2. Micro Forming Processes

The laser rod end melting process consists of two stages. The first step is the thermal upset process, which generates the material accumulation at the end of the rod. Here, the energy equilibrium and the solidification influence the reproducibility and the microstructure of the preform. In the second step, die forming or rotary swaging leads to the final geometry of the part. With regard to industrial applications, the manufacturing of linked part production is also implemented.

The laser melting process can also be applied to the rim of metal sheets. Using the lateral process design, a laser beam is deflected with a defined machining depth along the rim of a thin metal sheet [Woi15], as shown in Fig. 2.11. The material starts melting and a molten drop arises which stays connected to the sheet because of surface tension. By deflecting the laser beam along the rim, more material is molten and the melt pool moves along the rim. Due to the physical dimensions of the workpiece, the rear part of the melt solidifies rapidly so that the melt pool always has a specific length which depends on the process parameters and the thickness of the sheet. In general, the process can be used to generate continuous cylindrical preforms and, thus, preforms with irregularities at sheet rims (see Fig. 2.12b) are avoided (see Fig. 2.12a).

In [Brü17], the influence of the melt pool dimensions on the continuous generation of cylindrical preforms was investigated. Here, a length-to-height ratio of \( 3.0 \pm 0.4 \) of the melt pool was achieved for a blank thickness of 0.2 mm. Furthermore, an analytical model taking into account the surface area of the melt pool not only supports this result but is also able to predict the maximum allowable melt pool length to gain a continuous cylindrical melt pool. Otherwise, instabilities occur, which are comparable to the humping effect during laser welding. In Fig. 2.13, it is apparent that the local frequency of periodical maxima in a continuous preform is influenced linearly by the laser power and by the deflection velocity for sheet thicknesses of 25 up to 100 µm. Here, a high accordance to the results of humping during laser welding by Neumann [Neu12] is viewable. This happens despite the fact that Neumann conducted experiments with a laser power in the range of some kW and much higher travel speed than used in the current rim melting experiments.

The process can also be applied to closed rims, such as voids in metal sheets. Using the results obtained for the generation of continuous cylindrical preforms, it is for example possible to generate a preform with a height of 0.4 mm at a void of a metal sheet with a thickness of 200 μm, cf. Fig. 2.14a for the simulation result. Thus, it is possible to cut a thread of M2 inside [Sch17c]. Figure 2.14b shows the corresponding scanning electron microscope (SEM) image of one thread with a thickness of 400 μm.

The wide range of possibilities for the laser-based free form heading process is appreciated, which is expanded from the rod to the metal sheet, so that more new applications can be exploited and industrial integration can be expected.

Micro rotary swaging is an incremental open die forming process to reduce the cross-section of axisymmetric workpieces. Concentrically arranged dies are oscillating with a given stroke frequency f_st and a stroke height h_T. The dies strike simultaneously on the workpiece to deform it gradually from the initial diameter d₀ to the final diameter d₁ [Kuh13]. The main components as well as the kinematics (white arrows) are presented in a front view of a rotary swaging machine in Fig. 2.15.

The nominal diameter d_nom is defined as the inside diameter of the forming zone of a closed die set. The two main variants of the process are infeed rotary swaging and plunge rotary swaging. During infeed rotary swaging the workpiece is axially fed with the feed rate v_f into the swaging unit and is reduced over a length l₀ (see Fig. 2.16a). However, during plunge rotary swaging the workpiece is processed locally as the dies are fed radially with a feed rate v_r while oscillating (see Fig. 2.16b).

Besides the presented developments in micro rotary swaging, investigations on rotary swaging by other authors were made in the macro range and focus on the workpiece properties after forming and on new applications for the process. For example, Alkhazraji et al. found that both tensile and fatigue strength are enhanced in workpieces with ultra-fine grains made by rotary swaging [Alk15]. The process was also analyzed for joining tubes [Zha14] or for plating axisymmetric metallic parts [Sch16].

With regard to high productivity in the micro range, infeed rotary swaging can already facilitate several hundred parts per minute by a continuous process, for example as a preliminary stage for extrusion [Ish18]. But there is still potential for further productivity increases. Plunge rotary swaging enables the manufacturing of variable types of geometries. However, the productivity is considerably low [Kuh09a], due to the low feed rates v_r used to prevent an undesired flow of the workpiece material into the gaps between the dies. Still, for both process variants, high productivity can be achieved by controlling the material flow and the positioning of the workpiece.

The degree of incremental deformation φ_st is a common value in rotary swaging to describe and quantify the deformation. It is defined by the initial diameter d₀ and the effective feed per stroke of the die h_st (Eq. 2.2). For infeed rotary swaging h_st equals the axial workpiece feed per stroke l_st, which itself depends on the die angle α and on the ratio of the workpiece feed rate v_f, over the stroke frequency f_st (Eq. 2.3). For plunge rotary swaging, h_st depends on the ratio of the feed rate of the dies v_r over the stroke frequency f_st Eq. 2.4.

The previous equations show that the degree of incremental deformation φ_st does not consider the final diameter d₁. However, this parameter is involved in the volume per stroke V_st, which represents the material volume formed by the dies at each stroke. For an idealized forming, V_st for infeed rotary swaging can be determined with Eq. 2.5 and for plunge rotary swaging with Eq. 2.6. For plunge rotary swaging the deformed volume of the workpiece is assumed to have a cylindrical shape. In Eq. 2.6 k stands for k-th incremental step.

In order to improve the micro rotary swaging process, it is necessary to understand and control the material flow. Three methods to improve the rotary swaging in the micro range based on the material flow control are presented. In infeed swaging a higher axial feed rate is enabled by using an adjusted workpiece clamping [Mou18a]. In plunge rotary swaging the application of an elastic tube prevents flash formation [Mou15b, Mou15b] and with the application of external axial forces the part geometry can be controlled [Mou18b].

