Effect of equivalent feed amount per revolution on cold rotary forging process by 3D elastic

Abstract

Cold rotary forging is an advanced and very complex incremental metal forming process with multifactor coupling interactive effects. Previous research is mainly based on experimental and analytical methods and thus cannot provide full details on the deformation characteristics and mechanisms of cold rotary forging. In the current work, a decisive factor in cold rotary forging, namely equivalent feed amount per revolution , is first determined, and its mathematical expression is presented. A reasonable three-dimensional elastic–plastic dynamic explicit finite element model of cold rotary forging of a cylindrical workpiece was established under the ABAQUS software environment. Through numerous simulation calculations and the analysis of equivalent plastic strain, it has been found that there are three plastic penetrating states of the cylindrical workpiece under different . On the basis of these plastic penetrating states, the effect laws of on the metal flow, degree of inhomogeneous deformation of workpiece and force and power parameters have been investigated, and thus, the deformation characteristics and mechanisms of cold rotary forging have been thoroughly revealed. The results show that with increasing , the ‘mushroom’ effect of the deformed cylindrical workpiece becomes less obvious and the deformation becomes more homogeneous, while the maximum axial forging force and forging moment gradually increase. Second, the effect of by changing the inclination angle γ of the upper die on the cold rotary forging process is different from that by changing the feed rate v of the lower die or the rotational speed n of the upper die.

Introduction

Cold rotary forging is an advanced incremental metal forming process that has wide application in many industry fields, such as automobile, machine tool, electrical equipment, cutting tool and hardware. During the cold rotary forging process (shown in Fig. 1), the upper die continuously oscillates around the vertical machine axis. Simultaneously, the lower die pushes the workpiece vertically so as to cause it to be subjected to axial compression. Thus, after the workpiece is pressed repeatedly several times, the plastic deformation will be completed perfectly. The advantages of cold rotary forging include reduced noise and vibration, uniform quality, smooth surface, close tolerance and considerable savings in energy and materials cost.

Figure 1.

Schematic diagram of cold rotary forging of cylindrical workpiece

Up to now, many scholars have carried out research on the cold rotary forging process. These researches mainly focused on measuring the pressure distribution at the contact area,¹ 1,2 calculating and verifying the power parameters3 ^– 6 and analysing the metal flow7 ^– 16 by analytical and experimental methods. However, it is very difficult to obtain satisfactory results because of the limit of these methods. The finite element (FE) method has been proven to be a good method in analysing the metal forming process. However, the existing FE research on cold rotary forging17 ^– 21 is mainly based on rigid plastic theory, so it is difficult to obtain acute simulation results because the elastic deformation has an important effect on the cold rotary forging process. Moreover, these FE researches have not been able to provide full details on the deformation characteristics and mechanisms of cold rotary forging. Therefore, it is urgent to reveal the deformation characteristics and mechanisms of cold rotary forging by the elastic–plastic FE method. As described above, cold rotary forging is a complex incremental metal forming process under coupled effects with multiprocessing parameters, such as geometry sizes of the workpiece, feedrate of the lower die, rotational speed and inclination angle of the upper die, etc. Consequently, the results of studying any single processing parameter cannot reflect the deformation characteristics and mechanisms of cold rotary forging comprehensively. Therefore, a comprehensive and decisive factor, including multiprocessing parameters, has to be determined and presented so as to thoroughly reveal the deformation mechanisms of cold rotary forging.

Consequently, in this study, a decisive factor, namely equivalent feed amount per revolution , is first determined, and its mathematical expression is also presented. Through numerous simulation calculations and the analysis of equivalent plastic strain, it has been found that there are three plastic penetrating states of the cylindrical workpiece under different . On the basis of these plastic penetrating states, the effect laws of on the metal flow, degree of inhomogeneous deformation of workpiece and force and power parameters have been explored, and thus, the deformation characteristics and mechanisms of cold rotary forging of a cylindrical workpiece have been thoroughly revealed.

Determination of decisive factor in cold rotary forging

Definition and significance of equivalent feed amount per revolution Q

In the metal plastic forming process, the shape and size of the plastic deformation zone have a decisive effect on the forming process, such as metal flow, degree of inhomogeneous deformation of workpiece and force and power parameters. In this paper, based on the deformation characteristics of cold rotary forging, the length/height ratio of the plastic deformation zone K is put forward to describe the plastic deformation zone.

