© C. Li et al. Published by EDP Sciences 2025

1 Introduction

With rapid socio-economic development and rising expectations for quality of life, demand for elevator safety and comfort has grown significantly. Innovations in materials, technologies, and processes are now widely adopted in elevator manufacturing, design, and maintenance. In 2000, Otis Corporation proposed the composite traction belt technology. Unlike with traditional wire rope structures, traction belts have gained widespread market acceptance due to their advantages in safety, comfort, energy efficiency, and environmentally friendly [1]. However, prolonged using can lead to issues such as cracks, yellowing of the covering layer, or even wire breakage, significantly reducing their operational lifespan compared to the designed service life [2]. The national standard GB/T 39172-2020 “Non-wire rope suspension devices for elevators” prescribed type test conditions and performance requirements for traction belts, and with breaking strength identified as a critical performance parameter [3]. Although there are no standardized guidelines for replacing in-service traction belts, with replacements often relying on manufacturer-specific recommendations. Meanwhile, there is relatively limited research on fundamental theories and applications related to stress analysis and model analysis of traction belts. Therefore, considering the national standard requirements for key parameters in the type testing of traction belts, establishing a refined simulation model for elevator traction steel belts and utilizing numerical simulation methods to investigate stress distribution under typical faults has significant theoretical and practical value. Such efforts would enhance the understanding of failure mechanisms, reliability analysis, and performance optimization of traction belts.

The aforementioned research on elevator traction steel belts requires extensive experimentation for data collection and validation. However, most performance tests on traction belts are destructive, resulting in low experimental efficiency and high costs. Therefore, using the finite element method to numerically simulate traction belt behavior under typical faults not only reduces experimental costs but also improves research efficiency. Furthermore, this approach enables the simulation of various traction belts states under different fault scenarios and environmental conditions, demonstrating both practicality and feasibility.

Currently, numerical simulation research mainly focuses on modeling traction wire ropes and analyzing stress distribution under tensile conditions. However, numerical simulation studies of traction belts remain limited. Gu established a physical model of elevator traction components, and finite element analysis software is used to study the combined stress distribution [4]. Sun built the simulation models of asymmetric tube plates, analyzing stress distribution under various compressive conditions and optimizing the parameters based on the analysis results [5]. Li analyzed the structural characteristics of linear-contact wire ropes, established a wire rope model, and conducted numerical simulation research using ANSYS software to determine stress distribution under tension, verifying the accuracy of the filled wire rope model [6]. Chen researched developed a finite element model for the fatigue performance of defect-containing steel wire ropes, considering various stress effects, and through a high-precision mesh refinement method, analyzed the specific impact of defect location and orientation on fatigue life and load-bearing performance [7]. Fedorko designed a finite element model of triangular core wire ropes, obtaining stress distribution under tensile loads using finite element software [8]. Sekmen researched the influence of different types of corrosion and high-temperature degradation on the mechanical properties of elevator traction steel strips was studied and verified through experiments [9]. Han and others conducted experiments to study the bending fatigue characteristics of YS 9–8 × 19 braided wire rope, analyzed the relationship between the number of broken wires and its fatigue life, explored the fracture mechanism and wear morphology of the wire using microscopy techniques, and delved into the friction fatigue characteristics of the wire rope [10]. Zhu conducted numerical simulation research on mine-use wire ropes using the finite element method, summarizing stress distribution patterns between wire strands and related conclusions on fatigue characteristics [11].

Current research has primarily focused on theoretical modeling of wire ropes, while investigations of the internal stress variations of wire ropes have been limited, particularly regarding their stress states under extreme operating conditions. Therefore, there is a critical need to develop refined traction belt models to analyze stress distribution and variation for enhancing their reliability.

Owing to variations in raw materials, manufacturing processes, and assembly standards among elevator manufacturers, combined with the complex interaction of multiple environmental factors affecting traction belt elevators, such as dynamic traction loads, thermal fluctuations, humidity, UV exposure, and biological degradation, the mechanical properties, product structures, and failure mechanisms of these systems remain insufficiently studied by regulatory authorities and inspection agencies. This research deficiency presents substantial obstacles to establishing standardized protocols for the inspection, maintenance procedures, and replacement criteria of traction belt elevator systems.

