Ultrasonic Orbital Microforming—A New Possibility in the Forming of Microparts

: The demand for very small metal parts is growing rapidly due to the development of micromechanisms. In microtechnology, the dimensions of scale parts are below 1 + c mm, where c varies based on the process type. The “classic” processes usually cannot be simply scaled down, and tools require thorough structural changes. Microforming has been isolated from the area of “classic” metal forming and is governed by modiﬁed laws. The proposed new technological process ultrasonic orbital microforming (UOM) and its related phenomena are possible only on a microscale. UOM is a process that uses the broadly understood idea of orbital forging, which involves rolling on a closed road. This, however, is where the analogy ends. The UOM process uses completely different laws of physics. The process, the result of which is the axial-symmetrical micropart, consists of inducing a fast rotational movement of the billet by a punch that is vibrating at an ultrasonic frequency. The rotational speed is so fast that gyroscopic effect plays an important role. This work presents the concept of the process, preliminary research results, and their general interpretation. FEM-3d modeling of micro-orbital forming processes in geometrically similar conditions to the UOM process was also performed, obtaining shapes consistent with those obtained in the UOM.


Introduction
The twenty-first century brought an avalanche of development in microdevices applicable in almost every area of human activity (e.g., broadly understood technology, telecommunications, medicine, and defense). Microelectromechanical systems, micro-opto-electromechanical systems, microsensors, and microrobots are no longer futuristic, but reality. These devices need microparts, usually metal, and the demand for them grows rapidly. Perfectly mastered technologies for manufacturing parts on a macroscale face the challenge of reducing the size of products to the currently expected size. Such small parts must meet the requirements for dimensional accuracy and surface quality. These requirements can be met using microforming technology [1,2]. However, the direct "scaling" of this technology has encountered serious difficulties. The occurrence of the boundary size of the manufactured parts has been observed, below which the nature of physical interactions changes, and so the rules applied so far require verification. This limit size is 1 + c mm, understood as at least two dimensions of the classified object. The value of c varies depending on the type of process. As a result, a new branch of metal forming was created that deals with the production of objects that meet the above criterion: microforming technology [3,4]. Deviations from the current metal forming technological rules are called "scale or size effects" and can be applied to all the elements of the technological process. The reduction of the dimensions of the billet automatically increases the volume of the surface layer in its volume, which results in a phenomenon generally called the "surface effect". Size reduction also results in a significant deterioration of friction conditions [5][6][7][8], an increase in galling [9], and the creation of build-ups [10]. Because of this, other models of contact materials. Further miniaturization of these materials seems to be rather complicated and difficult due to complicated equipment. The process introduced in this publication does not have the above limitations. On the other hand, it can be used only for short bars and a group of products with one or both ends widened. The ultrasonic orbital microforming (UOM) process presented within this work is a new process partially based on the use of a dynamic effect. This discovery gives a new tool and thus expands the possibilities of ultrasonic-supported microprocesses. This is the first presentation of this method, which is in the development phase.

Materials and Methods
The experiment setup, seen in Figure 1, consisted of a testing machine (labeled 1), a ram (2), a force transducer (3), and a die set (4). On the lower plate of the die set, a micro-die set (5) and a camera (6) were mounted. An ultrasonic system, connected with a ram, consisted of a piezoelectric transducer (7), a booster (8), and a sonotrode (9) with a punch (10) (Figure 1c). An alternating voltage oscillating at ultrasonic frequency was applied by a separate power supply unit to the piezoelectric transducer. The booster and sonotrode worked as half-wavelength resonators, vibrating lengthwise with a standing wave at its resonant frequency. The frequency used was 20 kHz. miniaturization of these materials seems to be rather complicated and difficult due to complicated equipment. The process introduced in this publication does not have the above limitations. On the other hand, it can be used only for short bars and a group of products with one or both ends widened. The ultrasonic orbital microforming (UOM) process presented within this work is a new process partially based on the use of a dynamic effect. This discovery gives a new tool and thus expands the possibilities of ultrasonic-supported microprocesses. This is the first presentation of this method, which is in the development phase.