As shown in Fig. 1c , the shadow region is just the plastic deformation zone. The length/height ratio of the plastic deformation zone K is defined as (1) where L and H are the length and average height of the plastic deformation zone respectively.

The length L of the plastic deformation zone is defined as the axial projection length of the contact arc DE between the upper die and the cylindrical surface of the cylindrical workpiece, as shown in Fig. 1c . Obviously, arc DC shown in Fig. 1b is the axial projection arc of the contact arc DE. Thus, L can be obtained according to the geometric relationship shown in Fig. 1b (2) where R is the instantaneous radius of the cylindrical workpiece, and θ is the value of ∠COD shown in Fig. 1b .

The value of ∠COD can be expressed by3 (3) (4) where S is the feed amount per revolution, and v, n and γ are the feedrate of the lower die, the rotational speed and the inclination angle of the upper die respectively. From equation (4), it can be seen that Q denotes the ratio of the feed amount per revolution S to the instantaneous radius R of the cylindrical workpiece, so it is defined as the equivalent feed amount per revolution.

By substitute equations (2)–(4) into equation (1), we have (5) It can be found from equation (5) that K is mainly determined by Q. That is to say, Q has a decisive effect on the shape and size of the plastic deformation zone in cold rotary forging of the cylindrical workpiece, thereby affecting the forming process significantly. Additionally, it can be seen from equation (4) that Q is a comprehensive factor that is related to the main processing parameters, including the instantaneous radius R of the cylindrical workpiece, the feedrate v of the lower die, the rotational speed n and the inclination angle γ of the upper die. Based on the above analysis, it can be concluded that Q is a decisive factor and plays a decisive role in the cold rotary forging process.

Determination of mathematical expression of equivalent feed amount per revolution

However, it can be seen from equation (4) that for a given cold rotary forging process, Q is an instantaneous variable changing with time. Therefore, its average value over the total forming time T, namely , is adopted for the sake of mathematical convenience. Assuming that the cylindrical workpiece is still cylindrical in the cold rotary forging process, so according to the volume constancy principle, we have (6) where R ₀ and H ₀ are the initial radius and height of the cylindrical workpiece respectively, and t is the time variable.

By substituting equation (6) into equation (4), we have (7) Therefore, the equivalent feed amount per revolution can be expressed by (8) where T is the total forming time in the cold rotary forging process.

Determination of reasonable range of

In cold rotary forging, the value of cannot be selected randomly. Only when the value of is located in the reasonable range can the cold rotary forging process be performed successfully so as to obtain the desired products.

In cold rotary forging, the surface of the upper die is a conical surface, so the upper die contacts the workpiece only partially; otherwise, the cold rotary forging process has become the conventional forging. Therefore, according to the geometric relationship shown in Fig. 1b , we have (9) From equation (9), we have (10) For the sake of mathematical convenience, equation (10) can be modified by equation (11) (11) Therefore, for a given cold rotary forging process, the equivalent feed amount per revolution can be calculated according to equation (8), and its range can be approximately determined by equation (11).

Three-dimensional (3D) FE modelling of cold rotary forging

Based on the forming characteristics, a reliable 3D FE model of cold rotary forging of a cylindrical workpiece is developed under the ABAQUS/Explicit software environment, as shown in Fig. 2. Summarily, the proposed model has the following features:

Figure 2.

Three-dimensional FE model of cold rotary forging of cylindrical workpiece

because the elastic deformation that occurs in the cylindrical workpiece has a significant effect on the cold rotary forging process, the elastic–plastic FE method is adopted to improve the computational accuracy

ii.

the dynamic explicit FE procedure is used to avoid the huge computation time and convergence problem of the static implicit procedure

iii.

the upper and lower dies are defined as 3D analytical rigid bodies, while the cylindrical workpiece is defined as a 3D deformable solid body. The contact between the dies and the cylindrical workpiece is defined as surface to surface contact type, which allows sliding between the surfaces. The finite sliding formulation is adopted to account for the relative motion of two surfaces. Additionally, the relative sliding that exists between the dies and the cylindrical workpiece contributes to describe the friction condition of the contact pairs with a Coulomb friction model

iv.