This study focuses on the mechanical properties, structural characteristics, stress distribution, and related aspects of traction belts. A steel belt with a breaking strength of 43 kN was selected as the research object. Following national standards and referencing type test certification data for traction belts, the parameters, specifications, and boundary conditions for elevator traction steel belts were determined. Comprehensive and localized refined physical models for the traction belt were established. Using ANSYS finite element analysis software, numerical simulation research was conducted to study stress distribution within the traction belt and its internal steel wire ropes under extreme tensile loads. A comparison between the simulation results and the tensile test data validated the accuracy of the established traction belt model. Additionally, a virtual simulation model replicating traction belt failure mechanisms was developed, for analyzing stress characteristic distributions under typical faults. Specific recommendations were formulated for different stress conditions to improve traction belt reliability. This study provides theoretical support for the digitization of special equipment, detection warning systems, and fault simulation analyses.

2 Analysis of the load-bearing structure of the steel belt

In Figure 1, the dashed line delineates the traction sheave assembly of the steel belt elevator system. The traction belts, which are assembled side by side on the traction machine, form a core component of the steel belt elevator. The belts consist of steel wire ropes and a covering layer, the steel wire ropes are uniformly arranged in a longitudinal direction and encased within the wrapping layer. Specifically, the steel wire ropes composed of seven twisted strands, while the covering layer material is made of a thermoplastic polyurethane elastomer (TPU) rubber. The physical appearance of the traction belt is illustrated in Figure 1.

The steel wire rope is the primary load-bearing part of the traction belt, and analyzing the stress on the steel wire ropes under tension is fundamental to improving the reliability of the belt. Within the traction belt, the steel wire ropes are fabricated by helically twisting outer wires around a central core at a predetermined angle. This study conducts a stress analysis of the steel wire ropes based on principles from elastic mechanics, as depicted in Figure 2.

Since the steel wire rope primarily bears tensile loads during operation, it can be considered as a cohesive unit within the traction belt. In this scenario, the axial tension F₀ exerted on the steel wire rope is:

$$F_0=E\pi {R_0}^2{\epsilon }_0.$$(1)

In equation (1), E represents the elastic modulus of the steel wire rope, R₀ is the radius of the steel wire rope, ε₀ denotes the axial strain of the steel wire rope. The material, structure, and uniformity of force of the wire rope will cause changes in ε₀.

If each strand of the steel wire within the belt is considered as a cohesive unit, inter-wire friction can be treated as internal forces owing to effective wire lubrication. Thus, inter-facial friction between individual wires may be disregarded, and is excluded from the analytical model. Consequently, the mechanical response of the steel wire rope under tensile loads is similar to actual usage [9]. The axial tension F₁ exerted on the steel wire rope is:

$$F_1=F_2+F_3$$(2)

$$F_2=E\pi {R_1}^2{\epsilon }_1$$(3)

$$F_3=mE\pi {R_2}^2{\epsilon }_2.$$(4)

In equation (2), F₂ represents the axial tension experienced by the core of the steel wire rope, R₁ denotes the radius of the core of the steel wire rope, ε₁ signifies the axial strain of the core of the steel wire rope. Similarly, F₃ stands for the axial tension experienced by the strands of the steel wire rope, R₂ represents the radius of the strands of the steel wire rope, ε₂ indicates the axial strain of the strands of the steel wire rope, and m denotes the number of strands in the steel wire rope.

Fig. 1 The structure and diagram of the traction belt elevator.

Fig. 2 The simplified diagram of steel wire rope under stress.

3 The finite element analysis of the traction belt

3.1 The establishment and analysis of the traction belt model

3.1.1 The physical model and mesh division of the traction belt

The traction steel belt studied in this article is composed of steel wire ropes and covering layer. The steel wire rope is twisted into 7 strands, and 10 steel wire ropes are evenly arranged horizontally, and then wrapped with a covering layer. The covering layer material is thermoplastic polyurethane elastomer rubber, and the material of steel wire rope is 60 carbon steel. The picture and size of the steel belt we have selected are shown in Figure 3.

This paper analyzes the overall force distribution within the traction belt. Because the regular arrangement of the steel wire ropes and the uniformity of stress distribution, the coupling stress between the 7 strands of steel wire rope is neglected, and they are treated as a single steel wire rope to establish the physical model. The traction belt is classified based on the breaking strength into three primary categories: 32 kN, 43 kN, and 64 kN [12]. Among them, the 43 kN traction belt has the highest using in traction elevators due to its excellent traction performance and economical cost of use. Therefore, this study chooses the 43 kN traction belt as the subject for simulation research.

