- Email: [email protected]
Dynamic response of sand particles impacted by a rigid spherical object
Results in Physics 9 (2018) 246–251
Contents lists available at ScienceDirect
Results in Physics journal homepage: www.journals.elsevier.com/results-in-physics
Dynamic response of sand particles impacted by a rigid spherical object P. Youplao a,⇑, A. Takita b, H. Nasbey b, P.P. Yupapin c,d, Y. Fujii b a Electrical Engineering Department, Faculty of Industry and Technology, Rajamangala University of Technology Isan Sakon Nakhon Campus, 199 Village No. 3, Phungkon, Sakon Nakhon 47160, Thailand b School of Science and Technology, Gunma University, Kiryu, Tenjin-cho 1-5-1, 376-8515, Japan c Computational Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, District 7, Ho Chi Minh City, Viet Nam d Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, District 7, Ho Chi Minh City, Viet Nam
a r t i c l e
i n f o
Article history: Received 26 January 2018 Received in revised form 13 February 2018 Accepted 20 February 2018 Available online 24 February 2018 Keywords: Sand particle Collision response Dynamic force Inertial mass Optical interferometer
a b s t r a c t A method for measuring the dynamic impact responses that acting on a spherical object while dropping and colliding with dried sand, such as the velocity, displacement, acceleration, and resultant force, is presented and discussed. In the experiment, a Michelson-type laser interferometer is employed to obtain the velocity of the spherical stainless steel object. Then the obtained time velocity profile is used to calculate the acceleration, the displacement, and the inertial force acting on the observed sand particles. Furthermore, a high-speed camera is employed to observe the behavior of the sand during the collision. From the experimental results with the sampling interval for frequencies calculation of 1 ms, the combined standard uncertainty in the instantaneous value of the impact force acts on the observed object is obtained and approximated to 0.49 N, which is related to a corresponding 4.07% of the maximum value at 12.05 N of the impact force. Ó 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Introduction The mechanical behavior of soil, sand, dust and the other associated composite materials is receiving intensive attention and widely investigated by a variety of research methods, where there are many of relevant studies proposed, for an instant, an attempt to investigate mechanical behavior of geological materials in any considered conditions [1–3], where the lunar soil simulant with a geochemical reproduction of lunar regolith is examined to compare with the returned samples from the Moon, which aim to support the landing missions or facility constructions on the lunar surface [4–6]. The impact cratering process on brittle materials, such as borosilicate glass and a mixture of geophysical materials is investigated as well for improving parts of industrial products [7] and understanding impact craters on the Moon [8]. Furthermore, the dynamic behavior of an object impacts onto any material is received intensive attention [9–12]. One of the most important groups of the materials in both the geography and construction industry is sand [13,14], in which some studies employ the numerical simulations to evaluate the impact responses from testing materials [15–17]. However, it is still difficult to measure the dynamic mechanical quantities acting on an object during the
⇑ Corresponding author.
collision, such as the impact force on and from the material, which is under tested. Several authors have previously developed methods based on the law of momentum conservation for precision mechanical measurement, known as the Levitation Mass Method (LMM). In this method, the force due to a moving mass, levitated by a linear motion air bearing so that its velocity is at an almost constant, which is employed to be a reference force made to collide with testing objects. The LMM experiment has been conducted to evaluate mechanical quantities for some investigations such as the strength test for a general industrial product [18]. Measuring response calibration in dynamic conditions for a force transducer [19,20] and impact force measurement for a hard drive actuator arm have been reported [21]. In addition, the dynamic response of an object impacts onto a surface such as the water entry event can also be evaluated using the modified LMM [22]. By using the LMM, all necessary mechanical quantities during the collision of the observed object, such as the velocity, the displacement, and the acceleration, can be evaluated by an optical interferometer. The results were obtained in a good synchronization using numerical calculations of the motion-induced time-varying beat frequency of the optical interferometer. Finally, the resultant force acts on the observed object will be calculated directly according to the force definition as multiplying the mass of the whole object’s body by its acceleration.
E-mail address: [email protected] (P. Youplao). https://doi.org/10.1016/j.rinp.2018.02.046 2211-3797/Ó 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
P. Youplao et al. / Results in Physics 9 (2018) 246–251
247
In this paper, the LMM method has been modified for evaluating the dynamic responses of a mass in the vertical movement, which is suitable for impact measurement under the gravity and found in nature. In the experiment, by modifying the LMM, a method for evaluating the dynamic impact responses of a spherical object dropped onto the dried sand surface is presented. The experimental validity is demonstrated and discussed as well.
Experimental setup The interference-based experiment, of which the schematic diagram of apparatus setup illustrated in Fig. 1, is employed to evaluate the dynamic response that a rigid object drops impact onto the sand particles surface. In the experiment, the object is free to fall under the gravity before the collision. Therefore, the shape of the object that can provide the symmetry orientation of the laser beam is considered, where the spherical shape is suitable. Additionally, the simple drag force formula can be applied. Thus, the spherical object with a tempered surface of 30.2 mm in diameter is made up by machining a spherical stainless steel SUS440. A cube corner prism with a diameter of 12.7 mm has been firmly inserted into the object’s body afterwards so that the center of gravity of the object coincides with the optical center of the laser beam. The total mass of which, including the cube corner prism, is m = 93.88g. Fig. 2 details the photographs and dimensions of the spherical object. In operation, the time and the displacement, at the moment of the impact force is detected, will define to be the origin of each the time and displacement axis. Fig. 3 shows the photographs of the sand under test, which is a standard sand of JIS R 5201 provided for a cement strength test. It is employed for the experiment in order to keep the major properties and moisture content in the sand under test with the less possible contamination. The sand is specified by the Japanese Industrial Standard (JIS) and provided by the Japan Cement Association (JCA), a trade organization comprises all 17 cement manufacturers in Japan (as of April 2015). It is natural dried sand of which the criterions are less than 0.2% of moisture content, screened and preferably prepared to contain at least 98% of a silicon dioxide content. The density is 2640 kg/m3 (specific gravity of 2.64). The composition and particle size distribution of the sand are given in Table 1.
