Recursive Methods in Modeling and Control of Modular Robotic Systems

This paper addresses the dynamical modeling and control of reconfigurable modular robots. The modular actuators (brushless DC motors with Harmonic Drive gears) for the robots under consideration are connected by rigid links. This way the robot can be assembled in different configurations by rearranging these components. For dynamical modeling the Projection Equation in Subsystem representation is used, taking advantage of its modular structure. Due to the lack of position sensors at the gearbox output shaft, deflections caused by the elasticities in the gears can not be compensated by the PD motor joint controller. Therefore, a correction of the motor trajectory is needed, which can be calculated as part of a flatness based feed-forward control using the exact model of the robot. With the recursive approach proposed in this paper the concept of reconfigurability is retained. For validation a redundant articulated robot arm with seven joints is regarded and results are presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Detection of incipient gear failures using statistical techniques

Gears are important components in most power transmission mechanisms.Failures of gears can cause heavy losses in industry. Conditionmonitoring and fault diagnosis of gears is therefore importantto improve safety and reliability of gearbox operations andreduce losses caused by gear failures. This research proposesa new diagnostic approach based on the statistical analysisof data. It investigates the use of Principal Components Analysis(PCA) to detect growing local faults in a two-stage industrialhelical gearbox. In this research, the vibration signal is usedto monitor fault conditions and a broken tooth is simulatedas a local fault. Since the early detection of faults is a challenge,small fault conditions were tested first as well as severe faultconditions. In order to examine the ability of the PCA to detectfault conditions, first the PCA-based model was created fornormal operating conditions. Any unexpected event such as afault condition causes a significant deviation from the PCAmodel, which is obtained from the normal condition data of thegearbox. The Square Prediction Error (SPE) was calculated todetect the fault conditions. When the vibration signal fromthe gearbox is representative of normal operation, the valueof the SPE shows very little fluctuation and remains under acertain threshold value. However, in the presence of the faultthe SPE fluctuates considerably beyond the threshold value.It is shown that the PCA-based statistical approach cannot onlybe used to detect severe fault conditions, but that it alsoreveals small growing fault conditions at very early stage.The technique also provides information about the state of thefault such as the location of the fault as well as its severity. Received 5 March 2001. Revised 12 December 2001. Accepted 17 January 2002.     

Flow Past a Swept Wing with a Compliant Surface: Stabilizing the Attachment-Line Boundary Layer

Many aquatic species such as dolphins and whales have fins, which can be modeled as swept wings. Some of these fins, such as the dorsal fin of a dolphin, are semi-rigid and therefore can be modeled as a rigid swept wing with a compliant surface. An understanding of the hydrodynamics of the flow past swept compliant surfaces is of great interest for understanding potential drag reduction mechanisms, especially since swept wings are widely used in hydrodynamic and aerodynamic design. In this paper, the flow past a swept wing with a compliant surface is modeled by an attachment-line boundary layer flow, which is an exact similarity solution of the Navier–Stokes equations, flowing past a compliant surface modeled as an elastic plate. The hydrodynamic stability of the coupled problem is studied using a new numerical framework based on exterior algebra. The basic instability of the attachment line boundary layer on a rigid surface is a traveling wave instability that propagates along the attachment line, and numerical results show that the compliance results in a substantial reduction in the instability region. Moreover, the results show that, although the flow-field is three-dimensional, the qualitative nature of the instability suppression is very similar to the qualitative reduction of instability of the two-dimensional Tollmien–Schlichting modes in the classical boundary-layer flow past a compliant surface.     

A DAE formulation for geared rotor dynamics including frictional contact between the teeth

A DAE approach is presented for geared rotor dynamics simulations with rigid helical evolvent gears. It includes the normal contact force between the teeth as well as tangential components. Given the evolvent tooth flank geometry of gear 1 and gear 2 [1], the contact line and the velocity difference in the contact are found. The requirement of no penetration of the teeth yields a non-holonomic constraint and the contact normal force. The friction caused force and moment are obtained by applying Coulomb's friction model. This approach is used to investigate the dynamics of two ideal rotors with translational DoFs, which are connected by gears to one another. The driving rotor has a given angular speed, while the driven rotates unrestrainedly and is connected to a rotational damper. Because of the periodic friction terms, the solution is periodic. A direct time integration or a harmonic approach can be used for the numerical computation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A consistent theory for poroelastic plates

