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Mechanics of Materials
Effects of Punch Geometry on Formability and Forming Load —Forming of Tube with Differential Wall Thickness by Ironing of Inner Surface—
Nasa KawagoshiShohei TamuraTakeshi Kawachi
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2022 年 63 巻 12 号 p. 1631-1638

詳細
Abstract

With the focus on the forming of a tube with differential wall thickness by the ironing of the inner surface, the interaction of the effects of punch geometry (length of parallel part LP, semiangle αP and clearance CP) on the formability and forming load is investigated by experimentally consistent finite element analysis. Results of the analysis show that LP and αP significantly affect the forming load, while CP has little effect on the load. The punch with larger LP, or the punch with smaller αP or smaller CP, realizes a higher formability because the slipping of steel tube, which is a result of shape defects, does not occur even if Δμ is small. Furthermore, it is theoretically clarified, through discussions on the forces that suppress/induce the slipping of the tube, that slipping does not occur if a large surface pressure is generated on the parallel part of the punch. Since the surface pressure generated on the parallel part of the punch during tube forming varies depending on αP and the area of the parallel part of the punch varies depending on LP, LP and αP should both be taken into account in designing the punch. On the other hand, CP does not affect the other design factors and can be designed independently.

 

This Paper was Originally Published in Japanese in J. Japan Soc. Technol. Plasticity 62 (2021) 87–94.

Fig. 19 Relationship between punch shape and formability (Δμ = 0.10). Lines showing the forming limit for each αP.

1. Introduction

In recent years, with the aim of decreasing CO2 emissions, there is a growing need for the weight of automobiles to be reduced. In order to reduce weight while maintaining performance, the utilization of high strength materials and optimization of wall thickness distribution are being investigated. As part of these efforts, in order to optimize the wall thickness distribution of closed section members, studies are being performed of various methods to form tubes that have a wall thickness distribution in the circumferential or longitudinal direction (hereinafter, tubes with differential wall thickness).1)

The methods for forming tubes with differential wall thickness can be classified as formation from plates or formation from tubes. One method of formation from plates is to make a tailored blank by welding plates of different thicknesses, then form this blank into a tube. One method of formation from a tube is to employ a drawing process, but the difference in wall thickness is limited to 40% when steel tubes are used.2) Going forward, further weight reduction will require tubes with larger differences in wall thickness, and the technologies for forming such tubes.

Thus, this study focuses on a method in which the inner surface of a tube is ironed to partially thin its wall, thereby forming a tube with differential wall thickness.3) Figure 1 shows a steel tube with differential wall thickness formed using this method. Steel tubes with differential wall thickness that had differences in wall thickness of 40% or more were successfully formed without cracks or wrinkles.4) The authors revealed the effect on formability of the difference in coefficient of friction between the outer and inner surfaces of the steel tube (lubrication condition) and the punch shape.57) However, the interaction relating to punch shape is still not clear.

Fig. 1

Forming sample of tube with differential wall thickness formed by ironing of inner surface.

By means of numerical analysis using the finite element method (hereinafter abbreviated as the FEM), this article studies the interaction between the effects of punch shape (length of the parallel part of the punch LP, clearance of the punch CP and semiangle of the punch αP) on formability and forming load during ironing of the inner surface of the tube.

2. FEM Analysis Method and Conditions

Figure 2 schematically shows the method for forming a tube with differential wall thickness by ironing the inner surface of the tube. In the first process, one end of the tube is fixed with a stopper, and the tube is expanded by pushing the punch into the other end. Next, in the second process, the stopper is removed and, with the part expanded in the first process engaged with the die, the punch is pushed in so as to iron the inner surface of the tube and reduce its wall thickness. The punch is pushed in until the length of the ironed part has reached the target value. Finally, the punch is pulled back and removed. As a result of these forming processes, a tube with differential wall thickness consisting of a longitudinal expanded part (thick), ironed part (thin), and unprocessed part (thick) can be obtained.

