Winches and Reels: Tension in Line and Pressure on the Drum and Flanges

Study on the loads in winches and reels systems resulted from the tension in lines Draft version (2013-02-17) Marius Popa, MRINA, CEng, Ph.D. ([email protected]) Important Note: This document is a draft issued for the purpose of peer review from other engineers. The paper is not final yet therefore the use of this document is on the risk of the reader. A. 1.

The estimation of the tension in lines. The estimation of the pressure on the drums General equations

The scope of this paper is to study the influence of friction and eventually the influence of the line’s rigidity for the variation of tension in the line and the value of pressure on the drum. T= pi = µ= Pp = n= l= D1 = Ri=

tension in line pressure in each layer friction coefficient product pitch the number of layers in radial direction the number of layers along the drum the external diameter = drum diameter + n*Pp contribution of layer i to the total radial pressure on the drum

An infinite small segment dsi=Di/2*dφ is i=can be isolate from the line’s radial layer i. The loads acting on this segment are shown in Figure 1 below. Figure 1 – Loads acting on the line’s radial layer i segment dsi=Di/2*dφ

The segment is in equilibrium therefore the equations can be analysed. For vertical direction the equilibrium equation is pi*dA = pi-1*dA + (2*Ti+dTi)*sin(dφ/2) Assuming that dTi*sin(d φ/2) is very small (pi-p1-1)*dA = 2*Ti*sin(dφ/2) Assuming dφ is small => 2*sin(dφ/2) = dφ (pi-pi-1)*dA = Ti* dφ

=> => => [eq 1]

For horizontal direction some notations are proposed together with the equilibrium equation:

µ*pi-1*dA = Ff-(i-1) µ*pi*dA = Ff-i Ti+Ff-i= Ti+dTi+Ff-(i-1) => Ff-i – Ff-(i-1) = dTi => -µ*(pi-pi-1)*dA = dTi From Eq 1 and 2 => -µ*Ti* dφ = dTi

[eq 2] [eq 3]

Integrating Equation 3 => T= T0*e-µφ

[eq 4]

For φ=0 T is the puling at the free end => T0 is the puling at the free end. It is interesting to note that tension is decreasing with the increasing of φ because the friction consumes the tension. For the one layer spooled on the drum at the free end the pressure can be deduced as: p1*dA = 2*T* sin(dφ/2) and having dA= dφ*D1/2*Pp => p1*dφ*D1/2*Pp = T* dφ => p1 = 2*T/D1/Pp

=> [eq 5]

This formula can be deduced from [1] Ch. 2 Sec. 3 B.207 and 208. Considering dA= dφ*Di/2*Pp Equation 1 become: (pi-pi-1)* dφ*Di/2*Pp = T0*e-µφ* dφ (pi-pi-1) = 2* T0*e-µφi/Di/Pp Where Di= D1-(i-1)*Pp

=> [eq 6]

For multi layers the formulas in Equations 7 apply: p1= 2* T0*e-µφ1/D1/Pp (p2-p1)= 2* T0*e-µφ2/D2/Pp 2* T0*e-µφ3/D3/Pp (p3-p2)= … (pi-pi-1)= 2* T0*e-µφi/Di/Pp (pi+1-pi)= 2* T0*e-µφ(i+1)/Di+1/Pp … (pn-1-pn-2)= 2* T0*e-µφi/Dn-1/Pp 2* T0*e-µφ(i+1)/Dn/Pp (pn-pn-1)=

=> => =>

[eq 7.1] [eq 7.2] [eq 7.3]

=> =>

[eq 7.i] [eq 7.i+1]

=> =>

[eq 7.n-1] [eq 7.n]

Summing up the Equations 7 results that pn or the pressure at drum pdrum is: pdrum = 2 *

T0 e − µ *(ϕ 0 + 2*π *l *(i −1)) * ∑in=1 Pp D1 − (i − 1) * Pp

[eq 8]

where φi+1= φi + 2*π*l It is useful to note that the equation 7.i can be identified as the pressure contribution of layer i (Ri) to the total pressure on drum. It is interesting to note that the ratio between the contributions of each layer is quasi constant: Ri/Ri+1 = (pi-pi-1)/(pi+1-pi) = eµ*2π*l*Di/Di+1 Ri/Ri+1 = eµ*2π*l*(D1 – (i-1)*Pp)/(D1-i*Pp) If Pp/D1 = α then

=>

Ri/Ri+1 = eµ*2π*l*(1 – (i-1)*α)/(1-i*α)

[eq 9]

