Problems related to the design of multi layer drums for ... · PDF fileInnovative ropes and rope applications 2 determination of the behaviour under load of multi-layer wound hoisting

OIPEEC Conference / 3rd International Ropedays - Stuttgart - March 2009

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P. Dietz, A. Lohrengel, T. Schwarzer and M. Wächter ODN 08xx Technical University of Clausthal, Fritz-Süchting-Institute of Mechanical Engineering

Problems related to the design of multi layer drums for synthetic and hybrid ropes

Summary

Rope drum and rope – as parts of a hoisting system, must constantly be improved and modified concerning rising standards. To fulfil the requirement of a further weight reduction of the system, high strength chemical-fibre (man-made fibre) ropes or compound constructions, so called hybrids, shall be used in future when there is a multilayer winding of the drum. Their rope characteristics, that are different from those of common ropes, cause an entirely different drum load, which urgently requires an adaptation of the existing calculation bases to the new rope types. This paper shall give a review on current projects on designing and dimensioning rope drums with a multi-layer winding with synthetic or hybrid ropes and gives an outlook on further required steps to the adaptation of the calculation processes. 1 Introduction The current valid and standardised dimensioning specifications of hoists are based on the classification of winding systems into time-based and load-based collectives, for which geometry, loading and life time of the ropes are the leading criteria for dimensioning. In order to increase the performance of the hoisting drum winding system while keeping the dimensions of the drum constant, the safe working capacity of the ropes was increased by the implementation of new rope-making techniques and innovative wire materials. The different rope characteristics such as bending stiffness and Poisson’s ratio led to a dramatic increase in the load on the winding drums and at the same time to new damage mechanisms. This has resulted in stronger and therefore heavier dimensioning of the hoisting drum elements. At the Institute of Mechanical Engineering a variety of ropes were tested during different research projects. Their characteristics were determined and the influence on the load conditions of the winding drum was analysed [1]. Furthermore a combined theory for the calculation of the load on the drum cylinder and end plate as a total system was developed, which shows the critical points in the transition area also a function of the stiffness of the drum cylinder and the flanged wheels (flanges) [2]. Further research work was the inclusion of partly-ductile deformations which result in a clear calculated increase of bearing strength and the development of a non-rotationally symmetric load model for the

Figure 1: Broken flange wheel.

Innovative ropes and rope applications

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determination of the behaviour under load of multi-layer wound hoisting drums [3]. On the basis of those papers it was possible to develop the existing calculation method towards a weight reducing winding drum dimensioning. However, the potential for weight reduction for a given combination of drum and rope is almost exhausted at 20%. The usage of new rope materials like synthetics or compound materials as an alternative to the pure wire rope is essential for a further optimisation of the mass/performance ratio of future hoisting drum winding systems and therefore also the realisation of ultra-light weight constructions (with weight reductions of far more than 20%) on the whole area of the conveyer technique. Today’s commercially produced high-tensile light weight fibres like Dyneema und Aramid [4], [5], [6] and [7] have the same tensile strength as steel wires while saving weight by a factor 6 to 8. Table 1 compares the characteristics of these fibres to steel wire.

Dyneema SK60 Aramid LM Steel wire

Density (g/cm3) 0.97 1.44 7.85

Tensile strength (N/mm2) 2700 2700 1770

Young’s modulus (N/mm2) 87000 58000 200000

Ultimate strain (%) 3.5 3.7 2.6

Table 1: Characteristics of fibres and steel wire [6].

The following calculation example clarifies the potential for weight reduction, which becomes usable by implementing synthetic ropes in cranes. A lifting rope with a diameter of 23mm has a specific weight of ca. 3 kg/m. With a length of 800 m – a common length for mobile cranes- the total weight is 2400 kg. Assuming, that a synthetic rope is at least five times lighter than the wire rope, the rope weight is reduced by 1920 kg. In comparison the absolute weight reduction for a fitting rope drum is 74 kg (with the assumption of a reduction by 20%). For this reason synthetic ropes are predestined for the mobile service, since a high traction force/weight ratio is required here. Furthermore the loads on the winding drums decrease because of the lower self-weight of the rope as well as the smaller bending stiffness compared to wire ropes. Light weight constructions will so be possible. Moreover, the by far higher flexibility of synthetic ropes allows a minimisation of the dimensions of hoisting drum winding systems. A D/d ratio of 12/1 up to 15/1 could be achieved by using synthetic ropes [8]. 2 Problems with the usage of synthetic or hybrid ropes The development of synthetic-based light weight ropes is still in the prototype state. For this reason there is only a small number of scientific results for synthetic ropes. Basically until now, only research was done on the area of the maximum tensile force and the number of bending over sheave fatigue cycles.