Given the plasticity, high elasticity, and stress-strain hardening characteristics of the steel wire rope, this paper employs the Solid185 element in ANSYS to perform mesh partitioning for the solid model of the steel wire rope. As the main load-bearing component of the traction belt, the steel wire rope requires high computational accuracy in its mesh. Therefore, the SWEEP command in ANSYS is utilized to generate a hexahedral mesh for the steel wire rope model. The main function of the covering layer is to protect the steel wire rope, requiring less computational accuracy. So, the FREE command in ANSYS is applied to mesh the covering layer model, producing either tetrahedral or hexahedral meshes. The resulting model after meshing is shown in Figure 4.

Fig. 3 The picture and size of the steel belt.

Fig. 4 Mesh division of the steel wire rope and traction belt.

3.1.2 Calculation of material property parameters and setting boundary conditions

To ensure that the model parameters and boundary conditions of the traction belt align with the actual scenario, we conducted tensile tests on the steel wire rope following the type test requirements specified in the national standard ‘Non-steel wire rope suspension devices for elevators' (GB/T 39172-2020). The tensile strength and stress-strain diagrams of the steel wire rope were measured and recorded, from which key parameters were extracted for material property settings in the numerical simulation. The experiment's condition is shown in Table 1.

In the experiment, 3 steel wire ropes of the same specification (length: 300 mm) were tested using a universal testing machine. The stretching speed is 20 mm/min until the wire ropes fractured. The maximum force recorded at fracture was defined as the breaking load. The average of the 3 test results was taken as the measured tensile strength. The test results are presented in Table 2.

In Table 2, the yield strength of the steel wire rope is the stress at its yield point, its calculated as shown in equation (5):

$${\sigma }_{\text{b}}=\frac{F_{\text{b}}}{S}.$$(5)

In the equation (5), σ is the yield strength, F is the stress at the yield point, and S is the cross-sectional area of the steel wire rope.

The tensile strength and stress-strain diagrams of the steel wire ropes are shown in Figures 5–7. As shown, the steel wire rope remains in the elastic phase when subjected to a tensile force in the range of 0 to 900 N. Beyond this range, it transitions into the yielding phase. The material behavior of the steel wire rope aligns well with a bilinear material model.

The tangent modulus of the steel wire rope is defined as the slope between the yield limit and the ultimate strength limit. It can be calculated with equation (6):

$${\sigma }_{\text{t}}=\frac{{\sigma }_{\text{b}}-\sigma }{\mathrm{\Delta }\delta }.$$(6)

In equation (6), σ_t is the tangent modulus, Δδ is the average displacement difference between the fracture point and yield point of the steel wire rope. From Figures 4–6, Δδ = 0.03625-0.02 = 0.01625 mm, and by the calculation, the yield strength of the steel wire rope is determined to be 0.388 GPa, and the tangent modulus is 126.8 GPa.

As a result, the numerical simulation parameters for the traction belt are configured as follows: the elastic modulus of the steel wire rope material is 206 GPa, the yield strength is 0.388 GPa, the tangent modulus is 126.8 GPa, and the Poisson's ratio is set to 0.3; the elastic modulus of the covering layer is 60 MPa, and the Poisson's ratio is 0.47 [13].

To simulating the traction belt's tensile test, the numerical simulation is carried out. To replicate this condition, a 43 kN axial load is applied to the top of the traction belt model, and the bottom is subjected to fully constrained conditions.

Fig. 5 Tensile strength and stress-strain diagram of sample 1.

Fig. 6 Tensile strength and stress-strain diagram of sample 2.

Fig. 7 Tensile strength and stress-strain diagram of sample 3.

3.1.3 Calculation results and analysis

Following completion of mesh generation, material property assignment, and boundary condition definition, the traction belt finite element model was analyzed. The resultant Von Mises stress distribution provides valuable insight into the stress distribution characteristics within the traction belt under operational conditions. Additionally, it enables assessment of whether the embedded steel cables approach their tensile strength limits. Figure 8 presents the post-analysis stress distribution in the steel wire ropes.

The Von Mises stress distribution diagram indicates that the 8 central wire ropes exhibit substantially lower stress levels than the both end ropes, and stress concentrates are observed at the ends of the wire ropes, with a maximum stress of 5.152 GPa, far exceeding the breaking strength of the wire ropes. This indicates that the need for model refinement to better represent actual physical behavior.

