rotate on itself about its central axis C which is parallel to the axis of rotation A of the main roller 105.
However, it is not ruled out that, in certain special cases, the guide rollers 115 can also be shaped.
The guide rollers 115 preferably have the same diameter and are arranged on opposite sides with respect to an (ideal/imaginary) plane of symmetry S in which the axes of rotation A and B of the main roller 105 and the contrast roller 110 lie (see fig.2).
Preferably, the guide rollers 115 are idler rollers, i.e. they are able to rotate freely about their own axis of rotation C without being connected to any drive motor.
Each guide roller 115 is carried by (and pivotally mounted on) a respective swinging support arm 120, which is designed to oscillate by rotating about an axis of oscillation D that is parallel to and spaced from the axis of rotation C of the respective guide roller 115.
The axes of oscillation D of the two oscillating support arms 120 are preferably arranged symmetrically with respect to the aforementioned plane of symmetry S, and the distance separating the axis of oscillation D from the axis of rotation C of the respective guide roller 115 is preferably the same for both oscillating support arms 120.
Each oscillating support arm 120 can be driven to oscillate about its own axis of oscillation D by a respective actuator member 125, e.g. by a hydraulic piston cylinder assembly via a suitable linkage.
One function of these actuator members 125 is to hold the axes of rotation C of the guide rollers 115 in a desired/programmed position.
In some cases, this position may be the one (illustrated in the figures) in which the axes of rotation C of the guide rollers 115 are mutually symmetrical with respect to the plane of symmetry S.
In other cases, however, the oscillating support arms 120 can be controlled so that the position of the axes of rotation C of the guide rollers 115 is deliberately asymmetrical. The rolling mill 100 also includes a pair of tapered rollers, designated 130 and 135 respectively, each with a respective central axis of symmetry E.
A tapered roller is of course also understood to be a truncated cone roller, i.e. any roller with an axisymmetric side surface whose generatrices all converge at a point (vertex) on the central axis of symmetry E.
Preferably, the central axes of symmetry E of the two tapered rollers 130 and 135 lie coplanar in the plane of symmetry S.
Furthermore, the vertices V of the two tapered rollers 130 and 135, i.e. the (also ideal) vertices of the respective tapered side surfaces, are preferably aligned with each other along an (ideal/imaginary) axis Q that is parallel to the axis of rotation A of the main roller 105.
This axis Q is preferably interposed between the tapered rollers 130 and 135 and the main roller 105.
The two tapered rollers 130 and 135 (i.e. the respective tapered surfaces) are finally faced and oriented in such a way that the mutually closest generatrices of one and the other tapered roller 130 and 135 are parallel to each other and perpendicular to the axis of rotation A of the main roller.
For example, the tapered rollers 130 and 135 (i.e. their tapered side surfaces) can have the same angle at the vertex and their central axes of symmetry E can be mutually inclined by an angle equal to the angle at the vertex of each.
The angle at the vertex is generally understood to be the angle formed at the vertex by any pair of generatrices of the tapered surface lying coplanar to each other in a plane that also contains the central axis of symmetry E.
In the example illustrated, in which the axis of rotation A of main roller 105 is oriented vertically, the tapered rollers 130 and 135 are essentially superimposed, with the tapered roller 130 being arranged below the tapered roller 135.
In embodiments where the axis of rotation A of the main roller 105 is horizontal, the tapered rollers 130 and 135 would be oriented vertically and mutually flanked.
In each case, each of the tapered rollers 130 and 135 is adapted to rotate on itself about its central axis E.
In particular, each tapered roller 130 and 135 is preferably motorised, i.e. connected to at least one motor to place it in rotation.
The motors driving the two tapered rollers 130 and 135 are preferably independent of each other, so that the rotational speed of these rollers can be adjusted equally independently.
The tapered rollers 130 and 135 can also be associated with first movement members (not shown) adapted to move them relative to each other in a direction parallel to the axis of rotation A of the main roller 105.
For example, the first movement members can move the tapered (upper) roller 135 towards/ away from the tapered (lower) roller 130, which remains stationary, or vice versa, or move both.
Finally, the tapered rollers 130 and 135 can be combined with second movement members (not illustrated) to move them both (and simultaneously) towards and away from the main roller 105, along a direction perpendicular to the axis of rotation A and lying in the plane of symmetry S.
The operation of the rolling mill 100 described above starts with a semi-finished metal piece 200 (or blank) with a "doughnut" shape at high temperature, e.g. comprised between 900°C and 1000°C in the case of steels or even much lower, e.g. comprised between 250°C and 300°C in the case of copper or aluminium.
