Quasi-Equilibrium Stress Zone with Residual Displacement Causing Permanent Slippage in Shrink-Fitted Sleeve Rolls
Abstract
:1. Introduction
2. Simulation in Comparison with Experiment
2.1. Previous Experiment
2.2. Analysis Method of Residual Deflection
3. Analysis Results for Residual Deflection
3.1. Deflection under Loading and Residual Deflection after Unloading
3.2. Effect of the Friction Coefficient and the Magnitude of Load on the Residual Deflection
4. Discussion of Residual Deflection Generation Mechanism
4.1. Relative Slippage of the Sleeve to the Shaft
4.2. Residual Deflection Caused by the Stress State along the Shrinkage-Fitting Surface
4.3. Roll Deflection during Unloading Process and Stress Change along the Shrink Fitted Surface
5. Quasi-Equilibrium Stress Zone with Residual Displacement Causing the Permanent Circumferential Slippage in Shrink-Fitted Sleeve Roll
6. Conclusions
- (1)
- Residual deflection after removing the load W = 294 kN coincides with the previous experimental results within 15% error.
- (2)
- With increasing the friction coefficient μ, the residual deflection increases having a peak value around μ = 0.1–0.2, then decreases. The friction coefficient providing the peak varies depending on the magnitude of the load applied before removing the load.
- (3)
- (4)
- The same residual deflection can be obtained when the product of the quasi-equilibrium zone and the distance from this region to z = 0 is almost the same. Here, the quasi-equilibrium zone can be defined as the region where the shear force is balanced the friction as within 1 MPa difference.
- (5)
- The quasi-equilibrium stress zone and the residual displacement are strongly related to the residual deflection. The quasi-equilibrium stress zone can be seen in the circumferential direction between the sleeve and shaft may cause the circumferential interfacial slippage.
Author Contributions
Funding
Conflicts of Interest
References
- Lindsey, E.G. Backup Rolls and their Contribution to Gage Variation. Iron Steel Engr. 1960, 37, 91. [Google Scholar]
- Hohage, R. Support Rollers for Cold Rolling Mills. Steel Iron 1939, 59, 1197–1204. [Google Scholar]
- Hori, K. Model Test on the Mechanism of the Residual Deflection of Built-up Type Back-up Rolls; Technical Papers (Part II) for the 70th Grand Lecture Meeting of The Iron and Steel Institute of Japan: Tokyo, Japan, October 1965; pp. 200–202. [Google Scholar]
- Trinks, W. Pressures and Roll-Flattening in Cold Rolling. Steel Plant 1937, 25, 617–619. [Google Scholar]
- Ohkomori, Y.; Sakae, C.; Murakami, Y. Analysis of Mode II Crack Growth Behavior in Spalling Failure of Backup Roll. J. Soc. Mat. Sci. 2001, 50, 249–254. [Google Scholar] [CrossRef]
- Shimoda, H.; Onodera, S.; Hori, K. Study on the Residual Deflection of Large Sleeved Back-Up Rolls: 1st Report, Mechanism of the Deflection. Trans. Jpn. Soc. Mech. Eng. 1966, 32, 1–7. [Google Scholar] [CrossRef]
- Shimoda, H.; Onodera, S.; Hori, K. Study on the Residual Deflection of Large Sleeved Back-Up Rolls: 3rd Report, Effect of Condition at Shrink Fitting Interface, Welding at Barrel Ends and Other Factors on the Deflection. Trans. Jpn. Soc. Mech. Eng. 1966, 32, 440–446. [Google Scholar] [CrossRef]
- Shimoda, H.; Onodera, S.; Hori, K. Study on the Residual Deflection of Large Sleeved Back-Up Rolls: 4th Report, Residual Stresses of Sleeved Rolls. Trans. Jpn. Soc. Mech. Eng. 1966, 32, 689–694. [Google Scholar] [CrossRef]
- Shimoda, H.; Onodera, S.; Hori, K. Study on the Residual Deflection of Large Sleeved Back up Rolls: 5th Report, Analysis on the Machanism of the Deflection and the Efficacy of the Counter-measure of the Residual Deflection about Actual Rolls. Trans. Jpn. Soc. Mech. Eng. 1967, 33, 11–18. [Google Scholar] [CrossRef]
- Gruner, H. Investigations on Machine-Induced Influences on the Uniformity of Cold-Rolled Strips. Steel Iron 1957, 77, 347–353. [Google Scholar]
- Kawai, M.; Kitsuki, K.; Nozaki, Y.; Takeuchi, H.; Miura, K. On the Bending Deflection of Model Rolls, Investigation of bending deflection on the built-up type back-up rolls for 4 high strip mills I. In Proceedings of the Preprints for the 66th Grand Lecture Meeting of The Iron and Steel Institute of Japan, Tokyo, Japan, 1 September 1963; pp. 1613–1615. [Google Scholar]