Fig. 2

Schematic diagram of forming method for tube with differential wall thickness by inside ironing. *Wall thickness of original tube.

To study the effect of punch shape on the formability of a steel tube with differential wall thickness formed using this method, numerical analysis was conducted using the FEM. Figure 3 shows the dimensions of the steel tube with differential wall thickness that was analyzed in this study. Electric resistance welded tubes of outside diameter 60.5 mm, wall thickness 1.8 mm, length 120 mm, and approximate tensile strength 440 MPa were used as samples (yield strength: 433 MPa, tensile strength: 524 MPa, breaking elongation: 29.9%), and for the forming of the steel tube with differential wall thickness, an ironing rate of 50% (wall thickness 1.8 mm → 0.9 mm) and ironed part length of 90 mm were assumed.

Fig. 3

Dimensions of tube with differential wall thickness.

For the FEM analysis, general-purpose code Abaqus/Explicit Version 6.14 was used. The steel tube was divided in the wall thickness direction into five four-node axially symmetric elements (CAX4R) of element size approximately 0.5 mm. The die, punch, and stopper were treated as rigid bodies. The coefficient of friction between the steel tube and punch μP was set to values from 0.10 to 0.25, and the coefficient of friction between the die and steel tube μD was fixed at 0.25. Hereinafter, the difference in the coefficient of friction μD − μP is represented as Δμ. Figure 4 and Fig. 5 respectively show the shapes of the die and punch used in the FEM analysis. For punch shape, the length of the parallel part of the punch LP was varied from 1 to 30 mm, the clearance of the punch CP from 0.05 to 0.9 mm, and the semiangle of the punch αP from 5 to 30°. For material characteristics, the stress-strain curve obtained by conducting a uniaxial tensile test on JIS12B arc-shaped specimens was approximated using eq. (1) and the parameters shown in Table 1.8) In addition, the von Mises yield function was used. With regard to the boundary conditions, for the die and stopper, the three degrees of freedom were constrained, and for the punch, the two degrees of freedom other than longitudinal translation were constrained. The stopper was installed at a point 170 mm from the end with the expanding part of the die, and was removed for the second process.   

\begin{equation} \sigma = K(\varepsilon^{p} + a)^{\{ \bar{n} + \frac{1}{b(\varepsilon^{p} + c)} \}} \end{equation} (1)

Fig. 4

Die shape.

Fig. 5

Punch shape.

Table 1 Value of each parameter.

3. FEM Analysis Results

3.1 Validity of FEM analysis

This section describes the results of verification of the validity of the experiment and FEM analysis. It is known that with this method, if the difference in the coefficient of friction between the outer and inner surfaces of the steel tube Δμ is below a certain value, then a steel tube with the target wall thickness difference cannot be formed.5) This is because slip occurs on the surface of contact between the outer surface of the steel tube and the die, with the steel tube being drawn into the die by the punch. Figure 6 shows the state of the steel tube during ironing, as predicted by FEM analysis. First, the results of the FEM analysis were verified for the case in which Δμ exceeded a certain value, no slip occurred, and a steel tube with the target wall thickness difference was successfully formed, as shown in Fig. 6(a). Figure 7 shows the relationship between forming load (hereinafter referred to as load) and punch stroke during the ironing process. As shown in Fig. 2(b), the punch stroke at the end of the first process was set as 0 mm at the start of the second process. In the first process, the punch was pushed in until the distance between the tapered part of the punch and the inner periphery of the die of diameter 60.5 mm was equal to the wall thickness of the original tube t0. Load was taken to be the sum of the forces acting on the punch in the longitudinal direction at the current punch stroke, and was plotted for each 5 mm punch stroke increment. At a punch stroke of 0 to 5 mm, the tapered part of the punch is passing through the expanded part of the die, the forming of the ironed part is about to begin, and load is increasing rapidly. At a punch stroke of 5 to 20 mm, the parallel part of the punch is passing through the expanded part of the die, and load is increasing almost linearly. At a punch stroke of 20 mm or more, load is constant in both the experiment and FEM analysis results. Furthermore, in this range, the experiment and FEM analysis results show a similar punch push-in value.