In particular, this semi-finished piece 200 may comprise an annular wall, e.g. cylindrical in shape, which extends around a central axis and has an outer perimeter surface 205, an inner perimeter surface 210 and two opposing axial ends 215 and 220.
The semi-finished piece 200 is placed in the rolling mill 100 so that its axis is parallel to the axis A of the main roller 105 and its annular wall is interposed between the latter and the contrast roller 110.
In particular, the semi-finished piece 200 can be arranged so that the main roller 105 is positioned on the outside and the contrast roller 110 is positioned on the inside of the annular wall.
At this point, by bringing the contrast roller 110 closer to the main roller 105, the annular wall of the semi-finished piece 200 is gripped between these two rollers, with the main roller 105 remaining in contact with the outer perimeter surface 205 and the contrast roller 110 remaining in contact with the inner perimeter surface 210.
Thus, by placing the main roller 105 in rotation about the axis of rotation A, the semi-finished piece 200 is also rotated about its own axis.
To stabilise this rotation, the guide rollers 115 are also brought into contact with the outer perimeter surface 205 and, by the oscillation of the respective support arms 120, they are placed in a desired/prefixed position.
As mentioned above, this position can be chosen so that the axis of the semi-finished piece 200 is coplanar with the axes of rotation A and B of the main roller 105 and the contrast roller 110, i.e. lying on the plane of symmetry S.
In other words, the position assumed by the guide rollers 115 can be such that their points of contact with the outer perimeter surface 205 of the semi-finished piece 200 are mutually symmetrical with respect to the plane of symmetry S.
However, some rolling techniques may provide that, during certain rolling steps, the position of the guide rollers 115 is actively altered in order to "move" the ring 200 being processed with respect to the centreline of the rolling mill 100 (off-centre rolling), normally by a few degrees, and then "return it to the centre" at the end of rolling.
At the same time, the tapered rollers 130 and 135 are arranged on axially opposite sides of the semi-finished piece 200, preferably so that the axis Q, along which the vertices V of the respective tapered surfaces are aligned, coincides with the axis of the semi-finished piece 200 itself.
The tapered rollers 130 and 135 are then brought closer together in the axial direction, so that the tapered roller 130 is in contact with the axial end 215 of the semi-finished piece 200 while the tapered roller 135 is in contact with the opposite axial end 220.
As the semi-finished piece 200 continues to rotate about its own axis, the contrast roller 110 is progressively brought closer to the main roller 105 (in a direction perpendicular to the axis of rotation A), while the tapered rollers 130 and 135 are gradually brought closer together (in a direction parallel to the axis of rotation A).
In this way, the wall of the semi-finished piece 200 undergoes axial crushing and radial crushing, which simultaneously also causes an increase in diameter, until it reaches a ring of the desired height, thickness and diameter.
As the diameter of the semi-finished piece 200 increases, the guide rollers 115 gradually spread apart, while continuing (due to appropriate control of the actuator members 125) to perform their positioning function; for example, to maintain the axis of the semi-finished piece 200 in the plane of symmetry S of the rolling mill 100, or to maintain the axis of the semi-finished piece 200 in a desired/programmed "off-centre" position.
For this purpose, the support arms 120 carrying the guide rollers 115 can be controlled in pure position, force-limited position or more rarely in pure force.
At the same time, since the increase in diameter also entails a shift in the axis of the semi-finished piece 200 away from the main roller 105, the tapered rollers 130 and 135 are progressively shifted in the same direction, so that the vertices V of their tapered surfaces remain aligned along the axis of the semi-finished piece 200.
As long as the latter condition can be maintained, it is possible to rotate each tapered roller 130 and 135 about its respective axis of rotation E at a reference speed such that the tangential speed of said tapered roller 130 or 135 is equal to the tangential speed of the semi-finished piece 200 at all points of mutual contact.
In particular, this reference speed, which essentially depends on the geometry and rotational speed of the semi-finished piece 200, can be calculated and imposed on the tapered roller 130 via an appropriate command supplied to the respective motor.
In this way, there is no material creep in the semi-finished piece 200.
However, when the diameter of the semi-finished piece 200 increases beyond a certain value, it is no longer possible to keep the vertexes V of the tapered rollers 130 and 135 perfectly aligned with the axis of the semi-finished piece 200.
In this condition, it is possible to rotate each tapered roller 130 and 135 about its respective axis of rotation E at a reference speed such that the tangential speed of this tapered roller 130 or 135 is equal to the tangential speed of the semi-finished piece 200 at a single point of mutual contact, e.g. at a midpoint between the inner perimeter surface 210 and the outer perimeter surface 205.
