Impact of Increased Travel Speed of a Transportation Set on the Dynamic Parameters of a Mine Suspended Monorail

: The method of increasing the efﬁciency of using one of the most common means of auxiliary transport in underground coal mines—suspended monorails—is presented. Increase of velocity is one of the key parameters to improve the efﬁciency and economical effect related with the underground auxiliary transport. On the other hand, increasing the velocity results in bigger value of force acting on the suspended monorail route and its suspensions. The most important issue during increasing the velocity is ensuring the required safety for the passengers and not overloading the infrastructure. In order to analyze how increasing velocity inﬂuences the level of loads of the route suspension and the steel arch loads, the computational model of suspended monorail was developed. The computational model included both the physical part (embedded in the program environment based on the Multi-Body System method) and the components of the monorail control system. Two independent software environments were cooperating with each other through the so-called co-simulation. This model was validated on the base of results obtained on the test stand. Then, the numerical simulations of emergency braking with different values of velocity were conducted, which was not possible with the use of physical objects. The presented study can be used by the suspended monorail’s producers during the designing process, and leads to increase the safety on underground transportation routes.


Introduction
Suspended monorails are one of the basic auxiliary transportation means in underground mining plants. The design of the monorails allows the transportation of materials as well as the personnel. The design of the monorails is constantly developed to improve both transportation possibilities, safety [1][2][3], and at the same time, the distances between the shaft and the mining face are being extended, both as a result of the expansion of mining fields and as a result of organizational changes. As the length of the routes increases, the time the personnel spends commuting to the workplace also increases. The popularity of suspended monorails is due to many advantages, including: High lifting capacity and efficiency; the possibility of using long, branched routes; possibility of avoiding obstacles on the floor, and easy reloading of floor mounted railways. Moreover, in suspended monorails, the route is isolated from the floor, which, in certain geological and mining conditions, may uplift and deform [4][5][6].
The maximum permissible speed of a suspended monorail during the people movement depends on the country and the applicable law, and is 1-3.3 m/s. In some European countries, preparatory work to introduce legislative changes increasing the maximum permissible speed of suspended monorails during personnel movement has been underway in recent years [7][8][9]. Both manufacturers of suspended monorails, who improve their machines, and mining plants that use this type of transportation are interested in increasing this speed limit. The main benefit of increasing the speed of monorails is the extension of the effective working time of the personnel, which translates into measurable economic benefits and an increase in the profitability of the coal mining process.
Of course, for safety reasons, the speed limit will be increased on the route sections that are properly prepared and tested. Ensuring the load to a single roof support arch below 40 kN (in a certain case, a load of 50 kN is allowed with the consent of the mining plant operation manager, providing the results of the calculations) is one of the criteria the route must meet that the suspended monorail can move along it.
Contrary to railways, where the rails are stationary and integrated with the ground, there are extensive and detailed methods of identifying vibrations of the running components [10]. In suspended monorails the route is assembled, lifted, and stabilized by means of slings, which changes the flow of forces between the means of transport and its surroundings. Increasing the speed is possible with maintain the existing level of safety.
Determining the forces in slings with the use of analytical methods is difficult due to the fact that the suspended line is a system that is statically indeterminate. Therefore, the numerical MBS method was used.
As the weight of the suspended monorail used for the crew movement is much lower than the mass of the assembly dedicated to the transportation of heavy materials (e.g., powered roof supports or longwall shearer components), exceeding the maximum permissible load to the roof support arches is unlikely. However, three aspects should be taken into account in the context of increasing the maximum permissible speed of the monorail moving the personnel. The first one is the fact that the dynamic overloads in emergency situations, such as emergency braking, are greater than the loads resulting from static calculations. Second, increasing the travel speed will result in an exponential increase in kinetic energy and side-sway amplitude [11]. This energy must be dissipated during the emergency braking process. In connection with the above, it is necessary to verify the level of dynamic overloads in the suspensions of the suspended monorail route, which directly affect the yielding roof support [7,[12][13][14][15]. The results of the authors' analyses of loads to the suspensions of the suspended monorail's route in terms of the possibility of increasing the permissible speed of the monorail while moving the personnel is presented. Based on the emergency braking tests carried out on the test track, it was possible to validate the suspended monorail calculation model. This model was used in numerical simulations to assess the impact of changing the speed of a suspended monorail on the load to the route suspensions.