In the assumption that the diameter variation doesn’t make a significant contribution for Ri (the coefficient of diameter may increase on a rate significantly lower than the decreasing due to friction effect) the Equation 8 become: pdrum =

2 * T0 n −1 − µ *2*π *l *(i −1) * ∑e D1 * Pp i =1

[eq 10]

In this assumption the ratio between the contributions of each layer is constant and functions only of friction and the number of layers along the length of the drum: Ri/Ri+1 = (pi-pi-1)/(pi+1-pi) = eµ*2π*l [eq 11] This last approach is a development of the works in [2]. The variation of the pressure between layers with the diameter is considered also in [4] together with the self-weight. The self-weight is not considered in this approach because a separate application of this load would allow the correction with the dynamic involved by the installation on board of floating units (ships). The approach in [4] seems to not account the friction. 2.

Experiment by others

An experiment assumed relevant for this study is presented in [3] for a winch/rope arrangement. In [3] Figure 17 the variation of tangential stresses measured for a drum (assumed as hoop stresses) is presented. As known the hoop stress is direct proportional with the pressure on drum therefore the in the following logic the values of stress in the diagram are assimilated with drum pressures. The values read from the diagram can be reasonable approximated with the values below: layer R dR dRi/dR(i+1)

1 100 100

2 180 80 1.25

3 224 64 1.25

4 295 51 1.25

5 336 41 1.25

In the logic of Equation 11 results: eµ*2π*l = 1.25 => µ*l= ln(1.25)/2/π = 0.035 From [3] the cable diameter is declared 23 mm arranged on 5 layers. From Figure 15 the characteristics of the arrangement can be approximated as followings: • number of layers on length can be approximated to about 40 leading to friction coefficient of 0.0009 • the drum length about 40*0.023= 0.92 m say 1.0 m and proportional the outer diameter about 0.5 m. In this case the drum diameter results 0.5 – 2*(5*0.023)= 0.27 m. Using these values in Equations 10 and 11, the ration pdrum/p1 are computed in Table 1: Table 1 The only input value is friction coefficient µ= 0.0009

layer-n 1 2 3 4

layers-l 1 1.000 1.994 2.983 3.966

2 1.000 1.989 2.966 3.933

3 1.000 1.983 2.950 3.900

4 1.000 1.978 2.933 3.868

5 1.000 1.972 2.917 3.836

10 1.000 1.945 2.838 3.682

40 1.000 1.798 2.434 2.941

5

4.944

4.889

4.835

4.781

4.729

4.480

3.346

Using these values in Equations 8 and 9 (the effect of diameter effect included), the ration pdrum/p1 are computed in Table 2.1: Table 2.1 The only input values are: friction coefficient µ= 0.0009, D-drum= 0.270 m, Outside diameter D1= 0.500 m, product diameter Pp= 0.023 m, number of layers in radial direction n=5, number of layers along the length of the drum l=40

D-factor Layer-n 1.000 0.908 0.816 0.724 0.632

1 2 3 4 5

Layers-l 1 1.000 2.095 3.307 4.665 6.212

2 1.000 2.089 3.287 4.622 6.134

3 1.000 2.083 3.267 4.580 6.059

4 1.000 2.077 3.248 4.539 5.984

5 1.000 2.071 3.229 4.498 5.911

10 1.000 2.041 3.135 4.301 5.563

40 1.000 1.878 2.658 3.359 3.999

A better correlation with the experimental values is achieved if the friction coefficient is increased to 0.0013 – see Table 2.2 Table 2.2 The only input values are: friction coefficient µ= 0.0013, D-drum= 0.270 m, Outside diameter D1= 0.500 m, product diameter Pp= 0.023 m, number of layers in radial direction n=5, number of layers along the length of the drum l=40

D-factor Layer-n 1.000 0.908 0.816 0.724 0.632

1 2 3 4 5

Layers-l 1 1.000 2.092 3.298 4.646 6.177

2 1.000 2.083 3.270 4.585 6.067

3 1.000 2.075 3.242 4.525 5.959

4 1.000 2.066 3.214 4.466 5.855

5 1.000 2.057 3.187 4.409 5.752

10 1.000 2.015 3.056 4.137 5.278

40 1.000 1.794 2.432 2.950 3.378

1st Preliminary conclusions Taking into account the results below it is difficult to assess based on the information in [3] if the influence of diameter can be ignored or not. In any case, the good relation between the values resulted from experiment and the theoretical values demonstrate that the relations in Equations 8 to 11 are valid. It can be said that the Equations 8 and 9 are more general and providing more conservative results therefore more recommended. However the Equations 10 and 11 are simpler and requests no information about the geometrical characteristics of the arrangement therefore may represent a reasonable initial approximation. It is also interesting to note that: • The very small friction coefficient resulted from the logic above. Values like 0.0009 or 0.0013 are very small in comparison with the usual frictions coefficients (in the range of 0.05 to 0.30) however may have sense in the assumption of greased wires. • The inclusion of the diameter effect leads to an about 50% increase of friction coefficient for same pressure on the drum.

