Vibratory incremental sheet forming tool

Description

1. TECHNICAL FIELD

The invention relates to the field of sheet forming, and more particularly incremental sheet forming. Forming is a manufacturing process consisting of shaping a by-product, typically a plate or a sheet. Forming is conventionally carried out by compressing or pressing the by-product between two predetermined forms, referred to respectively as the die and counter die.

However, conventional forming is a rigid process, since a given pair of dies can only produce one given form. Thus, if you wish to change the shape of the product shaped by forming, even just marginally modify it, it is necessary to change the dies used. Conventional forming is also cumbersome to set up, particularly when the sheet to be shaped has large dimensions and requires very high forces to apply sufficient and uniform pressure to the sheet to be formed.

To address the shortcomings of conventional forming, incremental sheet forming (ISF) has been developed over the last two decades. Incremental sheet forming consists of iterative local deformation of a sheet to give it the desired shape. To achieve this, the sheet is locally deformed using a tool head (also referred to as a punch), and this process is iterated until the desired shape is achieved. To control incremental sheet forming, the position of the tool head is controlled. It is even possible to control the acceleration of the tool, so as to control the force that the punch exerts on the sheet.

Incremental sheet forming has a number advantages over conventional forming processes. The shape of the formed product results from the numerical control that controls the position of the tool head, and can thus be easily modified by changing the instructions at the origin of the numerical control (for example a 3D model), without having to change the sheet forming tool itself, unlike with conventional forming. Incremental sheet forming can advantageously be implemented by integrating the tool head at the end of a robotic arm or in a numerically controlled machine. The robotic arm or computer numerical control machine then controls the position of the tool head, thereby shaping the sheet metal.

Incremental sheet forming using a robotic arm is particularly advantageous in that it can be used to shape a large sheet at much lower cost than a CNC machine, and is even less costly than traditional forming with a die and a counter die (which are, by definition, the same size as the sheet to be formed).

Due to its flexibility and ease of use, incremental sheet forming has many advantages, and is ideal for the manufacture of prototypes or small production runs.

2. PRIOR ART

As explained above, incremental sheet forming is based on the local deformation of a metal sheet. This deformation is a result of the local application of a force (or pressure) to said sheet by the punch. This force thus produces in turn the elastic deformation of the robotic arm. If this deformation is too great, it moves the robotic arm and disrupts the control of the position of the punch. Thus, the forces that can be applied to the sheet to be formed are limited by the rigidity of the robotic arm with which the sheet is formed, and even more limited the thicker the sheet. Similar problems arise when a CNC machine is used for incremental sheet forming.

However, it has been discovered that vibrating the punch at frequencies in the kilohertz to low-frequency ultrasonic range, locally softens the sheet material, making it more ductile, thereby reducing the forces required to deform it. The springback of the sheet is thus reduced. These vibrations can be used to shape thicker sheets and/or allow the use of a robotic arm with smaller dimensions. The vibrations are typically generated by a piezoelectric actuator.

More precisely, when the vibrations are in a direction normal to the sheet (i.e. perpendicular to the sheet at the point of punch-sheet contact), these longitudinal vibrations would activate a dislocation movement and their propagation within the material, from which the observed softening potentially occurs. Transverse vibrations (i.e. perpendicular to normal vibrations) reduce the friction between the sheet and the punch, which also reduces the forces that the robotic arm needs to produce to carry out the incremental sheet forming. These transverse vibrations also limit the ‘stick-slip’ phenomenon, which also improves the quality of tool movement control and the surface finish of the sheet metal formed.

Vibrations normal and transverse to the sheet thus produce complementary effects which greatly reduce the effort required to perform incremental sheet forming. However, generating these vibrations in three directions (one normal and two transverse) is not easy.

The article by Kurniawan, R., Ali, S., Park, K. M., Li, C. P., & Ko, T. J. is known (2019): “Development of a three-dimensional ultrasonic elliptical vibration transducer (3D-UEVT) based on sandwiched piezoelectric actuator for micro-grooving”, International Journal of Precision Engineering and Manufacturing, 20 (7), 1229-1240, which describes a drilling tool comprising a stack of piezoelectric actuators placed in the centre of the sheet forming tool body. Each of the actuators in the stack can vibrate in one of the three directions, as a function of the electrical command it receives. The vibrations produced by the actuators are propagated by the tool body to the drill bit. Thus, this drill bit can vibrate in all three directions.

