The modeling of the swing winches of a cutter dredge in relation with simulators

S.A. Miedema[1]

Abstract

When developing a simulator for cutter suction dredges, the different processes have to be considered non-stationary and dynamical. A simulator usually consists of a combination of input by a user and hard- and software processing this input and generating output. In the case of a cutter suction dredge simulator the manual control of the swing winches, by means of joysticks, is one of the important inputs for the simulation process.

The position of the joysticks determines a set point for either the swing velocity or the revolutions of the hauling swing winch. By means of a control algorithm the hauling winch will generate a hauling torque, while the braking winch exerts a brake torque. This results in pulling forces in both the swing wires. These forces, combined with the cutting forces and the current forces, result in a rotation around the active spud. This rotation can be described with the equilibrium equation of the dredge around the active spud.

Introduction

The dredge motions consist of the six degrees of freedom of the pontoon complemented with the rotation of the ladder around the ladder bearings. This gives a total of 7 degrees of freedom (surge, sway, heave, roll, pitch, yaw and ladder rotation). For a dredge operating in still water, when wave forces are ignored, the motions in the horizontal plane are relevant (surge, sway and yaw) as well as the ladder rotation. The three pontoon motions can be reduced to the rotation around the spud if the spud is considered to be infinitely stiff. If the ladder rotation is considered not to be the result of a mass-spring system, but controlled by the ladder winch, only one equilibrium equation has to be solved, the rotation of the pontoon around the spud. The other 6 equilibrium equations are of interest when working offshore, when wave forces have to be taken into account, but using these equations increases the calculations to be carried out enormous.

The motions of the dredge

The equilibrium equation of rotation around the spud is a second order non-linear differential equation, with the following external forces:

The inertial forces of pontoon and ladder
The water damping on pontoon and ladder
The spring forces resulting from the swing wires
The external forces resulting from the current
The external forces resulting from the cutting process
The external forces resulting from the swing winches
The external forces resulting from the pipeline
The reaction forces on the spud

1. The inertial forces (moments) determine whether there is an acceleration or deceleration of the rotation around the spud. These forces are the result of the equilibrium equation and thus of the external forces.

Fig. 1: The display of the top view of the cutterdredge, also showing the channel.

2. The water damping and the current forces depend on the value and the direction of the current and on the rotational speed of the pontoon around the spud.

3. The spring forces resulting from the swing wires and the forces resulting from the swing winches strongly depend on the characteristics of the winches and the wires and the winch control system. The position of the anchors in relation to the position of the spud and the position of the swing wire sheaves on the ladder determines the direction of the swing wire forces and thus of the resulting moments around the spud. Figure 4 shows the winch output of a research simulator.

Fig. 2: The display of the back view of the cutterdredge, also showing the cross-sectional channel profile.

4. The forces and moment excerted on the pontoon by the current influence the rotation around the spud depending on the current speed and the swing speed. For small values of the current speed this effect can however be neglected. For high values of the current speed the influence depends on the direction of the current and the swing angle. It may occur that the swing winches do not have enough power to pull back the pontoon out of a corner due to the angle of the swing wires and a high current speed.

5. The cutting forces and the cutting torque strongly influence the rotation around the spud, these will be discussed in the paragraph concerning the cutting forces.

6. The winch forces and the winch moment strongly influence the rotation around the spud, these will be discussed in the paragraph concerning the swing winch characteristics.

7. The forces resulting from the pipeline can be neglected if the position of the swivel elbow is close to the position of the work spud, because in this case this force hardly influences the rotation of the pontoon around the spud.

8. The reaction forces on the spud can be determined by the equilibrium equations of forces and complement this equilibrium. These forces however do not contribute to the moment around the spud.

The rotation of the pontoon around the spud is dominated by the cutting forces, the winch characteristics, the inertia of pontoon and ladder and placement of the anchors, while damping and current play a less important role. The equilibrium equation can be formulated as:

(1)

The water damping is combined with the current moment, the wire spring force, the pipeline moment and the spud moment are not taken into consideration. Equation 1 thus reduces to:

(2)

The equilibrium equation in question is non-linear, while some of the data is produced by interpolation from tables. This implies that the equation will have to be solved in the time domain, using a certain time step. This is also necessary because the simulation program has to interact with the console (the user input). To simulate the motions of the dredge real time, a time step of at least two times per second is required. A time step of 5 to 10 times per second would be preferred.