During micro rotary swaging different limitations to the process occur [Kuh08a]. Furthermore, process parameters like the workpiece material, the die geometry, and the tribological conditions influence these limitations.

Typical limitations of the process can be divided into two categories (see Fig. 2.17). The limitations in the first category lead to a termination of the process. These are bending, torsion or breaking of the workpiece. The limitations in the second category are those that affect the workpiece quality. Examples are flashes, high surface roughness [Wil13] and shape deviation [Kuh09b]. A guiding element with a hole slightly larger than d₁ for the workpiece at the inlet in the swaging head is used to prevent premature limitations due, for example, to vibrations occurring in the process [Wil15]. Furthermore, the use of a guiding element, which is necessary and specific for the micro range, reduces the risk of the workpiece getting into the tool gap during the process and thus enables the application of higher strokes.

During rotary swaging material flow takes place predominantly in the axial and radial directions. The axial material flow occurs in both the positive and negative directions. Higher material flow against the axial feed direction induces an axial load that bends the workpiece when the critical bending load F_b,crit. is reached. This is a specific problem in micro rotary swaging due to the low stiffness of the slim workpieces. The application of a guiding channel for the workpiece minimizes the risk of bending.

Depending on the workpiece material and the diameter reduction, different maximal feed rates can be applied. Infeed rotary swaging experiments with three materials (AISI 304 steel, Cu-ETP, Al99.5) were carried out and the maximum feed rate with which 5 samples could be processed without process failure was determined. Workpieces with an initial diameter d₀ = 1.0 mm and a length of 110 mm were reduced by different tool sets with nominal diameters of 0.3, 0.4 and 0.5 [Kuh08b].

Forming was possible within a larger window of feed rate and thus higher V_st for materials with higher Young’s modulus (see Fig. 2.18). Forming with feed rates above the boundary (lines) for the specific material will lead to failure on the workpiece. From the failures in Fig. 2.17, predominantly bending and torsion occur in infeed rotary swaging.

The tribological conditions and the workpiece material influence the material flow. Especially in micro rotary swaging, due to the slim workpieces, the surface- to-volume ratio is very high, whereby the tribological conditions have a strong influence. During infeed rotary swaging of workpieces from alloy 304 and from Al99.5 with and without lubrication of the workpiece, opposite behaviors of the achievable feed rate are observed [Kuh12b]. While under the dry condition (without lubrication) lower axial feed rates than with lubricant can be achieved for alloy 304, the forming of Al99.5 at higher true strain becomes possible without lubricant. In some cases, Al99.5 rods can be formed only without lubricant, i.e. a reduction from d₀ = 1.5 mm to d₁ = 0.5 mm and even to 0.4 mm.

However, during forming of aluminum without lubricant, adhesive wear can occur on the tools due to the affinity between the workpiece and tool material. By using tools with amorphous diamond-like carbon coatings, adhesive wear can be avoided and the tool life considerably increased. The tools were coated using magnetron sputtering. Pin-on-disk tests have shown that such coating results in a considerable reduction of friction and wear against aluminum.

For high volume per stroke V_st, inadequate material flow in the radial direction can lead to flashes on the workpiece. Because the material cannot flow completely in the axial direction, the generated surplus flows against the direction of the closing motion of the dies, which means into the gaps between the dies. This can be observed both in infeed rotary swaging and in plunge rotary swaging. Furthermore, the inadequate material flow can cause inaccurate geometries (incomplete filling of cavities or asymmetry) or destroy the workpiece irreversibly.

Using the finite element method (FEM), the material flow during the process is investigated. Two-dimensional axisymmetric simulations are commonly used to simulate rotary swaging [Gha08]. The model for infeed rotary swaging consists of two parts: the workpiece (deformable) and the die (rigid) [Mou14a].

One approach to characterize the material flow in rotary swaging is by analyzing the behavior of the neutral zone (NZ). The NZ represents an area in the region of the workpiece being deformed in which the workpiece material features no flow in the axial direction. A position closer to the initial diameter means a higher material flow in the direction of the feed motion. The location of NZ can vary due to the tribology. With a higher friction coefficient, the position of the NZ is shifting in the direction against the feed motion (−z) [Ron06]. Furthermore, the NZ is influenced by v_f as well other process settings, like the final diameter. It was found that the NZ changes its position as well as its shape during a single stroke (see Fig. 2.28). The gray area of the workpiece represents the material flowing against the feed direction, the bright area the material flowing in the feed direction and the boundary between both is the NZ. By an increase of the coefficient of friction value µ, the material flow in the feed direction within one stroke seems to increase. In order to analyze the NZ, a stroke was divided into many small and constant time steps. The number of detected NZ was found not to be equal to the number of time steps but to vary with the friction, the strain and the feed rate. The number of NZ increased with µ and furthermore a shift of the NZ in the negative z-direction was noticed (see Fig. 2.28a and b). The increased number of NZ is a sign of more internal deformation. As the NZ shape can change from concave to convex, the internal deformations are cyclic. Less material flow against the feed direction was observed in experiments without lubricant and thus with higher friction coefficients as in the FEM (see Sect. 2.3.2). For higher axial feed rates a similar trend to that for higher friction was observed, which can be explained by the higher volume per stroke which is deformed (see Fig. 2.28b and c) [Mou14a]. From these results, the improvement of the feed rate and strain range in the forming of the Al99.5 without lubricant can be attributed to the material flow, and more precisely the behavior of the neutral zone.

A further method to characterize the material flow dependent on the process parameters is the history of the plastic strain development. The plastic strain at the outer region of the workpiece is more sensitive to the friction coefficient value (see Fig. 2.29). This can also be seen at the NZ, since the shape is more curved at the surface for higher friction coefficients. But compared to rotary swaged rods in the macro range, at which only the outer 20% of the diameter is sensitive to friction [Liu17], in the micro range the PEEQ (plastic strain) is influenced over almost the complete radius. This can be explained by the small cross-section of the workpieces in which the surface to volume ratio is very high, thus the tribological conditions have a stronger influence.