Materials and Methods
The experiment setup, seen in Figure 1, consisted of a testing machine (labeled 1), a ram (2), a force transducer (3), and a die set (4). On the lower plate of the die set, a micro-die set (5) and a camera (6) were mounted. An ultrasonic system, connected with a ram, consisted of a piezoelectric transducer (7), a booster (8), and a sonotrode (9) with a punch (10) (Figure 1c). An alternating voltage oscillating at ultrasonic frequency was applied by a separate power supply unit to the piezoelectric transducer. The booster and sonotrode worked as half-wavelength resonators, vibrating lengthwise with a standing wave at its resonant frequency. The frequency used was 20 kHz. The sonotrode acted as a displacement amplifier. The laser displacement transducer was used to measure the amplitude of vibrations on the face of the punch.
The course of the process and the shape of the product depend on the design of the tools, as shown in Figure 2a. This study envisaged the process of simple upsetting and the UOM process of cylindrical samples being produced in the microblanking process, with reduced clearance of a hardened aluminum sheet with a thickness of 1 mm. The sample is shown in Figure 2b. Reverse analysis in combination with FEM-2d modeling was used, to calculate parameters C and n of the yield curve (1), see Table 1. The remaining values: Young modulus-E, yield stress-Re and Poisson ratioν were adopted on the basis of the literature.
where σp is yield stress, ε is equivalent strain, and C, n are material constants. The sonotrode acted as a displacement amplifier. The laser displacement transducer was used to measure the amplitude of vibrations on the face of the punch.
The course of the process and the shape of the product depend on the design of the tools, as shown in Figure 2a. This study envisaged the process of simple upsetting and the UOM process of cylindrical samples being produced in the microblanking process, with reduced clearance of a hardened aluminum sheet with a thickness of 1 mm. The sample is shown in Figure 2b. Reverse analysis in combination with FEM-2d modeling was used, to calculate parameters C and n of the yield curve (1), see Table 1.
The remaining values: Young modulus-E, yield stress-R e and Poisson ratio-ν were adopted on the basis of the literature.
where σ p is yield stress, ε is equivalent strain, and C, n are material constants.  The processes were carried out at the stand shown in Figure 1 with the registration of process forces and video recording. Process parameters are shown in Table 2.

Results
In the upsetting conditions, without vibrations, the processes were stable and the registration of forces proceeded smoothly. The recorded sample runs are shown in Figure 3, curves a and b.  The use of the UOM process was supplemented with the limiting plate, as seen in Figure 2a, label 4. Under these conditions, various final sample heights were carried out. The results are shown  The processes were carried out at the stand shown in Figure 1 with the registration of process forces and video recording. Process parameters are shown in Table 2.

Results
In the upsetting conditions, without vibrations, the processes were stable and the registration of forces proceeded smoothly. The recorded sample runs are shown in Figure 3, curves a and b.
The processes were carried out at the stand shown in Figure 1 with the registration of process forces and video recording. Process parameters are shown in Table 2.

