Suppression of Machine Tool Chatter Using a Viscoelastic Dynamic Damper

1987 ◽  
Vol 109 (1) ◽  
pp. 58-65 ◽  
Author(s):  
K. J. Kim ◽  
J. Y. Ha
Keyword(s):  
Loss Factor ◽  
The Other ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Dynamic Damper ◽  
Single Degree ◽  
Machine Tool Chatter ◽  
Chatter Vibrations ◽  
Resonance Frequencies ◽  
Viscoelastic Element

Optimization procedures to install a viscoelastic dynamic damper into a single degree of freedom primary system is briefly reviewed. Excitation methods are shown to identify elastic modulus and loss factor of a viscoelastic material at given prestrain, which are needed in the optimum design of the damper. An optimum-designed damper is attached on the toolpost of a lathe and its excellent chatter-suppressing effects are observed under six cutting conditions in terms of integrated power of the accelerations around the chatter frequency. Because one of the resonance frequencies responsible for the chatter varies depending upon the location of the carriage on the sliding surface, the prestrain of the viscoelastic element, which is initially optimum-tuned and damped at a location of the carriage, is readjusted for optimum tuning at the other locations. The effects of the readjustment are discussed in terms of the reduction of structural compliances and magnitudes of chatter vibrations.

Application of Viscoelastic Material for a Dynamic Damper

1986 ◽  
Vol 108 (3) ◽  
pp. 378-381 ◽  
Author(s):  
K. J. Kim ◽  
T. I. Yeo
Keyword(s):  
Resonance Frequency ◽  
Viscoelastic Material ◽  
Optimization Procedure ◽  
Degree Of Freedom ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Dynamic Damper ◽  
Single Degree ◽  
Mass Damper

An optimization procedure in the design of a viscoelastic dynamic damper is proposed for a single-degree-of-freedom primary system with the effects of prestrain taken into account. The performance is compared with that by a conventional spring-dashpot-mass damper. Applicability of the proposed procedure to a resonance-frequency-varying system is also shown.

Deployable Prismatic Structures With Origami Patterns

2014 ◽  
Author(s):  
Sicong Liu ◽  
Weilin Lv ◽  
Yan Chen ◽  
Guoxing Lu
Keyword(s):  
Design Method ◽  
Kinematic Model ◽  
The Other ◽  
Dihedral Angles ◽  
Geometric Condition ◽  
Compatibility Conditions ◽  
Deployable Structures ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Geometric Compatibility

In order to find the general condition of the rigid origami pattern for the deployable prismatic structures, the kinematic model is proposed based on the mobile assemblies of spherical 4R linkages. The kinematic and geometric compatibility conditions of the mobile assemblies are derived. Two groups of 2n-side deployable prismatic structures are obtained. When n=2, one of them is with kite-shape intersection, while the other is with parallelgram. The variations of the unit are discussed. The straight and curvy multilayer prisms are built by changing the dihedral angles between the intersecting planes. The general design method for the 2n-side multilayer deployable prismatic structures is proposed with the geometric condition of the origami patterns. All the deployable structures constructed with this method can be deployed and folded along the central axis of the prisms with single degree of freedom, which makes the structures have wide engineering applications.

Tunable-with-energy intense modal interactions induced by geometric nonlinearity

2020 ◽  
pp. 095440622090862
Author(s):  
Alireza Mojahed ◽  
Lawrence A Bergman ◽  
Alexander F Vakakis
Keyword(s):  
Geometric Nonlinearity ◽  
Degree Of Freedom ◽  
Primary System ◽  
Energy Relation ◽  
Initial Angle ◽  
Modal Interactions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Energy Transfers ◽  
Wave Tailoring

