Technology optimization analysis of three-roll rotary piercing process for seamless steel pipe

A three-roll rotary piercing process (TRPP) with severe plastic deformation was conducted to fabricate stainless steel seamless tubes with high mechanical properties. To address production issues such as Front stuck (FS) - where the front end of the tube blank cannot be accessed, Back stuck (BS) - where the back end of the tube blank cannot be penetrated, and steel-heaping, the process parameters were optimized through simulation and testing in this study. Additionally, a new structure for the three-roll piercing machine was designed and developed. The changes in roll feed angle and plug advance were systematically analyzed for defects in the tubular billet. Numerical simulations of the TRPP were performed using commercially available FEM software (Simufact Forming) to analyze the stress, strain, and temperature distributions in the pierced tubes. Experimental analysis was conducted on seamless tubes with different diameter defects, leading to the discovery of optimal rules. Based on the experimental and numerical investigations, it was found that optimizing plug advance and roll feed angle can enhance the forming quality of the tubes.


Introduction
The seamless AISI304 stainless steel pipe has been an important pro le widely used in oil, transportation and national defense industries mainly due to its excellent corrosion and oxidation resistances and good performance under high and low temperatures [1].The initial stage of seamless tube manufacturing is known as the tube piercing phase (TPP).In this phase, a pre-cut billet with speci c dimensions and geometry is heated up to more than 80% of its melting temperature, until it is converted to plasticized form [2,3].
The three-roll perforator shares similar advantages with the two-roll perforator, including high e ciency, exible production, and the ability to penetrate long billets.However, its most notable feature lies in the deformation zone of the metal, which experiences three-way compressive stress [4,5].Unlike the two-roll perforator, the three-way compressive stress eliminates the occurrence of center rupture.As a result, the Three-Roll Rotary Piercing Process (TRPP) exhibits greater potential in enhancing the quality of the tubular billet and increasing production capacity [6].TRPP ensures high dimensional precision of the tubular billet and enables the perforation of a wide range of alloy steel pipes [7].Consequently, TRPP serves as a commendable model for promotion and possesses signi cant development potential [8].
The quality defects of the tubular billet can be categorized into two types.The rst type arises from inherent defects in the tube blank itself or defects that occur during the heating process [9].These defects are further ampli ed when the awed tube blank undergoes the perforation process [10].On the other hand, the second type of defect emerges during the perforation process due to incorrect design or adjustment of the process parameters, unfavorable shape of the perforating tool, and quality defects on the surface of the tool [11].The unquali ed tubular billets produced by the TRPP can be categorized into two main types: Front stuck (FS) and Back stuck (BS).In the case of FS, the front end of the tube blank is inaccessible, resulting in the formation of a cavity that cannot be engaged by the roller as shown in Fig. 1a.On the other hand, BS occurs when the plug fails to penetrate the tube blank, sometimes even falling inside the blank as shown in Fig. 1b.In severe cases, as depicted in Fig. 1c, the surface of the tubular billet becomes twisted, leading to the phenomenon of steel heaping [12,13].
Murillo-Marrodan et al. [14] addressed various friction models at the interface of plug and rollers during the TPP phase of 9Cr steel.The FEM software is used to understand thermo-physical phenomena during the TPP phase like cross roll force and torque to analyze power consumption, TPP process e ciency, and analysis of tube twisting.Li (2002) [15]reported that the three-roll skew rolling process results in a more obviously uneven deformation distribution on the round bar, compared with the two-roll process.Panov (2005) [16] studied shear stresses and their dependence on various process parameters in the helical rolling of solid semi-nished products.Panov's results indicated that an increase in tension increases the intensity of the negative shear stresses in the zones not in contact with the rolls, whereas an increase in thrust increases the positive shear stresses in the same zones.Gao et al. (2009) [17]used DEFORM-3D to create an FEM model of spiral n tube rolling using the three-roll skew rolling process.Shuang et al. (2017) [18] put forward the technology of combining RTP process with rolling process to prepare high precision tubes.Romanenko and Sizov (2014) [19] investigated the dimension uniformity of thick-walled tubes.Yu.V. Gamin [20] studied the temperature conditions and stress-strain states of the bar during radial shear rolling.
This study aims to investigate the impact of plug advance and roll feed angle on the defects of tubular billets in a new structure of the TRPP [21].By calculating the angle relationship between the displacement of the connecting rod and the feed angle of the roller, the study ensures the consistency and accuracy of the feed angle during the production process.The in uence of different plug advances on the tubular billets was analyzed through simulation [22].Furthermore, through production testing, the feed angle and plug advance parameters were optimized to ensure the production of quali ed tubular billets using the TRPP [23].
2. Design of key process parameters