the rigid motion of the rigid bodies in all degrees of freedom can be represented by the reference point, as shown in Fig. 2. The upper die is constrained to rotate only around the global two axis, while the lower die is constrained to translate only along the global two axis. Because of the oscillation of the upper die, the cylindrical workpiece may rotate together with it during the cold rotary forging process. Based on the deformation characteristics, the constraint type ‘distributing coupling’ is adopted to constrain the rotation of the cylindrical workpiece

in the cold rotary forging process, the contact surface between the upper die and the cylindrical workpiece is a portion of an Archimedes spiral surface. Thus, after the lower die stops the axial feed, the upper die still has to oscillate at least one revolution around the machine axis so as to make the upper surface of the cylindrical workpiece become a plane. The load curves of the upper and lower dies are shown in Fig. 3

vi.

the 3D linear reduction integration continuum element with eight nodes (C3D8R) is used to discretise the cylindrical workpiece. The number of elements in the cylindrical workpiece is determined by its size and computational efficiency and precision, and the adaptive mesh technology is employed to reduce the distortion of the elements

vii.

mass scaling technology is adopted in the simulation process; appropriate mass scaling factors are selected to improve the computation efficiency while the computational accuracy is also satisfied.

Figure 3.

Load curves of upper and lower dies

Verification of developed 3D FE model of cold rotary forging

In order to validate the proposed 3D FE model, experiments have been carried out on a T 200 cold rotary forging press at Hubei Automobile Axle Co., Ltd, China, as shown in Fig. 4. The processing parameters adopted in the simulation and experiment are shown in Table 1. The workpiece material used in this model is AISI 1020, and its mechanical properties are shown in Table 2. Figure 5 shows the initial blank and deformed cylindrical workpiece in the experiment. Figure 6 shows the comparison of the upper surface diameter of the cylindrical workpiece between simulation and experimental results. It can be seen from Fig. 6 that the simulation results are in good agreement with the experimental ones and that the maximum relative error is 3·76%. Thus, the 3D elastic–plastic dynamic explicit FE model of cold rotary forging is proved to be reliable experimentally, and further investigation can be carried out using the developed 3D FE model.

Figure 4.

T 200 cold rotary forging press

Figure 5.

a initial blank and b deformed cylindrical workpiece in experiment

Figure 6.

Comparison between simulation and experimental results

Table 1.

Processing parameters adopted in simulation and experiment

Parameters	Values
Initial radius of cylindrical workpiece R ₀/mm	20
Initial height of cylindrical workpiece H ₀/mm	15
Height reduction ΔH/H ₀/%	20
Feedrate of the lower die v/mm s⁻¹	1
Rotational speed of the upper die n/rev min⁻¹	300
Inclination angle of the upper die γ/°	2
Friction coefficient between dies and workpiece	0·15
Motion orbit of the upper die	Circle line

Table 2.

Mechanical properties of cylindrical workpiece

Material	AISI 1020
Density ρ/kg m⁻³	7800
Young’s modulus E/GPa	210
Poisson’s ratio μ	0·3
Constitutive equation σ = 850ε^0.25

Results and discussion

Calculation conditions

From equation (8), it can be seen that if the initial dimensions of the cylindrical workpiece are selected, the value of may change by changing v, n and γ, and thus, the effect laws of on the cold rotary forging process can be obtained. The calculation conditions in this study are presented as follows.

Condition 1: Select v = {0·2, 0·3, 0·6, 1, 2, 3, 4} (mm s⁻¹), n = 300 rev min⁻¹ and γ = 2°, while keeping the other processing parameters listed in ^{Table 1} Tables 1 and 2 unchanged. The corresponding values of according to equation (8) are = {0·027, 0·0407, 0·081, 0·136, 0·272, 0·407, 0·543} (rev⁻¹). Obviously, the calculated values of are located in the range determined by equation (11).