Fig. 2. Photographs and dimensions of the spherical object.
During the free fall motion and collision event, the total force that acts on the spherical object is considered a combination by three forces. The first is the force due to gravity that acts on the object, mg, the second is the reaction force acts on the object due to colliding with the sand, F sand , and the last is the other negligible forces (air drag force and magnetic force that used to hold and release the spherical object). Therefore, the resultant force acts on the spherical object, F object , can be expressed as:
F object ¼ mg þ F sand
ð1Þ
where g is the acceleration due to gravity of the Earth, which is estimated to be 9.799 m/s2 at the altitude of the experiment room. By
Fig. 1. The experimental setup for the proposed method, where BS is a beam splitter, PBS is a polarization beam splitter, CC is a cube-corner prism, GTP is a Glan-Thompson prism, PD is a photodiode, LD is a laser diode, ADC is an analog to digital converter, and DAC is a digital to analog converter.
248
P. Youplao et al. / Results in Physics 9 (2018) 246–251
Fig. 3. Photographs of the JIS R 5201 sand, (a) the package in polyethylene bag of 1350 g, (b) the sand in close up as a scale of 1 cm2.
Table 1 The composition and particle size distribution of the JIS R 5201 sand. Compositions (%)
Particle size distribution
Ignition loss SiO2 Al2O Fe2O CaO MgO Na2O K2O
Square mesh size (mm)
Cumulative sieve residue (%)
2.00 1.60 1.00 0.50 0.16 0.08
0 7±5 33 ± 5 67 ± 5 87 ± 5 99 ± 1
0.00 98.4 0.40 0.40 0.20 0.00 0.01 0.01
modifying the Eq. (1), the impact force due to colliding with the sand, F sand , can be expressed as:
F sand ¼ F object þ mg
ð2Þ
In addition, while the spherical object is moving with acceleration, the resultant force acts on the object, F object , can also be calculated by multiplying the object’s mass, m, by its acceleration, a. The acceleration of the object can be obtained by differentiating its related velocity, v , respect to time. The velocity calculated from the Doppler shift frequency, f Doppler , between the beat and the rest signal, which are obtained by the optical interferometer. These estimates can be expressed as:
v ðtÞ ¼ kair ½f Doppler ðtÞ=2
ð3Þ
f Doppler ðtÞ ¼ ½f beat ðtÞ f rest ðtÞ
ð4Þ
The wavelength of the laser beam that used in the experiment is kair ¼ 633 nm. The beat frequency, f beat , is the frequency of the interference fringe signal between the signal beam and the reference beam, obtained by the optical interferometer and related to the velocity of the spherical object. The rest frequency, f rest , is approximately of 3.0 MHz. The beat frequency will be equivalent to the rest frequency when the spherical object is at rest and no Doppler Effect result in the signal beam. The coordinate system used for all the evaluated mechanical quantities acting on the object will be considered positive in the upward direction of Fig. 1. A simple method with more accuracy for the first derivative, known as the central difference method, is employed to evaluate the acceleration of the spherical object. The numerical differentiation can be expressed as:
an ðtÞ ¼ ½v nþ1 ðtÞ v n1 ðtÞ=½t nþ1 t n1
ð5Þ
where an is the acceleration, v n is the velocity, and t n is the time, all at the position n of the experimental time-velocity profile.
The collision in the experiment is caused by only the free fall of the spherical object under the gravitational force with the drop distance of approximately 107 mm in height above the sand surface. Therefore, the materials are nondestructive and not have any effects after the collision. In the experiment, a hollow circular electromagnet is employed to hold and release the spherical object, by manually turning on/off the magnet. During the free fall motion and collision, the Doppler shift frequency is measured by a laser interferometer. A Zeeman-type He-Ne laser with two orthogonal polarization frequencies is used to be the light source of the interferometer. This light beam is divided into two coincident beams by a beam splitter. One of the beams is employed as the resting beam appears on the detector PD1 and results in the rest signal. Another beam propagates through to a polarization beam splitter. One of the polarized frequencies propagates through along the signal beam route and then reflects off the cube corner prism that placed inside the spherical object. Another polarized frequency concurrently reflects off the same polarization beam splitter and then propagates along the reference beam route. After propagating along the Michelson-type interferometer, the signal beam and reference beam will be finally transmitted through the GlanThompson polarizing prism with 45° respect to each the beam polarization. The beams thus interfered. As the beams have a slightly different in frequency, the interference of the beams will appear on the detector PD2 and results in the beat signal. A digitizer (NI PCI-5105, National Instruments Corp., USA) is used to record the beat and the rest signal with a resolution of 8 bits and a sampling frequency of 30 MHz. Thus, each channel obtains a dataset of 5 M samples in the measuring duration of 0.167 s. The digitizer is initiated by a triggered signal from the digital to analog converter, which will be activated by an external light switch (a laser diode and a photodiode) when the spherical object is released from the electromagnet. The Zero-Crossing Fitting method (ZFM) [23,24], which is a principle of frequency estimation that considering all the zero crossing times during each sampling interval period of a data waveform, is employed to determine f beat and f rest from the digitized signal waveforms. The sampling interval of the signal waveform is defined as N = 1000 periods, corresponds to 0.132 ms and 0.333 ms when f beat is at the maximum and minimum value of approximately 7.6 MHz and 3.0 MHz, respectively. A high-speed camera (NAC Memrecam GX-1, NAC Image Technology, USA), with a resolution of 135,424 pixels and a frame rate of 15,000 fps, is employed to capture the images while the spherical object is colliding with the sand.
