Calculation Method for Structural Dynamics of Material Ropeway under Startup and Shutdown Conditions with Single Concentrated Loads and Distributed Multiple Loads

In light of the unique structural features of material ropeway of transmission line, this paper presents a calculation method for the structural dynamics of material ropeway when subjected to single concentrated loads and distributed multiple loads. Taking into account the geometric nonlinearity and significant flexible deformation features of carrying rope and pulling rope in material ropeways, a finite mass point method is utilized for theoretical derivation to investigate the effects of varying load weights and speeds on tension fluctuations in carrying rope and pulling rope during the startup and shutdown processes. The results indicate that the proposed method can accurately calculate the tension and structural variations in carrying rope and pulling rope of multi-span material ropeway when subjected to single concentrated loads and distributed multiple loads. This method not only satisfies the requirements for transmission line engineering applications but also offers insights into the safe utilization of material ropeway of transmission line.


Introduction
Material ropeway of transmission line is extensively utilized in the material transportation associated with transmission line [1].The working rope consists of the carrying rope and the pulling rope.Given the substantial deformation flexibility and pronounced geometric nonlinearity of the carrying rope and pulling rope, the selection of an appropriate calculation method of the finite mass point method for these issues is essential [2,3].The finite mass point method is a numerical method for structural analysis, which is particularly adept at addressing nonlinear issues, such as substantial deformations and displacements, facilitating theoretical derivation and program implementation.
Upon the startup of the material ropeway, the drum of the driving device, situated at the starting side, begins to rotate, thereby drawing the pulling rope and sequentially propelling the load to move continuously along the carrying rope from the starting end of the ropeway.The abrupt acceleration of the pulling rope leads to drastic changes in its tension, which concurrently exerts an influence on the carrying rope [4].In the course of the ropeway's operation, the significant inertia of the concentrated load is likely to induce drastic tension changes in the carrying rope during an emergency require braking.Therefore, an analysis on the operational tension in the carrying rope and pulling rope under startup and shutdown conditions of the ropeway is of paramount importance [5,6].

Calculation Methods for Startup and Shutdown Conditions with Single Concentrated Loads and Distributed Multiple Loads
Upon the startup of the material ropeway, the drum of the driving device, situated at the starting side, begins to rotate, thereby drawing the pulling rope and sequentially propels the concentrated load to move continuously along the carrying rope from its initial suspension position, as shown in figure 1.In order to simulate the function of the ropeway driving device, a designated pulling force acting interval D is established at the end of the ropeway's pulling rope.This specified interval spans a width equal to the length of two pulling rope units, as shown in figure 2. The pulling rope is controlled by regulating the motion of its nodes within interval D, while nodes located outside this interval remain unaffected [7].The motion of nodes within interval D should remain horizontal to avoid generating additional tension in the pulling rope.To achieve this, upper and lower clamping rollers are positioned at the interval ends, as illustrated in figure 3. The spacing between upper and lower rollers is set to match the diameter of the pulling rope, thereby ensuring that rope nodes can move horizontally within the designated interval.Due to the fact that interval D spans the length of two pulling rope units, normally, there are 1-2 pulling rope nodes within interval D. In the calculation process, applying a displacement (and acting force if necessary) to the first node entering this interval is sufficient to simulate the function of the driving device, which is to power the ropeway operation.

Calculation of Operation Startup
Assume the startup speed of the driving device is v1, and the time step for the operation calculation is h, then subsequent to the suspension of the load and its attainment of near-static condition, apply a horizontal forward displacement dn to the first pulling rope node within the interval: Where, ev represents the unit vector in the forward horizontal direction.

Calculation of Operation Shutdown
To simulate the condition of the driving device braking and consequent operational shutdown, let the position x1 of the first pulling rope node within the interval be constant during the operation calculation.This means the ability to make an emergency shutdown during operation.
Where, the superscript n represents the calculation time step.

Analysis on Startup and Shutdown Processes
Basic Parameters for Material ropeway: A span of 350m, a height difference of 130m; the diameter of the carrying rope is φ30mm, with a unit length mass of 4.57kg/m, and an elastic modulus of 110GPa; the deflection coefficient is set to 0.03, resulting in an initial length of the carrying rope of 374.02m; the diameter of the pulling rope is φ26mm, with a unit mass of 3.4kg/m, and an elastic modulus of 110GPa.

Analysis on Startup Process
(1) Analysis on Operating Conditions: The conditions involve loads of 2t, 3t, and 4t, respectively, with an operational speed of 30m/min (at the startup position).The analysis on figure 4 to figure 8 reveals that the startup state has a marginal influence on the carrying rope, yet markedly affects the tension of the pulling rope.Additionally, there is a negative correlation between the weight of the load and the effect of the startup state on the pulling rope's tension.Specifically, lighter loads result in more significant fluctuations in the pulling rope's tension at startup.Moreover, a higher startup speed is associated with increased fluctuations in the tension of the pulling rope.Therefore, reducing the operational speed of the ropeway driving device during the ropeway startup is imperative.

Analysis on Shutdown Process
(1) Analysis on Operating Conditions: The conditions involve loads of 2t, 3t, and 4t, respectively, with an operational speed of 30m/min (at the shutdown position).The analysis on figure 9 to figure 10 reveals that the shutdown state has a marginal influence on the carrying rope, yet markedly affects the tension of the pulling rope.Furthermore, it is evident that an increase in load weight corresponds to a proportional rise in the carrying rope's tension.In the shutdown state, the carrying rope experiences minimal tension fluctuations, in contrast to the pulling rope, which demonstrates more pronounced tension fluctuations.Notably, the fluctuation amplitude of the pulling rope's tension tends to converge across various load weights.Moreover, a higher shutdown speed is associated with increased fluctuations in the tension of the pulling rope.Therefore, reducing the operational speed of the ropeway driving device during the ropeway shutdown is imperative.

Conclusion
This paper proposes a dynamic calculation method for analyzing material ropeway structures under startup and shutdown conditions when subjected to single concentrated loads and distributed multiple loads.It determines the effects of varying load weights and operational speeds on the working rope structures in material ropeway.The analysis on startup and shutdown processes reveals that these processes have a marginal effect on maximum tension fluctuations in the carrying rope, yet they substantially affect the maximum tension fluctuations in the pulling rope.Consequently, the impact of speed emerges as a critical factor warranting focused consideration.

Figure 9 .
Figure 9. Curves of Ropeway Tension Variations in Shutdown State with Different Loads.Analysis on Operating Conditions: The weight is set at 2t, with operational speeds of 15m/min, 30m/min, and 60m/min, respectively (at the shutdown position).

Figure 10 .
Figure 10.Curves of Ropeway Tension Variations in Shutdown State with Different Speeds.
Curves of Tension Variations during Startup with Load of 2 tons.Curves of Tension Variations during Startup with Load of 3 tons.