Method for Determining the Friction Coefficient in Cold Pilger Rolling

The study examined methods for determining the friction coefficient in metal forming processes, using a universal friction testing machine for this purpose. An assessment was made of the feasibility of determining the friction coefficient by this method for cold tube rolling in cold pilgering mills. The studies were carried out for two versions of cooling lubricants: No. 1 — emulsion, machine oil + water (50/50 %); cooling lubricant No. 2 — composition of cooling lubricant No. 1 + complex lithium grease containing 1.5 % nanodiamonds (50/50 %). During the experiments with cooling lubricant No. 1, we obtained the repeatability with a high degree of reliability. The recommended friction coefficient value for cooling lubricant No. 1 is λ₁ = 0.13, which falls within the range of friction coefficients reported by other researchers for this metal forming process. Experiments conducted with cooling lubricant No. 2, when reproducing the test, showed that the resulting dependence diagrams exhibit a completely different pattern of friction coefficient variation as a function of test duration, explainable by the segregation of nanodiamond additives, which is difficult to predict when mechanically adding a plastic grease modified with nanodiamond additives to the cooling lubricant No. 1 followed by mixing, but hereby, the initial friction coefficient values across different diagrams differed by no more than ± 2.150 % and lay within the range of 0.263. Thus, the method for determining the friction coefficient developed by the authors is also applicable to cold pilgering.

1. Tomilo V.A., Pilipenko S.V., Dudan A.V., Shtempel O.P., and Vigerina T.V. Development of a Method for Determining the Coefficient of Friction in Cold Sheet Rolling // Journal of Friction and Wear. — 2025 (46), no. 2, 82—85

2. Tomilo V.A., Pilipenko S.V., Dudan A.V., Shtempel O.P., and Vigerina T.V. Metod opredeleniya koefficienta treniya pri holodnoj prokatke osobo tonkih listov // Trenie i iznos. — 2024 (45), no. 3, 220—226 (in Russian)

3. Pilipenko S.V. Teoreticheskiye osnovy kholodnoy pil'gernoy prokatki trub. — Novopolotsk: Euphrosyne Polotskaya State University of Polotsk. — 2022 (in Russian)

4. Shevakin Yu.F. Calibration and efforts during cold rolling. — M.: Metallurgizdat. — 1963 (in Russian)

5. Azizoğlu Y., Sjöberg B., and Lindgren L.-E. Modeling of Cold Pilgering of Stainless-Steel Tubes // Journal of Manufacturing Processes. — 2024, no. 112, 112—125

6. Yarita I. Problems of Friction, Lubrication, and Materials for Rolls in the Rolling Technology // Transactions of the Iron and Steel Institute of Japan. — 1984 (24), no. 12, 1014—1035

7. Huda Z. Metal Rolling // Metal Forming Processes: Fundamentals, Analysis, Calculations. — Cham: Springer Nature Switzerland. — 2024, 75—97

8. Agrawal P., Aggarwal S., Banthia N., Singh U.S., Kalia A., and Pesin A. A Comprehensive Review on Incremental Deformation in Rolling Processes // Journal of Engineering and Applied Science. — 2022 (69), no. 1, 20

9. Younas S., Havinga J., Hol C., and Boogaard T. A Qualitative Study of the Contact Pressure Distribution in Cold Rolling // Materials Science Forum. — Trans Tech Publications Ltd. — 2026 (1183), 69—79

10. Grudev A.P., Zilʹberg Ju.V., Tilik V.T. Trenie i smazki pri obrabotke metallov davleniem. — M.: Metallurgija. — 1982 (in Russian)

11. Thakare N. and Scharifi E. Modelling of the Cold Rolling Process for Mild Steel Using Physics-Constrained Neural Network // Journal of Intelligent Manufacturing. — 2026, no. 1, 1—16

12. Vasilʹev Ja.D. Točnostʹ opredelenija koèfficienta fizičeskogo trenija pri xolodnoj prokatke metodami prinuditelʹnogo tormoženija polosy i krutjaščego momenta // Izvestija. Černaja metallurgija. — 2020, (63), no. 8, 639—643 (in Russian)

13. Garber È.A., Jagudin I.V., Ermilov V.V. Utočnenie zavisimosti koèfficienta trenija pri xolodnoj prokatke ot faktorov texnologičeskogo processa metodami regressionnogo analiza // Vestnik Čerepoveckogo gosudarstvennogo universiteta. — 2009, no. 3, 118—124 (in Russian)

14. Orlov G.A., Malanov A.A., Orlov A.G. Vlijanie texnologičeskix pogrešnostej na silovye parametry xolodnoj prokatki trub // Izvestija vysšix učebnyx zavedenij. Černaja Metallurgija. — 2018 (61), no. 5, 416—417 (in Russian)

15. Mazur V.L. and Nogovitsyn O.V. Theory and Technology of Sheet Rolling: Numerical Analysis and Applications. — London: CRS Press. — 2019

16. Nanoalmazy detonacionnogo sinteza: poluchenie i primenenie / pod obshch. red. Vityaz' P.A. — Minsk: Belarus. navuka. — 2013 (in Russian)

17. Dudan A., Vigerina T.V., Kravchuk V.I., Pilipenok I.I. Povyshenie iznosostojkosti detalej tyazhelonagruzhennyh uzlov treniya avtomobilej // Vestnik Polockogo gosudarstvennogo universiteta. Seriya B, Promyshlennost'. Prikladnye nauki. — 2022, № 10, 25—30 (in Russian)