The Mechanism of Forming Hollow Shafts with Constant Wall Thickness by Three-Roll Skew Rolling

Abstract

To solve the problem of the long forming process for hollow shafts with constant wall thickness (HSCWT), a new process for forming HSCWT, namely three-roll skew rolling, has been proposed. First, the working principle of the three-roll skew rolling process is presented. Then, the finite element model (FEM) of the three-roll skew rolling HSCWT is established. The strain-stress field and temperature field distribution rules of the three-roll skew rolling HSCWT are analyzed with FEM. The stress-strain field of the rolled piece is distributed uniformly along the axial direction but not uniformly along the radial direction. The variation of the temperature field is related to the axial traction velocity. The greater the axial traction velocity, the smaller the variation of the temperature field. The temperature of rolled pieces varies within 100 °C during rolling. Finally, the three-roll skew rolling experiment of the HSCWT is carried out. The results show that the three-roll skew rolling process can form HSCWT. The temperature field of the three-roll skew rolling HSCWT is evenly distributed. The selection of larger axial traction velocity is conducive to the forming of rolled pieces. The three-roll skew rolling technology has achieved near constant temperature forming of HSCWT.

1. Introduction

Compared with solid shafts, hollow shafts have significant lightweight advantages. Therefore, hollow shafts are widely used in aerospace, transportation, and other fields [1]. Generally, there are three main methods for manufacturing larger hollow shafts: One is to use a steel rod to forge a solid shaft and then use a deep hole to drill the inner hole. Another method is to use thick-walled hollow tubes to be cut and formed on a CNC lathe. The third method is to use hollow billets to be formed through the cross-wedge rolling process. The forming quality of the forged hollow shaft is good, but its production cost is high, and the processing efficiency is low. Although the efficiency of machining hollow shafts is high, the mechanical properties of the shaft will be reduced, and the material will be wasted [2]. Using cross-wedge rolling to form hollow shafts with constant hole diameters will cause the inner hole to lose roundness. Yan [3] investigated the impact of process parameters on thinning and necking in cross-wedge rolling of large-section multi-step shafts. Feng [4] compared the formability of TC4 titanium alloy and AISI 1045 steel hollow shafts formed by cross wedge rolling with a mandrel. Li [5] performed numerical and experimental studies on the hot cross wedge rolling of Ti-6Al-4V vehicle lower arm preforms. Shen [6] theoretically studied and predicted the reduction of the inner hole and critical mandrel diameter in the cross wedge rolling of hollow shafts. Yu [7] explored the microstructure evolution of aluminum alloy hollow shafts in cross wedge rolling without a mandrel. Currently, more and more researchers have begun to explore the feasibility of skew rolling to form shaft parts. Stefanik [8] theoretically and experimentally analyzed the forming process of aluminum rods by three-roll skew rolling. Gryc and Bajor [9] studied the influence of process parameters on the temperature of the rolled piece during the three-roll skew rolling process. Lin [10,11] proposed a new flexible skew rolling (FSR) process for manufacturing shafts and verified its feasibility through physical and numerical investigations. Cao [12] conducted an exploratory study and numerical simulation for manufacturing hollow shafts via flexible skew rolling with a mandrel. Zhang [13] analyzed the deformation characteristics and microstructure evolution of GH4169 alloy bars with δ-phase in flexible skew rolling. Pater [14] proposed the use of the three-roll skew rolling process to form elongated axisymmetric parts. Finite element analysis of three-roll skew rolling forming of a stepped shaft (solid and hollow) was carried out. Based on the analysis results, a three-roll skew rolling mill was designed and manufactured. Zhang [15,16] studied the wall thickness uniformity of three-roll skew rolled hollow shafts with constant hole diameters. The influence of different process parameters on wall thickness uniformity is explained. Wang [17] explored the wall thickness quality of three-roll skew rolling hollow shafts from the perspective of forming mechanism and experimental design, proposing a method to improve wall thickness quality using irregular billets. These studies primarily focus on the forming of solid shafts and hollow shafts with constant hole diameters.

