Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 1 Madrid, Junio 2005 Acoustics of wood Introduction * Acoustical parameters * Stress wave propagation in 1D and 3D * Stress wave velocity, relationship with MOE, MOR, density and fiber length * Practical application: - evaluation of urban trees, defect detection - wood selection for musical instruments 1 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 2 Madrid, Junio 2005 Acoustic parameters of wood are: - sound velocity, - acoustic impedance - damping, logarithmic decrement Sound velocity in homogeneous solids velocity: Wave forms: longitudinal (pressure) Vl = MOE ρ 1 −ν (1 + ν )(1 − 2ν ) transverse (shear) surface Vs = Vt 0,87 + 1,12ν 1 +ν MOE: modulus of elasticity G : shear modulus ν : Poisson ratio Stress wave is the mixture of the 3 wave forms. 2 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 3 Madrid, Junio 2005 Sonic velocities of orthotropic solids like wood: Longitudinal (p) waves: V11, V22, V33 Transverse waves V44 =VRT deduced from V23 and V32 Figure from V. Bucur: Acoustics of wood Longitudinal velocity surface Velocity depends on the direction of the propagation. Velocity of the p waves are the highest Figure from V. Bucur: Acoustics of wood 3 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 4 Madrid, Junio 2005 Hankinson’s formula V(α)=V0 V90/(V0 sin(α)n+V90 cos(α)n) n=2 5 Velocity (km/s) Hankinson Velocity (km/s) 4 Demonstration: Material: beech veneer 3 2 1 0 0 L 15 30 45 Angle (degree) 60 75 90 R 4 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 5 Madrid, Junio 2005 Attenuation figure from F. C. Beall article Acoustic impedance (z) : z=Vρ zwood⊥= 0,5 MPa s/m zwood =2,5 MPa s/m zair =0,4 KPa s/m Reflection coefficient (R) reflected wave energy/ incident wave energy Wave propagation is perpendicular to the surface: 2 R= (q − 1) (q + 1)2 q=z1/z2 z1 woodz1>z2 qwood/air=6000 Rwood/air=0,9993 z2 air 5 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 6 Madrid, Junio 2005 Damping characterisation by the logarithmic decrement (δ) δ=ln(A1/A2)=λT 1,5 A1 1 A2 0,5 Ae-λt T 0 0 1 2 3 4 5 6 7 -0,5 -1 Time Logarithmic decrement determination δ=ln(a1/a2)/dt/f vibration a1: amplitude (black) a2: amplitude at the spectra a1 delayed spectra (white) a1 dt: delay f : frequency a2 6 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 7 Madrid, Junio 2005 Experimental set-up for logarithmic decrement determination Sound propagation around knot 7 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 8 Madrid, Junio 2005 p-Wave propagation around knot in spruce lumber Grid size is 10 by 10 mm Pendulum was used for making uniform start signal 8 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 9 Madrid, Junio 2005 9 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 10 Madrid, Junio 2005 10 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 11 Madrid, Junio 2005 11 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 12 Madrid, Junio 2005 12 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 13 Madrid, Junio 2005 13 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 14 Madrid, Junio 2005 Determination of the stress wave time Amplitude starter signal receiver signal Measured time depends on the receiver signal level treshold Time 14 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 15 Madrid, Junio 2005 TOF slope technique for velocity determination time [µ s ] 400 y = 1,8039x + 6,9 R2 = 0,9999 300 200 100 0 0 50 100 150 200 dis tance [cm] Velocity is determined by the slope. Accurate test Stress wave velocity, relationship with MOE, MOR, density and fiber length MOEdynamic= ρ V2 MOEstatic < MOEdynamic (Reason is creep) Velocity is a good predictor of MOE 10,4 10,2 10,0 9,8 9,6 9,4 y = -0,1988x + 9,5186 9,2 2 R = 0,9875 9,0 8,8 -4 -2 0 MOE[GPa] Effect of time on MOE determination 2 4 log(characteristic time[s]) MOE and MOR correlation is rather high (0,7-0,8), so transitive there is correlation between V and MOR ( 0,6 - 0,7) (correlation coefficients are in the brackets) 15 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 16 Madrid, Junio 2005 Velocity and density There is no correlation between velocity in grain direction and density. Foresters in Australia and Japan are predicting density by stress wave velocity perpendicular to the grain. Velocity and fiber length There is correlation between fiber length and velocity in fiber direction. Longer fibers resulting higher MOE and MOR. Velocity and microfibril angle There is correlation between microfibril angle and velocity in fiber direction. Lower angle results higher velocity and MOE Practical applications: - Predicting tree stiffness - Evaluation of urban trees, defect detection 16 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 17 Madrid, Junio 2005 Stiffness grading of trees by stress wave velocity determination Background: MOE= ρV2 Director ST300 tool by Fiber-gen, NZ Stiffness grading of trees by stress wave velocity determination TreeSonic tool by Fakopp and Weyerhaeuser 17 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 18 Madrid, Junio 2005 Tree evaluation using the stress wave technique Sound propagates faster in intact than in decayed wood. By simply hitting on the tree and measuring the radial stress waves velocity, internal defects are detectable. Stress waves are generated by hitting the start transducer using a hammer. The principle Figure shows the sound propagation in an intact and in a decayed tree. 18 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 19 Madrid, Junio 2005 FAKOPP Microsecond Timer Measurement perpendicular to the grain Evaluation The evaluation is rather simple. If the measured velocity is lower than 90% of the velocity in an intact tree, the tree contains an internal defect, in the line between the transducers. Is the deviation is higher the defect size is also higher. The relative velocity change (RVC) is a measure of the defect size. RVC = Vreference − Vmeasured Vreference *100 19 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 20 Madrid, Junio 2005 Reference velocity examples: Tree species Radial velocity [m/s] Tree species Radial velocity [m/s] Poplar Spruce Silver fir Scotch fir Black fir 1140 1410 1360 1470 1480 Larch Oak Beech Linden Maple 1490 1620 1670 1650 1690 Examples: We are testing big trees. Poplar trees in a protected area. 20 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 21 Madrid, Junio 2005 The extention of the decay is the question. The extention of the decay is the question. 