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Numerical investigation of rope-core elasticity effects on rope–sheave traction

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Abstract

Fiber core wire ropes are widely used in rope–sheave traction equipment such as elevators, mine hoists, and cranes due to their excellent mechanical properties and low cost. However, the mechanical behavior of the rope core and its influence on the traction performance have not been thoroughly investigated. Therefore, this study aims to examine how the elasticity of the rope core affects the traction performance of wire ropes. A finite element model of a wire rope wrapped on a sheave was developed and validated by high-speed camera experiments. The results indicated that the core elasticity increased the stress in the outer wires, resulting in a reduction in the rope strength. According to the boundary conditions of our finite element model, a specific solution to a system of ordinary differential equations describing the tangential contact force at the traction interface is given. This particular solution reveals the tendency of the core elasticity to enhance the rope–sheave slip by increasing the tangential contact force. By monitoring the rope tension, the study discovered a correlation between rope–sheave traction and rope’s interwire friction, which has not been reported before. These findings enhance our understanding of the influence of rope core elasticity on traction and highlight the importance of considering the core elasticity in wire rope design.

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Abbreviations

\({T}_{1}\) :

Tension at the tight end of the rope

\({T}_{2}\) :

Tension at the loose end of the rope

\(f\) :

The equivalent coefficient of friction (COF) between rope and sheave

\(\theta\) :

The wrap angle between the rod and cylinder

\({E}_{1}\) :

Elastic modulus of the outer wires inside the rope

\({E}_{2}\) :

Elastic modulus of the core wire inside the rope

\({E}_{2}\) :

Elastic modulus of the traction sheave

\({E}^{*}\) :

Equivalent elastic modulus of the rope

\(\nu\) :

Poisson's ratio

\(\rho\) :

The density of the materials (g/cm3)

\({\mu }_{{\text{sw}}}\) :

COF between rope and sheave

\({\mu }_{{\text{wc}}}\) :

COF between the core wire and the outer wires inside the rope

\({\mu }_{{\text{ww}}}\) :

COF between the adjacent outer wires inside the rope

\({U}_{i}\) :

Translational displacement along \(x,y\) or \(z\)-axis

\({{{UR}}}_{i}\) :

Angular displacement along \(x,y\) or \(z\)-axis

\({{{VR}}}_{i}\) :

Angular velocity along \(x,y\) or \(z\)-axis

\({F}_{i}\) :

Force along \(x,y\) or \(z\)-axis

\({M}_{i}\) :

Torque along \(x,y\) or \(z\)-axis

\(Q\) :

Critic tension ratio

\(\alpha\) :

Winding angle

\(\tau (\alpha )\) :

Tangential contact stress between rope and sheave

\({k}_{{\text{s}}}\) :

Stiffness of a bristle

\(s(\alpha )\) :

Bristle deformation

\({T}^{\mathrm{^{\prime}}\mathrm{^{\prime}}}(\alpha )\) :

The second derivative of the rope tension with respect to the winding angle

\(R\) :

Radius of the traction sheave

\({v}_{1}\) :

Velocity of the rope

\(\omega\) :

Angular velocity of the sheave

\({E}^{*}\) :

Equivalent elastic modulus of the rope

\(A\) :

Equivalent cross-sectional area of the rope

\(N(\alpha )\) :

Normal contact force between rope and sheave

\({f}_{{\text{wc}}}\) :

Friction force between the rope core and the outer wires

\({L}_{{\text{w}}}\) :

Length of the outer wires at the loose end

\({L}_{{\text{c}}}\) :

Length of the rope core at the loose end

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Acknowledgements

The authors gratefully acknowledged the support of National Natural Science Foundation of China under Grant No. 519350

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Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Yunting Han, Gang Zhang, Songtao Hu & Xi Shi

  2. Shanghai Institute of Aerospace System Engineering, Shanghai, 201108, People’s Republic of China

    Xiaolong Ma

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Correspondence to Songtao Hu or Xi Shi.

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Han, Y., Ma, X., Zhang, G. et al. Numerical investigation of rope-core elasticity effects on rope–sheave traction. J Braz. Soc. Mech. Sci. Eng. 46, 90 (2024). https://doi.org/10.1007/s40430-023-04673-1

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