Fig. 3: The display of the side view of the cutterdredge, also showing the longitudinal channel profile.

The influence of the swing angle on the wire moment

With fixed anchor positions, the angle of attack of the swing wires relative to the axis system of the pontoon, changes continuously with the value of the swing angle. With large swing angles this may result in a large decrease of the effective pulling or braking moment of the swing wires. This decrease of course depends on the anchor positions relative to the pontoon.

In this paper the following coordinate system definitions are applied:

1. The origin is placed in the centerline of the work spud.

2. The two wire sheaves are positioned on the centerline through the work spud and the cutterhead.

3. The positive swing direction is counter clock wise, with an angle of zero degrees when the centerline of the dredge matches the vertical axis (y-axis).

4. The distance from the center of the workspud to the center of the sheaves is L_ss.

Fig. 4: The output of the winch parameters.

With the coordinates if the swing sheaves on the ladder x_ss and y_ss according to:

(3)

And

(4)

Fig. 5: The coordinate system with the dredge in the neutral position.

The length of the port wire and the angle of the port wire with the centerline of the channel can be determined according to:

(5)

and

(6)

The length of the starboard wire and the angle of the starboard wire with the centerline of the channel can be determined according to:

(7)

and

(8)

Fig. 6: The coordinate system with the dredge at a swing angle f_s.

The angle of the port wire with the centerline of the dredge is:

(9)

The angle of the starboard wire with the centerline of the dredge is:

(10)

The moment around the spud, resulting from the forces in the swing wires can now be determined by:

(11)

The relation between the rope speed of the port wire and the angular speed of the dredge is now:

(12)

The relation between the rope speed of the starboard wire and the angular speed of the dredge is now:

(13)

This results in loss of effective power of both winches. The power mobilized by the winches to the angular speed of the dredge is:

(14)

The power consumed by the winches is:

(15)

The winch characteristics

The torque speed characteristic of the winches consists of two parts if an electric drive is assumed. The first part runs from 0 revolution up to full revolutions and has a linear decrease of the torque, from a maximum at zero revolutions to the full torque at full revolutions. At this last point also the full power of the drive is reached. At higher revolutions the drive will use field weakening, while the power stays constant. In the simulator it is assumed that the characteristics for hauling and braking are equal.

If one winch is in hauling mode, the other one will always be in braking mode.

Fig. 7: The torque-speed characteristic of the winches.

The control system of the winches

The hauling winch is controlled by a setpoint for the winch revolutions. The braking winch is controlled by a setpoint for the braking torque. So for the hauling winch, the available torque results from the revolutions, while the pulling force also results from the drumdiameter and the number of layers on the drum. The mobilized torque also depends on the loads (cutter and current) and on the angular acceleration of the dredge around the spud pole.

Fig.8 shows the actual revolutions of the hauling winch, the setpoint of the hauling winch, the setpoint of the braking winch and the load curve for the hauling winch. The load curve includes the cutting process, the current and water damping and the braking winch. The difference between the available torque and the torque resulting for the loads is available for the acceleration of the pontoon. In the example given in fig. 8, it is assumed that the actual revolutions of the winch are smaller then the setpoint and that the available torque is larger then the required torque for compensating the loads.

The actual torque mobilized by the hauling winch, is always the resulting torque necessary to reach or stay on the setpoint. If in a certain situation, the torque available is less then the torque required, then the available maximum torque is assumed.

In this case the working point is the intersection point of the load curve with the vertical dotted line through the setpoint of revolutions. The maximum available torque is not fully mobilized.

Fig. 8: The torque-speed characteristic of the winches with the setpoints. Case where the required torque is sufficient.

Fig. 9: The torque-speed characteristic of the winches with the setpoints. Case where the required torque in the setpoint is not sufficient.