Fig. 6

Deformation behavior of steel tube during ironing process. (a) Without slip. (b) With small slip (less than 3 mm). (c) With large slip (more than 3 mm). *Thickness of expanded part, **Gap between die and punch shaft.

Fig. 7

Relationship between load and stroke (LP = 15 mm, αP = 15°, CP = 0.9 mm, Δμ = 0.15).

From the above, it is presumed that the forming of a steel tube with differential wall thickness can be simulated using FEM analysis if no slip occurs. Henceforth, a double circle (◎) represents a case in which a steel tube with the target wall thickness difference was successfully formed.

Next, the validity of the FEM analysis results for small Δμ was investigated. When Δμ is small, a small slip of 3 mm or less occurs in the initial stage of forming, as shown in Fig. 6(b), and, as a result, the steel tube comes into contact with the clearance part of the punch. After that, no slip occurs if CP is small, and ironing is possible. The convex part formed when the expanded part of the pipe comes into contact with the clearance part of the punch is flattened when the punch is retracted. Finally, a steel tube with the target wall thickness difference is eventually obtained. Henceforth, a circle (○) represents a case in which a small slip of 3 mm or less occurred in the initial stage of forming but a steel tube with the target wall thickness difference was successfully formed; together with ◎, this indicates the conditions under which it is possible to form a steel tube with differential wall thickness.

However, when Δμ is small and CP is large, as shown in Fig. 6(c), slip occurs continuously even after the steel tube comes into contact with the clearance part of the punch, and a steel tube with the target wall thickness difference cannot be formed. In the experiment, when lubricating oil with a high coefficient of friction was applied to the inner surface of the steel tube and forming was performed using a punch with large CP, then, as in the FEM analysis, slip occurred in the steel tube and a tube with the target wall thickness difference could not be formed.5) Henceforth, a triangle (△) represents a case in which slip of more than 3 mm and not exceeding 50 mm occurred, and a cross (×) represents a case in which slip occurred continuously from the start of forming the ironed part to the end of forming, these cases indicating conditions under which a steel tube with differential wall thickness cannot be formed.

From the above, it was confirmed that the deformation behavior observed in the experiment can be simulated by FEM analysis, and that the FEM analysis results were therefore valid. The following describes the results of an investigation of the factors that cause slip.

3.2 Effect of length of parallel part of punch LP

This section describes the effect of punch shape parameter LP on load and slip occurrence.

Figure 8 shows the relationship between load and punch stroke for different LP values. The markers in the figure indicate the point in time at which the parallel part of the punch has passed through the expanded part of the die. For all of the conditions shown in Fig. 8, no slip occurred during forming. Although the marker position changes depending on LP, the slope of the load remains the same even when LP changes. This means that the surface pressure generated on the tapered and parallel parts of the punch are not dependent on LP; details will be described in the discussion in Section 4.

Fig. 8

Relationship between load and stroke for three models of different LP values (αP = 15°, CP = 0.9 mm, Δμ = 0.15).

Figure 9 shows slip occurrence with different LP and αP values. As previously described, when forming a steel tube with differential wall thickness by ironing, as Δμ increases, slipping of the steel tube is suppressed, and this is advantageous to forming.5) In other words, forming becomes easier when the coefficient of friction between the steel tube and punch (inner surface of the steel tube) μP decreases and the coefficient of friction between the die and steel tube (outer surface of the steel tube) μD increases. From Fig. 9(a), when LP is large, forming is possible even if Δμ is small. However, Fig. 9(b) show that when αP is large, there is no change in the Δμ value at which forming is possible when LP is increased, indicating reduced effectiveness at suppressing slipping of the steel tube.

Fig. 9

Amount of slip when LP is changed (CP = 0.9 mm). (a) αP = 10°. (b) αP = 20°.

