A new analytical model of bolted flange structures in the rotor system and its verification

doi:10.1007/s10483-025-3312-7

Abstract

Abstract:

The bolted flange structure finds significant applications in fields such as aerospace, shipbuilding, and pipeline transportation. The investigation of its dynamic characteristics has consistently been a focal point for researchers; however, there remains a deficiency in the development of robust analytical models. This paper introduces a novel analytical model based on the finite element methods and the Timoshenko beam theory to accurately simulate the bolted flange structure. The stiffness, mass, damping, and inertia matrices of the rotor system are individually derived, and the dynamic equation is subsequently formulated. The model’s validity and accuracy are validated through both the experimental testing and the finite element analysis. This study aims to elucidate the relationship between the external loads and the influence of the geometric configuration on the stiffness and contact behavior of the bolted flange structure, thereby enabling a thorough and precise prediction of the static and dynamic load transfer pathways, as well as the distribution of vibrational energy within the structure, while also facilitating the incorporation of friction and slip effects. Simultaneously, this work provides a foundational framework for the optimization design of bolted flange structures, addressing the factors such as the number, size, and geometric distribution of bolts.

Key words: bolt flange structure, non-uniform beam, dynamical model, model test

2010 MSC Number:

TH122

Jin CHEN, Kuan LU, Haopeng ZHANG, Wentao ZHANG, Xiaohui GU, Chao FU, Shanmin TUO. A new analytical model of bolted flange structures in the rotor system and its verification. Applied Mathematics and Mechanics (English Edition), 2025, 46(11): 2115-2134.

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Figures/Tables 17

Fig.?1

Fig.?2

Fig.?3

Table?1

Fig.?4

Table?2

The torsion coefficient of rectangular section"

$H / B$	1	1.2	1.5	2	2.5	3	4	6	8	10	$∞$
$γ$	0.141	0.166	0.196	0.229	0.249	0.263	0.281	0.299	0.307	0.313	0.333

Table?2

Fig.?5

Fig.?6

Fig.?7

Fig.?8

Fig.?9

Table?3

Comparison of free end displacement of the cantilever beam with variable cross-section"

Displacement	$u x /mm$	$u y /mm$	$u z /mm$
Calculation results of this paper	$2.697 0 × 10 − 4$	$− 1.5 × 10 − 4$	$7.684 8 × 10 − 3$
Results of finite element software	$2.849 1 × 10 − 4$	$3.6 × 10 − 3$	$8.272 1 × 10 − 3$
The error/%	5.3	–	7.1

Table?3

Fig.?10

Fig.?11

Fig.?12

Table?4

The first six natural frequencies"

Natural frequency	The first-order	The second-order	The third-order	The fourth-order	The fifth-order	The sixth-order
Theoretical calculation in this paper/ Hz	451.1	1 432	1 445.8	2 771.2	3 104.2	3 168.1
Finite element simulation/ Hz	410.5	1 392.6	1 395	2 851.6	3 257.4	3 260.3
Experiment/ Hz	531.25	1 446.9	1 446.9	–	–	–
Relative error $A /%$	9	2.75	3.72	2.9	4.93	2.91
Relative error $B /%$	15.08	1.03	0.08	–	–	–
Note: error $A$ in the table represents the error analysis between the method and the finite element model; error $B$ represents the error analysis between the method and the experimental results

Table?4

Fig.?13

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Natural frequency	The first-order	The second-order	The third-order	The fourth-order	The fifth-order	The sixth-order
The integral flange plate	3 821.7	3 825.1	4 983.8	5 677.3	6 586.1	6 586.8
The discrete plate	3 894	3 894.9	5 142.2	5 183.9	7 203	7 210.7
Error/%	1.86	1.79	3.08	9.52	8.56	8.65