CHAPTER 6 CALCULATION OF REQUIRED DESIGN
6.1
Calculation from experimental results
In this section, we will calculate the hoop stress not only for the pulling load but also for the braking load for the 1st layer of rope on the drum body due to the compressive stress. Also, the pressure occurred when a loaded rope is wound onto a winch drum, wrap by wrap; each successive wraps compress the drum in its area of contact (Refer to section 3.4). Afterward, we will compare the hoop stress between design codes and calculated results for both of the loading conditions.
6.2
Calculation for required drum thickness
According to the experimental results, the loaded rope tension throughout the winch operation is decreasing from far end to near end of the drum whether there is a pulling load or braking load applied on the drum. As a result, it is shown that the assumption of uniform tension along the loaded rope is not supported by our experimental results. Thus, the calculation of hoop stress in this section will be used with decreasing pressure that acting on the drum by the th e rope tension tensi on due to the pulling pullin g or braking load lo ad (Figure 6.1).
As discussed in section 3.4.3 and 3.5, the Hampe’s solution method gives more realistic data to get an improve design. Moreover, one of the advantages of this solution has provided a calculation on each and every wraps continuously onto the
47
winch drum; which we can observe the deflection as well as hoop stress occurring in each positions under the respective warps on the winch drum in pulling or braking load conditions.
As mentioned in the Chapter 3, our analysis is based on one particular design of the winch, which is currently being used, with the following design parameters:
Drum diameter
=
1000 mm
Drum Length
=
1775 mm
Drum thickness
=
70 mm
Steel wire rope size (diameter)
=
65 mm
Applied tension load (pulling)
=
200 tons
=
1.96 MN
(1ton = 1000kg = 9810N) Applied tension load (braking)
=
300 tons
=
2.94 MN
(1ton = 1000kg = 9810N) Yield Stress for steel (ST 52.3)
=
520 MPa
The general formula based on the Hampe’s solution [9], the hoop stress, σh is:
σ h
=
N θ t
=
E R
[w
p
(ξ ) + S 1 F 7 (ξ ) + S 2 F 15 (ξ ) + S 3 F 16 (ξ ) + S 4 F 8 (ξ )
] = E [w] R
(6.1)
The derivation of the above equation and the various terms are discussed in Appendix A.
48
Deflection, w, is given by,
w = w p (ξ ) + S 1 F 7 (ξ ) + S 2 F 15 (ξ ) + S 3 F 16 (ξ ) + S 4 F 8 (ξ ) ]
where, the ordinates of deflection line, w p is: w p (ξ ) =
The non dimensional coordinate of ξ =
x L
P R 2 Et
(6.2)
(1 − ξ )
(6.3)
,
(6.4)
where (0 ≤ ξ ≤ 1): can be seen in Figure 6.1.
According to the above formulae, account is taken for the decreasing pressure applied to the drum as illustrated in Figure 6.1.
ξ=0.25
Pressure (P)
ξ=0.75 ξ=1
ξ=0 ξ
x
y =0.5 σ Drum
Near end
Drum thickness = t
x
R D
Far end
L
Rope Wraps Load
Fig 6.1 Illustration of cylindrical shells affected by external decreasing pressure
49
6.3
Calculated results for pulling load process
For a pulling load of 200 tons and drum thickness of 70 mm, the hoop stress exerts onto the drum due to the load at each respective ξ positions with the number of wraps on the drum is as shown in Figure 6.2. According to our calculated results, the highest hoop stress occurs when the applied load is at ξ =0.8 from the near end of the drum due to the pulling load. The details calculation of maximum hoop stress is as shown in Appendix A. However, the highest hoop stress caused by uniform pressure has a magnitude of 429 MPa according to Table 3.2 method III as drawn in dashed line. So that, the percentage difference of highest hoop stress between the design codes and our results is 19%.
