Mate Antali

56197460700

Publications - 13

Phase portraits and bifurcations induced by static and dynamic friction models

Mate Antali Balazs J. Bekesi G. Csernák

Publication Name: Nonlinear Dynamics

Publication Date: 2025-07-01

Volume: 113

Issue: 13

Page Range: 15863-15899

Description:

The paper discusses the phase-space structure of six variants of a simple mechanical system that differ in the applied friction model. It is shown that many properties of the Coulomb and the Stribeck models, such as the number of equilibria and their stability, are inherited by the Dahl and the LuGre dynamic friction models, respectively. Exploiting similar relationships, a Coulomb-based and a Stribeck-based version of the Generalized Maxwell-Slip model are also introduced. The detailed analysis of these models reveals a surprisingly rich variety of equilibrium types and bifurcations. Moreover, it is highlighted that the most frequently used values of the Stribeck exponent may lead to atypical results such that even a small deviation from these values changes the bifurcation scenario.

Open Access: Yes

DOI: 10.1007/s11071-025-10974-y

Harmonic expansion and nonsmooth dynamics in a circular contact region with combined slip-spin motion

Mate Antali

Publication Name: Nonlinear Dynamics

Publication Date: 2024-05-01

Volume: 112

Issue: 9

Page Range: 6785-6811

Description:

We analyse a rigid body in planar motion while touching a rough plane at a finite-sized, circular contact area. Assuming Coulomb friction between the tangential and normal pressure distributions, the resultant forces and torques can be expressed formally with a nonsmooth dependence on the kinematic variables. In the literature, the exact form of the tangential forces is available for special pressure distributions expressed by transcendent functions; recently, an approximate linear model was introduced. Now, we present a nonlinear extension of the approximation, which can be used effectively to characterise slipping-sticking transitions between the bodies.

Open Access: Yes

DOI: 10.1007/s11071-024-09462-6

Dynamics of Rolling Wheels with Elliptical Tread Profiles

Mate Antali Gabor Kupi

Publication Name: Advances in Transdisciplinary Engineering

Publication Date: 2024-01-01

Volume: 59

Issue: Unknown

Page Range: 255-262

Description:

In this paper, the dynamics of a loose wheel is considered rolling on a horizontal plane, where the tread profile of the wheel is ellipsoidal. From the equations of motion, a two-parametric family of steady motions are obtained, corresponding to the rolling motion on a circular or straight line with a uniform rotational speed and tilt angle. It is shown that compared to the geometries analysed in the literature, the elliptical tread profile leads to a significant change in the qualitative behaviour of the wheel.

Open Access: Yes

DOI: 10.3233/ATDE240553

Improved Equations of the Classic Hunting Problem of Railway Wheelsets

Mate Antali Ervin Finta

Publication Name: Advances in Transdisciplinary Engineering

Publication Date: 2024-01-01

Volume: 59

Issue: Unknown

Page Range: 240-247

Description:

In this paper, the equations of motion are derived for a railway wheelset by the systematic linearisation of the full nonlinear description. Compared to the standard approximate equations of the literature, the new form of differential equations improves the values of some coefficients and also adds the correct values of terms from gravity and gyroscopic forces. The resulting model can be used to describe the stability loss called hunting motion, and can be included in models of whole railway vehicles.

Open Access: Yes

DOI: 10.3233/ATDE240551

Analysis and Measurement of Bending Stiffness of Wound String According to Higher Order Frequencies

Mate Antali P. Szalai

Publication Name: Advances in Transdisciplinary Engineering

Publication Date: 2024-01-01

Volume: 59

Issue: Unknown

Page Range: 263-268

Description:

Bass strings of piano are manufactured by winding a wire around a core string. At these strings, the bending stiffness is not negligible. This effect modifies the higher harmonics of the string compared to the harmonic spectrum of the ideal string. This inharmonicity is even more significant in upright pianos. The effect has recently received renewed attention in the literature. In the present paper, the authors present a dynamic measurement for determining the bending stiffness of the piano strings. By using the so-called inharmonicity coefficient, the spectrum of the string is predicted, and the deviation from the ideal string is determined.