The article by Gao, J., & Altintas, Y. is also known (2019): “Development of a three-degree-of-freedom ultrasonic vibration tool holder for milling and drilling”, IEEE/ASME Transactions on Mechatronics, 24(3), 1238-1247 describes a machining tool that uses elliptical excitation of a stack actuators to couple vibration modes.

However, these solutions are not satisfactory. Firstly, it requires the use of several actuators (in the form of stacks), and therefore a multitude of power supplies to be controlled. In addition, since there are several actuators, each actuator is smaller (to respect the space limitations), and can therefore product less powerful vibrations. Finally, in practice these solutions are difficult to control, as multiple actuators interfere with the tool and it is not easy to control the vibration modes individually to produce the desired vibrations.

Furthermore, these solutions relate to machining and drilling, which are very different from incremental sheet forming.

There is a need to find a solution for vibrating a punch in a multidirectional manner which does not have the shortcomings of the prior art, in particular in terms of simplicity of implementation, size and ease of control.

The invention improves the situation.

3. DISCLOSURE OF THE INVENTION

The invention has been designed to overcome at least some of the disadvantages of the prior art.

To this end, the invention proposes an incremental sheet forming tool, characterised in that it comprises:

• • a tool body;
  • a tool head, integral with the body and terminated by a punch at its end;
  • a housing arranged within the body;
  • an actuator, located in the housing and capable of producing a vibration in a first direction, which can be propagated to the punch;
  • at least one means of transforming the first direction of vibration to a second direction of vibration, during its propagation to the punch.

Thus, due to this transformation means, the tool is able to transform a vibration produced by a unidirectional actuator (in the first direction) into a multidirectional vibration or at least in the second direction. For example, the tool is able, from an actuator producing an axial vibration (i.e. in a main axis of the body, also referred to as the axial direction or longitudinal direction), to produce a transverse vibration, i.e. orthogonal to this main axis, at site of the punch. The actuator can thus be a unidirectional actuator without this preventing the tool from vibrating in several directions (including one transverse and one axial direction). The actuator is for example a piezoelectric actuator. During an incremental sheet forming process, the punch is able to vibrate in directions normal and transverse to the metal sheet (i.e. in the main axis of the tool body and in one or more directions orthogonal to this main axis, respectively). The sheet is thus locally smoothed and friction between the tool head and the sheet is reduced. The springback of the sheet to the tool is therefore reduced. As the forces required to form the sheet are reduced, the springback of the arm is also reduced.

The actuator can excite tool head and cause it to vibrate by imposing a vibratory force on it to obtain, at certain frequencies, a large vibratory force at the punch by the structural resonance effect, particularly when the punch is in contact with a metal sheet.

This results in a gain on the machine side (i.e. a smaller size of the robotic arm or the CNC machine supporting the tool) but also on the quality of the formed part, since the lower springback and reduction in friction result in a better surface finish of the part after sheet forming.

According to one aspect, said at least one transformation means comprises at least one non-axisymmetrical portion with respect to a main axis of said tool.

Thus, the tool has a generally axisymmetrical shape, which improves its vibratory properties, in particular by separating the vibratory nodes of the punch in relation to a tool whose shape would be particularly dissymmetric. This also makes it possible to integrate the transformation means into a pre-existing tool, by partially modifying its axisymmetrical nature.

According to one aspect, the means for transforming the direction of vibration is arranged so that a unidirectional vibration parallel to a main axis of said tool and produced by the actuator causes the punch to vibrate in at least one direction orthogonal to the main axis.

The fact of being able to make the punch vibrate in several directions from a unidirectional vibration due to the transformation means also makes it possible to use a single unidirectional actuator, and therefore a more powerful actuator. The tool can therefore be smaller for equivalent actuator power, since the effects of reduced ductility and reduced friction are all the greater the higher the amplitude of the vibration.

In order to generate a controllable transverse vibration of the punch, the body and/or the head (in particular the non-axisymmetric portion of the transformation means) can be judiciously dimensioned, such that a given unidirectional vibration of the actuator at a given frequency delivers a given transverse vibration of the tool head. It is thus not only possible to generate a multidirectional vibration of the tool head using a unidirectional actuator, but also to control it precisely.

