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Analytical modeling of axial stiffness of tensile bolted joints under concentric external load

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Abstract

Stiffness of bolted joints is a critical parameter for determining deformations and natural frequencies of assemblies. In this study, the effect of external load on axial stiffness of bolted joints is clarified theoretically for the first time. The stiffness of stress zones between and beyond load planes is derived on the basis of the strain energy method and used to formulate the stiffness of bolted joints. The influence of the distance between the load planes of the external load, axial positions of the external load, and difference in the material of the clamped parts on the stiffness of the bolted joints are investigated by applying the proposed formulations and finite element method. Comparisons with finite element results indicate that the proposed formulation can accurately predict the stiffness of the bolted joints.

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Abbreviations

W :

Effective work

A b :

Sectional area of bolt (m2)

E b :

Young’s modulus of bolt (GPa)

E c :

Young’s modulus of clamped parts (GPa)

F cri :

Critical external load of bolted joint (N)

F E :

Critical external load of bolted joint (N)

F′E :

Dimensionless external axial load

F I :

Pretension force of bolt (N)

L :

Total grip length of bolted joint (m)

L 1,L 2 :

Thickness of clamped parts (m)

L′p :

Dimensionless position of load plane

U b :

Strain energy in bolt (J)

U c :

Strain energy in clamped parts (J)

U J :

Strain energy in bolted joint (J)

d :

Diameter of bolt (m)

k Ion :

Stiffness of stress zone beyond load planes in upper clamped part (N/m)

k Iin :

Stiffness of stress zone between load planes in upper clamped part (N/m)

k IIon :

Stiffness of stress zone beyond load planes in lower clamped part (N/m)

k IIin :

Stiffness of stress zone between load planes in lower clamped part (N/m)

k N :

Equivalent stiffness to normalize stiffness of bolted joint (N/m)

k J :

Axial stiffness of bolted joint (N/m)

k′J :

Dimensionless stiffness of bolted joint (N/m)

k b :

Axial stiffness of bolt (N/m)

k c :

Axial stiffness of clamped parts (N/m)

k c1,k c2 :

Axial stiffness of clamped parts (N/m)

k ci :

Axial stiffness of stress zone between load planes (N/m)

k co :

Axial stiffness of stress zone beyond load planes (N/m)

k g :

Axial stiffness of cylinder in bolt (N/m)

k sk :

Axial stiffness of bolt head (N/m)

r H :

Radius of bolt hole (m)

r h :

Radius of bolt head (m)

u, u i :

Axial displacement of joint of node I in finite element model (m)

Φn :

Load factor of bolted joint

ΔF b :

Variation of bolt load (N)

ΔF c :

Variation of clamping force (N)

ΔU b :

Variation of strain energy in bolt (J)

ΔU c :

Variation of strain energy in clamped parts (J)

ΔU :

Total variation of strain energy (J)

α :

Cone angle of pressure cone (rad)

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Acknowledgments

This research work is funded by the National Natural Science Foundation of China (Grant No. 11602071) and National Science and Technology Major Project (Grant No. 2017-IV-0008-0045).

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Authors and Affiliations

  1. School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China

    Peng He, Jiaxin Liu, Chengyuan Zhang & Zhansheng Liu

Authors
  1. Peng He
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  2. Jiaxin Liu
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  3. Chengyuan Zhang
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  4. Zhansheng Liu
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Corresponding author

Correspondence to Peng He.

Additional information

Recommended by Associate Editor Beomkeun Kim

Peng He is a lecturer at the School of Energy Science and Engineering, Harbin Institute of Technology in Harbin, China. He received his Ph.D. in Power Machinery and Engineering from the same institution. His research interests include rotordynamics, mechanics of discontinuous structures, and thermal-mechanical coupled mechanics.

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He, P., Liu, J., Zhang, C. et al. Analytical modeling of axial stiffness of tensile bolted joints under concentric external load. J Mech Sci Technol 33, 5285–5295 (2019). https://doi.org/10.1007/s12206-019-1020-8

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  • DOI: https://doi.org/10.1007/s12206-019-1020-8

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