3.3 Effect of semiangle of punch αP

This section describes the effects of punch shape parameter αP on load and slip occurrence.

Figure 10 shows the relationship between load and punch stroke for different αP values. The markers in the figure indicate the point in time at which the parallel part of the punch has passed through the expanded part of the die. For all of the conditions shown in Fig. 10, no slip occurred during forming. In the range of punch stroke between 0 mm and the marker, the slope of the load generated on the tapered and parallel parts of the punch becomes steeper as αP decreases. Figure 11 shows slip occurrence during forming for different values of αP and CP.

Fig. 10

Relationship between load and stroke when αP is changed (LP = 15 mm, CP = 0.9 mm, Δμ = 0.15).

Fig. 11

Amount of slip when αP is changed (LP = 15 mm). (a) CP = 0.9 mm. (b) CP = 0.5 mm.

Figure 11(a) show that forming is possible even if Δμ is small when αP is small. Even in the case shown in Fig. 11(b), where CP is small, the Δμ value required for forming decreases when αP is small, so that a slip suppression effect is observed for the steel tube. The range of ◎, where no slip occurs, is constant regardless of CP.

3.4 Effect of clearance of punch CP

This section describes the effect of punch shape parameter CP on load and slip occurrence.

Figure 12 shows the relationship between load and punch stroke for different CP values. In the figure, the solid and dashed lines indicate the results for ○ and ×, respectively. It is presumed that for all of the conditions, since LP is 15 mm, the effect of CP is observed at a punch stroke of 20 mm or more, for which the parallel part of the punch has finished passing through the expanded part of the die. For those cases where the result was ◎, the effect of CP was not observed even at a punch stroke of 20 mm or more, because the expanded part of the tube did not come into contact with the clearance part of the punch. The following describes how load changes in cases that give the results ○ and ×.

Fig. 12

Relationship between load and stroke when CP is changed (αP = 15°, LP = 15 mm).

Looking first at the results obtained with CP = 0.10 mm and Δμ = 0.05, and CP = 0.03 mm and Δμ = 0.05 mm, which are indicated by solid lines (○), the expanded part of the tube comes into contact with the clearance part of the punch at a punch stroke of 20 mm, but, following this, the ironing process proceeds stably and load is constant even at a punch stroke of 20 mm or more. The effect of CP on load is small, since in the case of ◎ and ○ load changes in almost the same manner.

Next, the results obtained with CP = 0.30 mm and Δμ = 0.00, which are indicated by dashed lines (×), show that load increases at a punch stroke of 20 mm or more. However, the results obtained with CP = 0.90 mm and Δμ = 0.00, for which slip also occurred, show decreasing load. Figure 13 shows slip occurrence during forming with different CP and LP values. From Fig. 13(a), forming is possible even if Δμ is small when CP is small. The same effect is observed in Fig. 13(b), which shows the results when LP is large. In particular, the range of ◎, in which no slip occurs, is constant regardless of CP. For large LP, slipping of the steel tube is suppressed when Δμ = 0.05, as is also the case in Fig. 13(a), but it readily occurs when Δμ = 0.00.

Fig. 13

Amount of slip when CP is changed (αP = 15°). (a) LP = 5 mm. (b) LP = 20 mm.

4. Discussion

4.1 Effect of punch shape on load

This section first discusses the effect of punch shape on the relationship between load and punch stroke. As shown in Fig. 7, when the punch stroke is between 5 mm and the point at which the parallel part of the punch has passed through the expanded part of the die, load increases linearly. This is presumably because surface pressure is generated between the parallel part of the punch and the die, causing friction. Until the parallel part of the punch has passed through the expanded part of the die, the area where surface pressure is generated increases linearly as the punch is pushed in further. The frictional force acting on a sliding flat surface subjected to uniform pressure is given by the product of the pressure, area of the flat surface, and coefficient of friction. Therefore, considered reasonable that if the surface pressure generated on the parallel part of the punch is constant, then load will increase linearly with respect to punch stroke. In addition, the smaller the value of αP, the larger the slope of the load, this presumably being because the surface pressure generated on the parallel part of the punch is large. Figure 14 shows the relationship between the surface pressure generated on the parallel part of the punch and αP. The average pressure value for the area over which surface pressure is generated at a punch stroke of 15 mm was used as the surface pressure generated on the parallel part of the punch. The above discussion confirmed the assumption that the surface pressure generated on the parallel part of the punch increases as αP decreases.

