Load and Energy Consumption Analysis of Rope Winches Used in Mining Rail Transport

Abstract

A central engineering concern in the use of such winches is their energy intensity, which is significantly influenced by operational factors such as the length and gradient of the transport route, the transported weight, and the target hauling velocity. These variables directly affect the drive system’s load and thus the power demand of the motor, which represents the primary component of the system’s energy consumption. While manufacturers typically provide structural, kinematic, and power-related specifications, the user must evaluate whether a given winch can operate efficiently within the energy constraints imposed by specific site conditions. To aid in this assessment, an analytical model, along with a computational software tool, has been developed. This solution enables the continuous determination of essential parameters, with particular attention paid to the energy requirements of the system, supporting informed selection and implementation of winches with appropriately rated motors to optimize energy consumption. For the analyzed case, it was calculated that doubling the transport distance results in an increase in energy consumption of approximately 50%. Moreover, an increase in the velocity of the transported weight by only 0.5 m/s leads to a rise in energy consumption of approximately 25%.

1. Introduction

For decades, the transport of various types of machinery, equipment, materials, and personnel has been conducted using traction drives based on ropes and winches [1]. This type of transport system is particularly widespread in underground horizontal and inclined tunnels (Figure 1) [2,3,4], as well as in vertical shafts of underground mines (Figure 2) [5,6].

This method involves the movement of loads using a rope or occasionally a chain as the traction element, where the transport vehicle is guided either by rail tracks or mechanical guides [7,8]. One typical example of such transport systems is rail haulage utilizing winches equipped with ropes. Most often, the transportation of materials or personnel in rail-wheel-based cars occurs along horizontal or inclined transport routes.

Such a transport system generally consists of a single- or double-drum winch, a rope, one or more transport cars with rail chassis, a return pulley with a rope tensioning mechanism, and the track system itself. In inclined underground tunnels at four degrees or more, additional safety devices are installed to prevent the uncontrolled rolling of transport vehicles in the event of rope or winch failure [9,10]. In contrast, in tunnels with an inclination of up to four degrees, such protective devices are not required and therefore not used. It is evident that the rope winch in this system serves as the primary drive unit [11,12].

For a prospective user considering the implementation of a rope winch transport system, key drive parameters are of interest, such as the load hauling speed, the maximum rope tension force, and the motor power. These parameters must be determined either analytically or empirically as functions of the transport route characteristics and the weight of the material to be conveyed. Manufacturers of this type of equipment do not provide calculation methods related to winch-based transport. Therefore, the aim of this article is to assist users of such systems in the process of calculating and selecting their basic parameters.

Figure 2. Hoist model with the rope winch [13].

Figure 2. Hoist model with the rope winch [13].

2. Analytical Model of a Transport System with a Rope Winch

As outlined earlier, the proper selection of a rope winch requires the precise specification of its technical characteristics, which is most effectively achieved through analytical evaluation. This creates the need to formulate a dedicated analytical model for the transport system incorporating a rope winch. A conceptual representation of such a system operating along an inclined mining route is shown in Figure 3. In the proposed configuration, the transport process is driven by a winch operating with a continuous (endless) rope. The rope may be wrapped around the winch drum multiple times in order to generate the necessary frictional contact (XP) between the rope and the drum. Alternatively, if the system design assumes that the rope or ropes are mechanically fixed to the drum, the frictional interaction can be disregarded in the analysis.

Then, using the principle of equilibrium on an inclined plane, the individual forces relevant to selecting the winch, rope, and rope tensioning mechanism were determined.

$$G_{\mathrm{m}\mathrm{l}}=G_{\mathrm{m}}·\sin {\alpha }_{\mathrm{u}}$$

(1)

$$G_{\mathrm{l}}=G_{\mathrm{l}1}+G_{\mathrm{l}2}$$

(2)

$$G_{\mathrm{l}1}={q_{\mathrm{l}}·(L}_u-L_{\mathrm{u}\mathrm{l}})·\sin {\alpha }_{\mathrm{u}}$$

