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Gas–solid coupling lateral vibration characteristics of high-speed elevator based on blockage ratio

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Abstract

To describe the dynamic behaviors of high-speed elevators in service environments, the motion of a high-speed elevator hoisting system and airflow and their coupling mechanism at the contact surface were analyzed using computational fluid dynamics and system dynamics theory. Based on time discretization, a gas–solid coupling method for high-speed elevators was proposed. Selecting a high-speed elevator with a speed of 7 m/s as the research object, the relationships between blockage ratio, deflection angle, and aerodynamic load were explored. The coupling between the car, guide rail, and airflow was analyzed, and a dynamic model of the airflow-car-guide rail coupling system for high-speed elevators with different blocking ratios was constructed. The effectiveness of the model was verified by experiments, and gas–solid coupling lateral vibration responses of the high-speed elevator under different blockage ratios were compared. The results showed that the aerodynamic load was approximately linearly positively correlated with the vibration state of the car at a fixed blockage ratio, while the blockage ratio was positively nonlinearly correlated with the aerodynamic load. The typical numerical characteristics of the elevator car’s lateral vibration acceleration in the coupled state were larger than those in the uncoupled state. When the blockage ratio was greater than 0.57, the typical numerical characteristics showed a nonlinear increasing trend with increasing blockage ratio. This study provided an effective method to analyze gas–solid coupled lateral vibrations of high-speed elevators and has theoretical guiding significance for the design and manufacture of high-speed elevators and the development of vibration-absorbing devices.

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Abbreviations

k :

Turbulent kinetic energy, J

ε :

Turbulent dissipation rate

μ :

Air dynamic viscosity, Pa s

μ t :

Turbulent viscosity coefficient

ρ :

Fluid density, kg/m3

C μ :

Empirical constant: Cμ = 0.09

C 1 :

Empirical value: C1 = 1.44

C 2 :

Empirical value: C2 = 1.92

σ k :

Empirical value: σk = 1.0

σ ε :

Empirical value: σε = 1.3

\(t\) :

Time, s

U :

Fluid velocity vector and U = [ux, uy, uz]T

u x, u y, u z :

Velocity components of U in the direction of x, y, and z axes, m/s

φ :

Generic variable and φ = [1, ux, uy, uz, k, ε]T

Γφ :

Generalized diffusion coefficient

CV:

Control volume, m3

\(A\) :

Surface area of the control volume, m2

\({\varvec{n}}\) :

External normal vector

S φ :

Generalized source item

Δt :

Time step, s

M, C, K :

Mass, damping and stiffness matrices of elevator lifting system

X, \(\dot{\varvec{X}}\), \(\varvec{\ddot{X}}\) :

Generalized displacement, velocity, and acceleration vectors of elevator lifting system

F r :

Generalized external excitation vector of elevator lifting system (excluding the aerodynamic load)

F x, F y, F z :

Aerodynamic forces along the x, y, and z axes, N

M x, M y, M z :

Aerodynamic moments around the x, y, and z axes, N m

p :

Airflow pressure, Pa

τ :

Viscous stress, Pa

S car :

Surface area of the car, m2

R a :

Position of the application of the load

R o :

Position of the car centroid

F a :

Generalized aerodynamic load vector acting on the car centroid

w cw :

Car width, m

w cd :

Car depth, m

h c :

Car height, m

w w :

Shaft width, m

w d :

Shaft depth, m

H :

Shaft height, m

w 1 :

Distance between car door and shaft, m

h 1 :

Distance between car upper surface and shaft upper surface, m

r a :

Blockage ratio

C f, C m :

Influence coefficient

m c :

Car mass, kg

J c :

Moment of inertia of the car, kg m2

x c :

Lateral displacement of the car, m

θ :

Deflection angle of the car, rad

m f :

Car frame mass, kg

J f :

Moment of inertia of the car frame, kg m2

x f :

Lateral displacement of the frame, m

θ f :

Deflection angle of the frame, rad

k p :

Equivalent stiffness between the car and car frame, N/m

k 1 :

Equivalent stiffness between the car frame and guide roller, N/m

c 1 :

Equivalent damping between the car frame and guide roller, N s/m

k 2 :

Equivalent stiffness between the guide roller and guide rail, N/m

c 2 :

Equivalent damping between the guide roller and guide rail, N s/m

m w :

Guide roller mass, kg

x wi(t):

Lateral displacement of the guide roller at time t (i = 1, 2, 3, 4), m

m r :

Mass per unit length of the guide rail, kg

EI :

Bending stiffness of the guide rail, N/m

c r :

Damping of the guide rail, N s/m

l :

Span of the guide rail, m

h :

Vertical distance between the upper and lower guide rollers, m

x rj(y,t):

Vibration displacement of the j-th guide rail at time t (j = 1, 2), m

r k(y):

Lateral displacement of the k-th guide rail at the contact point with the guide roller (k = 1, 2), m

y(t):

Position of the guide roller on the rail at time t, m

F 0 :

Preload between the guide roller and guide rail, N

F i :

Contact forces between the guide roller and guide rail (i = 1, 2, 3, 4), N

q 1, q 2 :

Generalized displacement of xr1 and xr2

PSD:

Power spectral density, m2/s3

RMS:

Root mean square

A95:

Value that greater than or equal to 95% of the sampled data

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Acknowledgements

The authors gratefully acknowledge the support of Shandong Provincial Natural Science Foundation, China (Nos. ZR2017MEE049, ZR2021ME245) and Shandong Provincial Key Research and Development Program (No. 2018GSF122004).

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Authors and Affiliations

  1. School of Mechanical and Electronic Engineering, Shandong Jianzhu University, Jinan, 250101, China

    Ruijun Zhang, Jie Liu, Mingxing Liu, Qing Zhang & Qin He

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  1. Ruijun Zhang
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Correspondence to Ruijun Zhang.

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Zhang, R., Liu, J., Liu, M. et al. Gas–solid coupling lateral vibration characteristics of high-speed elevator based on blockage ratio. J Braz. Soc. Mech. Sci. Eng. 44, 184 (2022). https://doi.org/10.1007/s40430-022-03500-3

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