Study on rigid-flexible coupling multi-body dynamic model and simulation for wind turbine

Ji-zhe HAI，Wen-lei SUN，Yu-jun ZHOU

(School of Mechanical Engineering，Xinjiang University，Urumqi 830047，China)

1 Introduction

The design life of wind turbine unit is generally up to 20 years during which it is hard for engineers and technicians to test and analyze the entity structure during the long term of operation.So，how to test and simulate the dynamic performance of virtual prototype in design phrase of wind turbine has become a concerned problem for researchers in wind power［1］.The early research of wind turbine system was based on rigid-body system.However，with the increase of overall dimensions of wind turbine，the influences of the flexibility of tower and blade structure to dynamics can’t be neglected.Dynamic analysis of multi-body system which contains the effect of flexible body can simulate the real operation conditions of the generator more accurate and reliable simulation data can be obtained from it.

A lot of research work on multi-body dynamics model construction and dynamic characteristics of wind turbine generator has been done by researchers in wind power both at home and abroad.Yanfeng Deng et al［2］based on the original put forward a modified Craig-Bampton modal synthesis method to analyze multi-body dynamics.Dynamic Substructure method considering the effect of elastic deformation was proposed by Yoo et al［3］which was based on the finite element method of nonlinear dynamics.Xiurong Dou［4］built a simplified dynamic model of a horizontal axis wind turbine by using elastic hinge method.By analyzing the vibration characteristics and coupled vibration characteristics of tower and blade the natural frequency and modal shape were obtained.Due to the deficiency of zero-order model Jiazhen Hong［5］explored a new model which studied the analysis of rigid-flexible coupling dynamics and rigid dynamic problem.Moreover，the accuracy of model was verified through comparative analysis.

In this paper，by using SIMPACK，a soft for analyzing multi-body dynamics，the model of a MW wind turbine was built based on the theory of coupled rigid and flexible multi-body dynamics analysis of mechanical system.Besides，natural frequency and modal shape were obtained from the modal analysis of wind turbine.The simulation of wind turbine unit was completed by defining internal unit controller and using AeroDyn，a soft for calculating aerodynamic loads.From above，the displacement，response of dynamic acceleration and deflection of leaf tip of tower parts under three different conditions which reflects the dynamics of wind turbine unit.

2 Model construction of wind turbine unit’s multi-body dynamics

The flexible multi-body dynamics model can be divided into three systems，blade-hub system，enginetransmission system and tower-foundation system.Flexibility of blades and tower should be considered in multi-body dynamics analysis.For flexible blades，first four step modal is usually considered which mainly includes first two step flapping modal and first two step shimmy modal.For flexible tower，first two step modal is always considered.

2.1 Calculation parameters and topology of wind turbine unit

The analysis model is a MW land-based wind turbine and the design code is by reference to IEC2005 wind turbine whose wind scale is class II and turbulence intensity is class A.In addition，the blade length is 61.5 m and single blade quality is 17，695 kg.The tower with quality of 1，935，346 kg，stands 120 m high which contains the upper half of steel tower drum and the lower half of concrete tower drum.The key calculation parameters are shown in Table 1.

Accurate topology graph of wind turbine operation is the key to build the analysis model of dynamics from which relative motion and force among the parts of wind turbine system can be reflected correctly and intuitively.Besides，the effects of flexible structure should be fully considered and the model should be simplified appropriately.Topology graph of wind turbine unit is illustrated in Fig.1.

