Applied

Steel Wire Rope Bending Cycle fatigue

Part One-Bending Cycle Counting

The series titled  Wire Rope Integrity Management is to be read in conjunction with the Whole Life management of Steel Wire ropes procedure  and consists of the following elements:

Part One – Bending Cycle Counting

Part Two – Initial Setting of Trigger Action and Trigger Discard Values

Part Three –  Empirical assessment of Steel Wire Rope Service Life using Bending fatigue Calculation

Part Four – Practical example of Bending fatigue Calculator Hardware

Part Five -  Structural Fatigue Cycle Counting


Definitions


Load Modifier

Multiplier applied to bending cycle count depending on applied load on the Wire


Load Collective Modifier

Multiplier applied to bending cycle count depending on Collective of Loads applied to Wire rope


Bending Fatigue Calculator Solution

A Hardware / Software solution as described in Part Four – Practical example of Bending Fatigue Calculator Hardware


Trigger Action Value (TAV)

Section line Bending Cycle Fatigue count to trigger some further action ( NDT, Cut back, determination of ABL etc)


Trigger Discard Value (TDV)

Extended  section line Bending Cycle Fatigue count that leads to discard of the Wire Rope. This is always greater than the TAV.


Summary






Determining Bending Cycles in a Reeved System (Cb)

Standard Bending Cycles

A Complete bending cycle is  considered to be one where the Rope passes from one state to another and then returns to its original state. An example could be a rope passing over a sheath. The rope is straight, it is then bent and is then returned to the straight state.


When a rope passes onto a drum this is considered a half cycle as the rope passes from a Straight State to a Bent State

Symbol


Where:

Cf = Bending fatigue Count

Cb = Bending Cycle Count

Ml = Load Modifier

Mlc -  Load Collective Modifier


Example

A Rope Running over two sheaths has  a Fatigue Cycle count of 2 (1+1)


A Rope running onto a drum in which there is no change in bending plane  has a fatigue cycle count of 1 ½ (1 + ½)


Reverse Bending Cycles

These are considered to be Two Standard Bending Cycles. The increased damaging relative effect of Reverse bending cycles on systems designed with generous D/d ratios is considered in the assignment of the Bending Cycle Modifier and the  Load Collection Modifier

Symbol


Examples

A Rope Running over two sheaths in which there is a change in plane of bending has  a Fatigue Cycle count of 4  [(1+1) x 2]


A Rope running onto a drum in which there is a change in bending plane  has a fatigue cycle count of 3

[(1 + ½) x 2]


Effects of Change of Plane

If the plain of action of the wire rope changes by 90’ or more,  this is to be considered a Reverse bending cycle


If A >90o then the Standard Cycles is doubled. In this case the effects of the plane displacement is to increased the Bending cycles from 2 to 4  from 2 to 4 [( 1+1) x 2]


1.1 Effects of Distance between Sheaves

Where sheaves are mounted within one Circumference of each other then they are to be considered as a reverse bending Cycle


If Ds <= 2πRs then the Standard Cycles is doubled. In this case from 2 to 4 [( 1+1) x 2]


1.1 Complex System Bending Cycles


These are considered to be systems in which there is a greater than one modifying value.



In the above system ( which appears as the double sheave arrangement on one vessel  for lowering the Lubricator Wire to deck level) the fatigue cycle count is 8 as the effects of having the sheaves close together and the reverse bend are experienced


(1+1) x 2 x 2]


Types of Reeved system for Bending Cycle Fatigue Calculation

For the purposes of bending fatigue calculation Reeved systems are considered to be one of tow forms

Simple – in which consistent values on cycle multipliers are applied

Complex – In which two or more multiplier values must be applied determined by  the effects of local geometry.

Simple

Examples of Simple reeving Systems are  all systems on the Well Intervention Towers and pod and guide wire systems


For simple systems the bending cycles are considered to effect ALL the rope within the Wire Rope in Compensated Zone evenly


Complex

Examples of complex Reeving Systems are the Lubricator Wire for one vessel and the Diving Bell Handling System on another vessel.


Complex systems are split into sections against which local Bending fatigue Cycle counts are applied.