Fig. 14

Relationship between surface pressure generated on the parallel part of the punch and αP (LP = 15 mm, CP = 0.9 mm, Δμ = 0.15, punch stroke = 15 mm).

When slip occurs, the behavior of load changes depending on CP. As shown in Fig. 6(c), if the gap between the clearance part of the punch and the die t2 is smaller than the wall thickness of the expanded part of the tube t1, then the thickness of the expanded part decreases when it is pulled in by the punch, generating surface pressure between the clearance part of the punch and die, and thereby causing friction between them. As a result, as the punch is pushed in further, the area over which surface pressure is generated increases linearly, and therefore, as shown in the case with CP = 0.30 mm and Δμ = 0.00 in Fig. 12, load increases almost linearly. However, if the gap between the clearance part of the punch and die t2 is almost the same as the wall thickness of the expanded part of the tube t1, then there is little decrease in the thickness of the expanded part, and accordingly, the surface pressure generated between the clearance part of the punch and die decreases. As a result, as shown in the case with CP = 0.90 mm and Δμ = 0.00 in Fig. 12, load decreases.

Figure 15 schematically shows the relationship between load and punch stroke for the conditions under which forming is possible. In the figure, β indicates the slope of the load up to where the tapered part of the punch has passed the expanded part of the die, and γ indicates its slope up to where the parallel part of the punch has passed the expanded part of the die, with (1) to (3) indicating the position of the punch at the time of the relevant punch strokes. β and γ depend on αP, increasing as αP decreases. The length from punch stroke 0 mm to (1) indicates the length over which the tapered part of the punch is in contact with the steel tube, and the length from (1) to (2) is equal to LP. Therefore, load in the steady state (3) can be represented by the sum of the load at (1) and the product of γ and LP.

Fig. 15

Schematic diagram of relationship between load and stroke (Length of taper part in contact with steel tube).

Figure 16 shows the surface pressure generated on the punch surface for different LP values at a punch stroke of 80 mm, and with αP = 15°, CP = 0.9 mm and Δμ = 0.15. To eliminate surface pressure variation due to the way of contact, the 5-node moving average of the surface pressure obtained by FEM analysis was used. Figure 16 shows that when LP = 20 mm, a constant surface pressure of approximately 330 MPa is generated over a range of approximately 5 to 15 mm in the longitudinal direction of the punch, which is presumed to correspond to the parallel part of the punch. When LP = 30 mm, the generated surface pressure remains constant but is generated over a range of approximately 5 to 25 mm in the longitudinal direction of the punch, so that the range over which the surface pressure is constant increases as LP increases. From the above, it is considered reasonable to assume that the surface pressure generated on the parallel part of the punch is constant.

Fig. 16

Surface pressure on the punch surface (αP = 15°, CP = 0.9 mm, Δμ = 0.15, stroke = 80 mm).

Next, a discussion follows of the interaction between the effects of LP, CP and αP on average load. Figure 17 shows average load under different conditions with Δμ = 0.15.

Fig. 17

Average load after the parallel part of the punch passes through the expanded part of the die under each condition (Δμ = 0.15). (a) Relationship between average load and LP when αP is changed (CP = 0.5 mm). (b) Relationship between average load and CP when LP is changed (αP = 15°).