This new type of tool thus allows incremental sheet forming using a robotic arm or a CNC machine (more generally any machine that supports the tool) of smaller dimensions than those usually used, since the springback is lower. Alternatively, larger and/or thicker sheets can be formed using the same robotic arm. Finally, there is less friction, which limits the stick-slip effect. This improves the quality of the tool head position control and the surface finish of the sheet once it has been formed.

According to one aspect, the housing is off-center with respect to a main axis of the body, constituting at least partially said non-axisymmetrical portion.

According to one aspect, the axis of attachment of the actuator within the housing is off-centre with respect to a main axis of said tool, constituting at least partially said non-axisymmetrical portion.

According to one aspect, the actuator is installed within the body in a substantially off-centre manner with respect to a main axis of the body, constituting at least partially said non-axisymmetrical portion.

Due to the offset of the housing and/or the actuator, the parallel vibration induced by a unidirectional actuator mounted in the housing causes a vibration transverse to the main axis of the tool body. By accurately dimensioning this offset, it is then possible to determine the transfer function between the vibration in the Z axis (axial direction) and the vibration in X, Y and Z directions (transverse radial, transverse tangential and axial direction respectively). This can be achieved for example by means of a simulation (for example, numerical analysis using the finite element method) based on a model of the tool obtained by computer-aided design (CAD). With good knowledge of this transfer function, it is possible to control the vibrations of the punch from the frequency control of the power supply to the actuator (i.e. the unidirectional vibration it produces in the housing).

According to one aspect, the body comprises an addition of material which is non-axisymmetrical with respect to a main axis of the body, said addition constituting at least partially said non-axisymmetrical portion.

Thus, an addition of material makes it possible to contribute to the propagation of the vibration in a non-axial direction. It should be noted that this non-axisymmetrical addition of material can perform a third function, such as acting as a behavior-shaping constraint in the assembly of the tool, making it possible to attach power supply means or sensors to the tool, etc. which saves pace by pooling the function within this addition.

According to one aspect, the body comprises at least one recess that is not axisymmetrical with respect to a main axis of the body, said at least one recess being provided within the body and constituting at least partially said non-axisymmetrical portion.

Here, the recess makes it possible to contribute to the propagation of the vibration in a non-axial direction. It should be noted that this non-axisymmetrical recess can perform a third function, such as providing access to parts of the tool, acting as a behavior-shaping constraint, housing power supply means or sensors etc., which makes it possible to save space by sharing the functions within this recess.

According to one aspect, the recess comprises at least one hole made in the body and forming an access to the housing from the outside of the body.

This hole has a dual function: it contributes to the non-axisymmetry of the tool and helps to power the actuator by allowing access to the housing (to run power cables). This saves space, as well as generating a transverse vibration in the punch.

It should be noted that the dissymmetry caused by the removal or addition of material or drilling is not incompatible with an offset of the housing and/or actuator. On the contrary, these two particular features can be combined to amplify the dissymmetry of the part, thereby improving the generation of a transverse vibration.

According to one aspect, the tool also comprises one or more shims installed in the housing so as to exert a preload on the actuator (particularly when the tool is in operation and in the absence of vibrations of the actuator).

According to this example, the compression of the actuator with a shim (or a set of shims) induces a preload, i.e. a force (or preload) applied to the actuator in the absence of any specific action (such as powering the actuator). The preload drastically improves the energy transfer between the actuator and the tool body (hence the gain in the transfer function described above). The preload also increases the transfer of the vibration produced by the actuator to the rest of the tool.

According to one aspect, the punch is also able to vibrate according to at least one resonance mode in reaction to a vibration generated by the actuator in a main axis, and the tool has at least one resonance frequency for said vibration mode for the transfer function defined by the relationship between the amplitude of a vibration of the punch according to the vibration mode and the amplitude of the vibration of the actuator parallel to the main axis, said resonance frequency being between 5 kHz and 30 kHz.

The transfer function has a resonance. This resonance advantageously makes it possible to improve the energy transfer, and therefore increase the amplitude of the vibration of the punch. The smoothness of a sheet to be formed is increased in this way and reduces the forces required to form the sheet.

This resonance is achieved by carefully selecting the dimensions of the tool, in particular its non-axisymmetrical portion, selected judiciously. This can be achieved using simulation means during computer-aided design, or empirically, the important factor being that in the end a resonance frequency is obtained for the desired mode or modes.

