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In order to explore a set of methods to analyze the structure of Lift-Drag Combined-Type Vertical Axis Wind Turbine (LD-VAWT), a small LD-VAWT was designed according to the corresponding Standards and General Design Requirements for small vertical axis wind turbines. The finite element method was used to calculate and analyze the static mechanical properties and modalities of main parts of a kind of small-scale LD-VAWT. The contours of corresponding stress and displacement were obtained, and first six-order mode vibration profiles of main parts were also obtained. The results show that the main structure parts of LD-VAWT meet the design requirements in the working condition of the rated speed. Furthermore, the resonances of all main parts did not occur during operation in the simulations. The prototype LD-VAWT was made based on the analysis and simulation results in this study and operated steadily. The methods used in this study can be used as a reference for the static mechanical properties and modal analysis of vertical axis wind turbine.

The vertical axis wind turbine (VAWT) has a simple structure and does not need special device to catch the wind. In addition, it is environmentally friendly; therefore, it has a rapid development in recent years. Among them, the Straight-Bladed Vertical Axis Wind Turbine (SB-VAWT) has been studied more deeply due to better power characteristics and higher transfer efficiency of wind energy. However, the starting characteristic is not well, which is one of the important factors restricting the development of SB-VAWT [

The model of LD-VAWT designed is shown in Figure

Basic structural parameters of LD-VAWT.

Name | Symbol | Value |
---|---|---|

Rated power [kW] | | 3 |

Rated wind speed [m/s] | | 10 |

Wind rotor diameter [mm] | | 4000 |

Wind rotor height [mm] | | 5200 |

Number of main blades | | 3 |

Chord length of main blade [mm] | | 400 |

Airfoil of main blade | | NACA0018 |

Attack angle of main blade [°] | | 0 |

Drag rotor diameter [mm] | | 700 |

Drag rotor height [mm] | | 2600 |

Mounting position of drag rotor [mm] | | 250 |

Model of LD-VAWT.

(1) Wind Rotor: The wind rotor of LD-VAWT is an important part, which can convert wind energy into mechanical energy. It is composed of main blade, drag rotor, beam, main axis, and so on. The main blade is made of FRP which has characteristics of being light, having high strength, having corrosion resistance, and being manufactured easily. The main blade is hollow and stiffened by two ribs, which can reduce the weight of blade. The main blade is shown in Figure

The structure of main blade.

The shape of drag rotor is a semicylindrical surface with thin wall thickness. In order to reduce the weight in the premise of strength requirement, the aluminum alloy material is selected. The thickness of aluminum plate is 3 mm. The structure of drag rotor is shown in Figure

The structure of drag rotor.

In Figure

(2) Nacelle: The nacelle consists of alternator, electromagnetic brake, main axis, and support bars as shown in Figure

The structure of nacelle.

The main axis in the nacelle is an important part in designing process. The diameter of axis is designed based on the analog method and empirical method. The minimum diameter of main axis is 40 mm and a pair of angular contact ball bearings with model number 7214 is used.

(3) Tower: The role of the tower is to support and fix the wind rotor and nacelle. The material of tower is Q235, the structure is shown in Figure

The parameters of tower.

Name | Value |
---|---|

Height [m] | 6 |

Outside diameter [mm] | 630 |

Inside diameter [mm] | 616 |

Wall thickness [mm] | 8 |

The loads of main blade during operation mainly include self-gravity

The static mechanical property of main blade is analyzed by finite element method (FEM). The tetrahedral element is selected as mesh type of main blade and the element type is Solid186. Finally, the finite element model of blade has 616368 elements and 212397 nodes. The material of main blade is FRP and the material properties are shown in Table

Material properties of main blade.

Name | Value |
---|---|

Density [kg/m^{3}] | 2 × 10^{3} |

Elastic Modulus [MPa] | 7.2 × 10^{4} |

Yield limit [MPa] | 450 |

Poisson ratio | 0.22 |

Allowable stress [MPa] | 320 |

In order to simulate the connected relation between main blade and beam, a fixed constraint is added at the connection point. Then the wind load is applied on the windward surface of main blade by pressure, the main blade weight is calculated by mass, and gravity acceleration and the centrifugal force are calculated by the rotational inertia load. The loads above are applied on the model of main blade. Finally, the contours of stress and displacement under the rated operation conditions can be obtained as shown in Figures

Equivalent stress contour of main blade.

Displacement variation contour of main blade.

From Figure

The calculating method of mechanical property of drag rotor is the same as main blade. The self-gravity

The solid 185 element is used to mesh and the number of elements and nodes are 457865 and 6956782, respectively. The material of drag rotor is aluminum alloy and the material properties are shown in Table

Material properties of drag rotor.