Results and discussion Fig. 4 shows the data manipulation process for evaluating the dynamic impact responses of the spherical object dropped onto the sand under test surface. The procedure starts from the quantity of each the frequency, f beat , and f rest , as a function of time, obtained by the ZFM [23,24]. Then, the velocity of the spherical object, v (m/ s), can be evaluated by using Eqs. (3) and (4). The acceleration, a (m/s2), and the displacement, x (m), of the spherical object is calculated afterwards by differentiating and integrating the velocity, respectively. Then, the total force acts on the spherical object, F object , will be calculated by multiplying the mass of the object by the acceleration. Finally, the evaluation of the impact force due to colliding with the sand, F sand , which relates to the total force acts on the observed object, F object , can be achieved. Fig. 5 shows the changes in the impact force, F sand , the velocity, v , and the displacement, x, against the time, t. The figure provides the captured images of the spherical object during the collision as well. While the spherical object is colliding with the sand, the
P. Youplao et al. / Results in Physics 9 (2018) 246–251
249
Fig. 4. Data manipulation process: the velocity, the displacement, the acceleration, and the forces acting on the spherical object, calculated by the two frequencies, f beat and f rest .
Fig. 5. The impact force acts on the observed object and of which the velocity and the displacement, each as a function of the time, together with the captured images from the high-speed camera.
250
P. Youplao et al. / Results in Physics 9 (2018) 246–251
impact force rises precipitously to its maximum value of Fsand = 12.05 N at the time of t = 3.4 ms and the displacement of x = 4.6 mm. After the collision, the spherical object is motionless and bogged down on the sand surface. As a result, the beat frequency becomes a constant value due to no Doppler shift result in the signal beam. The measurement was terminated at the time of t = 80 ms and the displacement of x = 15.3 mm. Fig. 6 shows the comparison of the changes in the impact force and of which the relative velocity and displacement for the 5-drop tests. The results are superimposed and coincide well indicate that the proposed method has a high-reliability for measurement and reproducibility. A slightly different value in each quantity is mainly derived from the differences in collision point on the sand surface, which are impossible to be the same for each drop test. The measurement value of the resultant force that acts on the observed object may have some degree of uncertainty, which derived from a variety of sources as follows: [S1] Optical alignment: The uncertainty in the optical alignment of the interferometer is mainly derived from the inclination angle of the laser beam, which is approximately of 1 103 rad and results in the velocity with a negligible uncertainty of 5 107 m/s. [S2] Noise in the signal: The data processing procedure starts with the calculated values of the two frequencies, f beat and f rest , which are obtained by the ZFM. Principally, the value of f beat will change depending on the velocity of the object, but the value of f rest is a constant. In practice, f rest is inconstant and vary around its mean value of 3.04269 MHz with a standard deviation of approximately 19 Hz due to the noise in the signal. In contrast, it is difficult to estimate the deviation in the f beat signal since it will change depending on the velocity. However, during the free fall phase, the noise in the f beat signal is considered to have similar properties with the noise in the f rest signal. Therefore, with the same standard deviation of approximately 19 Hz, corresponds to a deviation in the velocity of 12 106 m/s, the uncertainty due to noise in the signals can be neglected.
[S3] Mass calibration: A commercial digital electronic balance used for the mass measurement will typically have some uncertainty of results within 0.01 g, which is approximately 0.01% of the mass of the object. Corresponding to a negligible deviation of 1.2 mN respect to the maximum value of Fsand = 12.05 N. [S4] Acceleration due to the gravity: The acceleration due to gravity on the Earth’s surface (the experiment room) is estimated to be g = 9.799 m/s2 with an uncertainty of 0.01%, which can be neglected. [S5] Air resistance force: According to the drag equation [25], defined as F drag ¼ 12 qv 2 C d A, it can be employed to calculate the drag or the resistance force of an event as an object is moving in an environment, such as air or water. As the mass density of the air at 1 atmosphere (101.325 kPa) with the temperature of 25 °C is q = 1.184 kg/m3 (the experiment room), the air drag coefficient is Cd = 0.47, and the reference area of the sphere is A = pr2, where r = 15.1 mm. Therefore, during the maximum velocity of v = 1.45 m/s, the air resistance force is estimated to be Fdrag = 0.42 mN. [S6] The other derivations: The uncertainties that derived by the other sources are difficult to estimate as a separate quantity, such as the noise in optical interferometer, the numerical calculation for the force, the lateral misalignment of the laser beam, the rotation of the cube corner prism, the impact-excited modal oscillations, the change in moisture content of the sand, the different impact locations on the sand surface, etc. However, in practice, the dropping experiment can be considered as two separate events. The first is during the free fall motion and the seconds is while colliding with the sand. In the 5-drop test measurements, during only the free fall phase of 10–50 mm heights above the sand surface, the mean and the standard deviation of F sand (equals to F body þ mg) are 0.5 mN and 8.1 mN, respectively. For the colliding phase, the mean and the standard deviation of the maximum value of F sand are 12.4 N and 0.49 N, respectively. Therefore, for the colliding phase only, the combined standard uncertainty in measuring the impact force acts on the object is estimated to 0.49 N, which is corresponding to 4.07% of the maximum value of Fsand = 12.05 N. This uncertainty is mainly due to the collision points on the sand surface are not the same. The dynamic impact responses of the spherical object dropped onto the sand surface can be evaluated by using an optical interferometer as the experiment. The measured data that provided by the proposed method is valuable for improving the associated numerical simulation algorithm and for a deeper understanding of mechanical properties of sand. The impact response of the tested material or other geological materials can be applied for evaluating the other material properties such as smoothness and strength, especially for the other planet explorations by a robot. These impact responses are essential for supporting the spacecraft landing mission or facility constructions on the other planet’s surface, for instance, the Moon or Mars. In addition, the dynamic impact responses of systems with any build of a rigid object that moves in a vertical direction to collide with any materials can be evaluated using the same experimental method. The velocity at the moment of collision can be varied by changing the drop height above the testing material surface. The proposed method will be interesting to the fields of optical metrology, material science, measurement science, impact engineering, mechanical engineering, civil engineering, space engineering, lunar science, and geological.
Conclusion Fig. 6. Comparison of the impact force, the velocity, and the displacement, as a function of the time for the 5-drop test measurements.