Due to the substantial elastic modulus mismatch between the belt's covering layer and the steel wire ropes, under operational loading conditions, the covering layer undergoes substantial deformation, whereas the steel wire ropes experience minimal deformation. So, the steel wire ropes fail to achieve uniform load distribution, leading to a sharp increase in stress at both ends of the wire ropes, and this stress concentration introduces significant errors in the simulation results.

In accordance with the national standard GB/T 39172-2020, specifying traction belts type testing requirements, a connecting block was incorporated at the steel belt model interface. Positioned directly above the traction belt model, the block ensures uniform deformation between steel cables and polyurethane coating under tensile loading. This modification improves model fidelity to actual traction belt mechanical behavior. The modified belt model is illustrated in Figure 9.

To identify the optimal elastic modulus for the connection model, simulations were performed under identical load conditions with the elastic modulus of the connection model set to 1, 10, 100, and 1000 times that of the steel wire rope. The simulations followed the previously outlined steps, and Figure 10 presents the resultant stress distributions in the steel wire rope.

From Figure 10, it can be observed that with increasing of the elastic modulus ratio, the internal stress distribution evolves from irregular to uniform patterns. The stress becomes increasingly concentrated in the middle section of the steel wire rope, and the maximum stress gradually decreases.

At 1:1 elastic modulus ratio, the steel wire rope reaches a peak stress of 2.323 GPa, concentrated at the top end. The midsection average stress of 1.41 GPa represents a 64.7% reduction from peak stress. This substantial discrepancy demonstrates the inadequacy of unity elastic modulus ratio (1:1). At a ratio of 10:1, the maximum stress in the steel wire rope is 1.614 GPa, at the top end and the midsections on both sides. The midsection experiences an average stress of 1.406 GPa stress, differing by 14.75% from the maximum stress. The higher stress levels on the sides compared to the middle section suggest that an elastic modulus of the connection model 10 times that of the steel wire rope is also unsuitable. At 100:1 elastic modulus ratio, 1.489 GPa peak stress localizes at the top termination. The average stress in the middle section is 1.405 GPa, which is 6.98% lower than the maximum stress. While showing improvement through reduced stress gradient (6.98% differential), the 100:1 ratio still requires optimization. At 1000:1 elastic modulus ratio, the maximum stress in the steel wire rope is 1.447 GPa, concentrated at the top termination. The average stress in the middle section of the steel wire rope is 1.405 GPa, less than 5% lower than the maximum stress. With <5% stress variation and uniform bilateral distribution, this configuration proves acceptable. The observed axial symmetry further validates the 1000:1 elastic modulus ratio.

From Figure 11, it can be observed that the stress on the covering layer is concentrated at the top, where it interfaces the steel wire rope. However, the covering layer stresses remain substantially lower than those in the steel wire rope. These findings confirm that the primary function of the covering layer is to protect the steel wire rope from damage and to ensure the cohesive integrity of all steel wires.

To analyze the stress variation within the midsection of each steel wire, the steel wires were numbered from left to right as 1–10, the stress level in the midsection of each steel wire, as indicated by the red line in Figure 12, were then recorded.

Figure 13 presents the ANSYS-simulated stress distributions in wire midsections for various connection model elastic modulus ratios. During the steel belt tensile test, with bidirectional loading, midsection stresses maintain near-uniform distribution. At elastic modulus ratios of 1:1, 10:1 and 100:1, stress concentrations develop at midsection termini compared to central regions. As the elastic modulus increases, the material becomes stiffer and less susceptible to deformation, this load redistribution minimizes transmission errors to the wire bundle. At elastic modulus ratios of 1000:1, wire stress distributions achieve greater uniformity, and the stress distribution in the midsection aligns closely with expectations, exhibiting a trend consistent with the actual tensile test. This alignment confirms the authenticity and reliability of the traction belt model.

With increasing of the elastic modulus ratio, the internal stress within the steel wire becomes negligible, indicating uniform stress distribution. This implies that the load applied to the connection model becomes negligible, thereby reducing the error in the tensile load to the steel wire. The simulated stress distribution closely matches experimental tensile behavior, validating the 1000:1 elastic modulus ratio selection for this study.

Fig. 8 The Von Mises equivalent stress state cloud diagram of the traction belt and the internal steel wire ropes.

Fig. 9 Geometry and physical model of traction steel belt.

Fig. 10 Von Mises stress distribution in steel wire ropes with varying connection modulus ratios.

Fig. 11 The equivalent stress state cloud chart of the covering layer.

