Rotary forging with double symmetry rolls (DSRs) is a new metal plastic forming technology developed on the basis of conventional rotary forging with a single roll, which uses a pair of symmetrical cone rolls to realize continuous local pressure plastic deformation of the workpiece. Large-diameter, thin discs are a key component in nuclear power, aerospace, deep-sea exploration, and other fields. At present, the forming process of large-diameter discs mainly includes welding and multiple local upsetting, but these processes exhibit many defects and can not meet the requirements of industry. In this paper, a large diameter : thickness ratio disc is integrally formed by rotary forging with DSRs. Using theoretical calculation and finite element simulation methods, the stable rolling conditions and calculation formulas of force and power parameters of rotary forging with DSRs of a large diameter : thickness ratio disc are derived. Based on the reliable three-dimensional rigid-plastic finite element model, the plastic deformation characteristics of rotary forging with DSRs of discs are studied, the reliability of the stable rolling conditions and the calculation formulas of force and power parameters are verified, and the defects and causes of unstable rolling conditions are analysed. An experiment was carried out on a rotary forging press developed with double symmetry rolls, and the experimental results are in good agreement with simulation results, which demonstrated that rotary forging with DSRs is a reliable technology for forming large diameter : thickness ratio discs. The results of this research are helpful to promote the further development of rotary forging with DSRs.

With the development of modern industrial technology, large integral disc parts are more widely used in industrial fields and have important applications in deep-sea exploration, nuclear energy, military industry, aerospace, and other fields. The cylindrical shell of a large hydrogenation reactor and a large spherical tank for deep-sea exploration are both produced by the forging process of large-diameter discs. An integral disc with a diameter of more than 8 m is required for the head plate of the nuclear reactor high-pressure vessels. The spaceflight fuel tank needs a circular plate with a diameter of 4 to 5 m and a height of 0.008 m. At present, the main forming processes of large-diameter discs are welding, plate cutting, and multiple local upsetting of the plate. When the large-diameter disc is formed by welding, more forming defects will occur. When the large-diameter disc is formed by a cutting plate, the machining is large, and the material utilization rate is low. When the large-diameter disc is formed by multiple local upsetting of the plate, it requires a large forging strike force and high-tonnage equipment, and the thickness error of the disc formed is large. The large-diameter discs produced by these forming processes cannot meet higher safety grades and cannot meet the needs of nuclear power, aerospace, and military industry for large-diameter integrally formed discs.

Rotary forging is an innovative metal plastic forming process which is
widely used in manufacturing discs, rings, and gears (Yuan et al., 1999; Sheu
et al., 2008; Zhu et al., 2011), and it has many advantages of a low forging
pressure, a high machining accuracy, and a low level of noise and vibration. Owing
to its inherent advantages, many scholars have studied rotary forging. Zhang (1984) studied the force and power parameters in the rolling process and
derived the calculation formula of the force and power parameters. Canta et
al. (1998) carried out rotary forming with lead and steel materials and
obtained the energy distribution during the rotary forming processes. Choi
et al. (1997) analysed the rotary forging process, studied the velocity
field, and determined the upper-bound force by minimizing the total power
consumption. Zhou et al. (1992a, b) studied the metal flow laws and
forming defects in the process of rotary forging of the cylindrical
workpiece, which provided a reference for die design. Jin et al. (2018) put
forward a process optimization method for cold orbital forging of components
with a deep and narrow groove, analysed the cold orbital forging process under
three metal flow modes, and revealed defect mechanisms such as underfilling
and folding. Jin et al. (2016) proposed a new sheet blank rotary forging
process for thickening the rims of disc-like sheet blanks and studied the
effects of the main defects and process parameters on formation. Zhuang et al. (2016) studied the cold orbital forging technology of spur bevel gears and
analysed the influence of process parameters on the final step. Loyda et al. (2018) studied the influence of the rotary forging process on the microstructure
behaviour of nickel-based superalloys. Pérez et al. (2017) analysed the
microstructure and texture evolution of high-strength materials during the cold
rotary forging process. Han et al. (2009, 2014) studied the difference of
metal flow between cold rotary forging and conventional forging of
the cylindrical workpiece and proposed a method of forming non-rotary gear
parts by cold rotary forging. Han et al. (2016) proposed an innovative cold
orbital forging method for manufacturing gear racks and conducted the
accurate design of the die to ensure the forming accuracy of the gear rack.
Liu et al. (2019, 2020) analysed the influence of process parameters of
rotary forging on formation, defects, and preventive measures. For research
on the formation of discs and rings, Wang et al. (1999, 2005) studied velocity
fields and stress–strain fields of the ring workpiece in the rotary forging
process and revealed the deformation mechanism of rotary forging of the ring
workpiece. Hua et al. (2009) and Han and Hua (2011) studied the plastic deformation mechanism
of cold rotary forging of cylindrical parts, analysed the effect laws of the
feed rate of the lower die, rotational speed, and inclination angle of the
upper die on metal flow and predicted the wear of dies. Liu et al. (2000,
2004) studied the forming process of rotary forging with a single roll of the
cylindrical workpiece with a

