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

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

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

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

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

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

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

Where:

Cf = Bending fatigue Count

Cb = Bending Cycle Count

Ml = Load Modifier

Mlc - Load Collective Modifier

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)

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

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]

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]

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]

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]

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.

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

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

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

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

For Clarity reference is made to the reeving plan shown above

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

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

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

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)

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)

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]

Total Wire = Hook depth from Deck [m]

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]

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]

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)

Bending cycle count is multiplied based on the following :

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

Where:

Mlc = Load Collective Modifier;

V = Load Collective Value;

n = Number of Load Collectives;

Nc = Total Collective Count (LCM).

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

This is the modifying value whose value is determined below

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

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

The value for this determined as follows

Where

Nc = Total Collective Count

SL =Service Life [days]

U = Utilisation [%]

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

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

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

This is the modifying value whose value is determined below

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

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]

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

U =Is taken as 40%

VLow = 1

VMed = 0.999288754

VHigh = 0.9981034059

Using

E.g. for Vmed count

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

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.

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

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

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

These are ignored given impact expectations <1%

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