Open Access: Yes

DOI: 10.3233/ATDE240554

Dynamics of Railway Wheelsets with a Nonsmooth Contact Force Model

Mate Antali

Publication Name: Springer Proceedings in Mathematics and Statistics

Publication Date: 2024-01-01

Volume: 454

Issue: Unknown

Page Range: 41-53

Description:

The dynamics of a railway wheelset is investigated, focusing on the effect of the contact force models. For large values of creep velocities, the Coulomb model can be used as an asymptotic approximation of wheel-rail contact forces. Then, we get a nonsmooth dynamical system with codimension-2 discontinuities. At the discontinuity of the phase space, the so-called limit directions can be found, which correspond to the possible transitions between slipping and rolling. By this analysis, the nonsmooth model can complement the usual linear creep force model from the opposite direction, and we can explore more details about the qualitative behaviour of the wheelset.

Open Access: Yes

DOI: 10.1007/978-3-031-56496-3_4

Bifurcations of the limit directions in extended Filippov systems

Mate Antali

Publication Name: Physica D Nonlinear Phenomena

Publication Date: 2023-03-01

Volume: 445

Issue: Unknown

Page Range: Unknown

Description:

This paper explores special bifurcations that appear in dynamical systems possessing codimension-2 discontinuity sets in the state space. In these systems, the vector field has continuously many directional limits at the discontinuity set. It is shown that the trajectories can reach the discontinuity set along specific limit directions. The number and type of these organising objects characterise the behaviour of the dynamics in the vicinity of the discontinuity set. Thus, bifurcations of limit directions have a remarkable effect on the system. In the paper, two special bifurcations are explored; the tangency bifurcation and the saddle–node bifurcation of limit direction are followed through different formulations of the dynamical system. It is demonstrated that these bifurcations appear in rigid body dynamics in the presence of dry friction.

Open Access: Yes

DOI: 10.1016/j.physd.2022.133622

The Nonsmooth Dynamics of Combined Slip and Spin Motion Under Dry Friction

Mate Antali Peter L. Varkonyi

Publication Name: Journal of Nonlinear Science

Publication Date: 2022-08-01

Volume: 32

Issue: 4

Page Range: Unknown

Description:

We investigate the motion of rigid bodies subject to combined slipping and spinning over a rough flat surface in the presence of dry friction. Integration of Coulomb friction forces over the contact area gives rise to a dynamical system with an isolated discontinuity of codimension 3. Recent results about such vector fields are applied to the motion of flat bodies under the assumption of known, time-independent distributions of normal contact forces and to general bodies where kinematic constraints enforce a state-dependent normal contact force distribution with a discontinuity at the sticking state. In both cases, the equations of motion are transformed into a smooth slow–fast dynamical system. The fixed points of the fast flow indicate the possible directions of combined slip–spin motion immediately before a body stops. We also introduce an approximation of the frictional forces and moments by the leading-order term of a spherical harmonic expansion, which allows for an explicit formulation of the equations of motion. The approximate model captures important empirically observed features of the motion. It is proven analytically and illustrated by examples that the number of fixed points in the approximate model is 2, 4, or 6.

Open Access: Yes

DOI: 10.1007/s00332-022-09812-x

Computation of sensitivity of periodically excited dynamical systems

Mate Antali Zoltán Horváth

Publication Name: Journal of Engineering Mathematics

Publication Date: 2018-12-01

Volume: 113

Issue: 1

Page Range: 123-142

Description:

In the optimization of continuous-time dynamical systems, it can be important to numerically calculate the parametric sensitivity of some long-time-averaged quantities in the system. These computations are challenging for typical numerical methods in the presence of oscillations, which can originate from the internal structure of an autonomous dynamical system or be caused by an external periodic excitation. The case of periodic excitation is motivated by the problem of heat conduction in mechanical parts in engines, where the mean strength of the heat fluctuation can be an important parameter in the engineering design. In this work, approaches to transform periodically excited systems into autonomous systems appropriate for sensitivity analysis were investigated. The least-squares shadowing method is used to compute the sensitivities, and the effect of different kinds of transformation compared. The resulting numerical method is presented using the motivating example of heat conduction.