In terms of forming methods and forming quality, Mao [18] investigated the deformation characteristics and mechanism of tubes produced by the Tandem Skew Rolling (TSR) process, using numerical simulation and experiments with carbon steel 1045, high-strength steel 42CrMo, and magnesium alloy AZ31. Ji [19] focused on fabricating 45 carbon steel/316 L stainless steel (CS/SS) cladding tubes by the three-roll skew rolling bonding process, analyzing the deformation law, interfacial microstructure, and bonding mechanism. Jiang [20] presented a heat-assisted three-roll incremental rolling system for producing rods and tubes of various diameters without die/tool replacement, which is ideal for low-volume production or scientific research. Cao [21] introduced a new method of manufacturing hollow shafts via Flexible Skew Rolling (FSR), a near-net-shape rolling technology suitable for diversified production without special molds. Pater and Walczuk-Gągała [22] proposed a concept for manufacturing hollow axles using three skewed rolls, an axially moving chuck, and a moving mandrel, with numerical simulation confirming the method’s feasibility. Lin [23] described a novel flexible skew rolling (FSR) process for manufacturing large shafts, offering a good combination of flexible production and less loading. Murillo-Marrodan [24] studied the performance of various friction models in a skew rolling process numerical simulation, using FORGE^® software to analyze their effects on consumed power, plastic deformation, and surface temperature. Hu [25] conducted a microstructure study on large-sized Ti-6Al-4V bar three-high skew rolling based on a Cellular Automaton (CA) model, simulating the microstructure evolution process during rolling. Bulzak [26] investigated a new manufacturing technology for producing hollow railway axle forgings with a mandrel using three-roll skew rolling (TRSR) with a computer numerically controlled (CNC) rolling mill. Tomczak [27] explored the design and technological capabilities of a CNC skew rolling mill for producing elongated axisymmetric parts, presenting FEM modeling results and experimental validation. Pater [28] focused on predicting ductile fracture in skew rolling processes by comparing stresses and strains in bars produced by two and three rolls, proposing the use of classical fracture criteria for crack prediction. Overall, the above research highlights the significant advancements in rolling processes, emphasizing their potential for various industrial applications and the need for further exploration to optimize forming techniques for HSCWT.

The research process of the forming mechanism of HSCWT by three-roll skew rolling is as follows. Firstly, based on the structural characteristics of HSCWT, the working principle of the three-roller skew rolled HSCWT is proposed. Then, the forming process of the three-roll skew rolled HSCWT is analyzed by establishing a finite element model of the three-roll cross-rolled HSCWT. Finally, the stress field, strain field, and temperature field during the forming process are analyzed.

2. Forming Process and Finite Element Model

2.1. The Forming Principle of the HSCWT by Three-Roll Skew Rolling

HSCWT is a hollow stepped shaft with the same wall thickness everywhere, as shown in Figure 1. The billet used in the three-roll skew rolled HSCWT is a hollow tube blank with constant wall thickness.

The principle of three-roll skew rolling is that the three rolls rotate in the same direction to drive the rotation of the hollow billet. Simultaneously, the chuck pulls the hollow billet forward. The formation of different shaft steps can be achieved by precisely controlling the radial feed rate of the three rolls. Because the roll axis is inclined at an offset angle β relative to the rolling line (the rolling line in the three-roll skew rolling generally coincides with the axis of the billet), the billet can advance while spirally rotating so that the rolling process is gradually completed. The angle between the cone surface of the roll and the rolling axis is the forming angle α. The forming angle α is to facilitate the deformation of the material in the deformation zone of the rolled piece. Generally, −12° ≤ β ≦ +12°, 0 ≤ α ≦ 30°. The principle of the three-roll skew rolled hollow shaft is shown in Figure 2.

2.2. Finite Element Model of HSCWT for Three-Roll Skew Rolling

The material of the HSCWT is 30CrMoA steel. The material model of the HSCWT is shown in Equation (1) [29,30]. The finite element model of the three-roll skew rolling HSCWT is established in Simufact Forming V14.0 software. The FEM is shown in Figure 3. The billet diameter is 52 mm. The wall thickness is 10 mm. The length is 500 mm. The mesh employed consists of 8-node hexahedral elements. The mesh size is 2.5 mm, and the total number of mesh elements is 45,034. The friction model on the contact surface is shear friction, and the friction factor m is 0.8. The heat transfer coefficient between the billet and rolls is 1 × 10⁴ W/(m²·K). The process parameters for the simulation and experiment of three-roll skew rolling HSCWT are shown in Table 1.

