Gasch R., Twele J. (Eds.) Wind Power Plants: Fundamentals, Design, Construction and Operation

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322 9.4 Example: Rotor hub analysis - multi-axial stress state and isotropic material

9.4.2 Ultimate limit state analysis - critical section plane method

In contrast to the analysis of the wind turbine tower presented in section 9.3, there

are significant spatial and temporal changes of the principal stresses in the rotor

hub, due to its geometry and the temporal superposition of the loadings from the

rotor blades. This leads to a greatly increased analysis effort, especially for the

lifetime calculation.

A common approach for the periodically changing principal stress is the method of

the critical section plane. Fig. 9-10 shows the algorithm of this procedure

schematically; this is described briefly in the following:

- For each load acting on the hub a unit load case is calculated.

- Using these unit load cases the so-called “hot spots” are determined, which

are the zones of highest stress in the structure.

- For these zones of the hub shear and normal stress is then calculated for

each time step of the load time series. From these stresses an equivalent

stress is determined using common approaches.

- For the ultimate limit state analysis the result is now given since this load

case is only a “special case” of the fatigue strength analysis: it is one time

series with only one time step.

- The actual fatigue strength analysis is carried out, using a modified design

S/N curve (cf. section 9.4.3), by a rainflow classification followed by the

damage accumulation. This has to be performed individually for each

individual hot spot, each section plane and each time step.

- The following damage accumulation calculation of the partial damages

finally gives the plane of maximum damage.

Naturally, this procedure needs excessive computing time, so attempts are made to

reduce the effort by making a sensible reduction of the time series number.

9 Guidelines and analysis procedures 323

Component

- Roughness

- Residual stress

- Stress gradient

- Material

FE unit load

cases

Node selection

Stress tensor time function

Fragmentation into

n section planes

Calculation of equivalent stress for

each chosen node, for each time

step and each cutting plane

Rainflow

count +

damage

accumulation

Lifetime

Loads, time

Wöhler

Haigh



iekik

tFStS )]([)(

k = Node no.

i = Loads index

e = Unit load

Component

- Roughness

- Residual stress

- Stress gradient

- Material

FE unit load

cases

Node selection

Stress tensor time function

Fragmentation into

n section planes

Calculation of equivalent stress for

each chosen node, for each time

step and each cutting plane

Rainflow

count +

damage

accumulation

Lifetime

Loads, time

Wöhler

Haigh

Wöhler

Haigh



iekik

tFStS )]([)(

k = Node no.

i = Loads index

e = Unit load

Fig. 9-10 Flow chart of the lifetime fatigue strength analysis of rotor hubs [11]

9.4.3 Fatigue strength analysis - procedure-dependent S/N curves

While in section 9.3 the fatigue strength analysis was performed using the nominal

stress concept, the determined equivalent stresses of cast components are “local”

stresses which means that they already include the influence of the component

shape, local notches and supporting effects. Therefore, a different approach must

be selected for the applied S/N curves which takes into account in particular the

influences not considered up to now, for example the surface quality and the

porosity of the material.

For this purpose, synthetic S/N curves are generated which describe the influence

of exactly these boundary conditions. The procedure relevant for the certification

of wind turbines is described in [1]. The following Fig. 9-11 shows the construc-

tion of a synthetic S/N curve. In this diagram the reduction factors S

PÜ

and S

consider the survival probability and casting flaws including the inspection

method used.

324 9.5 Example: Rotor blades analysis - mono-axial stress state and orthotropic material

6 7 8 9

pü d A

2m-1

Fig. 9-11 Synthetic S/N curve according to [1]

9.5 Example: Rotor blades analysis - mono-axial stress state and

orthotropic material

In contrast to the components treated up to now, the particular difficulty in the

design of the rotor blades is the elementary relationship between geometry and

stresses.

If the shape of the rotor blade changes, there are fundamental consequences for

the load cases to be analyzed, for the stresses and last but not least for the

expected energy yield as well. Therefore, the blade design is an iterative process

and it is quite often necessary to run through it several times before the optimum

compromise between aerodynamic efficiency, weight and costs of the rotor blade

is found.

For design and analysis the rotor blade structure is divided into its functional

elements, cf. Fig. 3-9, 3-11, 3-12 and 9-12:

- Supporting structure: Chords, webs and other unidirectional reinforcing

elements

- Shells

- Connecting elements: blade bolts and bonding

9 Guidelines and analysis procedures 325

The material strength design concentrates on the dimensioning of the chords,

spars, the unidirectional layers and the connecting elements. For the structural

mechanics the rotor blade is reduced to a double-T beam. For the thin-walled shell

the key issue is its stability while, in the first approach, its contribution to the

supporting structure is ignored.

Fig. 9-12 Functional elements of a rotor blade (web, shell, flange)

9.5.1 Concept of admissible strain for analysis of the chords

In a first run a design of the rotor blade is created with the main dimensions and

aerodynamic profiles already determined and selected. The loads are then calcu-

lated for this design. Section by section these loads are used for the following

optimisation of the chord construction. For components made out of fibre reinforced

plastics the maximum strain occurring in the laminate serves as the design crite-

rion. For given internal sectional loads the strain behaviour may be influenced, on

the one hand, by changing the laminate construction, and on the other hand, also

by changing the geometry of the individual section, e.g. by modifying the thick-

ness ratio. Due to the anisotropic structure of the laminate the determination of the

strain has to be performed for each individual layer of the chord in order to take

into account the influence of the fibre direction.