The interaction between the dies and the workpiece during forming leads to material modifications, such as in the mechanical properties and the microstructure. Figure 2.30 presents the Martens hardness in five different regions along a deformed workpiece of alloy 304. The scatter of the Martens hardness after forming (regions I to IV and beginning of V) reaches up to 250 N/mm² compared to about 160 N/mm² before forming (end of region V). The high scatter occurred because of the inhomogeneity of the microstructure (soft austenite and hard strain-induced martensite) and also the distribution of the hardness across the diameter, as can be seen in detail in Fig. 2.30, where three hardness profiles in region II across the diameter [−r, +r] are presented. The observed distributions reflect inhomogeneous work hardening through the diameter.

Workpieces of AISI 304 steel after rotary swaging present a strong hardening, as the yield strength increases significantly (Fig. 2.31). This increase is generally attributed to work hardening during cold forming. However, further specific phenomena like phase transition as well as dynamic effects influence the development of the material properties.

As is known for AISI 304 steel, martensite usually develops during cold forming. Using a Fischerscope MMS PC that works according to the magnetic induction method, the martensite content can be estimated (Fig. 2.31). The development of martensite with regard to the feed rate in the presented case can be approximated by Eq. 2.7. The equation is derived from the profile in Fig. 2.31.

α_M is high for low v_f and decreases when v_f increases. As the workpieces have the same initial diameter and nominal true strain, this behavior can be attributed to the number of strokes experienced by the workpiece and to an adiabatic heating during forming. At each stroke, new volume fractions of austenite are transformed into martensite, hence more martensite is present at low feed rates. When the feed rate increases, the deformed volume at each stroke also increases, which means the deformation work is higher. As a result, the workpiece temperature increases and the martensitic transformation is reduced. The yield strength, determined by tensile testing, is also high for workpieces manufactured at low feed rates and decreases almost linearly for the feed rate range between 2 and 8 mm/s. While the amount of martensite is reduced from 60 to 10%, the yield strength is reduced only by about 30% within the investigated feed rate range. Therefore, the martensite-induced transformation in micro rotary swaging is sensitive to feed rate changes.

Micro rotary swaging is an eligible convenient process when parts with high strength and high surface quality are needed [Mou14b]. Due to its incremental characteristic, it allows larger cross-section reductions compared to other forming processes. Moreover, not only rotationally symmetrical cross-sections are possible but also polygons. The smaller dimensions of the workpiece compared to the dimensions of available machines open new possibilities for adjusting rotary swaging for micro rotary swaging. Besides the manufacturing in linked parts (Sect. 2.3.2) several workpieces can be formed at the same time (multi-forming) with adequate die geometries. Figure 2.32 presents examples of micro parts generated by micro rotary swaging.

Important factors for generating good parts in micro rotary swaging are a deep understanding of the flow behavior of dissimilar (a) or similar (b) materials; the control of the relative motion between the workpiece and the dies (b), (c); the control of the positioning in process and the tool design (e). The part (a) in Fig. 2.32 shows a composite component made of two different materials (copper in the core, and AISI 304 steel as shell) by infeed rotary swaging [Kuh10]. The softer material in the core guarantees a tight connection of the two components [Kuh12a]. Part (d) was made by joining two rods [Mou14c] in plunge rotary swaging, using a tube as the connecting component. In both cases (a) and (d), the connection between the joining partners can be a form and a force fit. The correct relative rotational motion between the workpiece and the dies not only allows further material modifications (Sect. 2.4) but also leads to more possible geometry variations. For (b) and (c) this relative rotation was kept to zero and the calibration zones of the dies were flat. Using a mandrel with tubes, polygons like (c) can be manufactured. In (e) nine notches (depth 0.25 mm) manufactured in three steps are presented. Because the notches are small the feed rates remain the same for one or more elements when manufactured at the same time, but the productivity is increased with regard to the number of geometries designed in the die.

By the control of the material flow in micro rotary swaging with different measures, the process can be improved in the sense of productivity, the accuracy of the final product or even material modifications. Using a spring-loaded clamping device, the axial material flow in infeed rotary swaging can be controlled and thus enables about four times higher axial feed rates. With intermediate elements around the workpiece in plunge rotary swaging, an undesired radial material flow into the gaps between the dies can be prevented and, as a result, the radial feed rate can be significantly increased. Furthermore, external forces applied on one or both ends of the workpiece allow the material shift to be guided, thus the final geometry of the product can be influenced.

In infeed rotary swaging, the final diameter can be constant or have a profile over the workpiece length, depending on the feed rate used. For low feed rates, the generated diameter is closer to the nominal diameter of the dies d_nom and is constant along the workpiece length, besides the tip. At high feed rates, an inhomogeneity of the diameter over the total part length is produced. The diameter increases with the feed rate and from the tip to the end of the deformed part. The diameter increase can be explained by the machine resilience, which leads to an incomplete closing of the dies during the forming with high feed rates as in the idle state. However, the rising value of the final diameter over the length of the workpiece can be overcome by using another machine with less resilience or by controlling the position of the dies by adding a radial feed during the infeed process.

In plunge micro rotary swaging, intermediate elements around the workpiece enable up to three times higher radial feed rates v_r compared to forming without these elements. This is because flashes on the workpiece can be prevented. However, the final diameter increases slightly, which depends on the stiffness of the elastic intermediate element, with bigger diameters for harder elements. This fact has to be considered during the die design.

A further approach to control the material flow during plunge rotary swaging involves the external forces at the workpiece ends. The material flow reacts very sensitively to these. Low forces at one side can direct the material flow so that it occurs in a preferred direction. A symmetrical material flow is possible if equal external axial forces are applied on both sides of the forming zone. Thus, the final shape of the workpiece can be controlled.

