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Reverse simulation using the simulation block technique and its application in the precision forging process
Joumalof
ELSEVIER
Materials Processing Technology Journal of Materials Processing Technology 63 (1997) 244-247
REVERSE SIMULATION USING THE SIMULATION BLOCK TECHNIQUE AND ITS APPLICATION L,," THE PRECISION FORGING PROCESS Luan Viguo, Sun Sheng Dept. Material Engineering & Science, Shandong l.Jniversity of Technolog): , Jinan City, Shandong Province, P. R China Abstract Referring to die forging as an example, the so-called reverse simulation of the forming process, regardless of whether it is hot or cold forging, is executed . Separating imaginarily the two half-parts of the forging die from their closed position, they move apart from each other progressively. As they move, material in the die cavity deforms and results in an opposite movement to that ofthe normal forming process. Finally an initial billet or a simplified preform forging is obtained. In this paper, basic points in the execution of reverse simulation with UBET are described. For the purpose of easy execution, a new approach named the Simulation Block Technique (SBT) is introduced. Example of successful applications in practice using the above methods are presented. Keyword: die forging, reverse simulation, simulation block technique
J. Introduction
The prevailing design method of metal forming at present is to obey the procedures edited into technological handbooks/text-books, combined with designers' experience, in order to determine the forming stages and to calculnte process/die parameters. This is effective, but it is difficult to exactly understand the quantitative flow of the process. Although a versed designer can exercise precise control with some parts, he might not be sure of spreading his experiences. Indeed, if it is common to consume an excessi'...e amount of raw material in return for success in design and production. Modern design methods for metal forming are quite different. Instead of referring to empirical procedures. they develop various practical simulation techniques for design, based on achievements of metal forming theory, using the computer. They are precise design methods aimed at optimizing such aspects as the saving of raw material or energ)', high product quality, low cost, etc. In some papers such work is called Net Shape Manufacturing (NSM). Many researchers know that preform design is the key point of NSM. Amongst papers in related to preform design, those that employ the reverse simulation technique are very novel: the present paper presents some contributions in this area. 2. Basic points of the reverse simulation technique With the die forging process as an example, reverse simulation starts at the final forging position, separating 0924-0136/97/$15,OO@ 1997 Elsevier Science SA All rights reserved PI! S0924-0136(96)02630-1
imaginarily the two half-parts of the forging die from each other. When executing simulation step-by-step, on the one hand some boundaries of the material in the die cavity leave the die walls, whilst on the other hand the deformed body contracts in the opposite direction to that of filling of the die cavity. Continuing this procedure, a series of simplified configurations and. finally, a biHet are produced. In reverse simulation, the initial forging state can be selected, such as a filled cavity with a pre-determined surplus of metal or without any scrap. If forward simulation is investigated with the billet resulting from reverse simulation, the same fmal forging state should be obtained. Indeed, reverse simulation is an approach to find a desirable forming process by setting the best selected final forging states and taking into account some conditions experienced in the course of forming. To execute reverse simulation. there is the need to deal with three basic problems: (i) the contraction technique of the free sides; (ii) the model for leaving the die walls of the free sides; and (iii) the end positions ofthe reverse simulation. The description of the detail concerning forward and reverse simulation is described in Ref.ll). 3. Simulation block techniquel 21 A complete simulation of a forming process, irrespective of whether it is forward or reverse. consists of a series of instant simulation steps. Although the forming conditions between respective steps are not the same. the steps are connected to
Luan Yiguo. Sun Sheng I Journal ofMaterials Processing Technology 63 (1997) 244-247
each other in the forming state. Amongst, man)' aspects, the most important is to simulate the geometrical contour changes of the deformed body, which latter contains two items: figure and sizes. In general, the technique deals with the size changes of the plastic process in the following way. Based on the known sizes of last step, the technique calculates all of the velocities around the contour after some optimization, then it uniformly expands the contour at the resolved speeds until the end of this step: thus the changed sizes are determined. Except for unbounded figure change resulting from size change, the previous figure has no essential effect on the figure change that the current step will take. The most important factors influencing the figure change is the fmal figure of the forming process or the die c.wity figure. In other words, to construct the figure change that is possible to appear during the forming process, reference has to be made to the die cavity.
