Dynamic loads during safety braking of the container with cargo

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Procedia Engineering 206 (2017) 248–253

International Conference on Industrial Engineering, ICIE 2017 International Conference on Industrial Engineering, ICIE 2017

Dynamic loads during safety braking of the container with cargo Dynamic loads during safety braking of the container with cargo R.B. Kuskil’din, M.A. Vasilyeva* R.B. Kuskil’din, M.A. Vasilyeva* Saint-Petersburg Mining University, 2, 21-st Line, Vasilyevskiy Island, St. Petersburg 199106, Russia

Saint-Petersburg Mining University, 2, 21-st Line, Vasilyevskiy Island, St. Petersburg 199106, Russia

Abstract Abstract The article presents the results of the investigation into the effect of dry friction forces on the magnitude of the dynamic load acting on the rope inthe theresults processofofthe safety braking. The of the process of safety braking are presented. The article presents investigation into equations the effect for of the dry analysis friction forces on the magnitude of the dynamic load The analysis of the process of changing the forces in the rope showed that the maximum forces in the rope arising in presented. the lifting acting on the rope in the process of safety braking. The equations for the analysis of the process of safety braking are modeanalysis of the load be reduced by a factor of three of the of natural movement thearising vessel.inModeled of The of thecan process of changing the forces in the ropeforces showed that theresistance maximumtoforces in the of rope the lifting suddenofexertion thebe brake forcebytoathe brake The resistance results of mathematical presented in the mode the loadofcan reduced factor of drum three in ofthe thelifting forcesmode. of natural to movement modeling, of the vessel. Modeled of form ofexertion graphs of in the the brake rope, confirm results. The data allows getting an expression for sudden ofchanging the brakeefforts force to drum in the the theoretical lifting mode. The results of obtained mathematical modeling, presented in the calculating the braking force, applied to the lifting container to eliminate head ropes during of safety braking. form of graphs of changing efforts in the rope, confirm the theoretical results. The data obtained allows getting an expression for © 2017 Thethe Authors. Published by Elsevier B.V. container to eliminate head ropes during of safety braking. calculating brakingPublished force, applied to the lifting © 2017 The Authors. by Elsevier Ltd. committee Peer-review under responsibility of Elsevier the scientific of the International Conference on Industrial Engineering. © 2017 The Authors. Published by B.V. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering Keywords:safety braking; partil braking of a lifting vessel; vessel relifting; rope blosing; dynamic loads on of aIndustrial rope. Peer-review under responsibility of the scientific committee of the International Conference Engineering. Keywords:safety braking; partil braking of a lifting vessel; vessel relifting; rope blosing; dynamic loads of a rope.

1. Introduction 1. Introduction Dynamic loads on the rope during safety braking are dangerous for several reasons. First, the overloads acting on theDynamic rope during safety braking can lead to itsbraking breakage loss of operability. the frequent implementation loads on the rope during safety areor dangerous for severalSecondly, reasons. First, the overloads acting on of safety braking leadsbraking to an increased fatigue wear oforsteel [1]. Reducing dynamic loads during the safety the rope during safety can lead to its breakage loss ropes. of operability. Secondly, the frequent implementation braking improve the durability of the fatigue ropes iswear an urgent problem further theoretical and experimental of safetytobraking leads to an increased of steel ropes.that [1].requires Reducing dynamic loads during the safety studies [2]. braking to improve the durability of the ropes is an urgent problem that requires further theoretical and experimental Despite studies [2]. the significant development of the theory of mine hoist to date remains unexplored possibility of reducing dynamic loadsdevelopment in the cable system the implementation its own braking effort of of Despitethethe significant of theintheory of mine hoistthetosafety date braking remains by unexplored possibility the container that demands theoretical studies. reducing the dynamic loads additional in the cable system inand the experimental implementation the safety braking by its own braking effort of the container that demands additional theoretical and experimental studies.

* Corresponding author. Tel.: +79062263218. E-mail address:author. [email protected] * Corresponding Tel.: +79062263218.

E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier B.V. Peer-review©under of the scientific committee 1877-7058 2017 responsibility The Authors. Published by Elsevier B.V. of the International Conference on Industrial Engineering. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering.

