Gábor Stépán

Budapest University of Technology and Economics · Department of Technical Mechanics

In many facets of industry, slender workpieces are formed by means of milling processes. These workpieces are especially prone to experience harmful chatter vibrations, which limits quality and productivity. In this paper, a novel solution is proposed where a robotic arm is used to support the workpiece, improving its modal properties and reducing...

The robustness of dynamical systems against external perturbations is crucial in engineering; however, it is often overlooked for the lack of methods for rapidly computing it. This paper proposes a novel algorithm for estimating the robustness of systems subject to time delay. More precisely, the algorithm iteratively estimates the so-called local...

Direct spring operated pressure relief valves connected to a constantly charged vessel and a downstream pipe have a complex dynamics. The vessel-valve subsystem is described with an autonomous system of ordinary differential equations, while the presence of the pipe adds two partial differential equations to the mathematical model. The partial diff...

The steering control of an autonomous unicycle is considered. The underlying dynamical model of a single rolling wheel is discussed regarding the steady state motions and their stability. The unicycle model is introduced as the simplest possible extension of the rolling wheel where the location of the center of gravity is controlled. With the help...

The robustness of dynamical systems against external perturbations is crucial in engineering; however, it is often overlooked for the lack of methods for rapidly computing it. This paper proposes a novel algorithm for estimating the robustness of systems subject to time delay. More precisely, the algorithm iteratively estimates the so-called local...

Hardware-in-the-loop (HIL) measurements of highly interrupted milling processes were conducted. A real spindle was used with a dummy tool on which the cutting forces were emulated with contactless sensors and actuators. During the experiments, Hopf- and period-doubling bifurcations were identified. The nonlinear dynamics of these period-doubling bi...

In turning operations, the harmful small-amplitude but high-frequency chatter vibrations are identified in hardware-in-the-loop (HIL) experimental environment by means of the application of a multi-dimensional bisection method. The dummy workpiece clamped to the real main spindle is excited by contactless electromagnetic actuators and the response...

Direct spring operated pressure relief valves are regular elements of high-pressure hydraulic systems; however, valve vibrations may still occur endangering the valve and the protected system. The damping of these vibrations is a crucial issue, whereas the external viscous damping at the valve cannot be increased boundlessly based on safety aspects...

The digital balancing of the Furuta pendulum is studied when the time delay related to the digital control and the dynamics of the actuator have essential effects on stability. Such cases occur when the sampling rate of the digital control is low, that is, the control cycles are slow due to complex signal processing strategies and/or the implementa...

A simplified mechanical model of vehicle towing is constructed. The towing procedure is modeled by means of two blocks connected with a linear spring that represents the elastic drawbar. The driver in the towing car controls the velocity of towing, while the driver of the towed vehicle tries to maintain a constant tension in the drawbar. Both contr...

The present work investigates the dynamics of a guided control situation when an automated vehicle is traveling in front of a human-driven vehicle, while the control of the automated vehicle contains the combination of a cruise control term and a backward looking term. The plant and string stability conditions of the underlying dynamical system are...

Hardware-in-the-loop (HIL) measurements of highly interrupted milling processes were conducted. A real spindle was used with a dummy tool on which the cutting forces were emulated with contactless sensors and actuators. During the experiments, Hopf- and period-doubling bifurcations were identified. The nonlinear dynamics of these period-doubling bi...

A nonlinear mechanical model of human balancing is established with the help of ankle stiffness measurements available in the literature. The stability analysis of quiet standing is studied analytically in the presence of the neural reaction delay. This analysis is followed by the investigation of the nonlinear dynamics: increasing reaction time re...

The paper investigates the nonlinear dynamics of the collocated position control of a trolley that carries a pendulum. Delayed proportional derivative control force is considered, which is based on the position and velocity of the trolley only. Stability charts are constructed for different parameter combinations, which show intricate structures in...

The REHAROB robotic upper limb rehabilitation system was improved with a custom-designed and developed hand/finger therapy module. The new module extends the scope of the applicable motion therapy from passive to active reach-to-grasp activities of daily living tasks, and the range of treated anatomical joints was also extended to every proximal an...

Two basic models of machine tool vibrations are presented. First, a simple model of orthogonal turning process is discussed where material is removed from the rotating workpiece by a tool. Vibrations of the tool are copied on the workpiece’s surface and, after one revolution, the tool cuts this wavy surface. This phenomenon is called surface regene...

Mechanical models of two human balancing tasks, quiet standing and stick balancing on the fingertip, are discussed with special attention to the reaction time delay. As in many control systems, time delay sets limitation to performance during balancing tasks. Human subjects cannot balance an arbitrarily short stick on the fingertip, because a short...

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...

This paper investigates the dynamics of a fuzzy controlled polishing machine where the effect of temporal sampling is also taken into account. Chaotic and transient chaotic behaviors are experienced for certain control parameter combinations. In the case of transient chaotic motion, closed-form algebraic expressions are determined for the expected...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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/...

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...

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...