Table1 Thekey calculation parametersof wholewind turbineunit

It can be concluded from Fig.1 that the wind turbine unit was divided into three parts，blade-hub system，engine-transmission system and tower-foundation system according to the direction of aerodynamic transmission.The model of blade and tower，the flexible body，were built in detail but the remaining parts were simplified in which the internal structure of the gear box was not considered.In topology of wind turbine，the simulation of relative movement between parts was completed by means of kinematic pair simulation and the force relation was by force element simulation.In general，there are six degrees of freedom of a moving part at most in three-dimensional space.The three directions of rotation and three of translation are expressed by α，β，γ andx，y，z.For corresponding to pitch-regulated mechanism，the relative movement between blade and variable propeller flange was simulated by degrees of freedom rotating aroundzaxis and 110th force element.The simulation of relative movement between draft and engine room was completed through the degrees of freedom rotating aroundxaxis and 210th force element which corresponds to brake system.Moreover，the movable tower foundation and ground was by means of kinematic pair simulation with six degree of freedom and 43rd force element.The remaining parts were connected by kinematic pair with zero degree of freedom.

2.2 Model construction of blade－hub system

Dynamic model of hub includes dome，flange and pitch-regulated mechanism.Because the geometric figure was neglected，the connection relation between blade and hub should be defined exactly.The built-in blade generator of SIMPACK make it more convenient complete the flexible body model of blade.In generator，.rbx format file indicated the detailed parameters of blade which includes the definition of rigid and flexible attribute，definition of marking points and segmental parameters such as centroid position，rotational inertia of unit length，pneumatic rigidity torsional angle in the direction of flap and lag，length of chord and airfoil thickness.Further，based on the .rbl format file，the .rbx format file defined the shape of airfoil section to build blade structure model［6］.Finally，on the basis of.rbx，the input file，the blade generator would output the flexible body file .fbi.And combining the flexible body interface module，the dynamic analysis model of blade was built.

Fig.1 Topology graph of wind turbine unit

2.3 Model construction of engine－transmission system

Dynamic model of engine-transmission system includes yaw system，the cover and base of engine room and transmission mechanism.For the method of simplified model，it is important to define the relative position，quality attribute and relative movement.Integrated model was applied in the engine-transmission system in which yaw system is mainly used to connect to the tower and the base of engine room，gearbox is simulated by simplified cube.As well，spindles and hubs are connected to gearbox expressed by two simplified bodies and the internal force of gearbox can be simulated by adding elastic force element.Because the active yaw is so hard to simulate that the passive yaw is applied in the calculation.Specifically，consolidating the yaw system and tower，yaw-steering is completed by adjusting wind direction.

2.4 Model construction of tower－foundation system

The tower-foundation bears multiple loads from wind turbine.Relative to ground the foundation is not immovable completely and it has six degrees of freedom in space structure.The foundation and tower are connected by flange which influences the dynamics of tower and even the whole unit.From the point of mechanics of structure，tower can be considered as a slender beam structure，a flexible structure.The model of this flexible structure is generated by means of importing the FE analysis model into SIMPACK through Flexible(modal)interface unit.At first，after obtaining the finite element model of tower，the Archive model of ANSYS writes out.cbd format swap file and calculates the reduced model from which the.sub and .tcms file are obtained.Secondly，the flexible body generation module of SIMPACK，FBI generation creates the .fbi file of flexible body.Finally，im-porting the.fbi file through the Flexible(modal)module，flexible model of tower is obtained.

2.5 Definition of wind turbine co－simulation model

Two input conditions are considered in this simulation analysis.The first is the load when the wind acts on the each parts of wind turbine.In this paper，241st force element is selected to complete the calculation under the action of wind by AeroDyn V13.This force element passes the operation parameters of unit structure from the sensor to AeroDyn and then applies the aerodynamic load from the calculation to the each parts of unit.The other one is the load that the input shaft end reacts on the transmission system.The load is simulated by 110th force element.Because the force element is connected to control solver so the load depends on control mode.

Moreover，eight kinds of control force element are defined in calculation which includes speed sensor force element，variable propeller angle output disturbance force element and variable propeller torque force element of three blades and control interface force element.In addition，243rd control interface force element，Wind Controller Interface，can complete the interaction between the controller and SIMPACK.In this paper，the control mode is set as dynamic model because the .dll format control file is a inner set file.Dynamics Analysis of Three-dimensional entity model of wind turbine see Fig.2 and wind turbine co-simulation model see Fig.3.