At all other points of mutual contact, however, there will be a tangential speed difference between each tapered roller 130 and 135 and the semi-finished piece 200, such that material creep may occur.
This material creep tends to move the semi-finished piece 200 to one side or the other, causing it to lose its correct position or leading to defects.
To overcome this drawback, the rotational speed of each tapered roller 130 and 135 is then adjusted to try to equalise the thrust force exerted by the semi-finished piece 200 on the two guide rollers 115 and to equalise the torque applied to the tapered rollers 130 and 135.
For this purpose, the rotational speed of the tapered rollers 130 and 135 can be adjusted using the control method shown in figure 3.
This control method first involves establishing (block S100) the aforementioned reference value v of the rotational speed of each tapered roller 130 and 135.
This value v can, for example, be calculated as a function of one or more parameters chosen from the group consisting of: rotational speed of the main roller 105, diameter of the main roller 105, geometry of the tapered rollers 130 and 135, rotational speed of the semi-finished piece 200, position of the semi-finished piece 200 between the tapered rollers 130 and 135.
Alternatively, the reference value v can be retrieved from a correlation matrix that receives as input one or more of the above parameters and outputs the corresponding reference value v of the rotational speed of the tapered rollers 130 and 135.
A correction d1 is then applied to this reference value v in order to obtain a first corrected value v*.
The correction d1 is a numerical value (of positive or negative sign as the case may be) which is preferably added to the reference value v of the rotational speed.
However, it is not excluded that, in other embodiments, the correction d1 may be a multiplicative or other factor.
In any case, the correction d1 depends in turn on at least a first feedback contribution r1 and possibly also on at least a first manual contribution m1.
These contributions r1 and m1 are also numerical values (of positive or negative sign as the case may be) which are preferably added together to obtain the correction d1. However, it is not excluded that, in other embodiments, the correction d1 can be calculated, again as a function of the contributions r1 and m1, but using a different mathematical relationship.
Regardless of these considerations, the feedback contribution r1 may be the one that performs the function of equalising the thrust force exerted by the semi-finished piece 200 on the two guide rollers 115.
For this purpose, the feedback contribution r1 can be obtained by first measuring the thrust force f1 that is exerted by the semi-finished piece 200 on a guide roller 115 (block S105) and the thrust force f2 that is exerted by the same semi-finished piece 200 on the other guide roller 115 (block S110).
These two thrust forces f1 and f2 can be measured by means of suitable force (or torque) sensors installed e.g. on the oscillating support arms 120 and/or in the respective actuator members 125.
The thrust forces f1 and f2 can then be subtracted from each other (block S115) to calculate a difference e1 (or error).
This difference e1 can then be provided as input to a controller S120, specifically a proportional-integrative (PI) or proportional-integrative-derivative (PID) controller, which returns the value of the feedback contribution r1 as output.
For example, in the case of a PID, the value of the feedback contribution r1 can be expressed by the following relationship in the time domain t: $r 1 (t) = K_{p} e 1 (t) + K_{i} \int_{t_{0}}^{t} e 1 (τ) dτ + K_{d} \frac{de 1 (t)}{dt}$
where e1 is the calculated difference between the thrust forces f1 and f2, K_p is a coefficient named proportional gain, K_i is a coefficient named integrative gain, and K_d is a coefficient named derivative gain.
The term $K_{p} e 1 (t)$
represents the proportional part of the controller S120; while the term $K_{i} \int_{t_{0}}^{t} e 1 (τ) dτ$
represents the integrative part; and the term $K_{d} \frac{de 1 (t)}{dt}$
represents the derivative part.
Equivalently, the value of the feedback contribution r1 provided at the output from the controller S120 can be expressed by the following relationship in the time domain t: $r 1 (t) = K_{p} (e 1 (t) + \frac{1}{T_{i}} \int_{t_{0}}^{t} e 1 (τ) dτ + T_{d} \frac{de 1 (t)}{dt})$
where T_i (=K_p/K_i) is a coefficient named integration time and T_d (=K_d/K_p) is a coefficient named derivation time.
In this case, the proportional part of the controller is represented by the term $K_{p} e 1 (t)$
while the integrative part is represented by the term $K_{p} \frac{1}{T_{i}} \int_{t_{0}}^{t} e 1 (τ) dτ$
and the derivative part is represented by the term $K_{p} T_{d} \frac{de 1 (t)}{dt}$
Should the controller S120 be a PI controller, the value of the feedback contribution r1 will be expressed by the same relations as above with the exclusion of the derivative part, i.e. considering a derivative gain K_d (or a derivation time T_d) equal to zero.