Angular relationship between connecting rod excursion and roll feed Angle
The axial force increases as the feed angle of the roller increases.On the one hand, the axial speed increases with the increase of the feed angle, and on the other hand, the unit compression amount increases with the increase of the roll feed angle [24].
Figure 2(a) shows the adjusting device of the left and upper rollers in the self-made piercing machine.Through the four-link rod device, the relation between the displacement of the connecting rod and the feed angle of the roller in the TRPP can be accurately calculated.The rotation of the motor drives the screw to rotate, so that the nut connected with the screw moves up and down.The connecting rod de ection drives the rotating-drum deviation, resulting in the change of roll feed angle.
Compared with the common three-link rod device, the new structure has higher accuracy, more reliable movement, and more convenient installation of roll rolling angle.
The relation formula of screw up and down movement and roll feed angle deviation is found out by using the principle of fourlink mechanism, and the schematic diagram of left and upper rollers are made, as shown in Fig. 3.
According to the cosine theorem of trigonometric functions, , , the x is the amount of screw movement.According to the sine theorem, , the is the calculation parameter of the roll feed angle.In the same way, the corresponding parameters of the right roll can be calculated as shown in Table 1.

Force analysis of the plug
When the advance of plug is too large, the front compression of the plug will be reduced, and the axial pulling force of the tube blank will be reduced.If the advance of plug is too smell, the resistance will increase when the tube blank is pierced into the end by the plug.The axial force also directly affects the forward speed of the tube blank, which further affects the product quality and output [25].where denotes the radius of the front end of the plug (mm); is the metal stress state coe cient at the front end of the plug, generally between 0.5 0.6; is the ow limit of metal.
The basic formula of the axial force acting on the entire plug is expressed as follows: where denotes the positive pressure applied to the plug; denotes the tangent angle of plug generatrix; denotes friction coe cient between tube blank and plug.
Due to the spiral motion of the tubular billet, the direction of contact friction force between the tube blank and the plug is not parallel to the piercing axis.The expression for the axial component of contact friction force is as follows: where denotes the direction angle of friction force between the tube blank and the plug.The above formulas are combined as follows: Excessive the advance of plug can create a large cavity in the center of the solid billet, especially when pierce stainless steel pipes, which signi cantly increases axial resistance.Due to the formation of the hole cavity, the surface roughness increases the contact friction force, and it is easy to stick to the plug, resulting in an increase in instantaneous axial force and causing the FS.When the plug advance is too small, the speed of TRPP increases, the slippage decreases, and the compression of unit increases, ultimately leading to an increase in axial force and causing the BS.
3. Finite element modeling and analysis

Finite element modeling
Finite element modeling of the TRPP was performed using the FEM-based Simufact Forming software.A geometrical model of the analyzed process is illustrated in Fig. 5.The model comprises the piercing section with three identical barrel-type rolls arranged symmetrically at an offset of around the rolling centerline, plug, push pedal, and the billet molded in the form of a cylindrical rod.
For the numerical simulation, a rigid plastic material model was employed.Material properties of AISI304 stainless steel were assigned to the billet, with 93mm in diameter and 100mm in length.The material model and the parameters were determined from the database library of the Simufact Forming software.The plastic material behavior of the billet is speci ed with a material ow stress function or ow stress data.The ow stress equation is dependent on the strain, strain rate, and temperature.Figure 6(a) and (b) presents the ow curves of AISI 304 stainless steel material, which depicts the variation of ow stress as a function of strain for different billet temperatures, at strain rates of 0.1 and 100 , respectively.The Normalized Cockcroft & Latham damage model is the model used in FEM.Mechanical work to heat speci es the fraction of mechanical work converted to heat.The operating parameters employed in the calculations corresponded to the parameters adopted for the rolling experimental tests.More speci cally, the entire volume of the material prior to the formation process was heated at a temperature of 1150℃, while the tools were maintained at a constant temperature of 150℃.
The simulation conditions are as follows: Shear friction is selected, the friction factor is 0.80, and the friction factor between the push pedal and the tube blank is 0.1.
The initial temperature of the solid tube is set to 1150°C and the initial temperature of the roller is 150°C.The heat transfer coe cient between the tube blank and tools is 31 .
In the experiment, the length of the tube blank is 100 mm, and the rotation speed of the roll is 160rpm.Table 2 shows the process parameters of three-roll rotary piercing.