•

[1] Ch. 2 Sec. 3 B.513 bases the rope anchorage design (for winches) on a coefficient of friction µ= 0.10. This value is 100 larger than the values deduced from the experiment in [3].

4.

Application of formula for Reels

A typical offshore reel may have the drum diameter of 6.0 m and flange diameter of 10.0 m, the drum length of 5.0 m. The number of layers may vary among 10 to 50 along the drum and among 4 to 20 in radial direction. If Pp is 0.1 m the n and l values are computed as 20 and 50. The results for Equation 8 (relative to the value of pressure at the outmost/first layer) and typical reel dimensions and pp=0.1 m, µ= 0.10, n= 20 and various values of l up to 50 are presented the Table 3.1 below. Table 3.1 Layers-l Layer-n

1

2

3

4

5

10

50

1

1.000

1.000

1.000

1.000

1.000

1.000

1.000

2

1.544

1.290

1.155

1.083

1.044

1.002

1.000

3

1.841

1.375

1.179

1.089

1.046

1.002

1.000

4

2.002

1.399

1.183

1.090

1.046

1.002

1.000

5

2.090

1.406

1.183

1.090

1.046

1.002

1.000

6

2.138

1.409

1.183

1.090

1.046

1.002

1.000

7

2.165

1.409

1.183

1.090

1.046

1.002

1.000

8

2.179

1.409

1.183

1.090

1.046

1.002

1.000

9

2.187

1.409

1.183

1.090

1.046

1.002

1.000

10

2.191

1.409

1.183

1.090

1.046

1.002

1.000

11

2.193

1.409

1.183

1.090

1.046

1.002

1.000

12

2.195

1.409

1.183

1.090

1.046

1.002

1.000

13

2.195

1.409

1.183

1.090

1.046

1.002

1.000

14

2.196

1.409

1.183

1.090

1.046

1.002

1.000

15

2.196

1.409

1.183

1.090

1.046

1.002

1.000

16

2.196

1.409

1.183

1.090

1.046

1.002

1.000

17

2.196

1.409

1.183

1.090

1.046

1.002

1.000

18

2.196

1.409

1.183

1.090

1.046

1.002

1.000

19

2.196

1.409

1.183

1.090

1.046

1.002

1.000

20

2.196

1.409

1.183

1.090

1.046

1.002

1.000

The results for Equation 10 (ignoring the effect of diameter variation), µ= 0.10, n= 20 and various values of l up to 20 are presented the Table 3.2 below. The results are relative to the value of pressure at the outmost/first layer. Table 3.2 Layers-l Layer-n

