Size effects on process performance and product quality in progressive microforming of shafted gears revealed by experiment and numerical modeling

As one of the indispensable actuating components in micro-systems, the shafted microgear is in great production demand. Microforming is a manufacturing process to produce microgears to meet the needs. Due to the small geometrical size, there are uncertain process performance and product quality issues in this production process. In this study, the shafted microgears were fabricated in two different scaling factors with four grain sizes using a progressively extrusion-blanking method. To explore the unknown of the process, grain-based modeling was proposed and employed to simulate the entire forming process. The results show that when the grains are large, the anisotropy of single grains has an obvious size effect on the forming behavior and process performance; and the produced geometries and surface quality are worsened; and the deformation load is decreased. Five deformation zones were identified in the microstructures with different hardness and distributions of stress and strain. The simulation by using the proposed model successfully predicted the formation of zones and revealed the inhomogeneous deformation in the forming process. The undesirable geometries of microgears including material unfilling, burr and inclination were observed on the shaft and teeth of gear, and the inclination size is increased obviously with grain size. To avoid the formation of inclination and material unfilling, the punch was redesigned, and a die insert was added to constraint the bottom surface of the gear teeth. The new products had then the better forming quality.


Introduction
In recent years, the demand for various microparts in many industrial fields is increasing continuously [1,2]. Micromanufacturing technologies such as additive manufacturing [3], ion beam etching [4], micro-discharge machining [5], laser processing [6], ultra-precision machining [7] play great roles in satisfying the different manufacturing demands, and among them, microforming [8] is a wide-applied technology, which has high productivity and great net-shape or near-netshape formation. However, the development of microforming is limited by the material feeding, handling, transporting and positioning [9]. Progressive microforming thus emerged aiming to address the above problems, which consists of progressive tooling and several forming operations with a given sequence [10]. Moreover, with scaling down to microscale, the material deformation is different from that in macroscale due to size effect. Many researchers have investigated how size effect affects microforming processes. Zheng et al. [11][12][13] developed a progressive forming system including blanking and extrusion operations, and they fabricated pinshaped plunger parts, plug-shaped parts and flanged parts to investigate the deformation load, formation accuracy and surface problem to analyze the size effect. Chan et al. [14] studied grain size effect in micro-compression experiments, and the results indicated that the properties of individual grains played great roles and would cause inhomogeneous Abstract As one of the indispensable actuating components in micro-systems, the shafted microgear is in great production demand. Microforming is a manufacturing process to produce microgears to meet the needs. Due to the small geometrical size, there are uncertain process performance and product quality issues in this production process. In this study, the shafted microgears were fabricated in two different scaling factors with four grain sizes using a progressively extrusion-blanking method. To explore the unknown of the process, grain-based modeling was proposed and employed to simulate the entire forming process. The results show that when the grains are large, the anisotropy of single grains has an obvious size effect on the forming behavior and process performance; and the produced geometries and surface quality are worsened; and the deformation load is decreased. Five deformation zones were identified in the microstructures with different hardness and distributions of stress and strain. The simulation by using the proposed model successfully predicted the formation of zones and revealed the inhomogeneous deformation in the forming process. The undesirable geometries of microgears including material unfilling, burr and inclination were observed on the shaft and teeth of gear, and the inclination size is increased obviously with grain size. To avoid the formation of inclination and material unfilling, the punch was redesigned, and a die 1 3 deformation with the decreasing number of grains. Chan and Fu [15] investigated microembossing process of microchannels and revealed the size effect on surface roughening and local deformation behaviors. Wang et al. [16] studied the fracture behaviors of materials in microscale, and they found the deformation behavior was influenced by the grain size effect and stress condition significantly.
Nowadays, micro-electro-mechanical system (MEMS) has been widely industrialized, which increases the demand for environmentally friendly and low-cost manufacturing of various microparts. As a type of indispensable actuating component in MEMS, the microgear is broadly applied for changing the speed, torque, direction and form of motion. The manufacturing of microgears has been tried in different ways by many investigators including powder metallurgy, milling technology, laser cutting, and microforming [17,18]. Debin et al. [19] proposed a hybrid process combining the isothermal closed forging process to manufacture miniature double gears. Tay et al. [20] successfully fabricated microgears through micro powder injection process by using 316L stainless steel powder. Liu et al. [21] investigated the mouldability of various zirconia microgears based on different binder systems, and the forming results indicated that the gears with a diameter below 0.5 mm were difficult to be molded due to sticking. Dong et al. [22] performed extrusion to fabricate microgears by using the 7075 aluminum alloy, and they found that good lubrication conditions and high temperatures made the extrusion load decline obviously and the gear surface quality better. Chen [18] investigated the grain size effect during the forging process of microgears and found that the material with large grains had a poor flow condition on the die substrate and a small maximum deformation load. Li et al. [23] developed a novel laser dynamic flexible stamping process using shockwaves as the punch, which could solve the problem of die alignment better compared with the traditional micro-stamping process. Vollertsen et al. [24] developed a method to form the microgear on the thickness direction of copper sheet, but the surface quality of the formed gear was poor due to the twisting operation at the end of production. Wang et al. [25] presented a process of microwire electrical discharge machining to achieve the precise fabrication of microgears, and the results indicated that the formation accuracy was high and the surface roughness was low.
Although various manufacturing technologies of microgears have been performed in the above literature review, there is still a lack of research on shafted gears by progressive microforming method using sheet metals, and the research on size effects in microforming processes is limited. In this research, a progressively extrusion-blanking microforming system was developed to fabricate shaft gears in two scales with various grain sizes to investigate size effect. The product quality and forming performance were analyzed through experiments and simulations using a proposed model from the aspects of deformation load, microstructures, distribution of stress and strain, undesirable geometry, microhardness, and surface quality. The proposed size-dependent constitutive model predicted precisely and reflected the inhomogeneous deformation in microscale. In addition, the causes of undesirable geometries were analyzed, and the forming system was thus improved to obtain better product quality.