Rotary forging is an advanced forming process which is widely used in the production of discs. At present, most of the research on rotary forging focuses on the forming of small-diameter discs or rings. Large diameter : thickness ratio discs (diameter : thickness ratio greater than 100) cannot be integrally formed, which limits the development of rotary forging technology. In order to meet the industry demand for large diameter : thickness ratio discs, this paper uses novel rotary forging with double symmetry rolls to integrally form large diameter : thickness ratio discs. Rotary forging with DSRs is a new metal plastic forming technology which is developed on the basis of conventional rotary forging with a single roll and uses a pair of symmetry rolls to realize local accumulated deformation of the workpiece. Rotary forging with DSRs has the advantages of a low forging force, high machining accuracy, and material saving. Based on the reliable three-dimensional rigid-plastic finite element model, the calculations of force and power parameters, stable rolling conditions, and plastic deformation characteristics of rotary forging with DSRs of large diameter : thickness ratio discs were studied. The experiments were carried out on the rotary forging press developed with double symmetry rolls, which verified the correctness of the calculation of force and power parameters and stable rolling conditions. The results of this research are helpful to promote the further development of rotary forging with DSRs of large diameter : thickness ratio discs.

The working principle of conventional rotary forging with a single roll is
shown in Fig. 1a. In rotary forging with a single roll, the conical upper die
with an inclination angle of

Schematic diagram of rotary forging.

The calculation of the force and power parameters and the stable rolling conditions of rotary forging with DSRs of large diameter : thickness ratio discs is important to the design of the rotary forging press with double symmetry rolls and the theoretical basis of the numerical simulation. The force condition of the workpiece during the process of rotary forging with DSRs is obviously different from that of conventional rotary forging with a single roll. Therefore, it is very important to establish accurate and reliable calculation formulas of the force and power parameters of the rotary forging press with double symmetry rolls and the stable rolling conditions. Based on the theories of rotary forging and metal plastic forming, the calculation of force and power parameters of the rotary forging press with double symmetry rolls and the stable rolling conditions is studied.

During the forming process of rotary forging with DSRs of large diameter : thickness ratio discs, the contour curve of the contact surface
between the cone roll and the workpiece is composed of the intersection
curve of the cone roll surface and the upper surface of the workpiece. The
contact surface between the cone roll and the workpiece is helical. Since
the feed amount of the lower die is much smaller than the radius of the
workpiece, the helical surface is regarded as a plane. The contact area
between the cone roll and the workpiece is shown in Fig. 2. In the process of
rotary forging with DSRs of discs, the surface of the disc can be divided
into two parts: contact area (1) and non-contact area (2). Due to the
symmetrical distribution of the two rolls, the contact area (1) between the
upper die and the workpiece is composed of two symmetrical parts, and the
contact area (1) is the active deformation area. The non-contact area (2) is
also distributed symmetrically, and the non-contact area (2) is the passive
deformation area. Therefore, this paper derives the calculation formula for
the contact area between the upper die and the workpiece, i.e. the
calculation formula for contact area (1). Due to the symmetrical distribution
of the two rolls, the contact area (1) can be divided into two areas: the area
OAB and the area ODE. These two surfaces are symmetrically distributed and
have an equal area, and the surface

Contact area between the cone roll and the workpiece.