In many fields of engineering thin porous components are used, e.g. as damping elements for noise insulation in cars or walls in buildings. Today these elements are often calculated using a numerical 3-D model. Because of numerical problems which occur using a 3-D model for thin transversly loaded structures a plate theory is advantageous. To take into account the porous structure as well as the damping effect of the porosity of these components a poroelastic plate theory is necessary. Several posibilities exist to establish plate theories. Generally, methods to derive a plate theory require a priory assumptions motivated by engineering intuition (like the classical Kirchhoff normal hypothesis). In this contribution a priori assumptions are not used. Plate theories of different orders are derived from the 3-D poroelastic theory using series expansion. For elastic plates this idea was introduced in [3]. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A FEM model for lifetime prediction of Ancorsteel1000C in rolling contact fatigue

Ancorsteel1000C is commonly used for important components including bearing rollers, gears, connecting rods, wheels and rails; most failures of these components are caused by rolling contact fatigue (RCF). In this study the fatigue damage indicator based on Fatemi-Socie critical plane were determined in a local hot spot area in finite element (FE) model in case of Hertzian stress with zero slip condition. The simulation results compared with respect to experimental data, which is in good agreement. Therefore, this approach can be implemented as a useful tool for lifetime calculations in RCF in the process of structure fatigue design. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear dynamics and dynamic instability of smart structural cross-ply laminated cantilever plates with MFC layer using zigzag theory

In this paper, a novel dynamic model for smart structural systems cross-ply laminated cantilever plate with smart material Macro fiber composites (MFC) layer is presented by using zigzag function theory. The nonlinear dynamic response and dynamic instability of the smart structural systems are studied for the first time. The plate is subjected to the uniformed static and in-plane harmonic excitation conjunction with electrically loaded under different electric boundary conditions. The partial layer-wise theory which the first shear deformation theory is expanded by introducing the zigzag function in the in-plane displacement components is adopted. The carbon fiber reinforced composite material T800/M21and macro fiber composites (MFC-d31) M8528-P3 are implemented. By Lagrangian equation and Chebyshev polynomial, the equations of motion are derived for the laminated plate. The validation and convergence are studied by comparing results with literatures. The dynamic instability regions and the critical buckling load characteristics can be obtained for different layer sequences, geometric dimensions and also the electromechanical effects are considered. Nonlinear dynamic responses of the laminated plate are studied by using numerical calculation. It can be seen that in certain state the plate will loses stability and the periodic, multiple period as well as chaotic motions of the plate are found.     

The Higher Frequency of Free Vibrations of Thin Annular Plates Made of Functionally Graded Material

Subject of this paper is a thin plate with a characteristic geometry: periodic in one direction and smoothly varying along the other. The aim of the contribution is to formulate and apply the averaged model which can describe higher frequencies of free vibrations. Problem of finding frequencies of free vibrations is very important. It could be applied to many engineering problems such as resonance phenomena, wave propagation, absorption of vibrations and many others. When the considered plate is made of an isotropic material, we can find the first, the second and the others frequencies in simply way. But if we consider plate made of a functionally graded material [1], which have varying properties and which is made of two components, this problem is more complicated. In this cause, apart from family of the base frequencies (first, second, etc), which depend on macroscopic properties of the plate, we have the higher frequency, which depends on a microscopic structure. We can find many papers describing the base frequencies of free vibrations for many different types of structures (for example [2] for considered type of plate). In this paper, we find the higher frequency. For solving this problem, we use the tolerance averaging technique described in [3]. This theory allows to take into account the microstructure size and to find the higher frequency of free vibrations. The equations have smooth coefficients. They can be solved numerically with help of the finite difference method, in polar coordinates for an annular plate. Next, we use special procedure for selecting of the higher frequencies of free vibrations, which depend on the microstructure size, from the list of all frequencies. After that we analyze an influence of ratios of material properties and the microstructure size on the higher frequency of free vibrations. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Eigenvalue sensitivity and parametric optimization of the large rotating systems

The contribution presents the modal synthesis method of the mathematical modelling of the large rotating systems. The condensed mathematical model is used for deriving analytical formula for eigenvalue sensitivity calculation. According to the sensitivity analysis suitable design parameters are chosen and the optimization process for the purpose of steady state response minimization in a certain operating speed area is performed. The theory is applied to a simple test‐gearbox. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Melnikov criterion of instability for random rocking dynamics of a rigid block with an attached secondary structure