For the process and especially for the material flow in micro rotary swaging, specific micro effects have to be considered. The first particularity are the slim workpieces, which tend to bend, break or even get into the die gaps, so a guiding element needs to be applied during forming. Furthermore, the surface-to-volume ratio is much higher and for that reason the friction condition has a greater effect on the process. The friction influences, for example, the plastic strain in a thicker area from the surface of the workpiece. In addition, the feasible axial feed rates reach such high values that the feed length during one stroke exceeds the workpiece’s initial diameter. For this reason, the radial forces are high and the outer ring of the swaging head expands, which leads to an inhomogeneous diameter evolution. The previous results present the potential of rotary swaging for micro manufacturing.

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Cold forming of complex workpieces is usually accompanied by work hardening and is usually realized by multi-stage forming processes. In addition, difficult to form materials have to be annealed between the forming steps due to the strain hardening. This heat treatment contributes to a substantial rise of costs for equipment and energy supply. One possibility to avoid this intermediate heat treatment and to improve the formability of the workpieces is a targeted conditioning of the workpieces for further forming. This conditioning includes adjusting the forming characteristics of the workpiece, the geometry (diameter) and the surface (roughness, lubrication pockets). Very good formability with such characteristics as good strength in combination with a sufficient ductility provide ultrafine-grained (UFG) materials. Refining of materials can be generated by applying severe plastic shear deformation, e.g. by pressing the workpiece into a die with an angular channel [Val00]. Further improvement of the forming process can be achieved by reducing the friction between the workpiece and the forming die. This can be realized, for example, by modifying the profile and the surface topology of the blanks [Ish17a].

Micro infeed rotary swaging not only changes the geometry and the surface of the swaged parts, but also influences the microstructure and, thus, the mechanical properties of swaged workpieces. Due to the special adjustments of the machine, it was possible to vary the produced diameter [Kuh13] and the roughness of the swaged parts [Ish15c]. Moumi et al. investigated the change of the microstructure after rotary swaging depending on the feed velocity as well as the increase or decrease of the martensite content with the variation of the forming temperature [Mou15a]. They deduced that rotary swaging could provide the opportunity to adjust the forming characteristics of the workpieces for further forming steps [Ish15a]. However, the process was to be enhanced in terms of tool geometry and process kinematics.

The analysis of the characterization curves reflected the possibility of conditioning of part properties by means of modifications in rotary swaging. The influence of the modifications in the swaging die design on the extrusion force is shown in Fig. 2.38. The stroke s of the pressing punch varied with the actual initial length of the samples. Curve NS represents the unswaged material during extrusion. The analysis revealed that rotary swaging with curve shaped dies increased the required extrusion force (curve I above curve NS). In contrast, using flat-shaped and double-flat-shaped dies decreased the required forces significantly (curves II and III are below curve NS). This difference can be explained by various aspects, for example a change of the microstructure, a reduction of the grain size or martensite and carbide formation [Ish17b].

The microstructures are shown in Fig. 2.39. Independent of the die design, a clear grain refinement in the radial direction resulted from the swaging process. However,, the grain boundaries after swaging with curve-shaped dies (Fig. 2.39b) were more easily detectable than after swaging with flat- or double-flat-shaped dies (see Fig. 2.39c and d).

Another aspect is the roughness and the topology of the surface. The surface roughness of the initial stage samples revealed a value of S_a = 0.92 ± 0.16 μm. The geometry (cross-section) of swaged stainless steel (alloy AISI304) specimens using the curve-shaped dies as well as the flat- or double-flat-shaped dies featured a circular geometry. However, the value of surface roughness S_a of the latter two grew to S_a = 1.50 ± 0.35 μm and S_a = 1.11 ± 0.61 μm compared to the conventional swaged workpieces with S_a = 0.41 ± 0.05 μm (settings II, III and I). Hence, the workpieces swaged with curve-shaped dies tended to provide smoother surfaces, but the flat- or double-flat-shaped dies promoted pocket formation on the sample surface. Consequently, different die designs, curved or flat, led to significantly different forming properties [Ish18].

Although flat-shaped dies allow a significant reduction of the yield stress [Ish17b, Ish15a] and work hardening, an increase of feed velocity from v_f = 1 mm/s (settings I and II) to v_f = 2 mm/s (settings I-a and II-a) decreased this improvement. The required extrusion force increased when forming with flat-shaped dies (curve II-a higher than curve II) (Fig. 2.40), while the feed velocity did not affect the extrusion force when using curve-shaped dies (curve I equals curve I-a).

The roughness of the workpieces swaged with flat-shaped dies was influenced by the feed velocity v_f as well (decreased to S_a = 0.94 ± 0.23 μm), while swaging with curve-shaped dies at a higher feed velocity v_f = 2 mm/s changed this insignificantly (S_a = 0.58 ± 0.18 μm) (Fig. 2.41).

These results correspond to the martensite content, which was more influenced by the feed velocity if flat-shaped dies were applied [Ish17b]. Additionally, the number of strokes was higher with lower feed velocity. The number of strokes influenced the cross-sectional shape more when using flat-shaped dies, due to the pockets on the surface (see Fig. 2.45). The microstructure was refined more by the higher degree of shear strain [Ish15a].

Another major influence on the extrusion characteristics was the modification of the process kinematics. The use of the eccentric flat-shaped dies changed the process kinematics by means of radial displacement of the center-line during the process and thus resulted in a higher shear strain. Due to a significant reduction of the grain size and the martensite content compared to the rotary swaging using double-flat-shaped dies [Ish17b], a reduction of the required press force during extrusion could be observed (Fig. 2.41, curve IV below curve III).