- Ookomori, Y.; Kitagawa, I.; Shinotsuka, K.; Miyamoto, R.; Yazaki, S. Study on Spalling of Hot Strip Mill Backup Roll. Tetsu-to-Hagané 1987, 73, 691–698. [Google Scholar] [CrossRef] [Green Version]
- Tsutsumi, S.; Hara, S.; Yoshi, S. The Residual Deflection of Sleeved Back-up Rolls. Tetsu-to-Hagané 1971, 57, 818–822. [Google Scholar] [CrossRef] [Green Version]
- Noda, N.N.; Sano, Y.; Wang, X.; Nakagawa, Y.; Guan, W.H.; Ono, K.; Hu, K. Residual Stress Simulation and Generation Mechanism for Hot Strip Composite Roll during the Quenching. J. Automot. Eng. 2015, 46, 831–837. [Google Scholar] [CrossRef]
- Sano, Y. Recent advances in rolling rolls. In Proceedings of the No. 148–149 Nishiyama Memorial Technology Course, Tokyo, Japan, 17 May 1993; pp. 193–226. [Google Scholar]
- Tanaka, T.; Kanzaki, M.; Terakado, R.; Tabe, H.; Kudo, K.; Goto, H. Survey on usage of back-up rolls: Roll and steel sheet investigation of continuous hot rolling mill II (thin plate processing/processing general, steel making processing). In Proceedings of the 74th Grand Lecture Meeting of The Iron and Steel Institute of Japan, Tokyo, Japan, 31 August 1967. [Google Scholar]
- Zhua, Z.; Sunb, D. Stress-Strain Analysis of Back-up Roll with Roll-Sleeve. Appl. Mech. Mater. 2012, 1, 139–142. [Google Scholar] [CrossRef]
- Dong, Y.; Wang, M.; Su, Y. Building the Mathmatical Model of Elastic Deformation for Rolls System by Four-High Mill Strip Rolling with a Composite Back-Up Roll. Adv. Mater. Res. 2012, 413, 320–325. [Google Scholar] [CrossRef]
- Frolish, M.F.; Beynon, J.H. Design criteria for rolling contact fatigue resistance in back-up rolls. Ironmaking Steelmaking 2004, 31, 300–304. [Google Scholar] [CrossRef] [Green Version]
- Takigawa, H.; Hashimoto, K.; Konno, G.; Uchida, S. Development of forged high-speed-steel roll for shaped steel. In Proceedings of the Current Advances in Materials and Processes: Report of the ISIJ Meeting, Tokyo, Japan, September 2003; pp. 1150–1153. [Google Scholar]
- Irie, T.; Takaki, K.; Tsutsunaga, I.; Sano, Y. Steel strip and section steel and thick rolling, processing. In Proceedings of the Japan Iron and Steel Institute 97th (Spring) lecture meeting, Tokyo, Japan, 7 March 1979. [Google Scholar]
- Noda, N.-A.; Suryadi, D.; Kumasaki, S.; Sano, Y.; Takase, Y. Failure Analysis for Coming out of Shaft from Shrink-Fitted Ceramics Sleeve. Eng. Fail. Anal. 2015, 57, 219–235. [Google Scholar] [CrossRef]
- Noda, N.-A.; Xu, Y.; Suryadi, D.; Sano, Y.; Takase, Y. Coming Out Mechanism of Steel Shaft from Ceramic Sleeve. J. ISIJ Int. 2016, 56, 303–310. [Google Scholar] [CrossRef] [Green Version]
- Soda, N. Bearing; Iwanami Shoten: Tokyo, Japan, 1964; pp. 196–203. [Google Scholar]
- Niwa, T. A Creep Mechanism of Rolling Bearings. NTN Tech. Review 2013, 81, 100–103. [Google Scholar]
- Murata, J.; Onizuka, T. Generation Mechanism of Inner Ring Creep. J. Koyo Eng. 2004, 166, 41–47. [Google Scholar]
Material Properties | Yield Points [MPa] | Tensile Strength [MPa] | Young’s Modulus [GPa] | Reduction of Area after Fracture [%] | Breaking Elongation [%] |
---|---|---|---|---|---|
Value | 616 | 970 | 216 | 53.5 | 18.5 |
Point | W [MPa] | μ | |||
---|---|---|---|---|---|
a | 588 | 0.04 | 122 | 578 | 6.32 × 104 |
b | 294 | 0.07 | 55 | 458 | 6.41 × 104 |
c | 294 | 0.15 | 22.5 | 389 | 6.10 × 104 |
d | 588 | 0.50 | 8.75 | 404 | 6.56 × 104 |
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Noda, N.-A.; Sakai, H.; Sano, Y.; Takase, Y.; Shimoda, Y. Quasi-Equilibrium Stress Zone with Residual Displacement Causing Permanent Slippage in Shrink-Fitted Sleeve Rolls. Metals 2018, 8, 998. https://doi.org/10.3390/met8120998
Noda N-A, Sakai H, Sano Y, Takase Y, Shimoda Y. Quasi-Equilibrium Stress Zone with Residual Displacement Causing Permanent Slippage in Shrink-Fitted Sleeve Rolls. Metals. 2018; 8(12):998. https://doi.org/10.3390/met8120998
Chicago/Turabian StyleNoda, Nao-Aki, Hiromasa Sakai, Yoshikazu Sano, Yasushi Takase, and Yutaro Shimoda. 2018. "Quasi-Equilibrium Stress Zone with Residual Displacement Causing Permanent Slippage in Shrink-Fitted Sleeve Rolls" Metals 8, no. 12: 998. https://doi.org/10.3390/met8120998