Steel Wire Ropes Service Life

Abstract

This paper demonstrates the low life expectancy of the steel wire rope that might be achieved by using the ISO 4308-Part1:2003 for the calculation of the reeving system of a S/R machine. The problem is illustrated with a case study: Calculation of one S/R machine steel wire rope service life. It is also shown that the application of the DIN 15020-Part1:1974, leads to better results on the steel wire rope service life. In response to increasingly demanding customer requirements for high throughput automatic storage systems, S/R machines and VTDs are being pushed to achieve higher number of cycles per hour. The S/R machines are under the scope of EN 528:2008, which states that the ISO 4308-Part1:2003 must be used to calculate and design the steel wire rope reeving system. This standard has been developed for cranes and it takes in account the lifting appliance mode of operation, through the mechanism classification group. However, even the consideration of the most demanding mechanism classification for the steel wire rope calculations may lead to a low service life of the rope. As stated previously, in this paper a S/R machine case study calculation of a steel wire rope service life is made. The lifting system is designed according to the ISO 4308-Part1:2003 and DIN 15020-Part1:1974, and the service life is calculated and compared with the typical requirements for an automatic storage and retrieval warehouse system. Methods like the one developed by Feyrer, may support the machine designer to increase the steel wire rope life expectancy. This method allows the assessment of the impact on the steel wire rope service life of one given improvement in the reeving system design, enabling the designer to balance improvement with cost.

Introduction

This document demonstrates the low life expectancy of the steel wire rope that might be achieved by using the ISO 4308-Part1:2003 [1] for the calculation of the reeving system of a S/R machine. The case study S/R machine steel wire rope reeving system is presented in Fig. 1. The S/R machines, commonly known as stacker cranes—STK, are under the scope of EN 528:2008 [2] and the VTDs are under the scope of EN 619:2002 + A1 [3]. The requirements of these standards must be fulfilled so that the conformity declaration under CE marking is ensured. Both types of machines are used to transfer loads, typically on the top of pallets, in and out of an automatic warehouse system. When calculating the machine under the scope of EN 528:2008 [2], the manufacturer must refer to ISO 4308-Part1:2003 [1]. When designing a VTD according to EN 619:2002 + A1 [4], it is acceptable to use other recognized codes of practice, therefore the DIN 15020-Part1:1974 [4], may also be used. For both machines the design is usually done considering the most demanding classification mechanism to define the steel wire rope diameter, the pulleys diameter, and the drum diameter. However, the requirements of the standard for the steel wire ropes and pulleys design, may not be enough to achieve a high service life, as it will be shown with the case study calculation.

Fig. 1

Reeving system of the case study S/R machine. Extracted from KSC-PT technical documentation [5]. Reprinted with permission

Requirements of EN 580, EN619, DIN 15020 and ISO 4308, for Steel Wire Rope Lifting Appliances

The vertical transfer devices–VTDs—are under the scope of EN 619:2002 + A1:2010[3].¹ According to this standard one VTD is a device with raising and lowering movements of more than 200 mm in the path of conveyors, in which unit loads can be transferred from one defined level to one or more defined levels by a carrying element, refer to Fig. 2. This standard defines the requirements for the suspension elements of the VTD.

Fig. 2

VTD definition. Steel wire rope VTD designed by the document author for KSC-PT

The rail-dependent storage and retrieval equipment—S/R machines, commonly known as stacker cranes are under the scope of EN 528:2008[2],² refer to Fig. 3, which states that wire rope, drum and pulley diameters shall be calculated according to ISO 4308-1:2003 [1], and defines the minimum values to be considered.

Fig. 3

S/R machine. Double mast stacker crane designed with the contribution of the document author for KSC-PT

Table 1 presents a synthesis of the requirements for a steel wire rope reeving system, according to the mentioned standards.

Table 1 Requirements of EN 528:2008 [2] and EN 619:2002 [3] regarding steel wire ropes

Thus, the standard EN 528:2008 [2], for S/R machines, refers to the ISO 4308:2003 [1] for the drive group requirements. The standard EN 619:2002 + A1:2010 [3], for VTDs, only defines that recognized codes of practice shall be considered.

Diameter of the Rope, Drum, and Sheaves on a System Designed According to DIN 15020-Part 1:1974 and ISO 4308-1:2003

Figure 1 shows the case study reeving system of a S/R machine. The pulley size, drum diameter, and steel wire rope diameter were calculated according to ISO 4308-1:2003 [1] and DIN 15020-Part1:1974 [4], and the minimum values of the EN 528:2008 [2] were exceeded. All the requirements for all the components of the reeving system were fulfilled.