In this investigation, we have demonstrated the dynamic impact responses of the rigid spherical object dropped onto the
P. Youplao et al. / Results in Physics 9 (2018) 246–251
testing material (the standard sand) can be evaluated by the proposed method. In the experiment, the velocity of the spherical object while dropping and colliding with the sand surface is measured using a Michelson-type laser interferometer. Afterward, the obtained velocity is useful for calculating the other required mechanical quantities such as the displacement and the acceleration. Finally, by multiplying the acceleration by the mass of the object, the dynamic impact force acts on the observed object during the collision can be achieved. Moreover, the behavior of the sand during the collision is also observed by the captured images from the high-speed camera. From the experimental results, with the sampling interval of approximately 1 ms, the combined standard uncertainties in measuring the impact force acts on the spherical object are estimated to 8.1 mN during the free fall motion and 0.49 N for the collision phase. These correspond respectively to 0.07% and 4.07% of the maximum impact force of 12.05 N. The uncertainty in the impact forces is primarily due to the differences in the collision points on the sand surface. Acknowledgments The authors would like to thank a research-aid fund of the Asahi Glass Foundation, a research-aid fund of the NSK Foundation for the Advancement of Mechatronics (NSK-FAM) and the grant-inaid for Scientific Research (B) 24360156 (KAKENHI 24360156) for providing the financial support.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.rinp.2018.02.046. References [1] Miao L, Houston SL, Cui Y, Yuan J. Relationship between soil structure and mechanical behavior for an expansive unsaturated clay. Can Geotech J 2007;44:126–37. [2] Estabragh AR, Beytolahpour I, Moradi M, Javadi AA. Mechanical behavior of a clay soil contaminated with glycerol and ethanol. Eur J Environ Civ En 2016;20:503–19. [3] Ghasemzadeh H, Sojoudi MH, Ghoreishian Amiri SA, Karami MH. Elastoplastic model for hydro-mechanical behavior of unsaturated soils. Soils Found 2017;57:371–83.
251
[4] Ray CS, Reis ST, Sen S, O’Dellc JS. JSC-1A lunar soil simulant: characterization, glass formation, and selected glass properties. J Non-Cryst Solids 2010;356:2369–74. [5] Mingjing J, Liqing L, Qijun Y. Experimental investigation on deformation behavior of TJ-1 lunar soil simulant subjected to principal stress rotation. Adv Space Res 2013;52:136–46. [6] Sun H, Yi M, Shen Z, Zhang X, Ma S. Developing a new controllable lunar dust simulant: BHLD20. Planet Space Sci 2017;141:17–24. [7] Anderson CE, Holmquist TJ. Application of a computational glass model to compute propagation of failure from ballistic impact of borosilicate glass targets. Int J Impact Eng 2013;56:2–11. [8] Michikami T, Hagermann A, Morota T, Haruyama J, Hasegawa S. Oblique impact cratering experiments in brittle targets: implications for elliptical craters on the Moon. Planet Space Sci 2017;135:27–36. [9] Mohagheghian I, Wang Y, Jiang L, Zhang X, Guo X, Yan Y, Kinloch AJ, Dear JP. Quasi-static bending and low velocity impact performance of monolithic and laminated glass windows employing chemically strengthened glass. Eur J Mech A Solids 2017;63:165–86. [10] Ravikumar K, Kiran K, Sreebalaji VS. Characterization of mechanical properties of aluminium/tungsten carbide composites. Measurement 2017;102:142–9. [11] Soulas F, Espinosa C, Lachaud F, Guinard S, Lepetit B, Revel I, Duval Y. A method to replace lightning strike tests by ball impacts in the design process of lightweight composite aircraft panels. Int J Impact Eng 2018;111:165–76. [12] Zhang R, Zhi XD, Fan F. Plastic behavior of circular steel tubes subjected to lowvelocity transverse impact. Int J Impact Eng 2018;114:1–19. [13] Liu T, Fleck NA, Wadley HNG, Deshpande VS. The impact of sand slugs against beams and plates: coupled discrete particle/finite element simulations. J Mech Phys Solids 2013;61:1798–821. [14] Chian SC, Tan BCV, Sarma A. Projectile penetration into sand: relative density of sand and projectile nose shape and mass. Int J Impact Eng 2017;103:29–37. [15] Roul P, Schinner A. Simulation study on micro and macro mechanical behaviour of sand piles. Powder Technol 2010;204:113–23. [16] Mao YQ, Fu YM, Chen CP, Li YL. Nonlinear dynamic response for functionally graded shallow spherical shell under low velocity impact in thermal environment. Appl Math Model 2011;35:2887–900. [17] Yu K, Tafti D. Impact model for micrometer-sized sand particles. Powder Technol 2016;294:11–21. [18] Suzuki T, Fujii Y, Valera J. Optical method for strength test for general industrial products. Mech Syst Signal Process 2006;20:735–44. [19] Fujii Y. Toward establishing dynamic calibration method for force transducers. IEEE Trans Instrum Meas 2009;58:2358–64. [20] Fujii Y. Measurement of impulse response of force transducers. Rev Sci Instrum 2001;72:3108–11. [21] Fujii Y, Shu DW. Impact force measurement of an actuator arm of a hard disk drive. Int J Impact Eng 2008;35:98–108. [22] Araki R, Takita A, Ishima T, Kawashima H, Pornsuwancharoen N, Punthawanunt S, Carcasona E, Fujii Y. Impact force measurement of a spherical body dropping onto a water surface. Rev Sci Instrum 2014;85:075108. [23] Fujii Y, Hessling JP. Frequency estimation method from digitized waveform. Exp Tech 2009;33:64–9. [24] Jin T, Takita A, Mitatha S, Yupapin PP, Jia HZ, Hou WM, Fujii Y. Method for acceleration measurement using a laser Doppler interferometer. Meas Sci Technol 2013;24:077001. [25] Clancy LJ. Aerodynamics. London: Pitman Publishing Limited; 1975.