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For safe operation of those ropes and therefore as well the loaded drive element (i.e. drums) the exact knowledge of the specific rope characteristics is essential. A change of the rope elasticity in longitudinal and transverse direction directly affects the way in which the load is transferred into the drum body material and in the flanged wheels. The lack of verified technical expertises on the characteristics affecting drum load, like the Young’s modulus in axial and transverse direction makes a stress related and weight optimised design at this time impossible. The same facts are valid for the winding behaviour of those ropes and thus the stiffness of the rope on the multi-layer winding of the drum cylinder. The main aim of IMW’s research is to determine the impact of the different rope characteristics on the drum load by undertaking experimental and analytical analysis. The results shall be incorporated into the existing calculation and dimensioning bases.

2.1 Analytical model of the different rope characteristics While – by using a mechanical analogous model for the winding of a drum with a steel coil – the rope is considered to be a spring, the damping of the used fibre material has to be considered at the usage of synthetic or hybrid ropes. Figure 2 shows an analogous model at the winding of the turn j in the layer i for such a rope.

Figure 2: Analogous model of the rope-drum system at the winding with a synthetic rope for one turn

j in the layer i.

The behaviour of a synthetic rope in the system rope-drum can be demonstrated by a spring and a damping element. The forces on the analogous model are hence the rope tensile force Fsi and the radial force Fri. The equilibrium state of the rope can be described by Equation (1) and Equation (2).

(1)

(2)

(t)FxKdtdxη rii1i

i1i =+

(t)FyKdtdyη sii2i

i2i =+


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The radial force Fri does not occur immediately or suddenly as it is assumed with a steel cable, but increases to its maximum value over time. It depends on the rotation of the drum by the angle ϑi. The radial force can be expressed as in Equation (3).

tωr(t)F(t)F

iLi

siri ϑ

= (3)

Since the pressure on the cylinder in position zj acts as a local force, it can virtually be distributed on the cylinder according to the Fourier series (Equation 4). Figure 3 for example shows the pressure under the turn on position zj. The drum cylinder is deformed by the radial force as shown in Figure 4.

( )∑ ++=∞

=1

0 sincos2

)(k

kk kzbkzaazp (4)

Figure 3: Pressure on the drum cylinder in the first layer on a rope diameter ds = 14 mm and a tensile force Fs = 20 kN under the turn in the position zj, length of the drum cylinder L = 500 mm; synthetic rope.

Pres

sure

[N/m

m2 ]

Figure 4: Deformation of the rope cylinder under the pressure of the turn j; synthetic rope.

Def

orm

atio

n [m

m]

Position zj [mm]

Position zj [mm]


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The rope is deformed by the radial force in the transverse direction. Depending on the damping the radial force reaches its maximum after the time ϑi/ω, at the maximum deformation. Figure 5 shows the deformation in the transverse direction as a function of the damping. A clear bow is noticeable at high damping in the slope of the deformation in transverse direction.

Figure 5: Rope deformation in transverse direction; synthetic rope.

The delay in the deformation caused by the damping induces an energy loss in the rope. The loss during the winding of one turn over the angle ϑi is shown in Figure 6. Here the impact of the damping according to the energy loss is clearly illustrated.

Figure 6: Energy loss in a synthetic rope.


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The winding of a rope on position zj takes pressure off the turn in position zj-1 - the so-called ‘loss elimination effect’ [9]. For the synthetic rope the decay in the initial load depends on the damping and occurs just like the deformation in transverse direction with a time delay. The time delay, combined with the physical characteristics of a rope and respectively the drum cylinder (surface quality, coefficient of friction) will affect the loss-elimination process (release process) of a synthetic rope in a different way to that of the steel cable. Figure 7 shows the decay of the rope’s initial load within 8 ms as a function of the rope damping – assuming the rope will not slip. The slip behaviour of the rope will be determined by the surface characteristics of the rope with respect to the drum and the construction specifications concerning geometry of the groove, the turn distance and respectively the length of ascendancy and the parallel area.

Figure 7: Course of the rope load relieving on the position zj-1 in dependency of the damping,

synthetic rope.

2.2 Numerical analysis of the impact of different rope characteristics on the cylinder load

In order to determine the impact of the different rope characteristics and thus the arising drum load when using a synthetic rope for multilayer winding, numerical analysis was undertaken using a simplified FE-model. The model was broken down to a simple rope drum with a rope package that is assumed to be rectangular (idealised 5 rope layers). A constant rope tensile force of FS = 20 kN was assumed in the model. Different combinations from transverse- and longitudinal Young’s modulus were assigned. To investigate the impact of the drum stiffness in the model, the diameter ratio of the cylinder’s diameter to the rope’s diameter were varied with D/d = 24 and D/d = 17 (while keeping the rope’s diameter constant).


