外文翻譯--均質(zhì)球體在三維振動下包裝的實驗研究（英文）

1、Experimental study on the packing of uniform spheres under three-dimensional vibrationC.X. Li a, X.Z. An a,?, R.Y. Yang b, R.P. Zou b, A.B. Yu ba School of Materials and Metallurgy, Northeastern University, Shenyang 1100

2、04, PR China b Laboratory for Simulation and Modeling of Particulate System, School of Materials Science and Engineering, University of New South Wales, Sydney 2052, Australiaa b s t r a c t a r t i c l e i n f oArticle

3、history:Received 27 August 2010Received in revised form 8 December 2010Accepted 31 December 2010Available online 15 January 2011Keywords:Particle packingDensification3D vibrationPacking densityBatch-wise feedingDensifica

4、tion of mono-sized sphere packings under three-dimensional (3D) vibration is experimentallystudied. The effects of an operational condition, such as vibration amplitude and frequency and feedingmethod, on packing density

5、 are systematically investigated. The results indicate that the dense packings canbe achieved by proper control of both vibration amplitude and frequency. The feeding method plays animportant role in densification. Highe

6、r packing densities can be obtained when the number of particles fed perbatch is less than one layer. Packing density decreases with increasing number of particles fed per batch, butkeeps constant when the number of part

7、icles per batch is larger than three layers. Through the extrapolationon packing density obtained from different sized containers, the maximum packing density is 0.69 for thetotal feeding method and 0.74 for the batch-wi

8、se feeding under the present experimental condition. Theformation of ordered structure is discussed based on the particle interlayer diffusion.© 2011 Elsevier B.V. All rights reserved.1. IntroductionParticle packing

9、 is an important subject in scientific research andindustrial applications [1–7]. Three reproducible states can beidentified in terms of packing density [2,9–12]: random loose packing(RLP, ρ≤0.60), random close packing (

10、RCP, ρ=0.64) and ordered FCC(face-centered cubic) or HCP (hexagonal closed packed) packings(ρ=0.7405). These states and their correlation (transition), asindicated in a phase diagram [13], attract increasing interests.Vi

11、bration is a common method to achieve the transition from looseto dense packings, and many efforts have been spent in this area [2,8–11,14–24]. We recently carried out a systematic study of thedensification of mono-sized

12、 spheres under vibration in the verticaldirection. The effects of vibration condition and feeding method wereinvestigated. The maximum packing density can reach 0.636 in thetotal feeding method and 0.663 using the batch-

13、wise feeding method,indicating different densification mechanisms.Previous studies, however, largely focused on one-dimensional(1D) vibration, and the maximum packing density obtained is stillrelatively low (0.64–0.66 de

14、pending on the feeding method). How toachieve physically the transition from a disordered (random) to anordered (regular) structure is still an open question [25,26]. Earlierwork conducted by Owe Berg et al. [15] on pack

15、ings of mono-sizedsteel ball-bearings indicated that 3D vibrations can produce a nearlyperfect HCP structure. While their vibration conditions are not quiteclear, their results indicated that 3D mechanical vibration is a

16、neffective way to obtain much higher packing density. Some studieshave also claimed to achieve ordered packings [12,15,27–33]; nearlyall of them were on the numerical basis or under special packingconditions in physical

17、experiments (e.g., packing spheres manually).Systematic analysis of vibrated densification of equal spheres under3D vibration in physical experiments has not been carried out.This paper is to systematically study the den

18、sification of spherepacking under 3D vibration. The roles of vibration parameters such asamplitude A and frequency ω, container size and feeding method willbe investigated. The focuses of this work are to reproduce physi

19、callythe transition from a disordered to an ordered state and to identify theformed ordered structure and densification mechanism.2. Experimental method and conditionsThe physical experiments were carried out using a 3D

20、vibrationdevice as shown in Fig. 1. This setup is able to vibrate independently inthree directions with different amplitudes and frequencies. Thevibrations in three directions are driven by three motors whoseamplitudes a

21、nd frequencies can be controlled independently by camsand transducers. In this work, we employed the same A and ω in thethree vibration directions, so the phase difference is zero in threecomponents and the movement is i

22、n a straight line. Under thiscondition, it is considered that the phase angle of vibration has noeffect. The experimental procedure was as follows: first, glass beads ofdiameter d=5.02 mm±0.065 and containers made o