(3)

$$G_{\mathrm{l}2}={q_{\mathrm{l}}·L}_{\mathrm{u}\mathrm{l}}·\sin {\alpha }_{\mathrm{u}}$$

(4)

$$G_{\mathrm{m}\mathrm{o}}=G_{\mathrm{m}}·\cos {\alpha }_{\mathrm{u}}$$

(5)

$$G_{\mathrm{l}\mathrm{s}}={q_{\mathrm{l}}·L}_u·\sin {\alpha }_{\mathrm{u}}$$

(6)

$$T_{\mathrm{m}}=G_{\mathrm{m}}·{\mu }_{\mathrm{p}\mathrm{m}}·\cos {\alpha }_{\mathrm{u}}$$

(7)

$$T_{\mathrm{l}1}={q_{\mathrm{l}}·{\mu }_{\mathrm{p}\mathrm{l}1}·(L}_u-L_{\mathrm{u}\mathrm{l}})·\cos {\alpha }_{\mathrm{u}}$$

(8)

$$T_{\mathrm{l}2}={q_{\mathrm{l}}·{\mu }_{\mathrm{p}\mathrm{l}2}·L}_{\mathrm{u}\mathrm{l}}·\cos {\alpha }_{\mathrm{u}}$$

(9)

$$T_{\mathrm{l}}=T_{\mathrm{l}1}+T_{\mathrm{l}2}=q_{\mathrm{l}}·{\mu }_{\mathrm{p}\mathrm{l}1}·\cos {\alpha }_{\mathrm{u}}{·(L}_{\mathrm{u}}-L_{\mathrm{u}\mathrm{l}})+q_{\mathrm{l}}·{\mu }_{\mathrm{p}\mathrm{l}2}·\cos {\alpha }_{\mathrm{u}}·L_{\mathrm{u}\mathrm{l}}$$

(10)

$$T_{\mathrm{l}\mathrm{s}}=q_{\mathrm{l}}·L_u·{\mu }_{\mathrm{p}\mathrm{l}}·\cos {\alpha }_{\mathrm{u}}$$

(11)

$$F_{\mathrm{s}}=G_{\mathrm{l}\mathrm{s}}\pm T_{\mathrm{l}\mathrm{s}}+0.5·F_{nwl}={0.5·F_{nwl}+q}_{\mathrm{l}}·L_u·(\sin {\alpha }_{\mathrm{u}}\pm {\mu }_{\mathrm{p}\mathrm{l}}·\cos {\alpha }_{\mathrm{u}})$$

(12)

$$F_{\mathrm{C}}={0.5·F}_{nwl}+G_{\mathrm{l}\mathrm{m}\mathrm{C}}\mp T_{\mathrm{m}}\mp T_{\mathrm{l}}$$

(13)

$$G_{\mathrm{l}\mathrm{m}\mathrm{C}}=G_{\mathrm{m}\mathrm{l}}+G_{\mathrm{l}}=(G_{\mathrm{m}}+{q_{\mathrm{l}}·L}_u)·\sin {\alpha }_{\mathrm{u}}$$

(14)

where

• q_l—unit weight of the rope [kN/m];
• G_l—component of the winding rope weight parallel to the floor [kN];
• μ_pm—rolling resistance coefficient for the transported weight;
• μ_pl—rolling resistance coefficient for the unwinding rope;
• μ_pl1—rolling resistance coefficient for the winding rope section from KZN to point A;
• μ_pl2—rolling resistance coefficient for the winding rope section from point A to the drive unit;
• F_C—tension force in the winding rope [kN];
• F_S—tension force in the unwinding rope [kN].