1

2

3

4

5

10

50

1

1.000

1.000

1.000

1.000

1.000

1.000

1.000

2

1.533

1.285

1.152

1.081

1.043

1.002

1.000

3

1.818

1.366

1.175

1.088

1.045

1.002

1.000

4

1.970

1.389

1.178

1.088

1.045

1.002

1.000

5

2.051

1.395

1.179

1.088

1.045

1.002

1.000

6

2.094

1.397

1.179

1.088

1.045

1.002

1.000

7

2.117

1.398

1.179

1.088

1.045

1.002

1.000

8

2.130

1.398

1.179

1.088

1.045

1.002

1.000

9

2.136

1.398

1.179

1.088

1.045

1.002

1.000

10

2.140

1.398

1.179

1.088

1.045

1.002

1.000

11

2.141

1.398

1.179

1.088

1.045

1.002

1.000

12

2.142

1.398

1.179

1.088

1.045

1.002

1.000

13

2.143

1.398

1.179

1.088

1.045

1.002

1.000

14

2.143

1.398

1.179

1.088

1.045

1.002

1.000

15

2.143

1.398

1.179

1.088

1.045

1.002

1.000

16

2.143

1.398

1.179

1.088

1.045

1.002

1.000

17

2.144

1.398

1.179

1.088

1.045

1.002

1.000

18

2.144

1.398

1.179

1.088

1.045

1.002

1.000

19

2.144

1.398

1.179

1.088

1.045

1.002

1.000

20

2.144

1.398

1.179

1.088

1.045

1.002

1.000

It can be observed that for larger friction coefficients (about 100 times more than resulted from [3]) the hypothesis that diameter variation may not be significant is confirmed by the results Tables 3.1 and 3.2. Moreover it can be observed that for friction coefficients in the range of 0.10 and number of layers along the drum l>5 the difference of pressure between layers (pressure increase) tend to 0 after the 2nd radial layer. A sensibility study was carried out for friction coefficient (µ) based on Equations 8 and 9. The results relative to the value of pressure at the outmost/first layer are presented only for the radial layers n= 2 (Table 4.1 and Figure 4.1) and n= 5 (Table 4.2 and Figure 4.2). For these positions [1] indicate amplifications relative to the value of pressure at the outmost/first layer of 1.75 respectively 3.0. 2nd Preliminary conclusions The values in Tables 4.1 and 4.2 suggest that for friction coefficients considered usual (µ=0.10) or quite low (µ=0.05) and more than 10 layers along the drum, the pressure on the drum might be just slightly larger than the pressure generated by the outmost radial layer (about 5% increase or no increase). Unfortunately typical values for the friction coefficients of the offshore products transported on offshore reels were not available therefore it is difficult make a comparison among the typical values resulted from the codes (normally designed for winches and wire ropes) and the values resulted for reels drums in the assumptions of this paper. Table 4.1 and Figure 4.1 – Variation of drum pressure with friction coefficient (without the effect of diameter) Layer-l layer 2 2 2 2 2 2

Friction 0.001 0.01 0.02 0.05 0.10 0.20 code

1 2.014 1.939 1.882 1.730 1.533 1.285 1.750

2 2.008 1.882 1.778 1.533 1.285 1.081 1.750

3 2.001 1.828 1.686 1.390 1.152 1.023 1.750

4 1.995 1.778 1.605 1.285 1.081 1.007 1.750

5 1.989 1.730 1.533 1.208 1.043 1.002 1.750

10 1.958 1.533 1.285 1.043 1.002 1.000 1.750

50 1.745 1.043 1.002 1.000 1.000 1.000 1.750

2.250 2.000 1.750 1.500 1.250 1.000 0

5

10

15

20

25

30

35

40

45

50

Table 4.2 and Figure 4.2– Variation of drum pressure with friction coefficient (with the effect of diameter) Layer-l layer 5 5 5 5 5 5

Friction 0.001 0.01 0.02 0.05 0.10 0.20 code

1 5.147 4.427 3.951 2.938 2.051 1.395 3.000

2 5.082 3.951 3.219 2.051 1.395 1.088 3.000

3 5.018 3.553 2.700 1.624 1.179 1.024 3.000

4 4.955 3.219 2.326 1.395 1.088 1.007 3.000

5 4.894 2.938 2.051 1.262 1.045 1.002 3.000

10 4.603 2.051 1.395 1.045 1.002 1.000 3.000

50 3.025 1.045 1.002 1.000 1.000 1.000 3.000

5.500 5.000 4.500 4.000 3.500 3.000 2.500 2.000 1.500 1.000 0

5.

5

10

15

20

25

30

35

40

45

50

Spring (straightening) effect

One effect was neglected in the general equation in Section 1 and this is the possible spring or straightening effect of the line. This effect represents the tendency of the line to oppose deformation and come back to the straight line. Obviously this effect is not important for soft lines but might be important for the lines having increased rigidity. For example the combination of very soft line and significant friction keep the product on the cotton reels but a combination of small friction (greased lines to avoid overheating due to the friction) and increased rigidity (due to the high loads supported by the line) can generate problems for the subsea lifting arrangements [6].

