Abstract
To study the horizontal vibration characteristics of high-speed elevators, a 6-DOF horizontal dynamic model of the nonlinear coupling system of guide rails, guide shoes, and elevator cabin was established. Four kinds of guide rail excitation models, namely, sinusoidal, triangular, stepped, and pulsed excitation, were established through an error and contact analysis of guide rails and rollers. The factors that influenced the horizontal vibration response, such as excitation models, stiffness of guide shoes, and cabin parameters, were analyzed by solving the vibration acceleration of the coupling system. Vibration acceleration was measured through experiments to verify the theoretical results. The vibration acceleration of the no-load elevator under stepped excitation was the largest. Reducing the stiffness of the guide shoes and straightness error of guide rails, reasonably arranging the spacing between the guide shoes at the top and bottom of the cabin, and increasing the cabin weight were beneficial to reducing the horizontal vibration response of the elevator cabin.
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Abbreviations
- m 0 and J :
-
Mass and moment of inertia of the cabin system, respectively
- m a :
-
Mass of the cabin and frame with half of the rated capacity (1000 kg)
- m b :
-
Mass of guide shoe seats
- x and θ :
-
Horizontal displacement and rotation angle of the cabin system, respectively
- m 1 :
-
Mass of the guide shoe roller
- k 1 :
-
Equivalent stiffness of the guide shoe rollers
- k 2 :
-
Spring stiffness of the guide shoes
- c 1 :
-
Equivalent damping coefficients of the guide shoe rollers
- c 2 :
-
Equivalent damping coefficients of the guide shoe base
- x 1, x 2, x 3, and x 4 :
-
Horizontal displacements of four guide shoes, respectively
- u 1, u 2, u 3, and u 4 :
-
Irregular excitation displacements of guide rails at each guide shoe
- l 1 and l 2 :
-
Distances between the centroid and guide shoes at the top and bottom of the cabin system in the z direction, respectively
- P, M, R, K, and Q (t) :
-
Variable, mass, damping, stiffness, and guide rail excitation matrices, respectively
- X, U, Y, A, B, C, and D :
-
State variable, input variable, output variable, system, input, output, and direct transformation matrices, respectively
- H and Δl :
-
Excitation amplitude and separation distance of the adjacent bracket, respectively
- v 0 :
-
Running velocity of the elevator
- ω :
-
Angular frequency
- r 0, r 1, and δ r :
-
Outer radius, inner radius, and thickness of guide rollers, respectively
- F r :
-
Normal contact force between the guide roller and rail
- p :
-
Hertz contact pressure
- m :
-
Half-width of the contact area
- σ H :
-
Stress distribution of the contact area
- σ max :
-
Most significant stress at the center
- E 1, E 2, v 1, and v 2 :
-
Elastic modulus and Poisson’s ratios of guide rollers and rails
- Δx :
-
Radial deformation of rubber guide rollers
- B :
-
Angle of the cylindrical coordinate system
- ω x and ω y :
-
Maximum bending deformation of guide rails in the x and y directions, respectively
- I x and I y :
-
Inertia moments relative to x-axis and y-axis of T-type guide rails, respectively
- A, b, c, and h :
-
Dimensions of the T-type guide rails shown in Fig. 7
- t 0 :
-
Delayed time between the guide shoes at the top and bottom of the cabin on the same side
- L :
-
Spacing between the guide shoes at the top and bottom of the cabin
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Acknowledgments
This work was supported by the Natural Science Foundation of China (Program No. 51805429) and Young Talent Fund of University Association for Science and Technology in Shaanxi, China (20190416). The authors would like to acknowledge the editors and anonymous reviewers whose insightful comments have helped improve the quality of this paper considerably.
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Danlong Song received his B.S. and Ph.D. degrees in aeronautics and astronautics manufacturing engineering from Northwestern Polytechnical University, China, in 2011 and 2016, respectively. He is currently an Associate Professor in the School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, China. His research interests include dynamics and structure optimization of mechanical systems and mechanical behavior of composite materials.
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Song, D., Zhang, P., Wang, Y. et al. Horizontal dynamic modeling and vibration characteristic analysis for nonlinear coupling systems of high-speed elevators and guide rails. J Mech Sci Technol 37, 643–653 (2023). https://doi.org/10.1007/s12206-023-0109-2
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DOI: https://doi.org/10.1007/s12206-023-0109-2