Vibration Methods. Basic idea

Transcription

1 Course in Non Destructive Testing of Wood 05 Vibration Pág. 1 Vibration Methods Basic idea Best conditions for vibration test are: - support sample at the nodal points - hit sample at amplitude maximum, - hitting direction is important - microphone locate at max amplitude location 1

2 Course in Non Destructive Testing of Wood 05 Vibration Pág. Fourier Transformation H ( f ) h( t) i = e πft dt i = 1 Discrete Fourier Transformation ( kt ) h k = 0,1,,3,..., N 1 H n NT T: time between two samples, T=1/f sampling N 1 = h k= 0 k iπn N ( kt ) e n = 0,1,,3,... N 1 Fast Fourier Transformation: h function is identical, H is almost the same, but computation time is shorter.

3 Course in Non Destructive Testing of Wood 05 Vibration Pág. 3 Dynamic MOE determination by longitudinal vibration MOE dyn, long = ρv V = Lf Dynamic MOE determination by bending vibration MOE dyn fn, bending C = n ml I 3 3

4 Course in Non Destructive Testing of Wood 05 Vibration Pág. 4 Timoshenko beam theory The effect of shear is included. 4 r EI 4 x r + ρa t E r ρi + βg x t ρ I r βg t where: b - shear factor (1/1. for prismatic beams), r - displacement, x - longitudinal coordinate, t -time, A - cross section, ρ - density, I - moment of inertia, E - bending modulus of elasticity, MOE G - shear modulus. Solution is available by iteration technique only. = 0 Solution of the Timoshenko equation Evaluation software presented by Dr. Chui, Canada. Input data are: - length - thickness - density - bending vibration frequency, mode 1 - bending vibration frequency, mode Demonstration E.exe 4

5 Course in Non Destructive Testing of Wood 05 Vibration Pág. 5 Euler beam theory Neglecting the shear Timoshenko theory turns to Euler beam theory 3 f n ml E = C n I where:f n - frequency measured in the nth mode, C n - mode factor (see Figure ),, m - specimen mass. Mode E - MOE I - Inertia Influencing factors are: - Geometry: Nodal distance/thickness - Damping - Static-dynamic correction 5

6 Course in Non Destructive Testing of Wood 05 Vibration Pág. 6 Nodal distance Nodal distance is the distance between two neighbouring nodal points. Nodal point Nodal distance / beam height 6

7 Course in Non Destructive Testing of Wood 05 Vibration Pág. 7 Effect of damping The measured frequency (f) and the not damped vibration frequency (f o ) is different Λ f 0 = f 1+ 4π Λ is the logarithmic decrement: Λ =β/f β is damping coefficient Logarithmic decremet for wood is 0,1-0,01, the damping correction is minor, less than 0,% x Damping coefficient: β A x 1 x 3 Ae -βt x x 4 t T 7

8 Course in Non Destructive Testing of Wood 05 Vibration Pág. 8 Static - dynamic correction One order of magnitude difference in the characteristics time causes a 1.7% change in the measured MOE value. stress wave 10,5 bending vibration, 3rd mode bending vibration, 1st mode 10,5 static, 100 mm/min 9,75 static, 10 mm/min static, 1 mm/min 9,5 static, 0.1 mm/min 9, MOE [GPa] 10 log(time[s]) Determination of shear modulus by torsion vibration G dyn, torsion Lf = n n ρi K t p B1 T1 B T B3 T3 8

9 Course in Non Destructive Testing of Wood 05 Vibration Pág. 9 Evaluation chart MOE and G evaluation example.xls Portable Lumber Grader setup 9

10 Course in Non Destructive Testing of Wood 05 Vibration Pág. 10 Longitudinal vibration, Portable Lumber Grader (PLG) PLG screen 10

11 Course in Non Destructive Testing of Wood 05 Vibration Pág. 11 PLG algorithm ( lf ) 0.9( 1 u 50) MOE mea = ρ + ρ: density l: length f: longitudinal vibration frequency u: moisture different = actual service condition MOE = MOEmea 6. CKDR Concentrated Knot Diameter Ratio The knot diameter is a distance between the two tangential lines parallel to arises (longitudinal direction) of a lumber surface in which the knot exists. If a knot diameter not less than.5 times as much as its smallest diameter, it shall be considered to have one half of its actual measured diameter. The knot diameter ratio (KDR) is a percentage of the diameter of a knot to the width of a lumber surface in which it exists. The concentrated KDR (CKDR) is the sum of KDR concerning the knots existing in any 15 cm length of a piece of the lumber. The highest - considering 4 faces - CKDR represents the piece of lumber. The CKDR value is between 0 and 1. 11

12 Course in Non Destructive Testing of Wood 05 Vibration Pág. 1 PLG decision table Example, by 4 material 1

13 Course in Non Destructive Testing of Wood 05 Vibration Pág. 13 Demonstration: PLG and rapture test 13