(1)$\dot{\epsilon }=3.67\times {10}^9{\left[\sinh \left(0.011{\sigma }_p\right)\right]}^{4.403}\exp \left[-261,850/RT\right],$

where $\dot{\epsilon }$ is the strain rate/s⁻¹; σ_p is the peak stress; R is the gas constant (8314 J·mol⁻¹·K⁻¹), and T is the temperature/K;

It is important to analyze the forming mechanism of rolled pieces during the forming process of HSCWT by three-roll skew rolling, which is the basis for subsequent process parameter optimization and forming quality analysis. According to the shape characteristics of the rolled piece, the forming process of the HSCWT by three-roll skew rolling can be divided into clamping section, reducing section, straight shaft section, ascending section, and surplus material section, and the deformation status of each section is different. As shown in Figure 4, Section A is the straight shaft section, Section B is the ascending section, and Section C is the reducing section. Analyzing the forming process of HSCWT in different sections of three-roll skew rolling is crucial for understanding and mastering the three-roll skew rolling technology of hollow shafts.

3. Simulation Results and Analysis

3.1. Analysis of Deformation Process

The process parameters for analyzing the deformation process of HSCWT during three-roll skew rolling are the initial temperature of the hollow billet at 1100 °C, the axial traction velocity of the chuck at 20 mm/s, and the rotational velocity of the roll at 60 rpm. During the forming process of HSCWT, the billet is always clamped by the chuck and fed axially. The deformation status of each section during the forming process of HSCWT by three-roll skew rolling is shown in Figure 5. In the ascending section, the conical surface section of the roll serves as the working surface to continuously roll the billet along the axial and radial directions while the roll moves radially away from the rolling piece, gradually forming the ascending section. In the straight shaft section, the roll only performs rotational motion, and the conical surface section of the roll rolls the billet along the axial and radial directions, thereby achieving the forming of the straight shaft section of the rolled piece. In the reducing section, the conical surface section and the finishing section of the roll together to roll the billet along the axial and radial directions, while the roll feed radially until the forming of the reducing section is completed.

3.2. Stress-Strain Distribution

The magnitude of stresses in the forming of HSCWT depends on the state of deformation of the rolled pieces during the rolling process. The effective stress field distribution at different stages in the forming process of three-roll skew rolling HSCWT is presented in Figure 6. The area of the larger effective stress is mainly concentrated in the part of the rolling contact with the rolling piece. The residual effective stress increases gradually along the rolling direction. After the rolling is completed, the residual effective stress of the rolled piece is not more than 30 MPa. As shown in Figure 6a, the stress distribution at the I section is uneven. Residual effective stress below 36 MPa, which is due to the deformation in this section, is larger, and the rolls are still in contact with this section. As shown in Figure 6b, the length of the II section is shorter, the diameter is larger, and the roll finishing section is still in contact with this section, so there are still some areas in this section where the effective stress is larger. As shown in Figure 6c, the stress distribution in the III section is uneven, but the effective stress values are smaller because this section has the largest diameter and the smallest deformation. As shown in Figure 6d, the effective stress in the IV section is small and evenly distributed because this section is longer and the deformation is smaller. As shown in Figure 6e, the overall effective stress distribution in the V section is more even, but the effective stress value is larger. The average effective stress is about 60 MPa. The distribution of effective stress in the V section is greatly affected by the forming of the reducing section, as it is immediately followed by the reducing section. As shown in Figure 6f, the distribution of effective stress in the VI section is also affected by the subsequent forming of the reducing section. The effective stress value in this section is large, reaching about 70 MPa. As shown in Figure 6g, the VII section is the last straight shaft section with the largest radial compression. The effective stress distribution near the residual section is not uniform, but the whole effective stress is not higher than 30 MPa.