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering. 10.1016/j.proeng.2017.10.469

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2. Materials and methods To determine the value of a rational braking force must first be determined the effect of the drag force on the value of dynamic loads on the rope. At sharp application of braking force in a period of uniform motion in a mode of lifting cargo on single-end winder, the force in the rope at the beginning of braking is equal to:

S0   mcar  mcon  g  Fres

(1)

where Fres - the force of natural resistance to the motion the container, N; mcar , mcon - weight of cargo and the container, respectively, kg; g - acceleration of free fall, m/sec2. The process of a safety brake should be divided into two stages: prior to locking the lifting machine and after [3]. Until a full stop lifting machines, movement ofcontainer with cargo described by a system of differential equations [4]:

mr .m x  c  x  y   Fbr   mcar  тcon  y   c  x  y    mcar  тcon  g  Fres

(2)

where mr .m - reduced mass of the lifting machine, kg; Fbr - the braking force on the drive drum, N; х , y  acceleration, correspondingly,lifting machine and cargo container, m/sec2; с – rope rigidity,N/m;х – the mass movement of mr .m , m; y– the mass movement of mcon  mcar . At the moment of maximum deceleration of the container with cargo,the force in rope reaches a minimum value, and, based on the resistance forces will be equal to:



S min  g  a max y

m

car

 mcon  g  Fres

(3)

– the maximum (amplitude) value of the acceleration of the container with cargo until a full stop of where a max y

lifting machine, m/sec2. The greatest force in the rope occurs in the first half-period of oscillation, after locking lifting machine.After a full stop of lifting machine motion of the container with cargo described by the equation [5]:  amp sign  y   y   12 y 

where 1 

mcar

(4)

Fres c - the oscillation frequency container with cargo, sec-1; abr  - acceleration of mcar  mcon  mcon

the container under the force of resistance, m/sec2; sign  y  - Kronecker function, which shows,that if changing the sign of the speed у  then change the direction of force Fconp . Mathematically, this function can be written as follows:

 1, when y '  0  sign  у    1, when y '  0  0, when y '  0 

(5)

The analytical solution of this equation is difficult, because the function undergoes a discontinuity at the moments of the change in the direction of the velocity. It is only known that at the moments of the change in the direction of the velocity, the amplitude of the acceleration decreases abruptly by an amount 2abr .

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However, only by analyzing the reduced system of equations (2) and expression (4) it is impossible to more fully determine the influence of the resistance forces on the magnitude of the resulting maximum force in the process of safety braking [6]. For this purpose, a detailed examination of the change in force in the rope is applied at the time when the lifting machine is completely stopped (Figure 1). The speed of the container at this moment may have different meanings within the scope of the velocity oscillations relative to the average velocity entirea lifting mechanism to the moment of locking the lifting machine [7]. Yet, the speed of the container will also be close to zero at the time of a full stopthe lifting machine, so the residual rate of the container can be neglected. The force in the rope at the time of locking the lifting machine is equal to: S min  ( g  a ystop )  mcar  тcan   Fres

(6)

where a ystop - slowing the container at the time of locking the lifting machine, m/sec2. Slowing the container at the time of locking the machine in general can take any value in the range of acceleration amplitude of oscillation until the stop [8]. The minimum value of the force in the rope will be the and, as we know, it takes three times the value of the average deceleration maximum deceleration a ystop  a max y values a max  2aav y

Fig. 1. Scheme of forces acting on the container in the extreme positions of the first half period of oscillation after locking the lifting machine in the operating mode:

ymin , ymax – extreme position of container in the first half period, S  y  – schedule elastic force changes depending on the coordinate y.

Work of the rope elastic forces Aelas and resistance forces Ares on a way  y to achieve maximum force in the rope is equal to the change of potential energy a container with cargo E p in a gravity field:

Aelas  Ares  E p

(7)

Work of elastic forces in the area  y is equal to:  Aelas S min  y 

c  y

2

2

The expression (4) takes the following form:

(8)

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Smin  y  c

 y2 2

 Fres  y  mcar  тcon   y

251

(9)

Reducing the expression (9) on  y , substitute the value Smin from (6), we obtain the following equation of motion:

 a ystop  mcar  тcon   2 Fres 

c y  0 2

(10)

It is seen from the diagram (Figure 1), what minimum force in the rope equals: S S max  c y min

(11)

The maximum force that occurs through the half cycle locking the lifting machine is:



Smax g  a ystop

m

car

 тcon   3Fres

(12)

i.e., the maximum force in the rope under the action of the resistance force is reduced by the amount 3Fres .This is true for both single-end and two-end lift mechanisms, becauseafter a full stop lifting laden part will carry the same fluctuations. 3. Modelling