326 9.5 Example: Rotor blades analysis - mono-axial stress state and orthotropic material

k0k

= z





0kkk

n = n

mmzn 

kSkk

kPk

S0 k

0k0P

n = C C

mC C





SSk

kkSk

PPkkSk

CzC

CC+zC



11 11k

14 k 11k

44 44k k 11k

czc

cc+zc

Fig. 9-13 Laminate matrix, fibre direction and transformation [12]

If the requirement is fulfilled that the admissible level of strain is not exceeded,

the fatigue strength analysis is performed as a last step. The zones of

unidirectional layers are critical. Depending on the material, the material values

are either found in the literature or, in most cases, material tests for this special

blade need to be performed. The strain and the characteristic material values give

the total bending of the blade which may not exceed the limiting value given for

the corresponding extreme load cases: the blade must neither come into contact

with the tower nor fail. If the structure of the rotor blade fulfils the given

requirements another load calculation is performed for the geometry and mass

distribution obtained. Often, there are now deviations from the original as-

sumptions, so one more loop of the iteration is necessary.

9 Guidelines and analysis procedures 327

9.5.2 Local component failure

In the next step following the design of the supporting structure (chord-web

system), single elements of the blades are investigated for local failure. Failure

from buckling may not occur, neither in the shell of the rotor blade nor at the webs

or chords. Critical zones are found in particular where the distance between

supports is large or where the compressive stress is at a high level. FEM models

are applied for the buckling analysis.

The bonded joints of the rotor blade must be investigated for shear and peeling.

The individual limiting values result from the properties of the chosen bonding

material.

The bolting zone of the blade root is investigated using FEM models as well

(cf. Fig. 9-12 mad 3-12). Here, depending on the chosen type of connection, the

forces that occur must be fed into the material by the bonding of the inserts, or by

the surface pressure of the transverse bolts. The blade bolts are analyzed by the

common procedure according to VDI 2230.

9.5.3 Choice of materials and production methods

The rotor blades for the first series of wind turbines in the 1980s were already

manufactured out of glass fibre fabrics in a polyester resin matrix. This material

combination is still widely used today because of the following advantages: the

purchase price of the basic materials is relatively low, the processability is good

and the endurance is relatively high. In parallel, epoxy resins were applied for the

matrix because of the better fatigue strength properties of these resin systems (cf.

Fig. 3-10.) and less shrinking during the hardening process. Moreover, alternatives

to the glass fibre structure are investigated time and again: the stiffness is a crucial

design parameter especially for large wind turbines. Therefore, carbon fibre struc-

tures are being increasingly used for rotor blades. However, the most relevant

obstacles to the application of carbon fibre are the high price, higher production

requirements and the problem of lightning protection since the blade structure is

then electrically conductive.

Apart from carbon fibre, wood is also applied in combination with epoxy resin

as rotor blade material. In this case, the stiffness is not such an issue, but the good

damping properties of wood are of importance. These rotor blades are often

applied for stall-controlled wind turbines where additional structural damping

improves operating behaviour.

Until the end of the 1990s rotor blades were manufactured manually, Fig. 9-14.

The laminate structure was built up layer by layer in a mould and then soaked with

resin.

328 9.5 Example: Rotor blades analysis - mono-axial stress state and orthotropic material

With growing piece numbers and component sizes the production is becoming

ever more automated. Two different approaches have been established:

- The pre-preg method (also common in the aircraft industry) using already

soaked glass or fibre fabrics which are hardened in a heatable mould or

- The vacuum infusion method where the glass or fibre structure is covered

with a plastic film to seal the mould, and the resin is soaked in automati-

cally under evacuation, cf. Fig. 3-11.

Both methods improve the product quality (e.g. less air inclusions which reduce

material strength), allow control of the amount of resin applied (material savings)

and reduce the holding times in the moulds (shorter production time).

Fig. 9-14 Manufacturing of rotor blades at LM, DK; laying of the glass fiber fabrics

References

[1] Germanischer Lloyd Industrial Services GmbH: Richtlinie für die Zertifizierung von

Windenergieanlagen (Guideline for the Certification of Wind Turbines), Hamburg

2003, 2010

[2] Risoe/DNV: Guidelines for Design of Wind Turbines, 2

ed. 2002

[3] DIBt (German Institute for Civil Engineering): Richtlinie für Wind turbinen

Einwirkungen und Standsicherheitsnachweise für Turm und Gründung (Regulation for

Wind Energy Conversion Systems, Actions and Verification of Structural Integrity for