The average load value from the time at which the parallel part of the punch has passed through the expanded part of the die to the time at which the end of the stroke is reached (punch stroke: 90 mm) was used as the average load. This corresponding to the period over which forming load is in a steady state. The lines in the figure represent straight line approximations.

Figure 17(a) shows the relationship between average load and LP for different αP values. For the same value of αP, average load increases linearly with respect to LP. This is because of the previously mentioned frictional force generated by the surface pressure between the parallel part of the punch and die, and the slope of the approximated straight line is equal to the product of the surface pressure generated on the parallel part of the punch, the area per unit length of the parallel part of the punch, and μP. Since the product of the area per unit length of the parallel part of the punch and μP is constant, the surface pressure generated on the parallel part of the punch is small when αP ≥ 20°. In addition, looking at the intercept of the approximated straight line drawn for each αP value, the intercept increases as αP decreases. Since the intercept corresponds to the condition where LP = 0 mm, and therefore equals the load generated on the tapered part of the punch, this shows that the load generated on the tapered part increases as αP decreases.

Next, Fig. 17(b) shows the relationship between average load and CP for different LP values. The load is not dependent on CP and is almost constant if no slip occurs as indicated by ◎ and LP is the same value. In addition, the load decreases slightly but is almost constant as CP increases if no slip occurred after a small slip as indicated by ○.

4.2 Forces acting during the ironing process

Figure 18 shows the forces acting during the ironing process. f1 to f8 in Fig. 18 indicate the forces acting on the surface of the steel tube in contact with the punch: f1 indicates the force required to reduce the diameter of the expanded part of the tube, and f2 the frictional force generated at that time; f3 indicates the force required to reduce the wall thickness of the expanded part, and f4 the frictional force generated at that time; f6 indicates the force acting on the parallel part of the punch, and f6 the frictional force generated at that time; and f7 indicates the force acting on the tapered part of the punch, and f8 the frictional force generated at that time. In addition, f1′ to f8′ indicate the forces generated on the surface of the steel tube in contact with the die in opposition to these forces. In what follows, the longitudinal and wall thickness directions are represented by z and r, respectively, and each direction component of a force is represented using a subscript.

Fig. 18

Schematic diagram of the load in ironing process. (a) Expanded part under successful forming conditions. (b) Punch parallel part and taper part.

The forces acting on the steel tube can be classified into those that induce slip (+z direction in Fig. 18) and those that suppress it (−z direction in Fig. 18). Henceforth, the forces that induce slip are represented as Fs, and those that suppress it as Fi. When Fi < Fs, slipping of the steel tube is considered to occur.

In the results indicated by ○, the forces that induce slip are represented by eq. (2), and those that suppress it by eq. (3).   

\begin{equation} F_{\text{s}} = f4 + f6 + f7_{\text{z}} + f8_{\text{z}} \end{equation} (2)
  
\begin{equation} F_{\text{i}} = f1'_{z} + f2'{}_{z} + f3'{}_{z} + f4'{}_{z} + f6' + f8' \end{equation} (3)
The difference is represented by eq. (4).   
\begin{align} F_{\text{i}} - F_{\text{s}}& = f1'_{z} + f2'{}_{z} + f3'{}_{z} + f4'{}_{z} + f6' + f8' \\ &\quad- (f4 + f6 + f7_{\text{z}} + f8_{\text{z}}) \end{align} (4)
Assuming that the effect of the circumferential stress is small, the forces in the wall thickness direction are in equilibrium, and so eq. (4) can be written as eq. (5).   
\begin{align} F_{\text{i}} - F_{\text{s}} &= f1'{}_{z} + f2'{}_{z} + f3'{}_{z} + f3\\ &\quad \times \varDelta \mu + f5 \times \Delta \mu + f7_{\text{r}} \times \Delta \mu - f7_{\text{z}} \end{align} (5)
f1′z and f2′z are determined by the die shape, and are constant regardless of the punch shape.

Among these forces, LP has an effect on f5. Since f5 is the product of the surface pressure generated on the parallel part of the punch and the area of the parallel part of the punch, it is proportional to LP. Fi therefore increases as LP increases, and so slip is less likely to occur.