Fig. 9 shows the case where the winch torque required in the setpoint is not sufficient. In this case, the working point is the intersection point of the load curve with the torque-speed curve. The maximum available torque is fully mobilized. The setpoint is not reached because there is not sufficient torque available.

Fig. 10 shows the case where the setpoint is smaller then the actual revolutions. In this case, the pontoon will decelerate. The working point is the intersection point of the vertical through the setpoint and a minimum torque required keeping the wire from going slack.

Fig. 10: The torque-speed characteristic of the winches with the setpoints. Case where the setpoint is smaller then the actual revolutions.

Case studies.

To show the behavior of the dredge-winch system two cases will be shown. In the first case the dredge starts on the centerline of the channel. The dredge and winch layouts are shown in Figure 11.

Fig. 11: The dredge, winch and channel layout.

Fig. 12: The dredge 30 degrees to port (left) and 30 degrees to starboard (right).

Case 1:

The winches have a drum diameter of 0.84 m, a full power of 158 kW at 8.87 rpm. The resulting full torque is 167 kNm. The anchor positions are symmetrical with respect to the centerline and are 65 m in horizontal direction and -21.5 m in vertical direction, away from the sheaves on the ladder. The ladder is not in contact with the bank and is moving free through the water.

The following actions are taken:

1. The setpoint for the swingspeed is set to 24 m/min to starboard.

2. The dredge swings from 0 to 30 degrees to starboard.

3. The setpoint for the swingspeed is set to 24 m/min to port.

4. The dredge swings from 30 degrees starboard to 30 degrees port.

5. The setpoint for the swingspeed is set to 24 m/min to starboard.

6. The dredge swings from 30 degrees port to the centerline.

Fig. 13 shows the rope speeds and pulling forces for both the port and the starboard winch. It is clearly shown in the graphs in Figure 13 that, while the rope forces increase instantly, the rope speed increases or decreases according to a first or second order system. This is caused by the mass-spring-damper system according to equation 1, but also by the inertia of the winches themselves. In the simulator, the winches are modeled as a first order system. The winches and the dredge need some time to accelerate or decelerate.

The deceleration requires more time in case 1 then the acceleration, because the braking force is set to 30% of the maximum force, which is about 180 kN. The pulling force however, can be much higher, depending on the characteristic of the winches. Setting the braking force to a higher value, will increase the speed of the deceleration.

Typical for this case is, that the pulling wire is more and more perpendicular to the ladder when the swing angle approaches 30 degrees. This results in a decreasing pulling force, which can be seen in Figure 13. The braking force is set to a constant value and will only differ from this value if the braking force is larger then the torque-speed curve permits it to be. In that case the braking force will follow the torque speed curve.

Fig. 13: The rope speeds and forces for case 1.

Case 2:

The winches have a drum diameter of 0.84 m, a full power of 158 kW at 8.87 rpm. The resulting full torque is 167 kNm. The anchor positions are symmetrical with respect to the centerline and are 65 m in horizontal direction and +3.5 m in vertical direction, away from the sheaves on the ladder, as is shown in Figure 15.

The ladder is not in contact with the bank and is moving free through the water.

The following actions are taken:

1. The setpoint for the swingspeed is set to 24 m/min to starboard.

2. The dredge swings from 0 to 30 degrees to starboard.

3. The setpoint for the swingspeed is set to 24 m/min to port.

4. The dredge swings from 30 degrees starboard to 30 degrees port.

5. The setpoint for the swingspeed is set to 24 m/min to starboard.

6. The dredge swings from 30 degrees port to the centerline.

Fig. 14 shows the rope speeds and pulling forces for both the port and the starboard winch. Because the anchors are moved 25 m forward in the channel, now the angle between the pulling wire and the ladder decreases when the dredge approaches the 30 degrees swing angle. This results in an increase of the pulling force as is visible in Figure 14. The start and stop behavior is almost equal to case 1.

Fig 14: The rope speeds and forces for case 2.

CONCLUSIONS

The modeling of the winches and the wires consists of solving the equilibrium equation of motions of the dredge around the spudpole in combination with the characteristics of the winches. The two cases show that it takes about 10 seconds to accelerate to a swing speed of 24 m/min. The time required for the deceleration is of the same magnitude, but depends of course on the setpoint of the brake force.