Name | Value |
---|---|

Density [kg/m^{3}] | 2.7 × 10^{3} |

Elastic Modulus [MPa] | 6.9 × 10^{4} |

Yield limit [MPa] | 276 |

Poisson ratio | 0.33 |

Tensile strength [MPa] | 350 |

In the analysis process, the nodes on the upside surface and downside surface of drag rotor are restrained. After calculation, the contours of stress and displacement under the rated condition are obtained as shown in Figures

Equivalent stress contour of drag rotor.

Displacement variation contour of drag rotor.

From Figure

The maximum load of beam happens at the rated speed 100 r/min of wind rotor. Therefore, analyses of the stress and deformation of beam are processed under the rated speed condition. Force and torque can be calculated as shown in Table

Load distribution of beam.

Name | Value |
---|---|

Self-gravity [N] | 115 |

Gravity of main blade [N] | 156 |

Gravity of drag rotor [N] | 105 |

Torque of main blade [N·m] | 119.2 |

Torque of drag rotor [N·m] | 645 |

Self-centrifugal force [N] | 120.4 |

Centrifugal force of main blade [N] | 3421.4 |

Centrifugal force of drag rotor [N] | 808.5 |

Material properties of beam.

Name | Value |
---|---|

Density [kg/m^{3}] | 7.86 × 10^{3} |

Elastic Modulus [GPa] | 211 |

Yield limit [MPa] | 196 |

Poisson ratio | 0.3 |

Tensile strength [MPa] | 235 |

The Degrees of Freedom (DOF) are constrained on the displacements of X, Y, and Z directions at the end of connection position of beam and main axis. Then the gravity load, centrifugal load, and torque load are applied on the model, respectively. The contours of stress and displacement of beam under the rated condition are obtained by calculation as shown in Figures

Equivalent stress contour of beam.

Displacement variation contour of beam.

From Figure

From the calculation,

The stiffness checking formula is shown as follows:

After calculating, ^{−3} m < [^{−3} m, the stiffness of beam under the rated speed meets the design requirements.

The main axis is mainly subjected to gravity load, centrifugal load, and aerodynamic load. The values of loads are shown in Table

Received force of main axis.

Name | Value |
---|---|

Gravity of main axis [N] | 630 |

Gravity of wind rotor [N] | 3250 |

Torque of wind rotor [N·m] | 1045 |

Centrifugal force of wind rotor [N] | 0 |

In the static mechanical analysis of main axis, tetrahedral element is used to mesh grids. The numbers of elements and nodes are 87536 and 159853, respectively. The material of main axis is 40Cr, and the properties are shown in Table

Material parameters of main axis.

Name | Value |
---|---|

Density [kg/m^{3}] | 7.86 × 10^{3} |

Elastic Modulus [MPa] | 2 × 10^{5} |

Yield limit [MPa] | 400 |

Poisson ratio | 0.3 |

Tensile strength [MPa] | 980 |

According to the assembly relation, the end of main axis connected with generator is constrained. The self-gravity load of main axis is applied with gravity acceleration, the gravity of wind rotor is applied at mounting position of flange, and the torque of wind rotor is also applied at mounting position of flange. The simulation results are shown in Figures

Equivalent stress contour of main axis.

Displacement variation contour of axis.

From Figure

According to formula (

The calculation result shows that the maximum deformation of main axis is 0.27 mm.

The tower is mainly subjected to horizontal thrust of the wind rotor, the gravity of wind rotor and nacelle, self-gravity, the torque of wind rotor, and the wind pressure acting on the tower. The values of loads distributing on the tower are shown in Table

Load distribution of tower.

Name | Value |
---|---|

Horizontal thrust [N] | 1132.4 |

Gravity of wind rotor and cabin [N] | 8330 |

Self-gravity of tower [N] | 8291 |

Torque of cabin [N·m] | 286.5 |

Wind pressure [N/m] | 27.1 |

The material of tower is Q235 and the solid 185 is selected as element type. The numbers of elements and nodes are 15696 and 30864, respectively.

The bottom of tower is constrained. The above loads are applied on the model of tower and the contours of stress and deformation of tower are shown in Figures

Equivalent stress contour of tower.

Total deformation contour of tower.

From Figure

When the wind turbine works in natural environment, the load is complex and changeable. The power of air, inertia force, and elasticity force applied on the blades of wind turbine can make blade and tower deform and oscillate. If the frequency of exciting force approaches the natural frequency of the structure, the resonance may lead to damage of wind turbine. In order to avoid resonance, the natural frequency of wind turbine should be different from the one of wild exciting force. Therefore, the modal analysis should be carried out during the structural design of wind turbine.