It is assumed that the bending of ds= D/2*dφ length of product request of the pressure ps (spring pressure). For a simple supported beam length ds, loaded uniform over the length with line load Pp*ps, the total deflection is the sum of bending deflection and shear deflection, maximum in the mid of the length. The total deflection is obtained from [5].4.10.1.7 as: w-total = w-shear + w-bending = (Pp*ps)*ds2/(8*G*As) + 5*(Pp*ps)*ds4/(384*E*Iy) Equation 13.1 can be re-write using the notation: 1/(8*G*As )= shear characteristics of the line ks= kb= 5/(384*E*Iy)= bending characteristics of the line ds= Di/2*dφ w-total = Di/2(1- cos(dφ/2))= Di/2*2*sin2(dφ/4)= Di*dφ2/16 = (Pp*ps)* Di2*dφ2/4 *(ks+ ds2*kb) => ps= 1/4/Di/Pp/(ks+ ds2*kb) It is normally acceptable to approximate ks+ ds2*kb as ks so ps= 1/4/Di/Pp/ks = 2*G*As/Di/Pp= 2*Ks/Pp/Di [eq 13] where is a characteristic of the shear rigidity of the line (for a compact steel section Ks= G*As). Note: The approach above is an attempt to approximate the pressure ps requested to compensate the spring effect. The following logic can be applied for a general value ps with the formulae corrected in consequence. The spring force (ps*dA) is included in the equilibrium equation for vertical direction (Equation 1) (pi-pi-1)*dA = Ti* dφ - ps*dA= Ti* dφ - 2*Ks/Pp/Di*Pp*Di/2*dφ (pi-pi-1)*dA = Ti* dφ - Ksdφ [eq 14] Equation 14 is used in the equilibrium equation for horizontal direction -µ*(pi-pi-1)*dA= dTi From Eq 1 and 2 => -µ*(Ti-Ks)* dφ = dTi or dTi/dφ = -µ*Ti + µ*Ks In order to integrate this equation a substitution of variable is made as followings: z= -T+Ks Due to the fact that Ks is constant dz/dφ = - dT/dφ so Equation 15 become: dz/dφ = -µ*z integrated as: z= w*e-µ*φ = -T+Ks therefore T= -w*e-µ*φ +Ks For φ = 0 (free end) equation 16 become T0= -w+Ks => w= Ks-T0 => T= (T0-Ks)*e-µ*φ +Ks Considering dA= dφ*Di/2*Pp Equation 14 become: (pi-pi-1)* dφ*Di/2*Pp = (Ti-Ks)*dφ = (pi-pi-1)* Di/2*Pp = (Ti-Ks) = (T0-Ks)*e-µφi (pi-pi-1) = 2*(T0-Ks)/Pp/Di*e-µφi

[eq 2] [eq 15]

[eq 16]

=> [eq 17]

Summing Equation 17 − µ *(ϕ 0+ 2*π *l*( i −1)) T0 − K s n e pdrum = 2 * * ∑ i=1 Pp D1 − (i − 1) * Pp

[eq 18]

It is noted that the term representing the force term makes the difference between equations 8 and 18. The direct conclusion of this equation is that the spring effect will decrease the tension in the line and in consequence the pressure on the drum. However the recent incidents and investigation of the deep subsea lifting arrangements [6] having the lines more rigid than the arrangements for lifting in air suggest that the effect is opposite.

In my opinion the only possible explanation still in coherence with the formulae 18 is the fact that a more rigid line leads to smaller friction coefficient (rigid lines means smaller contact areas between lines). It is obvious that a reduction with 50% of the force term leads to 50% reduction of the pressure on the drum. The estimation of the effect of friction coefficient variation is more complex therefore a numeric approach was used based on the equation not considering the effect of diameter. The relative pressure computed for the radian layer 5 (40 layers along the drum) and µ= 0.0009 is 3.346. The variation of the relative pressure with friction for the position above is provided below: µ= 0.000675 (75%) 3.665 +9.5% µ= 0.00045 (50%) 4.039 +20.7% µ= 0.000225 (25%) 4.480 +33.4% µ= 0.000 (0%) 5.000 +49.4% The variation is more significant if the number of layers in radial direction increases. The initial value for µ= 0.0009 is 4.886 µ= 0.000675 (75%) 6.193 +26.7% µ= 0.00045 (50%) 8.377 +71.4% µ= 0.000225 (25%) 12.319 +252% µ= 0.000 (0%) 20.000 +409% It is interesting to note that the reduction of the friction coefficient might be the result of well-greased lines. Well-greased lines are normal for subsea operations in order to minimize the amount of the heat dissipated as the effect of friction. However, as can be observed, the reduction of the heat generated by friction might means more load on the drum therefore the engineers might need to decide what effect among these two has a higher risk or cost and to work in that direction. Information received from industry [7] proposes an alternative method to minimize the pressure on the drum for the deep subsea arrangements: the spooling of the first layers on the drum with a reduced tension. It is supposed that these first layers will act like a protection cage for the drum. Equation 19 show that spooling with a tension close to the line’s spring (straightening) characteristic may generate less pressure on the drum or even if the tension goes below this value these layers may add an negative addition to the drum pressure somehow acting act indeed as protection cage. 3rd Preliminary Conclusion A more rigid line will reduce the basic tension in the line proportional with the rigidity. However this reduction of load can be compensated and overcome by the decrease of friction between layers as effect of the same increase in rigidity. The relation between the increasing of line rigidity and the reduction of friction coefficient between lines is not available. In consequence it is considered that are no sufficient data available to validate these equations and deductions therefore sound final conclusions are not possible at this stage.

