Power generation of the designed system

Due to power losses in both the electrical and mechanical subsystems, situations can occur where the amount of power produced by the system is lower than the energy consumed by the system to produce the requested PTO-force. This is because the system is optimised for performance rather than energy production. This results in a very high mechanical efficiency and a good motor efficiency, but due to the constant switching losses in the frequency inverter of the drive, the high efficiencies of the other components in the system make no difference with regard to the produced energy, as shown in Figure 19.

Figure 19: Sankey diagram of the electrical power generated for a test cond ition in which the average mechanical power absorption of the buoy is 50 W.

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6 Conclusion

A test rig for a scaled WEC that can actively control the motion of a buoy through the use a power take-off (PTO) has been designed based on preformulated design requirements and WEC-Sim input data. As the test rig must allow for an accurate database of wave interactions to be created, unquantifiable parameters must be avoided during the design. One major example of such a parameter is friction, which is minimised through the use of air bushings in the linear guide system. A stiff bearing configuration of three air bushings is used to convert any moment loads on the bearing system into pure radial forces while only allowing vertical displacement of the buoy.

The structural properties and performance of the mechanical design are evaluated for all wave conditions from the input data through the use of finite element methods. Furthermore, these methods are also used to iteratively dimension and thereby optimise the mechanical components of the system while remaining suitable for all test conditions.

The mechanical and electrical components of the power take-off have been dimensioned and optimised for the test conditions. The complete test rig, including the power take-off system is modelled in a Simulink system model where it is directly coupled to the WEC-Sim software. This model allows for evaluation of the test rig through comparison with an ideal system from the WEC-Sim library, thereby providing a new set of WEC-Sim input data based on a more realistic model of the system.

As the model can be simulated without the need to import time-dependent WEC-Sim simulation data, the hydrodynamic forces acting on the system are influenced by the performance of the designed PTO-system during the simulation. The position-, velocity and acceleration simulation results of the Simulink model using the designed test rig to apply the PTO-force to the system are nearly identical to those of the Simulink model using the ideal WEC-Sim translational PTO-system.

The position, velocity and acceleration of the system model using the designed test rig are slightly smaller in amplitude and show a seemingly insignificant amount of lag compared to the results obtained from simulations using the ideal PTO-system. This is due to the delay introduced by the designed test rig model where the PTO-force request is determined through measurement of the velocity of the buoy, which is then converted into a PTO-torque request for the motor. The motor then requires 5 milliseconds to attain the desired PTO-PTO-torque, resulting in a suboptimal timing of applying the PTO-force, which in turn causes the hydrodynamic forces to be smaller as these are determined by the velocity and position of the buoy, which both depend on the PTO-force.

In the next phase of the project, the designed test rig will be constructed from the bill of materials and tested in a scaled WEC-farm configuration. During the construction of the test rig, the Simulink model can be refined by adding motor and gearbox efficiency maps. After a first experimental test, the accuracy of the system model can be evaluated and based upon this data, it can be optimised. The system model can also be used as an emulator in software-in-the-loop tests for controller strategies before they are tested on the actual hardware.

26

References

[1] A. Techet, ‘Object Impact on the Free Surface and Added Mass Effect’, 2005.

[2] ‘Vessel theory: Stiffness, added mass and damping’. [Online]. Available:

https://www.orcina.com/SoftwareProducts/OrcaFlex/Documentation/Help/Content/html/Vesseltheory, Stiffness,addedmassanddamping.htm. [Accessed: 17-Dec-2018].

[3] T. S. Sarpkaya, ‘Hydrodynamic Damping’, in Wave Forces on Offshore Structures, Cambridge: Cambridge University Press, 2010, pp. 265–284.

[4] V. Stratigaki et al., ‘Wave Basin Experiments with Large Wave Energy Converter Arrays to Study Interactions between the Converters and Effects on Other Users in the Sea and the Coastal Area’, Energies, vol. 7, no. 2, pp. 701–734, Feb. 2014.

[5] A. Kortenhaus et al., Design features of the upcoming Coastal and Ocean Basin in Ostend, Belgium. 2016.

[6] Y.-H. Yu, K. Ruehl, J. Van Rij, and N. Tom, ‘WEC-Sim (Wave Energy Converter SIMulator)’. National Renewable Energy Laboratory and Sandia Corporation, 2015.