Therefore, it can be accomplished that the highest hoop stress, what we called a worse case scenario, occurs at ξ =0.8 from the near end of the drum and has a magnitude of 348.4 MPa. As a result, we can reduce certain amount of required drum thickness compared to the design codes. Hoop stres s on the drum after pulli ng load applie d at respective ξ position 0 Const
-90 a P -180 M n i s s -270 e r t S
ξ =0
-360
ξ =1
ξ =0.25 ξ =0.5 ξ =0.8
-450 1
4
8
13
Wraps
17
22
27
Fig 6.2 Hoop stress at each respective ξ positions on the drum applied by pulling load
50
6.4
Calculated results for braking load process
For a braking load of 300 tons and drum thickness of 70 mm, the hoop stress exerts onto the drum due to the load at each respective ξ positions with the number of wraps on the drum is as shown in Figure 6.3. According to our calculated results, the highest hoop stress occurs again at ξ =0.8 from the near end of the drum due to the braking load. The details calculation of maximum hoop stress is as shown in Appendix A. However, the highest hoop stress caused by uniform pressure has a magnitude of 643 MPa according to Table 3.2, method III as drawn in dashed line. This design codes maximum hoop stress is higher than the permissible stress level. However, our calculated maximum hoop stress is within the permissible level. Also, the percentage difference of highest hoop stress between the design codes and our results is 42%.
Therefore, it can be accomplished that the highest hoop stress, what we called a worse case scenario, caused by decreasing pressure occurs again at ξ =0.8 from the near end of the drum, whether the braking load is at that point or not and has a magnitude of 370.7 MPa. As a result, we can also reduce the certain amount of required drum thickness compared to the design codes.
51
HoopStress on the drumafter braking the loadat respective ξ position 0 -100
Const
-200 ) a P-300 M ( s -400 s e r t S-500
ξ=0 ξ=0.25 ξ=0.5 ξ=0.8
-600
ξ=1
-700 1
4
8
13
Wraps
17
22
27
Fig 6.3 Hoop stress at each respective ξ positions on the drum applied by braking load
52
6.5
Relationship between pulling and braking load
The main difference between these two process is the winding the rope on the drum. In the coiling (pulling) load process, the loaded rope is wound onto a winch drum in wrap by wrap starting from the near end to the desire position. Also, each successive wraps compress by radial pressure inwards on to the winch drum. As for the braking load, the unloaded rope was wound on the drum from the near end to the desired position before the load was being applied; unlike the process of coiling the loaded rope has been done on the drum. The comparison of loading type between these two applications can be clearly seen on the Figure 6.4 as below.
Braking load application
Pulling load application
Fig 6.4 Comparison of braking and pulling load in actual winch operation
Even though these two processes are different, the maximum hoop stress occurs in the same position, which is ξ=0.8 from the near end of the winch drum. In addition, the magnitude of maximum hoop stress in pulling and braking load application at ξ=0.8 is 348.4 MPa and 370.7 MPa, respectively.
53
In addition, Table 6.1 shows the comparison of maximum hoop stress at each respective ξ position between them. These calculated hoop stress will use to compute required design.
Table 6.1 Maximum hoop stress at respective ξ position for both applications
Maximum hoop stress (MPa) Applied load position Pulling Load 200 tons
Braking load 300 tons
ξ =0
-
-
ξ =0.25
110.4
141.8
ξ =0.5
220
242
ξ =0.8
348.4
370.7
ξ =1
335.7
345.6
As can be seen in the above Table 6.1, although the load applications and magnitude of load for each operations between the pulling load and braking load is different, the maximum hoop stress occurs at the same position of around third quarter (ξ=0.8) from the near end of the drum. In addition, our calculated maximum hoop stress between pulling load and barking are comparable as the different in percentage is only a 5%; the weight of braking load should be 1.5 times or less heavily than the weight of pulling loads.