Results
In the upsetting conditions, without vibrations, the processes were stable and the registration of forces proceeded smoothly. The recorded sample runs are shown in Figure 3, curves a and b.
(a) (b) The use of the UOM process was supplemented with the limiting plate, as seen in Figure 2a, label 4. Under these conditions, various final sample heights were carried out. The results are shown The use of the UOM process was supplemented with the limiting plate, as seen in Figure 2a, label 4. Under these conditions, various final sample heights were carried out. The results are shown in Figure 3. Recorded process forces (with the force transducer, as seen in Figure 1a, placed "before" the ultrasonic system), should be considered unreliable due to the occurrence of the so-called dynamic effect [57,58]. Their registration and analysis were abandoned. The only example is Figure 3a, where the h curve shows the friction forces in the die set guides. The dynamic effect meant temporarily losing contact between the punch face and the sample, according to the set frequency.
The microsystem then worked in a similar way to the work of a hammer on a macroscale. The course of the process was recorded with a camera (labeled as 6 in Figure 1b). Exemplary film frames are shown in Figure 4c. in Figure 3. Recorded process forces (with the force transducer, as seen in Figure 1a, placed "before" the ultrasonic system), should be considered unreliable due to the occurrence of the so-called dynamic effect [57,58]. Their registration and analysis were abandoned. The only example is Figure  3a, where the h curve shows the friction forces in the die set guides. The dynamic effect meant temporarily losing contact between the punch face and the sample, according to the set frequency. The microsystem then worked in a similar way to the work of a hammer on a macroscale. The course of the process was recorded with a camera (labeled as 6 in Figure 1b). Exemplary film frames are shown in Figure 4c.

Discussion
To analyze the results of upsetting without vibration, static modeling FEM-3d with remeshing was used with an elastic-plastic material model with strain hardening, as seen in Table 1. Friction was specified by friction coefficient μ = 0.2. The Simufact 14 package was used with the model shown in Figure 3b.
To compare the experiment with the FEM results, "loading device" deflection was taken into account. The method of analysis is described in detail in Appendix A, but results are shown in Figure  5a. On the basis of experimental curves a and b, trend lines c and d were used to construct the modified curves e and f. These curves eliminated the influence of elastic deflection on the load system and can be compared to the g curve resulting from the FEM modeling. The compared curves f and g showed good agreement.

