Gábor Stépán

Gábor Stépán
Budapest University of Technology and Economics · Department of Technical Mechanics

PhD

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395
Publications
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10,751
Citations

Publications

Publications (395)
Article
Mechanical systems with feedback control commonly contain time delays which usually tend to destabilize the system. With increasing accuracy requirements of data acquisition and calculation, investigation of the effect of the feedback delay including the computational time, actuating time, and signalling time is crucial for developing advanced chas...
Article
The system of a vessel and a direct spring operated pressure relief valve is extended by a downstream pipe. The presented mathematical model consisting of ordinary and partial differential equations can be transformed to a system of differential difference equations by means of the travelling wave solutions of the partial differential equations. Th...
Article
This paper is concerned with the material modelling of rubber balls applied for impulse excitation of high-speed rotating milling tools, which is essential for understanding the dynamics of various machining processes. For this purpose, a novel ball-shooter device was developed. The accurate finite element (FE) prediction of the ball impacts requir...
Article
In this work we present a quantitative measurement-based method to describe the stability behaviour of a periodic dynamical system. In-process response for impulse during milling is analysed to provide operational stability prediction. The proposed method combines chatter detection techniques with the theory of time-periodic delay differential equa...
Article
Full-text available
In this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of th...
Article
Full-text available
The interference of the elasticity of a single robotic arm and the unavoidable time delay of its position control is analysed from nonlinear vibrations viewpoint. The simplified mechanical model of two blocks and a connecting spring considers the first vibration mode of the arm, while the collocated proportional-derivative (PD) control uses the sta...
Article
Full-text available
In this paper, the stability properties of milling processes are presented when the axial component of the cutting force is also taken into account as a compressive force acting on the cutting tool. The mechanism of the material removal operation is described by a one degree-of-freedom oscillator subjected to the so-called surface regeneration effe...
Preprint
Full-text available
Nonholonomic models of automobiles are developed by utilizing tools of analytical mechanics, in particular the Appellian approach that allows one to describe the vehicle dynamics with minimum number of time-dependent state variables. The models are categorized based on how they represent the wheel-ground contact, whether they incorporate the longit...
Article
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We analyse the dynamics of a basketball which rolls around the rim of a basketball hoop. The rolling steady motions are determined, and we investigate falling, slipping, and instability. The qualitative behaviour of the global dynamics is analysed and the possible trajectories are categorised. We investigate the effect of initial conditions which c...
Article
Full-text available
Postural sway is a result of a complex action–reaction feedback mechanism generated by the interplay between the environment, the sensory perception, the neural system and the musculation. Postural oscillations are complex, possibly even chaotic. Therefore fitting deterministic models on measured time signals is ambiguous. Here we analyse the respo...
Article
Full-text available
Rolling resistance and angle constraint are important factors affecting the control performance and dynamics of Two-Wheeled Inverted Pendulums (TWIPs, for short), but they are usually neglected in previous studies. Taking both factors into account, this paper presents new control designs for the angle control of the pendulum, for the velocity contr...
Article
A stochastic dynamical model is presented to identify the difficulties in chatter detection during cutting processes. The theoretical implications are based on measurements related to the stochastic character of the cutting force. The stochastic model is validated in a Hardware-In-the-Loop (HIL) environment where the multiplicative component of the...
Article
Full-text available
Chatter suppression is investigated when time-periodic axial load is applied during the turning process of slender workpieces. The Euler-Bernoulli beam theory is used to construct the mathematical model of the workpiece that is clamped at the chuck and pinned at the tailstock. To improve the stability of the turning process, the workpiece is excite...
Article
Full-text available
Stability analysis has been always a key issue in nonlinear dynamics and engineering applications, and it is still a challenging task for time-delay control systems when tuning some parameters like feedback gains and delays. In this paper, firstly we propose a parametric continuation algorithm for calculating the rightmost characteristic root(s), b...
Article
Full-text available
The paper presents the first results of an exploratory research work, aiming the experimental evaluation of the mechanical contact between conforming surfaces of metallic bodies. The proposed procedure—that is based on the measurement of electric potentials—is able to determine the actual contact pattern and estimate the force distribution on the o...