Contents lists available at ScienceDirect
Results in Physics journal homepage: www.journals.elsevier.com/results-in-physics
Dynamic response of sand particles impacted by a rigid spherical object P. Youplao a,⇑, A. Takita b, H. Nasbey b, P.P. Yupapin c,d, Y. Fujii b a Electrical Engineering Department, Faculty of Industry and Technology, Rajamangala University of Technology Isan Sakon Nakhon Campus, 199 Village No. 3, Phungkon, Sakon Nakhon 47160, Thailand b School of Science and Technology, Gunma University, Kiryu, Tenjin-cho 1-5-1, 376-8515, Japan c Computational Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, District 7, Ho Chi Minh City, Viet Nam d Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, District 7, Ho Chi Minh City, Viet Nam
a r t i c l e
i n f o
Article history: Received 26 January 2018 Received in revised form 13 February 2018 Accepted 20 February 2018 Available online 24 February 2018 Keywords: Sand particle Collision response Dynamic force Inertial mass Optical interferometer
a b s t r a c t A method for measuring the dynamic impact responses that acting on a spherical object while dropping and colliding with dried sand, such as the velocity, displacement, acceleration, and resultant force, is presented and discussed. In the experiment, a Michelson-type laser interferometer is employed to obtain the velocity of the spherical stainless steel object. Then the obtained time velocity profile is used to calculate the acceleration, the displacement, and the inertial force acting on the observed sand particles. Furthermore, a high-speed camera is employed to observe the behavior of the sand during the collision. From the experimental results with the sampling interval for frequencies calculation of 1 ms, the combined standard uncertainty in the instantaneous value of the impact force acts on the observed object is obtained and approximated to 0.49 N, which is related to a corresponding 4.07% of the maximum value at 12.05 N of the impact force. Ó 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Introduction The mechanical behavior of soil, sand, dust and the other associated composite materials is receiving intensive attention and widely investigated by a variety of research methods, where there are many of relevant studies proposed, for an instant, an attempt to investigate mechanical behavior of geological materials in any considered conditions [1–3], where the lunar soil simulant with a geochemical reproduction of lunar regolith is examined to compare with the returned samples from the Moon, which aim to support the landing missions or facility constructions on the lunar surface [4–6]. The impact cratering process on brittle materials, such as borosilicate glass and a mixture of geophysical materials is investigated as well for improving parts of industrial products [7] and understanding impact craters on the Moon [8]. Furthermore, the dynamic behavior of an object impacts onto any material is received intensive attention [9–12]. One of the most important groups of the materials in both the geography and construction industry is sand [13,14], in which some studies employ the numerical simulations to evaluate the impact responses from testing materials [15–17]. However, it is still difficult to measure the dynamic mechanical quantities acting on an object during the
⇑ Corresponding author.
collision, such as the impact force on and from the material, which is under tested. Several authors have previously developed methods based on the law of momentum conservation for precision mechanical measurement, known as the Levitation Mass Method (LMM). In this method, the force due to a moving mass, levitated by a linear motion air bearing so that its velocity is at an almost constant, which is employed to be a reference force made to collide with testing objects. The LMM experiment has been conducted to evaluate mechanical quantities for some investigations such as the strength test for a general industrial product [18]. Measuring response calibration in dynamic conditions for a force transducer [19,20] and impact force measurement for a hard drive actuator arm have been reported [21]. In addition, the dynamic response of an object impacts onto a surface such as the water entry event can also be evaluated using the modified LMM [22]. By using the LMM, all necessary mechanical quantities during the collision of the observed object, such as the velocity, the displacement, and the acceleration, can be evaluated by an optical interferometer. The results were obtained in a good synchronization using numerical calculations of the motion-induced time-varying beat frequency of the optical interferometer. Finally, the resultant force acts on the observed object will be calculated directly according to the force definition as multiplying the mass of the whole object’s body by its acceleration.
E-mail address: [email protected] (P. Youplao). https://doi.org/10.1016/j.rinp.2018.02.046 2211-3797/Ó 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
P. Youplao et al. / Results in Physics 9 (2018) 246–251
247
In this paper, the LMM method has been modified for evaluating the dynamic responses of a mass in the vertical movement, which is suitable for impact measurement under the gravity and found in nature. In the experiment, by modifying the LMM, a method for evaluating the dynamic impact responses of a spherical object dropped onto the dried sand surface is presented. The experimental validity is demonstrated and discussed as well.
Experimental setup The interference-based experiment, of which the schematic diagram of apparatus setup illustrated in Fig. 1, is employed to evaluate the dynamic response that a rigid object drops impact onto the sand particles surface. In the experiment, the object is free to fall under the gravity before the collision. Therefore, the shape of the object that can provide the symmetry orientation of the laser beam is considered, where the spherical shape is suitable. Additionally, the simple drag force formula can be applied. Thus, the spherical object with a tempered surface of 30.2 mm in diameter is made up by machining a spherical stainless steel SUS440. A cube corner prism with a diameter of 12.7 mm has been firmly inserted into the object’s body afterwards so that the center of gravity of the object coincides with the optical center of the laser beam. The total mass of which, including the cube corner prism, is m = 93.88g. Fig. 2 details the photographs and dimensions of the spherical object. In operation, the time and the displacement, at the moment of the impact force is detected, will define to be the origin of each the time and displacement axis. Fig. 3 shows the photographs of the sand under test, which is a standard sand of JIS R 5201 provided for a cement strength test. It is employed for the experiment in order to keep the major properties and moisture content in the sand under test with the less possible contamination. The sand is specified by the Japanese Industrial Standard (JIS) and provided by the Japan Cement Association (JCA), a trade organization comprises all 17 cement manufacturers in Japan (as of April 2015). It is natural dried sand of which the criterions are less than 0.2% of moisture content, screened and preferably prepared to contain at least 98% of a silicon dioxide content. The density is 2640 kg/m3 (specific gravity of 2.64). The composition and particle size distribution of the sand are given in Table 1.