The model of main blade used in the modal analysis is the same as statistic analysis. The low-order mode of main blade has a great influence on stability and fatigue of blade, and the first six-order modes and the natural frequencies are calculated which are shown in Table

The first six-order mode natural frequency of main blade.

Order | Value |
---|---|

First order [Hz] | 18.0535 |

Second order [Hz] | 18.0543 |

Third order [Hz] | 28.2657 |

Fourth order [Hz] | 75.4023 |

Fifth order [Hz] | 80.6801 |

Sixth order [Hz] | 80.7842 |

The first six-order mode vibration profile of main blade.

First-order mode vibration profile

Second-order mode vibration profile

Third-order mode vibration profile

Fourth-order mode vibration profile

Fifth-order mode vibration profile

Sixth-order mode vibration profile

From Figure

The model of drag rotor used in the modal analysis is the same as the static analysis. Similarly the frequencies of first six-order modes are shown in Table

The first six-order mode natural frequency of drag rotor.

Order | Value |
---|---|

First order [Hz] | 50.2653 |

Second order [Hz] | 50.3117 |

Third order [Hz] | 50.3735 |

Fourth order [Hz] | 50.4092 |

Fifth order [Hz] | 50.4428 |

Sixth order [Hz] | 76.6961 |

The first six-order mode vibration profile of drag rotor.

First-order mode vibration profile

Second-order mode vibration profile

Third-order mode vibration profile

Fourth-order mode vibration profile

Fifth-order mode vibration profile

Sixth-order mode vibration profile

From Figure

The main axis is one of the important parts of wind rotor and nacelle, which not only needs to check the strength and stiffness but also avoid resonance phenomenon. Therefore, based on the model of static mechanical property analysis, the natural frequencies of first six-order modes of main axis are shown in Table

The first six-order mode natural frequency of main axis.

Order | Value |
---|---|

First order [Hz] | 8.35907 |

Second order [Hz] | 8.35938 |

Third order [Hz] | 52.2301 |

Fourth order [Hz] | 52.2319 |

Fifth order [Hz] | 145.56 |

Sixth order [Hz] | 145.565 |

The first six-order mode vibration profile of main axis.

First-order mode vibration profile

Second-order mode vibration profile

Third-order mode vibration profile

Fourth-order mode vibration profile

Fifth-order mode vibration profile

Sixth-order mode vibration profile

From Figure

Similarly the FEM model of tower in the modal analysis is the same as the static mechanical property analysis and the contact surfaces between tower and ground are constrained. The natural frequencies of first six-order mode of tower are shown in Table

The first six-order mode natural frequency of tower.

Order | Value |
---|---|

First order [Hz] | 15.2166 |

Second order [Hz] | 15.2166 |

Third order [Hz] | 88.6749 |

Fourth order [Hz] | 88.6749 |

Fifth order [Hz] | 120.362 |

Sixth order [Hz] | 168.738 |

The first six-order mode vibration profile of tower.

First-order mode vibration profile

Second-order mode vibration profile

Third-order mode vibration profile

Fourth-order mode vibration profile

Fifth-order mode vibration profile

Sixth-order mode vibration profile

From Figure

According to the design of LD-VAWT with the static mechanical property and modal analysis, the results show that the design of wind turbine structure is reasonable. A prototype of LD-VAWT was designed and made. It was tested in a farm of Northeast Agricultural University of China which is shown in Figure

Actual machine of wind turbine.

Based on the observation of its operation situation for a period of time, the wind turbine can work safely and stably according to the design goal, which shows that the design scheme is practicable and proves that the ideas and methods for LD-VAWT are correct. The paper provides references to analyze the structure of the LD-VAWT.

In order to explore a set of methods about designing and analyzing the structure of LD-VAWT, the paper took a small-scale LD-VAWT as an example and analyzes the static mechanical property and modal analysis by finite element method; the conclusions are as follows.

The corresponding contours of stress and deformation were obtained by using ANSYS to analyze the static mechanical property of main parts of wind turbine, which concludes that the structure of wind turbine meets the design requirements.

The first six-order mode vibration profiles of main parts were also obtained based on the modal analysis, which concludes that the resonance of each main part will not resonant during the operation.

The prototype LD-VAWT was made based on the analysis and simulation results in this study and operated steadily. The methods used in this study can be used as a reference for the static mechanical properties and modal analysis of vertical axis wind turbine.

The authors declare that they have no conflicts of interest.

This research is sponsored by the Project 2017MS02 supported by the Foundation of Key Laboratory of Wind Energy and Solar Energy Technology, Ministry of Education. The authors thank the supporter.