Preprint
Full-text available
Postural sway is a result of a complex action-reaction feedback mechanism generated by the interplay between the environment, the sensory perception, the neural system and the musculation. Postural oscillations are complex, possibly even chaotic. Therefore fitting deterministic models on measured time signals is ambiguous. Here we analyse the respo...
Conference Paper
Full-text available
In today’s automobile industry, every company tries to make a car as safe and comfortable as possible. The automotive industry is a big industrial and economic force worldwide. This industry makes almost 60 million cars and trucks per year. In this competitive market, every company tries to develop new systems, to optimize the old methods, and to c...
Article
Full-text available
In this paper, a nonsmooth model of towed wheels is analysed; this mechanism can be a part of different kind of vehicles. We focus on the transitions between slipping and rolling in the presence of dry friction. The model leads to a three-dimensional dynamical system with a codimension-2 discontinuity. The systems can be analysed by means of the to...
Article
Full-text available
During the milling of thin-walled workpieces, the natural frequencies might change radically due to the material removal. To avoid resonant spindle speeds and chatter vibration, a precise knowledge of the instantaneous modal parameters is necessary. Many different numerical methods exist to predict the changes; however, small unmodelled effects can...
Article
Full-text available
In hardware-in-the-loop (HIL) experimental environment, a local softening character of the emulated cutting force is observed during the emulation of turning, which affects the stability properties of the process. The real workpiece is substituted by a dummy one that is clamped to the real main spindle. It is excited in the lateral direction by an...
Article
Full-text available
The energy dissipation in assembled metal structures is mainly related to various physical phenomena – usually modelled as dry friction – on the contact surfaces. However, the reliable numerical modelling of assemblies is a challenging task due to the complexity of the contact mechanisms. To fit the models to experimental results, it is beneficial...
Article
Full-text available
Large-amplitude oscillations of turning operations are investigated, which can be modelled by a one degree-of-freedom damped oscillator subjected to the regenerative effect that introduces a relevant time delay in the system. In the case of large oscillations, when the cutting tool loses contact with the surface of the workpiece, the time delay is...
Article
Regenerative chatter is one of the main productivity limiting factors for thin-walled part milling due to their inherently low stiffness and damping properties. This paper presents a new concept called tuneable clamping table (TCT) for thin-walled part machining, which permits controlling the table mode through a rotary spring and eddy current modu...
Article
The paper presents a pseudospectral approach to assess the stability robustness of linear time‐periodic delay systems, where periodic functions potentially present discontinuities and the delays may also periodically vary in time. The considered systems are subject to linear real‐valued time‐periodic uncertainties affecting the coefficient matrices...
Article
This paper investigates a 3 degree-of-freedom shimmy model of vehicle front wheels with steering system and dependent suspension. The contact models of rigid ground and elastic tyre are analyzed from the viewpoint of predicting shimmy. Pacejka's Magic Formula and the Delayed Tyre Model are compared by means of stability charts in various parameter...
Article
Full-text available
Basic single-degree-of-freedom mechanical models of force control are presented to achieve desired contact forces between actuators and objects. Nonlinear governing equations are constructed for both collocated and non-collocated force sensor configurations. The models take into account large time delays in the feedback loop, which may occur, for e...
Article
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This paper studies the combined effect of sampling and dry friction on the dynamics of mechanical systems subjected to position control using discrete-time state feedback. This paper aims to highlight that even in case of a single degree-of-freedom mechanical subsystem, the controlled system cannot be characterized by a model with a single dominant...
Article
Full-text available
The dynamics of the one-degree-of-freedom model of a towed wheel is investigated with the help of delayed tyre model. The partial side slip in the contact region is also considered, leading to an infinite-dimensional, piecewise-smooth system of governing equations. The nonlinear behaviour of the system is explored by numerical continuation of the p...
Article
Full-text available
The prediction of chatter-free machining parameters is not reliable for industrial applications without guaranteed robustness against modeling uncertainties. Measurement inaccuracies, fitting uncertainties, simplifications and modeling errors typically lead to a mismatch between the mathematical model and the real physical system. This paper presen...