Modal interactions are distinct features of nonlinear systems that can be exploited in applications such as vibration and shock mitigation, targeted (irreversible) energy transfers (TET), and acoustic/stress wave tailoring. For such applications, different types of nonlinearities, e.g. hardening, softening, smooth, non-smooth, material or geometric, have been considered. In this work, we examine the geometric nonlinearity resulting from an initially inclined element consisting of a linear spring and a viscous damper connected in parallel, having an initial angle of inclination, [Formula: see text]. Because of its inclined configuration, this element possesses strong (and doubly tunable with respect to [Formula: see text] and energy) geometrically nonlinear stiffness and damping effects, despite the linear constitutive laws governing its constituent components. First, we consider a single-degree-of-freedom linearly grounded oscillator attached to the nonlinear inclined element. Omitting dissipative effects, we investigate the frequency–energy relation of this system by employing the canonical action-angle transformation and show that, depending on the initial angle of inclination and the energy-level, the resulting nonlinearity can be tuned to be softening, hardening or a combination of both. Next, we explore the efficacy of the geometric nonlinearity to induce strong modal interactions by considering a three-degree-of-freedom lightly damped primary system that is weakly coupled to a single-degree-of-freedom lightly damped attachment with the inclined nonlinear element, subjected to impulsive excitation. Varying [Formula: see text] and the input energy, we demonstrate strong modal energy-exchanges between the modes of the primary system and the nonlinear attachment over broad energy-dependent spans of [Formula: see text]. We show that the passive self-adaptiveness of the nonlinear damping and the hardening–softening geometric nonlinearity can induce narrowband or broadband frequency TET, including high-to-low frequency energy transfers. Interestingly, over a definitive range of [Formula: see text], these modal interactions may be limited only between the nonlinear mode of the attachment and the highest-frequency linear mode of the primary system, inducing strong high-frequency targeted energy transfer to the primary system.

scholarly journals Optimization of Multiple Tuned Mass Damper (MTMD) Parameters for a Primary System Reduced to a Single Degree of Freedom (SDOF) through the Modal Approach

2021 ◽  
Vol 11 (4) ◽  
pp. 1389
Author(s):  
Piotr Wielgos ◽  
Robert Geryło
Keyword(s):  
Degrees Of Freedom ◽  
Research Work ◽  
System Optimization ◽  
Degree Of Freedom ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Modal Approach ◽  
Single Degree ◽  
Novel Approach ◽  
The Impact

The research paper presents a novel approach toward constructing motion equations for structures with attached MTMDs (multiple tuned mass dampers). A primary system with MDOF (multiple dynamic degrees of freedom) was reduced to an equivalent system with a SDOF (single degree of freedom) through the modal approach, and equations from additional MTMDs were added to a thus-created system. Optimization based on ℌ2 and ℌ∞ for the transfer function associated with the generalized displacement of an SDOF system was applied. The research work utilized GA (genetic algorithms) and SA (simulated annealing method) optimization algorithms to determine the stiffness and damping parameters for individual TMDs. The effect of damping and stiffness (MTMD tuning) distribution depending on the number of TMDs was also analyzed. The paper also reviews the impact of primary system mass change on the efficiency of optimized MTMDs, as well as confirms the results of other authors involving greater MTMD effectiveness relative to a single TMD.

scholarly journals Optimization of Multiple Tuned Mass Damper (MTMD) Parameters for a Primary System Reduced to a Single Degree of Freedom (SDOF) Through the Modal Approach

2020 ◽  
Author(s):  
Piotr Wielgos ◽  
Robert Geryło
Keyword(s):  
Degrees Of Freedom ◽  
Research Work ◽  
System Optimization ◽  
Degree Of Freedom ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Modal Approach ◽  
Single Degree ◽  
Stiffness And Damping ◽  
The Impact

The research paper presents a new approach towards constructing motion equations for structures with attached MTMDs (multiple tuned mass dampers). A primary system, with MDOF (multiple dynamic degrees of freedom) was reduced to an equivalent system with a SDOF (single degree of freedom) through the modal approach, and equations from additional MTMDs were added to a thus-created system. Optimization based on H2 and H∞ for the transfer function associated with the generalized displacement of an SDOF system. The research work utilized GA (genetic algorithms) and SA (simulated annealing method) optimization algorithms to determine the stiffness and damping parameters for individual TMDs. The effect of damping and stiffness (MTMD tuning) distribution depending on the number of TMDs was also analyzed. The paper also reviews the impact of primary system mass change on the efficiency of optimized MTMDs, as well as confirms the results of other authors involving greater MTMD effectiveness relative to a single TMD.