From the above relationships, it is possible to determine the magnitudes of the relevant forces, with particular emphasis put on the tension in the winding and unwinding segments of the rope. This, in turn, enables the appropriate selection of the rope diameter d [14,15]. By specifying the transport velocity of the system and the weight of the material being conveyed, the required drive motor power N for the winch can be calculated [16,17]. The rolling resistance coefficients μ_pl1, μ_pl2, and μ_pl are typically introduced as empirical values, determined on the basis of practical assumptions. As a result, two scenarios may be considered. In the first, it is assumed that all coefficients take on equal values, in which case the following occurs:

$${\mu }_{\mathrm{p}\mathrm{l}1}={\mu }_{\mathrm{p}\mathrm{l}2}={\mu }_{\mathrm{p}\mathrm{l}}$$

$$T_{\mathrm{l}}=q_{\mathrm{l}}·{\mu }_{\mathrm{p}\mathrm{l}}·L_u·\cos {\alpha }_{\mathrm{u}}$$

(15)

$$F_{\mathrm{C}}={0.5 ·F}_{nwl}+{(G}_{\mathrm{m}}+{q_{\mathrm{l}}·L}_u)·\sin {\alpha }_{\mathrm{u}}\mp G_{\mathrm{m}}·{\mu }_{\mathrm{p}\mathrm{m}}·\cos {\alpha }_{\mathrm{u}}\mp q_{\mathrm{l}}·{\mu }_{\mathrm{p}\mathrm{l}}·L_{\mathrm{u}}·\cos {\alpha }_{\mathrm{u}}$$

$$F_{\mathrm{C}}={0.5 ·F}_{nwl}+G_{\mathrm{m}}·\sin {\alpha }_{\mathrm{u}}+q_l·L_u·\sin {\alpha }_u\mp G_{\mathrm{m}}·{\mu }_{\mathrm{p}\mathrm{m}}·\cos {\alpha }_{\mathrm{u}}\mp q_{\mathrm{l}}·{\mu }_{\mathrm{p}\mathrm{l}}·L_{\mathrm{u}}·\cos {\alpha }_{\mathrm{u}}$$

$$F_{\mathrm{C}}={0.5 ·F}_{nwl}+G_{\mathrm{m}}·(\sin {\alpha }_{\mathrm{u}}\mp {\mu }_{\mathrm{p}\mathrm{m}}·\cos {\alpha }_{\mathrm{u}})\mp q_l·L_u·\left(\sin {\alpha }_{\mathrm{u}}\mp {\mu }_{\mathrm{pl}}·\cos {\alpha }_{\mathrm{u}}\right)$$

(16)

In the second case, these coefficients have different values, and the lengths of the rope segments before and after point A also differ.

$${\mu }_{\mathrm{p}\mathrm{l}1}\ne {\mu }_{\mathrm{p}\mathrm{l}2 }, L_u\ge L_{\mathrm{u}\mathrm{l}} , L_{\mathrm{u}\mathrm{l}}\ne const$$

$$T_{\mathrm{l}}=q_{\mathrm{l}}·\cos {\alpha }_{\mathrm{u}}·\left[{\mu }_{\mathrm{p}\mathrm{l}1}·\left(L_{\mathrm{u}}-L_{\mathrm{u}\mathrm{l}}\right)+{\mu }_{\mathrm{p}\mathrm{l}2}·L_{\mathrm{u}\mathrm{l}}\right]$$

(17)

$$F_{\mathrm{C}}=0.5 ·F_{nwl}+{(G}_{\mathrm{m}}+q_{\mathrm{l}}·L_u)·\sin {\alpha }_{\mathrm{u}}{\mp G}_{\mathrm{m}}·{\mu }_{\mathrm{p}\mathrm{m}}·\cos {\alpha }_{\mathrm{u}}\mp q_{\mathrm{l}}·\cos {\alpha }_{\mathrm{u}}·\left[{\mu }_{\mathrm{p}\mathrm{l}1}·\left(L_{\mathrm{u}}-L_{\mathrm{u}\mathrm{l}}\right)+{\mu }_{\mathrm{p}\mathrm{l}2}·L_{\mathrm{u}\mathrm{l}}\right]$$

$$F_{\mathrm{C}}={0.5·F}_{nwl}+G_{\mathrm{m}}·(\sin {\alpha }_{\mathrm{u}}\mp {\mu }_{\mathrm{p}\mathrm{m}}·\cos {\alpha }_{\mathrm{u}})\mp q_{\mathrm{l}}·L_{\mathrm{u}}·\sin {\alpha }_{\mathrm{u}}\mp q_{\mathrm{l}}·\cos {\alpha }_{\mathrm{u}}·\left[{\mu }_{\mathrm{p}\mathrm{l}1}·\left(L_{\mathrm{u}}-L_{\mathrm{u}\mathrm{l}}\right)+{\mu }_{\mathrm{p}\mathrm{l}2}·L_{\mathrm{u}\mathrm{l}}\right]$$