23、f PMMA materialwere cleaned using distilled water and dried in an oven at 60 °C. ThenPowder Technology 208 (2011) 617–622? Corresponding author. Room 202, Metallurgy Building, School of Materials andMetallurgy, Nort

24、heastern University, Shenyang 110004, Liaoning, PR China. Tel.: +8624 83686465; fax: +86 24 23906316.E-mail address: anxz@mail.neu.edu.cn (X.Z. An).0032-5910/$ – see front matter © 2011 Elsevier B.V. All rights rese

25、rved.doi:10.1016/j.powtec.2010.12.029Contents lists available at ScienceDirectPowder Technologyjournal homepage: www.elsevier.com/locate/powtecω to have the dense packing. Similar effects of A on ρ have also beenidentifi

26、ed in our previous numerical and physical work [10,11,33].Therefore, proper choice of A and ω is the key to achieving the densestpacking.The combined influence of A and ω on ρ is shown in Fig. 5, indicatingthat a higher

27、packing density can be obtained with relatively smaller Aand larger ω or vice versa. It is known that the combined effect of A andω can be ascribed to vibration intensity (an indication of the peakacceleration) defined a

28、s Γ=Aω2. Variations in either A or ω givedifferent vibration intensities Γ, which creates effects on vibratedcompaction. A larger Γ not only accelerates the rearrangement ofparticles during densification, but also elimin

29、ates the “bridge” or “arch”structure formed in the initial packing. However, if Γ is too high, theresulted high vibration intensity will over-excite particles, which hasnegative effects on the formation of a dense struct

30、ure.The variation of packing density with Γ in Fig. 6 indicates thatdense packing can be formed when Γ is between 0.8 g and 1.5 g, whichis narrower than that in the case of 1D vibrated packing [11]. Alsodifferent packing

31、 densities can be obtained even if Γ has the samevalue, which confirmed our previous findings that Γ cannot be used tocharacterize packing densification, instead A and ω (or Γ and A or ω)should be separately considered [

32、10,11].3.1.2. Effect of container sizeIn addition to the effect of vibration condition, container size canalso create a significant effect on ρ. Fig. 7 shows the final packingdensity obtained with different sized contain

33、ers. It can be seen thatthe extrapolated packing densities for infinite sized container arehigher than the packing density of RCP (around 0.64), indicating that3D vibration is a simple way to realize a much denser packin

34、gcompared with 1D vibration. From the container wall, we couldobserve the partially ordered structure in the final packings, whichindicates that the packings are no longer completely random.3.2. Vibration with batch-wise

35、 feeding3.2.1. Effect of number of particles per batchIn the batch-wise feeding, the number of particles in a batch NB playsan important role in the densification. Fig. 8 indicates that packingdensity ρ decreases with NB

36、 for different vibration frequencies. There is0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.5720.5850.5980.6110.6240.6370.6500.6630.676Packing densityAmplitude, dω =30Rad/sω =50Rad/sω =55Rad/sω =60Rad/sω =65Rad/sω =80Rad/sFig. 4.

37、 Amplitude effects on packing density with different frequencies, whereD=229.70 mm.Fig. 5. Combined influence of amplitude and frequency on packing density, whereD=229.70 mm.0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.40.600.610.6

38、20.630.640.650.660.670.68A=0.2dA=0.4dA=0.6dA=0.8dA=1.0dPacking densityVibration intensity, gFig. 6. Vibration intensity effects on packing density with different amplitudes andfrequencies, where D=229.70 mm.0.01 0.02 0.0

39、3 0.04 0.05 0.06 0.070.6440.6510.6580.6650.6720.6790.6860.693ρ = -0.5545x + 0.6890ρ = -0.4871x + 0.6842ρ = -0.5913x + 0.6826ρ = -0.5238x + 0.6777ρ = -0.4673x + 0.6730Packing densityd/DFig. 7. Extrapolation of packing den

40、sity to avoid container wall effects in total feeding,where: (□), A=0.2d, ω=120Rad/s; (●), A=0.4d, ω=70Rad/s; (△), A=0.6d,ω=55Rad/s; (○), A=0.8d, ω=50Rad/s; and (☆) A=1.0d, ω=45Rad/s. Eachequation inside is the linear fi