Key Takeaways & Executive Findings
- •• • The four-DOF model incorporating normal motion eliminates the over-evaluation of system stability present in the three-DOF model, as validated by line testing; this prevents underestimation of chaotic stick–slip risk in high-speed train brake design. • • Tangential stiffness is the dominant factor inducing chaotic stick–slip vibration in the three-DOF model, whereas in the four-DOF model it primarily modulates amplitude; normal stiffness is identified as the critical parameter driving vibration chaos, necessitating distinct design strategies for each model fidelity. • • Damping has a minimal impact on the occurrence of chaotic stick–slip vibration, indicating that relying solely on damping adjustments is insufficient for suppression; instead, stiffness and inertia parameters must be prioritized. • • Optimal ranges for brake disc rotational inertia (5–9 kg·m² and 11–22 kg·m²) and friction pad mass (7–17 kg) effectively mitigate chaotic stick–slip vibration, providing actionable thresholds for industrial brake system design to reduce fatigue wear and enhance service life.
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Abstract
Stick–slip vibration in disc brake systems at low speeds arises from the interaction of multiple factors, posing persistent challenges for high-speed train safety and passenger comfort. This study establishes three- and four-degree-of-freedom (DOF) dynamic models that incorporate wheel–rail adhesion and nonlinear friction, validated through line testing. System stability, stick–slip bifurcation characteristics, and key influencing factors are analyzed via numerical simulation. Results demonstrate that the four-DOF model, by accounting for normal motion, avoids the over-evaluation of system stability inherent in the three-DOF model. In the three-DOF model, tangential stiffness is the primary factor inducing chaotic stick–slip vibration. In the four-DOF model, tangential stiffness predominantly affects vibration amplitude, while normal stiffness governs the onset of chaos. Damping exhibits minimal influence on chaotic stick–slip occurrence. Optimal parameter ranges are identified: brake disc rotational inertia of 5–9 kg·m² and 11–22 kg·m², and friction pad mass of 7–17 kg, which effectively mitigate chaotic stick–slip vibration. These findings provide quantitative guidelines for brake system design, enhancing operational reliability and reducing wear-related failures in high-speed rail applications.
1. Introduction
Disc brake systems are critical for high-speed train safety, dissipating kinetic energy through friction between pads and discs. However, at low speeds, stick–slip vibration at the friction pad generates complex flutter and creep groans, compromising passenger comfort and accelerating component fatigue. Existing experimental approaches have explored mitigation strategies such as micro-groove textures and brake pad sizing, yet the nonlinear nature of stick–slip vibration continues to pose a formidable challenge. Commercial brake designs often rely on simplified models that neglect normal motion, leading to over-optimistic stability assessments and unexpected vibration failures in service.
This study addresses the bottleneck by developing three- and four-DOF dynamic models that integrate wheel–rail adhesion and nonlinear friction, validated through line testing. The four-DOF model captures normal motion, revealing that tangential stiffness governs amplitude while normal stiffness drives chaotic behavior—a distinction absent in conventional analyses. By identifying optimal ranges for brake disc rotational inertia (5–9 kg·m² and 11–22 kg·m²) and friction pad mass (7–17 kg), the research provides quantitative guidelines to suppress stick–slip chaos, offering a pathway to more reliable and durable brake systems for high-speed rail.
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ZHOU Hangyu, WANG Zhiwei, WANG Quan, MO Jiliang, ZHAO Chunguang, WANG Kaiyun (2026). Dynamic Models and Analysis of Key Factors Influencing Stick–Slip Vibration in Disc Brake Systems. Railway Engineering Science (铁道工程科学). https://doi.org/10.1007/s40534-025-00379-3
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Frequently Asked Questions
What is the primary failure mechanism driving chaotic stick–slip vibration in the three-DOF versus four-DOF models?
In the three-DOF model, tangential stiffness is the main factor inducing chaotic stick–slip vibration. In contrast, the four-DOF model, which includes normal motion, identifies normal stiffness as the primary driver of vibration chaos, while tangential stiffness mainly affects amplitude. This distinction is critical because neglecting normal motion can lead to over-evaluation of system stability and inadequate vibration suppression.
How do the identified optimal parameter ranges for brake disc rotational inertia and friction pad mass compare to current industry standards?
The study specifies optimal ranges of 5–9 kg·m² and 11–22 kg·m² for brake disc rotational inertia, and 7–17 kg for friction pad mass. These ranges effectively mitigate chaotic stick–slip vibration. While direct comparisons to all industry standards are not provided, these values offer quantitative targets for design optimization, potentially reducing reliance on trial-and-error prototyping and lowering development costs.
What is the industrial scalability of implementing the four-DOF model for real-time brake control systems?
The four-DOF model incorporates wheel–rail adhesion and nonlinear friction, validated through line testing. Its computational complexity is higher than the three-DOF model, but it avoids over-evaluation of stability. For real-time control, model reduction techniques or precomputed stability maps based on the identified parameter ranges (e.g., inertia 5–9 kg·m², pad mass 7–17 kg) could enable practical implementation without sacrificing accuracy.
Why does damping have minimal impact on chaotic stick–slip vibration, and what are the implications for brake system design?
The study found that damping has a minimal impact on the occurrence of chaotic stick–slip vibration. This implies that increasing damping alone is insufficient to suppress chaos; instead, design efforts should focus on adjusting stiffness and inertia parameters. For industry, this shifts the emphasis from damping treatments to structural optimization of tangential and normal stiffness, and careful selection of rotational inertia and pad mass.
What are the cost and performance trade-offs of adopting the recommended parameter ranges in high-speed train brake systems?
Adopting the recommended ranges (disc inertia 5–9 kg·m² and 11–22 kg·m², pad mass 7–17 kg) can reduce chaotic stick–slip vibration, thereby decreasing fatigue wear and extending component service life. While specific cost data are not provided, the reduction in maintenance and replacement costs, along with improved passenger comfort, likely outweighs potential increases in material or manufacturing costs. Performance trade-offs may include changes in braking response, which require further validation.
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