Simulation analysis
Figure 7a and Fig. 7b show the stress-strain diagram of the tube blank in TRPP when it is FS.The plug advance is 55mm and the feeding angle is 6° for simulation.The maximum equivalent stress is 35.4Mpa and the maximum effective plastic strain is 4.3.The stress and strain are mainly concentrated at the inlet end of the tubular billet.Because the plug advance is too large, the stress is concentrated in the front end of the plug.The feed angle of rollers is too small, resulting in reduced axial force.
Therefore, the compression rate of plug is too low, and the pulling force in the front of deformation area is insu cient, resulting in the FS.
Figure 7c and Fig. 7d reveal the stress-strain diagram of the tube blank in TRPP when it is BS.The plug advance is 20mm and the feeding angle is 8.5° for simulation.The maximum equivalent stress is 46.4Mpa and the maximum effective plastic strain is 15.7.The stress is mainly concentrated at the end of the tubular billet, and the strain is concentrated at the contact position between the roller and the tube.The plug advance is too small, the feeding angle is too large, resulting in the increase of rolling force.When the tubular billet is pierced to the end of the tube, the tail of the billet cannot be penetrated due to the small plug advance and the insu cient reduction rate, resulting in the BS.
Figure 7e and Fig. 7f show the stress-strain diagram that can be normally penetrated in TRPP.The plug advance is 40 mm and the feeding angle is 7° for simulation.The tube blank can be penetrated normally.Therefore, excessive or insu cient plug advance and feed angle can cause tubular billet defects.During TRPP of the seamless steel tubes, the entire volume of the material was intensively utilized.The magnitude of stress needs to meet the compression rate of the pipe blank.The highest strain occurred in the outside surface of the formed steel tubes due to the highest reduction in the cross-section of the billet.
The strain reached moderate values inside the steel tube as well as at other places where reduction in the cross-section of the billet was low.Thus, the dominant direction of material ow is circumferential as a result of friction forces and of considerable redundant strains occurring in the product during the TRPP.
Figure 8 presents the temperature distribution in the seamless steel tubes during the TRPP.As expected, the maximum temperature was observed on the external surface of the formed steel tubes in the piercing section at approximately 1247 , which is about 150 to 200 higher than the temperature on the inside surface.A similar temperature difference was also observed using infrared thermometer in the experimental tests.
The aforementioned result demonstrates that the heat is carried away from the deforming material to the tools that are maintained at low temperature.During the TRPP, the temperature of the material in the piercing process increased, which was caused by the generation of heat as a result of deformation and friction.At the same time, before the material was subjected to the test machine at the end of the billets, the temperature was reduced or maintained at 1100 .We can therefore assume that temperature is one of the reasons for the tail ring and for the tail triangle in the three-roll piercing.The force applied to subject the material into the test machine resulted in the rapid decrease of the tail, the increase of the backward slip, and the rapid increase of radial expansion.
FEM allows a systematic analysis of forces during the TRPP. Figure 9 reveals the FEM data related to the roll force and the plug axial force.It can be concluded that the axial force of the plug is much greater than the axial force of the rolling roller.
Figure 10 shows the variation in the roll torques during the TRPP.Forces and moments vary in the TRPP in the form of oscillations that are typical during the process of metal forming.In addition, roll torque are almost identical, and only small differences have been observed due to a variation in the location of the billet among the rolls during the piercing process.

Test optimization
The test site of the three-roll piercing machine is shown in Fig. 11a.AISI304 stainless steel tube blank is heated in a heating furnace, as shown in Fig. 11b.Then, the tube blank is fed from the entrance table at a speed of 600mm/s into the three-roll piercing test machine, which uses a newly developed rotating-drum device of four-link rod mechanism in Fig. 11c.The tube blank contacts the rolling roller and maintains a temperature of 1150 before piercing the tube blank.The shape and size of the roll and head of the piercing machine are the same as the three-dimensional model.Table 3 shows the technical requirements of stainless-steel tube billets.
Table 3 Tube blank requirements project requirements Ingredient AISI304 stainless steel.
Curvature ≤ 2.5mm/m.The end of the tube blank is perpendicular to the axis of the tube blank.No ying thorns.Tangent slope ≤ 3°.

Surface quality
Cracks, folds, scars, and inclusions are not allowed on the surface.Scratches, dents, pits ≤ 0.5mm.