(18)

The use of a rope for transporting machinery, equipment, materials, and personnel in systems employing endless-rope winches [18] necessitates the implementation of a tensioning mechanism capable of applying the required initial rope tension force F_nwl. The value of this force is determined by the frictional coupling between the rope and the drum and is directly related to the tension in the pulling rope segment. The initial rope tension force F_nwl is typically either constant or adjustable, depending on the operational load. However, due to elongation or contraction of the rope under varying load conditions, compensation must be provided by the rope tensioning mechanism. Therefore, such a mechanism must be capable of delivering both an appropriate stroke length ∆F_nwl and a corresponding initial rope tension force F_nwl.

Assuming that ∆F_C represents the elongation of the rope under the action of the winding force, and ∆F_S the elongation under the action of the unwinding force, and that q_lw denotes the assumed unit elongation of the rope, the following relationship can be established:

$${∆F}_{\mathrm{C}}=q_{\mathrm{l}\mathrm{w}}·F_{\mathrm{C}}$$

(19)

$${∆F}_{\mathrm{S}}=q_{\mathrm{l}\mathrm{w}}·F_{\mathrm{S}}$$

(20)

Then, the elongation of the rope ΔF_nwl under the action of the initial rope tension force F_nwl is determined using Equation (22). In contrast, the elongation of the rope under the action of winding and unwinding forces can be obtained from Equation (21). The sum of these displacements corresponds to the minimum stroke of the return drum in the rope tensioning mechanism, as given by Equation (23).

$${∆F}_{\mathrm{C}\mathrm{S}}={∆F}_{\mathrm{C}}+{∆F}_{\mathrm{S}}=q_{\mathrm{l}\mathrm{w}}·(F_{\mathrm{C}}+F_{\mathrm{S}})$$

(21)

$${∆F}_{nwl}=q_{\mathrm{l}\mathrm{w}}·F_{nwl}$$

(22)

$$∆F={∆F}_{\mathrm{C}\mathrm{S}}+{∆F}_{nwl}$$

(23)

As previously noted, winch transport is conducted in underground tunnels with gradients ranging from 0° to 45°, encompassing horizontal, mildly inclined, and steeply sloped routes. These tunnels connect two vertically offset levels, separated by a height H_u (Figure 4). Knowing the value of H_u allows one to either assume or calculate the total length of the inclined tunnel, i.e., the transport distance L_u based on Equation (24), or conversely, to determine the achievable vertical difference H_u (25) or the tunnel inclination angle α_u (26). These relatively simple trigonometric relationships make it possible to define the geometric parameters of the transport path, which subsequently enable the calculation of the winch loading conditions and the appropriate selection of drive motor power. In the case of horizontal tunnels with an inclination of 0 degrees, Equations (24)–(26) do not apply, as the force values are not dependent on the inclination angle α_a. This issue arises only when α_a > 0.

$$L_u={\displaystyle \frac{H_{\mathrm{u}}}{\mathrm{s}\mathrm{i}\mathrm{n}\left({\alpha }_u\right)}}$$

(24)

$$H_{\mathrm{u}}=L_u·\mathrm{s}\mathrm{i}\mathrm{n}\left({\alpha }_u\right)$$

(25)

$${\alpha }_u=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}\left({\displaystyle \frac{H_{\mathrm{u}}}{L_{\mathrm{u}}}}\right)$$

(26)

Figure 4 illustrates the variation in the transport distance L_u as a function of the tunnel inclination angle α_u for a vertical difference of H_u = 300 m. This information is critical for users who must construct and equip such tunnels, and, most importantly, achieve the specified transport capacity. It should be noted, as mentioned previously, that these considerations apply only to tunnels where the tunnel inclination angle α_u does not exceed 45°. In practice, tunnels are most commonly encountered with tunnel inclination angles ranging between 10° and 20°. For instance, in this case, when α_u is 10°, the transport distance L_u is 1728 m, whereas for α_u at 20°, L_u is 877 m. The difference in length between these two scenarios is therefore 851 m.