Testing material
H75 brass (75% copper and 25% zinc, mass fraction) was chosen as the testing material in this study, which was widely applied in manufacturing of parts and structures for its good formability and ductility. The brass sheets with thicknesses of 0.6 and 1.0 mm were annealed with different temperatures viz., 450 • C , 550 • C , 600 • C and 700 • C for 1 h to obtain various grain sizes. The argon gas was filled in the furnace to avoid oxidation during annealing. To observe the microstructure of the cross-section along the thickness direction, the brass sheets were polished and etched in a solution of 5 g ferric chloride, 15 mL hydrogen chloride, and 85 mL water for about 15 s. The microstructure photos with the annealing temperatures and their corresponding grain sizes are shown in Fig. 1, which were captured by an optical microscope, Epiphot 200 Nikon. The grain sizes were measured according to the standard of ASTM E112. Moreover, the mechanical properties of brass sheets were obtained by conducting uniaxial tensile tests using the dog-bone-shape specimens with thicknesses of 1.0 and 0.6 mm under various grain sizes, and their dimension is shown in Fig. 2c. Two white points were marked on specific positions spacing 25 mm of the specimen to measure the elongation until fracture by a video extensometer. The speed of crosshead is 1.5 mm/min with the strain rate of 0.001 s −1 under a quasistatic condition. Three repeated tests were conducted for the same thickness and approximate grain size. The stress-strain curves are shown in Fig. 2d. It is revealed that the true stress decreases obviously with the growth of grain size since the grain boundary strengthening effect is weakened as the proportion of grain boundary declines.