Open Access: Yes

DOI: 10.1007/s10665-018-9977-3

Mechanics of the golf lip out

Mate Antali S. John Hogan

Publication Name: Royal Society Open Science

Publication Date: 2025-11-05

Volume: 12

Issue: 11

Page Range: Unknown

Description:

Sometimes, when a golfer attempts to putt a golf ball, it appears to enter the hole, only to re‑emerge almost immediately, hav‑ ing undergone an angle of turn around the hole rim that can exceed 180◦. We consider the problem from the point of view of mechanics. We show analytically that there are at least two distinct types of lip out: the rim lip out, where the centre of mass of the golf ball does not fall below the level of the green, and the hole lip out where it does. At the heart of both lip outs is a family of degenerate saddle equilibria of the dynamics on the rim (the golf balls of death). When perturbed one way, the golf ball executes a rim lip out. When perturbed another way, the golf ball enters the hole, only to re‑emerge (provided it does not touch the base of the hole) if it is spinning about an axis perpendicular to the wall of the hole.

Open Access: Yes

DOI: 10.1098/rsos.250907

Vibration Spectrum of an Act-and-Wait Controlled System With Significant Damping

Mate Antali P. Szalai

Publication Name: Iet Control Theory and Applications

Publication Date: 2026-01-01

Volume: 20

Issue: 1

Page Range: Unknown

Description:

Act-and-wait concept in control theory is a tool for enhancing the control quality by decreasing the destabilising effect of time delay. As was shown in other works, applying the act-and-wait concept to a PD position control increases the available range of proportional gains, which reduces the steady-state error of dry friction. In this paper, we focus on the vibration phenomena at the boundaries of the dynamic stability from the aspect of the vibration spectrum. We consider a single-degree-of-freedom mechanical model of DC actuators that contains significant effective damping. At different types of stability limits, new analytical and semi-analytical results are derived for the vibration spectrum. The results are validated by numerical calculations and experiments on a linear DC actuator.

Open Access: Yes

DOI: 10.1049/cth2.70111

Compensation of inharmonicity of piano strings with added masses

Mate Antali P. Szalai

Publication Name: Journal of Physics Conference Series

Publication Date: 2026-01-01

Volume: 3190

Issue: 1

Page Range: Unknown

Description:

Bass strings of piano consists of a core string and a wire wound around the core. Although this construction is essential for creating strings with low frequency in the presence of moderate tension force, the increased bending stiffness shifts the overtones of the strings. This inharmonicity is more significant for upright pianos with shorter string lengths. In the literature, we can find conceptual ideas for compensation of this effect that is considered acoustically unpleasant. In the present research, we analyse the effect of adding concentrated masses to reduce the amount of inharmonicity. We focus on improvements in the acoustically most significant overtones. The proper parameters are found by using both a finite-element method and experiments.

Open Access: Yes

DOI: 10.1088/1742-6596/3190/1/012002

Vibration characteristics of rolling elements in the presence of different friction and creep models

Mate Antali

Publication Name: Journal of Physics Conference Series

Publication Date: 2026-01-01

Volume: 3190

Issue: 1

Page Range: Unknown

Description:

Dynamics of wheels and other rolling elements in machines are significantly affected by the friction phenomena between the surfaces. When modeling the transitions between rolling and slipping motion, the simplest choice is applying the Coulomb friction model or the similar but improved models like the Stribeck model. However, when the local deformations are not negligible, often the so-called creep force models are used, which contain a coupled nonsmooth effect of the kinematic variables. This study investigates the effects of the different contact models on the properties of the vibrations. The models are demonstrated on 2D test problems of rolling elements. Mathematical methods of nonsmooth dynamics and singular perturbation are utilized to explore the details of the phenomena.

Open Access: Yes

DOI: 10.1088/1742-6596/3190/1/012001