13.15 a - Forces Experienced by Winch Drums ...- Marius Popa 3-6

DNV SERVING THE MARITIME AND OIL & GAS INDUSTRY

TECHNICAL PAPER

FORCES EXPERIENCED BY WINCH DRUMS AND REELS SYSTEMS AS A FUNCTION

OF ROPE CHARACTERISTICS AND VARYING LINE PULL – A THEORETICAL STUDY

DET NORSKE VERITAS

Cromarty House, 67-72 Regent Quay Aberdeen, AB11 5AR

E: [email protected] www.dnv.com

Forces experienced by winch drums and reels systems as a function of rope characteristics and varying line pull – a theoretical study

The 18th North Sea Offshore Crane and Lifting Conference 23rd - 25th April 2013, Stavanger Forum, Stavanger, Norway Marius Popa, FRINA, CEng, Ph.D. Principal Engineer, Lead Naval Architect, DNV Aberdeen Approval Centre TEEUK311 NOTE: This study is not intended and shall not be used to replace the basic requirements in section 5 of DNV Standard for the Certification of Lifting Appliances 2.22, with respect to design forces and stresses to be considered for winch drums and flanges; the concepts presented are intended to explore and stimulate a deeper understanding of two dominant phenomena involved. With further development and sufficient practical evidence, it may support the generation of “thorough documentation” as a means to alternative methods of design (reference is made to the DNV Standard for the Certification of Lifting Appliances 2.22 Ch. 2 Sec. 3 Guidance Note for the calculation of C coefficient for more than 2 layers). This paper presents in Part A a theoretical study of internal line friction, line rigidity and their influence on drum and flange pressures on single drum winches, with varying line tension. Part B of this It also develops in Part B, using the conclusion in Part A, an analysis of the effect of the rigidity of flange and line on the loads developed on the flange. The study in Part B was developed focusing on the structure of the reel flange however some conclusions may be of interest also for the structure of the winch flange.


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A. THE ESTIMATION OF LINE TENSION AND THE PRESSURE ON WINCH DRUMS 1. DEFINITIONS AND GENERAL EQUATIONS The equation [4] developed below is a generalization of the “capstan effect” equation [8] for a multi layers and multi windings arrangements. The pressure on the drum is estimated by the summation of the pressures between layers computed taking into account the general equation developed for the line tension. T = tension in line pi = pressure in each layer µ = friction coefficient Pp = product pitch n = number of radial layers l= number of windings along the drum D1 = external diameter (drum diameter + n*Pp) Ri= contribution of layer i to the total radial pressure on the drum An infinite number of small segments [dsi=Di/2*dφ is i] can be isolated from the line’s radial layer I, the forces acting on which can be seen in figure 1 below. FIGURE 1 – LOADS ACTING ON THE LINE’S RADIAL LAYER I SEGMENT DSI=DI/2*Dφ


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The segment is in equilibrium and the following equations are developed: In the vertical direction, the equation of equilibrium can be written as:

pi*dA = pi-1*dA + (2*T i+dTi)*sin(dφ/2) => Assuming that dTi*sin(d φ/2) is very small =>

(pi-p1-1)*dA = 2*T i*sin(dφ/2)

Assuming dφ is small => 2*sin(dφ/2) = dφ =>

(pi-pi-1)*dA = Ti* dφ [eq 1]

In the horizontal direction, some notations are proposed, together with the equation of equilibrium:

µ*p i-1*dA = Ff-(i-1) µ*p i*dA = Ff-i

Ti+Ff-i= Ti+dTi+Ff-(i-1) => Ff-i – Ff-(i-1) = dTi => -µ*(p i-pi-1)*dA = dTi [eq 2] From Eq 1 and 2 => -µ*T i* dφ = dTi [eq 3] Integrating Equation 3 =>

T= T0*e-µφ [eq 4]

For φ=0 T is the pulling force at the free end => T0 is the pulling force at the free end. It is interesting to note that tension decreases with increasing φ, since internal friction has a tendency to consume line tension. For one layer spooled onto the drum, the pressure at the free end can be deduced as follows:

p1*dA = 2*T* sin(dφ/2) and having dA= dφ*D 1/2*Pp => p1*dφ*D 1/2*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*D i/2*Pp, equation 1 becomes: (pi-pi-1)* dφ*D i/2*Pp = T0*e