The area

Feed amount per revolution.

In this paper, the slip line method is used to calculate the forging force
of rotary forging with DSRs of large diameter : thickness ratio discs. The
slip line field during the forming process is shown in Fig. 4. Where

Slip line field during the forming process.

The expression of the functional relation between

The schematic diagram of the decomposition of forging force is shown in
Fig. 5. The forging force of the cone roll on the workpiece can be decomposed
into two directions along the

Schematic diagram of the decomposition of the forging force.

Equation (23) can be obtained from Fig. 5.

The mechanical model of stable rolling of the workpiece is shown in Fig. 6.

Mechanical model of stable rolling of the workpiece.

Analysis of the static friction moment of the disc.

Only when the force of the lower die on the workpiece is greater than or
equal to the force of the cone rolls on the workpiece will the workpiece
not rotate with the cone rolls, i.e. it is stationary relative to the lower
die, then stable rolling can be achieved, and the

In this paper, DEFORM-3D software was adopted to simulate and analyse the forming process of rotary forging with DSRs of large diameter : thickness ratio discs. The three-dimensional finite element model of rotary forging with DSRs of large diameter : thickness ratio discs is shown in Fig. 8.

3D finite element model of rotary forging with DSRs.

In order to improve the calculation efficiency and accuracy of the results, the workpiece was discretized using a tetrahedral mesh with 32 000 elements and 5692 nodes. Because the elastic deformation is far less than the plastic deformation of the workpiece in the forming process of rotary forging with DSRs of large diameter : thickness ratio discs, the workpiece is defined as a rigid-plastic body. The workpiece material is AISI 1045, and its mechanical properties are shown in Table 1.

Mechanical properties of the workpiece material.

Boundary conditions are specified and enforced at the nodes or element edges
in the finite element mesh. The main boundary condition in rotary forging is
contact boundary condition, which is friction boundary condition. Friction
boundary conditions are generally divided into three categories: Coulomb
friction, maximum friction, and friction-invariant conditions. Since the
rotary forging adopted in this paper is a kind of forming method that belongs to
hot rotary forging, the maximum friction condition is selected in the
simulation. Friction in the model is defined as

Processing parameters for simulation of rotary forging with DSRs.

According to the stable rolling conditions, there are mainly three different kinds of plastic deformation of the workpiece.

The first case is that the feed amount per revolution

Deformation process of rotary forging with DSRs of a disc under the first deformation condition.

The second case is that the feed amount per revolution

Deformation process of rotary forging with DSRs of a disc under the second deformation condition.

The third case is that the feed amount per revolution

Deformation process of rotary forging with DSRs of a disc under the third deformation condition.

In order to explore the plastic deformation characteristics of rotary forging with DSRs of large diameter : thickness ratio discs, based on the plastic deformation process of stable rolling conditions, the surface and axial PEEQ (equivalent plastic strain) of the workpiece are analysed in detail. The surface PEEQ distribution of the disc is shown in Fig. 12. It can be seen from Fig. 12 that the PEEQ distribution on the surface of the workpiece diffuses from the centre to the edge, presenting an approximately central symmetrical distribution. In the initial stage of the forming process, due to the small feed amount, both the PEEQ value of the workpiece and the difference are small, as shown in Fig. 12a. As the forming process continues, large plastic deformation zones are generated. Due to the instability of deformation, the distribution of PEEQ is inhomogeneous, and the difference is large, as shown in Fig. 12b and c. In the final stage, when the workpiece is formed, the PEEQ value in the circumferential direction is much larger than that in the centre, and the distribution of the PEEQ in the circumferential direction is more uniform than that in radial direction, i.e. the PEEQ values are basically the same within the same radius, as shown in Fig. 12d.

