OPTICAL DETECTION OF SHORT COLLISION TIMES

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The 14 th International Conference of the Slovenian Society for Non-Destructive Testing»Application of Contemporary Non-Destructive Testing in Engineering«September 4-6, 2017, Bernardin, Slovenia

Petkovšek University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva cesta 6, 1000 Ljubljana, Slovenia E-mails: janez.rus@tum.de, * tomaz.pozar@fs.uni-lj.

1 The 14 th International Conference of the Slovenian Society for Non-Destructive Testing»Application of Contemporary Non-Destructive Testing in Engineering«September 4-6, 2017, Bernardin, Slovenia More info about this article: OPTICAL DETECTION OF SHORT COLLISION TIMES J. Rus, T. Požar * and R. Petkovšek University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva cesta 6, 1000 Ljubljana, Slovenia s: janez.rus@tum.de, * tomaz.pozar@fs.uni-lj.si, rok.petkovsek@fs.uni-lj.si ABSTRACT Determination of collision times is not only a crucial parameter in the basic studies of contact mechanisms. It is also important in a wide range of different applications related to: contact mechanics, tribology, shot peening, wear, erosion, rock falls, military ballistics, measurements of hardness at high strain rates and granular matter research. We introduced and demonstrated a stand-off method to measure short contact times during which small diameter balls collide with a stationary transparent cube. The measurements are based on the change of the total reflection properties at the dynamic contact mirror the surface elastically deformed by the impact. Deflection of the laser beam, illuminated on this surface, was monitored by a quadrant photodiode. A piezoelectric sensor was also used to detect the elastic waves released by the impact. The measured collision times of various ball diameters and approach velocities were compared with the results of the Hertz contact theory. By reducing these two parameters we estimated the minimum impact momentum of 40 nns that can still be detected with this method. Key words: Elastic impact, Contact time, Beam deflection probe, Piezoelectric sensor, Nondestructive testing 1. Introduction An idealized impact between two solid bodies consists of two major phases: the approach and the recoil phase [1]. In practice, the contact pressure often exceeds the critical yield stress of the material, what leads to a plastic deformation of the colliding bodies. These two phases occur in a time interval called the impact duration, the collision time or the contact time. This time is confined between the starting and the ending point of the contact when bodies firstly touch and then separate from each other. The contact time measurements are not only important in the basic studies of contact mechanisms, they are also important in different industrial applications especially in connection with the quality control. Due to its linear dependence on the ball diameter, the contact time can be a criterion for the size of the colliding particles. Even material properties (e.g. mass density, Young's modulus) of the colliding bodies can be determined from the collision time. Therefore, contact time measurements can be implemented in different fields ranging from contact mechanics, tribology, shot peening, wear, erosion, rock falls, military ballistics, hardness measurements at high strain rates to granular matter research [2]. 321