It is evident that increasing the inclination of the tunnel leads to a significant shortening of its length; however, this also results in higher power consumption by the winch motor, assuming that the transport parameters (transported weight, time of a single cycle, and total cycle time) remain unchanged. On the other hand, the notable reduction in the tunnel’s length considerably lowers the capital investment associated with its construction and commissioning. In this specific case (H_u = 300 m), assuming a linear increase in costs, the investment expense for the shorter tunnel is reduced by a factor of approximately 1.97. Therefore, it becomes imperative to determine the extent of the increased power demand of the winch motor while preserving the same transport parameters.

Figure 5 shows the velocity profile (time study) of the transport weight v_pj during a single cycle. It is assumed that the movement of the transported weight in the first section occurs with a velocity of v_pja (uniformly accelerated motion), starting from zero and increasing to a steady velocity v_pju over the acceleration time t_cp. This is followed by uniform motion at velocity v_pju for time t_cu, and finally, during time t_co, the transport system decelerates and comes to a complete stop (uniformly decelerated motion with velocity v_pjb).

The total time of a single transport cycle t_c (27) is the sum of the acceleration time t_cp, the uniform motion time t_cu, and the deceleration time t_co. During the time t_cp, the transport system moves with uniform acceleration a, covering a distance of L_up. Once the constant travel velocity v_pju is reached, the system moves with uniform velocity for time t_cu, covering a distance of L_uu. Breaking of the system, with deceleration b, occurs over a distance of L_uo (29).

$$t_{\mathrm{c}}=t_{\mathrm{c}\mathrm{p}}+t_{\mathrm{c}\mathrm{u}}+t_{\mathrm{c}\mathrm{o}}$$

(27)

$$L_u=L_{up}+L_{uu}+L_{\mathrm{u}\mathrm{o}}=0.5a·t_{\mathrm{c}\mathrm{p}}^2+v_{\mathrm{p}\mathrm{j}\mathrm{u}}·t_{\mathrm{c}\mathrm{u}}+0.5b·t_{\mathrm{c}\mathrm{o}}^2$$

(28)

$$L_u=0.5\left[a·t_{\mathrm{c}\mathrm{p}}^2+b·t_{\mathrm{c}\mathrm{o}}^2\right]+v_{\mathrm{p}\mathrm{j}\mathrm{u}}·t_{\mathrm{c}\mathrm{u}}$$

(29)

Assuming uniform motion along the entire transport distance L_u during the total cycle time t_c, the average transport velocity of the system v_pjsr can be determined using Equation (30). This is particularly useful during the stage of determining the tunnel inclination angle α_u (31), provided that mining and geological conditions, as well as the layout of the tunnels, allow for such optimization. In this context, the prospective user can select an appropriate value of α_u to minimize the capital investment required for the construction of the tunnel length L_u while still achieving the required transport capacity (v_pj, t_c).

In such a case, the transport capacity in the inclined tunnel using a winch system is measured by the number of transport cycles n_c that can be completed within a given time period T, i.e., the number of transport systems moved either upward or downward. The number of cycles n_c is then calculated as the ratio of the total available time T to the sum of the cycle time t_c and the preparation time t_pzj required to ready the transport system for travel (32). Accordingly, it is necessary to determine the required average transport velocity v_pjsr in order to complete the specified number of cycles n_c.