Table 2 presents the data for the case study S/R machine reeving system of Fig. 1.

Table 2 Data for calculation of the S/R machine reeving system

The requirements for a steel wire rope to be used in a VTD and a S/R machine are summarized in Table 1. According to EN 619:2002 + A1:2010 [3] and EN 528:2008 [2], the steel wire rope must have a tensile strength of individual wires equal or higher than 1570 N/mm², but not exceeding 1960 N/mm². The total number of wires shall be higher than 114. The steel wire rope with commercial name HD8K PPI [14] has 257 wires and tensile strength of individual wires of 1960 N/mm², therefore fulfilling the requirements, refer to Fig. 4 and Fig. 5. The name of this rope according to EN 12385–4:2002 [6] is 8xK26WS-ESWRC.

Fig. 4

Steel wire rope HD8KPPI data. Extracted from [14]. Reprinted with permission

Fig. 5

Steel wire rope HD8KPPI construction. Extracted from [14]. Reprinted with permission

Figure 6 explains the terminology of the elements of a steel wire rope. Figure 7 shows a non compacted steel wire rope. K means compacted steel wire rope, refer to Fig. 8. Figure 9 explains by itself the designation of the steel wire rope. ESWRC means that the rope core is enveloped with solid polymer, according to Fig. 10. A compacted steel wire rope is advantageous because of the increased filling factor, which decreases the coefficient C, thus decreasing the ${d}_{\mathrm{min}}$, according to formulae (5). The polymer enveloped rope core stabilizes the steel wire rope structure, acts as a shock absorber, and increases its fatigue life. The rope of this case study will be a Lang lay rope, Fig. 11. On a Lang lay rope the wires in strands and the strands of rope wind in the same direction. Lang lay ropes—zZ—have higher fatigue resistance than regular lay ropes. Regular lay ropes—sZ, Fig. 12, in which the wires wind in one direction and the strands in opposite direction, may be visually inspected, but on Lang lay ropes the internal wires usually break first, so they must be inspected magnetically. More information about steel wire ropes construction, common problems, maintenance, and handling may be found in references [7,8,9,10,11,12].

Fig. 6

Terminology of a steel wire rope elements. Adapted from reference[13]. Reprinted with permission

Fig. 7

Non-compacted steel wire rope [13]. Reprinted with permission

Fig. 8

Compacted steel wire rope [13]. Reprinted with permission

Fig. 9

Explanation of the steel wire rope name. Adapted from reference [13]

Fig. 10

Rope core enveloped with solid polymer [13]. Reprinted with permission

Fig. 11

Lang lay rope. Extracted from KSC-PT technical documentation [5]. Reprinted with permission

Fig. 12

Regular lay rope. Extracted from KSC-PT technical documentation [5]. Reprinted with permission

After some assessment of the system of Fig. 1, it is possible to observe that the total suspended mass is supported by $n_{{{\text{falls}}}}$ = 8 rope falls, in a differential system.

$$S = \frac{{\left( {\text{Deadload + Payload}} \right).g}}{{n_{{{\text{falls}}}} }}$$

(1)

Thus, from (1) the tension $S = 15{ }573{\text{ N}}$. The ${\text{Deadload}}$ is the load of the hoisting carriage plus the load handling devices (typically forks on S/R machines). The ${\text{Payload}}$ is the maximum load weight.

According to DIN 15020:1974 [4], the tension $S$ must be corrected taking in consideration the acceleration forces and the efficiency of the rope drive. Other correction factors shown on this standard are not applicable to S/R machines, since in this type of machines the hoisting carriage is guided along the mast by rollers (opposite from cranes where we have a hook). In a S/R machine, the acceleration force is only vertical. On appendix of this standard, a method is shown on how to calculate the efficiency of the rope drive, using formulae (2). Table 3 shows the values for the efficiency of the pulley block -$\eta_{F}$ that will be used to calculate the efficiency of the rope drive—$\eta_{S}$.

$$\eta_{S} = (\eta_{R} )^{i} .\eta_{F}$$

(2)

where

Table 3 Efficiency of the pulley block according to DIN 15020:1974 [4]

$\eta_{S}$: Is the efficiency of the rope drive.

