Chapter 12
The Dynamics of Eccentric Vibration
Mechanism (Part 2)
Leonid Igumnov, S. Vladimir Metrikin, V. Irina Nikiforova,
and Lubov N. Fevral’skikh
Abstract This paper presents a detailed study of the dynamics of the two-piston
vibro-impact mechanism with a crank vibration exciter. The mechanism has quite
a wide range of applications: It is effective for vibro-impact compaction of various
types of soil, sand and concrete in strained industrial conditions; for breaking the
ice and other harder objects; driving piles and structures, etc. The presented mathematical model (MM) is a substantially nonlinear dynamic system with a variable
structure. An original method for numerical–analytical study of dynamic characteristics, such as periodic motion modes with alternating impact interaction of pistons,
as well as complex motion modes with an arbitrary number of impacts, including
chaotic ones, has been elaborated on the basis of the point mapping method. Thus,
it was possible to obtain for the first time the engineering formulas for tuning the
mechanism into required mode of operation, at the stage of preliminary MM dynamic
analysis, using a special coordinate transformation and the geometry of the Poincaré
surface of section. The obtained engineering formulas allow us to indicate the regions
of various qualitative behavior of the mechanism in the parameter space. The bifurcation diagrams make it possible to determine the influence of the main parameters
on the processes of reorganization of motion modes, starting from the simplest to the
most complex modes, including chaotic ones. The obtained results and proposed
numerical–analytical approaches for investigating the dynamic characteristics of
crank-type vibro-impact mechanisms enable practitioners to use them for tuning
and analyzing the operational regimes of specific mechanisms.
Keywords Mathematical model · Point mapping · Stability · Bifurcation
diagrams · Chaos
L. Igumnov · S. V. Metrikin (B)
Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny
Novgorod, Nizhny Novgorod, Russia
e-mail: v.s.metrikin@mail.ru
V. I. Nikiforova · L. N. Fevral’skikh
National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_12
173
The Dynamics of Eccentric Vibration
Mechanism (Part 2)
Leonid Igumnov, S. Vladimir Metrikin, V. Irina Nikiforova,
and Lubov N. Fevral’skikh
Abstract This paper presents a detailed study of the dynamics of the two-piston
vibro-impact mechanism with a crank vibration exciter. The mechanism has quite
a wide range of applications: It is effective for vibro-impact compaction of various
types of soil, sand and concrete in strained industrial conditions; for breaking the
ice and other harder objects; driving piles and structures, etc. The presented mathematical model (MM) is a substantially nonlinear dynamic system with a variable
structure. An original method for numerical–analytical study of dynamic characteristics, such as periodic motion modes with alternating impact interaction of pistons,
as well as complex motion modes with an arbitrary number of impacts, including
chaotic ones, has been elaborated on the basis of the point mapping method. Thus,
it was possible to obtain for the first time the engineering formulas for tuning the
mechanism into required mode of operation, at the stage of preliminary MM dynamic
analysis, using a special coordinate transformation and the geometry of the Poincaré
surface of section. The obtained engineering formulas allow us to indicate the regions
of various qualitative behavior of the mechanism in the parameter space. The bifurcation diagrams make it possible to determine the influence of the main parameters
on the processes of reorganization of motion modes, starting from the simplest to the
most complex modes, including chaotic ones. The obtained results and proposed
numerical–analytical approaches for investigating the dynamic characteristics of
crank-type vibro-impact mechanisms enable practitioners to use them for tuning
and analyzing the operational regimes of specific mechanisms.
Keywords Mathematical model · Point mapping · Stability · Bifurcation
diagrams · Chaos
L. Igumnov · S. V. Metrikin (B)
Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny
Novgorod, Nizhny Novgorod, Russia
e-mail: v.s.metrikin@mail.ru
V. I. Nikiforova · L. N. Fevral’skikh
National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_12
173