Knowing the winding force F_C acting on the transport system and the average transport velocity v_pjsr, the required winch motor power N can be easily determined using Equation (33). The winding force F_C for a given transport system is primarily dependent on the inclination of the tunnel, expressed by the tunnel inclination angle α_u, while the energy consumption of the transport process E_ut depends on the transport distance L_u and either the single-cycle time t_c (34) or a defined total operational time T (35). Thus, the energy consumption of the winch-driven transport system may be analyzed either per cycle t_c or over a specified time interval T.

$$v_{\mathrm{p}\mathrm{j}\mathrm{s}\mathrm{r}}=\left\{0.5\left[a·t_{\mathrm{c}\mathrm{p}}^2+b·t_{\mathrm{c}\mathrm{o}}^2\right]+v_{\mathrm{p}\mathrm{j}\mathrm{u}}·t_{\mathrm{c}\mathrm{u}}\right\}·t_c^{-1}$$

(30)

or

$$v_{\mathrm{p}\mathrm{j}\mathrm{s}\mathrm{r}}=\left\{0.5v_{\mathrm{p}\mathrm{j}\mathrm{u}}\left(t_{\mathrm{c}\mathrm{u}}+t_{\mathrm{c}}\right)\right\}·t_c^{-1}$$

$${\alpha }_u=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}\left({\displaystyle \frac{H_{\mathrm{u}}}{v_{\mathrm{p}\mathrm{j}\mathrm{ś}\mathrm{r}}·t_{\mathrm{c}}}}\right)$$

(31)

$$n_c={\displaystyle \frac{T}{t_{\mathrm{c}}+t_{\mathrm{p}\mathrm{z}\mathrm{j}}}}={\displaystyle \frac{T}{\frac{L_{\mathrm{u}}}{v_{\mathrm{p}\mathrm{j}\mathrm{s}\mathrm{r}}}+t_{\mathrm{p}\mathrm{z}\mathrm{j}}}}={\displaystyle \frac{T·v_{\mathrm{p}\mathrm{j}\mathrm{s}\mathrm{r}}}{L_{\mathrm{u}}+t_{\mathrm{p}\mathrm{z}\mathrm{j}}·v_{\mathrm{p}\mathrm{j}\mathrm{s}\mathrm{r}}}}$$

(32)

$$N=F_{\mathrm{c}}·v_{\mathrm{p}\mathrm{j}\mathrm{s}\mathrm{r}}$$

(33)

$$E_{\mathrm{u}\mathrm{t}\mathrm{c}}=t_{\mathrm{c}}·N$$

(34)

$$E_{\mathrm{u}\mathrm{t}}=T·N$$

(35)

Figure 6 presents the run chart of the tunnel inclination angle α_u for H_u = 300 m and average transport velocities v_pjsr = 1.5, 2.0, and 2.5 m/s as a function of the single-cycle time t_c. Vertical lines indicate the values of t_c most commonly used by operators and recommended by winch manufacturers, while horizontal lines correspond to inclination angles α_u = 10° and 20°. Naturally, the higher the travel velocity v_pjsr, the shorter the achievable cycle time t_c, allowing for an increased number of cycles n_c for a given tunnel inclination angle α_u.

However, within the considered ranges of α_u (10°–20°), v_pjsr (1.5–2.5 m/s), and cycle times t_c (3, 6, 8, and 10 min), the values t_c = 8 or 10 min and possibly around 6 min can be taken forward for further analysis. This case is illustrated in Figure 7, where the selection of t_c depends on the assumed v_pjsr. In such scenarios, it may not be possible to achieve the required cycle time t_c unless the travel velocity v_pjsr is increased for a given inclination angle α_u. Therefore, average velocities of 2.0 and 2.5 m/s are recommended for further consideration. In both approaches, however, increasing the winch motor power is necessary.

Accordingly, for H_u = 300 m, the following technical parameters of the winch and the inclined tunnel are recommended for continued analysis:

–

Tunnel inclination angle α_u = 10°–20°;

–

Mean transport velocity v_pjsr = 2.0–2.5 m/s;

–

Single-cycle time t_c = 8–10 min.

Under these conditions, the transport distance L_u will range from 877 m (α_u = 20°) to 1728 m (α_u = 10°). Ignoring investment costs at this stage, the next step in the analysis must involve determining the required winch drive power N and the energy consumption of the process E_utc.

