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In order to study the strength of the composite material plate problems, need to adopt a nondestructive testing method to obtain the specimen surface under the effect of high-speed impact regularity of shape. The projection profilometry was used to measure the surface profile or the full field deformation. Furtherly, by using the Fourier transform algorithm, there is only one frame of captured image which is needed in the measurement, so that it can be introduced into the high speed impaction procedure measurement. An experimental system, which was contained with an impact setup and the projection profilometry measurement part, was constructed for the impaction action characteristic research. The metallic impact object can be launched by a gas gun or a spin fan, respectively. The detected object is manufactured by composite materials. In order to increase the surface deformation measurement accuracy, the calibration method and the error was discussed with different calibration specimen. And then, the proposed profilometry measurement method is proved by the gas gun and spin fan projectile test. The surface deformation of the manufactured composite plates and fan case are measured in the impaction procedure. So that the impact action details can be described much more clearly than the traditional video monitoring method.

As the developing of the Charge Coupled Device (CCD) camera and image processing algorithm are growing day by day, the 3-D optical and image measuring technology is widely used in the industry inspection [

In the projection grating profilometry of a dynamic impaction measurement, the parallel with cosine function modulated intensity is projected onto the detected object. The mainly two kinds of phase extracting methods are phase-shifting measurement profilometry (PMP) and Fourier transformation profilometry (FTP). The PMP is a mature method with high accuracy [

In this paper, the projection profilometry and the Fourier transform method are introduced into the surface deformation inspection of the manufactured composite plates. The experimental system is constructed to research the whole procedure of the impaction deformation. Some interesting experimental results are present to prove the feasibility of the proposed method.

As shown in

R S = P ( φ S − φ R ) / 2 π (1)

As QS is parallel to the incidence direction, point Q on the deformed object and point S on the reference surface would have the same phase angle. So

R S = P ( φ Q − φ R ) / 2 π (2)

From simple geometric, the surface height RQ is expressed as follow.

R Q = R S / tan α (3)

Substituting Equation (2) into Equation (3), we have

R Q = ( φ Q − φ R ) p 2 π tan α = ( φ Q − φ R ) k , (4)

Thus from Equation (4), the object surface height can be obtained, if the phase difference between the reference and the detected surface gratings can be measured. Furthermore, the coefficient k is defined to indicate the relationship. In order to reduce the system error, the coefficient can be obtained by a calibration test. As only one frame of fringe pattern can be captured by the high-speed CCD camera in every moment of the impact procedure, Fourier transform method is used to extract the phase change.

When the detected object is put on the reference plane, the deformed fringe pattern captured by a CCD camera can be expressed as:

I ( x , y ) = a ( x , y ) + b ( x , y ) cos [ 2 π f 0 x + Φ ( x , y ) ] (5)

where a ( x , y ) is the background intensity, b ( x , y ) is the amplitude of the gratings, f 0 is the spatial frequency, and Φ ( x , y ) is the phase change caused by the surface height of the object. The signal Φ ( x , y ) is modulated by a constant high-frequency signal f 0 . Thus, Equation (5) can be written as

I ( x , y ) = a ( x , y ) + c ( x , y ) exp ( j 2 π f 0 x ) + c * ( x , y ) exp ( − j 2 π f 0 x ) . (6)

where c ( x , y ) = [ b ( x , y ) / 2 ] exp { j [ Φ ( x , y ) ] } , and c * ( x , y ) is the complex conjugate of c ( x , y ) . The Fourier transform of I ( x , y ) with respect of x becomes

F [ I ( x , y ) ] = A ( f , y ) + C ( f − f 0 , y ) + C ∗ ( f + f 0 , y ) , (7)

where F[ ], A( ) and C( ) represent the Fourier spectra, and C * is the complex conjugate of C.

As the frequency of a ( x , y ) , b ( x , y ) and Φ ( x , y ) are much lower than f 0 , the function C ( f − f 0 , y ) can be filtered by an adequate window in the frequency domain. And then, C ( f , y ) can be obtained by spectrum shift center. Taking inverse Fourier transform of C ( f , y ) , we can get c ( x , y ) . The phase change of the deformed pattern is

Φ ( x , y ) = arctan { Im [ c ( x , y ) ] Re [ c ( x , y ) ] } + 2 n π = arctan G F + 2 n π = Φ ′ ( x , y ) + 2 π n . (8)

where F = Re [ c ( x , y ) ] and G = Im [ c ( x , y ) ] represent the real and imaginary parts of c ( x , y ) , respectively. Φ ′ ( x , y ) is the principal phase which is in the range of [ − π , π ] . A phase unwrapping procedure should be taken to get the continuous actual phase distribution Φ ( x , y ) .