-µφ* dφ =>


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(pi-pi-1) = 2* T0*e-µφi/Di/Pp

[eq 6] [where Di= D1-(i-1)*Pp] For multiple layers, the formulas in Equations 7 apply: p1= 2* T0*e

-µφ1/D1/Pp => [eq 7.1]

(p2-p1)= 2* T0*e-µφ2/D2/Pp => [eq 7.2]

(p3-p2)= 2* T0*e-µφ3/D3/Pp => [eq 7.3]

… (pi-pi-1)= 2* T0*e

-µφi/Di/Pp => [eq 7.i] (pi+1-pi)= 2* T0*e

-µφ(i+1)/Di+1/Pp => [eq 7.i+1] … (pn-1-pn-2)= 2* T0*e

-µφi/Dn-1/Pp => [eq 7.n-1] (pn-pn-1)= 2* T0*e

-µφ(i+1)/Dn/Pp => [eq 7.n] Equations in 7 result in pn or the pressure at drum pdrum:

pdrum = p

ilni

p PiD

e

P

T

*)1(**2

1

))1(***20(*

10

−−∑

−+−

=

πϕµ

[eq 8]

where φi+1= φi + 2*π*l It is noted that equation 7.i relates to the pressure at layer i (Ri), contributing to the total pressure on the drum and that the ratio between the contribution of each layer is quasi constant: Ri/Ri+1 = (pi-pi-1)/(pi+1-pi) = eµ*2π*l*D i/Di+1 => Ri/Ri+1 = eµ*2π*l*(D 1 – (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] Assuming that the variation in diameter does not significantly contribute to Ri (the coefficient of diameter may increase at a significantly lower rate than that due to the effect of friction) equation 8 becomes:

pdrum = ∑−

=

−−1

1

)1(***2*

1

0 ***2 n

i

il

p

ePD

T πµ [eq 10]


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Further, assuming that 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 work in [2]. Self-weight and the variation of the pressure between layers (with diameter) is considered in [4]; the effect of friction however appears to have been ignored. Self-weight is not considered in this approach since applying it separately would allow the correction with the dynamic involved by the installation on board of floating units (ships). 2. EXISTING EXPERIMENTAL RESULTS The results from [3] are considered relevant for the purposes of this study. From figure 17 in [3], the variation of tangential stresses measured for a drum (assumed as hoop stresses) is presented. As we know, hoop stress is directly proportional to the surface pressure acting on the drum – it can be reasonably deduced therefore that the values of stress in figure 17 [3] are proportional to applied drum pressure. The values taken from the diagram are approximated as follows:

layer 1 2 3 4 5

R 100 180 224 295 336

dR 100 80 64 51 41

dRi/dR(i+1) 1.25 1.25 1.25 1.25

From equation 11: eµ*2π*l

= 1.25 => µ*l= ln(1.25)/2/π = 0.035 With reference to [3] rope diameter is 23 mm, arranged over 5 radial layers. From Figure 15 [3], approximate characteristics of the arrangement are as follows: � number of windings along length is approximately 40, leading to a friction coefficient of 0.0009

� drum length therefore is approximately 40*0.023 = 0.92m (say 1.0m). Proportionally, the outer diameter and

the drum diameter is approximately 0.5m and 0.27m (i.e. 0.5 – 2*(5*0.023) respectively.


