New analytical formulation for torque specification of bolted joints considering external taper thread and internal parallel metric thread

Authors

DOI:

https://doi.org/10.35819/remat2025v11id7620

Keywords:

bolted joints, taper and parallel metric threads, length of engagement, tightening torque specification

Abstract

Specifying and applying the correct tightening torque to achieve the required tightening force is essential for obtaining a reliable tensile bolted joint. In order to avoid failure of any component and/or self-loosening, the effective length of engagement between the threads plays a major role. The analytical procedures available for these applications concern the assembly of internal and external parallel threads. However, there is not analytical procedure for an external taper thread with an internal metric parallel thread. So, the present work develops an analytical procedure for calculating the length of engagement, the number of threads effective engaged, the percentage of the maximum assembly preload supported by the first screw thread and thus the tightening torque to be applied during assembly of an external taper thread with an internal metric parallel thread. Results showed that, in this case, just a few threads effectively engage and the 1th engaged thread supports the major part of the clamp load (approximately 35%). To clarify this procedure, there is a solved example at the end of the article.

Downloads

Download data is not yet available.

Author Biography

  • Alexandre da Silva Scari, Universidade Federal de Minas Gerais (UFMG), Departamento de Engenharia Mecânica (DEMEC), Belo Horizonte, Minas Gerais, Brasil

References

ANSI/ASME B1.20.1. Pipe Threads: General Purpose (inch). New York: The American Society of Mechanical Engineers, 1983. Available at: https://standardsclub.com/wp-content/uploads/pdf/1529.pdf. Accessed on: June 17, 2025.

BHATTACHARYA, Anirban; SEN, Avijit; DAS, Santanu. An investigation on the anti-loosening characteristics of threaded fasteners under vibratory conditions. Mechanism and Machine Theory, v. 45, n. 8, p. 1215–1225, 2010. DOI: https://dx.doi.org/10.1016/j.mechmachtheory.2008.08.004. DOI: https://doi.org/10.1016/j.mechmachtheory.2008.08.004

BICKFORD, John H.; OLIVER, Michael. Accessibility symbol Accessibility Information Book Introduction to the Design and Behavior of Bolted Joints: Non-Gasketed Joints. 4. ed. New York: CRC Press, 2008. DOI: https://doi.org/10.1201/9780849381874

BUDYNAS, Richard G.; NISBETT, J. Keith. Shigley’s Mechanical Engineering Design. 10. ed. New York: Mcgraw-Hill, 2015.

CROCCOLO, Dario; DE AGOSTINIS, Massimiliano; VINCENZI, Nicolò. A contribution to the selection and calculation of screws in high duty bolted joints. International Journal of Pressure Vessels and Piping, v. 96-97, p. 38–48, 2012. DOI: https://doi.org/10.1016/j.ijpvp.2012.05.010. DOI: https://doi.org/10.1016/j.ijpvp.2012.05.010

DAADBIN, A.; CHOW, Y. M. A theoretical model to study thread loosening. Mechanism and Machine Theory, v. 27, n. 1, p. 69–74, 1992. DOI: https://doi.org/10.1016/0094-114X(92)90059-Q. DOI: https://doi.org/10.1016/0094-114X(92)90059-Q

FERNANDO, Saman. An Engineering Insight to the Fundamental Behavior of Tensile Bolted Joints. Steel Construction, v. 35, n. 1, p. 2–13, 2001.

ISO 898-1. Mechanical properties of fasteners made of carbon steel and alloy steel: Part 1 – Bolts, screws and studs with specified properties classes – Coarse thread and fine pitch thread. Geneva: International Organization for Standardization, Jan. 2013.

KIM, Jeong; YOON, Joo-Cheol; KANG, Beom-Soo. Finite element analysis and modeling of structure with bolted joints. Applied Mathematical Modelling, v. 31, n. 5, p. 895–911, 2007. DOI: https://doi.org/10.1016/j.apm.2006.03.020. DOI: https://doi.org/10.1016/j.apm.2006.03.020

LIU, Hangming; SONG, Yongpeng; HU, Shenghua; HE, Yuxian; WAN, Jifang; YI, Xianzhong; HOU, Song. Design and mechanical properties analysis of drill pipe’s joint thread with unequal taper under complex loads. Scientific Reports, v. 14, p. 30856, 2024. DOI: https://doi.org/10.1038/s41598-024-81691-6. DOI: https://doi.org/10.1038/s41598-024-81691-6

MILLER, David L.; MARSHEK, Kurt M.; NAJI, Mohammad R. Determination of load distribution in a threaded connection. Mechanism and Machine Theory, v. 18, n. 6, p. 421–430, 1983. DOI: https://doi.org/10.1016/0094-114X(83)90057-5. DOI: https://doi.org/10.1016/0094-114X(83)90057-5

MÍNGUEZ, José María; VOGWELL, Jeffrey. Theoretical Analysis of Preloaded Bolted Joints Subjected to Cyclic Loading. International Journal of Mechanical Engineering Education, v. 33, n. 4, p. 349–357, 2005. DOI: https://doi.org/10.7227/IJMEE.33.4.5. DOI: https://doi.org/10.7227/IJMEE.33.4.5

NASCIMENTO JR., Hermano. Estudo da relação torque X força tensora e do coeficiente de atrito em parafusos revestidos isentos de cromo hexavalente. 2003. Dissertation (Mestrado em Engenharia Mecânica) – Pontifícia Universidade Católica de Minas Gerais, Belo Horizonte, July 8, 2003. Available at: https://biblioteca.pucminas.br/teses/EngMecanica_NascimentoJuniorH_1.pdf. Accessed on: June 17, 2025.