Test Stand and Computational Model
Test stand was built at the premises of one of the manufacturers of suspended monorails. The stand uses an innovative type of 4 m long rails to stabilize the route and increase the personnel's comfort during travel. The rails design is the result of implementation of the European INESI project [7]. The length of the entire route on the test track was 90 m. Figure 1 shows the test stand. Each rail joint at the test stand was connected to a traverse, suspended from the stand frame with two chains. Successive pairs of chains were alternately installed vertically (perpendicular to the longitudinal axis of the rail) or they were deflected, forming the shape of the letter "V" (Figure 2).  Each rail joint at the test stand was connected to a traverse, suspended from the stand frame with two chains. Successive pairs of chains were alternately installed vertically (perpendicular to the longitudinal axis of the rail) or they were deflected, forming the shape of the letter "V" (Figure 2). Each rail joint at the test stand was connected to a traverse, suspended from the stand frame with two chains. Successive pairs of chains were alternately installed vertically (perpendicular to the longitudinal axis of the rail) or they were deflected, forming the shape of the letter "V" (Figure 2). Fourteen force transducers were fitted to the selected suspensions to record the tensile force in the suspension during the monorail travel or braking. The sensors were designed in such a way to replace three chain links in the suspension ( Figure 3). The suspended monorail was accelerated to the set speed with which it was moving along the test track, and at the end of the test track, the transportation set stopped. The second option was accelerating the transportation set and then initiating emergency braking at a selected point on the route. Apart from the tensile forces acting in the suspensions, the speed and acceleration of the monorail were recorded during the tests.
A computational model of the suspended monorail, consisting of two parts: the dynamic part and the dynamic part control module, was developed at the later stage.
Recreation of the suspended monorail with the route on the test stand is the dynamic part of the computational model. The dynamic part of the computational model Fourteen force transducers were fitted to the selected suspensions to record the tensile force in the suspension during the monorail travel or braking. The sensors were designed in such a way to replace three chain links in the suspension ( Figure 3). Each rail joint at the test stand was connected to a traverse, suspended from the stand frame with two chains. Successive pairs of chains were alternately installed vertically (perpendicular to the longitudinal axis of the rail) or they were deflected, forming the shape of the letter "V" (Figure 2). Fourteen force transducers were fitted to the selected suspensions to record the tensile force in the suspension during the monorail travel or braking. The sensors were designed in such a way to replace three chain links in the suspension ( Figure 3). The suspended monorail was accelerated to the set speed with which it was moving along the test track, and at the end of the test track, the transportation set stopped. The second option was accelerating the transportation set and then initiating emergency braking at a selected point on the route. Apart from the tensile forces acting in the suspensions, the speed and acceleration of the monorail were recorded during the tests.
A computational model of the suspended monorail, consisting of two parts: the dynamic part and the dynamic part control module, was developed at the later stage.
Recreation of the suspended monorail with the route on the test stand is the dynamic part of the computational model. The dynamic part of the computational model The suspended monorail was accelerated to the set speed with which it was moving along the test track, and at the end of the test track, the transportation set stopped. The second option was accelerating the transportation set and then initiating emergency braking at a selected point on the route. Apart from the tensile forces acting in the suspensions, the speed and acceleration of the monorail were recorded during the tests.
A computational model of the suspended monorail, consisting of two parts: the dynamic part and the dynamic part control module, was developed at the later stage.