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Using these values in equations 10 and 11, the ratio of pdrum/p1 are presented in Table 1: TABLE 1 [only input value being friction coefficient µ= 0.0009]

Winding-l

Radial layer

- n 1 2 3 4 5 10 40

1 1.000 1.000 1.000 1.000 1.000 1.000 1.000

2 1.994 1.989 1.983 1.978 1.972 1.945 1.798

3 2.983 2.966 2.950 2.933 2.917 2.838 2.434

4 3.966 3.933 3.900 3.868 3.836 3.682 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 (effect of diameter included), the ratio pdrum/p1 are computed in Table 2.1: TABLE 2.1 [Input values being: 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]

Winding-l

D-factor

Radial layer

- n 1 2 3 4 5 10 40

1.000 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000

0.908 2 2.095 2.089 2.083 2.077 2.071 2.041 1.878

0.816 3 3.307 3.287 3.267 3.248 3.229 3.135 2.658

0.724 4 4.665 4.622 4.580 4.539 4.498 4.301 3.359

0.632 5 6.212 6.134 6.059 5.984 5.911 5.563 3.999

A closer correlation with the experimental values is achieved if the friction coefficient is increased to 0.0013 – see Table 2.2


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TABLE 2.2 [input values being: 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]

Winding-l

D-factor

Radial

Layer - n 1 2 3 4 5 10 40

1.000 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000

0.908 2 2.092 2.083 2.075 2.066 2.057 2.015 1.794

0.816 3 3.298 3.270 3.242 3.214 3.187 3.056 2.432

0.724 4 4.646 4.585 4.525 4.466 4.409 4.137 2.950

0.632 5 6.177 6.067 5.959 5.855 5.752 5.278 3.378

PRELIMINARY CONCLUSIONS [1] Considering the results below and the information in [3], it is difficult to determine whether the influence of diameter (D1) can be ignored or not. The close correlation between experimental and theoretical values would appear to demonstrate the validity of equations 8 to 11. Equations 8 and 9 are more general and by their nature provide more conservative results. Equations 10 and 11 however are simpler, requiring no information with respect to geometrical characteristics and might therefore represent a reasonable initial approximation. It is also noted that: � Coefficients of friction considered above (i.e. 0.0009 - 0.0013) are extremely small in comparison with typical

values (e.g. 0.05 to 0.30 for steel on steel); well-maintained, lubricated wire rope may of course exhibit lower coefficients of friction, the values however are unknown.

� Rope anchorage design for winches, [1] Ch. 2 Sec. 3 B.513, is based on a coefficient of friction µ = 0.10; this value is 100 times larger than those deduced from [3].

� The inclusion of diameter effects leads to an increase in coefficient of friction (approx. 50%) for same drum pressure.


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3. APPLICATION OF FORMULAE FOR REELS A typical offshore reel (used for the transportation and offloading of umbilical products) may have drum and flange diameters in the region of 6.0m and 10.0m respectively, with a drum length of approximately 5.0m. The number of windings may vary from 10 to 50 along the length of the drum and the number of layers from 4 to 20 (radially). If we consider Pp = 0.1m, the n and l values are computed as 20 and 50 (typical products range in diameter from 80 to 300mm approximately). The results for Equation 8 (relating to pressure at the outmost/first layer) and typical reel dimensions (pp=0.1 m, µ= 0.10, n= 20 and values of l up to 50) are presented the Table 3.1 below. TABLE 3.1

Winding-l

Radial 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 varying diameter (µ= 0.10, n= 20 and values of l up to 20) are presented the Table 3.2. The results are relative to the value of pressure at the outmost/first layer.


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TABLE 3.2

Winding-l

Radial 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

For larger and perhaps more realistic coefficients of friction (approximately 100 times more than those in [3]), it can be seen from Tables 3.1 and 3.2 that variation in diameter may not be significant as previously postulated. Moreover it can be observed that for friction coefficients in the region of 0.10 and number of windings along the drum l > 5, differential pressures between layers (pressure increase) tend to 0, after the 2nd radial layer. A sensitivity study was undertaken for friction coefficients (µ), based on equations 8 and 9. The results relative to 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). [1] suggests a pressure increase of 1.75 and 3.0 at this location, relative to the value of pressure at the outmost/first layers.