245
that if "I is known, only two independent variables are permitted in
"2-
~'J '
v6' In other words. provided that the
input velocity is given, all of the velocities included on the boundaries and inside the block can be determined through optimization.
L. ! L
:="
tc"
-+-
it -T
-::..tIl---..,
~
l
I
7
-
.l~ !
,'L'", I Fig. 2 A complete rectangular block
-
Fig. I Figure change during simulation An example of a forging with an H cross-section is shown in Fig. 1, forward simulated UBET. Irrespective of its sizes change, there was a limited numbers of figures possible to undergo when the ingot filled the die cavity, form a billet to the final forging. Therefore, its figure change could be realized automatically. There are two ways to do this change, one being to set up a switch table about the figures, whilst another is to combine all possible figures together, based on the die cavity, and thus to construct an united block that can expand or compress, becoming any of figures possible to be taken by the deformed body. This kind of block and its changes technique are the so called Simulation Block Technique (SBT) in the present paper. Fig.2 presented a complete block with a rectangular crosssection. Based on UBET theory, it is divided into five elements, the side 2-3 being the entry of the block whilst the side 6-7 is the exit. The sides 1-2,3-4,5-6, 7-8 are the boundaries of the block, which are related to die walls. That the boundaries are bounded or free depends on whether or not they make contact with the die walls, Fig.3. The block has four normal boundary velocities: "I' "2' VI and vtj. Quantities v2 to Vs are the velocities between the elements inside the block. "I is the input velocity ofthe block, which usually is known, whilst "2 is output velocity of the block, which is often unknown. That VI and v6 are known or unknown depend on the state of their sides. Volume constancy controls the relationship between "I' u2' VI ' v6' so
Fig. 3 A block in the die Supposing that "1' v1 and v6 are known, the other boundary velocities of block are deduced as follows, referring to Fig. 2: According to the condition of keeping the total volume of the block constant ,and
2u t a(! -e) - v,(b z - a Z ) + v6 (b z - a Z )
-
2uzb(g- d) = 0
so that U
2au,. (f = _--'-...c.:.. z
e)+-'-_ (b z -_a Z )(V6 -_ ---'-'-~
VI) _'_'__
2b(g-d)
According to the condition of keeping the volume of element I constant: Vz
= VI
According to the condition of keeping the volume of element II constant:
uz(b therefore:
Z
-
a Z )_ v3 (b Z - a Z )+ 2u zb(g- f)
=0
246
Luan Yiguo, Sun Sheng / Journal ofMaterials Processing Technology 63 (1997) 244-247
and using the same method:
= -
V~
2u2 b(e-d) 2 2 + V4 (b -a )
The total upper bound power of the block is the sum of each element. the upper bound power of an element being resolved as follows: We=WrHVs+Wf where Wi is the plastic deforming power, Ws is the plastic shearing power between elements and is Wf friction power between an element and the die wall. As the above respective power items are related only to the element side velocity, the determination of the power can be attributed to tbe calculation of the element velocities. I
(a)
(b)
(c)
Referred to Fig.2. it is easy to construct a block with a rectangular cross-section used for plane deformation. Also other complex block can be designed on the basis of the above principles. Thus, joining in-series blocks and starting with the first block. a forward/reverse simulation can be spread outwards so as to be able to simplify the simulation of the forming process. 4. Application in production In this paper a method of controlling flash formation in dieforging process design has been used. Briefly speaking, this method is to make the metal almost till the die cavity before being forced out. It minimizes the effect of resistance on the die bridge. The method needs reverse simulation to determine a proper preform forging or an initial billet. In the paper a computer system including forward/reverse simulation and SBT has been established for analyzing and designing the axisymmetridplane die forging process. Fig.6 presents the designs resulting from reverse simulation, billets prepared according to simulation design and forged directly in to the tinal forging die. exhibiting a tilled die cavity and a uniform thin flash arrangement, as expected. Fig.7 presents a comparison of the forging results between the new design of this paper and the current design in forging shop.