Condition 2: Select n = {75, 100, 150, 300, 500, 1000, 1500} (rev min⁻¹), v = 1 mm s⁻¹ and γ = 2°, while keeping the other processing parameters listed in ^{Table 1} Tables 1 and 2 unchanged. The corresponding values of according to equation (8) are = {0·543, 0·407, 0·272, 0·136, 0·081, 0·0407, 0·027} (rev⁻¹). Obviously, the calculated values of are located in the range determined by equation (11).

Condition 3: Select γ = {0·5, 0·67, 1, 2, 3·3, 6·5, 10} (°), v = 1 mm s⁻¹ and n = 300 rev min⁻¹, while keeping the other processing parameters listed in ^{Table 1} Tables 1 and 2 unchanged. The corresponding values of according to equation (8) are = {0·543, 0·405, 0·272, 0·136, 0·082, 0·042, 0·027} (rev⁻¹). Obviously, the calculated values of are located in the range determined by equation (11).

Characteristics of distribution of plastic deformation zone

Figure 7 shows the equivalent plastic strain (PEEQ) distribution in the axial section of the cylindrical workpiece during the cold rotary forging process. At the early stage of the process, the plastic deformation zone is formed first at the central region of the upper surface of the cylindrical workpiece, as shown in Fig. 7b . With increasing height reduction ΔH/H ₀, the plastic deformation zone gradually develops axially towards the lower surface of the cylindrical workpiece, as shown in Fig. 7c . When ΔH/H ₀ = 15·94%, the plastic deformation zone penetrates the axial height at the region near the cylindrical surface, as shown in Fig. 7d . When keeping on increasing ΔH/H ₀, the entire axial height has been penetrated completely by the plastic deformation zone, as shown in Fig. 7e . From the above analysis, it can be concluded that the PEEQ distribution exhibits a transfer characteristic from the upper surface to the lower surface of the cylindrical workpiece. Figure 8 shows the selected viewpoints and the variation curves of their PEEQ with time. From ^{Figure 7} Figs. 7 and 8, it can be seen that the plastic deformation of the metal of the upper region is larger than that of the lower region at any time of the cold rotary forging process. Therefore, the deformed cylindrical workpiece exhibits the ‘mushroom’ effect (shown in Fig. 7), which is the main deformation characteristic of cold rotary forging.

Figure 7.

Equivalent plastic strain distribution in axial section of cylindrical workpiece

Figure 8.

Selected view points and variation curves of their PEEQ with time

Effect of on plastic penetrating states

From the distribution of the plastic deformation zone shown in Fig. 7, it can be concluded that cold rotary forging is a plastic penetrating process in which the plastic deformation zone gradually penetrates the axial height of the cylindrical workpiece from the upper surface to the lower surface. According to the slip line field theory, the depth of the plastic deformation zone increases with increasing length of the plastic deformation zone. As for cold rotary forging, the larger the length/height ratio of the plastic deformation zone K, the more easily the plastic deformation zone can penetrate the axial height of the cylindrical workpiece from the upper surface to the lower surface, and vice versa. Through a comprehensive analysis and summary, it is found that there exists three different plastic penetrating states in cold rotary forging under different :

when the value of is small (the value of K is also small), the plastic deformation zone cannot penetrate the entire axial height of the cylindrical workpiece from the upper surface to the lower surface at the end of the process, as shown in Fig. 9a

ii.

when the value of is large (the value of K also becomes large), the plastic deformation zone can gradually penetrate the entire axial height of the cylindrical workpiece from the upper surface to the lower surface, as shown in Fig. 9b

iii.

when keeping on increasing the value of (the value of K becomes larger), the plastic deformation zone can penetrate the entire axial height of the cylindrical workpiece from the upper surface to the lower surface more easily, as shown in Fig. 9c .

Figure 9.

Effect of on plastic penetrating states

Effect of on metal flow

In cold rotary forging of the cylindrical workpiece, the axial flow of the metal leads to the reduction in axial height, while both radial and circumferential flows of the metal result in the expansion in diameter. Under the same reduction amount in the axial height, the geometric dimensions and shape of the deformed cylinder workpiece may be different under different . Therefore, the growth rate of the upper surface diameter , the growth rate of the lower surface diameter and the roughness of the cylindrical surface φ _D of the deformed cylindrical workpiece are put forward to describe the metal flow laws, as shown in Fig. 10. Obviously, for a given cold rotary forging process, the larger φ _D is, the more obvious the ‘mushroom’ effect is, and vice versa.

