On the stabilization of steady-state motions of mechanical systems

1983 ◽  
Vol 47 (2) ◽  
pp. 253-259 ◽  
Author(s):  
E.M. Krasinskaia
Keyword(s):  
Steady State ◽  
Mechanical Systems

scholarly journals Degrading systems availability analysis: analytical semi-Markov approach

2021 ◽  
Vol 23 (1) ◽  
pp. 195-208
Author(s):  
Varun Kumar ◽  
Girish Kumar ◽  
Rajesh Kumar Singh ◽  
Umang Soni
Keyword(s):  
Steady State ◽  
Degradation Mechanism ◽  
Continuous Process ◽  
Mechanical Systems ◽  
Embedded Markov Chain ◽  
Steady State Probability ◽  
Opportunistic Maintenance ◽  
System Availability ◽  
Availability Analysis ◽  
Complex Mechanical Systems

This paper deals with modeling and analysis of complex mechanical systems that deteriorate with age. As systems age, the questions on their availability and reliability start to surface. The system is believed to suffer from internal stochastic degradation mechanism that is described as a gradual and continuous process of performance deterioration. Therefore, it becomes difficult for maintenance engineer to model such system. Semi-Markov approach is proposed to analyze the degradation of complex mechanical systems. It involves constructing states corresponding to the system functionality status and constructing kernel matrix between the states. The construction of the transition matrix takes the failure rate and repair rate into account. Once the steady-state probability of the embedded Markov chain is computed, one can compute the steady-state solution and finally, the system availability. System models based on perfect repair without opportunistic and with opportunistic maintenance have been developed and the benefits of opportunistic maintenance are quantified in terms of increased system availability. The proposed methodology is demonstrated for a two-stage reciprocating air compressor with intercooler in between, system in series configuration.

REACTANTS AND OTHER PARAMETERS OF MECHANICAL SYSTEMS

2020 ◽  
pp. 4-12
Author(s):  
I. P. Popov ◽  
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Electrical Engineering ◽  
Mechanical Systems ◽  
Phase Relations ◽  
Calculation Algorithm ◽  
Steady State Mode ◽  
Harmonic Oscillations ◽  
Harmonic Vibrations ◽  
Algebraic Operations

The traditional calculation of mechanisms for forced harmonic oscillations is often a difficult task. Most often, calculators are interested in the steady-state modes of harmonic oscillations. The purpose of this paper is to significantly simplify calculations by replacing the need to solve differential equations with simpler algebraic methods. A complex representation of harmonic and related quantities is used. This approach is widely used in theoretical electrical engineering. Parallel and serial connections of mechanical power consumers are considered. The velocities of elements of mechanical systems and the forces applied to them are determined algebraically from the known parameters of systems and the disturbing harmonic effect. The use of a symbolic (complex) description of mechanical systems under forced harmonic vibrations (in steady-state mode) allowed us to abandon the extremely cumbersome and time-consuming calculation algorithm associated with solving differential equations, and replace it with simpler and more visual algebraic operations. Due to this, the time of calculations is reduced significantly. Vector diagrams, not being a necessary component of the study of mechanical systems under harmonic influences, have substantial methodological significance, since they show quantitative and phase relations between the parameters of systems.

Cooling Effect of a MEMS Based Micro Capillary Pumped Loop for Chip-Level Temperature Control

2000 ◽  
Author(s):  
Jeffrey Kirshberg ◽  
Kirk Yerkes ◽  
Dave Trebotich ◽  
Dorian Liepmann
Keyword(s):  
Steady State ◽  
Temperature Control ◽  
Analytical Study ◽  
Mechanical Systems ◽  
Spot Size ◽  
Cooling Effect ◽  
Glass Wafer ◽  
Front Side ◽  
Capillary Pumped Loop ◽  
Micro Electro Mechanical Systems

Abstract Utilizing current Micro Electro Mechanical Systems (MEMS) technologies, a three-port micro-capillary pumped loop (micro-CPL) was designed, fabricated and tested to provide integral cooling to electronics or MEMS type devices. The two wafer design consists of one silicon and one borofloat glass wafer. An analytical study was used in determining the geometry of the device, including the evaporator dimensions (1000 μm × 2000 μm) and the length of the liquid and vapor lines (35 mm). Using laser spot heating, the finished device was run near steady-state. It was determined that the micro-CPL resulted in a backside cooling effect of at least 7 C when a laser delivering 7.5 W (+/− 0.2 W) with a spot-size diameter of 1.0 mm was focused on the front side of the evaporator region.

scholarly journals REACTANCES AND SUSCEPTANCES OF MECHANICAL SYSTEMS

2021 ◽  
pp. 64-75
Author(s):  
I.P. Popov ◽  
Keyword(s):  
Steady State ◽  
Mechanical System ◽  
Mechanical Systems ◽  
Harmonic Force ◽  
Parallel Connection ◽  
Electrical Circuits ◽  
Major Interest ◽  
Inert Body ◽  
Complex Mechanical Systems ◽  
External Harmonic Force

The classical solution to the problems associated with calculating the velocities and reactions of elements of complex mechanical systems under harmonic force consists in the compilation and integration of systems of differential equations and is rather cumbersome and time-consuming. In most cases, a steady state is of major interest. The purpose of this study is to develop essentially compact methods for calculating systems under steady-state conditions. The problem is solved by the methods which are typically used to calculate electrical circuits. Representation of harmonic quantities as rotating vectors in a complex plane and the operations with their complex amplitudes can greatly facilitate the calculation of arbitrarily complex mechanical systems under harmonic effects in the steady state. In the proposed method, a key role is played by mechanical reactance, resistance, and impedance for the parallel connection of consumers of mechanical power, as well as susceptance, conductance, and admittance for the serial one. At force resonance, the total reactance of the mechanical system is zero. This means that the system does not exhibit reactive resistance to the external harmonic force. At velocity resonance, the total susceptibility of the mechanical system is zero. This means that the system has infinitely high resistance to the external harmonic force. As a result, the stock of the source of harmonic force is stationary, although the inert body and the elastic element oscillate.

On the Steady State Motions Control Problem for Mechanical Systems with Relay Controllers

2021 ◽  
Vol 1 (1) ◽  
pp. 48-55
Author(s):  
Aleksandr Andreev ◽  
Olga Peregudova
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Asymptotic Stability ◽  
Control Problem ◽  
Mechanical System ◽  
Lyapunov Functions ◽  
Robot Manipulator ◽  
Mechanical Systems ◽  
Stabilization Problem ◽  
Stability Of The Solution

The paper presents the solution to the stabilization problem of steady state motions for a holonomic mechanical system by using relay controllers. This solution is achieved by proving new theorems on the asymptotic stability of the solution to a differential equation with a discontinuous right-hand side. The novelty of the theorems is based on the limiting inclusions construction and the use of semidefinite Lyapunov functions. As an example, the stabilization problem of steady-state motion for a five-link robot manipulator is solved by using relay controller.

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