54
6.6
Design code verses calculated results
According to the literature survey and our calculations, the DNV design guide gives more realistic, more suitable and more easier to compute the required design of winch drum, even though their formula are quite similar with SAA design guide. The only difference between these two design guides is the assumed maximum permissible stress. Therefore, the DNV design guide has been selected to compare with our calculated results and compute the maximum hoop stress condition. The detailed calculation of maximum hoop stress with actual operation data of DNV design code can be seen in Chapter 3, Section 3.1. Table 6.2 shows that the comparison between the DNV design guide and our calculated result output data.
Table 6.2 tabulates the maximum hoop stresses under the following conditions:
(a)
Uniform tension of the loaded rope in Design codes and Hampe’s Solution.
(b)
Decreasing tension of the loaded rope in Hampe’s Solution.
The percentage difference between the design codes and our results is 19% for the pulling load condition and 42% for the braking load condition, respectively. These percentage difference will be used to determine the required thickness of the improve design.
55
6 5
s s e r t S p o o H f o a t a d t l u s e r d e t a l u c l a c d n a e d o c n g i s e d V N D n e e w t e b n o s i r a p m o C 2 . 6 e l b a T
g h n t i i s w a e n r o c i t e ) a % D i r ( a v V e N g a D m t r n o f e i c n r e U P
e r u s s e r p
-
-
9 1
2 4
e r u s s e r p
-
-
0
0
g h n t i i d o s w h a t e a e r t c a M e d n D t o l i t u s u l e o r S d s e ’ t e a l p m r u o m c f l i a a n C H U
e r u s s e r p
0 2 5
2 4 4
4 . 8 4 3
7 . 0 7 3
e r u s s e r p
0 2 5
2 4 4
9 2 4
3 4 6
e d o C V N D
0 2 5
2 4 4
0 3 4
6 4 6
r a l u c i t r a P
, 3 . 2 5 T S l e e t a S P n M i s s e r t S d l e i Y
) s n o t 0 m 0 m 2 ( 0 d 7 ) a s e p o s σ e L n < g k h c σ n i i ( l h l t u h P t i
) s n o t 0 m 0 3 m ( 0 d 7 ) a s e p o s σ L e n g k > h n c σ i i ( k h a t r h t B i
a P M n i s s e r t S e l b i s s i m r o w e t P e u D
o w t e u D
6.7
Reinforced thickness for winch design
According to our calculated results, we found out that the other factor that can get a revamping profitable design is to reinforce the thickness only in the certain area of the winch drum, which will resist the higher compressive stress caused by the pulling or braking load in the winch operations. As refer to the Figure 6.1 and 6.2, it can be clearly seen that the maximum hoop stress occurred at around third quarter (ξ=0.8) from the near end of the drum with the drum thickness of 70 mm due to the pulling load. Moreover, the maximum hoop stress also occurred at the same position in the braking load process (Please see details in the section 6.4).
Even though the maximum hoop stress occurred at the same position between pulling and braking load condition, the improve design in reinforced thickness of winch drum will emphasize only on the pulling load condition as it gives more relevant data to see the clearer visualization of the continuous coiling. However, the suggested improve design guide will not only compute for pulling load, but also figure out for the braking load as well. For convenience calculations, we separated three sections as shown in Fig 6.6 which can apply the same formulae with this Hampe theory in separated sections for the reinforced application thickness of the drum.