Fig. 12 The stress diagram depicting the stress distribution within the midsection of the steel wire rope.

Fig. 13 Stress levels in the midsection of each steel wire under different elastic modulus connection models.

3.2 Finite element analysis of the refined simulation model of traction belt

3.2.1 The refined model of wire rope

Based on the belt model, the steel wire rope component was refined by replacement of the simplified single-wire approximation with an accurate representation of the 7-strand twisted wire rope matching field implementations. This refinement resulted in a higher-fidelity traction belt simulation model.

The steel wire rope consists of outer wires helically wound around a central core. The lay length of the outer steel wire is defined as the axial distance between corresponding points on adjacent wire turns along the rope's central axis. This parameter is measured parallel to the rope's central axis. The lay length T is calculated as follows:

$$T=\frac{2\pi R}{\tan \alpha }.$$(7)

In the equation, T is the lay length, R is the lay radius, and α signifies the lay angle of the outer steel wires in the wire rope.

During the measurement, it was obtained that the lay angle α = π/7, the lay radius R = 0.99mm, the wire rope twist distance is 14.78 mm, this distance represents the axial advance per helical revolution. Using this parameter, the wire rope model was developed as shown in Figure 14.

Fig. 14 Refined wire rope model.

3.2.2 Calculation results and analysis

With the previous parameters, the simulation results are shown in Figure 15.

From the Von Mises stress distribution diagram, it is evident that the steel wire rope exhibits a generally uniform stress distribution, stress concentrates at the top termination and midsection of the steel wire rope. The core midsection stress reaches 2.438 GPa, compared to 1.823 GPa in peripheral wires. A radial stress gradient exists from outer to inner wires, indicating radial contraction behavior. The symmetric stress distribution pattern closely matches experimental measurements under operational loading.

To analyze the stress distribution of individual steel wire ropes and between adjacent ropes, a single strand was isolated from the steel belt model, as shown in Figure 16. The steel wire rope core was labeled as 'A' and the side wires were labeled as 'B' The equivalent stress state cloud diagram of the entire steel wire rope is shown in Figure 17a, with detailed stress distributions for the core A and outer side wires B depicted in Figure 17b.

Figure 17a demonstrates uniform stress distribution under tensile loading, reflecting effective load sharing across the rope. This confirms the helical structure's efficacy in mitigating stress concentrations, thereby enhancing its strength and durability. Figure 17b shows that core strand stresses slightly exceed those in peripheral strands, and the core maintains uniform stress distribution, while peripheral strands show radial stress gradients from exterior to interior.

During the actual traction rope tensile test, the rope is subjected to axial tension from both sides, resulting in a uniform stress distribution. However, in the simulation, balance constraints must be applied to ensure the convergence of the calculated results. This leads to the simulation displaying maximum stress at both ends with uniform midsection stresses stress. This result correlates well with experimental observations. Therefore, midsection average stress serves as the representative rope stress in this paper.

From Figure 18, it shows uniform midsection stress distribution across all wire ropes, consistent with the simplified traction rope model. The calculated average wire rope stress is 1.916 GPa.

Fig. 15 The overall steel wire rope and the equivalent stress state cloud diagram at the top.

Fig. 16 Read the stress state diagram of individual steel wire ropes and between steel wire ropes.

Fig. 17 Partial steel wire rope equivalent stress state cloud diagram.

Fig. 18 The stress diagram for the middle section of each wire rope.

3.2.3 Validation of the accuracy of the refined simulation model for the traction belt

This method validates the refined traction belt model by comparing simulated strength limits with experimental tensile test results. Tensile testing used 300 mm minimum-length specimens secured in dedicated fixtures, with the temperature maintained between 25 °C, and specimen axes were aligned with clamp centerlines. After installation, the specimen is subjected to pre-tensioning as the required by national standard. The pre- and post-test conditions are shown in Figure 19, and the test results are summarized in Table 3.

The breaking force of the traction belt was determined by averaging the results of 3 tests, yielding an average breaking force of 54.92 kN for the belt sample. This value was applied to the refined traction belt model, producing the simulation results shown in Figure 20.

As the simulation applied the breaking load, the midsection average stress represents the tensile strength, the calculated strength limit was 2.447 GPa. To validate the accuracy of the model, this study used the CMT5305 computer-controlled electronic universal testing machine (as shown in Fig. 21) for conducting a tension test. Following the national standard (GB/T 39172-2020), 300-mm specimens were mounted in specialized fixtures. The pulling speed was set to 20 mm/min, and the machine recorded data from 0 kN until the steel wire rope fractured. 3 samples testes yielded an average breaking force of 5.63 kN (cross-section: 2.32 mm²), corresponding to 2.427 GPa tensile strength. The relative error between the simulation and experimental results was 0.84%, which, despite being a minor deviation, falls within an acceptable range for data comparison.