The methodology for generating these counts is identical to that of a simplex system other than it is repeated for each section. For clarity only the Simple system is considered in these calculations


Generating Bending Cycle count in a Reeved System

Key Assumption


Accumulative Compensation generated  Bending Cycles are considered to act upon the local  length of rope in the Compensated zone. Exception is given where distance between sheaves is less than the circumference of may be specially considered


A bending cycle is considered complete when the wire rope moves  one half the circumference of the  Sheaves


Shown Below is the reeving plan for Well Intervention System


Well Intervention System Reeving Plan


Bending Cycle Plan


The blue standard cycles indicate the sheaves which are in motion during compensation. The additional  Cycles are those that are employed during  deployment / recovery


= 5 in Compensation

= 7.5 in deployment / recovery


Rope Affected by  Compensation

For Clarity reference is made to the reeving plan shown above



Length of rope

Determined though Formula

This  is the distance from the  last Sheave after the live end of the wire rope that does not see rope movement ( in the above diagram this is Sheave 2) and some distance after the final sheave before the load.


Where

Rcz   = Wire Rope in compensated Zone [m]

Rsf   =Position of rope from dead end on drum to Final sheave before load [m]

Rsd  =  Position of Rope from dead end on drum to sheave after the live end of the wire rope that does not see rope movement when in compensation [m]

Rc = Movement of Rope   due to compensation



Estimated ( Well Intervention reeving)

In this calculation RC is taken as SWH(max) of the system.

Total Wire   =  (2-3) + (3-4) + (4-5) + (5-6) + (6-7) + SWH(max)  

 =SWH(max)  + 4.5[m] + 4.5[m] + 4.5[m] + 4.5[m] + SWH(max)  

Where 4.5m = length of wire between sheaths ( this is not the same as the areas over which the compensator works, this figure is taken to allow for variation in lay of wire relative to the Hull which will lead to wire being payed out or recover to ensure the compensator remains at mid stroke.

 =  18[m] + 2.SWH(max)  

 =26[m]

Where SWH(max) =4 [m]



Total affected wire length  = 30[m]  allowing for variation in lay of wire relative to the Hull which will lead to wire being paid out or recover to ensure the compensator remains at mid stroke



Position of Rope

Determined though Formula


The Commencement position of rope is to be considered the compensated distance before the first sheath with  the live zone. In the above reeving plan this can be considered sheath 3


Where

Rpc = commencement position of  rope in compensated  zone from  drum end [m]

Rsl  = Position of Rope from dead end on drum to sheave within  the live end of the wire rope that does  see rope movement when in compensation [m]

Rc = Movement of Rope   due to compensation


The Completion position of rope is to be considered the  compensated distance after  the final sheave  before the load. In the above reeving plan this can be considered sheath 7


Where

Rpe = Completion  position of  rope in compensated  zone from  drum end [m]

Rsf   =Position of rope from dead end on drum to Final sheave before load [m]

Rc = Movement of Rope   due to compensation


Estimated ( Well Intervention reeving)

In this calculation RC is taken as SWH(max) of the system.



Rope affected (Start)  = Hook Depth +Wire rope to Sheath 3 -  SWH

    =Hook Depth + 42M – SWH


Rope affect (End)   = Rope affect (Start) +30[m]


Simplified


Rope affected (Start)   = Hook depth + 40[m] ( rounded down to next multiple of 10)

Rope affect (End)     =Rope affect (Start) +30[m] ( rounded up to next multiple of 10)


Cycles Due to Compensation in Simple Reeving System


Where

Cc = Cycles  due to Compensation

Rc = Movement of Rope due to Compensation [m]

r = Sheave radius,   for generic systems this is considered to be 13 times the wire rope diameter [m]


Mdr =  Bending Cycle Plan Multiplier (see MAR/BBE/12/009)


Bending Cycles During Recovery Deployment

Length of rope

Calculated


Where

Rdz   =Rope length in deployment / recover Zone

Rsf   =Position of rope from dead end on drum to Final sheave before load [m]

Rw  = Position of rope from dead end on winch to Rope Position,  four  complete Wraps into Drum ( this may be taken where not known as 25m for simplification)   [m]

Rdr  = deployed Length of wire [m]


Estimated

Total Wire   =  Hook depth from Deck [m]


Position of Rope

Calculated


Where

Rdc   =Rope length in deployment / recover Zone

Rw  = Position of rope from dead end on winch to Rope Position,  four  complete Wraps into Drum ( this may be taken where not known as 25m for simplification)   [m]

Rdr  = deployed Length of wire [m]



The Completion position of rope is to be considered the  distance  from rope end at the Winch Drum to   the final sheave  before the load. In the above reeving plan this can be considered sheath 7


Where

Rpe = Completion  position of  rope in compensated  zone from  drum end [m]

Rsf   =Position of rope from dead end on drum to Final sheave before load [m]



Estimated

Rope affected (Start)  = Wire deployed from First Sheath

   =36[m]