Fig. 4 The varieties of the block Some changes can be developed from Fig.2, three examples being presented in Fig. 4. There is no to remember these changes separately. Indeed, Fig.4(a) was obtained by letting point S go on to point 6 and point 7 go on to point 8. In addition, if point 1 were to go on to point 2, then Fig.4(b) would appear. In this way a pancake billet (Fig.4(c» results from the overlapping of couples of points such as 1 and 2, 3 and 4, Sand 6, 7 and 8. Points 1 to 8 can be called contour nodes that are selected with reference to the die cavity. The relative positions of the contour nodes determine both sizes and figures at the same time. The block of Fig.2 provides an easy way to simulate forward/reverse forging, there being the need to pay attention to only to the position of the contour and the input velocity of the block. The forming process of a forging with a complex contour can be simulated easily. dividing it into a connecting series of several blocks. An example is shown in Fig.S in which the total deformed body is divided into two blocks that are connected with a common passage Pop. this passage being the exit of the first block and the entry of the second block. Each block is simulation in respect of its own cavity. Fig.S shows the complete course of reverse simulation with these two blocks. In summary. the simulation block is a deformed body that synthesizes figure changes based on the die cavity. It has basic functions such as: changing its contour sizes and figures through some particular optimization; checking the relationship between its boundaries and the die walls; having only one entry and one exit to connect with other blocks.
If) (\J
~"S
F--
'S. ~------
-------
t---~----r-~
f--~ 'S.
243 Fig. 6 Rod-Connection forging design(dimensions: mm)
Luan Yiguo, Sun Sheng / Journal ofMaterials Processing Technology 63 (1997) 244-247
Conclusion Based on UBET, this paper explains some technical problems in the execution of reverse simulation and presents an approach called the Simulation Block Technique. Using these methods, it is easy to simulate the forward/reverse forming process of a forging with a simple or a complex shape. The methods discussed in the paper have been tested successfully in practice. REFERENCES
NEvV
OLD
Fig. 7 Comparison of forging results
II) Sun Sheng, Luan Yiguo, J. of Mats Proc. Tech., 34(1992) 349-356 I2)Sun Sheng, Guan Tingdong, Chinese J. Mech. Eng. (Eng. Ed.), 4(3)(1991) 177-181 13) Sun Sheng, Luan Yiguo,Advances in Engineering Plasticity and its Application, W. B. LEE (Ed.), Elsevier, The Netherlands, (1993), pp. 887-892
247
ELSEVIER
Materials Processing Technology Journal of Materials Processing Technology 63 (1997) 244-247
REVERSE SIMULATION USING THE SIMULATION BLOCK TECHNIQUE AND ITS APPLICATION L,," THE PRECISION FORGING PROCESS Luan Viguo, Sun Sheng Dept. Material Engineering & Science, Shandong l.Jniversity of Technolog): , Jinan City, Shandong Province, P. R China Abstract Referring to die forging as an example, the so-called reverse simulation of the forming process, regardless of whether it is hot or cold forging, is executed . Separating imaginarily the two half-parts of the forging die from their closed position, they move apart from each other progressively. As they move, material in the die cavity deforms and results in an opposite movement to that ofthe normal forming process. Finally an initial billet or a simplified preform forging is obtained. In this paper, basic points in the execution of reverse simulation with UBET are described. For the purpose of easy execution, a new approach named the Simulation Block Technique (SBT) is introduced. Example of successful applications in practice using the above methods are presented. Keyword: die forging, reverse simulation, simulation block technique
J. Introduction
The prevailing design method of metal forming at present is to obey the procedures edited into technological handbooks/text-books, combined with designers' experience, in order to determine the forming stages and to calculnte process/die parameters. This is effective, but it is difficult to exactly understand the quantitative flow of the process. Although a versed designer can exercise precise control with some parts, he might not be sure of spreading his experiences. Indeed, if it is common to consume an excessi'...e amount of raw material in return for success in design and production. Modern design methods for metal forming are quite different. Instead of referring to empirical procedures. they develop various practical simulation techniques for design, based on achievements of metal forming theory, using the computer. They are precise design methods aimed at optimizing such aspects as the saving of raw material or energ)', high product quality, low cost, etc. In some papers such work is called Net Shape Manufacturing (NSM). Many researchers know that preform design is the key point of NSM. Amongst papers in related to preform design, those that employ the reverse simulation technique are very novel: the present paper presents some contributions in this area. 2. Basic points of the reverse simulation technique With the die forging process as an example, reverse simulation starts at the final forging position, separating 0924-0136/97/$15,OO@ 1997 Elsevier Science SA All rights reserved PI! S0924-0136(96)02630-1