Figure 10.

Definition of growth rate of upper surface diameter , growth rate of lower surface diameter and roughness of cylindrical surface φ_D of deformed cylindrical workpiece

The effect of on the metal flow is shown in Fig. 11. From Fig. 11, it can be seen that with increasing , and φ _D first decrease rapidly and then decrease slowly as exceeds 0·136 rev⁻¹, while first increases significantly and then increases slowly as exceeds 0·136 rev⁻¹. That is to say, the ‘mushroom’ effect becomes less obvious with increasing . The reason for this can be attributed to the different plastic penetrating states under different . When is a smaller value, the plastic deformation zone cannot penetrate the axial height of the cylindrical workpiece from the upper surface to the lower surface at the end of the process. Therefore, the upper region of the cylindrical workpiece produces large plastic deformation while the lower region is in an elastic or small plastic deformation state. That is, the reduction amount of the metal in the axial height mainly contributes to the expansion in the upper region diameter of the cylindrical workpiece, thus resulting in an obvious ‘mushroom’ effect. With increasing , the plastic penetration state gradually transforms from the first one to the second, and thus, the plastic deformation zone can gradually penetrate the entire axial height of the cylindrical workpiece from the upper surface to the lower surface. Therefore, the metal of both the upper and lower regions is involved in large plastic deformation, resulting in a less obvious ‘mushroom’ effect. When keeping on increasing the value of , the plastic penetrating state gradually transforms from the second one to the third, and thus, the plastic deformation zone has already penetrated the axial height of the cylindrical workpiece thoroughly. Therefore, the effect of on the metal flow becomes less significant as exceeds 0·136 rev⁻¹.

Figure 11.

Effect of on metal flow

It can also be seen from Fig. 11 that the effect of by changing γ on the metal flow is different from that by changing v or n. In calculating conditions 1 and 2 (change v and n while keeping γ unchanged), whenever v and n change, their effect laws on the metal flow are approximately unchanged as long as is kept unchanged. Meanwhile, it can be seen from equation (8) that when γ is kept unchanged, is determined by S. Therefore, the role of v and n in the metal flow can be attributed to the role of the feed amount per revolution S (S = 60v/n). It can also be found from Fig. 11 that v curve (change by v), n curve (change by n) and γ curve (change by γ) have the same values of , and φ _D at = 0·136 rev⁻¹, where they correspond to the same processing parameters. When the value of is larger than 0·136 rev⁻¹, the γ curve has smaller values of and and a larger value of than v and n curves, and vice versa. Therefore, in order to reduce the ‘mushroom’ effect, the increase in by decreasing γ is more effective than that by increasing v or decreasing n, while the decrease in by decreasing v or increasing n is superior to that by increasing γ. Further study from Fig. 11 reveals that when ranges from 0·027 to 0·543 rev⁻¹, the corresponding ranges of , and φ _D by changing v or n are located in the range of that by changing γ. That is to say, changing by γ is more effective to control the metal flow (‘mushroom’ effect) than that by v or n.

Effect of on degree of inhomogeneous deformation of cylindrical workpiece

According to an instability theory of fracture, ductile fracture will never occur in a homogeneous deformation. However, if the deformation becomes very inhomogeneous, the fracture will develop. Meanwhile, the deformation inhomogeneity has a significant influence on the microstructure inhomogeneity, thus affecting the properties of the deformed parts. In this paper, the difference between the maximum and minimum PEEQ is adopted to represent the degree of inhomogeneous deformation of the deformed cylindrical workpiece, namely φ _id = ϵ _max−ϵ _min. The larger φ _id is, the more inhomogeneous the deformation of the cylindrical workpiece is, and vice versa. Figure 12 illustrates the effect of on the degree of inhomogeneous deformation of the cylindrical workpiece. From Fig. 12, it can be seen that with increasing , the degree of inhomogeneous deformation first decreases rapidly and then decreases slowly as exceeds 0·136 rev⁻¹. That is to say, the deformation of the cylindrical workpiece becomes more homogeneous as increases. This can also be explained by the different plastic penetrating states under different . When the value of is smaller, the plastic deformation zone cannot penetrate the axial height of the cylindrical workpiece at the end of the process. Under this circumstance, less metal participates in the plastic deformation, and more metal is in the elastic or small plastic deformation state. Therefore, the deformation of the cylindrical workpiece becomes more inhomogeneous. With increasing , the plastic deformation zone can gradually penetrate the entire axial height of the cylindrical workpiece. Hence, more metal is in the plastic deformation state, and the deformation becomes more homogeneous. When keeping on increasing , the plastic deformation zone penetrates the axial height of the cylindrical workpiece thoroughly, and the deformation becomes very homogeneous. Therefore, the effect of on the degree of inhomogeneous deformation of the cylindrical workpiece becomes less significant as exceeds 0·136 rev⁻¹.

