Improved parametric resonance of a vibrating screen
Submitting InstitutionAberystwyth University
Unit of AssessmentMathematical Sciences
Summary Impact TypeTechnological
Research Subject Area(s)
Mathematical Sciences: Applied Mathematics, Mathematical Physics
Summary of the impact
A novel application of parametric resonance (PR) is described, which has
effectiveness of a vibrating screen used for size-sorting of crushed rock.
have had an economic impact on the Ukrainian company that makes the
screens: the mathematics
developed in Aberystwyth permits a stable, high amplitude PR-regime to be
found, reducing the
damage to the screen mesh and increasing its longevity. This new
technology is allowing the
company to reduce costs and equipment downtime and is enabling them to
gain a market
advantage by being able to sort wetter materials than previously.
Vibrating screens are used to separate crushed stone into different
sizes, for example in coal and
ore mining and various chemical industries. In the past, parametric
resonance has been mainly
considered as an undesirable phenomenon, but in 2007, L. Slepyan and V.
Slepyan realized that a
PR-based vibrating screen could eliminate many of the drawbacks of
existing screens. A PR-based
screen compares favourably with conventional size-sorting machines, in
oscillations are excited directly, because it has not only a larger
amplitude of vibration, but also
insensitivity to dissipation over a rather wide range. During L. Slepyan's
visit to the UK in 2007, he
worked with Movchan and Mishuris to start an intensive programme of
research on the topic, using
mathematical models of oscillations and waves in lattice structures.
In 2009, a patent was issued to the Slepyans on the excitation method and
structure of the screen
[3.1]. At that time, the nonlinear dynamics of such a machine had been
numerically simulated and
the first PR-based screen was built in Loginov and Partner Mining Company
(Kiev, Ukraine). L.
Slepyan subsequently visited Aberystwyth in 2010-12, and is now employed
here. He and Mishuris
have been actively working together within the EU FP7 IAPP project PARM-2
[3.5], coordinated by
Mishuris, to improve the screen and develop related theory [3.2,3.3].
The stable operation of a PR-based machine for the grading of granular
materials requires careful
design and set-up, which can be achieved on the basis of the mathematical
analysis of its
dynamics. Numerical simulations allow for the refinement of the domains of
where the parametric oscillations are excited and where the
analytically-obtained steady oscillation
regimes are stable. The models developed are also of use in other PR
applications, although this is
probably the largest machine to use PR at this time.
The modelling problem is described by a system of two coupled nonlinear
equations [3.4], which
permit an exact solution in the case that there is no damping associated
with the transverse
oscillations. In the fully nonlinear regime, harmonic analysis is used to
give explicit expressions for
the amplitudes of longitudinal and transverse oscillations as functions of
the external force
amplitude and frequency. It is remarkable that in the case of the resonant
excitation, where the
external force frequency coincides with the frequency of the free
longitudinal oscillations, the
amplitudes are independent of the viscosity of the granular material. In
addition, lattice waves and
pre-stress were studied, to induce particle fracture off-lattice.
The determination of the boundaries of the PR domain in the
frequency-amplitude plane is based
on the linear formulation. The PR arises in the nonlinear problem in
almost the same frequency
region predicted by the linear analysis, slightly shifted towards the
higher frequencies. The
transverse oscillations, both regular and irregular, abruptly decay on the
boundaries of the PR
References to the research
[3.1] V.I. Slepyan, I.G. Loginov and L.I. Slepyan, The method of
resonance excitation of a vibrating
sieve and the vibrating screen for its implementation. Ukrainian patent on
invention No. 87369,
[3.2] Slepyan, L.I., Mishuris, G.S., Movchan, A.B. (2010) Crack in a
lattice waveguide. Int. J. Fract.,
[3.3] Mishuris, G; Movchan, A; Slepyan, L. (2009) Localised knife waves
in a structured interface.
Journal of the Mechanics and Physics of Solids, 57, 1958-1979.
[3.4] Slepyan, L.I., and Slepyan, V.I., (2013) Modeling of parametrically
excited vibrating screen. J.
Phys.: Conf. Ser. 451, 012026.
[3.5] PARM-2, Vibro-impact machines based on parametric resonance:
modelling, experimental verification and implementation,
euro, 01/01/2012 - 31/12/2015.
Details of the impact
The research on PR and lattices by L. Slepyan and Mishuris has been
conducted in close
collaboration with V. Slepyan, Chief Designer at the Loginov and Partner
(LPMC), where a vibrating screen was designed and built based on the idea
LPMC now makes and sells equipment for size-sorting based on PR for field
testing, currently only
within the Ukraine; the equipment is known as GEPARD. They are popular
because they are
effective at separating wet granular material: in a traditional
vibrating lattice, the dissipation is
highest at the centre, and the material gathers there, but with PR not
only is the amplitude larger
for a given amount of input energy, but the dissipation is better
distributed so material does not
clump. This is expected to give LPMC a distinct market advantage.
At first, the screens broke too frequently (roughly every few hours), due
to cracks developing both
longitudinally and around the edges. As the Director General of LPMC
communication of V.I. Slepyan with Professors Leonid Slepyan and Gennady
(Aberystwith University) and the experiments carried out by the Company
resulted in better
understanding of the screening machine operation process and developing
solutions to increase
the fatigue strength of the screen and stabilize the parametric resonance.
As a result of the
solutions, the screening machine service life has been increased". By the
end of July 2013, the
operating time for the vibrating screen had been increased to a period of
The key improvements due to the mathematical modelling are:
- a more careful delineation of the parameter space in which the stable
PR modes are to be
- a suggestion to change the way in which the screen boundary is clamped
at its edges, so
as to eliminate edge cracks in the lattice;
- changing the lattice structure of the screens, to have a mesh with
elliptical or circular holes,
and a distribution of hole sizes which decrease towards the edges of the
- most significantly, inserting a small gap between the screen and the
exciter motor is
remarkably effective in preventing cracking of the lattice.
Each screen costs between one and eight-hundred dollars, depending on its
manufacture and the quality of the material. The whole vibrating machine
sells for only a few
thousand dollars. Thus the screens represent a significant proportion of
the running costs. The
result of the modelling — that is, the reduction in the frequency at which
the screens fail due to
cracking — is that there is less manual intervention required by the
operators, and a reduction in the
amount spent on replacement screens, currently by a factor of about four.
To increase the longevity of the screens, they are often used below
maximum efficiency, i.e.
outside the optimal PR regime. The industry standard is that a screen
should last for about 10
million cycles, roughly two weeks, and this is now the goal for modelling
and development of
refinements to the equipment.
Mathematical models developed for the oscillations and waves in lattice
structures and the
determination parameter space of the regular PR oscillations resulted in
the improvement of the
machine and opened a way for other PR applications.
Sources to corroborate the impact
[5.1] Letter and contact details for the Director General of LPMC.