imaginarily the two half-parts of the forging die from each other. When executing simulation step-by-step, on the one hand some boundaries of the material in the die cavity leave the die walls, whilst on the other hand the deformed body contracts in the opposite direction to that of filling of the die cavity. Continuing this procedure, a series of simplified configurations and. finally, a biHet are produced. In reverse simulation, the initial forging state can be selected, such as a filled cavity with a pre-determined surplus of metal or without any scrap. If forward simulation is investigated with the billet resulting from reverse simulation, the same fmal forging state should be obtained. Indeed, reverse simulation is an approach to find a desirable forming process by setting the best selected final forging states and taking into account some conditions experienced in the course of forming. To execute reverse simulation. there is the need to deal with three basic problems: (i) the contraction technique of the free sides; (ii) the model for leaving the die walls of the free sides; and (iii) the end positions ofthe reverse simulation. The description of the detail concerning forward and reverse simulation is described in Ref.ll). 3. Simulation block techniquel 21 A complete simulation of a forming process, irrespective of whether it is forward or reverse. consists of a series of instant simulation steps. Although the forming conditions between respective steps are not the same. the steps are connected to
Luan Yiguo. Sun Sheng I Journal ofMaterials Processing Technology 63 (1997) 244-247
each other in the forming state. Amongst, man)' aspects, the most important is to simulate the geometrical contour changes of the deformed body, which latter contains two items: figure and sizes. In general, the technique deals with the size changes of the plastic process in the following way. Based on the known sizes of last step, the technique calculates all of the velocities around the contour after some optimization, then it uniformly expands the contour at the resolved speeds until the end of this step: thus the changed sizes are determined. Except for unbounded figure change resulting from size change, the previous figure has no essential effect on the figure change that the current step will take. The most important factors influencing the figure change is the fmal figure of the forming process or the die c.wity figure. In other words, to construct the figure change that is possible to appear during the forming process, reference has to be made to the die cavity.
245
that if "I is known, only two independent variables are permitted in
"2-
~'J '
v6' In other words. provided that the
input velocity is given, all of the velocities included on the boundaries and inside the block can be determined through optimization.
L. ! L
:="
tc"
-+-
it -T
-::..tIl---..,
~
l
I
7
-
.l~ !
,'L'", I Fig. 2 A complete rectangular block
-
Fig. I Figure change during simulation An example of a forging with an H cross-section is shown in Fig. 1, forward simulated UBET. Irrespective of its sizes change, there was a limited numbers of figures possible to undergo when the ingot filled the die cavity, form a billet to the final forging. Therefore, its figure change could be realized automatically. There are two ways to do this change, one being to set up a switch table about the figures, whilst another is to combine all possible figures together, based on the die cavity, and thus to construct an united block that can expand or compress, becoming any of figures possible to be taken by the deformed body. This kind of block and its changes technique are the so called Simulation Block Technique (SBT) in the present paper. Fig.2 presented a complete block with a rectangular crosssection. Based on UBET theory, it is divided into five elements, the side 2-3 being the entry of the block whilst the side 6-7 is the exit. The sides 1-2,3-4,5-6, 7-8 are the boundaries of the block, which are related to die walls. That the boundaries are bounded or free depends on whether or not they make contact with the die walls, Fig.3. The block has four normal boundary velocities: "I' "2' VI and vtj. Quantities v2 to Vs are the velocities between the elements inside the block. "I is the input velocity ofthe block, which usually is known, whilst "2 is output velocity of the block, which is often unknown. That VI and v6 are known or unknown depend on the state of their sides. Volume constancy controls the relationship between "I' u2' VI ' v6' so
Fig. 3 A block in the die Supposing that "1' v1 and v6 are known, the other boundary velocities of block are deduced as follows, referring to Fig. 2: According to the condition of keeping the total volume of the block constant ,and