$\eta_{R}$: Is the efficiency of a rope pulley. For a rope pulley with ball bearings $\eta_{R} = 0,98$

$i$: Number or fixed pulleys.

$\eta_{F}$: Efficiency of the pulley block.

$$S_{{\text{cor max}}} = \left( {\text{Deadload + Payload}} \right).\frac{{\left( {g + a_{v} } \right)}}{{\eta_{S} }}$$

(3)

where $a_{v}$ is the hoisting acceleration.

The reeving system should be analyzed as if it is divided in two. Each of them begins on the one of the hoisting gearmotors drums, refer to Fig. 1, and ends on one side of the compensating pulleys. There are $i$ = 3 fixed pulleys in each of these systems. The number of rope plies, meaning deviations, on the drum and on the hanging pulleys of the hoisting carriage (moving up and down) is $n$ = 3. The compensating pulleys are not to be considered in this assessment. So, by Table 3, $\eta_{F}$ = 0,98. From formulae (2) $\eta_{S}$ = 0,92 and from formulae (3) $S_{{\text{cor max}}}$ = 17 401 N.

The standard DIN 15020:1974 [4] does not take in consideration the difference on the nominal strength of the individual wires of the ropes for 5 m drive groups, and sets $c = 0,132$ for all of them, refer to Table 4. From formulae (4), $d_{{{\text{min}}}} = 17,4 {\text{mm}}$.

$$d_{{{\text{min}}}} = c.\sqrt {S_{{{\text{cor}}}} }$$

(4)

Table 4 Coefficient ${\varvec{c}}{ }$ according to DIN 15020:1974 [4]

ISO 4308-1:2003 [1], Sect. 6.3, defines that the $S$ value must be defined taking in account the efficiency of the rope reeving system, but does not give any input on how to calculate it. $S_{{{\text{cor}}}}$ value will be considered the same as the one calculated by the DIN 15020:1974 [4] on this document.

Regarding the $C$ value³, ISO 4308-1:2003 [1] defines it for one example with a 6-strand steel wire rope, on Table 1. However, the steel wire rope that is going to be used in this case study is 8 strands. For other types of ropes, refers to ISO 2408:1985 [14] where the values shown in Table 5 are found.

Table 5 Numerical values for $K$ and $K^{\prime}$, according to ISO 2408:1985 [15]

The steel wire rope of this case study has got fiber core, but it is compacted. A more accurate value for $K_{1}^{\prime }$ is shown on the most recent ISO 2408:2017 [15], $K1 = 0.330$,⁴

Table 6 Values for compacted strand wire ropes, according to ISO 2408:2017 [16]

The rope selection factor – $C$, is calculated by the formulae (5).

$$C = \sqrt {\frac{{Z_{p} }}{{K^{\prime } .R_{o} }}}$$

(5)

where

$C$: Is the rope selection factor (minimum).

$K^{\prime}$: Is the empirical factor for minimum breaking load of a given rope construction (according to Table 3 of ISO 2408:1985 [14]), or provided by the manufacturer.

$R_{o}$: Is the minimum tensile strength of the wire used in the rope (N/mm²).

$Z_{p}$: Is the practical utilization factor.

The $Z_{p}$ values are defined in Table 1 of ISO 4308-1:2003 [1], for each mechanism classification group. For the most demanding classification group M8,⁵$Z_{p} = 9$. From formulae (5), with $R_{o} = 1960 {\text{N}}/{\text{mm}}^{2}$ and $K^{\prime} = K^{\prime} = K1 = 0,330$, $C = 0,118$, and from formulae (4) $d_{{{\text{min}}}} = 15,6 {\text{mm}}$.

To calculate the minimum drum, pulleys,⁶ and compensating pulleys diameter, DIN 15020:1974 [4] considers the coefficients $h_{1}$ shown in Table 7, and the formulae (6). The coefficient $h_{2}$ depends on the number of alternating bending stresses—$w$. In each machine cycle, composed by a hoisting movement up and down, a drum contributes with $w = 1$, a pulley that deflects the wire rope in the same direction contributes with $w = 2$ and a compensating pulley contributes with $w = 0$. Refer to DIN 15020:1974 [4], for more details on this assessment. For this case study, analyzing Fig. 1, $w_{t} = 11$. According to Table 8, with $w_{t} > 10$, $h_{2} = 1,25$ for drums and sheaves, and $h_{2} = 1$, for compensating pulleys. The values for the diameters of the components of the system shown in Fig. 1 are obtained by using the formulae (6) with the coefficients from Tables 7 and 8.