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Figure 8 shows the graphs of the arising flanged wheel deformation for a diameter ratio of D/d = 24 with different constant Young’s modulus in transverse direction ESQ and changing Young’s modulus in longitudinal direction ESL.

Figure 8: Flanged wheel deformation over Young’s modulus in longitudinal direction ESL; D/d=24.

A declining increase of the deformation is clearly recognisable for an increasing Young’s modulus in longitudinal direction ESL for all Young’s moduli in transverse direction ESQ. By comparing the lowest and the highest calculated Young’s modulus in transverse direction ESQ over the Young’s modulus in longitudinal direction ESL, there is reached approximately a doubling in the deformation of the end plates. The graphs of the deformation of the flanged wheels are identical for the smaller diameter ratio of D/d = 17. Deformations increase by factor 3 for all Young’s moduli in transverse direction ESQ. The same analysis was done for a constant Young’s modulus in longitudinal direction ESL for a changing the modulus in transverse direction ESQ. Figure 9 shows the calculated end plate deformations for the diameter ratio D/d = 24. There is a recognisable linear relationship in the calculation results between the flanged wheel deformation and the Young’s modulus in transverse direction ESQ. The highest deformation occurs for the lowest calculated Young’s modulus in the transverse direction, as for the analysis with variable modulus in the longitudinal direction. Figure 10 shows the radial flexural stress as a function of the rope’s Young’s modulus in longitudinal direction ESL for the diameter ratio D/d = 24. The graph for the radial bending stress for both diameter ratios shows similarities to the graphs of the flanged wheel deformations. The combination of the smallest Young’s modulus in transverse direction ESQ with the highest Young’s modulus in longitudinal direction ESL produces the highest deformations and therefore the highest occurring stress, too. The flexural stress is about 1/3 higher than for the diameter D/d = 17. The results of the numerical analysis show, that for a majority of combinations of the Young’s modulus in transverse and longitudinal direction, the flanged wheel deformations and the radial bending stress are much higher than with the usage of conventional wire ropes (cf. Figure 8 - Figure 10, value at ESQ = 1500 N/mm² and ESL = 120000 N/mm²). The Young’s moduli in transverse and longitudinal direction are notably reduced in comparison to the conventional rope.

-0,15

-0,1

-0,05

0

0,05

0,1

0,15

0 20000 40000 60000 80000 100000 120000

Longitudinal modulus ESL [N/mm²]

Defo

rmat

ion

[mm

]

ESQ = 400 ESQ = 600 ESQ = 800 ESQ = 1000 ESQ = 1500

0.15

0.1

0.05

0

-0.05

-0.1

-0.15


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The loads and deformations are mostly affected in a linear interrelationship by the Young’s modulus in the transverse direction. Furthermore the load increases for a decreased cylinder to rope diameter ratio (D/d).

Figure 9: Flanged wheel deformation over Young’s modulus in transverse direction ESQ; D/d=24

150

200

250

300

0 20000 40000 60000 80000 100000 120000

Longitudinal modulus ESL [N/mm²]

Stre

ss [N

/mm

²]

ESQ = 400 ESQ = 600 ESQ = 800 ESQ = 1000 ESQ = 1500

Figure 10: Radial bending stress at the flanged wheels over the Young’s modulus in longitudinal direction ESL; D/d=24.

2.3 Experimental analysis of rope characteristics The knowledge of the rope characteristics is very important for an exact dimensioning of a drum geometry as the rope’s longitudinal and transversal modulus have a strong influence on the rope package stiffness and thus on the drum’s loading. This is especially important in the case of multilayer winding. At the Institute of Mechanical Engineering two hybrid constructions were tested with regard to their rope characteristics during a research project (Figure 11). Several measurements with different longitudinal and transversal stress rates as well as different numbers of layers and layer arrangements were undertaken to determine the influence on the rope characteristics.

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-0,1

-0,05

0

0,05

0,1

0,15

200 400 600 800 1000 1200 1400 1600

Transverse modulus ESQ [N/mm²]

Defo

rmat

ion

[mm

]

ESL = 20000 ESL = 40000 ESL = 60000 ESL = 80000 ESL = 120000

0.15

0.1

0.05

0

-0.05

-0.1

-0.15


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Figure 11: Rope tensile force test stand for measurements of the rope characteristics.

