Study on the Load Conversion of Bolt-Nut Fasteners between Tightening and Service Conditions


At present, the common method to realize the pre-tightening effect of threaded fasteners is by applying an accurate tightening torque on them. However, when removing the tightening torque, the load characteristics will have a transient conversion, so that the pre-tightening loads will be significantly different from the tightening condition. For the aim of understanding the pre-tightening effect under the service condition, it is important to model the load conversion between tightening and service conditions. Based on the most basic mechanical equilibrium analysis, the load characteristics of bolt-nut fasteners under a round of the tightening and service conditions were studied. The torque equilibrium equations were built respectively, the load conversion between two conditions was analyzed and an approximate relationship between the applied tightening torque under the tightening condition and the pre-tightening torque under the service condition was obtained. In the meanwhile, a dynamic strain measuring system was proposed to accurately determine the pre-tightening loads in real time. Results verified that the thread torque and the bearing friction torque balance each other and act as pre-tightening torques under the service condition. The final pre-tightening loads can be roughly estimated to be larger than half of the difference in tightening torques by wrenches, but smaller than half of the sum of tightening torques, or can be accurately measured through dynamic strain measurements.


• We study on bolt-nut fasteners , load characteristics under tightening and service conditions.

• We model the relationship between the pre-tightening torque and the applied tightening torque.

• We verify that the pre-tightening torque is apparently determined by the friction on the contacting interface.

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We acknowledge the support received from the National Natural Science Foundation of China (NO. 51705298).

Author information




Xianyue Gang contributed significantly to the assumption rearrangement, theoretical verification and manuscript revision of the study; Shaojie Zhu performed the experiments, data analyses and manuscript revision; Di Liu contributed to write the original manuscript; Fan Zhang (CA) contributed to the conception, methodology, theoretical modeling of the study; Haizhi Wu helped perform the experiments and analyze the data.

Corresponding author

Correspondence to F. Zhang.

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A glossary of terms

Symbol Nomenclature
Tw The tightening torque
Tt The thread torque
Ts The bearing friction torque
F The axial pre-tightening force
r1 The flank radius of bolt
α The thread helix angle
μ1 The coefficient of friction between threads
r2 The effective friction radius under nut
μ2 The coefficient of friction between fastener and seat
Tw1 The tightening torque applied by wrench 1
Tt The reaction torque to Tt
Ts The friction torque between the bolt head and seat
r3 The effective friction radius under bolt head
μ3 The effective coefficient of friction between bolt head and seat
Tw2 The tightening torque from wrench 2
TT The thread torque under the service condition
TS The friction torque between the nut and seat under the service condition
TT The thread torque under the service condition, which is in opposite direction to TT
TS The bearing friction torques under the service condition, which is in opposite direction to TS
εi The measured strain of the i-th strain gage
εT The line strain component induced by the thread torque (Tt or TT under tightening and service conditions)
εF The line strain component induced by the axial clamping force F
εMxy The strain induced by torque in plane xy
εMxz The strain induced by torque in plane xz
εt The strain induced by temperature change
UBD The output voltage of the bridge
UAC The bridge excitation voltage of 5 V
K The sensitivity coefficient of strain gauge of 2.16
εout The instrument indicating strain of EX1629
εx The line strain in x axis
εy The line strain in y axis
γxy the shear strain in plane xy
G The shear modulus
E The modulus of elasticity
μ The poisson’s ratio
d The diameter of the bolt
C The coefficient of tightening torque

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Lv, C., Liu, A., Liu, D. et al. Study on the Load Conversion of Bolt-Nut Fasteners between Tightening and Service Conditions. Exp Tech (2021).

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  • Bolt-nut fastener
  • Tightening torque
  • Pre-tightening
  • Service condition
  • Strain measurement