Discussion
To analyze the results of upsetting without vibration, static modeling FEM-3d with remeshing was used with an elastic-plastic material model with strain hardening, as seen in Table 1. Friction was specified by friction coefficient µ = 0.2. The Simufact 14 package was used with the model shown in Figure 3b.
To compare the experiment with the FEM results, "loading device" deflection was taken into account. The method of analysis is described in detail in Appendix A, but results are shown in Figure 5a. On the basis of experimental curves a and b, trend lines c and d were used to construct the modified curves e and f. These curves eliminated the influence of elastic deflection on the load system and can be compared to the g curve resulting from the FEM modeling. The compared curves f and g showed good agreement. Careful analysis of the video recording showed that during the UOM process the sample was introduced into the rotary motion as soon as the punch touched the surface of the sample. This movement then disappeared and started again after a while. This sequence was repeated several times. The spinning sample was accompanied by sound. In the pauses between the centrifugation, the sample lost contact with the punch and laid motionless on the surface of the anvil. Detailed analysis of individual recording frames is shown in Figure 6a. The film frames were chosen in such a way that they were extreme cages of two states, motion and stillness. The punch positions corresponding to them are defined as a length of the red arrows in Figure 6a. These positions in connection with the known punch velocity allowed to determine the contact times of the punch and the sample (Figure 6b).  Careful analysis of the video recording showed that during the UOM process the sample was introduced into the rotary motion as soon as the punch touched the surface of the sample. This movement then disappeared and started again after a while. This sequence was repeated several times. The spinning sample was accompanied by sound. In the pauses between the centrifugation, the sample lost contact with the punch and laid motionless on the surface of the anvil. Detailed analysis of individual recording frames is shown in Figure 6a. The film frames were chosen in such a way that they were extreme cages of two states, motion and stillness. The punch positions corresponding to them are defined as a length of the red arrows in Figure 6a. These positions in connection with the known punch velocity allowed to determine the contact times of the punch and the sample (Figure 6b). Careful analysis of the video recording showed that during the UOM process the sample was introduced into the rotary motion as soon as the punch touched the surface of the sample. This movement then disappeared and started again after a while. This sequence was repeated several times. The spinning sample was accompanied by sound. In the pauses between the centrifugation, the sample lost contact with the punch and laid motionless on the surface of the anvil. Detailed analysis of individual recording frames is shown in Figure 6a. The film frames were chosen in such a way that they were extreme cages of two states, motion and stillness. The punch positions corresponding to them are defined as a length of the red arrows in Figure 6a. These positions in connection with the known punch velocity allowed to determine the contact times of the punch and the sample (Figure 6b).
(b) (c)  The UOM deformation effect was analogous to the classic orbital forming processes, as seen in Appendix B. The FEM model used to model the simple upset was supplemented by inserting the kinematics of the punch, parameterized in accordance with Figure 7a. The movement of the punch is described by the position of points P 0 (0,0,z 0 ) and P 1 (0,0,z 1 ) in relation to the face of the punch, tilt angle γ, angular velocity ω, axial velocity V, and the curve C along which point P 1 moves according to the equation: The use of the orbital forming process in the FEM simulation for free upsetting resulted in the sample of the upset cylinder being immediately thrown out of the working space, as shown in Figure 7c in row A. This was counteracted by the use of a limiting plate. In this case, by selecting the appropriate process parameters (Table 3), it was possible to obtain the shapes of deformed specimens analogous to those obtained in the UOM process, as seen in Figure 7c in the rows B-D. This confirmed the rotational nature of the UOM process.
The UOM deformation effect was analogous to the classic orbital forming processes, as seen in Appendix B. The FEM model used to model the simple upset was supplemented by inserting the kinematics of the punch, parameterized in accordance with Figure 7a. The movement of the punch is described by the position of points P0 (0,0,z0) and P1 (0,0,z1) in relation to the face of the punch, tilt angle γ, angular velocity ω, axial velocity V, and the curve C along which point P1 moves according to the equation: The use of the orbital forming process in the FEM simulation for free upsetting resulted in the sample of the upset cylinder being immediately thrown out of the working space, as shown in Figure  7c in row A. This was counteracted by the use of a limiting plate. In this case, by selecting the appropriate process parameters (Table 3), it was possible to obtain the shapes of deformed specimens analogous to those obtained in the UOM process, as seen in Figure 7c in the rows B-D. This confirmed the rotational nature of the UOM process.  The courses of the forces of the modeled processes in relation to the force of simple upsetting are shown in Figure 7b. The orbital forming forces were definitely smaller. This was related to the contact surface of the tool, as seen in Figure 7c. The courses of the forces of the modeled processes in relation to the force of simple upsetting are shown in Figure 7b. The orbital forming forces were definitely smaller. This was related to the contact surface of the tool, as seen in Figure 7c.
Despite the convergence of the specimen's shapes, which was obtained by the FEM simulations and the UOM process, the actual UOM process was definitely different from orbital forming without punch vibration. It was unique in its nature. Its course was influenced by the conditions and the phenomena that accompany it, which are listed below:

•
The process concerned microproducts and therefore there was a very large power reserve of the oscillatory system, which caused the system not to become damped, which then changed the system's parameters during the deformation process; • The so-called "dynamic effect" was present, which meant that in the conditions of the conducted process, periodic loss of contact between the punch and the sample was possible; • Punch vibration in connection with a periodic contact with a specimen caused an acceleration in rotational motion; and • Rapid rotational motion caused a gyroscopic moment, which stabilized the position of the sample in space.
Additionally, phenomena related to contact periodicity associated with rotational motion were expected, such as:

•
Local periodic temperature increases related to friction in temporary contact areas of the tool and the sample; • Local periodic temperature increases related to the generation of heat resulting from intense periodic plastic deformation in the contact areas; • Periodic homogenization of the temperature distribution during periods of material deformation, as seen in the free stroke in Figure 6; and • Thermally and mechanically generated structural changes as part of periodic deformation.
Consequently, the UOM is a unique deformation method that most likely proceeded as explained in Figure 8 and as described below.
The process started when, after a forward movement (phase S F1 , as seen in Figure 6c), punch 1 touched the surface of specimen 2. The low misalignment of the punch and the specimen caused an asymmetrical impact that initially moved the sample to the edge of limiting plate 3. On the other hand, this hit caused local deformation of the sample, raised it gently, put it on the edge, and gave the punch a rotary motion in the direction of p with a small precession of angle γ. To be precise, the punch precession evoked and maintained a series of eccentric beats caused by periodic loss of contact associated with the ultrasonic vibrations of amplitude A us . Due to its precession at the moment of contact with the sample, the punch gave it an angular acceleration. The S UOM phase began. The lifted sample rolled on anvil 4 along path C b in the direction w b , and along path C u toward the w u on the face of the punch. This resulted in the sample rotating around its axis toward the s. Contact of the sample with the punch and the anvil was only in the C u and C b zones, and was periodically lost due to ultrasonic vibrations (dotted lines w u , w b ). Initially, there was a slip on the contact surface between the punch and the sample. This slippage decreased as the deformation progressed, resulting in an angular acceleration at each subsequent contact of the punch and sample.
The sample was accelerated in a rotary motion, and the gyroscopic effect caused an increase in w p1 to w p2 , which meant increasing deformation. At some point, the effect of accelerating the rotary motion ended. The sample lost contact with the punch, and the punch lost precession.
The S F2 phase began. Friction forces and air resistance caused the sample rotation and gyroscopic effect to disappear, causing w p3 to decrease to zero. The sample returned to its initial position on the plane of the anvil.
A free space was created between the face of the punch and the face of the lying sample. The space was caused more by the sample under UOM conditions being deformed than by the axial displacement of the punch. If a further axial movement of the punch was planned, the S F2 phase started the next cycle. The S F2 phase continued until the punch face touched the sample surface. During the deformation of the UOM, many such cycles may occur. For example, four cycles occurred in this experiment, as seen in Figure 6b UOM, the presented mechanism of deformation, is qualitatively consistent with the experiment results, but the detailed course of phenomena and their quantitative assessment require further research and analysis.

Possible Industrial Applications
The process is in the development phase. At the current stage, it is intended for the production of short axial-symmetrical bars with variable diameters. It is a process that can be further miniaturized to a degree that is so-far difficult to determine. It also allows the processing of soft materials which are difficult to machine and grind. It achieves huge plastic deformations of the ends or end of microproducts analogous to those obtained in orbital forging on a macroscale. The parameters of the process are tool geometry, the frequency and amplitude of vibrations, progressive speed of the punch, and their mutual relations in connection with the properties and geometry of the processed billet. On the one hand, the complexity of the parameters makes their proper selection difficult, but on the other hand, it gives great possibilities for the variety of the process.

•
Using microforming conditions with the use of ultrasonic vibrations, it is possible to carry out a previously unknown method of metal forming, called ultrasonic orbital microforming.

•
The UOM method leads to obtaining microproducts with shapes analogous to the products obtained at the macroscale using classic orbital forming methods, which was demonstrated by FEM modeling.

•
The mechanisms of deformation in the UOM method are fundamentally different from those occurring in orbital forming macroprocesses, and cannot occur in such processes. The main difference is the use of dynamic effects, such as the gyroscopic effect.

•
The presented UOM mechanism is qualitatively consistent with the results obtained. However, the detailed course of phenomena and their quantitative assessment requires further research and analysis. UOM, the presented mechanism of deformation, is qualitatively consistent with the experiment results, but the detailed course of phenomena and their quantitative assessment require further research and analysis.

Possible Industrial Applications
The process is in the development phase. At the current stage, it is intended for the production of short axial-symmetrical bars with variable diameters. It is a process that can be further miniaturized to a degree that is so-far difficult to determine. It also allows the processing of soft materials which are difficult to machine and grind. It achieves huge plastic deformations of the ends or end of microproducts analogous to those obtained in orbital forging on a macroscale. The parameters of the process are tool geometry, the frequency and amplitude of vibrations, progressive speed of the punch, and their mutual relations in connection with the properties and geometry of the processed billet. On the one hand, the complexity of the parameters makes their proper selection difficult, but on the other hand, it gives great possibilities for the variety of the process.