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PRELIMINARY CONCLUSIONS [2] The values in Tables 4.1 and 4.2 suggest that for more realistic coefficients of friction (µ=0.05 - 0.10) and more than 10 windings along the length of the drum, the pressure on the drum might be marginally larger than the pressure generated by the outermost radial layer (i.e. no greater than 5% greater). Typical values for the coefficients of friction with respect to umbilical products transported on offshore reels were not available as part of this work. It is therefore difficult to extrapolate results from the references, normally associated with calculating pressures on winches (using wire ropes), with those for reel drums, based on the assumptions and equations developed herein. TABLE 4.1 AND FIGURE 4.1 – VARIATION OF DRUM PRESSURE WITH COEFFICIENT OF FRICTION (EFFECT OF DIAMETER INCLUDED) – REEL CONFIGURATION R-OUT= 5.0 / PP=0.1 M.

Winding-l

Radial

layer Friction 1 2 3 4 5 10 50

2 0.001 2.014 2.008 2.001 1.995 1.989 1.958 1.745

2 0.01 1.939 1.882 1.828 1.778 1.730 1.533 1.043

2 0.02 1.882 1.778 1.686 1.605 1.533 1.285 1.002

2 0.05 1.730 1.533 1.390 1.285 1.208 1.043 1.000

2 0.10 1.533 1.285 1.152 1.081 1.043 1.002 1.000

2 0.20 1.285 1.081 1.023 1.007 1.002 1.000 1.000

code 1.750 1.750 1.750 1.750 1.750 1.750 1.750

1.000

1.250

1.500

1.750

2.000

2.250

0 5 10 15 20 25 30 35 40 45 50


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TABLE 4.2 AND FIGURE 4.2 – VARIATION OF DRUM PRESSURE WITH COEFFICIENT OF FRICTION (EFFECT OF DIAMETER INCLUDED) – REEL CONFIGURATION R-OUT= 5.0 / PP=0.1 M.

Winding-l

layer Friction 1 2 3 4 5 10 50

5 0.001 5.147 5.082 5.018 4.955 4.894 4.603 3.025

5 0.01 4.427 3.951 3.553 3.219 2.938 2.051 1.045

5 0.02 3.951 3.219 2.700 2.326 2.051 1.395 1.002

5 0.05 2.938 2.051 1.624 1.395 1.262 1.045 1.000

5 0.10 2.051 1.395 1.179 1.088 1.045 1.002 1.000

5 0.20 1.395 1.088 1.024 1.007 1.002 1.000 1.000

code 3.000 3.000 3.000 3.000 3.000 3.000 3.000

1.000

1.500

2.000

2.500

3.000

3.500

4.000

4.500

5.000

5.500

0 5 10 15 20 25 30 35 40 45 50


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4. THE EFFECT OF LINE SPRING STIFFNESS One effect neglected in the general equation (section 1) was that of spring stiffness. This effect represents the lines’ ability to resist deformation and its natural tendency to return to its original form (straight line). This effect will obviously be more significant for lines demonstrating increased rigidity (e.g. larger diameter rope are naturally required for increasing loads and depths) and further exacerbated by lower coefficients of friction (e.g. when lubricated). These factors can pose significant challenges for subsea lifting arrangements [6]. It is assumed that the bending of ds=D/2*dφ length of product leads to the pressure ps (spring pressure). Considering a simply supported beam (length ds), loaded uniformly over its length, with a line load (Pp*ps), the total deflection is the sum of bending and shear deflection, with a maximum at midspan. The total deflection is obtained from [5].4.10.1.7: w-total = w-shear + w-bending = (Pp*ps)*ds2/(8*G*A s) + 5*(Pp*ps)*ds4/(384*E*Iy) Equation 13.1 can be re-write using the notation:

ks= 1/(8*G*As )= shear characteristics of the line 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)* D i

2*dφ2/4 *(ks+ ds2*kb) => ps= 1/4/Di/Pp/(ks+ ds2*kb)

It is normally acceptable to approximate ks+ ds2*kb as ks: ps= 1/4/Di/Pp/ks = 2*G*As/Di/Pp= 2*Ks/Pp/Di [eq 13] where Ks 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 required to counteract the spring effect. The following logic can be applied for a general value of ps with the formulae corrected accordingly. The spring force (ps*dA) is included in the equation of equilibrium for vertical direction (Equation 1)

(pi-pi-1)*dA = T i* dφ - ps*dA= T i* dφ - 2*Ks/Pp/Di*Pp*D i/2*dφ (pi-pi-1)*dA = T i* dφ - Ksdφ [eq 14]