In this paper we investigate the effect of structural flexibility on rocking motion of a system consisting of a free standing rigid block with an attached chain of uniaxially moving point masses. Motion is excited by random acceleration of the ground; instability is associated with overturning of the overall structure. The condition of instability is constructed by the stochastic Melnikov method. We demonstrate a twofold effect of structural flexibility on the rocking response. The attached structure may increase the critical angular displacement and velocity in comparison with the similar parameters of the single rigid block. At the same time, the enlargement of the domain of stability enhances the contribution of the random perturbation in the Melnikov process. As a result, a lower level of random forcing can result in overturning of the structure. As an example, an effect of a single-mass secondary structure on the dynamic behavior of the system is discussed. The paper is restricted to the consideration of seismic vulnerability of the structure. A similar approach can be applied to systems with wind or wave excitation.     

A new nonlinear blind source separation method with chaos indicators for decoupling diagnosis of hybrid failures: A marine propulsion gearbox case with a large speed variation

The normal operation of propulsion gearboxes ensures the ship safety. Chaos indicators could efficiently indicate the state change of the gearboxes. However, accurate detection of gearbox hybrid faults using Chaos indicators is a challenging task and the detection under speed variation conditions is attracting considerable attentions. Literature review suggests that the gearbox vibration is a kind of nonlinear mixture of variant vibration sources and the blind source separation (BSS) is reported to be a promising technique for fault vibration analysis, but very limited work has addressed the nonlinear BSS approach for hybrid faults decoupling diagnosis. Aiming to enhance the fault detection performance of Chaos indicators, this work presents a new nonlinear BSS algorithm for gearbox hybrid faults detection under a speed variation condition. This new method appropriately introduces the kernel spectral regression (KSR) framework into the morphological component analysis (MCA). The original vibration data are projected into the reproducing kernel Hilbert space (RKHS) where the instinct nonlinear structure in the original data can be linearized by KSR. Thus the MCA is able to deal with nonlinear BSS in the KSR space. Reliable hybrid faults decoupling is then achieved by this new nonlinear MCA (NMCA). Subsequently, by calculating the Chaos indicators of the decoupled fault components and comparing them with benchmarks, the hybrid faults can be precisely identified. Two specially designed case studies were implemented to evaluate the proposed NMCA-Chaos method on hybrid gear faults decoupling diagnosis. The performance of the NMCA-Chaos was compared with state of art techniques. The analysis results show high performance of the proposed method on hybrid faults detection in a marine propulsion gearbox with large speed variations.     

Strongly coupling of partitioned fluid–solid interaction solvers using reduced-order models

In this work a powerful technique is described which allows the implicit coupling of partitioned solvers in fluid–structure interaction (FSI) problems. The flow under consideration is governed by the Navier–Stokes equations for incompressible viscous fluids and modeled with the finite volume method. The structure is represented by a finite element formulation. The method allows the use of a black box fluid and structural solver because it builds up a reduced order model of the fluid and structural problem during the coupling process. Each solution of the fluid/structural solver in the coupling process can be seen as a sensitivity response of an applied displacement/pressure mode. The applied modes and their responses are used to build up a reduced-order model. The proposed model is used to predict the unsteady flow fields of a particular flow-induced vibrational phenomenon – a fixed cubic rigid body is submerged in an incompressible fluid flow (water), an elastic plate is attached to the rigid body in the centre of the downstream face, and the vortices, which separate from the corners of the rigid body upstream, generate lift forces which excite continuous oscillations of the elastic plate downstream. The computational results show that a fairly good convergence solution is achieved by using the reduced-order model that is based on only a few displacement and stress modes, which largely reduces the computational cost, compared with traditional approaches. At the same time, comparison of the numerical results of the model with available experimental data validates the methodology and assesses its accuracy.     