[7] N. Quartier, ‘Numerical implementation of the power-take-off (PTO) of two types of generic wave energy converters using WEC-Sim’, Ghent University, 2018.

[8] J. Boodts and A. De Schaepmeester, ‘Numerical study and experimental testing of heaving buoys for modelling of a wave energy converter for the WECwakes II project’, Ghent University, 2018.

[9] M. Folley, Numerical Modelling of Wave Energy Converters: State-of-the-Art Techniques for Single Devices and Arrays. Elsevier Science, 2016.

[10] ‘Siemens NX’. Siemens PLM Software, 2016.

[11] G. Tampier and L. Grueter, ‘Hydrodynamic analysis of a heaving wave energy converter’, Int. J. Mar. Energy, vol. 19, pp. 304–318, Sep. 2017.

[12] R. Boere, R. Goudswaard, T. Schneider, and B. van Vlijmen, ‘Interaction of Ocean Wave Energy Converters’, 2018.

[13] R. G. Coe, G. Bacelli, D. Patterson, and D. G. Wilson, ‘SANDIA REPORT Advanced WEC Dynamics &

Controls FY16 Testing Report’.

[14] ‘US Navy MASK basin’. [Online]. Available: http://www4.edesign.co.uk/portfolio/nswcdd-mask-basin-usa/. [Accessed: 18-Dec-2018].

[15] ‘New Way Air Bearings’. [Online]. Available: https://www.newwayairbearings.com. [Accessed: 18-Dec-2018].

[16] D. L. Bull, R. G. Coe, M. Monda, K. Dullea, G. Bacelli, and D. Patterson, ‘Design of a Physical Point-Absorbing WEC Model on which Multiple Control Strategies will be Tested at Large Scale in the MASK Basin’, Albuquerque, 2015.

[17] SKF Motion Technologies, ‘SKF: Linear ball bearings D-series catalogue’. [Online]. Available:

https://www.skfmotiontechnologies.com/sites/default/files/Linear_Ball_Bearings_D-series_catalogue.pdf. [Accessed: 17-Feb-2019].

[18] B. Automation GmbH, ‘System manual for Servo Drives AX5000’, 2018.

[19] Beckhoff, ‘AG2800 Planetary Gearbox datasheet’, 2017.

[20] Beckhoff Automation, ‘AM8832 datasheet - Stainless steel servomotor’. [Online]. Available:

https://download.beckhoff.com/download/Document/Catalog/Main_Catalog/english/separate-pages/Drive_Technology/AM8800.pdf. [Accessed: 26-May-2019].

1

Attachment

A. Gearbox and motor dimensioning

Selection of the servo gear unit

Step 1: Preliminary determination of the gear unit reduction ratio:

Determine maximum angular velocity of the gearbox output shaft.

Assumed rated motor speed of the servomotor (𝑛𝑅) = 3000 [rpm] with a 10% additional safety margin:

𝑖𝑝𝑟𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑟𝑦= 𝑛_𝑅 [𝑟𝑝𝑚] − (0.1 ∙ 𝑛_𝑅)[𝑟𝑝𝑚]

𝑛𝑜,𝑚𝑎𝑥 [𝑟𝑝𝑚]

= 3000 𝑟𝑝𝑚 − (0.1 ∙ 3000) 𝑟𝑝𝑚

666.9 𝑟𝑝𝑚 = 4.0845

Thus, the selected gear unit reduction ratio is 4. (AG2800-+HDV015S-MF1-4-1C1-AM883x planetary gearbox) The maximum input speed of the gearbox (𝑛𝑖𝑛,𝑚𝑎𝑥) is:

𝑛𝑖𝑛,𝑚𝑎𝑥 [𝑟𝑝𝑚] = 𝑖 ∙ 𝑛𝑜,𝑚𝑎𝑥 [𝑟𝑝𝑚] = 4 ⋅ 666.9 𝑟𝑝𝑚 = 2667.6 𝑟𝑝𝑚

This value must be below the maximum rated input speed of the selected gearbox.

2667.6 [𝑟𝑝𝑚] < 3000 [𝑟𝑝𝑚] (value from HDV015-datasheet, page 24/34 [19])

 Selection requirement fulfilled.