On the other hand, the manual contribution m1 is selected and adjusted as desired by an operator supervising the operation of the rolling mill 100 (block S125), e.g. through the manual operation of a handwheel or any other control or interface with the machine. The first corrected value v* obtained in this way is used to control the rotational speed of tapered rollers 135 and 130.
In particular, the first corrected value v* can be directly transmitted to a driver S130 that drives the motor of the tapered roller 135, so that the latter is driven to rotate at a speed exactly corresponding to the first corrected value v*.
At the same time, the first corrected value v* can also be used to drive the tapered roller 130, preferably after being further corrected by a second correction d2.
In this context, the first corrected value v* can be considered as a new reference value for controlling the rotational speed of the tapered roller 130.
Again, the correction d2 is a numerical value (of positive or negative sign as the case may be) which is added to the first corrected value v* of the rotational speed.
However, it is not excluded that, in other embodiments, the correction d2 may be a multiplicative or other factor.
The correction d2 may also depend in turn on at least a second feedback contribution r2 and at least a second manual contribution m2.
These contributions r2 and m2 are numerical values (of positive or negative sign as the case may be) which are preferably added together to obtain the correction d2. However, it is not excluded that, in other embodiments, the correction d2 can be calculated, again as a function of the contributions r2 and m2, but using a different mathematical relationship.
The feedback contribution r2 can be the one that performs the function of equalising the torque applied to the tapered rollers 130 and 135.
For this purpose, the feedback contribution r2 can be obtained by first measuring the torque t1 that is applied to the tapered roller 130 (block S135) and the torque t2 that is applied to the other tapered roller 135 (block S140).
These torques t1 and t2 can be measured by means of suitable torque sensors associated with the motors driving the tapered rollers 130 and 135.
The torques t1 and t2 can then be subtracted from each other (block S145) to calculate a difference e2 (or error).
This difference e2 can then be provided as input to a controller S150, specifically a proportional-integrative PI or proportional-integrative-derivative PID controller, which returns the value of the feedback contribution r2 as output.
For example, in the case of a PID, the value of the feedback contribution r2 can be expressed by the following relationship in the time domain t: $r 2 (t) = K_{p} e 2 (t) + K_{i} \int_{t_{0}}^{t} e 2 (τ) dτ + K_{d} \frac{de 2 (t)}{dt}$
where e2 is the calculated difference between the thrust forces, K_p is the proportional gain, K_i is the integrative gain, and K_d is the derivative gain; or equivalently by the following relationship: $r 1 (t) = K_{p} (e 1 (t) + \frac{1}{T_{i}} \int_{t_{0}}^{t} e 1 (τ) dτ + T_{d} \frac{de 1 (t)}{dt})$
where T_i (=K_p/K_i) is the integration time and T_d (=K_d/K_p) is the derivation time.
Should the controller S150 be a PI controller, the value of the feedback contribution r2 will be expressed by the same relations with the exclusion of the derivative part, i.e. considering a derivative gain K_d (or a derivation time T_d) equal to zero.
Naturally, the proportional part, the integrative part and the derivative part of the controller S150 are the same as those previously described with reference to the controller S120, while the coefficients K_p, K_i, K_d, T_i and/or T_d of the controller S150 may be different from the same coefficients of the controller S120.
On the other hand, the manual contribution m2 is selected and adjusted as desired by an operator supervising the operation of the rolling mill 100 (block S155), e.g. through the manual operation of a handwheel or any other control or interface with the machine. Correcting the first corrected value v* with the correction d2 provides a second corrected value v** of the rotational speed, which can be directly transmitted to a driver S160 driving the motor of the tapered roller 130, so that the latter is driven to rotate at a speed exactly corresponding to the second corrected value v**.
As part of this control method, it is provided that at least the coefficients of the proportional part and the integrative part of the controller S120 can vary (block S200) based on one or more physical parameters of the ring 200 being processed.
For example, the control method may provide to acquire (e.g., measure, calculate or otherwise receive as input) the value of one or more physical parameter(s) of the ring 200 being processed and, subsequently, use said value(s) to determine (e.g., calculate, establish or otherwise obtain) the values of the coefficients of the proportional and integrative part of the controller S120.
In this case, the physical parameters of the proportional and integrative parts of the controller S120 are the proportional gain K_p and the integration time T_i.
However, it is not excluded that, in other embodiments, the integration time T_i may be replaced by the integrative gain K_i.