Fig. 2. Photographs and dimensions of the spherical object.
During the free fall motion and collision event, the total force that acts on the spherical object is considered a combination by three forces. The first is the force due to gravity that acts on the object, mg, the second is the reaction force acts on the object due to colliding with the sand, F sand , and the last is the other negligible forces (air drag force and magnetic force that used to hold and release the spherical object). Therefore, the resultant force acts on the spherical object, F object , can be expressed as:
F object ¼ mg þ F sand
ð1Þ
where g is the acceleration due to gravity of the Earth, which is estimated to be 9.799 m/s2 at the altitude of the experiment room. By
Fig. 1. The experimental setup for the proposed method, where BS is a beam splitter, PBS is a polarization beam splitter, CC is a cube-corner prism, GTP is a Glan-Thompson prism, PD is a photodiode, LD is a laser diode, ADC is an analog to digital converter, and DAC is a digital to analog converter.
248
P. Youplao et al. / Results in Physics 9 (2018) 246–251
Fig. 3. Photographs of the JIS R 5201 sand, (a) the package in polyethylene bag of 1350 g, (b) the sand in close up as a scale of 1 cm2.
Table 1 The composition and particle size distribution of the JIS R 5201 sand. Compositions (%)
Particle size distribution
Ignition loss SiO2 Al2O Fe2O CaO MgO Na2O K2O
Square mesh size (mm)
Cumulative sieve residue (%)
2.00 1.60 1.00 0.50 0.16 0.08
0 7±5 33 ± 5 67 ± 5 87 ± 5 99 ± 1
0.00 98.4 0.40 0.40 0.20 0.00 0.01 0.01
modifying the Eq. (1), the impact force due to colliding with the sand, F sand , can be expressed as:
F sand ¼ F object þ mg
ð2Þ
In addition, while the spherical object is moving with acceleration, the resultant force acts on the object, F object , can also be calculated by multiplying the object’s mass, m, by its acceleration, a. The acceleration of the object can be obtained by differentiating its related velocity, v , respect to time. The velocity calculated from the Doppler shift frequency, f Doppler , between the beat and the rest signal, which are obtained by the optical interferometer. These estimates can be expressed as:
v ðtÞ ¼ kair ½f Doppler ðtÞ=2
ð3Þ
f Doppler ðtÞ ¼ ½f beat ðtÞ f rest ðtÞ
ð4Þ
The wavelength of the laser beam that used in the experiment is kair ¼ 633 nm. The beat frequency, f beat , is the frequency of the interference fringe signal between the signal beam and the reference beam, obtained by the optical interferometer and related to the velocity of the spherical object. The rest frequency, f rest , is approximately of 3.0 MHz. The beat frequency will be equivalent to the rest frequency when the spherical object is at rest and no Doppler Effect result in the signal beam. The coordinate system used for all the evaluated mechanical quantities acting on the object will be considered positive in the upward direction of Fig. 1. A simple method with more accuracy for the first derivative, known as the central difference method, is employed to evaluate the acceleration of the spherical object. The numerical differentiation can be expressed as:
an ðtÞ ¼ ½v nþ1 ðtÞ v n1 ðtÞ=½t nþ1 t n1
ð5Þ
where an is the acceleration, v n is the velocity, and t n is the time, all at the position n of the experimental time-velocity profile.
The collision in the experiment is caused by only the free fall of the spherical object under the gravitational force with the drop distance of approximately 107 mm in height above the sand surface. Therefore, the materials are nondestructive and not have any effects after the collision. In the experiment, a hollow circular electromagnet is employed to hold and release the spherical object, by manually turning on/off the magnet. During the free fall motion and collision, the Doppler shift frequency is measured by a laser interferometer. A Zeeman-type He-Ne laser with two orthogonal polarization frequencies is used to be the light source of the interferometer. This light beam is divided into two coincident beams by a beam splitter. One of the beams is employed as the resting beam appears on the detector PD1 and results in the rest signal. Another beam propagates through to a polarization beam splitter. One of the polarized frequencies propagates through along the signal beam route and then reflects off the cube corner prism that placed inside the spherical object. Another polarized frequency concurrently reflects off the same polarization beam splitter and then propagates along the reference beam route. After propagating along the Michelson-type interferometer, the signal beam and reference beam will be finally transmitted through the GlanThompson polarizing prism with 45° respect to each the beam polarization. The beams thus interfered. As the beams have a slightly different in frequency, the interference of the beams will appear on the detector PD2 and results in the beat signal. A digitizer (NI PCI-5105, National Instruments Corp., USA) is used to record the beat and the rest signal with a resolution of 8 bits and a sampling frequency of 30 MHz. Thus, each channel obtains a dataset of 5 M samples in the measuring duration of 0.167 s. The digitizer is initiated by a triggered signal from the digital to analog converter, which will be activated by an external light switch (a laser diode and a photodiode) when the spherical object is released from the electromagnet. The Zero-Crossing Fitting method (ZFM) [23,24], which is a principle of frequency estimation that considering all the zero crossing times during each sampling interval period of a data waveform, is employed to determine f beat and f rest from the digitized signal waveforms. The sampling interval of the signal waveform is defined as N = 1000 periods, corresponds to 0.132 ms and 0.333 ms when f beat is at the maximum and minimum value of approximately 7.6 MHz and 3.0 MHz, respectively. A high-speed camera (NAC Memrecam GX-1, NAC Image Technology, USA), with a resolution of 135,424 pixels and a frame rate of 15,000 fps, is employed to capture the images while the spherical object is colliding with the sand.