Equation 14 is used in the equation of equilibrium for horizontal direction

-µ*(p i-pi-1)*dA= dTi [eq 2] From Eq 1 and 2 => -µ*(T i-Ks)* dφ = dTi or

dTi/dφ = -µ*T i + µ*K s [eq 15]


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In order to integrate this equation, we can substitute the variables above as follows: 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 [eq 16] For φ = 0 (free end) equation 16 become T0= -w+Ks => w= Ks-T0 =>

T= (T0-Ks)*e-µ*φ +Ks

Considering dA= dφ*D i/2*Pp Equation 14 becomes: (pi-pi-1)* dφ*D i/2*Pp = (Ti-Ks)*dφ = =>

(pi-pi-1)* D i/2*Pp = (Ti-Ks) = (T0-Ks)*e-µφi

(pi-pi-1) = 2*(T0-Ks)/Pp/Di*e-µφi [eq 17]

Summing Equation 17

pdrum = p

ilni

p

s

PiD

e

P

KT

*)1(**2

1

))1(***20(*

10

−−∑

− −+−

=

πϕµ

[eq 18]

It is noted that the term representing the force term represents the difference between equations 8 and 18. From this equation we can conclude that the spring effect will tend to reduce line tension and as a consequence, pressure on the drum. Recent incidents and investigations surrounding deep water subsea lifting arrangements (where line rigidity is typically higher than for ‘normal’ in-air applications) however [6] appear to suggest that the effect is opposite. A feasible explanation, relating to formulae 18, is the possibility that more rigid products (with in theory smaller contact areas between layers) lead to smaller coefficients of friction. It is obvious that a reduction of the force term by say 50%, leads to a 50% reduction in drum pressure. Estimating the effect of varying coefficients of friction is more complex; a numerical approach based on the equation, excluding the effect of diameter was considered. The relative pressure calculated for the 5th radial layer (40 windings along the drum), with 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 the radial direction increases. The initial value for µ= 0.0009 is 4.886 µ= 0.000675 (75%) 6.193 +26.7%


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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 a reduction in the coefficient of friction may result from well-lubricated lines; being normal practise for subsea applications, used to minimize the amount of the heat dissipation from friction and prolong product life. As can be observed however, reducing the coefficient of friction might lead to more load on the drum. For deep sea applications in particular, the balance between operating procedures, maintenance routines, cumulative damage experienced by the wire due to heating/friction and pressures applied to the winch drum is a fine one and needs to be considered, in terms of safety, financial and technical constraints imposed on the design of such winches. Information contained in [7] proposes an alternative method to minimize the pressure experienced by winch drums for deep subsea arrangements; i.e. spooling the first layers on the drum with a reduced tension. These first layers will act in effect like a protective ‘cage’ for the drum, reducing the pressure and hoop stresses experienced by it. Equation 19 shows that spooling with a tension approximating or lower than the spring (straightening) characteristic of the line may generate less pressure on the drum and indeed offer a degree of ‘protection’ to the structure of the drum. PRELIMINARY CONCLUSION [3] Increasing line rigidity will reduce the basic tension in the line proportionally. However this reduction can be compensated and overcome by the reduction of friction between layers, an effect caused by the same increase in rigidity. The relationship between increased line rigidity and a reduced coefficient of friction between layers does not appear to be available in the literature. No sufficient data was available to validate these equations and deductions - firm conclusions in relation to this aspect are therefore not possible at the time of writing. B. AN ESTIMATION OF THE FORCES EXPERIENCED BY THE F LANGES OF REELS, CONSIDERING THE

INFLUENCE OF LINE ELASTICITY. Despite their differences, the requirements in [1] for the design of wire rope winches have often been adopted for the purpose of designing offshore reels (used for the transport and offloading of various pipe, cable and/or umbilical products). Some major differences include: � Reel structures (namely their core and flanges) tend to be significantly more flexible than those associated with

a typically more compact winch. � The transverse rigidity in particular of products carried by reels tend to be significantly less than that of a

typical wire rope.