As can be seen in the Figure 6.5, the graph was plotted for the 200 tons pulling loading condition throughout the winch drum with the required thickness of 60 mm. The details specification is as follows:
(I)
Drum diameter
=
1000 mm
57
(II)
Drum Length
=
1775 mm
(III)
Drum thickness
=
60 mm
(IV)
Diameter of Steel wire rope size
=
65 mm
(V)
Applied tension load (pulling)
=
200 tons
(VI)
Yield Stress for steel (ST 52.3)
=
520 MPa
(VII)
D/d ratio
=
15.4
=
Please see Table 6.3 row (1)
(VIII) Maximum hoop stress
6
= 1.96 x 10 N
Hoop stress on the 60 mm drum after pulling lo ad applied at respective ξ position 0 Const
-90 a P -180 M n i s s -270 e r t S
ξ =0
-360
ξ =1
ξ =0.25 ξ =0.5 ξ =0.8
-450 1
4
8
13
Wraps
17
22
27
Fig 6.5 Hoop stress at each respective ξ positions on the drum applied by decreasing pressure in uniform thickness of 60 mm
Table 6.3 Required thickness of the winch drum correlated with maximum load
Thickness of the drum
1
60
Maximum weight of
Hoop Stress in MPa
loading in Tons
and position
Pulling
200
Braking
Pulling
Braking
407
437
300
Permissible stress MPa
442 At ξ=0.8 (22nd wrap) 400
2
52
200
435
300
442 th
At ξ=0.66 (18 wrap)
58
As can be seen in the Figure 6.5 and Table 6.3, the maximum hoop stress occurs at ξ=0.8 which is around third quarter of the 60 mm drum and has a magnitude of 407 MPa and 437 MPa for puling and braking load, respectively. However, the winch drum had a capacity of 27 wraps of wire rope onto the full length of the drum.
According to the Figure 6.5 of pulling load application, the position of highest hoop stresses occurred at ξ=0.8 which is around third quarter of the drum, which means it occur between the (ξ=0.7) 19th to (ξ=0.88) 24th wraps on the drum. So that, the total of 6 wraps (from 0.7 to 0.88 ξ) which have to withstand the highest hoop stress between 382 to 407 MPa according to our calculated results. From this result, we could say that a quarter of total wraps on the drum has compressed the maximum hoop stresses on the drum. The rest of the wraps, other than between these wraps, withstand the hoop stresses are 366 MPa or less.
As a result, we can reduce the thickness the drum which is from near end (ξ=0) to 18
th
th
wraps (ξ=0.66) and 25 wraps (ξ=0.9) to far end (ξ=0). (The details illustration can be observed in Figure 6.6 and 6.7 as below). As can be seen in Table 6.4 row (2), the hoop stress occurred at the 18th wraps (ξ=0.66) and had a magnitude of 400 and 435 MPa in pulling and braking load, respectively for a 52 mm thickness of winch drum.
59
18 h wrap (ξ=0.66)
Pressure (P)
th
25 wrap (ξ=0.9) w
ξ
y x
Drum
R σ
2
Section 1 L
Near end
Section 3
D
Far end
t2=60mm thick t1=52 mm thick Load Fig 6.6 Illustration of cylindrical shells affected by external decreasing pressure in reinforced thickness of drum
Hoop stress on the variable thickn ess drum after pulling l oad applied at respective ξ position 0 ξ =0
-90 a P -180 M n i s s -270 e r t S
ξ =0.25 ξ =0.5 ξ =0.8 ξ =1
-360 -450 1
4
8
13
Wraps
17
22
27
Fig 6.7 Hoop stress at respective wraps on the drum applied by decreasing pressure in reinforced thickness of drum
The above Figures 6.6 and 6.7 shows that how the reinforced thickness of the winch drums should be fabricated and how the hoop stress exerted onto the drum in each and every position along the winch drum.