Internal quality
The microstructure, non-metallic inclusions, carbides, depth of non-uniform decarburization layer, and austenite grain size meet the experimental requirements.
There are three kinds of diameters for the solid tube blanks: 65mm (3 pieces), 88mm (6 pieces), 93mm (3 pieces), length 1000mm, material AISI304.Defective tubular billet resulting from different plug advance and feed angle, as shown in Table 4.
Defective tubular billet include Front stuck(FS)-the front end of tube blank cannot be accessed, Back stuck(BS)-The back end of the tube blank cannot be penetrated.After optimizing the advance of plug and feed angle of roller, two pieces of 65, 88 and 93 tube blanks were also tried on, and high-quality tubular billets could be penetrated as shown in Fig. 12.
The parameters of the successfully penetrated tubular billets, as illustrated in Table 5, were compared with those of the damaged tubular billets, as illustrated in Fig. 4. For the tubular billets of 65, the No. 1, No. 2, and No. 3 in Table 4 are compared with the No. 1 and No. 2 in Table 5.When the Pore-throat diameter is all 56, the plug advance is 38mm, and the feed angle is 6.3°, there is a phenomenon of FS.When the plug advance is 20mm, 23mm, and the feed angle is 7.9°, 7.8°, there is a phenomenon of BS.When the plug advance is 26mm, 32mm, and the feed angle is 7°, 7.1°, quali ed tubular billets can be penetrated.
For the tubular billets of 88, the No. 4, and No. 9 in Table 4 are compared with the No. 3 and No. 4 in Table 5.When the Porethroat diameter is all 76, the plug advance is 46mm, 47mm, 50mm, and the feed angle is 6.2°, 6.4°, 6.5°, there is a phenomenon of FS.The plug advance is 20mm, 25mm,30mm, and the feed angle is 7.4°, 7.6°, 8°, there is a phenomenon of BS.The plug advance is 38mm, 40mm, and the feed angle is 6.9°, 7°, quali ed tubular billets can be penetrated.
For the tubular billets of 93, the No. 10, No. 11, and No.12 in Table 4 are compared with the No. 5 and No. 6 in Table 5.When the Pore-throat diameter is all 80, the plug advance is 46mm, 48mm, and the feed angle is 6.3°, 6.6°, there is a phenomenon of FS.The plug advance is 34mm, and the feed angle is 7.5°, there is a phenomenon of BS.The plug advance is 38mm, 44mm, and the feed angle is 6.8°, 7.2°, quali ed tubular billets can be penetrated.

Summary and conclusions
This article aims to solve the problems of FS, BS, and steel-heaping during the TRPP of AISI304 stainless steel bars by adjusting the process parameters of feed angle and plug advance.The TRPP is optimized.In addition, the parameters causing the unquali ed capillary will also be related to temperature, throat diameter, roll speed and other parameters.In addition, other parameters such as temperature, Pore-throat diameter, and roller speed can also cause unquali ed tubular billet.
1.The optimization range of roller feed angle for pipe blanks with diameters of 65mm, 88mm, and 93mm through the TRPP is 6.8° to7.2°.The tube blank is not easy to be bitten by the roller because the roll feeding Angle is too small or the Angle is inconsistent, resulting in the FS.An increase in the feeding angle of the roller will also increase the axial force, and an excessive feed angle of the roller will also increase the pressure on the tube blank.When the Solid tube is forced into the TRPP it will cause the tube to BS, twist and even cause the phenomenon of steel-heaping.
2. When using TRPP for tube blank with a diameter of 65mm, the optimization range of the plug advance is around 28mm to 34mm.The optimization range of the plug advance for tube blank with a diameter of 88mm and 93mm is around 36mm to 44mm.Too much plug advance leads to too low forward compression rate of the plug and insu cient friction drag force in the front of the deformation area, which cannot meet the biting conditions of the tube blank, resulting in the FS.The plug advance is too small, the rolling force increases.However, at the end of the tube blank where the plug passes through the tube blank, due to the small plug advance and insu cient reduction rate, the tail of the tube blank cannot be penetrated, resulting in the BS.
3. During the TRPP, the central fracture did not occur at the piercing point due to the three-way alternating stress.
4. The optimization of plug advance and feed Angle has a good application prospect for the subsequent production of composite seamless pipe.

Declarations
Data availability statements As shown in Fig. 13, based on experimental veri cation, the optimized feed angle of the roller is between 6.8 ° to 7.2 °.When the diameter of tube blank is 65mm, the plug advance is 26 to 32mm.When the diameter of the tube blank is 88mm and 93mm, the protrusion of the plug is 38 to 44mm, which can produce high-quality tubular billets.Thus, it can be further veri ed that increasing the plug advance and reducing the feed angle during TRPP, results in a decrease in rolling force, an increase in the plunger force, which can easily cause the FS of pipe blank.On the contrary, reducing the plug advance and increasing the feed angle during TRPP, which can easily cause the BS of pipe blank.The distribution of temperature in the TRPP of steel tubes.
Page 16/18 FEM data relating roll force and plug axial force in the TRPP of producing seamless steel tubes.
Page 17/18 FEM data relating roll torque in the TRPP of producing seamless steel tubes.Specimen of seamless steel tube in the TRPP.
Figure 13 distribution view

Figure 4
Figure 4 exhibits the axial force Q of the plug, including: (1) the pressure acting on the front end of the plug.(2) The component of positive pressure acting on the plug.(3) The axial component of the contact friction force between the blank and the plug [26].The pressure acting on the front end of the plug is expressed as follows:

Figure 3 The schematic diagram of left and upper rollers Figure 4
Figure 3

Table 4
The parameters of unquali ed tubular billets