Article
In this study, surface error calculations and stability conditions are presented for milling operations in case of slender parts. The dynamic behavior of the flexible beam-type workpiece is modeled by means of Finite Element Method (FEM), while the varying dynamical properties related to the feed motion as well as the material removal process are i...
Article
Full-text available
The nonlinear dynamics of towed wheels is analysed with the help of the brush tyre model. The time delay in the tyre–ground contact and the non-smooth nature of the system caused by contact friction are considered simultaneously. Firstly, the centre manifold reduction is performed on the infinite-dimensional system transforming the governing equati...
Article
Full-text available
In the initial online version of the article, the poor alignment in the typeset matrices in Equations (44), (60), (61), (62), (70), (71), (81), (84), (85), (86), and (90) may have caused misinterpretation as vectors.
Article
The unsafe zone in machining is a region of the parameter space where steady-state cutting operations may switch to regenerative chatter for certain perturbations, and vice versa. In the case of milling processes, this phenomenon is related to the existence of an unstable quasi-periodic oscillation, the in-sets of which limit the basin of attractio...
Conference Paper
Tool geometry directly influences the dynamic performance of milling operations. Both surface properties and stability behavior are significantly influenced by the regeneration effect. The regeneration phenomenon is modelled by delay differential equations with delays originated from the time passed between consecutive flute passes. This work prese...
Article
Full-text available
In this paper, the nonsmooth dynamics of two contacting rigid bodies is analysed in the presence of dry friction. In three dimensions, slipping can occur in continuously many directions. Then, the Coulomb friction model leads to a system of differential equations, which has a codimension-2 discontinuity set in the phase space. The new theory of ext...
Article
Orthogonal planing experiments are conducted with high-speed camera recordings and simultaneous cutting force measurements in order to analyze chip formation during machine tool vibrations. By means of carefully designed periodic forcing of the cutting tool, non-stationary cutting experiments are performed including wave generation, wave removal an...
Chapter
The dynamic analysis of legged locomotion typically involves issues related to multibody dynamics, underactuation, motion planning and stability. In addition to biomechanics of humans and animals, the dynamic analysis of legged locomotion is also an important issue in the control development of pedal robots. For these robots, stable internal dynami...
Article
An efficient numerical method is presented to analyse the moment stability and stationary behaviour of linear stochastic delay differential equations. The method is based on a special kind of discretization technique with respect to the past effects. The resulting approximate system is a high dimensional linear discrete stochastic mapping. The conv...
Article
Regenerative chatter vibrations arising during machining operations are a severe problem affecting the manufacturing production of high-precision mechanical components. A relatively deep understanding of this phenomenon when the cutting tool has equally spaced cutting teeth without runout has been achieved by now. However, real cutting tools are al...
Article
Full-text available
Hardware-in-the-loop (HIL) experimental setup is presented to investigate the stability of turning processes. A dummy workpiece is fixed to a main spindle, which is excited in the radial direction by electromagnetic contactless actuators. The actuators emulate contact force characteristics including surface regeneration effect between the cutting t...
Article
Full-text available
In this paper, the influence of the chip thicknesses on the contact length between the rake face of the tool and the chip is investigated during orthogonal cutting. This is an important parameter in metal cutting, since it determines the cutting force over the rake face and the heat transfer between the tool and the workpiece. Therefore, it plays s...
Article
Full-text available
Cutting capacity can be seriously limited in heavy duty face milling processes due to self-excited structural vibrations. Special geometry tools and, specifically, variable pitch milling tools have been extensively used in aeronautic applications with the purpose of removing these detrimental chatter vibrations, where high frequency chatter related...
Article
Machine tool vibrations in turning processes are analyzed by taking into account the nonlinearity of the cutting force characteristics. Unstable limit cycles are computed for the governing nonlinear delay-differential equation in order to determine the bistable technological parameter region where stable stationary cutting and large-amplitude machi...
Conference Paper
Full-text available
This study investigates how the stability of the turning process changes when the tangential component of the cutting force is also taken into account as a compressive force acting on the cutting tool. The tool is modelled by a cantilever beam; the mathematical model is based on the Euler-Bernoulli beam theory. The effect of compression appears thr...