Recreation of the suspended monorail with the route on the test stand is the dynamic part of the computational model. The dynamic part of the computational model was built using the software analyzing the kinematics and dynamics of multi-body systems. This part of the model is shown in Figure 4. was built using the software analyzing the kinematics and dynamics of multi-body systems. This part of the model is shown in Figure 4. The model has 720 DOF (degrees of freedom). A 3D contact model was defined between: Braking pads and route rail; rollers and route rail; and drive gears and route rail. It was defined as combination of virtual spring and damper located between solid bodies being in contact. During interaction between these two bodies, the length of virtual spring decreases, and there is some penetration of one body into the second body (in this model, the maximum value of penetration is 1 × 10 −4 m). The next very important parameter of contact is contact force, which was calculated according the Formula (1) [16]: where: • F-contact force; • K-stiffness of the virtual spring; • x1-length of the virtual spring at the moment of the bodies contact; • x-instantaneous length of the virtual spring; • e-virtual spring linearity coefficient; e = 1 means a linear relationship; Computational model consists of: • 383 rigid bodies: Operator's cabin (7 rigid bodies); 2x rack-and-pinion drive (2x 6 rigid bodies); diesel power pack (11 rigid bodies); cabin for crew transportation (33 rigid bodies); braking trolley (24 rigid bodies); tension rod (5 rigid bodies); route rail (23 rigid bodies); components of the route suspensions (268 rigid bodies).
The model has 720 DOF (degrees of freedom). A 3D contact model was defined between: Braking pads and route rail; rollers and route rail; and drive gears and route rail. It was defined as combination of virtual spring and damper located between solid bodies being in contact. During interaction between these two bodies, the length of virtual spring decreases, and there is some penetration of one body into the second body (in this model, the maximum value of penetration is 1 × 10 −4 m). The next very important parameter of contact is contact force, which was calculated according the Formula (1) [16]: where: • F-contact force; • K-stiffness of the virtual spring; • x 1 -length of the virtual spring at the moment of the bodies contact; • x-instantaneous length of the virtual spring; • e-virtual spring linearity coefficient; e = 1 means a linear relationship; • c-damping coefficient of the virtual damper; •ẋ-relative speed of interacting bodies. The damping coefficient "c" doesn't have constant value, which change according the Equation (2) [16]: where: c-damping coefficient; c max -maximum damping coefficient; h-penetration depth of one solid into another; p-function describing dependence of the damping factor c on the depth of the solid penetration.
In the computational model contact parameter values were set as following: • 3D contact between rollers and gears with the rails: Virtual spring rigidity coefficient k = 7 × 10 9 N/m; damping coefficient c max = 7 × 10 4 N·s/m; maximum penetration depth h max = 1 × 10 −4 m; virtual spring linear coefficient e = 2.2.
The second part of the computational model, which is the implementation of the control system for the dynamic part of the computational model, was developed in the Matlab/Simulink environment. Then, by defining the input/output signals from each part of the computational model and by using the parallel simulation technique [17][18][19], numerical simulations using the developed computational model were carried out. This technique allows simulations in various software environments. In this way, it is possible to integrate various domains with each other, or to evaluate complex mechanical systems in the defined criteria states, e.g., cooperation of multi-body systems with hydraulic systems [20], thermal energy management in the mechanical systems [21], or verification of dynamic parameters of a moving vehicle in difficult land conditions [22]. The diagram of the signals flow between the various parts of the computational model is shown in Figure 5.
The simulations of the emergency braking process were carried out in accordance with the algorithm presented in Figure 5. The simulation process began with the activation of driving torque. The velocity of the suspended monorail was constantly monitored, during the simulation. After reaching the maximum value of the velocity (declared as a boundary condition), the driving torques were deactivated and the emergency braking procedure was started by activating the braking forces and torques. When the velocity of the suspended monorail was equal 0 m/s, the braking process was deactivated, and the simulation was stopped. In addition, the monorail acceleration values were recorded throughout the simulation. On their basis, it was determined whether during emergency braking there were excessive overloads affecting the operator and passengers of the transportation set.