$$D_{{{\text{min}}}} = h_{1} .h_{2} .d_{{\text{wire rope}}}$$

(6)

Table 7 Coefficients $h_{1} { }$ for calculation of the diameter of drums, pulleys, and compensating pulleys, according to DIN 15020:1974 [4]

Table 8 Coefficients $h_{2}$, for calculation of drums, pulleys, and compensating pulleys diameter, according to DIN 15020:1974 [4]

The diameters of the steel wire rope drive components are calculated according to ISO 4308-1:2003 [1], by using the formulae (7), and (8), with the factors shown in Table 9 and Table 10.

$$D_{1} = h_{{1^{\prime } }} .t.d_{{{\text{wire}}\;\;{\text{rope}}}}$$

(7)

$$D_{2} = h_{{2^{\prime } }} .t.d_{{\text{wire rope}}}$$

(8)

where 

Table 9 Selection factors for calculation of drums and sheaves diameter, according to ISO 4308-1:2003 [1]

Table 10 Rope type factor for calculation of drums and sheaves diameter, according to ISO 4308-1:2003 [1]

$D_{1}$: Is the minimum pitch circle diameter of the drum;

$D_{2}$: Is the minimum pitch circle diameter of the sheave;

$h_{1^{\prime } }$: Is the selection factor for the drum.

$h_{2^{\prime } }$: Is the selection factor for the sheave.

$t$: Is the rope type factor according to Table 10.

The steel wire rope of this case study is 8 strand and has got plastic impregnation, so $h_{1^{\prime } } = 25$, $h_{2^{\prime } } = 28$, and t = 0,95. With these coefficients and factors and formulae (7) and (8), the values of Table 11 were calculated.

Table 11 Calculation of diameter of the steel wire rope, drums, pulleys (sheaves), and compensating pulleys

Results: Steel Wire Rope Life Expectancy for the Case Study Reeving System

The Feyrer method [19] is going to be applied to estimate the steel wire rope life, considering that all the requirements from the previous standards have been fulfilled, and all the system was carefully designed.

The correction of the S value, with formulae (9), is detailed in the Feyrer reference [19]. The force factors and are shown in Table 12.

$$S_{{{\text{cor}}}} = \frac{Q.g}{{n_{t} }}.fs_{1} .fs_{2} .fs_{3} .fs_{4}$$

(9)

where

Table 12 Force factors according to Feyrer [19]

$Q$: Is the total load (kg)

$g$: Is the gravity acceleration (m/s²)

$fs_{1} \ldots .fs_{4}$: are the force factors according to Table 12.

$n_{t}$: is the number of load bearing wire ropes.

On the S/R machines and VTDs the hoisting carriage is guided by rollers, so $fs_{1} = 1.05$. $fs_{3} = 1.0$, because the sheaves are separated. The hoisting speed is 0,5 m/s, thus $fs_{4} = 1.1$. The rope efficiency factor—$fs_{2}$—is calculated by the ratios $\frac{{S_{{{\text{cor}}}} }}{{d_{{\text{wire rope}}}^{{2}} }}$ and $\frac{{D_{{{\text{sheave}}}} }}{{d_{{\text{wire rope}}} }}$, and formulae (13). The wire rope efficiency on one sheave – $\eta$ used for the calculation of the total efficiency of the rope drive—$\eta_{S}$ is shown in Table 13. Defensively, the value $\eta = 99,0$ was considered.

Table 13 Wire rope efficiency on one sheave – $\eta$, according to Feyrer [19]

According to Feyrer, the efficiency of the rope drive shall be calculated as follows.

$$\eta_{{{\text{stat}}}} = \eta^{{n_{{{\text{stat}}}} }}$$

(10)

$$\eta_{{{\text{hang}}}} = \frac{1 + \eta }{2}$$

(11)

$$\eta_{{\text{hang total}}} = \eta_{{{\text{hang}}}}^{{n_{{{\text{hang}}}} }}$$

(12)

$$\eta_{S} = \eta_{{{\text{stat}}}} .\eta_{{\text{hang total}}}$$

(13)

where

$\eta_{{{\text{stat}}}}$: Is the total stationary sheaves efficiency

$n_{{{\text{stat}}}}$: Is the total number of stationary sheaves, $n_{{{\text{stat}}}}$ = 3