Article
Full-text available
Models for the stabilization of an inverted pendulum figure prominently in studies of human balance control. Surprisingly, fluctuations in measures related to the vertical displacement angle for quietly standing adults with eyes closed exhibit chaos. Here we show that small-amplitude chaotic fluctuations (“microchaos”) can be generated by the inter...
Article
The prediction of chatter vibration is influenced by many known complex phenomena and is uncertain. We present a new effect that can significantly change the stability properties of cutting processes. It is shown that the microscopic environment of chip formation can have a large effect on its macroscopic properties. In this work, a combined model...
Article
Variable pitch milling cutters intend to increase performance, but off-the-shelf cutters do not ensure this generally. Depending on the milling process they are selected for, they can perform better or even worse than uniform pitch cutters do. Improved performance can be guaranteed by considering the reflected dynamic behaviour of the machine/tool/...
Article
This work presents dynamic finite element simulations of various pellet impacts in order to investigate their applicability during impulse excitation in modal analysis. Compared to the classical impulse excitation with modal hammer, the approach of pellet shots provides shorter impact time and reduces the multi-hitting effect leading a wider releva...
Article
Full-text available
Bifurcations of the periodic stationary solutions of nonlinear time-periodic time-delay dynamical systems are analyzed. The solution operator of the governing nonlinear delay-differential equation is approximated by a sequence of nonlinear maps via semidiscretization. The subsequent nonlinear maps are combined to a single resultant nonlinear map th...
Conference Paper
When modelling the contact of two rigid bodies in the presence of Coulomb friction, a special system of first-order differential equation is obtained , which is discontinuous on a codimension-2 submanifold of the state space. This leads to the concept of Extended Filippov Systems, which was introduced recently by the authors. By using the developed...
Article
A nonlinear model for human balancing subjected to a saturated delayed proportional-derivative-acceleration (PDA) feedback is analysed. Compared to the proportional-derivative (PD) controller, it is confirmed that the PDA controller improves local stability even for large feedback delays. However, it is shown that the saturated PDA controller typic...
Article
Full-text available
In spatial contact problems of rigid bodies, Coulomb friction results in dynamical systems with codimension-2 discontinuity manifolds, which are outside the scope of piecewise smooth dynamical systems. This motivated the authors to extend Filippov systems to codimension-2 discontinuity manifolds, which leads to the definition of extended Filippov s...
Article
A vehicle shimmy model using the Delayed Tyre Model to estimate the lateral tyre force is introduced. Stability charts are obtained for the linearized system. With reduced damping and stiffness parameters, a new vibration mode shows up at high speed range when the front wheels oscillate in opposite directions. Furthermore, the kinetic energy distri...
Article
Full-text available
Reliable stability predictions of machine tool chatter have high potential in the optimization of machining processes. Industrial applications can benefit from the corresponding stability lobe diagrams, which can guarantee improvement in the performance. However, predictions and experiments often do not match during cutting tests due to uncertain d...
Article
Full-text available
In order to predict the quality and the stability properties of milling processes, the relevant dynamics reduced to the cutting edges needs to be known. However, the dynamics varies through the workspace along the tool path during a given machining operation. This is the case for large heavy duty milling operations, where the main source of the rel...
Article
Full-text available
In this paper, we present the application of high-speed camera recordings in the mechanical analysis of machining processes. The modelling of the workpiece-machine-tool mechanical system is a very complex and challenging engineering problem having important features at multiple scales both in time and in space. The observation and experimental anal...
Article
Full-text available
A hardware-in-the-loop (HIL) experimental setup is presented to analyze the stability of turning process. In our test rig, the dummy workpiece in the spindle can be excited in radial direction by an electromagnetic contactless actuator. This actuator is utilized to emulate the contact (cutting) force that acts originally between the tool and workpi...
Article
Full-text available
The dynamical properties of the main spindle of a milling machine can have essential effect on the stability of milling processes. These dynamical properties often change with the rotational speed of the spindle, e.g. the stiffness and damping properties of the angular contact bearings of the spindle vary significantly with the spindle speed. Our s...
Article
Full-text available
In order to increase the material removal rate in milling, advanced cutting tools with complex geometry are typically applied under extreme cutting conditions which may trigger undesired chatter vibrations of the machining system. Recently some dynamic milling models were proposed in the literature which take into account the higher geometrical com...