While the simulated strength limit closely matches the actual wire rope tensile strength, a minor discrepancy persists. There are 3 primary factors for this discrepancy. Firstly, the simulation model did not account for environmental influences such as temperature and humidity. Secondly, the traction belt underwent a pre-stretching process prior to the tensile test, which was not replicated in the simulation. Lastly, in the traction belt test, there was a misalignment between the axis of the belt and the centerline of the dynamic fixture, whereas the simulation assumed an ideal alignment. These factors collectively explain the 0.84% lower simulated breaking strength.

Fig. 19 Fracture test of traction belt.

Fig. 20 The equivalent stress state cloud chart of the steel wire rope under the breaking force.

Fig. 21 Steel wire rope tensile strength test.

3.3 Force analysis of traction belt model under typical fault condition

This study examines internal stress variations in traction belt under typical fault conditions, such as covering layer damage, severe wear, and wire rope breakage. Based on the simulation results, recommendations are proposed for optimized belt design and inspection protocols.

3.3.1 Scratches on the belt's covering layer

During traction elevator operation, the belt experiences frictional sliding against the traction wheel axle. Surface scratches on the covering layer represent a common belt failure mode, as shown in Figure 22a. To simulate this failure, damage was introduced to the coating in the belt model, and tensile loading was then applied to the damaged model as shown in Figure 22b.

From Figure 22b, it can be observed that when the covering layer has been scratched and subjected to tension, the internal steel wire rope exhibits uniform stress distribution. The maximum stress reaches 5.306 GPa, 2.6% higher than fault-free wire rope. Most wire rope stresses range between 0.9–2.3 GPa, showing distribution patterns and magnitudes comparable to unscratched conditions. These results demonstrate that surface scratches minimally affect belt performance, confirming the coating's effective protection of internal steel cables while substantially mitigating failure risks.

Fig. 22 The model of the scratch fault and the Von Mises equivalent stress state cloud diagram of the steel wire rope.

3.3.2 Severe abrasion of the steel belt covering layer

During elevator operation, repeated friction between the sheave and belt occurs. Severe friction causes substantial coating wear, exposing steel wires and creating safety risks. Thus, severe coating wear represents a typical operational fault, as shown in Figure 23a. To simulate this fault, coating parameters were adjusted in the belt model. Tensile loading was then applied, as shown in Figure 23b.

Figures 23c and 23d compare stress distributions with and without severe wear, respectively. From the figures, it can be observed that reducing the thickness of the covering layer on one side of the traction belt model results in a maximum stress of 5.097 GPa on the wire rope. This represents 0.735 GPa(14.3%) increase over fault-free conditions. The worn side shows significantly increased stress, with an average stress of 2.045 GPa. In contrast, the unworn side exhibits reduced stress, with an average stress of 0.945 GPa. The stress on the severely worn side is 1.099 GPa higher than unworn side, a difference of 116.4%. This stress imbalance will reduce the belt reliability and these results confirm that severe wear significantly effects the reliability of the traction belt. So that, covering layer thickness reduction will affect the safety of the traction belt in elevator applications.

Fig. 23 Severe wear fault model and Von Mises equivalent stress cloud diagrams on both sides of the wire rope.

3.3.3 Wire rope breakage

During traction belts manufacturing, elevator installation and maintenance, internal wire breakage may occur. These problems could lead to misalignment between the traction belt, traction wheel, and deflection pulley, resulting in belt mis-tracking. This misalignment results in repeated friction between the traction belt and the grooves of the traction wheel and deflection pulley, leading to cover layer failure, wire ropes exposure, and subsequent abrasion. To simulate this fault mode, a broken wire was modeled by removing one strand. When a traction belt wire broken, it becomes inactive, so in the simulation model, it is simplified by removing one right-end strand and applying tensile loading, as shown in Figure 24a, and the cross-section at the top of the wire rope is illustrated in Figure 24b.