Microforming system and microgear
The design and dimensions of the microgear are illustrated in Figs. 3b and c, which has six gear teeth and two shafts on both sides. The scaling factors refer to the ratio of the brass sheet thickness to 1 mm to distinguish the two sizes in the following explanation, which are 1 and 0.6, respectively.
For microforming, it is important to consider the positioning between material and die, the transportation of material, and the ejection of final parts [9]. The microforming system was designed concerning the above factors and drawn by CAD software SolidWorks, as shown in Fig. 3a. This system adopts two progressive operations namely extrusion and blanking to form the shafted microgear. At the beginning, the shafts are simultaneously formed by extrusion, then the brass sheet is moved forward, and positioned by the preformed shaft. Next, blanking is performed to form the teeth of microgear. Figure 4 illustrates the forming process and the final part. Machine oil was used on the interface between brass sheet and die to reduce the interfacial frictional effect. The stroke speed was fixed at 0.005 mm/s in the whole process to make the strain rate effect neglectable. The whole microforming process was done by an MTS testing machine with a 50 kN capacity load cell.

Size-dependent material constitutive modeling
Knowing the mechanical properties of the testing material is important to predict the deformation behaviors in the microforming process. In this section, a size-dependent constitutive model considering the surface layer model (SLM) [26,27] and the Hall-Petch (H-P) [28] relationship is developed based on the tested results. where f IG , f SG , IG and SG are the fractions and flow stresses of SGs and IGs, respectively, and 0 ( ) and k( ) are constants at a given strain. As shown in Eq. (1), IG ( ) can be divided into two parts: one is independent of grain size (d) and the other one is grain-size dependent. 0 ( ) can be regarded as the flow stress of grain interior, and k( )∕ √ d can be considered as the strength contributed by additional resistance to dislocation motion due to grain boundaries. However, this theoretical model is phenomenological and empirical for analysis of meso-/micro-scaled deformation, so it is limited in study of crystalline structures.
As shown in Fig. 5, a sheet specimen is assumed to have only two layers of SGs since the width and length are much larger than the thickness, thus f SG and f IG can be designated as d∕t and 1 − d∕t , respectively. Therefore, Eq. (1) can be expressed as In Eq. (2), the flow stress has two partitions, where the former is size-independent, and the latter depends on the grain size (d) and thickness (t). A factor N is introduced to describe the interactive SEs of d and t. (2) is the size factor, which is related to d and t.

Experimental data fitting
0 ( ) and k( ) can be obtained by the data fitting method from ( )−N linear relation in power-law form with different d and t, as shown in Fig. 6a. Then the intercept and slope of the linear relation, which are 0 ( ) and k( ) respectively, can be obtained and fitted in power-law form, as shown in Figs. 6b and c. In this study, two thicknesses with four grain sizes in each of the brass sheets were selected, and their related N values are listed in Table 1. Finally, the following equations are obtained to describe the flow stress curves (4) 0 ( ) = 33 + 814 0.9 , k( ) = 16 0.1 .

Effect of grain orientation
The flow stress contributed by grain interior, 0 ( ) , can be written as follows in accordance with single-crystal theory and Schmid law [29] where R ( ) is the critical resolve shear stress (CRSS), the angle between the normal stress and the normal direction of the slip plane, and the angle between the normal stress and the slip direction. m is the orientation factor (Schmid factor) for the slip system, and ranges between 2 and 3.674 for facecentered-cubic (FCC) lattice with the mean value of 3.06 in the Taylor model [27]. Taking Eq. (5)