Results and discussion Fig. 4 shows the data manipulation process for evaluating the dynamic impact responses of the spherical object dropped onto the sand under test surface. The procedure starts from the quantity of each the frequency, f beat , and f rest , as a function of time, obtained by the ZFM [23,24]. Then, the velocity of the spherical object, v (m/ s), can be evaluated by using Eqs. (3) and (4). The acceleration, a (m/s2), and the displacement, x (m), of the spherical object is calculated afterwards by differentiating and integrating the velocity, respectively. Then, the total force acts on the spherical object, F object , will be calculated by multiplying the mass of the object by the acceleration. Finally, the evaluation of the impact force due to colliding with the sand, F sand , which relates to the total force acts on the observed object, F object , can be achieved. Fig. 5 shows the changes in the impact force, F sand , the velocity, v , and the displacement, x, against the time, t. The figure provides the captured images of the spherical object during the collision as well. While the spherical object is colliding with the sand, the
P. Youplao et al. / Results in Physics 9 (2018) 246–251
249
Fig. 4. Data manipulation process: the velocity, the displacement, the acceleration, and the forces acting on the spherical object, calculated by the two frequencies, f beat and f rest .
Fig. 5. The impact force acts on the observed object and of which the velocity and the displacement, each as a function of the time, together with the captured images from the high-speed camera.
250
P. Youplao et al. / Results in Physics 9 (2018) 246–251
impact force rises precipitously to its maximum value of Fsand = 12.05 N at the time of t = 3.4 ms and the displacement of x = 4.6 mm. After the collision, the spherical object is motionless and bogged down on the sand surface. As a result, the beat frequency becomes a constant value due to no Doppler shift result in the signal beam. The measurement was terminated at the time of t = 80 ms and the displacement of x = 15.3 mm. Fig. 6 shows the comparison of the changes in the impact force and of which the relative velocity and displacement for the 5-drop tests. The results are superimposed and coincide well indicate that the proposed method has a high-reliability for measurement and reproducibility. A slightly different value in each quantity is mainly derived from the differences in collision point on the sand surface, which are impossible to be the same for each drop test. The measurement value of the resultant force that acts on the observed object may have some degree of uncertainty, which derived from a variety of sources as follows: [S1] Optical alignment: The uncertainty in the optical alignment of the interferometer is mainly derived from the inclination angle of the laser beam, which is approximately of 1 103 rad and results in the velocity with a negligible uncertainty of 5 107 m/s. [S2] Noise in the signal: The data processing procedure starts with the calculated values of the two frequencies, f beat and f rest , which are obtained by the ZFM. Principally, the value of f beat will change depending on the velocity of the object, but the value of f rest is a constant. In practice, f rest is inconstant and vary around its mean value of 3.04269 MHz with a standard deviation of approximately 19 Hz due to the noise in the signal. In contrast, it is difficult to estimate the deviation in the f beat signal since it will change depending on the velocity. However, during the free fall phase, the noise in the f beat signal is considered to have similar properties with the noise in the f rest signal. Therefore, with the same standard deviation of approximately 19 Hz, corresponds to a deviation in the velocity of 12 106 m/s, the uncertainty due to noise in the signals can be neglected.
[S3] Mass calibration: A commercial digital electronic balance used for the mass measurement will typically have some uncertainty of results within 0.01 g, which is approximately 0.01% of the mass of the object. Corresponding to a negligible deviation of 1.2 mN respect to the maximum value of Fsand = 12.05 N. [S4] Acceleration due to the gravity: The acceleration due to gravity on the Earth’s surface (the experiment room) is estimated to be g = 9.799 m/s2 with an uncertainty of 0.01%, which can be neglected. [S5] Air resistance force: According to the drag equation [25], defined as F drag ¼ 12 qv 2 C d A, it can be employed to calculate the drag or the resistance force of an event as an object is moving in an environment, such as air or water. As the mass density of the air at 1 atmosphere (101.325 kPa) with the temperature of 25 °C is q = 1.184 kg/m3 (the experiment room), the air drag coefficient is Cd = 0.47, and the reference area of the sphere is A = pr2, where r = 15.1 mm. Therefore, during the maximum velocity of v = 1.45 m/s, the air resistance force is estimated to be Fdrag = 0.42 mN. [S6] The other derivations: The uncertainties that derived by the other sources are difficult to estimate as a separate quantity, such as the noise in optical interferometer, the numerical calculation for the force, the lateral misalignment of the laser beam, the rotation of the cube corner prism, the impact-excited modal oscillations, the change in moisture content of the sand, the different impact locations on the sand surface, etc. However, in practice, the dropping experiment can be considered as two separate events. The first is during the free fall motion and the seconds is while colliding with the sand. In the 5-drop test measurements, during only the free fall phase of 10–50 mm heights above the sand surface, the mean and the standard deviation of F sand (equals to F body þ mg) are 0.5 mN and 8.1 mN, respectively. For the colliding phase, the mean and the standard deviation of the maximum value of F sand are 12.4 N and 0.49 N, respectively. Therefore, for the colliding phase only, the combined standard uncertainty in measuring the impact force acts on the object is estimated to 0.49 N, which is corresponding to 4.07% of the maximum value of Fsand = 12.05 N. This uncertainty is mainly due to the collision points on the sand surface are not the same. The dynamic impact responses of the spherical object dropped onto the sand surface can be evaluated by using an optical interferometer as the experiment. The measured data that provided by the proposed method is valuable for improving the associated numerical simulation algorithm and for a deeper understanding of mechanical properties of sand. The impact response of the tested material or other geological materials can be applied for evaluating the other material properties such as smoothness and strength, especially for the other planet explorations by a robot. These impact responses are essential for supporting the spacecraft landing mission or facility constructions on the other planet’s surface, for instance, the Moon or Mars. In addition, the dynamic impact responses of systems with any build of a rigid object that moves in a vertical direction to collide with any materials can be evaluated using the same experimental method. The velocity at the moment of collision can be varied by changing the drop height above the testing material surface. The proposed method will be interesting to the fields of optical metrology, material science, measurement science, impact engineering, mechanical engineering, civil engineering, space engineering, lunar science, and geological.
Conclusion Fig. 6. Comparison of the impact force, the velocity, and the displacement, as a function of the time for the 5-drop test measurements.