21 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 22 Madrid, Junio 2005 The extention of the decay is the question. The extention of the decay is the question. 22 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 23 Madrid, Junio 2005 A huge plane tree in a play ground Some defect found by stress wave technique. Defect was invisible on the outside. 23 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 24 Madrid, Junio 2005 Acoustic tomography Using multiple measurements in a plane, 2D imaging of a decay is possible. Experiment with artificial defect. Velocity decreases greater than 7% are indicated by bold numbers. 24 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 25 Madrid, Junio 2005 Self calibration Self calibration is possible based on the velocity measurement between the neighboring sensors. This direction is near tangential. Wood material close to the bark, between two neighboring sensors is usually healthy, or a defect is visible from outside, like frost vibs. The average of the near tangential velocity data of the healthy sections is the basic reference velocity data. Ratio of the stress wave velocity measured in different anatomical orientations, relative to the neartangential direction. Valid for the 6point setup. 25 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 26 Madrid, Junio 2005 Acoustic tomography Typically 6 to 32 acoustic sensors are placed around the tree at the level to be tested. Each sensor is equipped with a spike which is tapped through the bark, into contact with the wood material. A hammer tap on a sensor generates stress waves propagates through the tree, which are received and measured by all the other sensors. A software takes all of transit time data. Using the distance between sensors, velocity is calculated. The end result is a two dimensional velocity distribution (tomogram) of the tree at the test level. Decay or cavity appear on the tomogram image. Detecting internal decay by sensors located at the surface is possible, because decay modify the sound propagation. Sound propagation Oak disk, grid size is 2 by 2 cm, time resolution is 20 µs. 26 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 27 Madrid, Junio 2005 Sound propagation in a larch disk Grid size is 3 by 3 cm, time resolution is 20 µs 20 µs 27 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 28 Madrid, Junio 2005 40 µs 60 µs 28 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 29 Madrid, Junio 2005 80 µs 100 µs 29 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 30 Madrid, Junio 2005 120 µs 140 µs 30 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 31 Madrid, Junio 2005 160 µs 180 µs 31 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 32 Madrid, Junio 2005 200 µs 220 µs 32 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 33 Madrid, Junio 2005 240 µs 260 µs 33 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 34 Madrid, Junio 2005 280 µs 300 µs 34 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 35 Madrid, Junio 2005 320 µs 340 µs 35 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 36 Madrid, Junio 2005 360 µs Acoustic tomography systems: - PICUS SONIC TOMOGRAPH - ARBOTOM ® - FAKOPP 2D Timer 36 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 37 Madrid, Junio 2005 PICUS SONIC TOMOGRAPH Image source is www.tree-test.com ARBOTOM® Image source: www.rinntech.de 37 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 38 Madrid, Junio 2005 FAKOPP 2D Timer 38 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 39 Madrid, Junio 2005 Example images: Linden and Nut tree 39 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 40 Madrid, Junio 2005 Evaluation methods • Relative line velocity decrease • Cell based backprojection • Filtered backprojection Relative line velocity decrease 1. Calculate reference velocity from the average of line velocities between neighboring sensors. 2. Select a line between any two sensors as a „defect line” if its velocity is lower than 85% of reference velocity 3. Draw a spot where two defect lines intersecting each other. 40 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 41 Madrid, Junio 2005 Example image, Relative line velocity decrease method Cell based backprojection 1. Divide the area into cells. 2. The slowness (reciprocal of velocity) of each cell is calculated by the average of line slownesses intersecting the cell. 41 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 42 Madrid, Junio 2005 Example image, Cell based backprojection Filtered backprojection • • Theoretical basis by J. Radon in 1917 Used in: - Medicine (CT, NMR) - Geology - Astronomy - Ocean research - Wood NDT - etc. 42 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 43 Madrid, Junio 2005 • Radon transform of f(x,y): • Our case: where ti,j is the time measured between the ith and jth sensors Xj and Xj are the coordinates of the ith and jth sensors v(x,y) is the velocity at the (x,y) point We know ti,j and need v(x,y) => INVERSION • Solution: projection-slice theorem by Bracewell: connection between Radon and Fourier transform where: : Radon transform : 1-dimensional inverse Fourirer transform : 2-dimensional Fourirer transform • Discrete version: filtered backprojection algorithm 43 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 44 Madrid, Junio 2005 Example image, Filtered backprojection „3D” test 44 Course in Non Destructive Testing of Wood ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid 02 Acoustics – Pág. 45 Madrid, Junio 2005 Acoustic tomography demonstration in the arboretum 45