Fig.2 Three-dimensional entity model of wind turbine

3 Analysis method of flexible multibody dynamics

In general，the floating coordinate-system is selected to express the large-scale motion of flexible multibody system and the elastic deformation of each part.The modal comprehensive analysis and finite element method are selected to realize the discretization relative to a datum coordinate system of flexible parts.The node coordinates is always used when the elastic deformation should be expressed by lumped mass method.Moreover，modal coordinates is selected to analyze the elastic deformation by dynamic substructure modal method［7］.

Fig.3 Wind turbine co-simulation model

Differential equation of flexible body motion:

Solution method of differential algebraic equations is usually classified into augmented method and reduction method.In the following，it is the ODAE decoupling method proposed by F.A.Potra on the basis of overdetermined differential algebraic equations group method［8］.

The complete dynamical equations of multi-body system are as follows:

Whereq，，∈Rnis respectively the position vector，speed vector and acceleration vector of system.And λ∈Rmis lagrange multiplier vector，t∈Ris time，M(q，t)∈Rn×nis mass matrix of mechanical system，Φq(q，t)= ∂Φ/∂q∈Rm×nis constraint jacobian matrix，f(q，，t)≡QA(q，，t)∈Rnis external force vector，Φ(q，t)∈Rmis the position constraint equation and υ，η is respectively the speed tight term and acceleration right term.

In order to guarantee the existence of equations above，it is necessary to make the following assumptions:

1)RankΦq(q，t)=m，m＜n

2)For anya∈KerΦq(q，t)anda≠0，aTM(q，t)a＞0，theKeris the kernel of matrix.

4 Dynamic response analysis of wind turbine unit

4.1 Modal analysis of whole unit

The first six step natural frequency and modal shape of wind turbine was obtained from the calculation of first four modal of tower and blade;see Table 2.It can be seen from the Table 2 that system damping ratio of each step vibration mode is different.Furthermore，the literature ［9］indicates that resonance of wind turbine does not occur if the relative difference between blade rotating frequency，impeller passing frequency and each-step frequency is greater than 10 percent.In this paper，the rated speed is 12.1 r/min so that blade rotating frequencyfris 0.201 7 Hz and impeller passing frequencyftis 0.605 1 Hz.Table 2 also shows that the first step nature frequency，0.245 34 Hz，and two step，0.247 12 Hz，of wind turbine are similar.Comparing them with the blade rotating frequency and impeller passing frequency，it can be concluded that the resonance does not occur which means the unit operates in the safe range.Moreover，the three to five step natural frequency of whole unit is at approximately 0.68 Hz and the resonance also does not occur as well as at the other high step frequency.Thus，the operation of wind turbine is smooth.

Table2 The calculation results of first six step modal

4.2 Dynamic response analysis of wind turbine under different operating condition

According to the design code of IEC wind turbine，three operating sub-conditions were selected to conduct the simulation of multi-body dynamics.The condition includes the normal operating condition of 14 m/s constant wind speed model，14 m/s gust extreme operating model and the pause operating condition of 14 m/s constant wind speed model.Specifically，under the normal operating condition the effect of brake should be neglected.Under the pause operating condition，the connection of generator and transmission system should be disconnected，the control system and brake should be turned off and the initial propeller pitch angle should be defined at 90°.Fig.4 and Fig.5 respectively shows the wind speed and direction change curve of 14 m/s constant wind speed model and gust model.It can be seen that with the increase of time，the wind direction appears linear growth.Before 80 s，the wind speed of gust model was at 14 m/s constantly while after 80 s，the speed changed sharply and exceeded 18 m/s.The highest speed lasted 10 s and it returned to constant 14 m/s during which the wind direction kept invariant.