During normal operation of the suspended monorail and in emergency situations, such as emergency braking, the operator and transported crew are affected by vibrations and dynamic overloads related to the change of the acceleration/deceleration level. The analysis of these values allows for the acquisition of appropriate knowledge in order to increase the level of comfort and safety of passengers, in particular operators who are more exposed to the occurrence of vibrations [23][24][25][26][27]. The results of the work related to the analysis of the impact of vibrations and dynamic overloads on the human body and the method of their minimization have been published in [28]. The simulations of the emergency braking process were carried out in accord with the algorithm presented in Figure 5. The simulation process began with the ac tion of driving torque. The velocity of the suspended monorail was constantly monito during the simulation. After reaching the maximum value of the velocity (declared boundary condition), the driving torques were deactivated and the emergency bra procedure was started by activating the braking forces and torques. When the veloci the suspended monorail was equal 0 m/s, the braking process was deactivated, and simulation was stopped. In addition, the monorail acceleration values were recor throughout the simulation. On their basis, it was determined whether during emerge braking there were excessive overloads affecting the operator and passengers of transportation set.
During normal operation of the suspended monorail and in emergency situati such as emergency braking, the operator and transported crew are affected by vibrat and dynamic overloads related to the change of the acceleration/deceleration level. analysis of these values allows for the acquisition of appropriate knowledge in orde increase the level of comfort and safety of passengers, in particular operators who more exposed to the occurrence of vibrations [23][24][25][26][27]. The results of the work relate the analysis of the impact of vibrations and dynamic overloads on the human body the method of their minimization have been published in [28].

Validation of the Computational Model
Time processes of the force in the selected transducers, the forces measured du stand tests, and those calculated in numerical simulations, were compared to verify correct operation of the computational model. Two passes were selected for compari first for speed 3 m/s and one for 5 m/s. For each speed, the forces were compared in pair of vertical suspensions and one pair of diagonal suspensions. When the set passing at a speed of 3 m/s, the forces in vertical suspensions marked with the sym (C5 and C6) and diagonal suspensions marked with the symbol (C2 and C4) were c pared. In addition, for the travel speed of 5 m/s, the forces in vertical suspensions mar (C5 and C6) and diagonal suspensions marked with symbols C8 and C9 were comp ( Figure 6).

Validation of the Computational Model
Time processes of the force in the selected transducers, the forces measured during stand tests, and those calculated in numerical simulations, were compared to verify the correct operation of the computational model. Two passes were selected for comparison; first for speed 3 m/s and one for 5 m/s. For each speed, the forces were compared in one pair of vertical suspensions and one pair of diagonal suspensions. When the set was passing at a speed of 3 m/s, the forces in vertical suspensions marked with the symbol (C5 and C6) and diagonal suspensions marked with the symbol (C2 and C4) were compared. In addition, for the travel speed of 5 m/s, the forces in vertical suspensions marked (C5 and C6) and diagonal suspensions marked with symbols C8 and C9 were compared ( Figure 6). The time curves of forces in vertical suspensions are presented in Figure 7. The time curves of forces in vertical suspensions are presented in Figure 7.        Forces in the vertical suspensions at travel speed 5 m/s are presented in Figure 9.  Figure 10. Forces in the diagonal suspensions at travel speed 5 m/s are presented in Figure 10.   Table 1 shows the maximum forces in the selected suspensions, recorded on the test stand and calculated by numerical simulations. The percentage difference of the results obtained in the numerical calculations in relation to the values measured on the stand is also given.  Table 1 shows the maximum forces in the selected suspensions, recorded on the test stand and calculated by numerical simulations. The percentage difference of the results obtained in the numerical calculations in relation to the values measured on the stand is also given. The biggest difference was observed in the case of C8 and C2 suspensions. They are diagonal suspensions. The role of diagonal suspensions is to stabilize the suspended monorail track in the axis of travel. Depending on how the monorail is accelerated (acceleration in the speeding up phase), different forces acting on the rail are generated. As a result of these forces, the route of the monorail moves, and the role of the diagonal suspensions is to limit the range of this movement. In a situation when the suspensions chains are loosened, position of the traverse of a given rail joint can change. This results in an increase in the range of the monorail route movement, and the disproportions between the forces in a pair of diagonal suspensions increase. The described phenomenon explains large differences in the values of the maximum forces recorded on the test stand in the sensors installed diagonally

Analysis of the Results
After the verification of the calculation model, emergency braking of the suspended monorail assembly from the speeds equal to 1, 2, 3, 4, 5, and 6 m/s was simulated. During the simulation, the forces were recorded in each suspension of the monorail route. As only forces in the selected suspensions were measured on the test stand, in the computational model, the marking and numbering of the following suspensions were changed. Figure 11 shows the markings and numbers of each suspension along the section, where emergency braking took place.