As Figures 24c and 24d are shown, wire removal from the belt model causes the wire rope to experience peak stresses reaching 7.052 GPa. This constitutes a 1.88 GPa (36.3%) increase compared to intact cables. This stress concentration results from load redistribution to remaining wires, significantly elevating stresses in intact wires. Stresses reach 2.707 GPa near the break versus 2.032 GPa in unaffected regions, representing a 0.676 GPa (33.3%) increase. The break-adjacent region sustains significantly higher stresses, with dangerous stress concentrations developing at termination points. These results demonstrate wire breaks' significant reliability impacts.

Fig. 24 Model and Von Mises stress distribution of broken wire rope.

3.4 Comparison of internal stress within the steel wire rope

To accurately analyze the stress distribution and variations in each segment of the steel wire rope, each rope was numbered from left to right as 1–10, as shown in Figure 25a.

The Von Mises stress distribution in the 10th steel rope midsection is shown as Figure 25b. It is evident that the midsection stress increases radially inward, concentrating at the core, and the radial stress pattern indicates steel rope contraction behavior, matching experimental tensile test results. Using the probing command in Solidworks, the central stresses of the 7 strands were measured, and their average was taken as the central stress of the steel wire rope. The 10 cables' midsection average stress was calculated as 1.916 GPa.

Fig. 25 Von Mises of the steel wire rope midsection.

3.4.1 Abrasion of the steel belt covering layer

For the cover layer abrasion fault condition, midsection stress distributions versus fault-free condition are presented in Figure 26.

From Figure 26, it shows that in the case of the scratching fault type of the covering layer, the steel wire rope midsection average stress is 1.911 GPa, only 5 MPa stress difference exists between faulted and pristine conditions. The maximum stress difference occurs in the 7th wire, with a deviation of 17 MPa, while maintaining overall stress distribution patterns. This indicates that the scratching has a negligible impact on the traction belt.

Fig. 26 Comparison of steel wire rope midsection stress under cover layer abrasion.

3.4.2 Severe wear of steel belt covering layer

When the fault type is severe wear of the covering layer, the stress change is shown in Figure 27a.

Figure 27b shows the stress in the midsection of the wire rope under covering layer severe wear, the average midsection stress reaches 1.961 GPa, an increase of 66.7 MPa, and 3.5% increase compared to the fault-free condition. The maximum stress difference occurs at the 4th strand, with a deviation of 82 MPa, indicating significantly higher stress on the severely worn side. This stress imbalance compromises belt reliability, confirming severe wear's significant reliability impact, and raising safety concerns for the elevator applications.

Fig. 27 Stress comparison and Von Mises of midsection of the steel wire rope under severe wear.

3.4.3 Wire rope breakage

When the wire rope breakage, the stress variation is shown in Figure 28a.

Figure 28b shows the stress distribution of the wire rope core. Following a wire breakage, adjacent wires experience significant stress increases. The stress decreases radially from the break point, and the wire rope core stress reaches 2.787 GPa, a 0.336 GPa (17.5%) increase over intact conditions. Prolonged operation with wire breaks causes dangerous load imbalances, potentially resulting in safety hazards.

Fig. 28 Stress comparison and Von Mises of midsection of the steel wire rope with rope breakage.

3.5 Analysis of failure types and recommendations

• For abrasion faults, a simplified abrasion model was applied to the covering layer simulation. The simulation results showed negligible structural impact from abrasion, maintaining uniform wire rope stress distribution comparable to undamaged conditions. As severe piercing or core exposure were not simulated, visual inspection for scratches, piercing or core exposure is required. If any of these issues are identified, the traction belt must be replaced immediately to ensure elevator safety.

• For severe coating abrasion, the covering layer parameters were modified in the belt model. Simulation results showed significantly elevated stress on the abraded side reduced stress on the opposite side. The average stress on the steel wire rope increased by 66.7 MPa, representing a 3.5% difference compared to the undamaged condition. This stress imbalance compromises reliability, and accelerating belt replacement, increasing operational costs. To improve reliability and service life, machine room or guide wheel layout optimization or operational wear mitigation measures are recommended. Regular inspection of sheave-guard clearance is also recommended to prevent belt impact.

• For wire breakage faults, the model simulated breakage by removing one right-end strand. Simulation results showed that when single-strand breakage, the adjacent strand stresses increases drastically, creating dangerous stress imbalances and being a serious safety hazard. To solve the problem, the inspection department should prioritize wire breakage inspections. In the regular checks, specialized resistance testing should be routinely performed for internal break detection, and inspection personnel should be proficient in using real-time detection devices, to facilitate immediate replacement and accident prevention.