The purpose of the spectrum shift center procedure is to remove the linear term in the phase. However, because of the limitation of the image resolution, there will be a residual linear term error. Fortunately, the fringe pattern image of the reference plane can be used to obtain the linear term of phase in advance. After subtracting the reference phase, the real phase can be obtained by the Fourier transform without spectrum shift.

The schematic diagram of the experimental system is shown in

In order to obtain the surface deformation of the composite plates, the proposed projection grating profilometry was used with the measurement part. The deformation measurement experimental setup is constructed by a high-speed CCD camera, a digital projector, and a personal computer. The camera manufactured by NAC Image Technology Inc. has a very low noise rating, and it also boasts the highest dynamic range to 64 dB. It has high speed and high resolution (800 × 528, 60,000 fps), which is suitable for the impact procedure measurement research. By using the digital projector, only one frame of parallel fringe pattern with cosine function modulated intensity is projected onto the detected object with an incidence angle. The classical fringe patterns are shown in

The high-speed CCD camera is fixed normal to the reference plane, and the distance between the camera and the detected object depends on the size of the composite plate and the parameter. When the impact object was launched, the camera would be triggered by input signal. So that the deformed fringe patterns modulated by the surface profile of the detected object can be captured in the impact procedure. Here, the most important thing is how to keep the impaction and the capturing in Synchronize. And then, the deformed fringe pattern images are recorded in the personal computer for the next calculation. After a measurement system calibration test, the surface profile can be extracted by calculating the fringe deformation between the reference and the detected surface.

In order to obtain the coefficient k defined in Equation (4), the calibration test should be carried out before the impact test. A specimen with a special shape, which is shown in

In order to improve the calculation accuracy of the calibration test, some different calibration specimens were designed to investigate the calibration error. The maximum height of the 3D printed specimen is 10, 20, 30, 40, 50, 60 mm, respectively. Calibration can be obtained through the calculation of arithmetic average specimen surface height of the maximum value. The calculated value of the phase difference with the different height is shown in

Firstly, the manufactured composite plates are tested by a gas gun impact testing system. The compressed gas was used as the propellant to launch the impact object. In order to simulate different impaction situation, the angle between the projectile and the target can be changed during the testing. The size of the manufactured composite plate was approximately 180 mm × 400 mm, and the plate was fixed to a rigid testing fixture. The fringe pattern was projected onto the target, and then high speed camera was used to record the images during the impaction procedure. In this test, the time interval of the high speed camera was set as 27 μs. Totally, there are 150 frames of image are captured and restored. The out-of-plane deformation can be extracted by using the projection grating profilometry method.

One of the composite plate impact test results are shown as follow.

was contained in that distortion. By using Fourier transform algorithm, the extracted phase distribution without unwrapping is shown in

In this part, the measurement method was used to obtain the deformation of a fan case which was also manufactured by the same composite material as previous test. The impaction experiment was simulated by a spin fan testing, and the projectile was launched by a motor at a high speed up to 400 m/s. In this research, we have two different tests to study the different impact energy influence of the fan case strength. The experimental results are shown as follow. Comparing the captured fringe patterns of composite plate which were shown in

In order to study the characteristics of the fan case surface deformation in the whole impaction procedure, five points were selected to compare the deformation in different area and different period of the case. The compared results are shown in

of the fan case in test-B present different characteristics. Because the impaction energy is much smaller than that in the test-A, so the fan case was keeping completely in the whole impaction procedure. From the experimental results shown in

The surface impaction deformation can be measured by the projection profilometry method. An experimental system was combined by the impaction and the deformation inspection parts. By using the high speed image capturing and recording system, the Fourier transform is successfully applied for the phase difference extracting. From the experimental results, it is found that the calibration error is about 5 - 7 percent, which is acceptable for the measurement in the impact deformation. The detected composite plate and circle fan case were used to prove the feasibility of the proposed method.

The author gratefully acknowledges support from the National Natural Science Foundation of China (Grant No. 51875568).

The authors declare no conflicts of interest regarding the publication of this paper.

Hu, E.Y. (2020) Application of 3D Projection Profilometry in the High Speed Impaction Surface Deformation Measurement Research. Journal of Signal and Information Processing, 11, 103-115. https://doi.org/10.4236/jsip.2020.114006