tween the forces in a pair of diagonal suspensions increase. The described phenomenon explains large differences in the values of the maximum forces recorded on the test stand in the sensors installed diagonally

Analysis of the Results
After the verification of the calculation model, emergency braking of the suspended monorail assembly from the speeds equal to 1, 2, 3, 4, 5, and 6 m/s was simulated. During the simulation, the forces were recorded in each suspension of the monorail route. As only forces in the selected suspensions were measured on the test stand, in the computational model, the marking and numbering of the following suspensions were changed. Figure 11 shows the markings and numbers of each suspension along the section, where emergency braking took place. Moreover, emergency braking was simulated in two variants, differing in the value of the braking force. In the first simulation variant, emergency braking with full force of braking devices was used. In the second variant, the braking force was reduced by 50%.
Such an approach was aimed at emphasizing the high impact of the braking method on the forces loading the route suspensions while increasing the speed of the monorail. Moreover, emergency braking was simulated in two variants, differing in the value of the braking force. In the first simulation variant, emergency braking with full force of braking devices was used. In the second variant, the braking force was reduced by 50%.
Such an approach was aimed at emphasizing the high impact of the braking method on the forces loading the route suspensions while increasing the speed of the monorail. The maximum tensile forces in each suspension, recorded during the simulation of emergency braking at different speeds, are presented in Tables 2 and 3    During emergency braking, the highest forces were recorded in the suspensionsstabilizing the position of the suspended monorail route. With the increase of the speed at which the emergency braking took place, the recorded dynamic overload in the suspensions increased. The maximum forces in the suspensions recorded for each analyzed driving speed of the set are shown in Figure 12. During emergency braking, the highest forces were recorded in the suspensions-stabilizing the position of the suspended monorail route. With the increase of the speed at which the emergency braking took place, the recorded dynamic overload in the suspensions increased. The maximum forces in the suspensions recorded for each analyzed driving speed of the set are shown in Figure 12. Based on the presented results, the increase in the force in the most loaded suspensions was calculated in relation to the value recorded at the lowest analyzed speed of 1 m/s (Table 4) and in relation to the maximum speed of the suspended monorail, accepted by the legal regulations during transportation of people, i.e., 2 m/s ( Table 5). The tables show the base value to which the other values were compared. The difference in forces was presented as force increase expressed in [N], and as a percentage increase in relation to the base value, both in relation to the simulation with full braking force and simulation Based on the presented results, the increase in the force in the most loaded suspensions was calculated in relation to the value recorded at the lowest analyzed speed of 1 m/s (Table 4) and in relation to the maximum speed of the suspended monorail, accepted by the legal regulations during transportation of people, i.e., 2 m/s ( Table 5). The tables show the base value to which the other values were compared. The difference in forces was presented as force increase expressed in [N], and as a percentage increase in relation to the base value, both in relation to the simulation with full braking force and simulation in which the braking force was reduced by 50%.

Discussion
The fact that the suspended monorail route is not rigid, and both the route and the neighboring rails can change their orientation in relation to each other (possibility of movement in the rail joint) is one of the reasons for the appearance of dynamic overloads. As a result, the suspension may be momentarily loosened and then dynamically loaded.