According to one aspect, the vibration mode belongs to the group comprising a vibration parallel to the main axis, a vibration orthogonal to the main axis and parallel to a direction of misalignment of the non-axisymmetric portion, a vibration orthogonal to the main axis and to the direction of misalignment of the non-axisymmetric portion, and a combination thereof.

The direction orthogonal to the main axis and parallel to a direction of misalignment of the non-axisymmetric portion (typically the offset of the actuator and/or the housing, or the direction of misalignment of a hole or an addition of material) is the radial transverse direction (X axis). The direction orthogonal to the main axis and to the direction of misalignment of the non-axisymmetric portion is the tangential transverse direction (Y axis). The possible combination(s) of these three directions X, Y and Z is referred to as the coupled mode(s).

The fact that the punch can vibrate in an axial mode, a radial mode, a tangential mode or a coupled mode makes it possible to obtain different effects on the sheet metal that are softened by vibrations. In particular, forces generated by transverse vibrations reduce friction at the point of contact between the sheet and the punch during sheet forming, as axial vibrations would activate dislocations in the sheet at the microscopic level, thus softening the sheet. The various coupled modes (in particular axial/radial and axial/tangential), for their part, would make it possible to combine these effects. Coupled modes also make it possible to anticipate variations in the trajectory of the punch, and therefore to maintain the transverse direction of the vibration of the punch co-linear with the feed direction of the tool, which in turn improves the reduction in punch/sheet friction. In other words, the direction of the transverse vibration of the tool can be controlled so that it is tangential to the movement of the punch. These modes of vibration can also be single, double or triple, i.e. inducing single, double or triple bending of the tool head, respectively.

4. BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages of the invention will become clearer on reading the following description of a particular exemplary embodiment, given merely as an illustrative and non-limiting example, and of the accompanying drawings, in which:

FIG. 1 shows a perspective view of a tool according to an exemplary embodiment of the invention;

FIG. 2 shows a perspective view from below of the tool of FIG. 1;

FIG. 3 shows a cross-sectional view of the top of the tool in FIG. 1;

FIG. 4 shows a cross-sectional view of the side of the tool in plane IV-IV of FIG. 3;

FIG. 5 shows a side view of the tool of FIG. 1;

FIG. 6 shows a detailed view VI of FIG. 4 according to another embodiment of the invention;

FIG. 7 shows an exploded view of the tool of FIG. 1;

FIG. 8 shows a variant of the tool head of the tool of FIG. 1;

FIG. 9 shows a frequency response of the tool of FIG. 1 in all three directions; and

FIG. 10 shows detail IX of FIG. 9.

5. DETAILED DESCRIPTION

5.1. General Principle

As explained above, the general principle of the disclosure is to produce vibrations in the desired direction by modifying the structure of the sheet forming tool and in particular by providing, within the tool, means for transforming the vibrations produced by the actuator. This aspect is clear from the description of the following figures, which represent one of the exemplary embodiments. The vibrations are produced at one or more given frequencies. In this application, vibration is defined as a mechanical wave at a certain frequency (or a plurality of superimposed frequencies) within the medium in which the vibration propagates. This vibration can be observed in the form of a vibratory force (for example at the actuator mounted in the housing) or in the form of a vibratory movement (or oscillations, for example observable at the punch when the latter is free, i.e. not in contact with a metal sheet). This vibration is also manifested physically in the form of a vibratory energy, i.e. the combination of a vibratory force and a vibratory movement.

With reference to FIGS. 1 to 5, a sheet forming tool 1 according to the invention is described. The tool 1 comprises a tool body 2, a tool head 3 and an actuator 4. The tool body 2 and the tool head 3 are fixed to one another. The actuator 4 is housed in the tool body 2 and/or the tool head 3.

The tool body 2 and the tool head 3 can be made of steel (but not necessarily the same steel). The tool body 2 and the tool head 3 can more generally be made from any material capable of withstanding the sheet forming forces induced by the incremental sheet forming process.

The tool body is generally axisymmetrical around a main axis 20, which defines a first direction Z referred to as the axial direction. For the remainder of this description, two directions X and Y are defined as orthogonal to direction Z and to each other. The directions X, Y and Z form an orthonormal reference framework (X, Y, Z), shown in FIG. 4.

The tool head 3 comprises a punch 30 at one of its ends. The punch is intended to come into contact with a metal sheet during an incremental sheet forming process.

