Dynamic simulation of a multi-cable driven parallel suspension platform with slack cables

Mathematical Problems in Engineering

Xiao

Liu

2019

A coal mine hoisting system includes two parts, one is a constant-length cable system, and the other is a variable-length cable system. In this paper, the nonlinear dynamic modeling of a coal mine hoisting system is established through Hamilton’s principle. The nonlinear partial differential equations of the coal mine hoisting system are discretized into ordinary differential equations by the fourth-order Galerkin truncation. The nonlinear dynamic responses and four key kinematic and structural parameter analysis of the coal mine hoisting system in the acceleration phases, constant velocity phases, and deceleration phases are given. The results show that the axial vibration displacements of the constant-length cable are an order of magnitude smaller than that of the variable-length cable. The load has the greatest effect on the axial vibration displacement of the hoisting cable. Adversely, the speed has the least effect on the axial vibration displacement of the hoisting cable.

Section: Introductionmentioning

confidence: 95%

Dynamic Modeling and Analysis of a Mine Hoisting System with Constant Length and Variable Length

Mathematical Problems in Engineering

Xiao

Liu

2019

“…e coupled longitudinal and torsional vibration equations of the multicable hoisting system in mine construction are derived through the constrained Lagrange equation. e results of numerical calculations are verified by Adams software [21].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Behavior of Winding Hoisting Rope under Head Sheave Axial Wobbles

Xiao

et al. 2019

Shock and Vibration

Axial wobbles of the head sheave due to manufacturing accuracy and installation technology can exert periodic lateral excitations to the winding hoisting rope. A hoisting rope consists of a constant catenary rope from the drum to the head sheave and a variable vertical rope from the head sheave to the conveyance. e longitudinal and lateral vibration responses of the hoisting rope are coupled to each other. In this paper, the coupled lateral-longitudinal governing equations of the winding hoisting system under the axial wobble excitations of the head sheave are established by the Hamilton principle. e governing equations are nonlinear infinite-dimensional partial differential equations, which are discretized into the finite-dimensional ordinary differential equations through the Galerkin method. e dynamic responses of the hoisting rope under the head sheave axial wobbles are given by MATLAB simulation when the winding hoist is lifting or lowering. e results show that lateral vibration displacements of the vertical rope under the head sheave axial wobbles are larger than those of the catenary rope. e axial wobble amplitude range of the head sheave is given to limit the lateral vibration displacements of the hoisting rope.

“…In this case, the tension differences between the cables may cause the platform apply pressure on the shaft wall. An even worse situation is that when the length differences are large enough, one or more cables might become slack, and when the slack cables become tensioned again, a shock will be applied on the platform [1]. Due to its flexibility, the suspension cable will undergo longitudinal vibrations, and the dynamic responses of the platform, which is suspended by several parallel cables, will be more complicated.…”

Section: Introductionmentioning

confidence: 99%

“…Y. Wang [24] investigated the dynamic responses of the multi-cable driven platform by using multibody dynamics modelling method with considering the longitudinal-torsional-coupled characters of the cable, but the cable slackness property is not considered. Y. Wang [1] solved the non-smooth cable problem with considering the unilateral property of the cable in longitudinal direction (which means the cable may become tensionless when been pushed in longitudinal direction) and the bilateral property in transversal and torsional directions (which means the cable may provide negative force). However, since the platform in Ref.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic modelling of a multi-cable driven parallel platform with guiding devices

Mathematical and Computer Modelling of Dynamical Systems

Kou

Cao

2020

Self Cite

In this paper, a mathematical model is presented to numerically simulate the dynamical responses in a multi-cable suspension platform taking into account the slack cables and guiding devices. The state change of the cable (slack versus tensioned) is considered and is described mathematically by a complementary condition equation, and the interactions between the guiding wheels and the shaft wall are described by the Heaviside step function. The Lagrange's equation with constraints is used to derive the dynamic equations of the system, and a non-smooth generalized-α algorithm for nonsmooth phenomena of multibody dynamics is applied to numerically solve the equations. The simulation results have shown the dynamic responses of the platform and the cable tension characters when different cables are excited by different longitudinal excitations. Moreover, the results have illustrated how the cable tension differences may affect the pressure on the shaft wall applied by the guiding devices.