Eccentric rotary swaging influenced also the development of the microstructure. As a result, the transformed martensite showed a strong reduction compared to the amount of martensite after conventional rotary swaging. Thus, pre-forming of the workpieces in this special way affected work softening, reduction of yield stress, and increase of the plastic strain [Ish17b]. The grain boundaries were detectable in the core area of the processed workpieces while they were not visible any more in the outer regions (Fig. 2.42b). Furthermore, the specimens exhibited typical eddy patterns and a spiral grain orientation, which were more pronounced with a feed velocity of v_f = 2 mm/s (setting IV-a) (see Fig. 2.42c). Moreover, the shape of these workpieces was a polygon with eight corners. Using this method, the surface roughness was also influenced by the feed velocity. The workpieces swaged at a feed velocity of v_f = 1 mm/s (setting IV) featured a roughness of S_a = 1.09 ± 0.26 μm, which rose at the increased feed velocity of v_f = 2 mm/s (setting IV-a) to a value of S_a = 1.36 ± 0.48 μm.

A variation of the stroke-following angle ∆ϕ allowed the production of parts with polygonal geometries. The shape of the conventional swaged workpieces using curve-shaped dies was actually circular. The usage of flat-shaped dies or double-flat-shaped dies in combination with the targeted adjustment of the stroke-following angle ∆ϕ delivered polygonally shaped parts with several facets. The shaping correlates to Eq. 2.9, where n is the number of corners:

With the increasing number of facets the characterization curves became flatter (Fig. 2.43).

In dependence on the stroke-following angle ∆ϕ, not only the microstructure but also the surface roughness was influenced. A stroke-following angle ∆ϕ = 60° (setting III-a) delivered a hexagon (see Fig. 2.44a), with a surface roughness of S_a = 0.45 ± 0.16 μm. The round shaped workpieces formed by ∆ϕ = 51° (setting III-b) featured the highest surface roughness value for these experiments with S_a = 0.72 ± 0.26 μm. Workpieces swaged by ∆ϕ = 40° (setting III-c) developed the shape of a nonagon (see Fig. 2.44c), and a surface roughness of S_a = 0.66 ± 0.36 μm. All dodecagons were swaged by ∆ϕ = 30° (setting III-d) (see Fig. 2.44d), and had a roughness of S_a = 0.53 ± 0.17 μm.

The workpieces swaged with curve-shaped dies revealed a circular cross-section and a smooth surface (Fig. 2.45a). Swaging with the stroke-following angle of Δϕ = 51° (non-rotating workpiece, setting III-b) using double-flat-shaped dies led also to a round geometry (Fig. 2.44b), but many small bevels (see Fig. 2.45b), which are dependent on the feed velocity v_f. The swaging dies did not strike along the same line of the workpiece any more and the resulting shape formed was not a polygon. The surface roughness increased to the value of S_a = 0.72 ± 0.26 μm.

Deep drawing is a well-suited technology to produce such parts due to its excellent qualities for mass production. However, the downscaling of the forming process leads to new challenges in tooling and process design. Cheng et al. investigated how the interaction of free surface roughening and the size effect affect the micro-scale forming limit curve [Che17]. They modified the original Marciniak-Kuczynski model by introducing free surface roughening to describe the decrease of the micro-scale forming limit curve as a result of the geometry and grain size effects.

Saotome et al. showed that the process window decreases with increasing ratio between the punch diameter and sheet thickness when thin foils are used [Sao90]. In preparation for the deep drawing process, Gau et al. expanded the process window for forming micro cups with cup height to outer diameter ratios by annealing stainless steel 304 sheets at temperatures not less than 900 °C for more than 3 min  [Gau13]. In 2014, a novel technique in micro sheet metal forming was presented by Irthiea et al. [Irt14]. They used a flexible die to produce micro metal cups from stainless steel 304 foils. The die consisted of a cylindrical tank filled with a rubber pad. Forming parameters like anisotropy of SS 304 material and friction conditions at various contact interfaces were investigated experimentally as well as in simulation with this setup.

Messner et al. demonstrated that increasing punch forces can be expected in the micro range due to increasing friction [Mes94]. Furthermore, Michel et al. showed that the yield point and stress decrease with decreasing foil thickness [Mic03]. Besides material and friction, the geometry of the forming tools has a significant impact on the process forces, stress states and the process window of the deep drawing process.

Aminzahed et al. present in [Ami17] a piezoelectric actuator as a new approach in a deep drawing operation to draw rectangular foils. They also studied blank holder effects on thickness distributions, punch force and spring-back and used experiments and simulations to obtain results.

Wagner et al. demonstrated that the punch radius has a significant influence on the process force and that higher punch radii are beneficial for the process [Wag05]. Thus, the quality of the produced parts depends on the choice of suitable geometric parameters of the forming tools. In conventional deep drawing processes, manufacturing deviation in the sub-millimetre range in tooling do not affect the deep drawing process since these deviations are neglectable in size compared to the dimensions of the tools. Moreover, small deviations are compensated by the formability of the workpiece material. Due to size effects, the tribology changes in the micro range, which leads to smaller process windows in micro deep drawing [Vol09]. If scaled down, the deep drawing process becomes more sensitive to process deviations. This is due to the relative deviations of the tool geometry, caused in tool manufacture. These increase with decreasing size in the micro range because the accuracy of manufacturing reaches its limits [Hu09]. Figure 2.46 illustrates the effect of larger relative manufacturing deviations in the micro range. Due to these effects, micro forming processes cannot be simply transferred to the micro range and further investigation is needed. Therefore, the aim of this study is to determine the influence of tool geometry on micro forming processes to allow a specific process design and improved process stability as well as a quantitative assessment of the effect of wear- and production-related deviations of tool geometry.