Checking this statement on the mathematical model of a single-end lifting system with an average deceleration  1.5 104 N and adjusted by the value of the coefficient of elasticity сfor monitoring the acp  3 m/sec2, Fres maximum value of the dynamic force in the rope a res y  2 aav [9]. Parameters of the single-end mechanismare shown in Table 1. Table 1. The parameters a lifting mechaism The reduced mass of the moving parts of the lifting mechanism

mr .m

10·104 kg

Containerweightwithload

тcon  тcar

2.5·104 kg

Calculations show that the minimum and maximum amount of effort into the ropes will be equal to: Smin 

 g  a m

S max 

 g  a m

stop y

stop y

car

car

 тcon   Fres 

 9.8  2  3  3 1.5 104 

1.1 105

 тcon   3Fres  2.5 104  9.8  2  3  3 1.5 104  3.5 105

Simulation of the braking was carried out in the program Mathcad 14. The results are shown graphically in Figure 2. are shown diagrams efforts in the rope, the velocity diagrams, acceleration of the lifting machine and the  1.5 104 N [10]. container with cargo at sharp braking force application for single-end mechanism Fres

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Fig. 2. Diagrams efforts in the rope, the velocity diagrams, acceleration of the lifting machine and the container with cargo at sharp braking force application for single-ends mechanism: respectively;

vx  t   x, v y  t   y 

changeeffort in the rope;

ax  t   x , a y  t   y - graphics acceleration the lifting machine and containers with cargo,

– graphics of the speedsof lifting machine and container with cargo, respectively;

S  t  – a graph of

t - time; T and T1 - period of oscillation of the container to a standstill the lifting machine and after stopping, respectively;

M 2 g - weight of container with cargo.

4. Results

This confirms that the effect of the braking force on the vessel with the load when operating in the safety braking mode, the maximum effort in the cable system is reduced by a factor of three of the forces of natural resistance to movement of the vessel. Therefore, the braking of the vessel with the load should be considered as an effective way to eliminate the dynamic overload during the safety braking on mine hoisting systems in the mode of lifting the load. The expression to calculate the necessary braking force in order to eliminate the dynamic overload of the rope during a safety braking is as follows:

 Fres

1 (mcar  mcon )a ystop 3

(13)

5. Conclusion

The magnitude of acceleration at the time of locking the container lifting machine ܽ௬௕௥ in the general case, may have different values. But to determine the amplitude of change of acceleration of the lifting of the container can determine the sufficient braking force is to avoid excess force in the rope over static values at rest. Also, the slowdown of the container with cargo at the time of the safety brake does not require determining the value of the oscillation period of the container with cargo.

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References [1] O.A. Goroshko, Evolution of the dynamic theory of hoist ropes, International Applied Mechanics. 43(1) (2007) 64–67. [2] S. Kaczmarczyk, W. Ostachowicz, Transient vibration phenomena in deep mine hoisting cables. Part 1: Mathematical, Journal of Sound and Vibration, pp 219–244. [3] N.K. Kuznetsov, Hoist safety braking mode estimation, Proceedings of IRGTU. 11 (2015) 31–34. [4] A.K. Malinovsky, Y.A. Sidash, E.I. Voronko, A.S. Ustinova, Dynamics of safety brake mine hoist systems, Mining information and analytical bulletin. 5 (2013) 269–275. [5] R.B. Kuskildin, V.I. Alexandrov, M.A.Vasilyeva, Partial braking of a laden container in the process of precautionary braking of a singleextended winding plant, Proceedings of the universities, Mining Journal. 1 (2016) 94–101. [6] S.K. Srirangam, K. Anuram, C. Kasbergen, A. Scarpas, V. Cerezo, Study of Influence of Operating Parameters on Braking Friction and Rolling Resistance, Transportation research record. (2015) 79–90. [7] J.N. Yao, X.M. Xiao, Effect of Hoisting Load on Transverse Vibrations of Hoisting Catenaries in Floor Type Multirope Friction Mine Hoists, Shock and vibration, 2016. [8] G.H. Cao, Z.C. Zhu, W.H. Peng, International conference on measuring technology and automatization, 2009, pp. 615–618. [9] E.V. Kurmyshev, Transverse and longitudinal mode coupling in a free vibrating soft string, Phisics letters, 2003, pp. 148–160. [10] D.G. Wang, D.K. Zhang, S.R. Ge, Determination of fretting parameters of hoisting rope in coalmine and fretting-fatigue behavior of steel wires, Industrial Lubrication & Tribology. 65(6) (2013) 436–448.