Vibrations Of Mechanical Systems Research Articles

Spectral-based direct multi-substructure analysis of mechanical system vibration response

A new spectral-based multi-substructure theory is formulated to compute the frequency responses of mechanical systems that are subdivided into multiple inter-connected substructures. The proposed approach employs the free substructure frequency response functions at the coupling, response and excitation coordinates of interest to construct the complete system model using a single efficient coupling step. Even though this proposed approach is conceptually similar to the conventional transfer path analysis, it is more extensive because of the capability to analyze structural systems with arbitrary numbers of substructures and coupling coordinates. Hence, the proposed methodology can be applied to treat complex multi-substructure mechanical structures commonly found in automotive and aerospace systems. In the present study, several lumped parameters mass-spring-damper systems are analyzed to validate the proposed theory. The comparison results show excellent agreement between the multi-substructure predictions and the single complete system calculations.

Method of Static Characteristics Calculation of Vibroinsulators with Rectilinear and Circular Working Sections in a Non-Linear Approach

An implementation of full-metal vibroinsulators is one of the most effective measures for an elimination of harmful effects of vibration in mechanical systems. However, in a contemporary literature an issue of an analytical calculation of vibroinsulators of that type, considering a non-linearity of the characteristics, is addressed insufficiently. In the presented study, by an implementation of exact theory of bending of elastic rods, the methodology of load characteristics calculation of full-metal vibroinsulators with elastic elements of rectilinear and circular shape of initial axial lines was developed. A groundlessness of Euler equation's implementation was demonstrated in a case of large displacement of linear rods, commensurable with their length. The method allows to increase designer's capabilities, to improve an accuracy of the calculation and to reduce time spent for a final adjustment of a product, which will ultimately lead to cost reduction final products.

Determination of mass, damping coefficient, and stiffness of production system using convolution integral

Discrete event simulation (DES) is most widely used tool for modelling complex production systems. DES model requires skilful mapping of actual production process in a framework used for DES modelling. It also calls for extensive data collection for arriving at probability distributions followed by the time required by various activities involved in production processes and also the probability distribution of various occurrences affecting production process. System dynamics (SD) has also been used to model production system. SD model requires forming causal loop model (stock–flow diagram) showing interrelated influential variables affecting production process, their rates and mathematical relation between cause and effect. Continuous and discrete flow models had also been used for modelling production system. This work proposes a tool for simulating the production output which is simpler as compared to these two techniques. This investigation attempts to establish relationship between inputs to the production system, state of production system and number of units produced. Second-order differential equation analogizing production system with mechanical vibration system is devised and the constants of differential equation are determined. These constants signify mass, damping factor and natural frequency of mechanical vibration system. Differential equation formed for production system helps to simulate the production output in response to forces such as supply order, breakdown and preventive maintenance.

Method of Static Characteristics Calculation of Adjustable Two-Ring Type Full-Metal Vibroinsulators in a Non-Linear Approach

Full-metal vibroinsulators with circular elements are widely spread and effectively reduce a harmful impact of vibration in mechanical systems. However, in a contemporary literature an issue of a regulation of that kind of vibroinsulators and their study, considering non-linearity of the characteristics, is addressed insufficiently. In the presented study by a joint implementation of Mohr's method and finite element method the method of a calculation of loading characteristics of adjustable full-metal vibroinsulators with elastic elements in the form of an ellipse and a system of two ellipses was developed. Broad (in a few hundreds of times) capabilities to regulate their rigidity characteristics were demonstrated. The presence of zone of quasi-zero rigidity is detected. The method allows to accurately determine parameters of a vibroinsulator, which increases quality of final products.

Passive Reduction in Vibration Considering the Desired Amplitude in the Case of Damping Proportional to the Mass

The paper presents and solves the problem of a discrete reduction in vibration in mechanical systems depending on the desired dynamic properties. The methods for determining the passive values of vibration elements reducing vibrations to the desired amplitude value were formulated. Synthesis was done, using the methods of a discrete synthesis of vibration systems and introducing an assumption concerning the damping element existing in the required system and taking a rheological model as a mass damping model.

ドライブトレインベンチの低慣性化制御技術と実路走行負荷模擬制御への応用

Drivetrain bench system is utilized to test powertrain components of a vehicle such as transmission, torque converter, etc. Conventional drivetrain bench system emulates the moment of inertia of a vehicle body. In order to simulate real road loads of the powertrain components, it is necessary that the dynamometer of the drivetrain bench emulates the moment of inertia of a tire. The moment of inertia of the tire is lower than the moment of inertia of the dynamometer. So, the dynamometer needs low inertia emulation control. The drivetrain bench is mechanical vibration system. The principal factor of the vibraion is stiffness of a drive shaft. In this paper, we propose a low inertia emulation control method for vibration system and its application to simulating real road loads. Basic idea of the proposed low inertia emulation control method is feedforward of torque that is necessary for accelerating emulated inertia. By numerical simulations, it is shown that real road loads tests can be implemented with the proposed control method.