Surface PEEQ distribution of the disc.

PEEQ distribution in the axial direction of the disc.

Comparison of the contact area between the cone rolls and the workpiece between theoretical calculation and simulation.

In order to explore the plastic deformation characteristics of rotary forging with DSRs of large diameter : thickness ratio discs, the axial PEEQ of the workpiece is analysed in detail. The PEEQ distribution in the axial direction of the disc is shown in Fig. 13. It can be seen from Fig. 13 that the cone roll first contacts the metal on the upper surface of the workpiece, and the metal on the upper surface of the workpiece first satisfies the yield condition, and plastic deformation occurs, and the plastic deformation zone gradually expands along the radial and axial direction, as shown in Fig. 13a. As the forming process continues, the thickness of the workpiece decreases gradually. The plastic deformation zone penetrates from the upper surface to the lower surface of the workpiece, and the whole workpiece enters the plastic deformation state, as shown in Fig. 13b and c. In the final stage, the workpiece is basically formed. It can be seen that the PEEQ gradually decreases from the upper surface to the lower surface of the workpiece in the axial direction, and the PEEQ value on the lower surface of the workpiece is smallest, as shown in Fig. 13d. During the whole forming process, the maximum PEEQ value is 17.02 mm/mm, and the minimum PEEQ value is 4.57 mm/mm.

Comparison of force and power parameters between theoretical calculation and simulation.

500 t rotary forging press with double symmetry rolls.

Compared with conventional forging technology, the obvious difference of rotary forging with DSRs is that the cone rolls and the workpiece are in partial contact during the forming process. The contact area between the cone rolls and the workpiece is constantly changing due to the continuous revolution of the cone rolls and the continuous change of the diameter of the workpiece. The comparison of the contact area between the cone rolls and the workpiece between theoretical calculation and simulation is shown in Fig. 14. From the contact area curve of simulation in Fig. 14, it can be seen that in the initial stage of forming process, the cone rolls contact the upper surface of the workpiece, and the contact area increases rapidly from zero to a certain value. Since the cone rolls and the workpiece are in partial contact, the workpiece surface warps slightly, and the contact area between the cone rolls and the workpiece fluctuates slightly. As the forming process continues, the diameter of the upper surface of the workpiece is larger than that on the lower surface. It is difficult for the metal to flow on the upper surface of the workpiece, and the diameter increases slowly. Therefore, the contact area between the cone rolls and the workpiece increases slowly. In the final stage of the forming process, after the lower die stops feeding upward, the cone rolls continue to rotate so as to make the upper surface become a plane, and the contact area decreases rapidly. It can be seen from the curve of contact area between the cone rolls and the workpiece that the contact area is always in dynamic change, which is highly nonlinear and nonstationary. According to the comparison between the contact area calculated by Eq. (8) and the contact area of simulation, the error between the theoretical calculation result and the simulation result is small, which proves that the formula derived in this paper is correct.

Discs formed on the 500 t rotary forging press with double symmetry rolls.

Force and power parameters are the important basis for designing and manufacturing rotary forging presses and guiding experiments. Force and power parameters in the forming process of rotary forging with DSRs of large diameter : thickness ratio are studied in detail. The comparison of force and power parameters between theoretical calculation and simulation is shown in Fig. 15. It can be seen from Fig. 15 that the curve of the axial forging force and forging moment is divided into three stages. In the first stage, the cone rolls first come into contact with the upper surface of the workpiece, resulting in the plastic deformation of the upper surface of the workpiece, and thus the axial forging force and forging moment increase rapidly from zero to a certain value. In the second stage, with the gradual stabilization of the forming process and the reduction of the thickness of the workpiece, the plastic deformation zone penetrates from the upper surface to the lower surface, and the whole workpiece has entered the steady deformation stage, and thus the axial forging force and forging moment increase slowly up to the maximum value. In the final stage, the lower die stops feeding upward, while the cone rolls continue to rotate, so as to make the upper surface become a plane, thus resulting in less metal participating in plastic deformation. So the axial forging force and forging moment decrease rapidly. In the forming process, the maximum axial forging force and forging moment are 3521 kN and 23 848 N m, respectively. According to Eqs. (20) and (28), the axial forging force and forging moment of theoretical calculation are obtained respectively. Compared with the axial forging force and forging moment of simulation, the error between theoretical calculation results and simulation results is small. The error of forging force is less than 10 %, and the error of forging moment is less than 15 %. The maximum axial forging force and forging moment of theoretical calculation are 3713 kN and 26 409 N m, respectively.

