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Geometry evolution prediction and process settings influence in profiled ring rolling

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Abstract

A kinematic-based analytical model was developed for estimating the geometrical expansion of profiled rings during the ring rolling process and validated against own and literature experimental results. The model, based on the volume conservation principle, describes the material redistribution between radial and circumferential directions due to the employed process parameters and friction conditions. The comparison between analytical and experimental ring diameters evolutions, carried out considering various materials, process conditions, and profiled ring shapes, showed maximum and average deviations equal to 4.9% and 2.1%, proving the reliability of the implemented kinematic solution. The penetration and biting-in conditions, well-known in flat ring rolling, showed to be applicable and effective also in profiled ring rolling, allowing to define the suitable ranges for the mandrel feeding speed and the main roll rotation speed. The proposed solution was utilized, coupled with thermo-mechanical FEM simulations, to investigate the influence of the ring preform shape and the process parameters on the geometrical expansion of both wall and flange of the ring during the process. Furthermore, the range of validity of the developed analytical model was investigated as well.

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Availability of data and material

The data that support the findings of this study are stored in an online repository and available on request from the corresponding author [Prof. Luca Quagliato, Ph.D.].

Code availability

The simulation files relevant for this research are stored in an online repository and available on request from the corresponding author [Prof. Luca Quagliato, Ph.D.].

Abbreviations

\(\omega_{R}\) :

Main roll rotation speed

\(R_{R}\) :

Main roll radius

\(R_{M}\) :

Mandrel radius

\([v_{M} ]_{0} \, , \, [v_{M} ]_{F}\) :

Initial and final mandrel feeding speed ranges

\(\beta_{R}\) :

Friction angle

\(R_{0}\) :

Ring preform outer radius

\(r_{0}\) :

Ring preform inner radius

\(R_{F}\) :

Final ring outer radius

\(r_{F}\) :

Final ring inner radius

\(R_{w,0} \, , \, R_{w,i} \, , \, R_{w,i + 1}\) :

Profiled ring wall radius (initial, i-round, and i + 1 round)

\(s_{w,0} \, , \, \overline{s}_{w,i} \, , \, \overline{s}_{w,i + 1}\) :

Profiled ring thickness (initial, i-round, and i + 1 round)

\(t_{1}\) :

Mandrel time for the first round of the process

\(t_{i} \, , \, t_{i + 1}\) :

Mandrel time for the i-round and the i + 1 round

\(t_{j}\) :

Generic process time within the mandrel feeding time

\(V_{w,0} \, , \, V_{w,i}\) :

Ring wall volume (Initial and i-round)

\(R_{in,0} \, , \, R_{in,i}\) :

Ring inner radius (Initial and i-round)

\(h_{w} \, , \, h_{f}\) :

Ring wall and ring flange heights

\(\lambda\) :

Wall-flange height factor

\(\overline{R}_{wc}\) :

Average radius of the ring wall

\(R_{f}\) :

Radius of the ring flange

\(\tau\) :

Friction stress

\(k\) :

Yield strength

\(m\) :

Friction factor

\(\upsilon\) :

Velocity parameter

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Funding

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2019R1I1A1A01062323). Prof. Dr. Luca Quagliato was supported by RP-Grant 2021 of Ewha Womans University.

Author information

Author notes

  1. Irene Mirandola and Luca Quagliato equally contributed to this work.

Authors and Affiliations

  1. Department of Management and Engineering, University of Padua, 36100, Vicenza, Italy

    Irene Mirandola, Guido A. Berti & Roberto Caracciolo

  2. Division of Mechanical and Biomedical Engineering, Ewha Womans University, 03760, Seoul, Republic of Korea

    Luca Quagliato & Seok Chang Ryu

  3. Zamperla S.P.A, 36077, Vicenza, Italy

    Mattia Perin

  4. Department of Mechanical Engineering, Sogang University, 04107, Seoul, Republic of Korea

    Naksoo Kim

Authors
  1. Irene Mirandola
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Contributions

Conceptualization (IM, LQ, GAB), methodology (IM, LQ, GAB), software (IM, MP), validation (IM, MP), formal analysis (IM, LQ, MP), investigation (IM, LQ), resources (SCR, NK, RC), data curation (IM, LQ), writing – original draft (IM, LQ), writing – review and editing (IM, LQ), visualization (IM, LQ), supervision (NK, RC), project administration (LQ, GAB, RC), funding acquisition (LQ, SCR).

Corresponding authors

Correspondence to Luca Quagliato or Naksoo Kim.

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Appendices

Appendix 1 Temperature-dependent properties of Inconel 718 and 42CrMo4 alloys

Fig. 13
figure 13

Temperature-dependent Young’s modulus, thermal conductivity, and specific heat capacity properties for the Inconel 718 material

Full size image
Fig. 14
figure 14

Temperature-dependent Young’s modulus, thermal conductivity, and specific heat capacity properties for the 42CrMo4 material

Full size image

Appendix 2 Detailed simulation levels for the process settings influence investigation (Table 2 of the paper)

Parameters

Ring#1A

Sub-case numbering

A1-1

A1-2

A1-3

A1-4

A1-5

A1-6

A1-7

A1-8

A1-9

Main-roll rotational speed [rad/s]

2

3

4

Initial mandrel feeding speed [mm/s]

0.26

1.88

3.33

0.4

2.86

5.08

0.54

3.85

6.84

Final mandrel feeding speed [mm/s]

0.16

1.75

3.19

0.24

2.68

4.86

0.33

3.6

6.54

Mandrel active time [s]

139

19.2

10.8

90

12.6

7.08

66.7

9.34

5.26

Total process time [s]

160

25.2

15.2

105

16.8

12.3

74.5

13.9

9.8

Parameters

Ring#2A

Sub-case numbering

A2-1

A2-2

A2-3

A2-4

A2-5

A2-6

A2-7

A2-8

A2-9

Main-roll rotational speed [rad/s]

2

3

4

Initial mandrel feeding speed [mm/s]

0.35

2.7

4.8

0.5

4

7.2

0.7

5.5

9.7

Final mandrel feeding speed [mm/s]

0.2

2.4

4.37

0.3

3.6

6.65

0.4

4.9

8.9

Mandrel active time [s]

140

18.15

10.21

98

12.25

6.79

70

8.91

5.05

Total process time [s]

158

22.9

15.2

108

16.5

11.2

76.3

13.6

9.7

Parameters

Ring#3A

Sub-case numbering

A3-1

A3-2

A3-3

A3-4

A3-5

A3-6

A3-7

A3-8

A3-9

Main-roll rotational speed [rad/s]

2

3

4

Initial mandrel feeding speed [mm/s]

0.46

3.45

6.14

0.7

5.26

9.37

0.94

7.08

12.59

Final mandrel feeding speed [mm/s]

0.28

3.22

5.87

0.43

4.92

8.96

0.58

6.62

12.05

Mandrel active time [s]

139.5

18.55

10.42

91.34

12.16

6.83

67.92

9.04

5.08

Total process time [s]

159.5

24.5

15.2

97.8

16.5

11.7

76.2

14.5

9.7

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Mirandola, I., Quagliato, L., Berti, G.A. et al. Geometry evolution prediction and process settings influence in profiled ring rolling. Int J Adv Manuf Technol 122, 799–819 (2022). https://doi.org/10.1007/s00170-022-09928-0

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