The examined hybrid ropes are based on a widely used construction for hoisting ropes as they combine good flexibility because of their 8 outer strands with a high wear resistance because of the compaction of those strands. In the following a fibre core in the hybrid variants replaced the standard construction of the rope core (Figure 12). The cross-sectional area of this core amounts about 25% of the total cross-sectional area. The two examined variants have the same construction (based on a Turboplast) but a different fibre core material. The core materials are Aramid fibres with different mechanical characteristics. Those fibres have a very high tensile strength combined with a low density and a low strain. Compared to a common steel wire the characteristic values of the used fibre types are shown in Table 2. The main difference is the E-Modulus of the particular fibre.

Fibre type Tensile strength [MPa]

Breaking strain [%]

E-Modulus [GPa]

Density [g/cm³]

Standard Module (SM) 3250 3.7 75 1.44

High Module (HM) 3100 2.7 105 1.45

Wire 1770 2.6 200 7.85

Table 2: Comparison of fibre and wire characteristics [6].

As comparison for the determined characteristic values two common constructions for hoisting ropes are used: the PDD 1315 CZ and the PC EUROLIFT. These are full steel wire ropes with a different rope construction. All ropes have a nominal diameter of 23 mm and a minimum breaking load Fmin depending on the particular construction between 410 kN and 490 kN.


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The presented analysis refers in the first place to the determination of the rope’s transversal modulus ESQ as the rope’s longitudinal modulus ESL is determined and stated by the rope manufacturer when specifying the breaking load. In Figure 13 the particular transversal modulus depending on the longitudinal stress rate kL with a constant transversal stress rate kQ = 0.07 is illustrated. In the diagram an increase of the transversal modulus with an increase of the longitudinal stress rate with respect to the tensile force is shown for all examined ropes. The hybrid construction with the fibre core (SM) has the lowest transversal modulus in all measurements. The transversal modulus of the rope with the HM fibre core is at all measurement points 1.5 times higher than the standard variant. Of great significance is the fact that the determined transversal moduli of the hybrid

Figure 12: Cross section of the tested hybrid wire, left the core, right the complete rope

0

400

800

1200

1600

2000

0,0 0,1 0,2 0,3 0,4

Longitudinal stress rate KL

E SQ [N

/mm

²]

Turboplast SM Turboplast HM

PC Eurolift PDD 1315 CZ

Figure 13: ESQ as a function of kL; kQ = 0.07; 1. Layer.


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construction are close to those of the PC Eurolift construction (kQ = 0.07), which is a full steel wire rope construction. The PDD 1315 CZ has a much higher transversal stiffness than the Eurolift. Increasing the transversal stress rate to kQ = 0.1 leads to an almost identical pattern as in the previous statement. Because of the higher longitudinal pre-stressing and thus a compaction of the rope’s cross-sectional area, the determined transversal moduli are 25 to 35% higher than with a transversal stress rate of kQ = 0.07. In Figure 14 the particular transversal modulus depending on the number of layers with a constant transversal stress rate of kQ = 0.07 is illustrated.

In general, a declining decrease of the stiffness with a constant increase of the number of layers can be detected at the layer-related demonstration of the transversal modulus. It will lead to a constant value with higher number of layers. The differences concerning the transversal stiffness especially in the first layer diminish with an increase in the number of layers, thus there is just a small variation from the third layer on. In this case the determined transversal moduli with kQ = 0.1 are almost identical to those before. The transversal stiffnesses of the two hybrid constructions are also almost identical in higher ranges of layers of the examined transversal stress rates. The higher longitudinal pre-stressing leads to a higher transversal modulus in the first two layers (analogy to the examination of one layer). The determined values for both rope constructions are in the usual range for those rope cross-sectional areas and constructions [1], [2]. 3 Conclusion and outlook The article shows that synthetic or hybrid ropes – as running ropes – can push the light weight constructions on the area of hoisting devices, last but not least due to

0

400

800

1200

1600

2000

0 1 2 3 4 5

Layer number

E SQ [N

/mm

²]