2u t a(! -e) - v,(b z - a Z ) + v6 (b z - a Z )
-
2uzb(g- d) = 0
so that U
2au,. (f = _--'-...c.:.. z
e)+-'-_ (b z -_a Z )(V6 -_ ---'-'-~
VI) _'_'__
2b(g-d)
According to the condition of keeping the volume of element I constant: Vz
= VI
According to the condition of keeping the volume of element II constant:
uz(b therefore:
Z
-
a Z )_ v3 (b Z - a Z )+ 2u zb(g- f)
=0
246
Luan Yiguo, Sun Sheng / Journal ofMaterials Processing Technology 63 (1997) 244-247
and using the same method:
= -
V~
2u2 b(e-d) 2 2 + V4 (b -a )
The total upper bound power of the block is the sum of each element. the upper bound power of an element being resolved as follows: We=WrHVs+Wf where Wi is the plastic deforming power, Ws is the plastic shearing power between elements and is Wf friction power between an element and the die wall. As the above respective power items are related only to the element side velocity, the determination of the power can be attributed to tbe calculation of the element velocities. I
(a)
(b)
(c)
Referred to Fig.2. it is easy to construct a block with a rectangular cross-section used for plane deformation. Also other complex block can be designed on the basis of the above principles. Thus, joining in-series blocks and starting with the first block. a forward/reverse simulation can be spread outwards so as to be able to simplify the simulation of the forming process. 4. Application in production In this paper a method of controlling flash formation in dieforging process design has been used. Briefly speaking, this method is to make the metal almost till the die cavity before being forced out. It minimizes the effect of resistance on the die bridge. The method needs reverse simulation to determine a proper preform forging or an initial billet. In the paper a computer system including forward/reverse simulation and SBT has been established for analyzing and designing the axisymmetridplane die forging process. Fig.6 presents the designs resulting from reverse simulation, billets prepared according to simulation design and forged directly in to the tinal forging die. exhibiting a tilled die cavity and a uniform thin flash arrangement, as expected. Fig.7 presents a comparison of the forging results between the new design of this paper and the current design in forging shop.
Fig. 4 The varieties of the block Some changes can be developed from Fig.2, three examples being presented in Fig. 4. There is no to remember these changes separately. Indeed, Fig.4(a) was obtained by letting point S go on to point 6 and point 7 go on to point 8. In addition, if point 1 were to go on to point 2, then Fig.4(b) would appear. In this way a pancake billet (Fig.4(c» results from the overlapping of couples of points such as 1 and 2, 3 and 4, Sand 6, 7 and 8. Points 1 to 8 can be called contour nodes that are selected with reference to the die cavity. The relative positions of the contour nodes determine both sizes and figures at the same time. The block of Fig.2 provides an easy way to simulate forward/reverse forging, there being the need to pay attention to only to the position of the contour and the input velocity of the block. The forming process of a forging with a complex contour can be simulated easily. dividing it into a connecting series of several blocks. An example is shown in Fig.S in which the total deformed body is divided into two blocks that are connected with a common passage Pop. this passage being the exit of the first block and the entry of the second block. Each block is simulation in respect of its own cavity. Fig.S shows the complete course of reverse simulation with these two blocks. In summary. the simulation block is a deformed body that synthesizes figure changes based on the die cavity. It has basic functions such as: changing its contour sizes and figures through some particular optimization; checking the relationship between its boundaries and the die walls; having only one entry and one exit to connect with other blocks.
If) (\J
~"S
F--
'S. ~------
-------
t---~----r-~
f--~ 'S.
243 Fig. 6 Rod-Connection forging design(dimensions: mm)
Luan Yiguo, Sun Sheng / Journal ofMaterials Processing Technology 63 (1997) 244-247
Conclusion Based on UBET, this paper explains some technical problems in the execution of reverse simulation and presents an approach called the Simulation Block Technique. Using these methods, it is easy to simulate the forward/reverse forming process of a forging with a simple or a complex shape. The methods discussed in the paper have been tested successfully in practice. REFERENCES
NEvV
OLD
Fig. 7 Comparison of forging results
II) Sun Sheng, Luan Yiguo, J. of Mats Proc. Tech., 34(1992) 349-356 I2)Sun Sheng, Guan Tingdong, Chinese J. Mech. Eng. (Eng. Ed.), 4(3)(1991) 177-181 13) Sun Sheng, Luan Yiguo,Advances in Engineering Plasticity and its Application, W. B. LEE (Ed.), Elsevier, The Netherlands, (1993), pp. 887-892
247