Application of Electric Subsystem as Implementation of Reduction of Mechanical Vibrations

This work presents methods of reduction of the vibration of mechanical systems by means of active elements as well as examples of implementation of active reduction of vibration by means of electrical elements [1], [2]. This work also describes a structural and parametric synthesis, which can be defined as the design of systems meeting specific requirements. These requirements refer to the frequency values of the systems’ vibration. The presented approach i.e. a non-classical synthetic method applied in designing mechanical systems with elements reducing unwanted vibrations. As a result of the synthesis, one can obtain the structure and parameters of the system of required properties. The synthesis may also be applied to modify the already existing systems in order to achieve a desired result [1–3].

Research of shaft seals made of porous wire «metal rubber» material

The possibility of using elastic porous elements made of "metallic rubber" (MR) as rotor seals is discussedin the paper. The technology of manufacturing of such elements is developed for the mechanical dampingof vibration in mechanical systems where they are widely used. Comparative analysis of rating curves of labyrinth,honeycomb, brush seals and seals made of MR material has shown that seals made of MR material havebetter rating curves than labyrinth and honeycomb seals, but slightly worse ones than those of the brush design.Therefore, the use of porous MR material shows promise for making parts of the seals for gas or oil cavities ofrotors. Seals made of MR material are designed for optimum performance in the most demanding aerospace sealingapplications where high speed and vibration are the norm, and where axial shaft movement takes place. Aninstallation imitating conditions of using rotor seals is designed for the purpose of analyzing seals made with theuse of MR material.

Effects of Mechanical Resonance on Vibrations of Mechanical Systems With Permanent Magnet Machines

In this paper, we describe the effects of mechanical resonance on the vibrations of mechanical systems with permanent magnet (PM) machines. Electromagnetic vibration sources produced by a PM machine were calculated using finite element analysis (FEA) solutions. Subsequently, the harmonic orders related to the mechanical vibrations of the PM machine itself were investigated experimentally by driving the machine at various rotor speeds. To investigate the effects of mechanical resonance, a cantilever beam whose mechanical resonance frequency can be changed by adjusting its length was employed. Finally, the resonance condition was achieved by matching the natural frequency of the cantilever beam with the vibration frequencies produced by the PM machine. The natural frequency mode shapes were validated using 3-D FEA solutions, and the results were confirmed through modal analyses of the frequency response function results from impact tests. Comparisons of the measured vibration data of the PM machine with and without the cantilever demonstrated that mechanical resonance significantly influenced the vibrations of mechanical systems using PM machines.

Fretting instability characteristics for gear shaft shoulder

In order to solve fretting instability problem of gear shaft shoulder due to torsional vibration in mechanical system, the mathematical model of fretting instability vibration of gear shaft shoulder was established by adopting the method of combining kinematics and tribology, and the numerical analysis was applied to the fretting instability mechanism of gear shaft shoulder by introducing the friction instability damping ratio. The numerical results show that the main factors causing the unstable and vibrating gear shaft shoulder are the large tightening torque and too large static friction coefficient. The reasonable values of the static friction coefficient, the amount of interference and tightening torque can effectively mitigate the fretting instability phenomenon of gear shaft shoulder. The experimental results verify that damping plays a significant role in eliminating the vibration of gear shaft control system.

Control of Vibration of Mechanical Systems Using Electrical Subsystems

The reduction or elimination of undesired vibration can be achieved by applying various methods. The most commonly applied methods are: passive, semi-active and active.This work presents methods of reduction of the vibration of mechanical systems by means of active elements as well as examples of implementation of reduction of vibration by means of electrical elements. This work also introduces a structural and parametric synthesis, which can be defined as the design of systems meeting specific requirements. These requirements refer to the frequency values of the systems vibration. The presented approach i.e. a non-classical synthetic method applied in designing mechanical systems, one (as early as at the design and construction stage) may verify future systems. As a result of the synthesis one can obtain the structure and parameters of the system of required properties. The synthesis may also be applied to modify the already existing systems in order to achieve a desired result.

Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and Groebner bases

This paper is devoted to the study of vibration of mechanical systems with geometric nonlinearities. The harmonic balance method is used to derive systems of polynomial equations whose solutions give the frequency component of the possible steady states. Groebner basis methods are used for computing all solutions of polynomial systems. This approach allows to reduce the complete system to an unique polynomial equation in one variable driving all solutions of the problem. In addition, in order to decrease the number of variables, we propose to first work on the undamped system, and recover solution of the damped system using a continuation on the damping parameter. The search for multiple solutions is illustrated on a simple system, where the influence of the retained number of harmonic is studied. Finally, the procedure is applied on a simple cyclic system and we give a representation of the multiple states versus frequency.

Vibration suppression of four degree-of-freedom nonlinear vehicle suspension model excited by the consecutive speed humps

It is well known that chaos phenomenon is harmful for a nonlinear mechanical vibration system. For a running vehicle, chaotic vibrations may lead to early damage to road and the component of vehicle or even bring physical injury to crew member. In this paper, we first studied the possibility of chaotic vibration of the four degree-of-freedom half vehicle model under consecutive speed control humps on the highway. Then, a direct variable feedback control is proposed to eliminate the influence of chaos on vehicle nonlinear vibrations and how to select proper control parameters is discussed.

