*Fabian Malm, summer semester 2012***Artikel auf Deutsch**

Within the scope of inspection and continuous monitoring processes automated testing methods become more and more significant. Frequent inspections of, for instance, rotor blades of wind power systems that have to be carried out every four to five years, are at the moment restricted to simple visual inspections and localised tapping for cavities. Using **local acoustic resonance spectroscopy** provides a non-destructive testing method which facilitates and improves these regular inspections.

## History

The theoretical basis of the mechanisms involved were already described by Cawley and Adams in 1988. ^{[1]} Following the theory of wave motion in elastic solids by Goldsmith (^{[2]}) in the 1950s, Cawley numerically simulated the effects of impacts with a hammer and a simply supported beam. He connected non-linearities occurring due to changes in the number of modes and the dependency of energy dispersions and damping by the excitation force (magnitude) with the non-rigid physical behaviour.

## Principle

The principle of “local resonance spectroscopy” relies on the method of resonance analyses. The component’s surface is tapped with an impact hammer and thus individual areas of the component are excited. If flaws exist inside the component, the oscillation behaviour changes followed by a change in the acoustic pattern. The acoustic pattern is recorded with a microphone. The resulting analysis of the frequency can eventually provide conclusions about faulty components with cavities and delaminations. In contrast to the common resonance analysis only a local oscillation is generated and not excitation to natural oscillation of the entire component.

Fig. 1: Schematic test set-up Quelle: Untersuchung von GFK-Bauteilen mit akustischen Verfahren am Beispiel der Rotorblätter von Windenergieanlagen, Dr.-Ing. Anne Jüngert http://elib.uni-stuttgart.de/opus/volltexte/2010/5289/pdf/DissJuengert.pdf |

## Physical fundamentals

### Measurement method

The *measurement method* is based on classic mechanics. The surface is excited by an impulse hammer and the resulting excitation force is recorded via a force sensor. With this partly-elastic collision, a proportion of the energy is converted into heat and elastic waves, expressed by a collision parameter. Elastic waves excite the material which then emit longitudinal waves into the air and these are ultimately recorded with a microphone. The contact time of hammer and the surface to be examined plays a decisive role here. The softer the surface structure, the longer the contact time and the smaller the impact coefficient.

The contact time is dependent on the contact stiffness of the excited material, which can also be considered the spring stiffness \begin{array}{l}k_c\end{array}. Contact stiffness describes the deformation of two touching solids under the influence of a normal force \begin{array}{l}F\end{array}.

\begin{array}{l}\dfrac{1}{k_c} = \dfrac{d \delta}{dF}\end{array} (1)

Deflection \begin{array}{l}δ\end{array} gives the deflection of a body which is dependent on the respective Young’s modulus \begin{array}{l}E\end{array}, Poisson ratio \begin{array}{l}v\end{array} and the respective geometry of the solid. In this case, the deflection is mostly in a non-linear relation to the impacting force \begin{array}{l}F\end{array}. Thus, for *local resonance spectroscopy*, the impacting force \begin{array}{l}F\end{array} should be kept as constant as possible.

Distinguishes the examined structure e.g. due to a flaw in the material, an audible difference in sound occurs at the interface. It is caused by a different contact stiffness between intact and damaged areas. In the case of a flaw, damage stiffness \begin{array}{l}k_d\end{array} reduces the actual stiffness which results in a longer contact time between impact hammer and surface. The result is a different amplitude spectrum and thus a different sound. For such a surface to be diagnosed, the results have to be described by a significant feature and have to show the properties of the amplitude spectrum. One possibility is the signal processing of the excitation force. The half-width of a force signal characterises the excitation. It shows how broad a signal at its half-height is and serves as a measurement of the time of contact between hammer and material. In the case of short contacts with the surface, the same force is applied to the surface in a very short time. The signal has a short half-width but possesses a higher maximum amplitude.

