Stiffness modeling of robotic manipulator with gravity compensator

The paper focuses on the stiffness modeling of robotic manipulators with gravity compensators. The main attention is paid to the development of the stiffness model of a spring-based compensator located between sequential links of a serial structure. The derived model allows us to describe the compensator as an equivalent non-linear virtual spring integrated in the corresponding actuated joint. The obtained results have been efficiently applied to the stiffness modeling of a heavy industrial robot of the Kuka family

A user's guide to the SUDAN computer program for determining the vibration modes of structural systems

The use of the SUDAN computer program for analyzing structural systems for their natural modes and frequencies of vibration is described. SUDAN is intended for structures which can be represented as an equivalent system of beam, spring, and rigid-body substructures. User-written constraint equations are used to analytically join the mass and stiffness matrices of the substructures to form the mass and stiffness matrices of the complete structure from which all the frequencies and modes of the system are determined. The SUDAN program can treat the case in which both the mass and stiffness matrices of the coupled system may be singular simultaneously. A general description of the FORTRAN IV program is given, the computer hardware and software specifications are indicated, and the input required by the program is described

Definition of a linear equivalent model for a non-linear system with impacts

Modal characteristics of non-linear system are typically studied through response to harmonic excitation and using various definitions of non-linear modes. However, few results are available for systems under broadband excitation. The end objective sought here is to generate a linear system, in some sense equivalent to the non-linear system, whose modal characteristics evolve with a level of non-linearity. The considered application is the contact non-linearity found between the tubes of heat exchangers and their support plates. Such tubes, present in nuclear plants, participate to the nuclear safety and can be significantly excited by the fluid flow, so that their dynamic behavior is critical. The turbulent nature of the flow implies broadband excitation and the small gaps between the tubes and the support plate generate very significant non-linear behavior. The proposed equivalent linear system is based on a bilateral contact law whose stiffness and damping characteristics evolve with the amplitude of excitation. A non-linear model is first validated by correlation with experiments. It is then shown that three different indicators (bandwidth of main resonance, operational modal analysis of non-linear power spectral density and correlation of operational deflection shapes) lead to similar values of contact stiffness and damping in the equivalent linear model. This model is hus shown to be a very efficient tool to analyze the impact of the amplitude dependence of the non-linear behavior in the considered system

Embedding negative structures to model holes and cut-outs

It has now been established that geometric boundary conditions and continuity conditions can be modelled by using either positive or negative stiffness or inertia type penalty term [1-5]. The experience of working with negative stiffness and inertial parameters has led to the question: what if both stiffness and mass were to be taken as negative? Changing the sign of all stiffness and inertial terms of a structure is simply equivalent to multiplying both sides of an eigenvalue equation by minus one, which does not change its frequencies or modes. Basically, a negative structure in such a sense has the same vibratory properties as that of its positive counterpart, although the structure itself may not have a physical meaning

Random excitation of a system with bilinear hysteresis

An analysis is made of the response of a system with bilinear hysteresis to random excitation. It is shown that for moderately large inputs, the additional damping created by the bilinear hysteresis decreases the mean squared deflection compared with that for a linear system with the same viscous damping. However, for large inputs, the decrease in the stiffness of the system due to the bilinear hysteresis causes the mean squared deflection to increase over that for the equivalent linear system

Dynamic tooth loads and stressing for high contact ratio spur gears

An analysis and computer program were developed for calculating the dynamic gear tooth loading and root stressing for high contact ratio gearing (HCRG) as well as LCRG. The analysis includes the effects of the variable tooth stiffness during the mesh, tooth profile modification, and gear errors. The calculation of the tooth root stressing caused by the dynamic gear tooth loads is based on a modified Heywood gear tooth stress analysis, which appears more universally applicable to both LCRG and HCRG. The computer program is presently being expanded to calculate the tooth contact stressing and PV values. Sample application of the gear program to equivalent LCRG (1.566 contact ratio) and HCRG (2.40 contact ratio) revealed the following: (1) the operating conditions and dynamic characteristics of the gear system an affect the gear tooth loading and root stressing, and therefore, life significantly; (2) the length of the profile modification affect the tooth loading and root stressing significantly, the amount depending on the applied load, speed, and contact ratio; and (3) the effect of variable tooth stiffness is small, shifting and increasing the response peaks slightly from those for constant tooth stiffness

Validity of the one-dimensional limp model for porous materials

A straightforward criterion to determine the limp model validity for porous materials is addressed here. The limp model is an "equivalent fluid" model which gives a better description of the porous behavior than the well known "rigid frame" model. It is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the Frame Stiffness Influence FSI based on porous material properties. The critical values of FSI under which the limp model can be used, are determined using a 1D analytical modeling for a specific boundary set: radiation of a vibrating plate covered by a porous layer.Comment: 12th International Student Conference on Electrical Engineering, Prague : Tch\`eque, R\'epublique (2008

Effect of fluid forces on rotor stability of centrifugal compressors and pumps

A simple two dimensional model for calculating the rotordynamic effects of the impeller force in centrifugal compressors and pumps is presented. It is based on potential flow theory with singularities. Equivalent stiffness and damping coefficients are calculated for a machine with a vaneless volute formed as a logarithmic spiral. It is shown that for certain operating conditions, the impeller force has a destablizing effect on the rotor

Persistent Currents in the Heisenberg chain with a weak link

The Heisenberg chain with a weak link is studied, as a simple example of a quantum ring with a constriction or defect. The Heisenberg chain is equivalent to a spinless electron gas under a Jordan-Wigner transformation. Using density matrix renormalization group and quantum Monte Carlo methods we calculate the spin/charge stiffness of the model, which determines the strength of the `persistent currents'. The stiffness is found to scale to zero in the weak link case, in agreement with renormalization group arguments of Eggert and Affleck, and Kane and Fisher.Comment: 14 pages, 7 figures, 2 tables, no changes to paper, author list changed on archiv

Self-Healing Multiblock Copolypeptide Hydrogels via Polyion Complexation

Diblock, triblock, and pentablock copolypeptides were designed and prepared for formation of polyion complex hydrogels in aqueous media. Increasing the number of block segments was found to allow formation of hydrogels with substantially enhanced stiffness at equivalent concentrations. Use of similar length ionic segments also allowed mixing of different block architectures to fine-tune hydrogel properties. The pentablock hydrogels possess a promising combination of high stiffness, rapid self-healing properties, and cell compatible surface chemistry that makes them promising candidates for applications requiring injectable or printable hydrogel scaffolds