This paper postulates that such differences have the potential to influence the design offshore reels and studies the influence of these factors in relation to the approach taken in [1], adopted regularly by the industry, for the assessment and design of reels.


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The phenomenon involved are complex and the limitations of a completely theoretical approach were considered too many for a brief study of this nature; it is therefore supplemented by a numerical approach (using FEM), providing what is considered to be a more realistic estimation of the behaviour of a typical system. It is still understood however that the computational limitations (FEM file used for one simulation is approximately 8Mb) used, together with the lack of information about the real-life characteristics of the product modelled, limits the results of this study to the parameters used. Two-dimensional stick-models were generated (using DNV Nauticus 3D Beam software) simulating a radial section through a reel. Modelling restrictions limited the arrangement to 5 windings along the drums’ length and 10 layers in radial direction. The product simulated has a diameter of 100mm - various wall thicknesses were considered. Contact between the rings and between the rings and the flanges is represented by short rigid dummy beams (approx 5mm long), with compressive characteristics only. Two spooling configurations are considered, representing two classic arrangements, i.e.: � Rectangular cell arrangement (figure 5.1) � Triangular cell arrangement (figure 5.2) For each arrangement a number of different product (6 no) and spoke/flange (5 no) rigidities are modelled. Each radial layer is loaded with decreasing loads, in accordance with Equation 4 in A.1, with an initial value T0= 100 and e-2*π*5*µ= 0.61, resulting in a coefficient of friction µ = 0.0157 (see values in Table 5). It is noted that this value is small in comparison with the benchmark value 0.10 in [1]; nevertheless, it is still approximately 10 times more than the values deduced from the experiment in [3].


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TABLE 5

Layer Coeff dR R

1 1.00 100 100

2 0.61 61 161

3 0.37 37 197

4 0.22 22 220

5 0.14 14 233

6 0.08 8 241

7 0.05 5 246

8 0.03 3 249

9 0.02 2 251

10 0.01 1 252

Table 6.1 describes the various sections assessed, with increasing line rigidity from 1 to 6. Transverse rigidity (kp) of each ring is represented by a simple 2-D beam model (Figure 6); logarithmic values of which are used for the graphical presentation of results.

TABLE 6.1 – LINE (PRODUCT) PROPERTIES

Section 1 (soft) 2 3 4 5 6 (rigid)

Line Iy= 0.667 1.333 2.000 2.667 3.333 52.080

Line A= 200 400 600 800 1000 2500

dy for 100kN= 5.742 0.889 0.593 0.445 0.356 0.054

kp=1e5/dy= 17416 112429 168645 224861 281073 1867797

ln(kp)= 4.241 5.051 5.227 5.352 5.449 6.271


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FIGURE 5.1 FIGURE 5.2


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FIGURE 6

Varying spoke stiffnesses are presented in table 6.2; the rigidity of each being determined using a simple beam model. Again, logarithmic values are listed, providing a more direct comparison with the line characteristics.

Section 1 (soft) 2 3 4 5 (rigid)

Spoke Iy= 2873 5796 8776 11443 42817

Spoke A= 4000 4750 5300 5700 8800

Square

dy for 100kN= 9.170 4.747 3.247 2.559 0.852

ks=1e5/dy= 10905 21064 30798 39078 117371

ln(ks)= 9.297 9.955 10.335 10.573 11.673

Triangular

dy for 100kN= 4.770 2.525 1.756 1.401 0.507

ks=1e5/dy= 20964 39612 56948 71378 197239

ln(ks)= 9.951 10.587 10.950 11.176 12.192

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


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FIGURES 7 – a - b

Typical shear force and bending moment diagrams for the spoke elements are presented in Figures 8 (square arrangement) and Figures 9 (triangular arrangement):


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FIGURES 8 a - c

FIGURES 9 a - c

Product characteristics are represented, increasing in stiffness from left to right.