The distribution of effective stress fields in the transverse and longitudinal sections of the rolled piece is shown in Figure 7. The figure demonstrates that the whole, effective stress field distribution of the rolled piece is not uniform. The residual effective stress gradually increases along the rolling axis. The surface effective stress at the end of the rolled piece is the largest, reaching 45 MPa. In the radial direction of the rolled piece, the effective stress of the outer surface layer of the rolled piece is the largest, followed by the inner surface layer. And the effective stress of the core layer is the smallest. In the circumferential direction of the rolled piece, the effective stress distribution of the outer surface and the inner surface is uniform. The effective stress distribution of the core layer in the C, E, F, and G sections is uniform. The area with smaller effective stress in the A, B, and D sections is a crescent-shaped distribution. From cross-section A to cross-section G, the circumferential effective stress of each layer of the rolled piece gradually increases. The outer surface layer gradually increases from 10 MPa to 45 MPa. The inner surface layer gradually increases from 10 MPa to 30 MPa. The core layer gradually increases from 10 MPa to 45 MPa. The overall distribution of the effective stress field is non-uniform, which is caused by the deformation state of the rolled piece during the forming process and the principle of the three-roll skew rolling process. Because the deformation of the rolled piece varies greatly in different sections, the local stress of the rolled piece is concentrated in the rolling process.

The distribution of effective plastic strain field at different stages in the forming process of three-roll skew rolling HSCWT is shown in Figure 8. The axial effective plastic strain distribution of the rolled piece is not uniform, which is due to the rolled piece being mainly axial deformation. The effective plastic strain at each stage of the rolled piece forming is related to the radial compression and the length of the area to be formed. The larger the radial compression is, the larger the effective plastic strain is. The longer the area to be formed, the greater the effective plastic strain in the deformation zone. As shown in Figure 8a, the rolling direction of the effective plastic strain gradually increases in the I section. The area with the largest effective plastic strain is mainly concentrated at the end of this section. And the maximum value reaches 5.3. The effective plastic strain of the contact area between the conical surface of the roll and the deformation zone of the rolled piece increases gradually along the axial direction. The effective plastic strain of the contact area between the finishing section of the roll and the rolled piece is the largest. As shown in Figure 8b, the effective plastic strain of the II section is large but evenly distributed, which is due to the deformation being large but evenly deformed in this section. As shown in Figure 8c, the effective plastic strain of the III section is small and the distribution is uniform, which is due to the deformation being smaller in this section. As shown in Figure 8d, the effective plastic strain distribution of the IV section is not uniform, which is due to the fact that surface deformation is not uniform in this section. As shown in Figure 8e, the surface effective plastic strain of the V section is small and the distribution is uniform, which is due to the deformation being uniform in this section. As shown in Figure 8f, the effective plastic strain distribution of the VI section is not uniform, which is due to the subsequent deformation section affecting this section. As shown in Figure 8g, the effective plastic strain of the VII section gradually increases along the axis direction, which is because no subsequent deformation sections are affecting this section.

The effective plastic strain distribution of the rolled piece is shown in Figure 9. The whole effective plastic strain distribution of the rolled piece is not uniform. The effective plastic strain in the transition section between the reducing section and the straight shaft section is smaller than that in the transition section between the ascending section and the straight shaft section. The axial effective plastic strain distribution is uniform in the straight shaft section. In the radial direction, the effective plastic strain decreases gradually from the outer surface to the inner surface in each section. In the circumferential direction, the effective plastic strain distribution of each layer of the rolled piece is more uniform. Comparing sections A, B, C, and D, and sections E, F, and G, it can be seen that the greater the radial compression, the greater the effective plastic strain of the rolled piece. Comparing section B and section F, it can be seen that the effective plastic strain of the ascending section is larger than that of the reducing section under the same compression. The above analysis shows that the deformation direction of the metal inside the rolled piece is mainly circumferential and axial.