In this investigation, we have demonstrated the dynamic impact responses of the rigid spherical object dropped onto the
P. Youplao et al. / Results in Physics 9 (2018) 246–251
testing material (the standard sand) can be evaluated by the proposed method. In the experiment, the velocity of the spherical object while dropping and colliding with the sand surface is measured using a Michelson-type laser interferometer. Afterward, the obtained velocity is useful for calculating the other required mechanical quantities such as the displacement and the acceleration. Finally, by multiplying the acceleration by the mass of the object, the dynamic impact force acts on the observed object during the collision can be achieved. Moreover, the behavior of the sand during the collision is also observed by the captured images from the high-speed camera. From the experimental results, with the sampling interval of approximately 1 ms, the combined standard uncertainties in measuring the impact force acts on the spherical object are estimated to 8.1 mN during the free fall motion and 0.49 N for the collision phase. These correspond respectively to 0.07% and 4.07% of the maximum impact force of 12.05 N. The uncertainty in the impact forces is primarily due to the differences in the collision points on the sand surface. Acknowledgments The authors would like to thank a research-aid fund of the Asahi Glass Foundation, a research-aid fund of the NSK Foundation for the Advancement of Mechatronics (NSK-FAM) and the grant-inaid for Scientific Research (B) 24360156 (KAKENHI 24360156) for providing the financial support.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.rinp.2018.02.046. References [1] Miao L, Houston SL, Cui Y, Yuan J. Relationship between soil structure and mechanical behavior for an expansive unsaturated clay. Can Geotech J 2007;44:126–37. [2] Estabragh AR, Beytolahpour I, Moradi M, Javadi AA. Mechanical behavior of a clay soil contaminated with glycerol and ethanol. Eur J Environ Civ En 2016;20:503–19. [3] Ghasemzadeh H, Sojoudi MH, Ghoreishian Amiri SA, Karami MH. Elastoplastic model for hydro-mechanical behavior of unsaturated soils. Soils Found 2017;57:371–83.
251
[4] Ray CS, Reis ST, Sen S, O’Dellc JS. JSC-1A lunar soil simulant: characterization, glass formation, and selected glass properties. J Non-Cryst Solids 2010;356:2369–74. [5] Mingjing J, Liqing L, Qijun Y. Experimental investigation on deformation behavior of TJ-1 lunar soil simulant subjected to principal stress rotation. Adv Space Res 2013;52:136–46. [6] Sun H, Yi M, Shen Z, Zhang X, Ma S. Developing a new controllable lunar dust simulant: BHLD20. Planet Space Sci 2017;141:17–24. [7] Anderson CE, Holmquist TJ. Application of a computational glass model to compute propagation of failure from ballistic impact of borosilicate glass targets. Int J Impact Eng 2013;56:2–11. [8] Michikami T, Hagermann A, Morota T, Haruyama J, Hasegawa S. Oblique impact cratering experiments in brittle targets: implications for elliptical craters on the Moon. Planet Space Sci 2017;135:27–36. [9] Mohagheghian I, Wang Y, Jiang L, Zhang X, Guo X, Yan Y, Kinloch AJ, Dear JP. Quasi-static bending and low velocity impact performance of monolithic and laminated glass windows employing chemically strengthened glass. Eur J Mech A Solids 2017;63:165–86. [10] Ravikumar K, Kiran K, Sreebalaji VS. Characterization of mechanical properties of aluminium/tungsten carbide composites. Measurement 2017;102:142–9. [11] Soulas F, Espinosa C, Lachaud F, Guinard S, Lepetit B, Revel I, Duval Y. A method to replace lightning strike tests by ball impacts in the design process of lightweight composite aircraft panels. Int J Impact Eng 2018;111:165–76. [12] Zhang R, Zhi XD, Fan F. Plastic behavior of circular steel tubes subjected to lowvelocity transverse impact. Int J Impact Eng 2018;114:1–19. [13] Liu T, Fleck NA, Wadley HNG, Deshpande VS. The impact of sand slugs against beams and plates: coupled discrete particle/finite element simulations. J Mech Phys Solids 2013;61:1798–821. [14] Chian SC, Tan BCV, Sarma A. Projectile penetration into sand: relative density of sand and projectile nose shape and mass. Int J Impact Eng 2017;103:29–37. [15] Roul P, Schinner A. Simulation study on micro and macro mechanical behaviour of sand piles. Powder Technol 2010;204:113–23. [16] Mao YQ, Fu YM, Chen CP, Li YL. Nonlinear dynamic response for functionally graded shallow spherical shell under low velocity impact in thermal environment. Appl Math Model 2011;35:2887–900. [17] Yu K, Tafti D. Impact model for micrometer-sized sand particles. Powder Technol 2016;294:11–21. [18] Suzuki T, Fujii Y, Valera J. Optical method for strength test for general industrial products. Mech Syst Signal Process 2006;20:735–44. [19] Fujii Y. Toward establishing dynamic calibration method for force transducers. IEEE Trans Instrum Meas 2009;58:2358–64. [20] Fujii Y. Measurement of impulse response of force transducers. Rev Sci Instrum 2001;72:3108–11. [21] Fujii Y, Shu DW. Impact force measurement of an actuator arm of a hard disk drive. Int J Impact Eng 2008;35:98–108. [22] Araki R, Takita A, Ishima T, Kawashima H, Pornsuwancharoen N, Punthawanunt S, Carcasona E, Fujii Y. Impact force measurement of a spherical body dropping onto a water surface. Rev Sci Instrum 2014;85:075108. [23] Fujii Y, Hessling JP. Frequency estimation method from digitized waveform. Exp Tech 2009;33:64–9. [24] Jin T, Takita A, Mitatha S, Yupapin PP, Jia HZ, Hou WM, Fujii Y. Method for acceleration measurement using a laser Doppler interferometer. Meas Sci Technol 2013;24:077001. [25] Clancy LJ. Aerodynamics. London: Pitman Publishing Limited; 1975.