In the example described here, the tool head 3 forms the punch 30 at one end, and is connected (fixed) to the tool body 2 at an opposite end. The punch 30 forms a tip of the tool head 3. The punch 30 may be hemispherical, which allows the angle of contact with the sheet metal to be varied continuously. The tool head 3 also comprises a base 32 via which the tool head 3 is secured to the tool body 2. The base 32 and the punch 30 are connected to one another by a section 34. The punch 30 and the section 34 can thus form a finger projecting from the base 32. The tool head 3 has a substantially axisymmetrical form. The tool head 3 has a profile which tapers from the base 32 to the punch 30. Here, the section of the tool head 3 has a substantially progressive cross-section, without any sharp angles, between the base 32 and the punch 30, so as to improve the mechanical properties of the part formed by the tool head 3. This also reduces the overall size of the tool, making it possible to obtain more varied shapes. In particular, the slender nature of the tool head 3 (i.e. its finger shape) makes it possible to form concave parts with a steeper resulting sheet angle and greater depth.

In the examples described here, the tool head 3 and the tool body 2 are described as separate parts, and are fixed together using screws, for example. Alternatively, the tool head 3 and tool body 2 may be in one piece, with access to an interior of the tool body 2 from the end opposite the tool head 2.

The interior of the tool body 2 forms a housing 22, shown in particular in FIG. 4. The housing 22 is suitable for receiving the actuator 4. The tool head 3 can close a first end of the housing 22, also referred to as the proximal end, as shown in FIG. 4. Alternatively, this first end of the housing 22 (close to the punch) can be closed by the tool body 2 itself. The tool 1 may comprise a cover 24, fixed to the tool body 2, and closing a second end (also referred to as the distal end of the housing 22, as it is remote from the punch) of the housing 22. Alternatively, the tool body 2 itself may close this second end.

The actuator 4 is installed in the housing 22. The actuator 4 may comprise an actuator interface 42 capable of controlling the actuator. The actuator 4 is capable of generating vibrations. The vibrations produced by actuator 4 are propagated throughout tool 1, and in particular to punch 30. The actuator 4 is able to vibrate in Z direction, i.e. parallel to the main axis 20. When the actuator 4 vibrates, it generates a vibration which can propagate to the rest of the tool 1. The actuator 4 may be unidirectional, i.e. capable of vibrating specifically in Z direction.

The tool 1 comprises means for transforming the direction of vibration, hereinafter referred to as transformation means. The transformation means is capable of modifying the direction of the vibrations as they propagate from the actuator 4 in the housing 22 to the punch 30.

The transformation means comprises a non-axisymmetric portion of the tool with respect to the main axis 20. In other words, the transformation means comprises at least one non-axisymmetrical portion (or element) with respect to this main axis 20.

This non-axisymmetrical portion of the tool 1 may comprise the actuator 4 itself, offset relative to the main axis 20 by an actuator offset 40, shown in FIG. 4. Here, the housing 22 is axisymmetrical relative to the main axis 20 of the tool body 2 and the actuator 4 is mounted off-centre in the housing 22. Alternatively, the housing 22 may be offset with respect to the main axis 20 and the actuator 4 housed centred in the housing 22 (this causes the offset 40). It is possible to combine an offset of the housing 22 and an off-center mounting of the actuator 4 in the housing 22.

The dissymmetry induced by the offset of the actuator 4 (whether by placing it off-center in a symmetrical housing 22 or by having a housing 22 itself off-center) enables axial vibrations of the actuator 4 to be transformed into transverse vibrations at the punch 30. These transverse vibrations occur in particular for particular frequencies of vibrations corresponding to bending modes of the tool. The actuator can thus be unidirectional while having a punch capable of vibrating axially and transversely. In the example shown in FIGS. 3 and 4, the actuator 4 is fixed to the tool head 3 by a hole 46 formed in the tool head 3, in line with the axis of the actuator 4 but offset from the tool body 2 and the tool head 3.

As the actuator can be unidirectional, this actuator can be significantly more powerful than a multidimensional actuator (for example a stack of small piezoelectric actuators, each layer of the stack being able to vibrate in its own direction). The amplitude of the vibrations at the level of the punch 30 is then much greater, which allows incremental sheet forming of better quality (surface finish) and on thicker metal sheets, for the same size of tool and machine supporting the tool.