For the deep drawing experiments described in this investigation, blanks were cut out using a picosecond pulsed laser with a wavelength of 1030 nm in order to prevent burr formation at the edge of the blank. The diameters were checked with a Keyence VHX 1000 digital microscope. For the tools, ledeburitic powder-metallurgical steel 1.2379 (X153CrMoV12) was used. The relevant geometric parameters of the tools used in the experiment were measured using a laser scanning microscope Keyence VK 9700. The drawing process was carried out on a single-axis micro forming press with a maximum punch force of 500 N and a constant punch velocity of 10 mm/s using HBO 947/11 as lubricant. The punch force was measured with a Kistler 9217A piezo load cell with an accuracy of 0.01 N. The punch stroke was measured with a Heidenhain LS477 linear scale with an accuracy of 1 μm. The press was driven by a servo motor controlled by a NI 9514 servo drive interface. The blank holder acts passively. It uses its own weight and is supported by two springs. The blank holder pressure can be adjusted by changing the spring tension. The blank positioning was realized by an automated positioning system. The blank was positioned with a pneumatic gripper that is driven by a linear direct drive cross table. The position of the blank was then measured using an Allied Vision G 917 B monochrome CCD camera with a resolution of 9 MP equipped with a telecentric lens with built-in coaxial illumination and a magnification of 0.75. With this setup the blanks can be positioned within a radius of 10 µm from the center of the drawing die.

The Finite Element Method (FEM) is a proven tool for routine calculation tasks and is used in plant and mechanical engineering as well as in vehicle construction. This method enables largely realistic statements in the stages of concept finding and the development of components and structures using computer-assisted simulations of physical properties. This results in a significant reduction of product development time [Kle15]. For FEM analysis, the software Abaqus 6.14 was used. A 3-dimensional model for micro deep drawing was used. All tools are defined as analytical rigid shell objects and the blank was defined as a deformable body using the 8-node linear brick 3D-stress element C3D8R for the mesh. Within the sheet thickness four elements were used. In order to save computational time, only one half of the blank was considered. For the elastic plastic material model of the foil, tensile tests were performed to determine the required flow stress curves.

The punch force presents an important parameter to assess the process stability of deep drawing processes. In [Beh13] the influence of variation of the tool geometry on the punch force is given. By using experimental data and FEM simulation, each geometry variation is classified regarding its impact on the punch force and therefore on the process stability, as shown in Fig. 2.47.

Figure 2.47 shows that the change of punch diameter and drawing gap resulted in the greatest impact on the punch force and therefore should be carefully controlled during tool manufacturing. Changes in the punch radius, drawing die radius and edge shape, on the other hand, proved to be of minor importance.

The limiting drawing ratio LDR describes the maximum value of the drawing ratio that can be achieved under the given process conditions. A larger achievable LDR acts as an indicator of a more stable deep drawing process and therefore makes it attractive for industrial use. In [Beh16] the influence of the blank material and tool geometry variation on the LDR is described. It is shown that, regardless of the tool geometry, the austenitic steel 1.4301 enables the largest process window compared to the foil materials Al99.5 and E-Cu58, and therefore proves to be most stable in micro deep drawing processes, as shown in Fig. 2.48.

For all the materials used, the die clearance and die radius have the biggest influence on the LDR. While the die radius should be increased, a decrease of the drawing clearance below 1.25 times the foil thickness is beneficial to the drawing process.

The investigation of the influence of a tool geometry deviation on the part geometry is mentioned in [Hei17]. In this case, the influence of an uneven drawing radius deviation was investigated for different drawing ratios using experimental data and FEM simulation. The deviation of the die radius is described by the ratio of curvature (ROC), which is defined as the ratio between the maximum and minimum curvature of the die edge. This sort of variation has a significant influence on the part shape, resulting in uneven cup height after the drawing process due to stronger stretching of the cup wall at positions with a smaller die radius. This effect increases with higher drawing ratios. Furthermore, it is shown that by using FEM simulation an initial blank displacement sufficient to result in an even cup height can be found. However, the effect of an uneven drawing radius cannot be compensated entirely. While an appropriate blank displacement results in an even cup height when an uneven drawing radius is used, a significant difference in strain remains in the part, as shown in Fig. 2.49. This is explained by the different mechanisms that result in an uneven cup geometry. While blank displacement leads to material surplus on one side of the cup, an unsymmetrical radius deviation on the other hand generates uneven stretching of the cup wall. It can be concluded that the effect of an uneven radius geometry proves to be of major importance to produce accurately shaped micro cups.

The investigation of the interactions between individual sub-processes in multi-staged micro deep drawing and their impact on the overall process is time-consuming and cost-intensive when done only experimentally. Thus, a simulation model of a two-stage micro deep drawing process is developed in  [Tet15] and showed that this model can display the first and second stroke in one forming simulation in accordance with the experiments conducted. Figure 2.50 shows the overview of the two-stage micro deep drawing process simulation model. It consists of two pairs of dies and punches with different diameters and a blank holder impinging the blank with pressure. After the first stroke, the second punch clamps the cup on the radius of the second die while the first punch and die move backwards. Then, the second punch with a smaller diameter starts moving, which draws the first cup into the second die, which results in a second cup with a smaller diameter and higher cup walls.

This model is the basis for further investigations with two-stage simulation models with varied tool geometries. This enables an identification of the influence of opportune or inopportune in series connected tool geometry. The investigated characteristics are the curvature of the rib, the mean wall thickness alteration and the maximum punch force. The geometry is varied in the range of ±3.5% around the initial tool geometry to investigate these influences. This variation represents unpreventable deviations that occur when fabricating real tools. It also makes it possible to use a maximum and minimum tool geometry in the simulation model. Hence, these options are expressed in two adjustments. On the one hand, (+) expresses the positive deviation of +3.5% to larger tool dimensions from the initial tool geometry, while (−) represents the negative deviation of −3.5% to lower dimensions. For example, a die with smaller dimensions (−) than the ideal is used in the first stroke and combined with a die with greater dimensions (+) than the ideal during the second stroke. As identified in [Beh13], the drawing gap variation has a significant influence on the punch force. Consequently, the punch diameter is held constant while the drawing gap is varied by using the two mentioned adjustments for the die diameters during the simulative investigations. Moreover, the die radius is varied in the same range as the diameter.