2 An impact of a dropped ball with a static plate is often used as a source of ultrasonic waves. Understanding the collision properties is also important when these waves are used as a known input signal for sensor calibration [3]. There are substantial methods for measuring collisional properties. When using conductive materials, it is a reasonable way to measure the contact time by observing changes of the current, when the colliding objects are connected in the electric circuit. This method was firstly realized in 1970 by using 50-mm-diameter spheres [4]. Similar experiments were made with 25.4-mmdiameter [5] and with 38.1-mm-diameter balls [6]. In these experiments, a pendulum was used. It enables to connect wires with colliding objects less intrusively. Real free fall conditions took place in the experiment made in 2015, where contact duration was studied for different lubrication conditions by application of complex impedance measurement. Disadvantage of this method is the inaccuracy caused by the wire that has to be connected with a 30-mm-diameter colliding particle. Electrical circuit method becomes unreliable for small ball diameters, because the dynamics of the colliding balls is affected too much by the connected wires [7]. The evolution of the contact force (and thereby also contact time) can be measured also using a piezoelectric film placed between the colliding bodies [8]. With this, the collision properties are influenced significantly. Experiments were performed for different ball materials and different drop heights. The collision time was approximately 1 ms. The contact time can be also indirectly determined from the width of the ultrasonic waves released during the impact and propagating within the collided solids [9, 10, 11]. Ball-plate and ball-rod experiments were realized. Long-enough rods were used in the experiment to eliminate the disturbance caused by the wave reflections. The wave properties are measured at the free end of the rod (opposite of an impact). In the first realization, the impact force was determined from the velocity of the free end, measured with laser-doppler vibrometer [9]. In the second realization, the contact times of approximately 0.1 ms were measured with a fringe-counting Michelson-type interferometer [10]. It was used to measure the displacement of the free end of the rod caused by the pressure wave generated at the impact. The motion lasts a time interval equal to the collision time. All of the mentioned methods are suitable only for balls with diameters larger than 10 mm, except the one, where the contact times of 0.4- to 2.5-mm-diameter balls were determined [11]. In the latter experiment, the ultrasonic waves induced by the ball collision with the solid plate were observed. Temporal distribution of the force during the contact was deconvolved from the displacement detected with the piezoelectric sensor located on the other side of the plate beneath the location of the contact. Employing the method described in this paper, it is possible to determine contact times more precisely also for small diameter balls. We demonstrate the stand-off methodology of measurements of short collision times of small diameter particles with stationary surface. The measurements are based on the change of the total reflection properties at the contact mirror the surface, deformed by the contact. Fast response of photodiode allows us to measure signals with frequency up to 100 MHz. The contact time for 0.5- to 2.5-mm-diameter balls was experimentally determined and compared with Hertz s contact theory [12, 13, 14]. By reducing the impact velocity and the ball diameter, we estimate the minimum impact momentum this method is still capable of detecting. 2. Experimental setup The method is based on the change of total reflection properties, when the ball impacts a massive transparent body. Due to the deformation of the material during the impact, the initially plane surface geometry is changed into a depression. The local slope of thus-formed surface causes a 322

deflection of the laser beam from its undisturbed path, as is shown in Fig. 1. The deflection of the beam is detected with the quadrant photodiode. Fig. 1: Deflection of the laser beam, reflected from the contact mirror.

3 deflection of the laser beam from its undisturbed path, as is shown in Fig. 1. The deflection of the beam is detected with the quadrant photodiode. Fig. 1: Deflection of the laser beam, reflected from the contact mirror. The experimental setup is shown in Fig. 2. A He-Ne laser (1) (λ = 633 nm) was used as a light source. In order to achieve a small beam diameter at the total reflection, a lens (2) was positioned before the glass cube. The laser beam was collimated again with second lens after the cube. By reducing the beam diameter at the point of the total reflection, the sensitivity was increased. Fig. 2: Experimental setup consists of laser source (1), two lenses (2), electromagnet (3), piezo sensor (4) (located at distance d from the impact point) and quadrant photodiode (5). α is the entry angle and β is the total-reflection angle in the glass. The ball was dropped on the glass cube (6) from the height h. Steel and sapphire balls were dropped using a magnetic release mechanism (3). It allowed us to generate impacts rapidly and more accurately on the reflection area of the laser beam. The ball drop was initiated by turning off the electromagnet for 50 ms. The ball was caught and halt via two electromagnet power levels: when the ball rebounded from the glass surface, it was caught by the magnetic pulse just strong enough to overcome the potential energy lost by impact; after it the ball was halt with the low electromagnet power. By lowering the magnetic field to the minimum value that still held the ball, we tried to provide ideal free-fall condition and to minimize the magnetic force that acted on the ball after turning off the electromagnet. 323