OLIVER, M. P.; JAIN, V. K. Effect of Tightening Speed on Thread and Under-Head Coefficient of Friction. Journal of ASTM International, v. 3, p. 1–8, 2006. DOI: https://doi.org/10.1520/JAI13072. DOI: https://doi.org/10.1520/JAI13072

PAI, N. G.; HESS, D. P. Experimental Study of Loosening of Threaded Fasteners due to Dynamic Shear Loads. Journal of Sound and Vibration, v. 253, n. 3, p. 585–602, 2002. DOI: https://doi.org/10.1006/jsvi.2001.4006. DOI: https://doi.org/10.1006/jsvi.2001.4006

PAI, N. G.; HESS, D. P. Influence of fastener placement on vibration-induced loosening. Journal of Sound and Vibration, v. 268, n. 3, p. 617–626, 2003. DOI: https://doi.org/10.1016/S0022-460X(03)00369-9. DOI: https://doi.org/10.1016/S0022-460X(03)00369-9

PAI, N. G.; HESS, D. P. Three-dimensional finite element analysis of threaded fastener loosening due to dynamic shear load. Engineering Failure Analysis, v. 9, n. 4, p. 383–402, 2002. DOI: https://doi.org/10.1016/S1350-6307(01)00024-3. DOI: https://doi.org/10.1016/S1350-6307(01)00024-3

REIFF, J. D. A Method for Calculation of Fastener Torque Specifications Which Includes Statistical Tolerancing. Journal of ASTM International, v. 2, n. 3, p. 1–12, 2005. DOI: https://doi.org/10.1520/JAI12878. DOI: https://doi.org/10.1520/JAI12878

REIFF, J. D. A Procedure for Calculation of Torque Specifications for Bolted Joints with Prevailing Torque. Journal of ASTM International, v. 2, n. 3, p. 1–8, 2005. DOI: https://doi.org/10.1520/JAI12879. DOI: https://doi.org/10.1520/JAI12879

SANCLEMENTE, J. A.; HESS, D. P. Parametric study of threaded fastener loosening due to cyclic transverse loads. Engineering Failure Analysis, v. 14, n. 1, p. 239–249, 2007. DOI: https://doi.org/10.1016/j.engfailanal.2005.10.016. DOI: https://doi.org/10.1016/j.engfailanal.2005.10.016

SASE, N.; FUJII, H. Optimizing study of SLBs for higher anti-loosening performance. Journal of Materials Processing Technology, v. 119, n. 1, p. 174–179, 2001. DOI: https://doi.org/10.1016/S0924-0136(01)00935-9. DOI: https://doi.org/10.1016/S0924-0136(01)00935-9

SASE, N.; NISHIOKA, K.; KOGA, S.; FUJII, H. An anti-loosening screw-fastener innovation and its evaluation. Journal of Materials Processing Technology, v. 77, n. 1, p. 209–215, 1998. DOI: https://doi.org/10.1016/S0924-0136(97)00419-6. DOI: https://doi.org/10.1016/S0924-0136(97)00419-6

SCARI, Alexandre da Silva; MACEDO, Bruno Luiz; OLIVEIRA, Herbert Tadeu Vilaboim; FIGUEIREDO, Tiago Petermann; MORAIS, Espedito Alves de. Influence of a New Component on a Bolted Joint. In: SAE BRASIL 2010 CONGRESS AND EXHIBIT, 2010. SAE Technical Paper 2010-36-0276. [S.l.]: SAE Brasil, 2010. DOI: https://doi.org/10.4271/2010-36-0276. DOI: https://doi.org/10.4271/2010-36-0276

SCHNEIDER, R.; WUTTKE, U.; BERGER, C. Fatigue analysis of threaded connections using the local strain approach. Procedia Engineering, v. 2, n. 1, p. 2357–2366, 2010. DOI: https://doi.org/10.1016/j.proeng.2010.03.252. DOI: https://doi.org/10.1016/j.proeng.2010.03.252

SHIGLEY, Joseph E.; MISCHKE, Charles R. Standard Handbook of Machine Design. 2. ed. New York: McGraw-Hill, 1996.

STEPHENS, R. I.; BRADLEY, N. J.; HORN, N. J.; ARKEMA, J. M.; GRADMAN, J. J. Influence of Cold Rolling Threads Before or After Heat Treatment on the Fatigue Resistance of High Strength Coarse Thread Bolts for Multiple Preload Conditions. Journal of ASTM International, v. 3, n. 3, p. 1–13, 2006. DOI: https://doi.org/10.1520/JAI13075. DOI: https://doi.org/10.1520/JAI13075

VDI-2230. Systematic Calculation of High Duty Bolted Joints: Joints with One Cylindrical Bolt. Berlin: Verband Deutscher Ingenieure, Feb. 2003.

ZADOKS, R. I.; YU, X. An Investigation of the Self-Loosening Behavior of Bolts Under Transverse Vibration. Journal of Sound and Vibration, v. 208, n. 2, p. 189–209, 1997. DOI: https://doi.org/10.1006/jsvi.1997.1173. DOI: https://doi.org/10.1006/jsvi.1997.1173

ZHANG, D.; GAO, S.; XU, X. A new computational method for threaded connection stiffness. Advances in Mechanical Engineering, v. 8, n. 12, p. 1–9, 2016. DOI: https://doi.org/10.1177/1687814016682653. DOI: https://doi.org/10.1177/1687814016682653

Downloads

Published

2025-08-20

Issue

Section

Mathematics

How to Cite

SCARI, Alexandre da Silva. New analytical formulation for torque specification of bolted joints considering external taper thread and internal parallel metric thread. REMAT: Revista Eletrônica da Matemática, Bento Gonçalves, RS, Brasil, v. 11, p. e305, 2025. DOI: 10.35819/remat2025v11id7620. Disponível em: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/7620. Acesso em: 11 jun. 2026.