The first characteristic is the curvature γ along the cup wall. The curvature is a result that can be found in both the simulation and experiment and results from an oversized drawing gap [Klo06]. It describes lip forming and bulge at the rib of a cup, which are defects along the cup wall and thus criteria for whether a cup is usable or not. This curvature is the maximum distance between a tangent and a point A. Both are located at the outer cup wall. The tangent goes through two points that mark the two local maximum peaks given by the lip forming and the rib of the cup wall. The point A is between these two peaks and marks the local minimum of the cup’s wall topography. Figure 2.51 gives a pictorial representation of the curvature.

The influence of the adjustment of the first and second die diameters on the curvature γ is shown in Fig. 2.52. The abscissa labels the die diameter deviation from the ideal geometry for a minimum (−) and maximum value (+), while the ordinate displays the curvature in µm. Furthermore, the main influence of the adjustment of D₂ on γ is represented by a black dotted line. The main influence of D₂ means that the influence of the adjustment of D₁ on γ is not considered. Two courses happen and show that a large die diameter in the first stroke and a large one in the second stroke reduce the curvature. For an explanation, it is important to differentiate between the outer and inner cup wall. A close look at these two sides reveals that the second stroke relocates the curvature from the outer to the inner wall. Responsible for this is the second die radius, which shifts the curvature to the inner wall by straightening the outer. The greater the curvature is after the first stroke, the better this mechanism works. If the curvature is low after the first stroke, this mechanism does not occur and the measured curvature after the second stroke gets worse.

Another deep drawing quality feature is a homogeneous wall thickness over the entire cup wall. As a measure for this, the mean wall thickness alteration Δ is used. The development is shown in dependency on the adjustment of die diameter D₁ in Fig. 2.53. As in Fig. 2.52, the abscissa labels the die diameter deviation from the ideal geometry for a minimum (−) and maximum value (+), while the ordinate displays the mean wall thickness alteration in µm. Furthermore, the main influence of the adjustment of D₂ on Δ is represented by a black dotted line. It can be seen that the mean wall thickness alteration is held almost constant by choosing a small diameter D₁ in the first deep drawing step and a small D₂ in the second one. Choosing a small die diameter leads to small drawing gaps in both deep drawing steps. The small drawing gap effects a levelling on deviations of the large wall thickness. Especially in the area of the punch radius at the cup wall, a thinner wall can be found. Otherwise, the wall thickness increases at the end of the rib due to the missing influence of the blank holder when the blank emerges under it. Between those zones, the cup wall thickness is in the range of the initial blank thickness. If this maximum deviation is reduced by applying a large die diameter in the second stroke, the smaller drawing gap reduces the mean wall thickness alteration and improves the homogeneity of the wall thickness distribution. Nevertheless, a small thickness deviation remains due to the drawing gap being larger than the blank thickness, leaving enough space for minimum alterations to occur.

The punch force is one of the most important considerations in metal forming. This force correlates with the tool wear, surface quality and the parameters of the conferred forces [Beh13]. Therefore, the influence of the adjustment of die diameter D₂ on the maximum punch force F_p,max is shown in Fig. 2.54. As in Fig. 2.52 the abscissa labels the die diameter deviation from the ideal geometry for a minimum (−) and maximum value (+), while the ordinate displays the maximum punch force in N. Furthermore, the main influence of the adjustment of D₂ on F_{p, max} is represented by a black dotted line. The diagram shows that a large diameter D₁ in the first stroke as well as a large diameter D₂ in the second stroke lead to stronger decreasing maximum punch forces than choosing a small D₁ and a large D₂. The decrease in the force is due to the reduced contact between the tools and workpiece. This contact does not only appear among the radii of the die and punch and the blank, but it also counts for the inner walls of the die and the blank. Contact connected with relative movement between a contact pair is always accompanied by friction. In the micro range, the punch force is affected by friction between the tool and workpiece [Beh13]. Therefore, a large diameter D₂ decreases the punch force, because it leaves enough space for the blank to avoid contact with the inner die walls. Additionally, a larger diameter D₂ reduces the contact pressure between the blank and die radius. This pressure arises from the contact conditions between the die radius and blank, ending in greater friction. And finally, a lower drawing ratio decreases the punch force. The maximum punch forces for the second stroke in dependency on D₁ differ strongly, because of the remaining stresses in the cup wall. A smaller D₁ causes greater stresses than a larger D_1. The punch must additionally overcome more stress during the second stroke. This increases the maximum punch force.

Compared to deep drawing of circular parts, there is a significant increase in complexity when rectangular parts are formed. As additional steps such as handling, or trimming become increasingly difficult when scaling processes to the micro range, it was the aim to produce accurately shaped parts only through deep drawing. A commonly used method to achieve near net shaped parts in deep drawing is blank shape optimization. However, due to size effects this method cannot be transferred unadjusted for the optimization of micro deep drawing processes. For example, there is a significant increase in friction with decreasing process dimensions. This effect has a fundamental influence on the shape of the final deep drawn part. In [Hu11] it is shown that, if the material model and friction coefficient are adjusted to the actual condition in the micro range, it is possible to determine the optimal blank shape in a size-dependent FEM simulation and accordingly produce near net shaped parts in rectangular micro deep drawing, as shown in Fig. 2.55.

Furthermore, the work carried out showed that material characteristics are even more important than friction and that the results of the FEM simulation are in good agreement with experimental findings. Using Al99.5, rectangular parts with no remaining flange can be formed. In [Hu11] these findings can be transferred to blanks made of E-Cu58 and 1.4301. The influence of tool geometry deviation on the punch force in rectangular micro deep drawing has been investigated in Behrens et al. [Beh15]. It is demonstrated that increasing the corner radius or decreasing the die radius increases the resulting punch force and therefore has a negative effect on the drawing process. Additionally, the results show that the influence of a die radius variation on the punch force is far more prominent in rectangular deep drawing compared to the forming of circular parts, which can be explained by the different composition of the punch force.

