A new rope-sheave traction contact force model incorporating complex geometric features developed through parameter identification methods

doi:10.1007/s10483-025-3300-7

Abstract

Abstract:

The complex geometrical features of mechanical components significantly influence contact interactions and system dynamics. However, directly modeling contact forces on surfaces with intricate geometries presents considerable challenges. This study focuses on the helically twisted wire rope-sheave contact and proposes a contact force model that incorporates complex geometric features through a parameter identification approach. The model’s impact on contact forces and system dynamics is thoroughly investigated. Leveraging a point contact model and an elliptic integral approximation, a loss function is formulated using the finite element (FE) contact model results as the reference data. Geometric parameters are subsequently determined by optimizing this loss function via a genetic algorithm (GA). The findings reveal that the contact stiffness increases with the wire rope pitch length, the radius of principal curvature, and the elliptic eccentricity of the contact zone. The proposed contact force model is integrated into a rigid-flexible coupled dynamics model, developed by the absolute node coordinate formulation, to examine the effects of contact geometry on system dynamics. The results demonstrate that the variations in wire rope geometry alter the contact stiffness, which in turn affects dynamic rope tension through frictional energy dissipation. The enhanced model’s predictions exhibit superior alignment with the experimental data, thereby validating the methodology. This approach provides new insights for deducing the contact geometry from kinetic parameters and monitoring the performance degradation of mechanical components.

Key words: complex contact geometry, contact force modeling, parameter identification, helical wire rope, rigid-flexible couple dynamics modeling

2010 MSC Number:

O302

Yunting HAN, Hui HU, Haoran SUN, Xi SHI. A new rope-sheave traction contact force model incorporating complex geometric features developed through parameter identification methods. Applied Mathematics and Mechanics (English Edition), 2025, 46(10): 1983-2006.

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Figures/Tables 17

Fig. 1

Table 1

Table 2

Boundary conditions of the FE model"

Parameter	Rope’s left end	Rope’s right end	Sheave (pre-tightening stage)	Sheave (rotation stage)
$U x$	0	0	0	0
$U y$	0	–	0	0
$U z$	0	–	0	0
$U R x$	0	0	0	–
$U R y$	0	0	0	0
$U R z$	0	0
$V R z$	0	0
$F y$	–	$− 615$ N	0	0

Table 2

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Table 3

Contact force modeling parameters corresponding to the wire rope with different pitches"

Pitch/mm	$R x (1)$ /mm	$R y (1)$ /mm	$R x (2)$ /mm	$R y (2)$ /mm	$θ$ /rad
60.00	6.475 0	10.582 8	-5.478 1	196.824 1	0.314 69
61.75	6.540 7	10.654 6	-5.485 1	196.824 1	0.316 70
63.50	6.603 5	10.824 3	-5.495 6	196.824 1	0.317 20

Table 3

Fig. 9

Table 4

Comparison of parameter identification results of elliptic eccentricity of wire rope with different pitch lengths in contact with traction sheave with FE models"

Pitch/mm	$e$ (FE model)	$e$ (solved)	Relative error/%
60.00	0.719 0	0.714 5	0.626
61.75	0.816 6	0.815 6	0.122
63.50	0.857 3	0.862 7	0.630

Table 4

Fig. 10

Fig. 11

Fig. 12

Fig. A1

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Parameter	Outer wire	Rope core^[35–39]	Sheave
Elastic modulus/GPa	85	10	210
Poisson’s ratio	0.3	0.39	0.3
Density/(g · cm^-3)	7.85	1.00	7.85