•
Using microforming conditions with the use of ultrasonic vibrations, it is possible to carry out a previously unknown method of metal forming, called ultrasonic orbital microforming.

•
The UOM method leads to obtaining microproducts with shapes analogous to the products obtained at the macroscale using classic orbital forming methods, which was demonstrated by FEM modeling.

•
The mechanisms of deformation in the UOM method are fundamentally different from those occurring in orbital forming macroprocesses, and cannot occur in such processes. The main difference is the use of dynamic effects, such as the gyroscopic effect.

•
The presented UOM mechanism is qualitatively consistent with the results obtained. However, the detailed course of phenomena and their quantitative assessment requires further research and analysis.

Conflicts of Interest:
The author declares no conflict of interest.

Appendix A. Compensation of the Elastic Deflection of the Load System
A precise comparison of the experimental recording of the process force with the result of the simulation required consideration of the correction resulting from the elastic deflection of the entire load system. This system is usually not included in the modeling. The force recording must therefore be corrected on the basis of an unloading curve: The procedure is explained in Figure A1. The local component of correction due to the elastic deflection corresponding to the point i is given by Equation (A2), where Y i is the recorded process force corresponding to point i on the unloading part of the process force, k represents the directional coefficients of the lines approximating the relief, and δx i represents the local components of correction due to elastic deflection. The elastic correction of the position of the point corresponding to the process force is equal to the sum of all components of the elastic corrections up to the considered force point, and is given by the formula where ∆x i represents the corrections of the displacement positions due to elastic deflection. The procedure is explained in Figure A1. The local component of correction due to the elastic deflection corresponding to the point i is given by Equation (A2), 1 δ , 1,2,..., .
where Yi is the recorded process force corresponding to point i on the unloading part of the process force, k represents the directional coefficients of the lines approximating the relief, and δxi represents the local components of correction due to elastic deflection. The elastic correction of the position of the point corresponding to the process force is equal to the sum of all components of the elastic corrections up to the considered force point, and is given by the formula where Δxi represents the corrections of the displacement positions due to elastic deflection. Figure A1. Modification of process force F to Fmod, meaning the reduction of elastic deflection of the load system.
The recorded process force, which is a set of measuring points after the modification consisting of taking the elastic correction into account, is transformed into a set according to the equation where F is a set of measured points and Fmod is a set of points taking into account the correction due to elastic deformations of the load system (i.e., the machine, tools, and tooling).

Appendix B. Orbital Forming
Orbital forming [59,60] is analogous to rolling along a closed path. The punch moves around the circumference, affecting only a part of the surface of the deformed product. It is an incremental process, which involves reducing the maximum process force in relation to the classical upsetting force [61]. A comparison of the classical and orbital processes is shown in Figure 1a. The recorded process force, which is a set of measuring points after the modification consisting of taking the elastic correction into account, is transformed into a set according to the equation where F is a set of measured points and F mod is a set of points taking into account the correction due to elastic deformations of the load system (i.e., the machine, tools, and tooling).

Appendix B. Orbital Forming
Orbital forming [59,60] is analogous to rolling along a closed path. The punch moves around the circumference, affecting only a part of the surface of the deformed product. It is an incremental process, which involves reducing the maximum process force in relation to the classical upsetting force [61]. A comparison of the classical and orbital processes is shown in Figure 1a.
The kinematics of presses that implement this type of process usually consist of the submission of two circular movements with independent drives [44]. Such a machine has the theoretical possibility of implementing the entire path area described by Equation (A5) and shown in Figure A2: where r is the radius of the curve and P, Q, are parameters resulting in the type of path of movement, as seen in Figure A2 [62]. where r is the radius of the curve and P, Q, are parameters resulting in the type of path of movement, as seen in Figure A2b