4 Piezo sensor (4) was located on the upper surface of the glass cube. It measured the surfacepropagating Rayleigh wave emanating from the impact point. Because of the good repeatability of the piezo signal, it was used to trigger the measurements. The beam deflection was measured using a fast quadrant photodiode (5). Two signals were obtained: the first one (UD channel) represented the difference between the intensities of the upper and lower quadrants (UL+UR) (DL+DR), while the second (LR channel) was represented as the difference between the intensities of the left- and right-hand quadrants (UL+DL) (UR+DR). The first signal (UD) corresponds to the beam deflection in the vertical direction, while the second (LR) portrays the beam deflection in the horizontal direction. The signals from the quadrant photodiode and piezo sensor were captured by a digital oscilloscope. The glass cube (6) was made of soda lime glass with refractive index of at 633 nm. Material properties of the glass and balls are shown in Table 1. Table 1: Material properties BK7 / K9 glass cube (Refractive index at 632 nm) AISI Cr6 Chrome steel balls R 1 = 0.5 mm ± 1 µm to 2.5 mm ± 1 µm Ruby doped sapphire (Al 2O 3) ball R 1 = 0.15 mm ± 2.5 µm Mass density [kg/m 3 ] Young s modulus [GPa] Poisson s ratio 2532 ± 8 78 ± ± ± ± ± ± ± ± Results and discussion Typical signal shapes and their dependence from the impact location are shown in Fig 3. The ball with a 2.5-mm radius was dropped from the height h of 29 mm. For every impact location five signals from each photodiode channel (UD and LR) were captured. The impact of the ball was moved relatively to the total reflection area in direction perpendicularly to the laser beam. From the leftmost point, the location of the contact was discretely displaced by 0.2 mm steps approaching the center of the laser beam (first row in Fig. 3). Moving across the center of the laser beam, the signal shape was measured every 0.1 mm (second and third row in Fig. 3). In the last row in Fig. 3 the step size was again increased to 0.2 mm. In the first and in the last row in Fig. 3, when the ball impacts on the margins of the laser beam, the signals of all 5 measurements appear overlying. Due to the Gaussian distribution of the laser beam intensity along the beam radius, the signal amplitude is smaller here. When approaching the center of the laser beam, the signal amplitudes increase. The LR signal from the quadrant photodiode is negative (laser beam is deflected to the right), when the ball impact on the left side of the beam (first row in Fig. 3). Oppositely, the laser beam is deflected to the left, when the ball impacts on the right side of the laser beam (last row in Fig. 3). Up-down signals are positive for all the impact locations, as the laser beam is deflected up. Near the edges of the impact, the signals shapes are strictly convex or concave. In the vicinity of the laser beam center (measurements at 1.1 mm and 1.2 mm), the shape of the signals becomes more complex. At distances 0.9 mm, 1 mm, 1.3 mm and 1.4 mm from the start point of the measurements, the signals are flattened at 0.3 V, since the part of the laser beam, deflected on the contact mirror, fully illuminates solely one half of the quadrant photodiode. 324

5 Fig. 3: Different UD and LR signal shapes while scanning the ball impact location relatively to the laser beam. Starting from the leftmost point, the impact location was moved perpendicularly to the laser beam. The ball with 2.5 mm radius was dropped from 29 mm height. Though the signal shape is strongly dependent on the ball impact location, the duration of the signal progress remains the same, what allows us to determine the contact time repeatedly. For contact time evaluation, the signals at distances 0.9 mm, 1 mm, 1.3 mm and 1.4 mm from the start point of the measurements were used. The contact time was measured for 0.5- to 2.5-mm-radius steel balls. The balls were dropped from the height h of 31.5 mm. For the each ball radius more than 20 measurements were captured, except for the 0.5-mm-radius ball, where the contact time was measured 13 times. The measurements (black dots in Fig. 4) were compared with the contact times calculated using the Hertz s contact theory (blue line in Fig. 4) [12, 13, 14]. It predicts the following contact time t 25 ρ 15 = Rv E, 1 C * 1 (1) which depends on the ball radius R1, its mass density ρ1, the approach velocity v and the effective material constant 1/Ε = (1 µ 1 2 )/E 1 + (1 µ 2 2 )/E 2, with the Young s moduli E 1 (ball), E 2 (glass cube) and Poisson s ratios µ 1 (ball), µ 2 (glass cube). 325