60
The detailed specification for modified winch drum in reinforced thickness is as follows:
(I)
Drum diameter
=
1000 mm
(II)
Drum Length
=
1775 mm
(III)
Drum thickness, t1
=
52 mm
(The thickness of 52 mm is from near end (ξ=0) to 18th wraps (ξ=0.66, 1170 mm) and 25th wraps (ξ=0.9, 1560 mm) to far end (ξ=0)) (IV)
Drum thickness, t2
=
60 mm from 1170 (ξ=0.66) to 1560 mm (ξ=0.9)
(V)
Diameter of Steel wire rope size
=
65 mm
(VI)
Applied tension load (pulling)
=
200 tons
= 1.96 x 106 N
(VII)
Applied tension load (braking)
=
300 tons
= 2.94 x 106 N
(VIII) Yield Stress for steel (ST 52.3)
=
520 N/ mm2 = 520 MPa
(IX)
D/d ratio
=
15.4
(X)
Maximum hoop stress in 60mm
=
407 MPa in pulling load
(XI)
Maximum hoop stress in 52mm
=
400 MPa in pulling load
(XII)
Permissible stress of material
=
442 MPa
(XIII) Maximum hoop stress in 60mm
=
437 MPa in braking load
(XIV) Maximum hoop stress in 52mm
=
435 MPa in braking load
61
As above calculated thickness and their position, we can predict that the general form of reinforced thickness into the certain area of the drum for fabrication is,
Length of the drum
=
L
Smaller thickness of the drum t1 is from 0 to 0.66 L and 0.9 L to L. Larger thickness of the drum t2 is from 0.66 L to 0.9 L.
6.10
Recommended required design thickness
According to our calculated result, the following table 6.4 and 6.5 tabulate the recommended thicknesses correlated with highest loadings for uniform thickness and reinforced thickness, respectively.
62
3 6
d a o l m u m i x a m h t i w d e t a l e r r o c m u r d h c n i w e h t f o s s e n k c i h t m r o f i n u d e d n e m m o c e R 4 . 6 e l b a T
r e t e e p o m a R i D
5 5 5 6 6 6
o d t / i a D R
3 . 3 . 3 . 5 5 5 1 1 1
l a d s a i s P 0 0 0 r e l e e 2 2 t i r M 2 5 5 5 a Y t s M e a l b P i s s i M s s m e r r e t P s g n i p a a k d o o P a o r L h M B m n u i m s s i g e x n d r i a t l a S l o M u l P g s t n d n h i o g k a i a o e T l r n B w i g m n g u i d m n d i a i x l a o l a l o u l M f o P e d h t e ) d f m n e o m s ( m s e m n m u o k r c c d e i R h T . r S
2 2 2 4 4 4 4 4 4
5 3 7 7 0 3 3 4 4
9 6 7 4 7 0 3 3 4
0 0 0 0 0 0 3 3 3
0 0 0 0 0 0 2 2 2
0 5 0 7 6 6
. . . 1 2 3
r e t e e p o m a R i D o d t / i a D R d a o l m u m i x a m h t i w d e t a l e r r o c m u r d h c n i w e h t f o s s e n k c i h t d e c r o f n i e r d e d n e m m o c e R 5 . 6 e l b a T
s s l a e i r a t r s P e t a d l e M M i Y e a l b P i s s M i s s m e r r e t P s g 1 n t i p k n o i a o r h a B P t s e M g s h n s g i i e l l r H t u S P 2 p t o n o i h a P m u M m s i s x e a t r M S
f o s t n h o g T i e n w i g m n u i d m i a x o a l M
5 5 5 6 6 6
3 . 3 . 3 . 5 5 5 1 1 1
0 0 0 2 2 2 5 5 5
2 2 2 4 4 4 4 4 4
7 2 5 7 1 3 3 4 4
7 9 1 4 7 0 3 3 4
g n i k a r B
5 3 7 7 0 3 3 4 4
g n i l l u P
9 6 7 4 7 0 3 3 4
g n i k a r B
0 0 0 0 0 0 3 3 3
g n i l l u P
0 0 0 0 0 0 2 2 2
) d f e 1 0 5 2 o m d t 6 5 5 m s n ( e s e m k n m u m r c d o i c 2 0 5 0 e t e h 7 6 6 T h R t . . . . r 1 2 3 S
. n o i t a c i r b a f r o f 1 t s i t s e r e h t d n a L 9 . 0 o t L 6 6 . 0 m o r f s i 2 t , n o i t a l u c l a c s s e n k c i h t d e c r o f n i e r 7 . 6 n o i t c e S n i s l i a t e d d e n o i t n e m s A
