Offshore crane shock absorber

An offshore crane shock absorber is a gas spring with hydraulic damping used to reduce dynamic loads during offshore lifting. The lifting capacity of the offshore crane can be increased significantly during lifting in high sea states if a shock absorber is fitted. ^[1]

Crane design load

Offshore lifting capacity is governed by classification society rules. The fundamental rule is that the design load should not be exceeded. The design load is given by:
${\displaystyle F_{m}=\psi m_{s}g}$

Where:
${\displaystyle F_{m}}$ - Crane design load
${\displaystyle \psi }$ - Dynamic coefficient
${\displaystyle m_{s}}$ - Safe working load
${\displaystyle g}$ - Acceleration of gravity

The classification societies require that ${\displaystyle \psi }$ ≥1.3 for offshore cranes. This means that ${\displaystyle m_{s}}$ cannot exceed ${\displaystyle {\frac {F_{m}}{\psi g}}}$ even for platform lifts. ^{[2] [3] [4]}

Dynamic load

To calculate the dynamic load the classification societies use energy equations. The kinetic energy of the load is expressed as:
${\displaystyle E_{k}={\frac {1}{2}}m_{s}v_{r}^{2}}$

Where:
${\displaystyle E_{k}}$ - Kinetic energy of the load
${\displaystyle v_{r}}$ - Relative velocity between crane hook and load

Energy absorbed by the crane is given by:
${\displaystyle E_{c}={\frac {1}{2}}ky^{2}}$

Where:
${\displaystyle E_{c}}$ - Spring energy stored in crane structure
${\displaystyle k}$ - Stiffness of offshore crane
${\displaystyle y}$ - Vertical displacement of crane hook

The spring force is given by:
${\displaystyle F_{c}=ky}$

Combining the two previous equations yields an alternative description of the energy stored in the crane structure:
${\displaystyle E_{c}={\frac {1}{2}}k({\frac {F_{c}}{k}})^{2}={\frac {F_{c}^{2}}{2k}}}$

During an offshore lift the crane does not start to absorb energy from the load before the force in the crane wire exceeds the static weight of the load, which means that we can write the energy absorption of the crane as:
${\displaystyle E_{c}={\frac {(m_{s}\psi g-m_{s}g)^{2}}{2k}}}$

Setting ${\displaystyle E_{c}}$ equal to ${\displaystyle E_{k}}$: ${\displaystyle {\frac {(m_{s}\psi g-m_{s}g)^{2}}{2k}}={\frac {1}{2}}m_{s}v_{r}^{2}}$

And solving for ${\displaystyle \psi }$:
${\displaystyle \psi =1+{\frac {v_{r}}{g}}{\sqrt {\frac {k}{m}}}}$

The dynamic factor will always be larger than 1 because there will always be a velocity difference between the crane hook and the load during offshore lifts. The value of ${\displaystyle \psi }$ determines the lifting capacity as a function of ${\displaystyle v_{r}}$ which is dependent on the significant wave height. If the offshore crane has a shock absorber mounted it will absorb energy according to:
${\displaystyle E_{a}=\eta \mu Sm_{s}g(\psi -1)}$

Where:
${\displaystyle E_{a}}$ - Energy absorbed by shock absorber
${\displaystyle \mu }$ - Stroke utilization (safety factor), standard value 0.9
${\displaystyle \eta }$ - Efficiency of shock absorber, usually possible to get close to 0.9
${\displaystyle S}$ - Stroke length

Adding this to the energy balance yields:

Dynamic coefficient versus relative velocity

${\displaystyle {\frac {(m_{s}\psi g-m_{s}g)^{2}}{2k}}+\eta \mu Sm_{s}g(\psi -1)={\frac {1}{2}}m_{s}v_{r}^{2}}$

Again solving for ψ:
${\displaystyle \psi =1+{\frac {{\sqrt {(\mu \eta Sk)^{2}+m_{s}kv_{r}^{2}}}-\mu \eta Sk}{m_{s}g}}}$

The plot to the right shows the effect of the shock absorber stroke length.

Estimating relative velocity

The relative velocity is defined by several classification societies as:
${\displaystyle v_{r}={\frac {1}{2}}v_{L}+{\sqrt {v_{d}^{2}+v_{c}^{2}}}}$

Where:
${\displaystyle v_{L}}$ - Maximum crane lifting velocity at this SWL
${\displaystyle v_{d}}$ - Vertical velocity of the deck which the load is placed on
${\displaystyle v_{c}}$ - Vertical velocity of the crane tip due to wave motion

${\displaystyle v_{L}}$ has to be gathered from crane user manual or be measured. The deck velocity can be estimated from Table 1.

Table 1: Deck velocity estimation

Lifting from or to	${\displaystyle v_{d}}$
Platform or fixed structure	${\displaystyle 0}$
Supply boat or barge	${\displaystyle 0.6H_{s}}$ if ${\displaystyle H_{s}}$ ≤3 ${\displaystyle 1.8+0.3(H_{s}-3)}$ if ${\displaystyle H_{s}}$>3

The crane tip velocity, ${\displaystyle v_{c}}$, can be estimated by Table 2.

Dynamic factor versus significant wave height

Table 2: Crane tip velocity

Lifting from or to	${\displaystyle v_{d}}$
Platform or fixed structure	${\displaystyle 0}$
Tension leg platform or Spar	${\displaystyle 0.05H_{s}}$
Semisubmersible	${\displaystyle 0.082H_{s}^{2}}$
FPSO or drillship	${\displaystyle 0.164H_{s}^{2}}$

These estimations are conservative and for large ships/rigs they may deviate significantly from reality. A plot of the dynamic factor versus significant wave height for a crane mounted on a semisubmersible and lifting from supply boat is shown above to the right.

References

1. The Engineers Guide Safelink AS
2. EN13852-1:2004 Cranes - Offshore cranes - Part 1: General - purpose offshore cranes
3. DNV Standard For Certification No. 2.22 Lifting Appliances October 2011
4. API 2C 7th Ed. Specification for Offshore Pedestal-mounted Cranes