B.

The estimation of the effect of elasticity of line and flanges for the loads on reel’s flanges

By tradition, the requirements in [1] for the winches drums are used for the design of the offshore reels. However, it was noted that the offshore reels for transport of pipes, cables or umbilicals have some important difference to the winches: - The reel’s flange is more elastic than the winch flange - The reel’s product (pipes, cables or umbilicals) may have transverse rigidity smaller than the wire ropes usually loading the winches. These differences may be very important for the design of the flanges of the offshore reels.

The scope of this paper is to study the influence of these factors in relation with design hypothesis in [1] used on a regular basis by the industry for the design of the reels. The phenomenon involved in this process are quite complex therefore an analytic approach (as in Part A of this study) was considered not effective for a brief study like this. In consequence a numeric approach by FEM was considered sufficient to provide a general estimation of the behaviour of these systems. However, the computational limitations (the FEM file used for one simulation is about 8 Mb) and the lack of information about the characteristics of the line/product spooled on the reels may limit the results of this study. Some very simple 2D sticks models (DNV Nauticus 3D Beam software) are done simulating a section with a plan along a radial and the longitudinal central axis of a reel. Due to modelling restrictions only 5 layers are modelled along the drum’s length and 10 layers in radial direction. The product is simulated as a ring of 100 mm with various wall thicknesses. The contact between the rings and between the rings and the flange’s spoke is modelled by short rigid dummy beams (about 5 mm long) acting only compression. Two variants of models were done simulating the two classic arrangements of the layers: - The rectangular cell arrangement (figure 5.1) - The triangular cell arrangement (figure 5.2) For each arrangement 6 rigidities of the product (wall thicknesses) and 5 rigidities of the flange’s spoke are modelled. Each model has every radial layer (rows in the model) loaded with loads decreasing in accordance with the Equation 4 in A.1 for an initial value T0= 100 and e-2*π*5*µ = 0.61 resulting a µ= 0.0157 (see values in Table 5). This value is quite small comparative with the benchmark value 0.10 in [1] however still about 10 times more than the values deduced from the experiment in [3].

Layer 1 2 3 4 5 6 7 8 9 10

Table 5 Coeff dR 1.00 100 0.61 61 0.37 37 0.22 22 0.14 14 0.08 8 0.05 5 0.03 3 0.02 2 0.01 1

R 100 161 197 220 233 241 246 249 251 252

The various characteristics of the line wall sections are presented in table 6.1. For each ring the rigidity kp is computed with a simple beam model (Figure 6). The logarithm ln(kp) values will be used for the graphic presentation of the results.

Section Line Iy= Line A= dy for 100kN= kp=1e5/dy= ln(kp)=

Table 6.1 – Line (product) properties 1 (soft) 2 3 4 5 0.667 1.333 2.000 2.667 3.333 200 400 600 800 1000 5.742 0.889 0.593 0.445 0.356 17416 112429 168645 224861 281073 4.241 5.051 5.227 5.352 5.449

6 (rigid) 52.080 2500 0.054 1867797 6.271

Figure 5.1

Figure 5.2

Figure 6

The various characteristics of the spoke’s section are presented in table 6.2. For spoke (and corresponding length) the rigidity k is computed with a simple beam model. The logarithm ln(k) is listed in order to provide a comparison with the line characteristics.

Section Spoke Iy= Spoke A= Square dy for 100kN= ks=1e5/dy= ln(ks)= Triangular dy for 100kN= ks=1e5/dy= ln(ks)=

1 (soft) 2873 4000

2 5796 4750

3 8776 5300

4 11443 5700

5 (rigid) 42817 8800

9.170 10905 9.297

4.747 21064 9.955

3.247 30798 10.335

2.559 39078 10.573

0.852 117371 11.673

4.770 20964 9.951

2.525 39612 10.587

1.756 56948 10.950

1.401 71378 11.176

0.507 197239 12.192

Typical deformations for the square and triangular configurations are presented below in Figures 7: Figures 7

Typical variations of the shear force and bending moments in spokes are presented in Figures 8 (square arrangement) and Figures 9 (triangular arrangement):

Figures 8

Figures 9

First pictures are for the softest ring, the picture in the middle for a medium elastic/rigid ring and the figure at right is for the hardest, most rigid ring.