FE model for the microforming process
To validate the proposed constitutive model, FEM was applied to simulate the extrusion operation of microgear forming of two scenarios with different scaling factors and grain sizes, as shown in Fig. 8. The natural-like polycrystalline tessellation was created in FEM model by a controlled Voronoi method [30]. After the generation of polycrystalline structures, each grain needed to be assigned material properties based on its orientation factor m using Abaqus Script. In this study, the orientation factor of each grain was generated in the valid range randomly with a given mean value. However, due to the limitations of theoretical model, the FEM model needs to have sufficient grains to be involved in deformation, and the deviation between the modeling and natural material can thus be reduced to an acceptable value. The distributions of the orientation factors in these two scenarios are illustrated in Figs. 9b, d. It can be found that the distributions are close to the normal distribution with a large number of grains involved in the statistic. In addition, the ranges of flow stress for all grains involved in the two workpieces are plotted in Figs. 9a, c, which presents the different properties among various grains, thus the inhomogeneous microstructures in micro-scaled workpiece can be reflected. In the simulations, the second-ordered CPS3 element was used for meshing to adapt irregular grain shapes and interfaces. The punch and die were rigid body. The strokes of punch were 0.2 mm for Case 1 and 0.4 mm for Case 2. The friction coefficient between the die and the sheet was 0.1. The lateral edges of the sheet were set as Y-symmetric. The simulations were conducted in Abaqus/Standard environment. In addition, the conventional FEM model was adopted for comparison, and the model generally used the stress-strain relation obtained from uniaxial tensile tests and applied homogeneous material properties. The grain orientations and material inhomogeneity are usually not considered.

Deformation load
The curves of deformation load and stroke in the experiments are shown in Fig. 10. By the comparison between two scaling factors, it is revealed that the deformation load is reduced with the grain size growing, caused by the grain boundary strengthening effect. Dislocations movement could be blocked by the grain boundaries, which results in the hardening of material. When the grains are large, the proportion of grain boundary decreases, thus the hardening effect is weakened a lot. In addition, the comparison of the load  Fig. 11. It is found that the simulation curves are little higher than the experimental curves, which could be induced by the difference between the boundary condition and the actual conditions. As shown in Fig. 11a, the simulations using the proposed model and the conventional method are conducted with the scaling factor of 1.0 and grain size of 125 µm. The results of two simulations are very close, which proves the accuracy of the proposed model in the prediction of deformation load. Figure 12 shows the microstructures on the cross-section of the formed microgears. Five domains on the cross-section of the gear teeth can be identified according to the material flow behaviors. Thus, Zones I to V are illustrated in Figs. 13a-d. Zone I is a less deformed area out of the extrusion region. Two dead zones (Zones II, IV) could be found on the cross-section, which have relatively less deformation and almost no material flow. Zones II and IV have a semicircular shape, which gradually becomes larger with grain size increasing due to a smaller number of grains bearing the distortion. The grains within Zone III are obviously elongated and rotated. This zone is located in the middle of gear teeth and gets narrower with the grain size rising. Zone V appears at the gear teeth edge due to shearing in the blanking operation, where the grains are seriously deformed. In addition, it can be found that there are grain cracks on the coarse-grained material, as illustrated in Figs. 13e, f. Since only a few grains are participating in the deformation, each grain deforms more seriously, resulting in a larger shear angle in single grains, which leads to the occurrence of crack within grains. The grain cracks could increase the risk of failure of the deformed parts, so it is necessary to avoid using largely coarse-grained material as the original material.

Distribution of stress and strain
Based on the proposed modeling method, numerical simulations of the extrusion operation were performed and compared with the conventional method. The results of stress and strain distribution are shown in Fig. 14. As shown in the stress results, the distributions on the central undeformed area are similar, but the distributions on the extrusion area are obviously different. The conventional method can only predict an average stress value on the deformed area, but the simulation using the proposed model can obtain an inhomogeneous stress distribution, which is the result of the different mechanical properties among the grains involved in the deformation. There is about 210 MPa deviation between the maximum and minimum value in the extrusion area. This result cannot be obtained by the conventional method. On the other hand, the strain distributions by both methods show generally similarities but local differences. The division of shear band from the result of the conventional method is clearly identified, but the simulation using the proposed model shows localized inhomogeneity. Meanwhile, through the comparison between the two grain sizes, it is revealed that the stress concentration can be reduced in fine-grained material, and the distribution of strain distribution is more uniform due to the increased number of grains involved in deformation. Similar results are also found in the smallscaled one, as shown in Fig. 15. The coarse-grained case has larger area of large stress, while fine-grained case has smaller and discrete large stress area. The simulation results also comply with the phenomenon of grain crack in Figs. 13e and f with the coarse-grained material, where individual grains are prone to cracking due to their large deformation.
By comparison with the experimental observation, the deformation domains can be identified from the distribution  Fig. 16, Zones II and IV are almost symmetrical near the upper and lower edges, but in the simulation results, they are not. However, for the smaller scaled one in Fig. 17, the deformation zones in simulation are different from them in experiments, which could be induced by the hard controlling of stroke in microscale, further resulting in the undesirable microstructural distribution.