3. Computer Application

Further analysis of the technical parameters of the winch and the mine tunnel, in the context of selecting the winch motor power N and the energy consumption of the transportation process E_utc, requires the adoption of more detailed data. Utilizing the previously described analytical model and a proprietary computer application, relevant calculations were conducted for a selected transport system equipped with a rope winch installed in an underground inclined tunnel. These calculations aimed to determine the values of N and E_utc as functions of the tunnel inclination angle α_u = 10°–20°, transport velocity v_pjśr = 2.0–2.5 m/s, and the time of a single cycle t_c = 8–10 min (Figure 8). Additionally, the correctness of the selection of the return drum stroke of the rope tensioning mechanism was verified.

The following parameters were used for the calculations:

–

Tunnel inclination angle, α_u = 10°–20° (10, 20°);

–

Transported weight, G_m = 467 kN;

–

Rolling resistance coefficient for G_m, μ_pm = 0.05;

–

Mean transport velocity, v_pjśr = 2.0–2.5 m/s (2.0, 2.5 m/s);

–

Rolling resistance coefficient for the unwinding rope, μ_pl = 0.05;

–

Rolling resistance coefficient for the winding rope section from K_ZN to point A, μ_pl1 = 0.05;

–

Rolling resistance coefficient for the winding rope section from point A to the drive unit, μ_pl2 = 0.05;

–

Time of one cycle t_c = 8–10 min (8, 10 min).

For this purpose, a preliminary rope diameter of d = 42 mm was assumed, corresponding to a transported weight G_m = 467 kN and a unit rope weight q_l = 0.08 kN/m. Additionally, an initial rope tension force F_nwl = 20 kN and a stroke of the return drum ΔF = 1000 mm were adopted. As a result of the calculations (Figure 8), the tension force in the winding rope was determined to be F_C = 189.35 kN, while the tension force in the unwinding rope was F_S = 38.18 kN. These values confirm the adequacy of the selected rope parameters as well as the assumed initial rope tension force F_nwl.

However, the stroke of the return drum in the rope tensioning mechanism was found to be ΔF = 1126.81 mm during descent and ΔF = 1387.18 mm during ascent. This indicates an increase of 387.18 mm above the initially assumed value, necessitating the modernization of the physical installation. Naturally, similar calculations can be performed with different input parameters to verify whether the actual performance aligns with the computed outcomes.

The data adopted for the calculations also enabled, as previously mentioned, the determination of the winch drive power and the energy consumption of the transport process. The results of these computations are shown in Figure 9 and Figure 10. As expected, both the power demand and energy consumption of the transport process decrease with increasing transport distance L_u. A similar trend is observed with respect to t_c and v_pjsr. It is evident that doubling the transport distance L_u leads to an approximate 50% increase in power consumption. Likewise, energy consumption follows the same pattern. Increasing the transport velocity v_pjsr from 2.0 to 2.5 m/s results in a roughly 25% increase in power demand, with energy consumption exhibiting a comparable trend.

Ultimately, the decisive parameter for selecting both L_u and v_pjsr and thus for determining the required winch motor power N should be the single-cycle time t_c, which directly defines transport efficiency, as expressed by the required number of cycles n_c.

4. Conclusions

The analytical model of the rope winch transport system, as previously mentioned, serves as a supporting tool in the selection process of the winch and other system parameters under specific conditions determined by the site of application. Therefore, the prospective user must be familiar with and able to specify the technical requirements for the winch, rope, transport distance, and safety devices.

In the context of winch determination of its technical parameters such as transport velocity, transported weight, rope tension force, drive power, and stroke of the return drum, the analytical model presented earlier proves to be particularly useful. Hence, when considering rail transport systems with rope winches, it is recommended that the selection procedure begins with defining the required transport capacity, i.e., the target number of operational cycles.

This allows for the determination of the necessary transport time and mean transport velocity. Subsequently, taking into account the existing network of tunnels and the vertical elevation difference, the user can determine and select the most advantageous tunnel inclination angle and, consequently, its length.