Nor can it be ruled out that some embodiments may also involve varying, based on the above-mentioned physical parameters of the ring 200, the coefficient(s) of the derivative part, e.g. the derivative gain K_d or equivalently the derivation time T_d.
The physical parameters of the ring 200 being processed can be chosen from the group consisting of: weight of the ring 200 being processed, volume of the ring 200 being processed, annular wall thickness of the ring 200 being processed (also called "section" or "wall"), height of the ring 200 being processed and finally diameter (e.g. outer or inner diameter) of the ring 200 being processed.
It should be noted here that the thickness of the ring 200, denoted by P in figure 2, is to be understood as the dimension of the ring wall measured along a radial direction, i.e. along a direction orthogonal to and incident with the axis of the ring 200.
In other words, the thickness can be considered as half the difference between the outer diameter and the inner diameter of the ring 200.
The height of the ring 200, indicated by H in figure 1, is instead to be understood as the dimension of the ring wall measured along a direction parallel to the axis of the ring 200. Having said this, it is preferable that the coefficients of the proportional part and the integrative part of the controller S120 (and possibly also those of the derivative part) can be varied at least on the basis of the weight of the ring 200 being processed (or equivalently its volume), and possibly on the basis of at least one additional parameter chosen from among those that change during the rolling of the ring 200, such as thickness or height.
Some of these parameters can be measured directly (such as ring diameter), while others can be derived from the position (height) and dimensions of the rollers in contact with the workpiece (such as thickness and height), and still others can be calculated from the measured parameters or known a priori from the set data (volume/weight).
For example, the volume of the ring 200 being processed can be known a priori on the basis of the dimensions of the initial blank.
The weight of the ring 200 being processed can be calculated as a function of the volume and density of the material.
The diameter of the ring 200 being processed can be measured with any suitable sensor.
To be precise, the diameter of the ring 200 is preferably measured by means of a laser gauge (usually of the triangulation type) or by means of a mechanical probe made by means of an idler wheel held in thrust on the outer perimeter surface 205 of the ring 200 by an air cylinder "acting as a spring" and connected to a linear measuring system (optical scale or other transducer).
These devices can be located between the two tapered rollers 130 and 135 (in the case of the mechanical touch probe) or in a position behind them (in the case of the laser gauge), so that the linear measurement taken is always on the centreline of the rolling mill 100, i.e. along a direction lying in the plane of symmetry S.
The height of the ring 200 being processed can be calculated based on a measurement of the relative position of the tapered rollers 130 and 135 and their dimensions.
For example, considering the illustrative case in which the tapered roller 130 remains stationary and the rolling mill 100 is equipped with an actuator adapted to modify the position of the tapered roller 135 along a vertical "axis", the height of the ring 200 will in fact correspond to the height of the tapered roller 135 along said "axis" (apart from its dimensions), which can be measured by a very precise measuring system (e.g., an optical scale or a temposonic transducer) already present on the rolling mill 100 and which is mainly used to control the displacements of the tapered roller 135 along that axis. The thickness of the ring 200 being processed can be calculated based on a measurement of the relative position between the main roller 105 and the contrast roller 110 and their dimensions.
For example, considering the illustrative case in which the main roller 105 remains stationary and the rolling mill 100 is equipped with an actuator adapted to modify the position of the contrast roller 110 along a horizontal "axis", the thickness of the ring 200 will in fact correspond to the position of the contrast roller 110 along said "axis" (apart from its dimensions), which can be measured by a very precise measuring system (e.g., an optical scale or a temposonic transducer) already present on the rolling mill 100 and which is mainly used to control the displacements of the contrast roller 110 along that axis.
Regardless of these considerations, each of the variable coefficients K_p and T_i of the controller S120 can be acquired from a correlation matrix (or table) in which a plurality of such coefficient values are stored and individually correlated to a corresponding value of at least one of the aforementioned physical parameters of the ring 200 being processed, or to corresponding values of a t-uple of said physical parameters.
Thus, by providing as input the values of the physical parameter(s) of the ring 200 being processed, the control method can retrieve the corresponding values of the coefficients K_p and T_i of the controller S120 from the correlation matrix.
The correlation matrix can be determined empirically during a preliminary configuration step of the control method.
