Estimation of the rope tension in trucklift slope hoisting system with varying profile of track

This paper focused on a study concerned with the estimation of the rope tension in Trucklift slope hoisting system with varying profile of track. In this system, the profile of track is not straight and there exists the segment where the sagged rope moves between the edges on the inclined track, and the rope tension always varies by the movement of platforms with empty and laden trucks. So co-simulation of ADAMS and MATLAB/Simulink was used to estimate the rope tension when the platforms move on the track, because there is a moving rope with sagged inclined segment in this system. From simulation results were analyzed the variation of the rope tension according to the position of platform and the influence of the angle of slope of track and the mass of platform when platforms move on the track. In the case of using Koepe winder, the simulation results could be used as more important reference data for the design and operation of Trucklift slope hoisting system with varying profile of track.


Introduction
The Trucklift slope hoisting systems which have various advantages were developed to accelerate and cheapen transport in open pit mines recently.The Trucklift slope hoisting systems have various types according to condition and environment of open pit mines [1].The track of the Trucklift slope hoisting system may be linear or nonlinear along the surface of open-pit mine.In the case of the nonlinear track, the angles of slope of profile along track vary, and this system is called Trucklift slope hoisting system with varying profile of track.In this system, the profile of track is not straight and there exists the segment where the sagged rope moves between the eages on the inclined track, and the rope tension always varies by the movement of platforms with empty and laden trucks.It is important to estimate the rope tension for design and operation of this system.Especially, it should be considered when Koepe winder is installed in this system.Many studies on sagged ropes have focused on the vibration of inclined rope with two immovable pinned-supports.Linear models for in-plane free vibrations of inclined taut ropes have been proposed by Wu et al. [2] and Zhou et al. [3].A numerical model has been developed by Sorokin et al. [4] for linear vibrations of arbitrarily sagged extensible inclined ropes in a quiescent viscous fluid.An experimental study on the inclined rope has been proposed by Rega et al. [5].Free undamped vibrations of ropes of arbitrary sag and inclination have been investigated according to the catenary theory by Mansour et al. [6].The three-node curved isoparametric finite element model has been investigated by Ni et al. [7].Ricciardi et al. [8] have investigated a continuous model for dynamics of large-diameter sagged horizontal cables.Reduced-order model capable of analyzing the vortexinduced vibration of catenary riser in the ocean current has been developed by Srinil et al. [9].A geometrically exact mechanical formulation has been proposed by Arena et al. [10] for threedimensional motions of flexible ropes.A modelling method and an accurate numerical procedure have been investigated to simulate the dynamical responses of a multi-cable driven parallel suspension platform system by Wang et al. [11].Han et al. [12] simulated the motion process of the platform by the motion of truck on the platform and the effect of rope hitched to the platform in Trucklift slope hoisting system during truck changing, using ADAMS and MATLAB/Simulink.By this simulation method, the effect of various factors on the movement of platform and the tension of rope could be considered quantitatively.Kim et al. [13] presented an alternative way to get the numerical solution of the motion of sagged inclined rope by using flexible part in ADAMS and its application to simulate the platform motion during truck changing in Trucklift slope hoisting system.Using ADAMS, they simulated the platform motion at the lower loading station in the Trucklift slope hoisting system with varying profile of track.However, seldom have we read the similar research data to estimate the rope tension in the Trucklift slope hoisting system with varying profile of track when the platforms move on the track.In this paper presents a method to estimate the rope tension in the Trucklift slope hoisting system with varying profile of track when the platforms move on the track, using ADAMS and MATLAB/Simulink.Then the variation of rope tension and the influence of various factors on it are analyzed and proposed the important data for design of system.

Estimation of the rope tension
The track of Trucklift slope hoisting system with varying profile of track consist of several segments with different slopes along the surface of open-pit mine as shown in figure 1.To calculate the rope tension in Trucklift slope hoisting system with varying profile of track, we can use following assumptions i) Eccentricity of sheave is neglected.ii) There is no force acting to side of platform, platforms only move along the profile.
iii) There is an inclined sagged segment in the rope when the platform moves on the lowest inclined segment of profile.When platform moves on the lowest inclined segment of profile, the rope is sagged between points B 1 and B 2 .
iv) The sag of rope between neighbored guide rollers is neglected because there are enough guide rollers on the profile.
v) The mass center of platform with truck is constant when the platform moves on the track.Because there is the inclined sagged rope in Trucklift slope hoisting system with varying profile and we have to solve some nonlinear partial differential equations to estimate the rope tension, we would to solve this work by using MSC.ADAMS and MATLAB software.MSC.ADAMS simulation is an alternative way to investigate the motion of platform and the rope tension in Trucklift slope hoisting system with varying profile.Using MSC.ADAMS, we can build models of Trucklift slope hoisting system with varying profile and simulate it.ADAMS/View as the general purpose rigid body dynamics package, can work with the ADAMS/Controls module to interface with MATLAB.By the co-simulation with MSC.ADAMS and MATLAB, we can also find the optimal design among multiple design variations quickly.