### Example

A sphere with the radius \begin{array}{l}r\end{array} in contact with an elastic half-space has a deflection of \begin{array}{l}δ\end{array}

\begin{array}{l}\delta = \left (\dfrac{9 F^2}{16 E^{*2}} \right )^{\frac{1}{3}}\end{array} (2)

with \begin{array}{l}\dfrac{1}{E^*} = \dfrac{1 - v_1^2}{E_1} + \dfrac{1 - v_2^2}{E_2}\end{array} (3)

\begin{array}{l}ν_1, ν_2\end{array}: Poisson’s ratio of both solids

\begin{array}{l}E_1, E_2\end{array}: Young’s modul of both solids

This equates to, solved in relation to the spring stiffness \begin{array}{l}k_c\end{array} (1):

\begin{array}{l}k_c = \dfrac{3}{2} \left (\dfrac{9 F^2}{16 E^{*2}} \right )^{\frac{1}{3}} * F^{1/3}\end{array} (4)

For a steel sphere (\begin{array}{l}E_1 = 210 \frac{kN}{mm^2}\end{array}, \begin{array}{l}ν_1 = 0.29\end{array}) with 8 mm in diameter on a GFRP half-space (\begin{array}{l}E_2 = 13 \frac{kN}{mm^2}\end{array},\begin{array}{l}ν_1 = 0.25\end{array}).

The damage stiffness of a round flaw with a diameter of \begin{array}{l}d\end{array} in a depth \begin{array}{l}h\end{array} can be calculated as follows:

\begin{array}{l}D = \dfrac{E h^3}{12(1 - v^2)}\end{array} (5)

Due to the proportionality to the third power of the flaw’s depth and the anti-proportionality to the square of the flaw’s diameter, delaminations closer to the surface have a more sensitive effect on the damage stiffness. A flaw with a 7 mm in diameter in a depth of 1 mm provokes the same change as a flaw of 20 mm in diameter in a depth of 2mm.

Fig. 2: Comparison of half-widths at a segment of a wind power plant rotor blade with flaws visible in the photograph. |

## Applications

- Detection of delaminations and cracks in structures that can be excited with sound vibrations e.g. CFRP and GFRP.
- With larger and more heterogeneous examination objects where only a localised area can be excited with a hammer blow e.g. rotor blades at wind energy power plants.
- Detection of different (inner) structures in the material. For this, the material does not necessarily need to be damaged.

## Advantages

- Advantage opposite to natural frequency methods where only one damage detection is possible.
- Damages that provoke a change in sound are in the immediate neighbourhood of the corresponding point of excitement.
- Automatisation with robots possible.
- Applicable for production quality control and semi-manual use.
- Easy and useful measurement with reduced need for equipment.
- No coupling of sensors necessary.

## Disadvantages

- Many points have to be tapped in the case of large components.
- Geometric effects significantly influence measurement assessments.
- Penetration depth is very dependent on the materials contact stiffness. Flaws at a depth of several centimetres can no longer be resolved.
- Flaw depth not determinable from measurement data.
- In the case of a limitation of the sample, natural oscillations can be excited.

## Literature

- Cawley, P.; Adams, R.D.:
*The Mechanics of the Coin-Tap Method of Non-Destructive Testing*. In:*Journal of Sound and Vibration*. 1988. - Goldsmith, W.:
*Impact, The Theory and Physical Behavior of Colliding Solids*. Edward Arnold. London, U.K., 1960. - Jüngert, A.; Grosse, C.; Aderhold, J.; Meinlschmidt, P.; Schlüter, F.; Förster, T.; Felsch, T.; Elkmann, N.; Krüger, M.; Lutz, O.:
*Zerstörungsfreie robotergestützte Untersuchung der Rotorblätter von Windenergieanlagen mit Ultraschall und Thermographie*. ZfP-Zeitung 115. p. 43 - 49. 2009. - Jüngert, A.; Grosse, C.; Krüger, M.:
*Inspektion der Rotorblätter von Windenergieanlagen mit akustischen Verfahren*. Proc. DACH Jahrestagung 2008 DGZfP. Berlin, 8.2008. - Jüngert, A.:
*Untersuchung von GFK-Bauteilen mit akustischen Verfahren am Beispiel der Rotorblätter von Windenergieanlagen*. Dissertation, Universität Stuttgart. Stuttgart, 2010.