$\eta_{{{\text{hang}}}}$: Is the hanging sheave efficiency

$\eta_{{\text{hang total}}}$: Is the total efficiency of the hanging sheaves

$n_{{{\text{hang}}}}$: Is the total number of hanging sheaves, $n_{{{\text{hang}}}} = 2$

$\eta$: Is the wire rope efficiency of one sheave, according to Table 13

$\eta_{S}$: Is the total efficiency of the rope drive

Considering $\eta = \frac{{99{\text{\% }}}}{{100{\text{\% }}}} =$ 0,99, and with the ISO 4308–1:2003 [1] values for the pulleys, sheaves, and steel wire ropes diameter, from formulae (10), $\eta_{{{\text{stat}}}} = 0,97$, from (3) $\eta_{{{\text{hang}}}} =$ 0,995, and from (12), $\eta_{{\text{hang total}}} =$ 0,99. The total efficiency of the rope drive is $\eta_{S} = 0,96$. In Table 14, $S_{{\text{cor max}}}$ is the tension on the steel wire rope when a load with maximum weight is on the hoisting carriage, and $S_{{\text{cor min}}}$ is the tension on the steel wire rope when there is no load on the hoisting carriage. The $S_{{\text{cor max}}}$ and $S_{{\text{cor min}}}$ values will be calculated through formulae (9), to build Table 14.

Table 14 Calculation of $fs_{2} {\text{ and}} S_{{{\text{cor}}}}$

This data are going to be used as input values on the calculation program developed by the Stuttgart University [20]. It is out of the scope of this document to dive deeply on the calculation, however for some clarification, the calculation program will compute the number of bending cycles by the formulae (14), with constants and endurance factors given has example in Tables 15 and 16.⁷

$$\log N = b_{0} + \left( {b_{1} + b_{3} .\log \frac{D}{d}} \right).\left( {\log \frac{S}{{d^{2} }} - 0,4.\log \frac{{R_{0} }}{1770}} \right) + b_{2} .\log \frac{D}{d} + \log f_{d} + \log f_{l} + \log f_{c}$$

(14)

where

Table 15 Example of constants $b_{0} { }$ to $b_{3}$ for discard number of bending cycles calculation for a given 8 strands steel wire rope, according to Feyrer [18]

Table 16 Example of endurance factors $f_{d} { }$, $f_{L} { }$ and $f_{c} { }$, for the discard number of bending cycles calculation for one 8 strands steel wire rope, according to Feyrer [19]

$D$: Is the sheave diameter (mm).

$d$: Is steel wire rope diameter (mm).

$R_{o}$: Is the minimum tensile strength of the wire used in the rope (N/mm²).

$S$: Is the rope tensile force (N).

The constants $b_{0} { }$ to $b_{3}$ and the endurance factors $f_{d}$, $f_{L}$ and $f_{c}$ are rope construction related and were gathered by experimentation. They can be found on reference [19], refer to Tables 15 and 16.

The values of the previous paragraphs are now used as inputs on the calculation program. As an example, in Table 17, the input data according to ISO 4308–1:2003 [1], see Table 11, is introduced for calculation of the number of working cycles $Z_{A10}$ with the maximum load on the hoisting carriage – $S_{{\text{cor max}}}$. $Z_{A10}$ is the number of hoisting cycles which, with a certainty of 95%, no more than 10% of the ropes have to be discarded. The bending length-$l$, is the length of the wire rope that, in this case study, runs in the higher number of sheaves, thus $l = 2 \times {\text{Hoisting stroke}}$, approximately, once it is a differential system.

Table 17 Inputs and results of the application of the calculation program [20]. Example: Calculation of the number of working cycles under the maximum load $S_{{\text{cor max}}}$, with the values of sheave diameter, wire rope diameter calculated according to ISO 4308, refer to Table 11

EN 528:2008 [2] does not define a minimum value for the steel wire rope service life. However, in complex systems like the one shown in Fig. 1, due to the requirement for low maintenance stopping times, the typical minimum expectation from the customer would be one year, but 2 years working in two shifts of 8 h, 5 days week would be a good target.