Building a mechanical model of Trucklift slope hoisting system with varying profile of track
The 3D geometry of Trucklift slope hoisting system with varying profile of track to investigate the rope tension, consists of two tracks and a platform with a laden truck, a platform with an empty truck, as shown in fig 3 .The mass of truck is 15t and the track is modeled with β 2 =19º , β 1 =6~12º , Δβ=0~3º (Δβ = β 3 -β 1 ) in Figure 2. In this system, mass of platform could be 6~33t.That could be built by using the SolidWorks software and the profile should be added during assembling those components.This 3D geometry could be exported into MSC.ADAMS model file (*.amd) by using Motion modul in SolidWorks.Then the constraint between platform and path could be added by using Path Mate function so that platform moves along the path.Because the mass center of every component in the geometry should to be located on same plane, two paths are located as shown in Figure 3.After importing the 3D geometry (*.amd) in MSC.ADAMS software, we can build a mechanical model of this Trucklift slope hoisting system by eliminating unnecessary constraints and adding some elements(Cable, Pulley, Motor, FE Part, etc.).The Adams Machinery Cable module provides for the modeling of cable systems within the Adams View environment.Two cable systems could be added to the mechanical model of this Trucklift slope hoisting system by using Cable module in MSC.ADAMS software.Each cable system consists of a rope and two pulleys.And the diameters of the pulleys of sheave and winder are 4m, 5m, respectively.The center of lower pulley with diameter of 5m was located at origin and the vertical distance between two cable systems could be 50m.In this model, the winder could be modeled by using two motors as shown Figure 3, and they have same value of velocity but move oppositely each other.The motors are controlled by a function and its distance and velocity, motor force are specified as measured variables in MSC.ADAMS software.In co-simulation with MSC.ADAMS and MATLAB/Simulink, the acceleration of motor should be specified as Input variable, distance and velocity of motor, motor force as Output variable in MSC.ADAMS software.

Co-simulation with MSC.ADAMS and MATLAB/Simulink
Adams/Controls is a part of the Adams suite, and it is a plugin to MSC Software.Using Adams/Controls, we can add sophisticated controls to our Adams model and connect our Adams model to block diagrams that we have developed with control applications such as MATLAB.Input variable and Output variable are specified by using Controls tool in MSC.ADAMS software and files for MATLAB are created.In MATLAB/Simulink, the control block diagram as shown in Figure 4 is constructed by using adams_sub block and some blocks in the library.

Result and discussion
In the case of the mass of platform m platform = 15t, β 1 = 10°, Δβ = 2°, the simulation results of this system are as follows.The platform moves 42.78m in accelerating period and then acceleration decreases to 3•10 -4 m/s 2 , so the motion of platform could be considered as constant motion.
The greater the absolute value of acceleration, the greater the force acting on truck.If β 1 and Δβ increase, acceleration decreases and if the mass of platform increases, it is varied by β 1 and Δβ.The rope tension according to the position of platforms is shown in Figure 5  When m platform , β 1 , Δβ vary, the maximum resistant torque of winder appears in final interval of acceleration period in Figure 6.The overall period according to m platform , β 1 , Δβ is calculated.According to increasement of m platform , the overall period decreases in initial period and then increases.According to increasement of β 1 , Δβ, the overall period decreases.
Our study provides additional support for the design and operation of Trucklift slope hoisting system with varying profile of track, predicting the rope tension and the resistant torque of winder when platforms move along the track.The more correct simulation result could be given if more practical operating condition is considered.

Conclusions
This paper estimated the rope tension by using MSC.ADAMS and MATLAB/Simulink in Trucklift slope hoisting system with varying profile of track.Thus, the influence of various factors on the rope tension could be considered quantitatively.The acceleration of platform in this system varies according to not only the mass of platform but also the angle of slope of track.And the rope tension, transport period and resistant torque of winder vary according to acceleration of platform.The rope tension hitched to the platform with laden truck is greater than the one with empty truck.By the simulation result, the maximum rope tension appears in the final interval in acceleration period.Generally, the mass of platform should be determined reasonably in Trucklift slope hoisting system where the Koepe winder is installed, and it is also important to determine reasonably the angles of slope of track in Trucklift slope hoisting system with varying profile of track.The results given from the considered simulation method are the reference data for the design and operation in the Trucklift slop hoisting system with varying profile of track.

Figure 2 .
Figure 2. Schematic diagram to estimate the rope tension in TruckLift slope hoisting system with varying profile of track

Figure 3 .
Figure 3. Model of hoisting system in MSC.ADAMS software 1motor, 2pulley, 3path, 4rope, 5flexible body, 6truck, 7platform Ends of cable are connected to the motor and FE Part, respectively.The FE Part (flexible body) consists of small pieces which are accurate for very large deformation cases.The behavior of each element is well known under all possible support and load scenarios.The elements have common points called nodes where section properties are assigned.FE Part is used to modeling the inclined sagged rope and its properties (diameter, mass per meter, etc.) are same as cable properties.The other end of FE Part is connected to platform.

Figure 4 .
Figure 4. Control block diagram in MATLAB/Simulink Using T 10 and T 20 given from adams_sub block, T 1 and T 2 as shown in Figure 2 are calculated as follows.a D x l p T T OE

Figure 5 .
Rope tension according to the position of platforms a) Rope tension in overall period; b) Rope tension in accelerating period; c) Rope tension in decelerating period As shown in above figure, the rope tension is not same along the overall length of track.The maximum tension of rope hitched to platform with laden truck appears at the final interval in acceleration period.And the minimum tension of rope hitched to platform with empty truck appears at the initial interval in acceleration period.

Figure 6 .
Figure 6.Resistant torque of winder according to the position of platform.When m platform , β 1 , Δβ vary, the maximum resistant torque of winder appears in final interval of acceleration period in Figure6.The overall period according to m platform , β 1 , Δβ is calculated.According to increasement of m platform , the overall period decreases in initial period and then increases.According to increasement of β 1 , Δβ, the overall period decreases.