The tool body 2 may comprise at least one hole 44; in FIG. 1, the tool body 2 comprises two holes. Hole 44 is formed in a side wall of the tool body 2 and opens into housing 22. When there are several holes 44, these holes 44 may not be equally spaced on the tool body 2, so as to contribute to the asymmetry of the tool body 2, and therefore of the tool 1. In addition to the asymmetry, the hole 44 allows access to the inside of the housing 22 so that the actuator 4 can be powered. the hole 44 can also be made in the tool head 3 or in the cover 24 to allow access to the housing 22. The asymmetrical appearance of the holes 44 is particularly apparent in FIG. 3, where it is clear that they are only formed on one side of the tool. The hole also enables the heat produced by the actuator during operation to be dissipated.

Alternatively, or in combination with the hole 44, a material recess can be made in the tool body 2, also producing a dissymmetry of the tool body 2, the cover 24 or the tool head 3.

5.2 Transfer Function

The different parts of the tool 1, in particular the tool body 2, the tool head 3 and the actuator 4, can be carefully dimensioned so as not only to cause the transformation of the direction of vibration (as it propagates from the actuator 4 housed in the tool body 2 to the punch 30), but also so as to know precisely the nature (amplitude, frequency) of the vibration of the punch 30 as function of the vibrations of the actuator 4. The vibration frequency of the tool corresponds to the excitation frequency of the actuator. The excitation of the system in a given mode (i.e. at a given frequency) does not cause the excitation of other modes.

This dimensioning can be the result of a computer simulation, for example as part of computer-aided design. It is also possible to replace or complete this simulation with empirical measurements on a tool prototype. In developing the present invention, the inventors were thus able to combine these two methods (simulation and experiment) to obtain a tool with satisfactory vibration properties, particularly in terms of vibration control.

The vibration of the punch can be measured using a laser vibrometer, the reflection of which on the punch makes it possible to determine the displacement of the punch, and therefore its vibrations. This measurement of the vibration of the punch can be observed by controlling the actuator and generating a frequency sweep of the excitation of the actuator by a sinusoidal command and observing the vibratory response of the punch. The frequency of the sweep (i.e. of the sinusoidal command) can evolve linearly or logarithmically.

For example, firstly a rapid frequency sweep is carried out over the whole spectrum (for example from 1 kHz to 22 kHz), then the frequency for which the gain between the displacement measured at the end of the tool by a laser vibrometer (or acceleration by an accelerometer) and the supply voltage to the actuator (image of the force) is maximum is recovered, and which is therefore most likely to be close to a resonance frequency (i.e. an own mode of the tool).

A second, finer frequency sweep is then carried out around the maximum frequency or frequencies obtained above, which makes it possible to obtain a precise gain profile in the vicinity of the resonant frequency or frequencies.

The punch 30 can vibrate in several vibration modes: unidirectional modes (axial Z, radial X or tangential Y), or coupled modes ((X,Z), (X,Y) or (Y,Z), or (X,Y,Z)).

For a given mode, it is possible to determine (by experiment and/or simulation) the associated transfer function, i.e. the function taking as input the vibration of the actuator 4 in Z direction (amplitude, frequency) and as output the vibration of the punch 30 in this given mode (amplitude, frequency).

The tool 1 as a whole is also dimensioned so that for at least one vibration mode, its associated transfer function comprises a resonance frequency of between 5 and 30 kHz. There may be several resonance frequencies for a transfer function of a given mode, i.e. several peaks in which the energy transfer from the actuator 4 to the punch 30 is at a maximum (at least locally).

In some embodiments, the tool 1 has several transfer functions, each with its own resonance in the 5-30 kHz range. These resonances can be disjointed, i.e. when a given frequency is selected for which there is resonance in a given mode, there is no resonance in another mode. If the excitation frequency does not correspond to the specific frequency of a mode, then the vibratory response of the punch is a linear combination of all the own modes. This allows for the precise control of which resonance mode is preferred for a given incremental sheet forming process.

5.3 Preload

Reference is now made to FIG. 6 and FIG. 7.

In this embodiment, the tool 1 also comprises a shim 46 (or a set of shims) housed in the extension of the actuator in Z direction. The shim 46 exerts a preload on the actuator 4 when the housing 22 is closed. The shim 46 can be dimensioned by a suitable chain of dimensions, for example a chain of dimensions relating to the body 3, the head 2 and the cover 24 together forming the walls of the housing 22.