For example, the correlation matrix can be determined (or constructed) by carrying out a multiplicity of empirical tests, each time using rings with different characteristics and, during each test, empirically establishing which coefficients K_p and T_i of the proportional and integrative part of the controller S120 allow a stable adjustment of the correction to be obtained, to apply to the rotational speed of the tapered rollers 130 and 135 (e.g. that does not oscillate or has oscillations that tend to dampen rapidly) reducing the error as much as possible and, consequently, leading to a uniform and regular growth of the ring (free from fluctuations and undulations) without giving rise to significant shape defects, such as circularity, flatness and cylindricity defects.
In particular, empirical tests can be carried out with rings of different weights (i.e. volume) and repeated, for each ring, at different stages of its "growth" in the rolling process (generally corresponding to different cross-sections, diameters and heights).
Using the coefficients thus determined, it is then possible to populate one or more matrices (or tables) which, for each value of the ring's physical parameters (e.g. weight, volume, cross-section, etc.), associate a corresponding value of the coefficients K_p and T_i of the controller S120.
Alternatively, each of the variable coefficients K_p and T_i of the controller S120 can be calculated by means of a mathematical function that relates the physical parameter(s) of the ring 200 being processed to the variable coefficient of the controller S120.
In this way, the control method can calculate the values of the coefficients K_p and T_i of the controller 120 from time to time as a function of the values of the physical parameter(s) of the ring 200 being processed.
The mathematical function can also be obtained empirically, e.g. by interpolating the values of the coefficients K_p and T_i obtained from the empirical tests outlined above. However, it is not excluded that, in other embodiments, the mathematical function can be obtained on a theoretical basis.
It should be noted here that the variation of the coefficients K_p and T_i of the controller S120 is preferably performed repeatedly and continuously during the rolling of the ring 200 being processed.
In other words, it is preferable that, during the rolling process of the ring 200, the coefficients K_p and T_i of the controller S120 vary continuously as the physical parameters of the ring 200 (e.g. cross-section, diameter and height) change.
This ensures that the dynamic response of the controller S120 is always the most appropriate at any time during the rolling of the ring 200 being processed.
However, it is not excluded that, in other embodiments, the coefficients K_p and T_i of the controller S120 can be varied (adjusted) as part of a preliminary setting step that is carried out before ring 200 rolling begins and then kept constant.
This solution could be implemented if the coefficients K_p and T_i of the controller S120 were to be varied solely on the basis of the weight (or volume) of the ring 200 being processed, as these parameters remain essentially constant throughout the entire rolling process.
All of the above considerations naturally also apply to the coefficients K_d or T_d of the derivative part of the controller S120, should they be expected to vary.
In much the same way as described above, the control method of the rolling mill 100 also provides that (at least) the coefficients of the proportional part and the integrative part of the controller S105 can vary (block S205) based on one or more physical parameters of the ring 200 being processed.
For example, the control method may provide to acquire (e.g., measure, calculate or otherwise receive as input) the value of one or more physical parameter(s) of the ring 200 being processed and, subsequently, use said value(s) to determine (e.g., calculate, establish or otherwise obtain) the values of the coefficients of the proportional and integrative part of the controller S150.
In this case, the physical parameters of the proportional and integrative parts of the controller S150 are the proportional gain K_p and the integration time T_i.
However, it is not excluded that, in other embodiments, the integration time T_i may be replaced by the integrative gain K_i.
Nor can it be ruled out that some embodiments may also involve varying, based on the above-mentioned physical parameters of the ring 200, the coefficient(s) of the derivative part, e.g. the derivative gain K_d or equivalently the derivation time T_d.
As in the previous case, the physical parameters of the ring 200 being processed can be chosen from the group consisting of: weight of the ring 200 being processed, volume of the ring 200 being processed, annular wall thickness of the ring 200 being processed (also called "section" or "wall"), height of the ring 200 being processed and finally diameter (e.g. outer or inner diameter) of the ring 200 being processed.
In particular, it is preferable that the coefficients of the proportional part and of the integrative part of the controller S150 (and possibly also those of the derivative part) can be varied at least on the basis of the weight of the ring 200 being processed (or equivalently of its volume), and possibly on the basis of at least one additional parameter chosen from among those that change during the rolling of the ring 200 being processed, such as thickness or height.