Figure 12.

Effect of on degree of inhomogeneous deformation of cylindrical workpiece

From Fig. 12, it can also be found that the effect of by changing γ on the degree of inhomogeneous deformation is different from that by changing v or n. The role of v and n in the degree of inhomogeneous deformation can be attributed to the role of the feed amount per revolution S. the v, n and γ curves have the same value of degree of inhomogeneous deformation at = 0·136 rev⁻¹. When the value of is larger than 0·136 rev⁻¹, the γ curve has a smaller value of degree of inhomogeneous deformation than the v and n curves, and vice versa. Therefore, in order to make the deformation become more homogeneous, the increase in by decreasing γ is more effective than that by increasing v or decreasing n, while the decrease in by decreasing v or increasing n is more favourable than that by increasing γ. Just as the metal flows, the variation range of the degree of inhomogeneous deformation by changing γ is larger than that by changing v or n. That is to say, changing by γ is a more effective method to control the degree of inhomogeneous deformation of the cylindrical workpiece than that by v or n.

It can be concluded from the above analysis that it is the inhomogeneous deformation that results in the occurrence of the ‘mushroom’ effect of the cylindrical workpiece. However, the ‘mushroom’ effect has duality. In the riveting process, the ‘mushroom’ effect can be utilised to realise the loose and tight riveting. With increasing , the ‘mushroom’ effect becomes less obvious, and the rod of the rivet is in the large plastic deformation state; thus, the tight riveting can be achieved. Inversely, when the value of is smaller, the ‘mushroom’ effect becomes obvious. Therefore, the rod of the rivet is in an elastic or small plastic deformation state, and the loose riveting can be achieved. As described above, changing by γ is more effective to control the metal flow (‘mushroom’ effect) and the degree of inhomogeneous deformation than that by v or n. That is to say, it is relatively difficult to change the degree of loose and tight riveting by changing v or n. Therefore, the method of changing by γ is usually adopted to change the degree of loose and tight riveting in the practical riveting process.

Effect of on force and power parameters

Figure 13 illustrates the variation curves of the axial forging force and forging moment during the cold rotary forging process. It can be seen from Fig. 13 that the cold rotary forging process has experienced three forming stages. At the first stage, the upper die begins to contact the cylindrical workpiece. Therefore, the axial forging force and forging moment increase rapidly from zero to a certain value. At the second one, the axial forging force and forging moment increase slowly up to their maximum values, indicating that the process has entered the steady forming stage. At the end of the process, because the lower die stops the axial feed while the upper die still oscillates so as to make the upper surface of the cylindrical workpiece become a plane, the axial forging force and forging moment decrease rapidly. Additionally, it can also be seen from Fig. 13 that the axial forging force and the forging moment oscillate with time. This is because cold rotary forging is a complex dynamic contact, highly non-linear and non-steady state deformation process.

Figure 13.

Variation curves of a axial forging force and b forging moment with time

Figure 14 provides the effect of on the maximum axial forging force and forging moment. From Fig. 14, it can be seen that as increases, the maximum axial forging force and forging moment gradually increase. This is because when the value of is larger, the deformation of the cylindrical workpiece becomes more homogeneous, and more metal is in the plastic deformation state. Thus, more energy is needed to produce the plastic deformation. Inversely, when the value of is smaller, the deformation of the cylindrical workpiece becomes more inhomogeneous, and more metal is in an elastic or small plastic deformation state. Therefore, less energy is consumed to produce the plastic deformation.

Figure 14.