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The variation of shear force and bending moment at the base of the spokes are presented in figures 10 & 11 below, as a ratio of the values expected from the method used in [1]. In addition, the position of the equivalent point of load application (z = M/F) was determined and is presented in figure 12. TABLE 10 - F-COMPUTED/F-CODE

F/F-code Kp-1 Kp-2 Kp-3 Kp-4 Kp-5 Kp-6

log(kp) 4.241 5.051 5.227 5.352 5.449 6.271

ks-1 R 2.803 1.495 1.316 1.196 1.109 0.365

ks-2 R 3.206 1.752 1.528 1.399 1.296 0.426

ks-3 R 3.424 1.918 1.686 1.532 1.418 0.465

ks-4 R 3.556 2.026 1.785 1.622 1.501 0.492

ks-5 R 4.032 2.567 2.289 2.091 1.938 0.631

ks-1 T 0.665 0.488 0.443 0.413 0.390 0.182

ks-2 T 0.755 0.536 0.487 0.454 0.435 0.205

ks-3 T 0.821 0.568 0.514 0.479 0.453 0.218

ks-4 T 0.851 0.588 0.533 0.495 0.468 0.227

ks-5 T 0.881 0.686 0.623 0.580 0.547 0.269


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FIGURE 10 – F-COMPUTED/F-CODE

0.000

0.250

0.500

0.750

1.000

1.250

1.500

1.750

2.000

2.250

2.500

2.750

3.000

3.250

3.500

3.750

4.000

4.250

4.000 4.500 5.000 5.500 6.000 6.500


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TABLE 11 - M-COMPUTED/M-CODE

M/M-

code kp-1 kp-2 kp-3 kp-4 kp-5 kp-6

log(kp) 4.241 5.051 5.227 5.352 5.449 6.271

ks-1 R 2.623 0.925 0.728 0.610 0.530 0.098

ks-2 R 3.351 1.269 1.006 0.843 0.733 0.135

ks-3 R 3.754 1.512 1.202 1.014 0.883 0.161

ks-4 R 4.006 1.670 1.346 1.133 0.989 0.180

ks-5 R 4.935 2.580 2.139 1.847 1.623 0.303

ks-1 T 0.368 0.190 0.150 0.125 0.107 0.031

ks-2 T 0.579 0.245 0.194 0.163 0.142 0.040

ks-3 T 0.737 0.288 0.223 0.188 0.164 0.046

ks-4 T 0.793 0.317 0.247 0.205 0.180 0.051

ks-5 T 0.774 0.467 0.375 0.318 0.277 0.080


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FIGURE 11 - M-COMPUTED/M-CODE

0.000

0.250

0.500

0.750

1.000

1.250

1.500

1.750

2.000

2.250

2.500

2.750

3.000

3.250

3.500

3.750

4.000

4.250

4.500

4.750

5.000

5.250

4.000 4.500 5.000 5.500 6.000 6.500


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TABLE 12 - Z-COMPUTED/Z-CODE