The variation of shear force and bending moment at the base of the spoke are compared with the values expected from the application of the hypothesis in [1]. In addition to the loads above, the position of the equivalent point of application of load (z= M/F) was monitored too. All the values above are presented below as ratio to the values resulted from [1].

Table 10 - F-computed/F-code

ks-1 ks-2 ks-3 ks-4 ks-5 ks-1 ks-2 ks-3 ks-4 ks-5

F/F-code log(kp) R R R R R T T T T T

Kp-1 Kp-2 Kp-3 Kp-4 Kp-5 Kp-6 4.241 5.051 5.227 5.352 5.449 6.271 2.803 1.495 1.316 1.196 1.109 0.365 3.206 1.752 1.528 1.399 1.296 0.426 3.424 1.918 1.686 1.532 1.418 0.465 3.556 2.026 1.785 1.622 1.501 0.492 4.032 2.567 2.289 2.091 1.938 0.631 0.665 0.488 0.443 0.413 0.390 0.182 0.755 0.536 0.487 0.454 0.435 0.205 0.821 0.568 0.514 0.479 0.453 0.218 0.851 0.588 0.533 0.495 0.468 0.227 0.881 0.686 0.623 0.580 0.547 0.269

Figure 10 – F-computed/F-code 4.250 4.000 3.750 3.500 3.250 3.000 2.750 2.500 2.250 2.000 1.750 1.500 1.250 1.000 0.750 0.500 0.250 0.000 4.000

4.500

5.000

5.500

6.000

6.500

Table 11 - M-computed/M-code

ks-1 ks-2 ks-3 ks-4 ks-5 ks-1 ks-2 ks-3 ks-4 ks-5

M/Mcode log(kp) R R R R R T T T T T

kp-1 4.241 2.623 3.351 3.754 4.006 4.935 0.368 0.579 0.737 0.793 0.774

kp-2 5.051 0.925 1.269 1.512 1.670 2.580 0.190 0.245 0.288 0.317 0.467

kp-3 5.227 0.728 1.006 1.202 1.346 2.139 0.150 0.194 0.223 0.247 0.375

kp-4 5.352 0.610 0.843 1.014 1.133 1.847 0.125 0.163 0.188 0.205 0.318

kp-5 5.449 0.530 0.733 0.883 0.989 1.623 0.107 0.142 0.164 0.180 0.277

kp-6 6.271 0.098 0.135 0.161 0.180 0.303 0.031 0.040 0.046 0.051 0.080

Figure 11 - M-computed/M-code 5.250 5.000 4.750 4.500 4.250 4.000 3.750 3.500 3.250 3.000 2.750 2.500 2.250 2.000 1.750 1.500 1.250 1.000 0.750 0.500 0.250 0.000 4.000

4.500

5.000

5.500

6.000

6.500

Table 12 - Z-computed/Z-code

ks-1 ks-2 ks-3 ks-4 ks-5 ks-1 ks-2 ks-3 ks-4 ks-5

Z/Zcode log(kp) R R R R R T T T T T

kp-1 4.241 0.936 1.045 1.096 1.126 1.224 0.553 0.768 0.897 0.932 0.878

kp-2 5.051 0.619 0.724 0.789 0.825 1.005 0.390 0.456 0.507 0.539 0.681

kp-3 5.227 0.554 0.658 0.713 0.754 0.935 0.338 0.398 0.434 0.464 0.601

kp-4 5.352 0.510 0.603 0.661 0.698 0.883 0.302 0.360 0.393 0.413 0.549

kp-5 5.449 0.478 0.566 0.623 0.659 0.837 0.276 0.325 0.363 0.384 0.506

kp-6 6.271 0.268 0.316 0.345 0.366 0.480 0.173 0.196 0.212 0.225 0.298

Figure 12 - Z-computed/Z-code 1.250

1.000

0.750

0.500

0.250

0.000 4.000

4.500

5.000

5.500

6.000

6.500

It is noted that all values estimated for the triangular arrangement are below (in general significantly below) the reference values in [1]. The values estimated for the square arrangement are mixed: Excepting the arrangements with the most rigid spoke the forces estimated at the base of the spoke are larger than the references values in [1]. For the values estimated for the moment at the base of the spoke the combination of soft line with rigid spokes provides values larger than the reference values in [1]. However the values of the