In order to enable the possibility of predicting component failure in deep drawing like bottom fracture using FEM simulation in addition to experimental investigations, it is necessary to integrate the material failure as an input variable into the simulation. Conventional methods like hydraulic or pneumatic bulge tests are available to determine forming limit curves even for thin foil materials. With these methods, only positive minor strains are measurable. Therefore, a scaled-down Nakajima test was developed and described in Veenaas et al. [Vee15]. Using an evaluation method adapted to the micro range, complete forming limit curves (FLC) can be determined. Especially for deep drawing processes, negative minor strains and the left side of a forming limit diagram are more important [Vee15]. It was possible to determine forming limit strain curves for the micro range for the foil materials Al 99.5, E-Cu58, 1.4301 and for PVD-sputtered Al–Zr, both for the positive and for the negative side of minor strain, as shown in Fig. 2.56.

Tolerance engineering is an approach for assessing influences in multi-stage processes but is also applicable in a single-stage process. The aim is the possibility of extrapolating the permissible tool geometry deviations in every process step from geometrical requirements on the final product geometry prescribed by operators. This becomes necessary because each process step increases or decreases the actual deviation of the workpiece. In order to describe this change of deviation, so-called “tolerance functions” are formulated. These functions answer the question, what is the necessary tolerance or admissible wear to get sound parts. For a process chain, the outcome can be calculated by a series of tolerance functions.

An example of data useful for tolerance engineering is given in Brüning [Brü15c] and is described by using upsetting of preforms with cone shaped cavities. In this example, four different dies are compared regarding their forming results. These results depend on the radii of the dies and preforms after upsetting as well as on the relative preform volumes. It is shown that the preforms generated by the laser rod end melting process can be calibrated well within a single-stage cold forming operation. Furthermore, for average natural strains φ* ≤ 0.7, the tolerable eccentricity of the preform is determined to 25 µm and increases with decreasing relative volume of the preform. This volume can scatter within 3% without a negative influence on the filling of the cavity. The influence of the calibration step on the eccentricity of the preform after the laser rod end melting process for one die is shown in Fig. 2.57.

The figure shows that the scattering field of the deviations regarding the position in the z- and r-direction is subjected to a shift. This shift is in the direction of the origin. Additionally, the scattering field of deviations after the calibration step is much smaller than the one after the laser rod end melting process. As Fig. 2.57 shows, it is possible to improve the scattering field and the position of its centroid by decreasing the field’s width and length and relocating the center point in the direction of the origin.

According to tolerance engineering, it is now important to know the allowed deviation of the laser rod end melting process so that the subsequent process step is able to calibrate those deviations and create a sound part. Therefore, matrices are used to transform the deviations from the cold forging process into the allowed deviations of the previous step by multiplying them with damping factors and subtracting the shift of the mean deviations of both processes. An exemplary equation is shown in the following Fig. 2.58.

On the left side of the equation, the mean deviation (r_i z_i) and the scatter of the laser rod end melting process (±Δr_i/2 ±Δz_i/2) are mentioned. The mean deviation results from the movement velocity of the laser in the lateral direction to the rod, while the scatter develops, for example, from the flow of the inert gas during preforming. On the right side of the equation, the mean deviation of the cold forging (r_i+1 z_i+1) and the scatter of this process (±Δr_i+1/2 ±Δz_i+1/2) is mentioned. In the case of the mean deviation, it results from positioning deviations of the upper and lower die in relation to each other, and the scatter develops from differences in the form filling of the die by the preform. The factors \( {\text{b}}_{11}^{{{\text{i}} + 1}} \) and \( {\text{b}}_{22}^{{{\text{i}} + 1}} \) are damping factors with values greater than one if the (i+1)th process step decreases the scatter, or with values greater than zero and less than one if the (i + 1)th process step increases the scatter. These values result from the reverse calculation, which means the calculation of the scatter of the (i − 1)th process step from the deviations of the prior step. The factors have to be evaluated prior to the calibration process by using simulations or experiments. In Fig. 2.58 two examples of the parameter b₁₁ and b₂₂ are given. In the first row the parameters for the cold forging process after the laser rod end melting process are mentioned. In this case, the parameters show that the scattering field is decreased. The second row includes the parameter for the scattering field of the preform diameter after a thermal upsetting. As can be seen, the values for the parameters are also greater than one and therefore describe a decreasing of the scatter. Finally, the shifting of the centroid of the scattering field from the cold forging to the laser rod end melting has to be considered. This shifting is expressed by the difference between the two centroids.

If a process comprises more than two process steps, a series of tolerance functions is used to calculate the necessary tolerance to get sound parts. An example of such a series of functions is given by the following Fig. 2.59.

As can be seen, the left side of the equation in Fig. 2.59 is the same as in Fig. 2.58 and so is the part of the equation in the tall square brackets, but with different exponents and indices due to the three-stage process chain. This last part still describes the transformation of the (i + 2)th scattering field of the final product into the (i + 1)th scatter of the previous step. Now, the process chain consists of three process steps and the transformation of the scatter from the (i + 1)th step into the ith step has to be considered. The part between the tall square brackets can be understood as the (i + 1)th centroid and its scattering field, and is now multiplied with the damping factors for this (i + 1)th step and relocated by the last mathematical term. As before, the damping factors have to be evaluated in simulation or experimentally in the first place.

To receive a tolerance function for an arbitrary n-stage process chain, the following steps have to be considered. Firstly, the starting point is always the mathematical description of the center point and the scatter of the nth process step. Secondly, the first of the overall n − 1 shifts takes place. Therefore, the center point and the scatter are multiplied with the damping factors of the (n − 1)th process step. Then, the difference between the center points of the nth and (n − 1)th steps is subtracted. The result is the center point and the scatter of the (n − 1)th step. Thirdly, the (n − 2)th shift has to be done, and so on. This procedure is repeated until the (n − (n − 1))th shift is done. Finally, a series of tolerance functions is received that describes the development of the allowed deviations or the tolerable tool wear through the overall process chain.