4 Conclusion

This study analysis stresses in the traction belt's wire rope under tensile loading, the main conclusions are as follows:

• A traction steel belt model was developed with defined simulation parameters. Using a 43 kN specification belt as the research subject and adhering to national standard requirements, using a computer-controlled electronic universal testing machine for wire rope tensile tests, and the material properties for simulation were experimentally determined, and an ANSYS-based finite element model was developed.

• A refined traction belt model was developed and validated. Stress distribution in both the wire rope and covering layer were comprehensively analyzed. Simulations showed a 2.447 GPa average stress in the wire rope under extreme loading, and a 0.84% discrepancy between experimental and simulated results validated the model's accuracy.

• Based on the model, the stress distribution and magnitude variations of the wire rope under different fault conditions were investigated. Compared to fault-free conditions, abrasion caused negligible belt stress changes, however, severe abrasion created 66.7 MPa stress imbalances, compromising belt reliability, and wire breakage posed greater risks, increasing stresses by 0.336 GPa under normal loading. Some recommendations were provided to enhance reliability and service life, and also support special equipment management, warning systems, and fault simulation.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by Zhejiang Province Market Regulatory Administration scientific research project (ZC2025025) and China Association of Special Equipment Inspection Soft Science Research Project (CASEI-RKT2024-15). We also acknowledge the financial support of Zhejiang Provincial Administration for Market Regulation “Eagle Plan” Cultivation Project (CY2023212).

Conflicts of interest

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Author contribution statement

Conceptualization, C.L., Y.H.; Methodology, Z.Z., Q.W.; Software, C.Z., F.X.; Validation, Y.H.; Q.W.; Formal Analysis & Simulation, C.L.; Investigation, C.L., C.Z.; Resources, C.L.; Y.H.; Writing, Review & Editing, C.Z.; F.X.; Supervision & Funding Acquisition.

References

All Tables

All Figures

	Fig. 1 The structure and diagram of the traction belt elevator.
In the text

	Fig. 2 The simplified diagram of steel wire rope under stress.
In the text

	Fig. 3 The picture and size of the steel belt.
In the text

	Fig. 4 Mesh division of the steel wire rope and traction belt.
In the text

	Fig. 5 Tensile strength and stress-strain diagram of sample 1.
In the text

	Fig. 6 Tensile strength and stress-strain diagram of sample 2.
In the text

	Fig. 7 Tensile strength and stress-strain diagram of sample 3.
In the text

	Fig. 8 The Von Mises equivalent stress state cloud diagram of the traction belt and the internal steel wire ropes.
In the text

	Fig. 9 Geometry and physical model of traction steel belt.
In the text

	Fig. 10 Von Mises stress distribution in steel wire ropes with varying connection modulus ratios.
In the text

	Fig. 11 The equivalent stress state cloud chart of the covering layer.
In the text

	Fig. 12 The stress diagram depicting the stress distribution within the midsection of the steel wire rope.
In the text

	Fig. 13 Stress levels in the midsection of each steel wire under different elastic modulus connection models.
In the text

	Fig. 14 Refined wire rope model.
In the text

	Fig. 15 The overall steel wire rope and the equivalent stress state cloud diagram at the top.
In the text

	Fig. 16 Read the stress state diagram of individual steel wire ropes and between steel wire ropes.
In the text

	Fig. 17 Partial steel wire rope equivalent stress state cloud diagram.
In the text

	Fig. 18 The stress diagram for the middle section of each wire rope.
In the text

	Fig. 19 Fracture test of traction belt.
In the text

	Fig. 20 The equivalent stress state cloud chart of the steel wire rope under the breaking force.
In the text

	Fig. 21 Steel wire rope tensile strength test.
In the text

	Fig. 22 The model of the scratch fault and the Von Mises equivalent stress state cloud diagram of the steel wire rope.
In the text

	Fig. 23 Severe wear fault model and Von Mises equivalent stress cloud diagrams on both sides of the wire rope.
In the text

	Fig. 24 Model and Von Mises stress distribution of broken wire rope.
In the text

	Fig. 25 Von Mises of the steel wire rope midsection.
In the text

	Fig. 26 Comparison of steel wire rope midsection stress under cover layer abrasion.
In the text

	Fig. 27 Stress comparison and Von Mises of midsection of the steel wire rope under severe wear.
In the text

	Fig. 28 Stress comparison and Von Mises of midsection of the steel wire rope with rope breakage.
In the text