equivalent point of application of load is in general below the reference values in [1] with the exception of a very soft line in combination with increased rigid spokes. A soft line with a rigid spoke leads to loads far higher than the references values in [1]. It is like the product is stuffed inside the reel. Same effect can be noted also for the triangular arrangement but with at a significantly smaller amplitude. In the triangular arrangement the rings seems to use the space in between to deflect loading less the spokes. As expected a rigid line in combination with a soft spoke provides the lowest loads. 4th Preliminary conclusion This brief study is an attempt to demonstrate the importance of the elasticity/rigidity of the element of the offshore reels assembly for the estimation of the loads in the system. It is unfortunate that values are not available for the transverse rigidity of the lines/products loaded on the offshore reels. It is unfortunate that real measurements values are not available for reel assemblies (e.g. at least the deflection at the tip of the flange after a controlled spooling onshore and having the spooling tension maintained in the line – obviously tension marks measurements over the spooling process would be better). Moreover it is not clear how realistic is to assume the square arrangement for the lines. The square arrangement is not an energetic stabile arrangement but the information received from the industry reports situations when this type of arrangement is requested. However, it looks that in this situations the spooling process might be different and the assumptions in this study might not be valid (e.g. wood pieces are arranged between layers). The triangular arrangement is the natural arrangement (the most stabile arrangement from energetic point of view) and the values estimated by this study might be significantly lower than the values used for design. However this study considers a “perfect match” between the ring’s arrangement and the drum length and doesn’t take into account the well-known increase of load effect of a side ring arranged in an imperfect triangular cell (so angle between line of ring’s centre and horizontal less than 60º). Most probable the balancing of these two phenomena is among the causes why the reels failures are not reported. C.

Conclusions

The study in Part A doesn’t accounts other characteristics of the line spooled on a drum. For example, the axial elasticity of the line is considered as having a significant potential to influence the pressure on the drum. However, I trust that the study demonstrates how important are friction and the spring/straightening effect for the understanding of the loads acting on the system spooled line/drum and the necessity for the consideration of these effects for the development of safer winch arrangements. The study in Part B has also significant limitation due to the very simple method chose for the analysis of the effects of the elasticity of line and spoke. However, I trust that the study demonstrate how important is the understanding of these effects for the design of the reel arrangement. The effects studied in Part A together with the effects studied in Part B may provide a differenced approach for the reels considered by the designer a kind of mega winches. For this equipment the inertia effects might have at least the same strength effect as the effect of the line spooling tension. I like to think that both directions in Part A and B worth to be explored further. In my personal opinion the experiments or measurement in field are what it is missing the most in this moment for the in-deep clarification of the aspects discussed in this study. I trust that this entire study can be seen as a part of a “thorough documentation” as requested by [1] for the estimation of C values (practically the ration between the drum pressure and the pressure on first layer or the reference layer).

References: [1]

DNV Standard for Certification 2.22 Lifting Appliances, edition October 2011

[2]

Mircea Florian Teica - “Research into good design practice for reels”, MSc Thesis Subsea Engineering 2011-2012, University of Aberdeen http://www.scribd.com/doc/116737626/Research-Into-Good-Design-Practice-for-Reels [3]

P. Dietz, A. Lohrengel, T. Schwarzer and M. Wächter – “Problems related to the design of multi layer drums for synthetic and hybrid ropes”, OIPEEC Conference / 3rd International Ropedays - Stuttgart - March 2009 http://www.imw.tuclausthal.de/fileadmin/Forschung/Veroeffentlichungen/Stuttgart_Seiltagung_IMW.pdf [4]

Gerhard Rebel, Roland Verreet – “Radial Pressure Damage Analysis of Wire Ropes Operating on Multi-layer Drum Winders” http://www.seile.com/bro_engl/Rebel_-_Radial_Pressure_Rev_C_from_GR.pdf [5]

Liviu Stoicescu – “Strength of material”, Dunarea de Job University, Galati, Romania

[6] Song, K.K., ODECO Engineers Inc.; Rao, G.P., ODECO Engineers Inc.; Childers, Mark A., ODECO Engineers Inc. – “Large Wire Rope Mooring Winch Drum Analysis and Design Criteria” Note: accessed only the abstract via the link below http://www.onepetro.org/mslib/servlet/onepetropreview%3Fid%3D00008548%26soc%3DSPE [7] Stephen M. Pearlman, David R. Gordon, Michael D. Pearlman – “Winch Technology - Past Present and Future A Summary of Winch Design Principles and Developments” Paper on InterOcean Systems, Inc. site http://www.interoceansystems.com/winch_article.htm Note: All the internet references were available at the date of drafting of this paper (February 2013).