Z/Z-code kp-1 kp-2 kp-3 kp-4 kp-5 kp-6

log(kp) 4.241 5.051 5.227 5.352 5.449 6.271

ks-1 R 0.936 0.619 0.554 0.510 0.478 0.268

ks-2 R 1.045 0.724 0.658 0.603 0.566 0.316

ks-3 R 1.096 0.789 0.713 0.661 0.623 0.345

ks-4 R 1.126 0.825 0.754 0.698 0.659 0.366

ks-5 R 1.224 1.005 0.935 0.883 0.837 0.480

ks-1 T 0.553 0.390 0.338 0.302 0.276 0.173

ks-2 T 0.768 0.456 0.398 0.360 0.325 0.196

ks-3 T 0.897 0.507 0.434 0.393 0.363 0.212

ks-4 T 0.932 0.539 0.464 0.413 0.384 0.225

ks-5 T 0.878 0.681 0.601 0.549 0.506 0.298

FIGURE 12 - Z-COMPUTED/Z-CODE

0.000

0.250

0.500

0.750

1.000

1.250

4.000 4.500 5.000 5.500 6.000 6.500


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THE FOLLOWING IS NOTED FROM FIGURES 10 – 12: With respect to the triangular arrangement, all values are found to be significantly below the reference values, determined by the formulae in [1]. With respect to the square arrangement, the values estimated are mixed, i.e.: With the exception of the spokes with the highest rigidity (Kp6), the forces estimated at the base of the spoke are larger than the reference values in [1]. Estimated bending moments at the base of the spokes are larger than the reference values in [1] when a combination of a ‘soft’ line and a ‘rigid’ spoke is considered. The equivalent point of load application [z] however is in general lower than the reference values in [1], with the exception of a very soft line (kp-1) and increasingly rigid spokes. From the study conducted, it can be seen that a softer product with a more rigid spoke tends to result in far higher forces and moments on the reel flanges than the reference values in [1], as the product is ‘forced’ into the space confined between the flanges and adjacent product. A similar effect can be seen for the triangular arrangement, but of a significantly smaller magnitude. It would appear that in the case of a triangular arrangement, the product has the capacity to take up the space between layers more readily, in effect reducing the horizontal load imparted by it onto the flanges. As expected, it is estimated that a rigid line in combination with a soft spoke provides the lowest flange loads. PRELIMINARY CONCLUSION [4] This brief study attempts to demonstrate the influence of product elasticity on the forces imparted into the offshore reels that are used to transport them. Figures relating to the transverse rigidity of actual product were unfortunately unavailable for the purposes of this study, as were representative measurements taken from actual reel assemblies (e.g. strain gauge measurements or flange tip deflections, associated with controlled constant tension onshore spooling). Such information would obviously be valuable for the purposes of validating these theories. Assuming a square arrangement for a spooled-on product may or may not be realistic. It is not a naturally stable one, but the information received from industrial users of reel structures, suggest at least that there are situations when it is specified / requested by the end-user. It may be of course that actual spooling procedures differ from the assumptions made herein, e.g. partitions in various combinations with flexible filling materials may in some cases be used between windings along the drum. The triangular arrangement is obviously the more natural and therefore stable one; this study indicates that the loads and forces experienced by the flanges at least are in effect significantly lower than the values typically used for the purposes of design. This study does however consider a ‘perfect fit’ between the ring arrangement and the drum length; it does not therefore account for the well-known increase in load associated with a side-ring arranged in an imperfect triangular cell (angle between line of rings’ centre and horizontal less than 60º). Structural failure


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of offshore reels does not appear to have been reported in the literature, perhaps partly as a result of these two phenomena cancelling one another out. C. CONCLUSIONS Part A of this study does not consider various characteristics associated with the line (whatever it may be) spooled onto a drum. For example, axial elasticity can have a significant effect on the pressure experienced by a winch drum. Part B also has significant limitations due to the simplistic analysis methods employed for assessing the effects of product and flange elasticity. Part A however demonstrates the relative importance of friction and the spring/straightening effect for the better understanding of loads acting on the system and the necessity for these effects to be considered for the development of in some cases more optimum and safer winch arrangements. At the same time, part B demonstrates the importance of understanding the effects that relative elasticity has on the design of offshore reel structures. The effects studied in Part A together with those in part B should provide the designer with a more thorough understanding of the phenomena at work and it is hoped some stimulation for further investigation and work towards a different, perhaps more appropriate design methodology for reels structures, considered by the designer as a kind of ‘mega-winch’. For this equipment the inertia effects might have at least the same strength effect as the effect of the line spooling tension. It is the opinion of the Author that both directions explored in parts A and B are worthy of further work, with empirical measurements and data being the major exponents missing from the development of final conclusions and incorporation of them into relevant codes and standards. This study may in part be considered as supporting information as far as “thorough documentation” is requested

in [1], for the estimation of lower C values (i.e. the ratio between the drum pressure and the pressure on first

layer or the reference layer) than are recommended in the same. ACKNOWLEDGEMENTS The author would like to thanks to Det Norske Veritas for the support offered for this paper and to Alex Doig for reviewing and editing the text. A special mention is made also for author’s wife who accepted that a significant number of evenings to be spent for the completion of this study.


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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.tu-clausthal.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 [8] Capstan equation - From Wikipedia, the free encyclopaedia http://en.wikipedia.org/wiki/Capstan_equation Note: All the internet references were available at the date of drafting of this paper (February 2013).

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13.15 a - Forces Experienced by Winch Drums ...- Marius Popa 3-6