6 Fig. 4: Contact time versus ball diameter for the steel balls dropped from 31.5 mm height compared with the Hertz s theory. In Fig 5, the UD and LR signals from quadrant photodiode are shown during the impact of a tiny 0.15-mm-radius sapphire ball. The measured contact time is only 0.9 µs, what is slightly smaller than 1.0 µs predicted by the Hertz theory. Fig. 5: UD and LR signal from the photodiode when the 0.15-mm-radius sapphire ball was dropped from the height of 25 mm. The dashed lines represent the approximate beginning and end of the contact. 4. Conclusions We have introduced a stand-off optical method to measure collision times of steel balls with the transparent glass cube. The described method is sensitive enough to discern contact times on the µs scale and does not require any demanding data post-processing. Photodiode signal shapes were observed as the impact location was moved relatively to the reflection area of the laser beam. We found that the impact location does not affect the contact time measurements as long as the impact area and the reflection area sufficiently overlap. 326

7 We have shown that this method is sensitive enough to determine the collision time of a 0.3- mm-diameter ball with an approach momentum of only 40 nns which equals the momentum carried by a 12 J laser pulse. The photodiode signal shapes can be used to sense the evolution of the contact mirror deformation. 5. References [1] Goldsmith W.: Impact: The theory and physical behavior of colliding solids, Edward Arnold, UK, [2] Antipov D., Elliott J.A.: Effect of particle size on energy dissipation in viscoelastic granular collisions, Physical Review, Vol. 84(2), 2011, [ [3] McLaskey G.C., Glaser S.D.: Acoustic Emission Sensor Calibration for Absolute Source Measurements, Journal of Nondestructive Evaluation, Vol. 31, 2012, [ [4] Bokor A., Leventhall H.G.: The measurement of initial impact velocity and contact time, Journal of Physics D, Journal of Applied Physics, Vol. 4(1), 1971, [ [5] Stevens A.B., Hrenya M.C.: Comparison of soft-sphere models to measurements of collision properties during normal impacts, Powder Technology, Vol. 154, 2005, [ [6] Hessel R., Perinotto A.C., Alfaro R.A.M., Freschi A.A.: Force-versus-time curves during collisions between two identical steel balls, American Journal of Physics, Vol. 74, 2006, [ [7] Nihira T., Manabe K., Tadokoro C., Ozaki S., Nakano K.: Complex Impedance Measurement Applied to Short-Time Contact Between Colliding Steel Surfaces, Tribology Letters, Vol. 57(3), 2015, [ [8] Bacon M.E., Stevenson B., Stafford Baines C.G.: Impulse and momentum experiments using piezo disks, American Journal of Physics, Vol. 66, 1998, [ [9] Seifried R., Schiehlen W., Eberhard P.: Numerical and experimental evaluation of the coefficient of restitution for repeated impacts, International Journal of Impact Engineering, Vol. 32, 2005, [ [10] Freschi A.A., Hessel R., Yoshida M., Chinaglia D.L.: Compression waves and kinetic energy losses in collisions between balls and rods of different lengths, American Journal of Physics, Vol. 82, 2014, [ [11] McLaskey G.C., Glaser S.D.: Hertzian impact: Experimental study of the force pulse and resulting stress waves, The Journal of the Acoustical Society of America, Vol. 128, 2010, [ [12] Kocur G.K.: Deconvolution of acoustic emissions for source localization using time reverse modeling, Journal of Sound and Vibration, Vol. 387, 2017, [ [13] Johnson K.L.: Contact Mechanics, Cambridge University Press, Cambridge, [ [14] Hertz H.: (1882) Über die Berührung fester elastischer Körper, Journal für die reine und angewandte Mathematik (Crelle's Journal), Vol. 92, 1882, [ 327

C. Wassgren, Purdue University 1. DEM Modeling: Lecture 07 Normal Contact Force Models. Part II

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