3.3. Temperature Field Distribution

Three-roll skew rolling HSCWT process is a hot working process. The variation of the temperature field during the rolling process has a significant impact on the forming quality of rolled pieces. The factors that cause changes in the temperature field of rolled pieces during the rolling process include thermal radiation, heat transfer, and temperature rise caused by plastic deformation. The temperature field distribution of different stages in the forming process of the rolled piece is shown in Figure 10. The whole temperature field of the rolled piece changes evenly. The temperature field of the rolled piece changes within 100 °C from the beginning to the end of the rolling process, which is conducive to improving the forming quality of the rolled piece. As shown in Figure 10a, the surface temperature of the I section does not change significantly. The temperature in the contact area between the rolling piece and the rolls decreases by a larger amount. As shown in Figure 10b, the temperature decreases obviously in the II section, because this section is short and has a large contact area with the rolls. As shown in Figure 10c, the surface temperature decreases slightly in the III section, which is due to the small deformation and contact area with the rolls in this section. As shown in Figure 10d, the whole temperature decreases obviously in the IV section, which is due to the longer rolling time in this section. As shown in Figure 10e–g, the temperature of these three sections decreases significantly in the contact area with the rolls, while the temperature field changes in other areas are not significant. The rolling time of these three sections is relatively short, so the temperature field changes less.

The temperature field distribution in the cross-section and longitudinal section of the rolled piece is shown in Figure 11. As shown in the figure, the temperature field distribution in the rolled section of the rolled piece is relatively uniform. The average temperature of the rolled piece is about 1000 °C. From section A to section G, it can be seen that the radial distribution of temperature is more uniform along the rolling direction with the rolling sequence advancing. This is because the surface temperature of the rolled section rises with the rolling process so that the radial temperature distribution becomes uniform.

In order to describe and analyze the change of temperature field more accurately. A total of 12 points are selected for observation in the middle of three sections of the billet, namely sections I, IV, and VII, as shown in Figure 12a. By tracking these feature points, the temperature changes at each point during the rolling process are analyzed, as shown in Figure 12b–d. It can be seen from the figure that the temperature of the outer layer of the rolled piece is lower than that of the core layer and the inner layer. This is due to the large contact area between the outer layer and the air, which causes the temperature of the outer layer to decrease faster than that of the core layer and inner layer. The temperature of the outer layer of the rolled piece decreases rapidly due to the heat conduction in the contact area between the rolls and the rolled piece. However, the temperature of the core layer and inner layer in the contact area is increased due to plastic deformation heat. After rolling, the whole temperature of the rolled piece is reduced from 1100 °C to about 1000 °C. The temperature drop of the rolled piece is small, which is beneficial for improving the forming quality of the rolled piece.

4. Three-Roll Skew Rolling Experiment with HSCWT

The three-roll skew rolling HSCWT experiment was carried out on the CNC three-roll skew rolling mill at the Lublin University of Technology in Poland. The CNC three-roll skew rolling mill is shown in Figure 13.

The process of conducting rolling experiments based on simulation parameters is shown in Figure 14. The rolling process can effectively remove the oxide scale on the surface of the rolled piece.

Experimental Analysis of Temperature Field

The process of three-roll skew rolling HSCWT is shown in Figure 15. The temperature field of the rolled piece is measured by capturing the initial, intermediate, and final stages of the rolling process using an infrared camera. Overall, the temperature change of the rolled piece during the rolling process is not significant. Due to thermal conduction, the surface temperature of the rolled piece decreases in the contact area between the roll and the rolled piece. As shown in Figure 15a,b, the initial temperature of the rolled piece does not affect the variation of the temperature field during the rolling process. According to Figure 15b–d, it can be seen that the higher the axial traction velocity, the smaller the temperature loss of the rolled piece from the initial stage to the end stage. When the axial traction velocity is 10 mm/s, the temperature loss of the rolled piece from the initial stage to the end stage is significant. The significant impact of axial traction velocity on the temperature field is because the larger the axial velocity, the shorter the rolling time, and thus, the smaller the temperature loss of the rolled piece. The smaller the change in the temperature field of the rolled piece, the more conducive it is to the stable progress of the rolling process and the forming quality of the rolled piece. Therefore, a higher axial traction velocity should be selected as much as possible during the rolling process.

The experimental rolled piece of the three-roll skew rolling HSCWT is shown in Figure 16. After the rolling is completed, the rolled piece is immediately water-quenched. The surface of the rolled piece is relatively smooth except for the obvious spiral marks in the reducing section.