Step 2: Determine the static and dynamic torques:

The first static torque (𝑀𝑠𝑡𝑎𝑡𝑖𝑐,1) can be calculated using the rms-value of the maximum PTO-Force:

𝑀𝑠𝑡𝑎𝑡𝑖𝑐,1 [𝑁𝑚] = 𝐹𝑃𝑇𝑂,𝑚𝑎𝑥 [𝑁] ∙ 𝐷𝐿 [𝑚]

_{𝐿𝑜𝑎𝑑}⋅ 2 ⋅ √2

= 230 𝑁 ⋅ 0.042441 𝑚 0.98 ⋅ 2 ⋅ √2

= 3.521 𝑁𝑚

The second static torque (Mstatic,2) can be calculated when the buoy is being lifted out of the water with a constant velocity:

2 The dynamic torque (𝑀𝑑𝑦𝑛) has to be calculated over the trajectory of the buoy when it is lifted out of the water as this is the most demanding cycle for the PTO-system.

The first dynamic torque (𝑀𝑑𝑦𝑛,1) is the torque required to accelerate the buoy upward with a constant

The second dynamic torque (𝑀𝑑𝑦𝑛,2) is the torque required to decelerate the buoy during its upward motion before locking it in place. A constant deceleration of 4 m/s² is applied throughout the deceleration process.

𝑀_{𝑑𝑦𝑛,2} [𝑁𝑚] = (𝑔 [𝑚 𝑠⁄ ] − 𝑎 [𝑚 𝑠² ⁄ ]) ⋅ 𝑚 [𝑘𝑔] ⋅ 𝐷² _𝐿 [𝑚] ⋅_{𝐿𝑜𝑎𝑑} 2

= (9.81 𝑚 𝑠⁄ ²− 4 𝑚 𝑠⁄ ) ⋅ 36.7283 𝑘𝑔 ⋅ 0.042441 𝑚 ⋅ 0.98² 2

= 7.801 𝑁𝑚

Step 3: Determine the peak output torque (𝑀𝑜,𝑝𝑒𝑎𝑘) and select the gear unit size:

As the PTO-force to extract energy from the buoy is no longer applied during the lifting, the largest torque from the static- or dynamic torques calculated in step 2 is the largest output torque of the system. This torque value, multiplied by a safety factor of 1.4 as the system is a hoisting application, must be less than the maximum rated output torque of the selected gearbox to fulfil the maximum output torque requirement.

𝑀𝑜,𝑝𝑒𝑎𝑘 [𝑁𝑚] = 𝑀_{𝑑𝑦𝑛,1}[𝑁𝑚] ⋅ 1.4 = 10.983 𝑁𝑚 ⋅ 1.4

The mean output speed of the gearbox output shaft must be lower than the rated output speed of the gearbox output shaft (𝑛_𝑘), with a 10% additional safety margin.

𝑛_{𝑜,𝑎𝑣𝑔} [𝑟𝑝𝑚] ≤ 𝑛_𝑘  471.57 rpm ≤ (3000 𝑟𝑝𝑚 − 0.1 ⋅ 3000 𝑟𝑝𝑚)

4 = 675 𝑟𝑝𝑚

 Design requirement fulfilled.

Step 5: Ensure that the permitted thermal torque of the gearbox (𝑀𝑇𝐻) is not exceeded:

The maximum output torque and speed are used to calculated the thermal torque of the application (𝑀𝑇𝐻,𝑎𝑝𝑝).

This torque value must be a factor 1.2 lower than the rated gearbox torque (𝑀𝑅𝑎𝑡𝑒𝑑).

𝑀_{𝑇𝐻,𝑎𝑝𝑝} [𝑁𝑚] = √𝑇_{𝑤𝑎𝑣𝑒} [𝑠] ⋅ 𝑛_{𝑜,𝑚𝑎𝑥} [𝑟𝑝𝑚] ⋅ (𝐹_{𝑃𝑇𝑂,𝑚𝑎𝑥} [𝑁] ⋅ 𝐷_𝐿 [𝑚]

 Design requirement fulfilled, no risk of thermal overload in the gearbox.

3 Selection of the servomotor

Step 6: Convert the maximum output moment during normal operation to the motor side:

𝑀_{𝑖𝑛,𝑚𝑎𝑥}= 𝑀𝑜,𝑚𝑎𝑥

𝑖 ⋅_{𝑔𝑒𝑎𝑟}

= (230 𝑁 ⋅ 0.042441 𝑚 0.98 ⋅ 2 )

4 ⋅ 0.97 = 1.284 𝑁𝑚

The gear efficiency (_{𝑔𝑒𝑎𝑟}) is the efficiency that is provided by the HDV015-gearbox datasheet on page 24/34.