Rope affected (End)   = Rope Affected(start) + Hook depth + length of rope in Sheaths (midstroke)

   =36[m] + hook depth + 24[m]

   =Hook depth + 60[m]


Simplified

Rope affected (Start)   = 30[m] ( rounded down to next multiple of 10)

Rope affect (End)     = Hook depth + 60[m]



Cycles Due to Deployment recovery in Simple Reeving System


Where

Cdr = Cycles in Deployment OR Recovery

D = Movement of Hook during Deployment / recovery [m]

r = Sheave radius,


Mdr =  Bending Cycle Plan Multiplier (see MAR/BBE/12/009)


1.0 Load Multiplier (Ml)

Bending cycle count is multiplied based on the following :


Load Collective Modifier (Mlc)

Key Assumption

A Wire rope which sees a higher proportion of heavy lifts will have a significantly shortened in Service life


Calculation of LCM


Where:

Mlc  =  Load Collective Modifier;

V  =  Load Collective Value;

n  =  Number of Load Collectives;

Nc  = Total Collective Count (LCM).


Load Collective Modifier (Mlc)

This is the numeric modifier value which is used to increase the modified Fatigue Cycle count


Load Collective Value (V)

This is the modifying value whose value is determined below


Number of Collective Counts (n)

This is the number of collective counts during the period for which the LCM is to be calculated


Total Collective Count (Nc)

This is the total number of collective counts in the service life of the wire rope as calculated below. The Collective count is based around a  typical period of base of [Day]  or one  24 hour period, although this can be modified to method of assimilation of Load Collection modifier into bending fatigue Cycle calculator



Determination of Total Collective Count (CN)


The value for this  determined as follows


Where

Nc  = Total Collective Count

SL  =Service Life [days]

U  = Utilisation [%]



Service Life (SL)

This is the is the estimated service life of the  Wire rope  which is subject to Low Load Collectives only. This is given in days


Utilisation (U)

This is  the estimated period of utilisation of the Wire Rope during the service life as a percentage



Total Collective Count (Nc)

This is the total number of collective counts in the service life of the wire rope as calculated below


Determination of Load Collective Values


Load Collective Value (V)

This is the modifying value whose value is determined below


Total Collective Count (Nc)

This is the total number of collective counts in the service life of the wire rope as calculated below



Worked Example ( Calculating the Default Total Collective Count and Load Collective Values for Intervention / Derrick)

This worked example generate the default values for  use when initially setting up a Wire Rope fatigue Monitoring System. The Units for the Total Collective Count is the default  [ Day]


Calculating total Collective Count (Nc)


SL = Is in accordance is taken initially as 4 years  of  365 days = 1460

U  =Is taken as 40%


Calculating the Load Collective Values (V)


VLow = 1


VMed  =  0.999288754


VHigh   =  0.9981034059


Using

E.g. for Vmed count

Determining  in-service systemic  Load Collective magnitude

The load collective is calculated via  consideration of load over a the Unit period of the Total Collective Count (Nc). The Default value is [Day]  and this is utilised in this description


Each Nc [Day] is divided into a Number of  Collection Periods. At these points an immediate snapshot is taken of the current load. This load is used to determine an Index value which is summated over the Unit Period for the total Collective count. The value of this summation provides the  Load Collective magnitude.


Where

It = Summated value for Index Values

Pc = Number of Collection Periods in the Total Collective Count Unit

Iv =  Index value dependent on Load determined as followed


The Averaged  Index value (It/Pc) is then used to determine the applied Load Collective Value


Collection Periods (Pc) per day

This is determined by the method Load date is collected. Typically it involves snapshot of the  current load on the crane on a fixed periodic base. Longer Collection periods simplifies data management but may exclude the effects of short period lifting operations.  Shorter periods provide a greater degree of accuracy but may exaggerate the effects of short term overloading.



Not Considered

The following are not considered in the calculation of bending Cycle count but are used  in  setting the Trigger Action values as described in Wire Integrity management

Part Two – Initial Setting of Trigger Action and Trigger Discard Values,   and

Part Three –  Empirical assessment of Steel Wire Rope Service Life using Bending fatigue Calculation


Sheath Losses

As these are accepted as a fixed percentage it is ignored in the counting


D/d ratio

As the Fatigue Cycle Counter described is based around empirical setting of limits the fixed values of D/d ratio means it is ignored in this


Tension – Tension Stresses

These are ignored given  impact expectations <1%   


Effects of Fleeting Angle


Example of flowchart for building in an LCM into a cycle counter