Undesirable geometries
Material unfilling is a common problem in metal forming processes, which can further result in the generation of undesirable geometries, as shown in Fig. 18. For the material unfilling on the shaft end in Fig. 18a, the trapped gas is a possible inducement. The pressure of trapped gas increases significantly with the material filling in the closed cavity, which would make the further material compression very hard even impossible [31]. Another inducement is the friction between material and die, which makes the outside material flow more slowly than the central material. So, the shaft end of microgear forms the domed shape finally.
As shown in Fig. 18b, burr and inclination are inevitably generated in the blanking operation. To quantitatively study the size effect on the formation of these undesirable geometries, their sizes on the formed parts with various material conditions were measured and illustrated in Fig. 19. The length of the burr has no obvious trend with the variation of grain size, since its formation is affected by multifactor such as lubricant, die clearance, original metal material thickness, and grain size simultaneously. The length of inclination grows up with the grain size for two scaling factors, especially for scaling factor 0.6. When there are a bit grains along the sheet thickness direction involved in deformation, the grain boundary strengthening effect is weakened to make the brass sheets easily deform. Therefore, the inclination size rises with the grain size.

Microhardness
Hardness is an important quality index that can determine the service life of parts. Due to the plastic deformation in metal forming, work hardening happens by the initiation and shift of dislocations within the crystal structure [32], which largely increases the hardness of part. To evaluate the hardening behaviors during microforming, the microhardness on the different positions of the polished cross-section of the final microgears was measured through the Future Tech Group FM7 Vickers hardness tester, as shown in Fig. 20. By comparing the hardness of original material and formed parts, the hardness increases significantly after the extrusion and blanking operations, but it varies a lot in different positions due to the different deformation conditions. As shown in Figs. 20c-e, the maximum value of microhardness occurs at the position 4 of the formed part. The most serious material flow occurs at this domain, resulting in the highest hardness. Meanwhile, it is also the area that has the largest strain in simulation. The hardness at positions 2 and 6 is the second highest, where the material flows through to form two shaft features, thus grains in this area undergo serious plastic deformation, and strain is accumulated in this area. The distribution of high hardness positions conforms to the formation of Zone III in Fig. 16. On the other hand, positions 1 and 7 have the lowest hardness, which indicates less material flow and strain accumulation at these areas, and they locate at the two dead zones (Zones II, IV). For the same scaling factor, the hardness on the same position decreases

Surface quality
The surface morphology was observed by scanning electron microscope (SEM) to study the surface forming quality of microgears. As shown in Fig. 21, the main surface defects include bulge, fracture, micropits, burr, voids, and uneven surface. The fracture resulting from microvoid growth and nucleation occurs at the edge of gear teeth during the blanking operation. The grain size effect on the quality of blanking surface is illustrated in Fig. 22. For the scaling factor of 1.0, the surface quality of gear teeth does not change greatly when the grain size varies. For the scaling factor of 0.6, however, the surface quality of gear teeth is worsened obviously with grain size increasing. When grains are larger, there are fewer numbers and a more random distribution of grains. Anisotropic single grain prefers to deform in a specific direction, making the whole deformation process more inhomogeneous.
To analyze the size effect on surface quality quantitively, the surface roughness of the gear teeth with different grain sizes was measured, and the results are illustrated in Fig. 23. It can be found that for the scaling factor of 0.6 the roughness grows up obviously with grain size increasing, which means the surface quality is worsened. For the scaling factor 5 Improvement of the microforming system