Tower and Foundation), series B, vol. 8 DIBt Berlin, 2004

9 Guidelines and analysis procedures 329

[4] Schneider: Bautabellen für Ingenieure (Construction tables for engineers),

ed., Werner Verlag Neuwied

[5] Gudehus, H.; Zenner, H.: Leitfaden für eine Betriebsfestigkeitsrechnung, Empfehlung

zur Lebensdauerabschätzung von Maschinenbauteilen (Guideline for fatigue strength

analysis, recommendations for the lifetime estimation of machinery components) , 3

ed., Verlag Stahleisen mbH, Düsseldorf 1995

[6] European Convention for Constructional Steelwork: Recommendations for the Fatigue

Design of Steel Structures, ECCS Publication 43, 1985

[7] Haibach, E.: Betriebsfestigkeit: Verfahren und Daten zur Bauteilberechnung (Methods

and data for component design), Düsseldorf, VDI-Verlag 1989

[8] Schaumann P., Seidel M., Messenburg L.: Weiterentwicklung des Beulnachweises von

WEA-Türmen mit elasto-plastischen FEM-Analysen (Improvement of the buckling

analysis of wind turbine towers using elasto-plastic FEM analysis), DEWEK 1998

[9] Petersen C.: Stahlbau - Grundlagen der Berechnung und baulichen Ausbildung von

Stahlbauten (Steel construction – Basics of the dimensioning and the constructional

formation of steel constructions), 3

revised and enhanced edition. Braunschweig/

Wiesbaden: Vieweg 1993

[10] Seidel, M.: Zur Bemessung geschraubter Ringflanschverbindungen von

Windenergieanlagen (On the dimensioning of bolted ring flange connections of wind

turbines), PhD thesis at the Institute of Steel Construction, University of Hannover

2001

[11] Willmerding, G., Häckh, J., Schnödewind K.: Fatigue Calculation using winLIFE;

NAFEMS-Tagung Wiesbaden 2000

[12] Wiedemann J.: Leichtbau (Lightweight construction), Vol. 1: Elements, Vol. 2:

Construction, Springer-Verlag, Berlin, 1996

[13] International Electrotechnical Commission: IEC 61400, preview documents on WWW

(Oct. 2010): http://webstore.iec.ch/

R. Gasch and J. Twele (eds.), Wind Power Plants: Fundamentals, Design, Construction 330

10 Wind pump systems

The application of wind mills for water pumping is of lesser importance today

than in the past centuries. However, for several reasons, it is useful to discuss this

type of wind energy application in a wind energy book targeted at development

and planning engineers as well as students.

A wind pump system for water supply is an energy system which serves to illus-

trate the interaction of the system components: wind turbine, water source and the

other system components for the water utilization. An optimum configuration of

the complete system is only possible when considering the interaction of the

system components with their individual operating behaviour and characteristics.

Moreover, it is likely that the significance of wind pump systems will grow

again with the increasing acceptance of renewable energies, particularly in the

developing countries. They may contribute significantly to rural development [1].

Today, there are ideas for new fields of application for wind pump systems, not

only for water pumping but also for oil pumping in remote and windy areas of the

world, e.g. sites in the southern parts of Chile and Argentina.

10.1 Characteristic applications

In Europe, utilizing wind energy for water pumping has a long tradition reaching

back to the 1500s. Historical examples of applications which were of great eco-

nomic importance are the drainage of coastal areas in the Netherlands lying below

sea level, the irrigation of potato plantations in the Cretan plateau of Lassithi, and

the wind pumps on cattle farms in the American Midwest. Today, industrialized

countries seldom use wind energy for water pumping. However, in developing

countries, where many regions are not connected to a local infrastructure with

electrical grid and public water supply, the utilization of wind energy constitutes

an economical and environmentally friendly option for improving the water

supply.

A schematic diagram of the conversion of wind energy into hydraulic energy

by the wind pump system is shown in Fig. 10-1. In the following sections, distinc-

tion is made between the wind pump consisting of the wind turbine, the gearbox

and the pump, on one hand, and the wind pump system combining the wind pump

and the hydraulic system, on the other.

10 Wind pump systems 331

well

pump

power

transmission

wind turbinewind energy

lost energy

hydraulic

energy

hydraulic plant

wind pumping system

wind pump

water

storage

Pipe at the

pressure side

of the pump

well

pump

power

transmission

wind turbinewind energy

lost energy

hydraulic

energy

hydraulic plant

wind pumping system

wind pump

water

storage

Pipe at the

pressure side

of the pump

Fig. 10-1 Schematic diagram of the conversion of wind energy into hydraulic energy by the

wind pump system

Wind energy is a stochastic input. Losses occur in the course of its conversion into

hydraulic energy. Most wind pump systems with a mechanical coupling operate

without a control mechanism with the exception of an overspeed control. There-

fore, any variation in wind speed directly leads to a change in the hydraulic oper-

ating point, particularly in the flow rate. Moreover, the energy conversion is also

influenced by varying pumping conditions, e.g. the varying height of the water

level in the well or increasing friction losses due to corrosion of the piping system.

Fig. 10-2 shows the general design of a wind pump system with a mechanical

coupling of wind turbine and pump by gearbox, shaft and belt drive.

The characteristic applications of wind pumps are mainly found in developing

countries. There are four types of applications:

- Drinking water supply,

- Livestock watering,

- Irrigation and

- Drainage.