Modeling, simulation and design optimization of a hoisting rig active heave compensation system

Abstract

The objective of this paper is to present an approach in developing a virtual active heave compensation system for a draw-works on a hoisting rig. A virtual system enables quicker overall product development time of a physical system as well as flexibility in optimizing the design parameters. Development of the virtual system started with the modelling of the draw-works and hoisting rig dynamics. Simulations of this model were run in two operational modes while subject to a sinusoidal wave: heave compensation and seabed landing of a payload. The results were analyzed and used for optimization in terms of cost and performance. This lays the groundwork for further testing either through hardware-in-the-loop testing (HIL) or using an actual prototype.

Appendix A. SimulationX model

1.1 Mechanical model implementation

This section shows how the simulation model was implemented from the equations of motion for the mechanical system. The system was set up from the payload and upwards toward the active drum. The structure of each major part: combined payload, wire dynamics, sheave system, bearing-pin friction are explained briefly. The actual values and references used in the simulation blocks are included in the sections below.

1.2 A.1 Combined payload

1.2.1 External forces

The payload is modeled by a mass component. It is attached to by five external forces. These are the forces described in Eq. 1. For clarification, Pulling Force in the simulation model consists of the wire forces pulling the payload. PayloadIni gives the initial position of the payload so that it starts in a position where the wires are very close to outstretched to reduce initial oscillations. It is derived in this way:

$$ x_{ini} = \frac{F}{n \times k} $$

where n is the number of wires connected to the combined payload. The other blocks are self-explainable.

1.2.2 Inertia

The Mass block automatically calculates the linear inertia from the parameters put into it, thus not requiring any additional input from the user.

1.2.3 Seabed dynamics

Seabed dynamics is implemented by adding the damping force component with the spring force component and feeding the result into the SeabedDynamics function. The important thing about the seabed dynamics is that it must only activate if the payload position is at −5 m. An if-else statement is made in Damping and Stiffness to account for this.

1.3 A.2 Wire dynamics

The Wire dynamics part includes the equations for wire forces (Eqs. 2, 3, 4 and 5), elongation (Eqs. 6, 7, 8 and 9) and rate (Eqs. 11, 12, 13 and 14. Additionally, there are function blocks with data of outer and inner wire section masses: halfwmass0 and halfwmass1 respectively.

To aid calculation of the total lower wire mass Nr is multiplied with PerMeter and halfwmass1. The Nr block is for the number of wire sections and PerMeter is for the mass per meter datum derived from the mass per 100 m from the Certex wire catalogue. This datum is included in the payload block in the CombinedPayload part.

1.3.1 Wire force

The wire forces are implemented in the WireForce block. The spring stiffness and damper coefficients are fed into these blocks through the WireStiffness and WireDamping blocks. The wire cross-sectional area is written in block SpringArea and used in finding the wire stiffness.

The inner wire forces (WireForce1, WireForce2) calculated in this part is used in the PullingForce block in part Combined Payload. Both inner and outer wire forces are used in calculating sheave and drum torques (SheaveTorque and Active blocks) and normal force in bearing-pin friction (Normal blocks).

1.3.2 Elongation and rate

Equations for wire elongation and rate are put in the Elongation and Rate blocks. Their outputs are sent to the WireForce blocks.

1.3.3 Wire mass and inertia

The blocks halfwmass0 and halfwmass1 depict half the outer and inner wire section masses respectively. They are used in

• the blocks DrumTorque, sheavetorque 1 and 2 to account for the wire mass’ effect on the drum and outer sheave torques.

• The normal forces in the bearing-pin friction part (Normal blocks).

• the payload block as part of the combined payload, thereby having the lower wire section mass’ inertia modeled. Its effect on the elongation will also be included by doing this.

1.4 A.3 Sheave system

This part contains the sheaves, active and passive drums and a subpart called Component Dimensions which have Function blocks containing data for the component dimensions.

1.4.1 Sheave mass and inertia

The travelling block sheave’s mass is included in the payload block in the Combined Payload part. This accounts for the linear inertia of the sheave. The crown block sheaves have no linear inertia in relation to the power source so they are not included. The sheave’s rotational inertia is implemented through the Inertia block. This value is calculated from Eq. 30.

1.4.2 Sheave torque

The sheaves’ torques are modeled by attaching External Torque blocks to the inertia blocks with equations from Eqs. 27, 28 and 29.

1.4.3 Active drum

The active drum is set up in the same fashion as the sheaves with Inertia blocks representing the inertia calculated in Eq. 32. The active drum torque is also modeled by attaching an External Torque block to its inertia block. The External Torque block had to be connected from the right side of the Inertia block because of the need of a Preset block. Doing this makes the torque act against the coordinate direction, thus the value inside this block needs to have a minus sign to reverse this effect. The preset allows the user to set a prescribed state of motion. For example, to hold the drum still a fixed state can be set. This function will prove useful in verifying the static analysis results. When the mechanical model is attached to the hydraulic model later on this preset is removed and attached to the gearing.

1.4.4 Component dimensions

In this subpart the radius for the active drum, sheaves and sheave bearings are stored in function blocks. The inertia of the active drum and sheave are also stored in function blocks along with the sheave mass. The outputs of these blocks are subsequently referred to the inertia and External Torque blocks for the active drum and sheaves. The SheaveMass is used in the bearing-pin part.

1.5 A.4 Bearing-pin friction

The Bearing-Pin Friction part of the simulation model contains functions of the normal forces that are used to calculate the bearing-pin frictions. The Eqs. 21, 22 and 23 are implemented in these blocks. The data in the Normal blocks are referred to the sheavetorque blocks where they are multiplied with the bearing radius and bearing-pin friction coefficient to include the effects of friction on the sheaves’ torques. The data in the Normal blocks are absolute values.

1.5.1 Function 1, 2, 3

These Function blocks include if-else statements that create a transitional slope <1 for when the friction moment changes direction. Before implementing this feature, SimulationX would have issues simulating the system due to the sharp directional changes of the sheaves.

1.5.2 Heave motion

This part has one signal block generating a sine wave with the parameters of the heave motion as per Eq. 10. Its output is included in the Elongation blocks to account for the heave motion’s effect on wire elongation Fig. 22.

Fig. 22

Curves for relative valve stroke for the two servo valves during load case 2

1.5.3 Hydraulic model

Implementation of the hydraulic model follows the same method as that of the mechanical one. The relevant simulation components with the correct dimensions are used. The result is the model seen in Fig. 23.

Fig. 23

SimulationX model of the hydraulic system with three sheaves

1.5.4 Model fusion

Putting the mechanical and hydraulic models together is achieved by connecting the gear component to the active drum component.