On stability and self-excited vibrations in fluid-structure-interaction

In flexible channels conveying fluid the steady state may loose stability by divergence or flutter. The aim of this contribution is to investigate the basic excitation mechanisms of flow-induced vibrations and to evaluate the influence of various parameters on the stability behaviour of the coupled problem. Therefore, a simple, yet general model is proposed. The fluid is assumed to be inviscid and irrotational and both incompressible and compressible flow is considered. It is guided by a planar, rectangular channel with a rigid wall and a thin, flexible wall. The latter is modelled as a one-parametric continuum on an elastic foundation, which exhibits bending and extensional stiffness. By examining the energy balance over one oscillation circle it is possible to reveal the mechanisms of energy transfer between the coupled components of the system. Based on this analysis a physical explanation of the arising instabilities is possible. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical Justification of an Obstacle Problem in the Case of a Plate

In this paper the modeling of a thin plate in unilateral contact with a rigid plane is properly justified.Starting from the three-dimensional nonlinear Signorini problem,by an asymptotic approach the convergence of the displacement field as the thickness of the plate goes to zero is studied.It is shown that the transverse mechanical displacement field decouples from the in-plane components and solves an obstacle problem.     

Boundary stabilization of structural acoustic interactions with interface on a Reissner–Mindlin plate

Boundary stabilization of a structural acoustic model comprised of a wave and a Reissner–Mindlin plate is addressed. Both the components of the dynamics are subject to localized nonlinear boundary damping: the acoustic dissipative feedback is restricted to the flexible boundary and only a portion of the rigid wall; the plate is damped only on a segment of its edge.Derivation of stabilization/observability inequalities for a coupled system requires weighted energy multipliers dependent on the geometry of the domain, and special microlocal trace estimates for the Reissner–Mindlin plate. The behavior of the energy at infinity can be quantified by a solution to an explicitly constructed nonlinear ODE. The nonlinearities in the feedbacks may include sub- and superlinear growth at infinity, in which case the decay scheme presents a trade-off between the regularity of trajectories and attainable uniform dissipation rates of the finite energy.     

The applicability of a hereditary model of wear with an exponential kernel in the one-dimensional contact problem taking frictional heat generation into account

An analytic solution is obtained for the contact problem for a stiff thermally insulated plate and an elastic heat-conducting layer, subject to the conditions of wear and frictional heating, when the contacting bodies are not drawn nearer. The evolution of the contact pressure, the temperature and the wear are traced. Conditions for the occurrence of thermoelastic instability are established. The conditions under which the wear model considered is applicable are given.     

Linear stability analysis of oscillating Ekman boundary layers

The analysed Ekman layer is generated in a fluid layer rotating around an axis normal to its two bounding rigid plates. One of the plates is stationary, the other moving at certain Reynolds numbers. An additional oscillation is added to the moving plate at different amplitudes and frequencies. The linear stability of this system is determined via a Floquet analysis and a Galerkin-approximation of the corresponding Navier-Stokes-Equations. If the frequencies of the oscillations are small the critical Reynolds numbers of the Type I and Type II instabilities do not differ much from steady Ekman layers. Also for a purely oscillating system the critical values of the instabilities are almost consistent with those for a steady system. Interestingly, for higher frequencies the Type II instability does not appear any more. Instead the boundary layer becomes unstable only in terms of a Type I instability. In comparison with findings of other authors these results seem to be quite reasonable. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Primary elements in formal modules

The stability of an elastic plate in a supersonic gas flow is considered in the presence of a boundary layer formed on the surface of the plate. The problem is solved in two statements. In the first statement, the plate is of large but finite length, and a coupled-mode type of flutter is examined (the effect of the boundary layer on another, single-mode, type of flutter has been studied earlier). In the second statement, the plate is assumed to be infinite, and the character of its instability (absolute or convective) is analyzed. In both cases, the instability is determined by a branch point of the roots of the dispersion equation, and the mathematical analysis is the same. It is proved that instability in a uniform gas flow is weakened by a boundary layer but cannot be suppressed completely, while in the case of a stable plate in a uniform flow the boundary layer leads to the destabilization of the plate.     

Influence of the contact model on the onset of sprag-slip

In systems with sliding-friction often strong self-excited vibrations do occur. One of the possible underlying mechanisms is the so-called sprag-slip instability. In the present work the onset of sprag-slip is investigated by a simple model in which an inclined elastic beam slides over a rigid belt moving with constant velocity. For a Coulomb friction law and a contact model with constant contact stiffness for a certain range of parameters the system loses its static solution corresponding to the steady sliding state. Simultaneously with this loss of existence of the static solution the qualitative properties of the system's flow field in phase space change, resembling a transition from stable to unstable behavior. To investigate the influence of contact models and related parameters on the details of this onset of sprag-slip also Hertz theory of elastic contact is applied. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)