Effect of Third Harmonic Vibratory Force on a Linear Spring-Mass System

1963 ◽  
Vol 67 (636) ◽  
pp. 799-803
Author(s):  
C. L. Kirk
Keyword(s):  
Resonant Frequency ◽  
Elastic System ◽  
Rate Of Change ◽  
Degree Of Freedom ◽  
The Other ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Third Harmonic ◽  
Single Degree ◽  
Linear Spring

SummaryThe response of an elastic system having a single degree of freedom, to a vibratory force whose waveform can be varied, is examined. The variable waveform is produced by a system of two pairs of unbalanced rotors in which one pair rotates at three times the speed of the other pair. The waveform depends on the frequency of excitation, the phasing of the rotors and the ratio of their amounts of unbalance. If the rotors are run at a speed at which the faster pair rotates above resonance while the slower pair rotates below resonance, a frequency is found at which the rate of change of amplitude with respect to frequency is zero. At this point, however, the waveform is quite sensitive to small changes in the frequency of excitation. If the rotor speeds cannot be maintained constant, and if stable vibration waveforms are required, it is necessary to run the slowest rotor well above the resonant frequency where both the amplitude and waveform will be virtually independent of frequency.

Extended Camus Theory and Higher Order Conjugated Curves

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Stationary Point ◽  
Higher Order ◽  
Degree Of Freedom ◽  
The Other ◽  
Body System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Pair Generation ◽  
Three Body ◽  
Two Bodies

According to Camus’ theorem, for a single degree-of-freedom (DOF) three-body system with the three instant centers staying coincident, a point embedded on a body traces a pair of conjugated curves on the other two bodies. This paper discusses a fundamental issue not addressed in Camus’ theorem in the context of higher order curvature theory. Following the Aronhold–Kennedy theorem, in a single degree-of-freedom three-body system, the three instant centers must lie on a straight line. This paper proposes that if the line of the three instant centers is stationary (i.e., slide along itself) on the line of the instant centers, a point embedded on a body traces a pair of conjugated curves on the other two bodies. Another case is that if the line of the three instant centers rotates about a stationary point, the stationary point embedded on a body also traces a pair of conjugated curves on the other two bodies. The paper demonstrates the use of instantaneous invariants to synthesize such a three-body system leading to a conjugate curve-pair generation. It is a supplement or extension of Camus’ theorem. Camus’ theorem may be regarded as a special singular case, in which all three instant centers are coincident.

scholarly journals Evaluation of the Methods for Response Analysis under Non-Stationary Excitation

1999 ◽  
Vol 6 (5-6) ◽  
pp. 285-297 ◽  
Author(s):  
R.S. Jangid ◽  
T.K. Datta
Keyword(s):  
Soil Structure ◽  
Solution Procedure ◽  
The Other ◽  
Soil Structure Interaction ◽  
Response Analysis ◽  
Single Degree Of Freedom ◽  
Structure Interaction ◽  
Sdof System ◽  
Single Degree ◽  
Stationary Analysis

Response of structures to non-stationary ground motion can be obtained either by the evolutionary spectral analysis or by the Markov approach. In certain conditions, a quasi-stationary analysis can also be performed. The first two methods of analysis are difficult to apply for complex situations such as problems involving soil-structure interaction, non-classical damping and primary-secondary structure interaction. The quasi-stationary analysis, on the other hand, provides an easier solution procedure for such cases. Here-in, the effectiveness of the quasi-stationary analysis is examined with the help of the analysis of a single degree-of-freedom (SDOF) system under a set of parametric variations. For this purpose, responses of the SDOF system to uniformly modulated non-stationary random ground excitation are obtained by the three methods and they are compared. In addition, the relative computational efforts for different methods are also investigated.

scholarly journals Passive Gravity Balancing with a Self-Regulating Mechanism for Variable Payload

Machines ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 145
Author(s):  
Diego Franchetti ◽  
Giovanni Boschetti ◽  
Basilio Lenzo
Keyword(s):  
Potential Energy ◽  
The Other ◽  
Robotic Systems ◽  
Single Degree Of Freedom ◽  
System Parameters ◽  
Single Degree ◽  
Energy Consumptions ◽  
Simulation Results ◽  
Practical Implications ◽  
Auxiliary Mechanism

Gravity balancing techniques allow for the reduction of energy consumptions in robotic systems. With the appropriate arrangements, often including springs, the overall potential energy of a manipulator can be made configuration-independent, achieving an indifferent equilibrium for any position. On the other hand, such arrangements lose their effectiveness when some of the system parameters change, including the mass. This paper proposes a method to accommodate different payloads for a mechanism with a single degree-of-freedom (DOF). By means of an auxiliary mechanism including a slider, pulleys and a counterweight, the attachment point of a spring is automatically regulated so as to maintain the system in indifferent equilibrium regardless of the position, even when the overall mass of the system varies. Practical implications for the design of the mechanism are also discussed. Simulation results confirm the effectiveness of the proposed approach.

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