The lightest motor series, suited for the environment and compatible with the selected gearbox, is the AM883x-motor series. The AM8832-AM883x-motor from the AM8800 stainless steel servoAM883x-motor catalogue ([20] page 3/10), has a rated torque (𝑀𝑁) of 1.4 Nm. Further characteristics of this motor are:

Peak torque (𝑀𝑚𝑎𝑥) [Nm] 6.3

Step 7: Check the additional motor torque for acceleration:

𝑀_{𝑚𝑜𝑡𝑜𝑟}=𝐽_{𝑚𝑜𝑡𝑜𝑟}[𝑘𝑔𝑚²] ⋅ 𝑎_𝑚𝑎𝑥[𝑚 𝑠⁄ ] ⋅ 𝑖 ⋅ 2² 𝐷_𝐿 [𝑚] ⋅_𝐿⋅_{𝑔𝑒𝑎𝑟} ⁼

0.795 ⋅ 10⁻⁴ 𝑘𝑔𝑚²⋅ 8.471 𝑚 𝑠²⁄ ⋅ 4 ⋅ 2 0.042441 𝑚 ⋅ 0.98 ⋅ 0.97

= 0.1335 𝑁𝑚

The PTO generator torque is however proportional to the velocity of the buoy, which is shifted a quarter of a wave period out of phase with the acceleration. Because of this, the motor acceleration does not increase the maximum motor torque request when the PTO-force is at its maximum. However, the motor acceleration does have an impact when the buoy is accelerated at 4 m/s² while being lifted out of the water. The torque required for this operation must be lower than the peak torque value of the motor (𝑀𝑚𝑎𝑥).

𝑀_{𝑚𝑜𝑡𝑜𝑟}=𝐽_{𝑚𝑜𝑡𝑜𝑟}[𝑘𝑔𝑚²] ⋅ 𝑎_{𝑙𝑖𝑓𝑡}[𝑚 𝑠⁄ ] ⋅ 𝑖 ⋅ 2²

 Design requirement fulfilled, even with the 1.4 safety factor for hoisting applications.

Step 8: With the rms motor torque and speed, the working point of the most extreme regular wave test condition can be marked:

4 To ensure no thermal overloading of the motor arises in dynamic applications, the rms motor torque value should be less than S1-torque value of at 1886 rpm divided by 1.2.

𝑀𝑆1,1886 𝑟𝑝𝑚 [𝑁𝑚] = 1.148 𝑁𝑚 𝑀𝑆1,1886 𝑟𝑝𝑚 [𝑁𝑚]

1.2 =1.148 𝑁𝑚

1.2 = 0.956 𝑁𝑚 > 0.908 𝑁𝑚

 Design requirement fulfilled, no thermal overloading of the motor occurs, even when combining the largest PTO-force with the highest angular velocity of all conditions.

Step 9: Inertia ratio calculation:

Writing out in Word unfinished as of now, but results are:

Inertia ratio = 13 for the AM8832 motor, which is tolerable according to the SEW-manual for rack and pinion or toothed belt applications with gearbox and motor.

Acceleration torque due to inertia of the gear unit: 0.095 Nm => Ieff,motor [A] can be calculated with the motor torque constant, Ieff,motor = 0.6126 Arms

 AX5101 servo drive [18]

Rated output current = 1.5 A

Maximum output current = 4.5 A = Motor maximum current (for 6.3 Nm torque) EMC category = checked, 25 m cable connection (One Cable Technology, OCT) Power loss in S1 mode: 35 W (including power supply unit)

Maximum braking power of external resistor = 15 kW (minimum resistance = 47 ) Pbrake,peak = 346.2 W

Pbrake,rms = 170.5 W

5

B. Overhanging mounting position

Figure 20: Assembly of the test rig in the overhanging mounting position.

Figure 21: Rendering of how a scaled WEC-farm can be constructed with the designed test rigs in overhanging mounting position.

6

C. Design optimisation iterations

Table 4: Overview of the exported output of the iterative design optimiser from the Siemens NX software.

7

D. Bill of materials