The time domain dynamic response of tower displacement and acceleration under three different operating conditions were obtained while the simulation time was 100 s and output step was 0.05 s.See Fig.6.It is seen from Fig.6(a)that before 80 s，the timedisplacement curve of constant wind speed model and gust model is totally the same.Specifically，the speed increases continuously under the load of constant wind within 24 s and at 24 s，the maximum displacement，0.52 m，appears at tower top.Afterwards，the impeller speed becomes constant under the action of controller and after a period of fluctuation the displacement of tower top comes to level off within 50－80 s at 0.3 m.From 80-90 s，the tower top displacement of gust model matches the gust time-displacement curve in which the maximum positive displacement is 0.68 m and maximum negative displacement is 1.5 m.After 90 s，the gust disappears and tower top displacement comes to level off under the controller.However，after 80 s，the tower top displacement of constant wind speed model increases slightly with the wind shift and at 100 s the maximum displacement is approximately 0.32 m.As for under pause operating condition，in the upwind direction the tower top displacement fluctuates in the vicinity of 0m.Additionally，the acceleration is at a high value from the beginning and afterwards decreases slowly.From 24-30 s，maximum acceleration，0.3 m/s2，of constant wind speed model and gust model appears and then decreases slowly.Until up to 80 s，under normal operating condition，the acceleration of gust model begins to fluctuate and the maximum is 0.68 m/s2，but it also slows down.At last，the acceleration dynamic response of three operating conditions fluctuates in the vicinity of 0m.See Fig.6(b).

Fig.4 Time-history curves of wind speed under different condition

Fig.5 Time-history curves of wind direction under different condition.

Fig.6 Tower top displacement and acceleration in the upwind direction

Fig.7 shows the blade tip deflection in three coordinate directions under different operating conditions.Fig.7(a)shows the blade calculating reference frame and Fig.7(b)shows the blade tip deflection in theXdirection under different operating conditions.Under the normal operating condition，the maximum deflection，5.5 m，appears at about 25 s and after that，it decreases to about 1.5 m but increases again periodically.However，under the gust condition，the deflection mutates at 88 s and it decreases below 0m.The blade tip deflection under pause operating condition is 0 m.Fig.7(c)shows the blade tip deflection in theYdirection.Under the normal operating condition，deflection curve change law of constant wind speed model and gust model are similar in which the maximum is 0.6 m and minimum is －0.7 m.As for pause operating condition，deflection fluctuates greatly and the maximum is 1.3 m but after 20 s it decreases from 0.75 to 0.5 m.Fig.7(d)shows the blade tip deflection in theZdirection.It can be seen that the blade tip initial length relative to blade root is 61.5 m in theZdirection.Under the normal operating condition，the maximum deflection，－0.4 m，of constant wind speed model and gust model appears at approximately 23 s.Additionally，the deflection under gust condition is greater than constant wind condition’s and the maximum is-0.35 m.Under pause operating the blade tip deflection condition almost keeps invariant at 0 m.

Fig.7 Blade tip deflection in three coordinate directions

5 Conclusions

In this paper，selecting a WM wind turbine as research object，the model of coupled rigid and flexible multi-body dynamics was built and it analyzed the vibration characteristics of turbine.The co-simulation completed the analysis of dynamic response under three different operating conditions and studied the dynamic response characteristics of flexible blade and tower.The following conclusions can be drawn from the study.

1)On the basis of self-designed topology of wind turbine machine movement，the model of coupled rigid and flexible multi-body dynamics was built which considered the structure flexibility of blade and tower.The analysis of mode calculation showed that the wind turbine avoids the resonance frequency of key speed interval which ensures the operating stability to some extent.

2)The co-simulation between whole unit analysis model and the software of external load calculation and control was completed through interface force element.The displacement dynamic response，acceleration dynamic response and blade tip deflection in three coordinate directions of tower in the upwind direction were obtained under three operating condition which includes normal operating condition of 14 m/s constant speed model，normal operating condition of 14 m/s extreme gust model and pause operating condition of 14 m/s constant speed model.From above analysis it can be concluded that extreme gust makes the tower structure displacement increases suddenly and the twinkling fluctuation occurs sharply which would damage the tower structure.Additionally，the maximum blade tip deflection appears in the X direction and it may make the blade collide with tower which would influence the operation safety of wind turbine.

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