5. Conclusions

• The HSCWT can be formed through a three-roll skew rolling process. This process is particularly well-suited for the hot forming of shaft components, especially large, long, and hollow shaft parts. The specifications of the rolled hollow shaft components are primarily constrained by the size of the rolling mill;

• The area with the highest effective stress in the rolling piece is mainly concentrated in the contact area between the roll and the rolling piece. The effective stress on the outer layer of the rolled piece is the highest, while the effective stress on the core layer is the lowest. The effective plastic strain of the rolled piece gradually decreases from the outer layer to the inner layer after rolling;

• Due to the effect of heat conduction, the temperature varies significantly in the contact area between the rolling piece and the roll. However, the whole temperature field of the rolling piece varies relatively uniformly. The temperature field of the rolling piece varies within 100 ℃ during the entire rolling process;

• Choosing a larger axial traction velocity is beneficial for reducing the temperature loss of the rolled piece, as well as improving the stability of the rolling process and the forming quality of the rolled piece.

Author Contributions

Conceptualization, X.S.; methodology, S.Z. and Z.L.; software, J.W. and Y.X.; validation, Z.P., J.T., Y.X. and T.B.; formal analysis, H.X. and S.Z.; investigation, S.Z. and Z.L.; resources, Z.P. and X.S.; data curation, S.Z., J.T. and T.B.; writing—original draft preparation, S.Z. and J.W.; writing—review and editing, S.Z. and X.S.; visualization, H.X. and S.Z.; supervision, X.S.; project administration, X.S.; funding acquisition, S.Z. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding authors.

Acknowledgments

We are deeply grateful for the assistance of Pater’s team from the Lublin University of Technology in supporting the experimental section of this paper.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Table

Figure 1. Dimensions of hollow shaft.

Figure 2. Principle of three-roll skew rolling HSCWT.

Figure 3. Finite element model of HSCWT formed by three-roll skew rolling.

Figure 4. Three-roll skew rolled HSCWT by finite element simulation.

Figure 5. Shape changes at different sections of the HSCWT by three-roll skew rolling.

Figure 6. The effective stress field at different stages of the rolled piece by three-roll skew rolling: (a) I section, (b) II section, (c) III section, (d) IV section, (e) V section, (f) VI section, (g) VII section.

Figure 6. The effective stress field at different stages of the rolled piece by three-roll skew rolling: (a) I section, (b) II section, (c) III section, (d) IV section, (e) V section, (f) VI section, (g) VII section.

Figure 7. Effective stress field distribution in transverse and longitudinal sections of the rolled piece.

Figure 8. The effective plastic strain field at different stages of the rolled piece by three-roll skew rolling: (a) I section, (b) II section, (c) III section, (d) IV section, (e) V section, (f) VI section, (g) VII section.

Figure 9. Effective plastic strain distribution of the rolled piece by three-roll skew rolling.

Figure 10. Temperature field at different stages of the rolled piece by three-roll skew rolling: (a) I section, (b) II section, (c) III section, (d) IV section, (e) V section, (f) VI section, (g) VII section.

Figure 11. Temperature field distribution of the rolled piece by three-roll skew rolling.

Figure 12. Temperature changes at different sections during the rolling process of the rolled piece.

Figure 13. CNC Three-roll skew rolling mill. 1—Electric motor, 2—Drive unit, 3—Frame, 4—Radial displacement unit, 5—Roll system, 6—Chuck system, 7—Axial displacement unit, 8—Power and control system.

Figure 14. Rolling experiment of HSCWT.

Figure 15. The temperature field of the rolled piece during the rolling process.

Figure 16. The HSCWT by three-roll skew rolling.

Table 1

Process parameters for three-roll skew rolling HSCWT.

Parameter	Unit	Value
Heating temperature of hollow billet	°C	1000, 1100
Rotational velocity of the roll	rpm	60
Axial traction velocity of the chuck	mm/s	10, 20, 30
Radial loading velocity of the roll	mm/s	0–3.5, 0–7, 0–10
Roll offset angle β	°	5
Roll forming angle α	°	20
Finishing section width of the roll	mm	12
Roll diameter	mm	150

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