The two cases also show, that the shape rope speed and force as a function of time, strongly depend on the position of the anchors relative to the sheave positions at the ladder. The two cases describe symmetrical configurations, which of course is not always the case. An infinite number of configurations can be chosen. Which configuration is the best depends on the work to be carried out and on the boundary conditions of the work to be carried out.

Recommendations

In a next paper the control system of the winches will be described in greater detail. Also the influence of the current and the cutting process will be included more extensively.

Fig. 15: The dredge and anchor layout for case 2.

REFERENCES

Cox, C. M., Eygenraam, J. A., Granneman, C. C. O. N., and Njoo, M., A Training Simulator for Cutter Suction Dredgers: Bridging the Gap between Theory and Practice, Proceedings of World Dredging Congress, WODCON XIV, Amsterdam, The Netherlands, November, 1995.

Digital Automation and Control Systems (DACS), Hydraulic Dredging Simulator, Houston, Texas, 1994.

Miedema, S. A. Considerations in Building and using Dredge Simulators, Proceedings of the Western Dredging Association XIX Technical Conference and 31^st Texas A&M Dredging Seminar, Louisville, KY, Center for Dredging Studies, Texas A&M University, College Station, TX, May 15-18, 1999.

Miedema, S. A. Modeling and Simulation of the Dynamic Behavior of a Pump/Pipeline System, Proceedings of the WEDA Technical Conference and Texas A&M Dredging Seminar, New Orleans, June 1996.

Miedema, S. A., Production Estimation Based on Cutting Theories for Cutting Water Saturated Sand, Proceedings of World Dredging Congress, WODCON XIV, Amsterdam, The Netherlands, November, 1995.

Randall, R. E. and Albar, A. Cutter Suction Dredge Simulator Training Manual, Center for Dredging Studies, Ocean Engineering Program, Civil Engineering Department, Texas A&M University, College Station, Texas, January 2000.

Randal, R.E. and deJong, P.S. and Miedema, S.A., Experiences with Cutter Suction Dredge Simulator Training. Proceedings of the WEDA Technical Conference and Texas A&M Dredging Seminar, Rhode Island, June 2000.

LIST OF SYMBOLS USED

c_yaw	Spring constant of the yaw motion	kNm/rad
F_pw	Rope force of the port wire	kN
F_sw	Rope force of the starboard wire	kN
I_yaw	Mass moment of inertia of pontoon in yaw direction	kNms²/rad
k_yaw	Damping coefficient of pontoon in yaw direction	kNms/rad
L_pw	Length of the port wire	m
L_ss	Distance from working spud to swing sheaves on ladder	m
L_sw	Length of starboard wire	m
M_current	Moment around the spud exerted by the current	kNm
M_cutting	Moment around the spud exerted by the cutting process	kNm
M_pipe	Moment around the spud exerted by the floating pipeline	kNm
M_spud	Moment around the spud exerted by the spud	kNm
M_wires	Moment around the spud exerted by the swing wires	kNm
n_full	Full revolutions of the swing winch	rpm
P_pw	Power of the port winch	kW
P_pwm	Power of the port winch mobilized on the dredge	kW
P_sw	Power of the starboard winch	kW
P_swm	Power of the starboard winch mobilized on the dredge	kW
P_w	Power of both winches	kW
P_wm	Power of both winches mobilized on the dredge	kW
T_acc	Winch torque available for acceleration or deceleration	kNm
T_full	Full torque of the winches	kNm
T_max	Maximum torque of the winches	kNm
v_pw	Rope speed of the port winch	m/sec
v_sw	Rope speed of the starboard winch	m/sec
x_pw	X coordinate of the port anchor	m
x_ss	X coordinate of the swing sheaves on the ladder	m
x_sw	X coordinate of the starboard anchor	m
y_pw	Y coordinate of the port anchor	m
y_ss	Y coordinate of the swing sheaves on the ladder	m
y_sw	Y coordinate of the starboard anchor	m
f_s	Swing angle	rad
j_pw	Port wire angle	rad
j_sw	Starboard wire angle	rad