Turboplast SM Turboplast HM

PC Eurolift PDD 1315 CZ

Figure 14: ESQ in dependence of the layer number; kL00.2; kQ = 0.07


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their weight advantage in comparison to wire ropes with the same load capacity. There are only a few scientific researches done on that application; the problem of a multilayer winding was not investigated yet. This lack of information prevents a wide industrial use of those ropes as running ropes. The numerical and analytical analyses resulted that the load behaviour of the rope drums changes when used with synthetic ropes. A reduction in the Young’s modulus in transverse direction results in an increase of the load in the drum flanges on the one hand, while on the other hand the load on the drum cylinder is reduced. Furthermore an energy loss, which is converted to heat, is induced in the system by the damping in the synthetic ropes. All those effects must be considered in the existing dimensioning models, which finally allow a stress related, weight optimised drum design for the usage of synthetic or hybrid ropes. The performed experimental examinations for measuring rope characteristics have shown that using the hybrid constructions with different fibre material leads to a reduced transversal modulus because of the fibre core. Furthermore one can get into the range of normal wire rope constructions by varying the fibre material. Because of this alteration in the rope characteristics there is also a changing of the drum’s loading behaviour. Currently on the Institute of Mechanical Engineering experimental measurements on a 5 layer winding (Figure 15) are carried out for a hybrid wire rope in order to validate the theoretical models. Figure 16 shows the 32 applied strain gauges with the cabling inside the test drum to measure the axial and tangential elongations.

Figure 16: Applied strain gauges at the test drum

Figure 15: Hybrid construction on test stand


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Figures 17 and 18 show examples of the tangential stress and axial stress variation over the time during the test run for a 23 mm steel rope. In both an increasing stress pattern over the test time is visible in every layer. At higher layer numbers the increase of the stress under constant tensile force reduces due to different relaxation effects [2]. The results of this measurement are the basis for the running comparison with the hybrid wire rope.

Figure 17: Characteristics of the measured tangential stress.

Figure 18: Characteristics of the measured axial stress.

-350

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0

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00:00 01:26 02:53 04:19 05:46 07:12 08:38 10:05 11:31 12:58 14:24 15:50 17:17 18:43

time [mm:ss]

stre

ss [N

/mm

2 ]

1st layer

2nd layer

3rd layer

4th layer 5th layer

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-20

-10

0

10

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00:00 01:26 02:53 04:19 05:46 07:12 08:38 10:05 11:31 12:58 14:24 15:50 17:17 18:43

time [mm:ss]

stre

ss [N

/mm

2 ]

1st layer 2nd layer 3rd layer 4th layer 5th layer


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4 References [1] Henschel, J. Dimensionierung von Windentrommeln, Dissertation TU Clausthal,

Verlag und Vertriebsgesellschaft mbH, Düsseldorf, 2000. [2] Mupende, I. Beanspruchungs- und Verformungsverhalten des Systems

Trommelmantel – Bordscheiben bei mehrlagig bewickelten Seiltrommeln unter elastischem und plastischem Werkstoffverhalten, Dissertation, TU Clausthal, Curvillier Verlag Göttingen, 2001.

[3] Otto, St. Ein nicht-rotationssymmetrisches Belastungsmodell für die Ermittlung des Beanspruchungsverhaltens mehrlagig bewickelter Seiltrommeln, Diss. TU Clausthal 2003.

[4] Jacobs, M. and Dingenen, J. Zugkräftig. Leichtfasern für Hochleistungsseile, Draht Welt Heft 3, 1991.

[5] Rebel, G., Verreet, R. and Ridge, I.M.L. Lightweight ropes for lifting applications, in I.M.L. Ridge ed. Proceedings of the OIPEEC Conference “Trends for Ropes: design, application, operation”, Athens, Greece 27th - 28th March 2006, pp 33-54, ISBN: 978-0-9552500-0-2.

[6] Ridge, I.M.L., O’Hear, N., Verreet, R., Grabandt, O. and Das, C.A. High strength fibre cored steel wire rope for deep hoisting applications, in I.M.L. Ridge, ed., Proceedings of the OIPEEC Conference “How to get the most out of your ropes” Johannesburg, South Africa, September 2007, ODN 0820, 225-240, ISBN: 978-0-9552500-1-9.

[7] O'Hear, N., Grabandt, O., Hobbs, R.E. Synthetic fibre ropes for mine winding, in: I.M.L. Ridge, ed, Proceedings of the OIPEEC Conference “Trends for Ropes: design, application, operation”, Athens, Greece 27th - 28th March 2006, pp 17-32, ISBN: 978-0-9552500-0-2.

[8] Foster, G. New fibre rope technologies drive increased applications, Sea technology Heft 7, 1989.

[9] Dietz, P. Ein Verfahren zur Berechnung ein- und mehrlagig bewickelter Seiltrommeln; Dissertation, TH Darmstadt, Darmstadt, 1971.

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Problems related to the design of multi layer drums for ... · PDF fileInnovative ropes and rope applications 2 determination of the behaviour under load of multi-layer wound hoisting