(521f) Measurement of Particle Impact Velocities in Vibrationally Fluidized Granular Flows

A probe consisting of a high-speed laser displacement sensor was
developed to measure directly the surface-normal impact
velocities of spherical steel and porcelain particles
in the vibrationally-fluidized granular flow produced by a tub vibratory finisher.  Measurements were made in various locations and
directions within the flow (Fig. 1). 

Vibratory
finishing is widely used to deburr, polish, burnish, harden and clean metal, ceramic
and plastic parts.  In a tub vibratory finisher, a container filled with granular
media is oscillated by an eccentric rotating shaft so that it develops a vibrationally-fluidized
circulatory bulk flow of the media that is largely two-dimensional.  The media
have both a large-scale bulk flow velocity and a much smaller-scale local
impact velocity.  Therefore, work-pieces that are entrained in the flowing
media are subjected to the repetitive, high-frequency impacts of the
surrounding particles. 

Within
a vibratory finisher, surface interactions such erosive wear and plastic
deformation are affected strongly by the velocity, frequency, and direction of
particle impacts.  High impact velocities can cause fracture and fragmentation
while low impact velocities can make the process less efficient.  The impact
velocity is also closely related to the breakage of granular materials in many
processes such as drug tablet coating within rotating drums, bulk materials
handling, food processing, and particle attrition in vibratory finishing. 
Large particle impact velocities may also result in excessive erosion of
machine components in processes such as vibratory sieving and mixing. 

Measurement
of local quantities such as the impact velocity of vibrating particles in a vibrationally-fluidized
granular media is challenging, because of the relatively small scale of the
motion and difficulties in designing probes capable of measuring local
quantities without disturbing the media.  Therefore, most
existing research in the field of flowing granular media has focused on the
bulk flow of the media.  In some of these studies, discrete element modeling (DEM)
simulations have been used to predict the bulk flow behavior of granular
media and the numerical results have been verified experimentally.  Generally,
these investigations have shown that discrete element simulations give
reasonable predictions of bulk flow velocity and volume fraction in both
fluidized and non-fluidized flows. 

Only a few studies have
focused on the local behavior of the media in
granular flows.  In most of these studies, DEM predictions of collision
scale quantities such as impact velocity, collision frequency or impact energy
were not validated experimentally. Therefore, it is not known if the commonly
used approaches and parameters in DEM simulations yield correct predictions of
the impact velocity.  This remains a significant limitation since the impact
forces that govern erosion, wear and fracture in granular flows are
fundamentally linked to the particle impact velocity and kinetic energy. 

There
are several different methods to measure particle velocity in fluidized beds:
laser-Doppler velocimetry, photographic and video techniques, optical fiber
probes and laser displacement sensors.  Photographic methods have been used to
measure bulk flow properties, but the limited spatial resolution of these
approaches makes them unsuited to the measurement of local impact velocities. 
Laser-Doppler velocimetry is restricted to the low solid concentrations (loose
media).  Optical fiber probes have been used to measure bulk flow velocities
and the void fraction of media passing transversely across the end of the
sensor.  Some designs can measure displacements along the optical probe axis
using a correlation with the amount of reflected light, but such devices become
inaccurate when the light reflected by the particle varies because of a
significant transverse velocity across the probe tip that causes the particle
to move out of the incident beam. 

Therefore,
laser displacement sensors were chosen to measure the impact velocity of 6 mm
diameter steel and porcelain balls inside a relatively packed granular flow
produced in a tub vibratory finisher.  Laser displacement sensors measure the
distance to an object using triangulation.  Laser light reflected from the
object is concentrated on a linearized charge-coupled device such that its
position depends on the distance to the object.  The accuracy of the impact
velocity measurement using the laser displacement sensor was assessed in a drop
test.  The disruption to the particle bulk flow was minimized by enclosing the
sensor in a streamlined elliptical tube.

The displacement signals from the laser sensors were analyzed to
obtain the probability distribution functions of the impact velocity of the particles. 
The output was also interpreted to give the frequency with which media passed
the sensor and hence a measure of the particle packing.  Both the impact
velocity and the packing density were found to vary significantly with the orientation
of the laser probe (direction in which the laser was pointing) and its location
in the tub vibratory finisher.  The impact velocity was found
to vary by up to 38% depending on the orientation of the laser at a single
location in the tub, and by up to 24% at various locations within the tub.  The
packing density varied by up to 55% with orientation at a single location and by
46% at different locations.  The average impact
velocity of the lighter and stiffer porcelain balls was 15% greater than that
of the steel balls for the same tub vibration.  These
laser sensor impact velocity measurements compared reasonably well with those
obtained in a previous study using an impact force sensor. 

The measurements can help to elucidate the distribution of impact
energy within a vibratory finisher and improve the understanding of processing
speed and uniformity.  The data can also serve to guide the development of DEM
simulations that attempt to predict local impact velocities in vibrationally
fluidized beds of granular materials.

Fig. 1:
Schematic of the test apparatus used to measure the impact velocity of steel
and porcelain balls in the vertical direction in the tub vibratory finisher.