The shim 46 can be housed in a recess 48 formed in the cover 24 in extension of the housing 22. Here, the shim 46 is housed on the cover side 24, but the shim 46 could be arranged on the tool head 3 side. In the case of a set of shims 46, one portion of the set of shims 46 can be on the cover 24 side and another portion on the tool head 3 side. Here, the shim 46 on the cover 24 side sandwiches the interface 42 with the actuator 4.

In the example shown in FIG. 7, the set of shims comprises one shim of greater thickness and three shims of smaller thickness.

The shim 46 precisely reduces the length of the housing 22 in which the actuator 4 is housed. Thus, the shim 46 exerts a preload on the actuator 4. When this preload is sufficient, it considerably increases the efficiency of the energy transfer between the actuator 4 and the rest of the tool 1. The inventors have estimated that a preload of in the order of 80 to 85 kN is optimal for a prototype that has been developed, in order to maximise the energy transfer without damaging the actuator 4. More generally, the preload is in the order of several tens of kN to a few hundreds of kN depending on the dimensions of the prototype. This preload can also be adjusted by tightening the screws 32 to a certain torque (for example with a torque spanner) to ensure control of the screw tightening force.

5.4 Non-Axisymmetrical Head

In one embodiment, the head 3 is non-axisymmetrical with respect to the main axis 20. In the example shown in FIG. 8, the punch 30 is offset from the main axis 20. The base 32 of the head 3 is substantially axisymmetrical with respect to the main axis 20.

The dissymmetry of the head 3 means that the head 3 vibrates non-axisymmetrically when the actuator 4 produces vibrations along the main axis 20. The punch 30 can therefore vibrate transversely (radially X or tangentially Y). This makes it advantageous to install a non-axisymmetrical head 3 on a pre-existing axisymmetric tool.

The punch 30 is connected to the base 32 by a section 34 whose cross-section becomes thinner the closer it is to the punch 30. The section 34 has a smooth profile, with no edges or corners.

The asymmetry of the head 3 is compatible with the other non-axisymmetrical portions described above to constitute the transformation means.

5.5. Example of Transfer Function

Reference is now made to FIG. 9, which represents a frequency response of the tool 1, or in other words the transfer function of this tool 1.

FIG. 9 comprises three graphs, each representing a frequency response of the punch 30 (i.e. the amplitude of the vibration produced at the punch) according to the excitation frequency of the actuator, in the X, Y and Z directions respectively (from top to bottom).

The frequencies studied here vary between 4 kHz to 16 kHz, and the x-axis (which represents the frequency) is on a linear scale. The gain studied (i.e. the ratio of the amplitude of the vibration of the punch to the amplitude of the vibration generated by the actuator) is measured in dB.

In this example, the transfer function has:

• • a coupled mode (X, Y) around 4.5 kHz (with a substantially higher gain in the Y direction compared to the X direction),
  • a coupled mode (X, Y, Z) around 14 kHz, and
  • an own mode in X direction around 7.5 kHz.

With specific reference to the transfer function around 14 kHz, cf. FIG. 10 which shows this transfer function along the X, Y and Z axes around 14 kHz, it can be seen in reality that the transfer function has two very similar own modes around 14 kHz:

• • a first coupled mode 100 at around 14.2 kHz which corresponds to a resonance peak in the three directions X, Y and Z, and a second own mode 102 in Y direction at around 14 kHz. In this second resonance mode 102 the frequency responses in X and Z both show a very marked dip (and so that the punch does not vibrate; this phenomenon being known as anti-resonance and being more marked in Z direction), whereas the frequency response in Y is close to the resonance peak. The frequency response of the punch is therefore particularly “pure” in the Y direction (in other words, the punch does not vibrate in X and Z directions).

The transfer function also has a third mode 104 which is very close to the first mode 100.

Thus, in this example, the tool has simple modes of vibration (e.g. at 14 kHz in the Y direction or at 7.5 kHz in the X direction) and coupled (in X, Y and in X, Y, Z). As the transfer function is linear, it is possible to excite each of these modes independently, by superposing frequencies in the excitation of the actuator 4. In this way, the vibration produced by the punch 30 can be finely controlled by adjusting the control of the actuator 4, while maintaining a unidirectional actuator 4.