More specifically, it is preferable that the coefficients K_p and T_i of the controller S150 are varied on the basis of the same physical parameters of the ring 200 being processed that also determine the variable coefficients K_p and T_i of the other controller S120.
Naturally, the physical parameters of the ring 200 can be measured, calculated or otherwise received as input in the same manner as described above with reference to the controller S120.
Also analogous to the first controller S120, each of the variable coefficients K_p and T_i of the controller S150 can be acquired from a correlation matrix (or table) in which a plurality of such coefficient values are stored and individually correlated to a corresponding value of at least one of the aforementioned physical parameters of the ring 200 being processed, or to corresponding values of a t-uple of said physical parameters.
Thus, by providing as input the values of the physical parameter(s) of the ring 200 being processed, the control method can retrieve the corresponding values of the coefficients K_p and T_i of the controller S150 from the correlation matrix.
The correlation matrix can be determined empirically during a preliminary configuration step of the control method.
For example, the correlation matrix can be determined (or constructed) by carrying out a multiplicity of empirical tests, each time using rings with different characteristics and, during each test, empirically establishing which coefficients K_p and T_i of the proportional and integrative part of the controller S150 allow a stable adjustment of the correction to be obtained, to apply to the rotational speed of the tapered rollers 130 and 135 (e.g. that does not oscillate or has oscillations that tend to dampen rapidly) reducing the error as much as possible and, consequently, leading to a uniform and regular growth of the ring (free from fluctuations and undulations) without giving rise to significant shape defects, such as circularity, flatness and cylindricity defects.
In particular, empirical tests can be carried out with rings of different weights (i.e. volume) and repeated, for each ring, at different stages of its "growth" in the rolling process (generally corresponding to different cross-sections, diameters and heights).
Using the coefficients thus determined, it is then possible to populate one or more matrices (or tables) which, for each value of the ring's physical parameters (e.g. weight, volume, cross-section, etc.), associate a corresponding value of the coefficients K_p and T_i of the controller S150.
Alternatively, each of the variable coefficients K_p and T_i of the controller S150 can be calculated by means of a mathematical function that relates the physical parameter(s) of the ring 200 being processed to the variable coefficient of the controller S150.
In this way, the control method can calculate the values of the coefficients K_p and T_i of the controller 150 from time to time as a function of the values of the physical parameter(s) of the ring 200 being processed.
The mathematical function can also be obtained empirically, e.g. by interpolating the values of the coefficients K_p and T_i obtained from the empirical tests outlined above. However, it is not excluded that, in other embodiments, the mathematical function can be obtained on a theoretical basis.
It should also be emphasised here that the variation of the coefficients K_p and T_i of the controller S150 is preferably performed repeatedly and continuously during the rolling of the ring 200 being processed, for example at the same time as the variation of the coefficients K_p and T_i of the controller S120.
In other words, it is preferable that, during the rolling process of the ring 200, the coefficients K_p and T_i of the controller S150 vary continuously as the physical parameters of the ring 200 (e.g. cross-section, diameter and height) change.
This ensures that also the dynamic response of the controller S150 is always the most appropriate at any time during the rolling of the ring 200 being processed.
However, it is not excluded that, in other embodiments, the coefficients K_p and T_i of the controller S150 can be varied (adjusted) as part of a preliminary setting step that is carried out before ring 200 rolling begins and then kept constant.
This solution could be implemented if the coefficients K_p and T_i of the controller S150 were to be varied solely on the basis of the weight (or volume) of the ring 200 being processed, as these parameters remain essentially constant throughout the entire rolling process.
All of the above considerations naturally also apply to the coefficients K_d or T_d of the derivative part of the controller S150, should they be expected to vary.
The control method outlined above can advantageously be performed automatically by an electronic processing unit (not shown) of the rolling mill 100, which is connected to the various actuators and sensors and is configured/programmed to perform the described operations.
Obviously, a person skilled in the art may make several technical-applicative modifications to all that above, without departing from the scope of the invention as claimed hereinbelow.