However, in Fig. 13, for αP = 15° and Δμ = 0.00, slip is more likely to occur when LP increases, which is presumably because f5 is slightly larger than f5′ due to the effect of circumferential stress. For αP = 15°, LP = 20 mm, CP = 0.05 mm and Δμ = 0.05, the f5 and f5′ in the FEM analysis results are 277 kN and 275 kN, respectively. Therefore, it is presumed that for Δμ = 0.00, slip is more likely to occur as LP increases.

The following is a discussion of the effect of αP on the forces acting on the steel tube. αP affects f5 and f7.

When ironing the outer surface, it is known that, denoting the die semiangle as αD, the surface pressure generated on the tapered part of the die increases as the differential friction factor (Δμ cot αD) decreases. When ironing the inner surface, the relationship between the die and punch is reversed, and the surface pressure generated on the tapered part of the punch therefore increases as the differential friction factor (Δμ cot αP) increases. Hence, it is reasonable to suppose that when Δμ ≥ 0, surface pressure increases as αP decreases. When αP is small, f5 and f7z increase and f7r decreases,9) suppressing slip.

In addition, it is presumed that because cot αP changes significantly when αP is small, the slope of the load is markedly steep for αP = 5° but changes little for αP ≥ 20°. Therefore, for αP ≥ 20°, the force that suppresses slip generated on the parallel part of the punch increases little even if LP increases, so that the effectiveness of suppressing steel tube slip by increasing LP is reduced.

CP affects f3′z and f3, with f3′z and f3 increasing as CP decreases. This is because, the smaller the value of CP, the greater the amount by which the thickness of the expanded part of the tube decreases. Therefore, as CP decreases, the force suppressing the slip of the steel tube increases, and so slip is less likely to occur. In addition, because the forces that suppress and induce slip are in equilibrium, load is equal to the maximum force suppressing slip or the maximum force inducing slip, whichever is smaller. Therefore, when slip does not occur, load is f4 + f6 + f7z + f8z. Because f4 = 0 under the conditions for ◎, it is reasonable to assume that load is not dependent on CP. In addition, for the results indicated as ○ in Fig. 17, load increases slightly as CP decreases, due to f3 and f4 increasing.

From the above, it was confirmed that the effect of LP on slip occurrence slipping of the steel tube occurs and on load is greatly affected by αP. In contrast, it was also confirmed that the effect of CP on the aforementioned is little affected by LP or αP. When a steel tube with differential wall thickness is formed using this method, LP and αP should not be designed separately.

Figure 19 shows the relationship, obtained from the above discussion, between punch shape and formability when a steel tube with the target wall thickness difference is formed with Δμ = 0.10. It was confirmed that as αP decreases and LP increases, the formable range becomes wider, but when αP is large, the slip suppression effect produced by LP is very small. Although Fig. 19 does not show load, it must be noted that, in practice, the formable range is limited by the maximum load of the press used.

Fig. 19

Relationship between punch shape and formability (Δμ = 0.10). Lines showing the forming limit for each αP.

5. Conclusion

By means of FEM analysis, this article has investigated the interaction between the effects of punch shape (length of the parallel part of the punch LP, clearance of the punch CP and semiangle of the punch αP) on formability and forming load when a tube with differential wall thickness is formed by ironing the inner surface of the tube in order to partially reduce the wall thickness. The findings obtained are given below.

In the steady state, load is dependent on αP and LP.

Larger LP and smaller αP and CP are more advantageous to forming.

When Δμ > 0.00, slipping, which is a type of forming defect, is less likely to occur as the surface pressure generated on the parallel part of the punch increases.

Since the surface pressure on the parallel part of the punch during forming is dependent on αP, LP and αP must be considered simultaneously when designing the punch.

The effect of CP on slip occurrence of the steel tube occurs and on load is little affected by LP or αP.

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