The Optimal Control Method of Impulse Response in Prosthetic Leg

Passive control and semi-active control of vibration in mechanical systems have recently successfully been used in automobiles and airplanes suspension systems. These control techniques are able to guarantee the performances of all vibration structures. Unfortunately, the knowledge and data has not been readily applied to human prosthetics. The information collected can be directly applied to accelerate research into dampening for prosthetics. A focus of this paper is on modeling and controlling vibrations by a given impulse onto prosthetic legs. Simulations of using passive control and idealized skyhook dampening are using Matlab to complete. Through model analysis, control variable, simulation procedures and comparison of two modeling, the models have been refined and with idealized skyhook dampening suspension provide significant improvement of the body characteristics compared with passive suspensions.

進化計算を用いた機械システムのロバスト振動制御

This paper presents a feedforward control technique for the suppression of residual vibrations in mechanical systems with parameter variations. We deal with the Point-To-Point (PTP) motion of the pendulum system consisting of an unactuated pendulum attached to the end of a horizontal rotating arm, and demonstrate the effectiveness of the proposed method through numerical simulations and experiments.

Natural Oscillations of Viscoelastic Lamellar Mechanical Systems with Point Communications

We investigated the natural oscillations of dissipative inhomogeneous plate mechanical systems with point connections. Based on the principle of virtual displacements, we equate to zero the sum of all active work force, including the force of inertia which obtain equations vibrations of mechanical systems. Frequency equation is solved numerically by the method of Muller. According to the result of numerical analysis we established nonmonotonic dependence damping coefficients of the system parameters.

Evaluation of some improper integrals with aid of the determinant of the Hurwitz matrix

A relation between some improper integrals of complex variable and a ratio of two determinants of n-th order matrices is derived in the presented paper. (A determinant of the Hurwitz matrix is a denominator of this ratio.) Moreover, a similar relation with integration along the imaginary axis is proved as a corollary. An algorithm implemented in Mathematica software for evaluation of integrals mentioned above is presented. Obtained results are suitable for calculation of some quantities used in random vibration of mechanical systems, for calculation of the quadratic performance index in closed loop systems in process control, for calculation of root mean square error - a statistical measure that represents the dierence between measured and predicted data points, etc.

Warren Blazier and his contributions to noise rating criteria

Warren Blazier was well known for his work with sound and vibration in mechanical systems, e.g., HVAC equipment. As such, he was particularly active at ASHRAE in addition to the ASA meetings. Although I was always focused more on the “room acoustics” side of the design, I none-the-less offered to help edit the 1999 ASHRAE Handbook chapter 43 with Warren and Chuck Ebbing. This section dealt with “Indoor Sound Criteria,” and what an eye opening event this turned out to be. You might say that I jumped into the fire as there was an ongoing “tug-of-war” over which rating system should be adopted to describe background noise in buildings from mechanical systems. NC, RC, RC mark II, NCB … several of these had been used up to this point and lots of controversy existed as to what to include in the re-write. A somewhat historic special meeting of ASHRAE TC2.6 was held in Boston on the evening of Sunday 27 June 1997 from 3:30 to 6:30 pm where this was discussed to resolve the issue. Both Warren and Leo Beranek were asked to make presentations on the merits of the competing approaches. And this is what was decided!!

Minimizing residual vibrations for non-zero initial states: Application to an emergency stop of a crane

This paper presents an approach to design command inputs for the reduction of residual vibrations in mechanical systems for nonzero initial states. The technique starts with the development of a standard input shaper in a second order oscillator, and adds the initial states of the system to the formulation. However, it is proven that the obtained input shaper does not guarantee a null residual vibration when it is convolved with any unshaped command. To obtain an analytically proven zero-vibration response, it is required to include the parameters that characterize the response of the system to a selected normalized unshaped command in the formulation. By introducing an appropriate processing time delay and by measuring the initial states using a feedback sensor, the proposed method has been applied in a real time scenario where an emergency stop of a crane is required, assuming that initially the payload is swaying. The analyzed systems are those that can be modeled as discrete linear ones and can be described with constant parameter motion equations. Experimental results show the efficacy of the developed method with its application to a scaled crane test platform.

Electrical Elements in Reduction of Mechanical Vibrations

This work presents methods of reduction of the vibration of mechanical systems by means of active elements as well as examples of implementation of active reduction of vibration by means of electrical elements [. This work also describes a structural and parametric synthesis, which can be defined as the design of systems meeting specific requirements. These requirements refer to the frequency values of the systems vibration. The presented approach i.e. a non-classical synthetic method applied in designing mechanical systems, one (as early as at the design and construction stage) may verify future systems [1-. This work presents the description of vibration reduction methods. The most popular methods are passive, active and semi-active. An important aspect of this work is the presentation of several possibilities of the physical implementation of active subsystems. In examples active subsystems consisted of the following electric elements is coil with a movable core. In this work is presents influence of electrical subsystem to basic mechanical system. Designer should analyse the resultant systems and investigate the interaction between the subsystems and the basic system [4-.