Study on the Energy Absorption Characteristics of Tapered Threaded Tubes Under Oblique Loading

WANG Chao, ZHANG Ning, ZHANG Chuanliang, TIAN Xiaogeng
(State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University)

Oct. 2025 10. 11776 / j. issn. 1000-4939. 2025. 05. 010

Abstract

Thin-walled structures are widely utilized in fields such as transportation due to their lightweight nature, low manufacturing costs, and high energy absorption efficiency. To improve the energy absorption performance of traditional straight and corrugated tubes, this study proposes a tapered thin-walled tube featuring a helical corrugated pattern, referred to as a tapered threaded tube. The crushing behavior and energy absorption characteristics of these tapered threaded tubes under oblique loading were investigated using the finite element method. The study analyzes the effects of various geometric parameters and loading angles on key performance indicators, including initial peak force, average crushing force, energy absorption, and specific energy absorption.

The results indicate that while oblique loading generally limits the energy absorption performance of a structure, the tapered tube can withstand oblique loads as effectively as axial loads. The introduction of the threaded pattern significantly reduces the initial peak force of the tapered tube—by a maximum of $78\%$ compared to a smooth tapered tube. Furthermore, the crushing force efficiency increased by a maximum of $50\%$, markedly reducing load fluctuations, although the specific energy absorption experienced a slight decrease. These research findings provide a theoretical basis for the design of related energy-absorbing structures.

Keywords: Thin-walled structures; Oblique loading; Energy absorption; Tapered spiral tube

1. Introduction

Thin-walled structures serve as critical passive safety components designed to protect passengers and sensitive equipment by dissipating kinetic energy through plastic deformation during collisions. While axial crushing has been extensively studied, real-world collision scenarios frequently involve oblique loading, which can lead to global buckling and a significant reduction in energy absorption efficiency.

To address these challenges, researchers have explored various geometric modifications, such as multi-cell structures, functionally graded thicknesses, and corrugated walls. Tapered tubes, in particular, have demonstrated better stability under oblique loads compared to straight tubes because their increasing cross-sectional area helps resist lateral bending. This study proposes a tapered spiral tube, combining the advantages of tapered geometries with spiral reinforcements to further enhance crashworthiness performance under multi-axial loading conditions.

2. Numerical Modeling and Validation

2.1 Design Method of Tapered Threaded Tubes

As shown in [FIGURE:1], the structure features a spiral pattern similar to that of a conch shell found in nature. This geometry is generated by sweeping a sine wave along a spiral path on the surface of a straight tapered tube. The expression for the sine wave is given by:

$$y' = A \sin (x' \cdot 2\pi / P)$$

The geometry is primarily defined by the thread amplitude ($A$), the thread pitch ($P$), and the taper angle of the tube ($\theta$). As shown in [TABLE:1], each geometric parameter is assigned specific values to investigate their effects on mechanical performance. In this study, the height ($H$) and top diameter ($D_1$) of the tapered threaded tube are fixed at 120 mm and 40 mm, respectively, while the bottom diameter varies according to the taper angle. By varying these geometric factors, a total of 27 different configurations were obtained and tested under three different loading angles ($0^\circ$, $10^\circ$, and $20^\circ$).

2.2 Finite Element Model

The finite element analysis was performed using the explicit solver in Abaqus/Explicit to simulate the static compression process. As shown in [FIGURE:1], the tapered threaded tube is positioned between two rigid plates. The tube is fixed to the bottom rigid plate, which is fully constrained. The top rigid plate is restricted to translational motion along the longitudinal axis. To ensure a quasi-static response where the ratio of kinetic energy to internal energy remains below $5\%$, the loading duration was set to $0.05\text{ s}$. The total compression distance was defined as $70\%$ of the tube height.

For the finite element mesh, S4R shell elements were employed with five integration points through the thickness. A global mesh size of $1.0\text{ mm}$ was selected. Contact interactions were defined using a surface-to-surface formulation between the tube and the plates, while self-contact was assigned to the tube walls with a friction coefficient of $0.2$. The material used is Q235 mild steel, utilizing an elastoplastic constitutive model.

2.3 Performance Indicators

The performance of tubular thin-walled structures is evaluated based on the following indicators:

1. Initial Peak Force ($IPF$): The maximum force required to initiate deformation.
2. Energy Absorption ($EA$): The area under the load-displacement curve, expressed as $E_{EA} = \int P(s) ds$.
3. Mean Crushing Force ($MCF$): The average force over the stroke, $P_m = E_{EA} / d_{max}$.
4. Crushing Force Efficiency ($CFE$): The ratio of mean crushing force to maximum peak force, $CFE = P_{mean} / P_{max}$.
5. Specific Energy Absorption ($SEA$): Energy absorbed per unit mass, $E_{SEA} = E_{EA} / m$.

2.4 Finite Element Validation

The accuracy of the FE analysis was verified by comparing results with experimental data from literature for sinusoidal spiral tubes and tapered tubes. The deformation modes and force-displacement curves obtained from the FE analysis were fundamentally identical to experimental results, with trends in force-displacement curves showing high consistency. The errors between simulation and experimental performance indicators were within acceptable limits, confirming the model's reliability.

3. Results and Discussion

3.1 Force-Displacement Characteristics

The plateau force of the tapered threaded tube (STT) is lower than that of the straight tapered tube because the threaded surface acts as a deformation trigger, effectively reducing the initial peak force. While all tube types experience their highest peak forces under axial loading, these values are significantly lower for the STT. As the loading angle increases, the force-displacement curve shifts downward, leading to a reduction in the plateau force.

3.2 Deformation Modes

Under oblique loading, the tubes primarily undergo axial progressive crushing or global bending. At low loading angles ($0^\circ$ to $10^\circ$), axial progressive collapse dominates. At larger angles, the mode transitions to global bending, which reduces energy absorption efficiency. Increasing the taper angle helps delay this transition. For instance, at a taper angle of $15^\circ$, the critical angle for bending transition increases to $20^\circ$–$30^\circ$.

3.3 Parametric Analysis

• Amplitude and Pitch: Increasing thread amplitude and decreasing pitch helps achieve a lower initial peak force. However, reducing amplitude can result in higher $SEA$. A small pitch is suitable for low loading angles, while a large pitch is more effective for high loading angles.
• Thickness and Taper Angle: $SEA$ and $MCF$ increase with wall thickness and taper angle. At low loading angles, the structure maintains high resistance to failure, comparable to axial compression performance.

4. Conclusion

1. The tapered threaded tube transitions from axial crushing to global bending at specific loading angles. Increasing the taper angle is beneficial for resisting bending and enhancing energy absorption.
2. Increasing thread amplitude and decreasing pitch effectively reduces the initial peak force.
3. Compared to conventional tapered tubes, the proposed STT reduces the initial peak force by $21.5\% \sim 45.4\%$ and improves crushing force efficiency by up to $63.7\%$, demonstrating excellent compression stability.
4. Compared to tapered corrugated tubes, the STT exhibits a maximum $SEA$ increase of $15.3\%$.