Quality problems of microgears
The inclination defect is caused directly by the blanking operation, which could be resulted from the interactive influences of grain size, die constraint, and fracture [33]. For the inclination on gear teeth in this study, the lack of die constraint is a major reason causing this undesirable geometry. To get desirable geometries of teeth, a constraint die contacted with the bottom surface should be adopted. As the results in the above sections, the inclination increases with the growth of grain size.
On the other hand, the punch for forming the upper shaft in the microforming system has a closed cavity, the trapped air in the closed die cavity is continuously squeezed in the forming process, thus its pressure increases with the When the air pressure in the closed die cavity is increased to a certain value that equals the sum of the punch pressure and the atmospheric pressure, the material will no longer be filled into the die cavity, which results in the domed shape of the upper shaft of microgear.

Improved design of tooling
Considering the industrial application of microgears, the inclination of gear teeth and material unfilling of the shaft are serious problems. According to the above analysis, tooling redesign is one of the efficient ways to solve these problems, and the improved design of the microforming system is illustrated in Fig. 24. Marked by the red dashed boxes in Fig. 24a, the original holed punch was changed to the punch pin with a sleeve, so the fit clearance could be used for venting during extrusion to avoid air pressure rising. Hence, the material unfilling can be improved. On the other hand, to avoid the inclination of the gear teeth, a die insert was added into the original die of the blanking operation, which acted as the constraint to the bottom surface of teeth and shaft, as shown in Fig. 24b. In this case, a slight forging was performed after blanking, which could adjust the undesirable inclination to the desired shape to some extent.   The improved forming process of the redesigned system is shown in Fig. 25a. In the first operation namely extrusion, the gear shafts on two sides are formed first. Then the brass sheet was moved along the feed direction by a certain distance after the release of blank holder. In the second operation namely blanking, the formed shafts are used for positioning, the gear teeth are cut off from the brass sheet by shearing. With the punch moving down, an additional forging is performed with the constraints of the die insert, and the inclination formed in blanking can be improved.
The microstructures of the microgears before and after redesigning are illustrated in Fig. 25b to show the differences obviously. Three features are identified from the cross-sections, where Features I and II are induced by material unfilling, and Feature III is the inclination formed during blanking. It is found that the gear teeth inclination is improved visibly for both scales. Moreover, the material filling of the gear shafts becomes more sufficient, but unfilling still exists due to the interfacial friction. In addition, Fig. 25c shows the qualitative comparison before and after redesigning. It is revealed that all the undesirable features are reduced, and for the smaller Scenario 2, the reduction is more significant. Therefore, the improved design can effectively solve the problems of inclination and material unfilling in the progressive forming of microgears.

Conclusions
Two scaled shafted gears with various grain sizes were manufactured by progressive forming, and the fabricated part and microforming process were analyzed in terms of deformation load, microstructures, undesirable geometries, microhardness, and surface quality. A size-dependent model was proposed and applied in FEM simulation  of the whole process to reveal the deformation behaviors of the forming process. Based on the forming problems, the forming system was redesigned, which could fabricate microgears with better quality. The following conclusions are drawn.
(i) The deformation load is decreased with the increase of grain size, and the simulation using the proposed model can accurately predict the deformation load. (ii) Five zones of the microstructure in the final parts are identified, and their areas vary with grain size and scaling factor. The zones have the characteristic stress and strain distributions and different hardness reflecting the extent of deformation. The simulation using the proposed model can predict the formation of these zones and the inhomogeneous deformation during forming process. Fine-grained material can reduce the effect of inhomogeneous deformation of individual grains and obtain more uniform deformation distributionsin forming of the parts. (iii) Material unfilling of the shaft and the inclination of the gear teeth are two undesirable geometries of the microformed gears. The inclination gets worsened with the larger grains. The microforming system is redesigned to solve these problems, and the newly fabricated parts have obviously better forming quality than before. In addition, the side surface of the teeth has poor quality and deteriorates with the increase of grain size and the small scaling factor.