Comparison of axial forging force between experiment and theoretical calculation.

In order to verify the reliability of the stable rolling conditions,
calculation formulas of force and power parameters, and finite element
simulation of rotary forging with double rolls of large diameter : thickness
ratio discs, experiments were carried out on a 500 t rotary forging
press developed with double symmetry rolls. The 500 t rotary forging press with double
symmetry rolls used in the experiment is shown in Fig. 16. The discs formed
on the 500 t rotary forging press with double symmetry rolls are shown in
Fig. 17. A disc formed under unstable rolling conditions with the lower die
feed rate

The comparison of axial forging force between experiment on the 500 t rotary forging press and theoretical calculation is shown in Fig. 18. It can be seen from Fig. 18 that the theoretical calculation results are in agreement with the experimental results, and the error is relatively small, which proves that the calculation formulas for force and power parameters of rotary forging with DSRs of large diameter : thickness ratio discs are reliable.

In this paper, a novel forming process of large diameter : thickness ratio
discs is studied, namely rotary forging with double symmetry rolls. At the
same time, the plastic deformation law and related calculation formula of
large diameter : thickness ratio discs are studied. The following conclusions
can be drawn.

In this paper, the stable rolling conditions and the calculation formulas for force and power parameters of rotary forging with DSRs of large diameter : thickness ratio discs are derived, which are the theoretical basis of simulation process parameters and experiments.

The stable rolling conditions are verified by numerical simulation. When
the feed amount per revolution

Based on the plastic deformation process of stable rolling conditions, the surface and axial PEEQ of the workpiece are analysed. The PEEQ distribution on the surface of the workpiece diffuses from the centre to the edge, presenting an approximately central symmetrical distribution. The plastic deformation zone first occurs on the upper surface of the workpiece. With the feed of the lower die and the revolution of the cone rolls, the plastic deformation zone penetrates from the upper surface to the lower surface. The PEEQ value decreases from the upper surface to the lower surface of the workpiece in the axial direction, and the PEEQ value of the lower surface of the workpiece is smallest.

Experiments were carried out on a 500 t rotary forging press developed with double symmetry rolls. The experimental results are in agreement with the theoretical calculation results, which proves that the stable rolling conditions and the calculation formulas of force and power parameters are reliable.

Data can be made available upon reasonable request. Please contact Chun Dong Zhu (zcdzcd6252@sina.com).

CDZ put forward the method of rotary forging with double symmetry rolls (DSRs) to form large diameter : thickness ratio discs, and he conducted the final examination of the whole paper. RFM studied the theoretical formula derivation, conducted the numerical simulation analysis, and wrote the article. YFG and ZHW performed the experiments to verify the reliability of the theoretical formula and the numerical simulation.

The authors declare that they have no conflict of interest.

The authors would like to thank the National Natural Science Foundation of China (grant no. 51875427) for the support given for this research. In addition, the authors would like to thank the Suizhou-WUT Industry Research Institute (grant no. suikefa [2019]9).

This research has been supported by the National Natural Science Foundation of China (grant no. 51875427) and the Suizhou-WUT Industry Research Institute (grant no. suikefa [2019]9).

This paper was edited by Giovanni Berselli and reviewed by two anonymous referees.