Considering that the S/R machine is with the maximum load 2/3 of the cycle time⁸ (combined cycle), $Z_{A10}$ is calculated with formulae (15). Table 18 summarizes the results from the application of the formulae (15), with the input values given by the calculation program [20]⁹.

$$Z_{A10} = \frac{{N_{{A10(S_{{\text{cor max}}} )}} . N_{{A10(S_{{\text{cor min}}} )}} }}{{N_{{A10(S_{{{\text{cor min}})}} }} .t_{{S_{{\text{cor max}}} }} + N_{{A10\left( {S_{{\text{cor max}}} } \right)}} .t_{{S_{{\text{cor min}}} }} }}$$

(15)

where

Table 18 Summary of  the results of the application of the Feyrer method for calculation of the number of  working cycles of a steel wire rope

$N_{{A10\left( {S_{{\text{cor max}}} } \right)}}$: is the number of working cycles $Z_{A10}$, under the maximum load $S_{{\text{cor max}}}$

$N_{{A10 (S_{{\text{cor min)}}} }}$: is the number of working cycles $Z_{A10}$, with no load on the hoisting carriage (only deadload) $S_{{\text{cor min}}}$

$t_{{S_{{\text{cor max}}} }}$: is the time fraction with maximum load $S_{{\text{cor max}}}$ (2/3).

$t_{{S_{{\text{cor min}}} }}$: is the time fraction without load $S_{{\text{cor min}}}$ (1/3).

$Z_{A10}$ (90% wire ropes will achieve this life before discard criteria)

$Z_{{{\text{Am}}}}$ (50% wire ropes will achieve this life before discard criteria)

Remark 1: According to Feyrer [18], the values of the table would need to be corrected considering deviations from the optimum design. These $F_{N1}$ to $F_{N4}$ correction parameters take in account a non-perfect lubrication, sheaves groove radius smaller than the defined one, for example. In this document it is considered that the design fulfilled all these requirements, so all the $F_{N} = 1.$

Remark 2: On this calculation it is considered that the drum diameter is equal to the sheave diameter. The minimum sheaves diameter is bigger than the minimum drum diameter, according to Table 11.

Conclusions

In this case study it was not possible to ensure the minimum number of cycles defined in ISO 4308-1:1986 with the application of the ISO 4308-1:2003 calculated steel wire rope diameter and sheaves diameter. Moreover, the minimum number of 43 200 cycles is very low in comparison with the duty cycles that the S/R machine may achieve working 2 years in 2 shifts of 8 h, 5 days a week.

The machine will probably not work these two daily shifts constantly with a 30 cycles/hour throughput, and the load on the hoisting carriage may not be always the maximum. However, the number of cycles $Z_{A10} =$ 27 192 is so far from the required 240 000, that it is possible to say that the required number of cycles will certainly not be achieved. The fact that the ISO 4308–1:2003 does not take in account the number of steel wire rope bendings on each lifting cycle, leads to these poor results on the rope life expectancy. Refer to DIN 15020-Part2:1974 [21] for more information about the discard criteria for a steel wire rope.

By the application of the DIN 15020:1974, the expected number of cycles $Z_{A10}$, was more than three times higher than the one that resulted from the application of the ISO 4308-1:2003. This happens due to the consideration of the factor $h_{2}$ = 1,25 on the sheave diameter calculation. Notice that the $R_{o}$ of the steel wire rope is not considered for the calculation of the $c$ parameter, for the most demanding mechanism classes. The $c$ value is the same for steel wire ropes with different $R_{o}$, and this value is bigger than the $C$ defined by ISO 4308-1:2003. As a result, the calculated steel wire rope diameter $d_{{{\text{min}}}}$ is higher than the one obtained from the application of ISO 4308-1:2003. However, this increased $d_{{\text{wire rope}}}$ will have a big economic impact on the machine, and the manufacturer may try to reach to a similar number of cycles by using other solutions with lower economic impact.¹⁰ Nevertheless, it was not possible to reach the $Z_{A10}$ = 240 000 cycles, but it is possible to admit that more than 50% of the ropes would reach 240 000 cycles before discard, since $Z_{{{\text{Am}}}} =$ 289 457. $Z_{{{\text{Am}}}}$, occurs before $Z_{10}$. $Z_{10}$, is the number of hoisting cycles which, with a certainty of 95%, no more than 10% of the ropes break. This means that it may be possible to estimate that 90% of the steel wire ropes would last the 2 years working 2 shifts of 8 h, 5 days a week, before breaking.

References like Feyrer and the new ISO 16625, currently under ballot, introduce methods to estimate the steel wire rope service life, so that is possible to study the impact on the life expectancy of the rope, of the improvements in the reeving system design. Feyrer, also allows a clearer determination of the $S$ value, setting clearer correction parameters $f_{s}$.