Claims

A method for controlling an axial radial rolling mill (100) for rings (200),
wherein the axial radial rolling mill (100) comprises:
- a main roller (105) adapted to stay in contact with an outer perimeter surface (205) of the ring (200) being processed,

- a contrast roller (110) having an axis of rotation (B) coplanar to the axis of rotation (A) of the main roller (105) and adapted to stay in contact with an inner perimeter surface (210) of the ring (200) being processed,

- a pair of guide rollers (115) having axes of rotation (C) parallel to the axis of rotation (A) of the main roller (105) and adapted to stay in contact with the outer perimeter surface (205) of the ring (200) being processed, and

- a pair of tapered rollers (130, 135) having coplanar axes of rotation (E) on said plane of symmetry (S), which are respectively adapted to stay in contact with the opposite axial ends (215, 220) of the ring (200) being processed,

wherein the control method provides for adjusting the rotational speed of each tapered roller (130, 135) by means of the steps of:
- establishing a reference value (v) of the rotational speed of the tapered roller (130, 135),

- applying a correction (d1, d2) to said reference value (v) to obtain a corrected value (v*, v**) of the rotational speed of the tapered roller (130, 135),

- actuating the tapered roller (130, 135) at a rotational speed having the corrected value (v*, v**), and

wherein the correction (d1, d2) comprises at least one feedback contribution (r1, r2) provided by a controller (S120, S150) of the proportional-integrative or proportional-integrative-derivative type,
characterized in that the control method provides for varying at least the coefficients of the proportional part and of the integrative part of the controller (S120, S150) on the basis of the value of at least one physical parameter of the ring (200) being processed.
A method according to claim 1, wherein said coefficients of the proportional part and of the integrative part are the proportional gain and the integration time.
A method according to claim 1 or 2, wherein said physical parameter of the ring (200) being processed is selected from the set consisting of: weight of the ring (200) being processed, volume of the ring (200) being processed, thickness of the ring (200) being processed, height of the ring (200) being processed, diameter of the ring (200) being processed.
A method according to any one of the preceding claims, wherein each of the variable coefficients of the controller (S120, S150) is provided by a correlation matrix in which a plurality of values of the variable coefficient are stored and individually correlated to a corresponding value of said at least one physical parameter of the ring being processed.
A method according to any one of the preceding claims, wherein each of the variable coefficients of the controller (S120, S150) may be calculated by means of a mathematical function which relates said at least one physical parameter of the ring being processed to the variable coefficient of the controller.
A method according to any one of the preceding claims, wherein said variation of the coefficients of the proportional part and of the integrative part of the controller (S120, S150) is performed repeatedly during the rolling of the ring (200) being processed.
A method according to any one of the preceding claims, wherein the feedback contribution (r1) of at least one of the tapered rollers (135) is obtained by means of the steps of:
- measuring the force (f1, f2) applied by the ring (200) being processed on each guide roller (115),

- calculating a difference (e1) between the measured forces,

- using said difference (e1) as an input of the controller (S120) which outputs said feedback contribution (r1).
A method according to any one of the preceding claims, wherein the feedback contribution (r2) of at least one of the tapered rollers (130) is obtained by means of the steps of:
- measuring the torque (c1, c2) applied to each tapered roller (130, 135),

- calculating a difference (e2) between the measured torques (c1, c2),

- using said difference (e2) as an input of the controller (S150) which outputs said feedback contribution (r2).
an axial radial rolling mill (100) for rings (200), comprising:
- a main roller (105) adapted to stay in contact with an outer perimeter surface (205) of a ring (200) being processed,

- a contrast roller (110) having an axis of rotation (B) parallel to the axis of rotation (A) of the main roller (105) and adapted to stay in contact with an inner perimeter surface (210) of the ring (200) being processed,

- a pair of guide rollers (115) having axes of rotation (C) parallel to the axis of rotation (A) of the main roller (105) and adapted to stay in contact with the outer perimeter surface (205) of the ring (200) being processed,

- a pair of tapered rollers (130, 135) having coplanar axes of rotation (E) on said plane of symmetry (S), which are respectively adapted to stay in contact with the opposite axial ends (215, 220) of the ring (200) being processed, and

- an electronic processing unit configured to perform the control method outlined above.
A software comprising a computer code which, when executed by an electronic processor, enables the electronic processor to execute the method of any one of claims 1 to 8.