Examples of rail displacements during emergency braking are presented in relation to rail No. 5, during braking from a speed of 5 m/s. Figure 13 shows the rail displacement along the longitudinal axis (Y axis) in line with the direction of travel of the monorail set, both in simulations with full and reduced braking force. The maximum rail displacement in this axis was 0.05 m when using the full braking force, while when using the braking force reduced by half, this displacement was 0.0141 m.   Figure 14 shows the displacement of the rail No. 5 in the vertical axis (Z axis). The maximum rail displacement in this axis was 0.0193 m when using the full braking force, while when using the braking force reduced by half, the displacement was 0.0024 m.   Figure 14 shows the displacement of the rail No. 5 in the vertical axis (Z axis). The maximum rail displacement in this axis was 0.0193 m when using the full braking force, while when using the braking force reduced by half, the displacement was 0.0024 m.   Figure 14 shows the displacement of the rail No. 5 in the vertical axis (Z axis). The maximum rail displacement in this axis was 0.0193 m when using the full braking force, while when using the braking force reduced by half, the displacement was 0.0024 m.   Displacement of rails changes the traverse position in suspensions, which leads to loosening of one suspension and excessive load to the other one of the pair of diagonal suspensions stabilizing the monorail route. The successive stages of changing the position of the traverse in the rail suspension and the way of loading the suspensions are shown in Figure 15. Before braking, the suspensions are symmetrically loaded (state 1). Then, in a result of braking and action of inertia forces, the route moves forward and up-the traverse in the rail suspension rotates, and as the result, the L11 suspension is significantly more loaded (preventing against further movement of the route), and the L12 suspension is loosened and relieved (state 2). Then the track and rails return to their previous position, and the position of the traverse as a result of the action forces the suspension position changes, and the L12 suspension is dynamically hit and overloaded while loosening the L11 suspension (state 3). Stabilization and return to the balanced position and symmetrical load to the L11 and L12 suspensions is the last stage.
The analysis of the recorded forces allows us to conclude that with the increase in the maximum speed of the suspended monorail, the dynamic overloads during emergency braking with full force increase. However, reducing the braking force by half results in a significant reduction of the increase of the forces loading the route suspension. The conclusion is that along with increasing the speed of the suspended monorail, proper selection of the force and method of braking is extremely important.

Conclusions
The analysis shows the risk of significant dynamic overloads in the route suspensions. The diagonal suspensions stabilizing the suspended monorail's route are exposed to the greatest overload. With the increase in the maximum driving speed, the accelerations and overloads, as well as the vibrations acting on the operator and passengers of the suspended monorail also increase. These aspects were presented in other studies [29]. The simulations showed that in situations such as emergency braking, short dynamic overloads occur already when braking from the speed of 3 m/s. However, it should be mentioned that during tests a new type of rail, longer than the current one, was used (4 m long). The use of such rails improves the comfort of people travel by providing a more stable route and minimizing vibrations and overloads affecting people in the monorail, caused by improper assembly of the route. However, to distribute the weight of the suspended monorail and rails over a greater number of roof support arches, the rails require applying the special traverses at the rail joints. The analysis of the simulation results indicates that this solution may contribute to the development of dynamic over- Before braking, the suspensions are symmetrically loaded (state 1). Then, in a result of braking and action of inertia forces, the route moves forward and up-the traverse in the rail suspension rotates, and as the result, the L11 suspension is significantly more loaded (preventing against further movement of the route), and the L12 suspension is loosened and relieved (state 2). Then the track and rails return to their previous position, and the position of the traverse as a result of the action forces the suspension position changes, and the L12 suspension is dynamically hit and overloaded while loosening the L11 suspension (state 3). Stabilization and return to the balanced position and symmetrical load to the L11 and L12 suspensions is the last stage.
The analysis of the recorded forces allows us to conclude that with the increase in the maximum speed of the suspended monorail, the dynamic overloads during emergency braking with full force increase. However, reducing the braking force by half results in a significant reduction of the increase of the forces loading the route suspension. The conclusion is that along with increasing the speed of the suspended monorail, proper selection of the force and method of braking is extremely important.

Conclusions
The analysis shows the risk of significant dynamic overloads in the route suspensions. The diagonal suspensions stabilizing the suspended monorail's route are exposed to the greatest overload. With the increase in the maximum driving speed, the accelerations and overloads, as well as the vibrations acting on the operator and passengers of the suspended monorail also increase. These aspects were presented in other studies [29]. The simulations showed that in situations such as emergency braking, short dynamic overloads occur already when braking from the speed of 3 m/s. However, it should be mentioned that during tests a new type of rail, longer than the current one, was used (4 m long). The use of such rails improves the comfort of people travel by providing a more stable route and minimizing vibrations and overloads affecting people in the monorail, caused