Effect of on a maximum axial forging force and b maximum forging moment

It can also be seen from Fig. 14 that the effect of by changing γ on the maximum axial forging force and forging moment is different from that by changing v or n. The role of v and n in the maximum axial forging force and forging moment can be attributed to the role of the feed amount per revolution S. When the value of is larger than 0·136 rev⁻¹, the γ curve has larger values of the maximum axial forging force and forging moment than the v and n curves, and vice versa. Therefore, in order to reduce the axial forging force and forging moment, the decrease in by increasing γ is more effective than that by decreasing v or increasing n, while the increase in by increasing v or decreasing n is superior to that by decreasing γ. Further study from Fig. 14 reveals that just like the metal flow and the degree of inhomogeneous deformation, changing by γ is more effective to control the maximum axial forging force and forging moment than that by v or n.

Conclusions

In this paper, a decisive factor in cold rotary forging, namely, equivalent feed amount per revolution , is first determined, and its mathematical expression and reasonable range are also deduced. Based on a reliable 3D elastic–plastic dynamic explicit FE model of cold rotary forging, the effect laws of on the metal flow, degree of inhomogeneous deformation of workpiece and force and power parameters have been explored, and thus, the deformation characteristics and mechanisms of cold rotary forging of a cylindrical workpiece have been thoroughly revealed. The results of this research are shown as follows:

The equivalent feed amount per revolution is a decisive factor and plays a decisive role in the cold rotary forging process.

There exists three different plastic penetrating states in cold rotary forging under different : when the value of is smaller, the plastic deformation zone cannot penetrate the entire axial height of the cylindrical workpiece from the upper surface to the lower surface at the end of the process; when the value of is larger, the plastic deformation zone can gradually penetrate the entire axial height of the cylindrical workpiece; and when keeping on increasing the value of , the plastic deformation zone can penetrate the entire axial height of the cylindrical workpiece more easily.

With increasing , the ‘mushroom’ effect of the deformed cylindrical workpiece becomes less obvious, and the deformation becomes more homogeneous, while the maximum axial forging force and forging moment gradually increase. The effect of by changing γ, v and n on the cold rotary forging process (metal flow, degree of inhomogeneous deformation of workpiece and force and power parameters) is different. The role of v and n in the cold rotary forging process can be attributed to the role of feed amount per revolution S. In order to reduce the ‘mushroom’ effect and make the deformation of workpiece more homogeneous, the increase in by decreasing γ is more effective than that by increasing v or decreasing n, while the decrease in by decreasing v or increasing n is superior to that by increasing γ. In order to reduce the maximum axial forging force and forging moment, the decrease in by increasing γ is more effective than that by decreasing v or increasing n, while the increase in by increasing v or decreasing n is superior to that by decreasing γ. Additionally, changing by γ is more effective to control the metal flow, degree of inhomogeneous deformation of the cylinder workpiece and force and power parameters than that by v or n.

The results of this research thoroughly reveal the deformation characteristics and mechanisms of cold rotary forging of a cylindrical workpiece and help to optimise the processing parameters so as to precisely control the cold rotary forging process.

Footnotes

Acknowledgements

The authors would like to thank the Natural Science Foundation of China for Distinguished Young Scholars (grant no. 50725517), Natural Science Foundation of China (grant no. 51105287) and State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology (grant no. 2011–P05) for the support given to this research.

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Effect of equivalent feed amount per revolution on cold rotary forging process by 3D elastic–plastic dynamic explicit FE method

Abstract

Introduction

Determination of decisive factor in cold rotary forging

Definition and significance of equivalent feed amount per revolution Q

Determination of mathematical expression of equivalent feed amount per revolution

Determination of reasonable range of

Three-dimensional (3D) FE modelling of cold rotary forging

Verification of developed 3D FE model of cold rotary forging

Processing parameters adopted in simulation and experiment

Mechanical properties of cylindrical workpiece

Results and discussion

Calculation conditions

Characteristics of distribution of plastic deformation zone

Effect of on plastic penetrating states

Effect of on metal flow

Effect of on degree of inhomogeneous deformation of cylindrical workpiece

Effect of on force and power parameters

Conclusions

Footnotes

Acknowledgements

References