Semiempirical identification of nonlinear dynamics of a two-degree-of-freedom real torsion pendulum with a nonuniform pl
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ORIGINAL PAPER
Semiempirical identification of nonlinear dynamics of a twodegree-of-freedom real torsion pendulum with a nonuniform planar stick–slip friction and elastic barriers Bartłomiej Lisowski . Clement Retiere . Jose´ Pablo Garcia Moreno . Paweł Olejnik
Received: 15 November 2019 / Accepted: 5 May 2020 Ó The Author(s) 2020
Abstract The purpose of this study is to identify the nonlinear dynamics of the double torsion pendulum with planar friction and elastic barriers. The original experimental stand consists of a disk-shaped body that rotates freely on top of a forced column with a system of barriers limiting the torsional vibrations of the pendulum bodies that create an nonuniform planar rotational friction contact. Two beam springs form soft barriers modeled by Voigt elements that limit the angular displacement of one of the pendulum bodies— the disk, while the second limiting system, made of a much more rigid barrier, limits the movement of the pendulum’s second body. The dynamic behavior of the asymmetrical system of two degrees of freedom with discontinuities is identified with the use of the described strategy, numerical solutions of the derived mathematical model and the Nelder–Mead simplex algorithm. The actual measurement series and numerical solutions show a good similarity of the dynamical reaction of the mechanical system and its virtual analog. B. Lisowski C. Retiere J. P. G. Moreno International Faculty of Engineering, Lodz University of _ Technology, 36 Zwirki Str., 90-001 Lodz, Poland P. Olejnik (&) Department of Automation, Biomechanics and Mechatronics, Faculty of Mechanical Engineering, Lodz University of Technology, 1/15 Stefanowski Str., 90-924 Lodz, Poland e-mail: [email protected]
Keywords Parameter identification Optimization Numerical modeling Impacts Torsional vibrations
1 Introduction With the introduction of useful computer software focused on solving dynamic problems, many researchers focused on identifying and predicting the behavior of various dynamic objects. These include double pendulums with torsional friction. Scientific research is based on a relatively simple theory of friction, describing this phenomenon in the contact zone between the surfaces of two bodies existing in nature. In this context, two main types of friction should be distinguished, i.e., the static and kinetic friction. Their occurrence depends on the phase of movement of interacting bodies. In dynamic systems, such as pendulums, friction has a structural form with energy dispersion, which is directly related to the contact surface properties and range of motion. Nevertheless, friction can be analyzed in both solids and liquids by testing for mechanical energy losses [1–3]. Looking at the history of the development of the description of the phenomenon of friction, one of the first models of full friction was developed by Coulomb. The author stated that static friction is not constant and causes kinetic friction fluctuations. In recent de
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