scholarly journals Investigation of the forced spatial vibrations of a wood shaper, caused by rotor’s unbalance of its electric motor and by cutting forces

2020 ◽  
Vol 317 ◽  
pp. 02001
Author(s):  
Valentin Slavov ◽  
Georgi Vukov
Keyword(s):  
Mechanical System ◽  
Analytical Solutions ◽  
Electric Motor ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Damping Properties ◽  
System Of Differential Equations ◽  
Numerical Investigations ◽  
Matrix Modeling ◽  
Analysis And Synthesis

Mechanic-mathematical matrix modeling of the forced spatial vibrations of a wood shaper is performed in this study .The wood shaper is modeled as a mechanical system of three rigid bodies, which are connected by elastic and damping elements with each other and with the motionless floor. This mechanical system has 18 degrees of freedom. Formulas and algorithms are developed for computer calculating, analysis and synthesis of designing and investigating of this machine. This study renders an account the geometric, kinematic, mass, inertia, elastic and damping properties of the machine. A system of differential equations is derived. Analytical solutions are presented. The study presnts results of the numerical investigations of the forced spatial vibrations by using parameters of a particular machine. They allow to select parameters that reduce harmful vibrations for people and constructions.

scholarly journals Modelling and researching of forced spatial vibrations of axial fans

2019 ◽  
Vol 287 ◽  
pp. 03006
Author(s):  
Valentin Slavov ◽  
Georgi Vukov
Keyword(s):  
Mechanical System ◽  
Human Body ◽  
Degrees Of Freedom ◽  
Forced Vibrations ◽  
Rigid Bodies ◽  
Axial Fan ◽  
Analysis And Synthesis ◽  
Axial Fans ◽  
Standards And Regulations ◽  
Matrix Modelling

This work presents a mechanic - mathematical matrix modelling of the forced spatial vibrations of an axial fan. The axial fan is considered as a mechanical system consisting of three rigid bodies and with 18 degrees of freedom. The differential equations of the forced vibrations are derived. They take into account the mass, inertial, elastic, damping and geometric characteristics of this mechanical system. Algorithms are developed for computer calculating, analysis and synthesis of the design of this axial fan. These algorithms are a prerequisite for achieving the required operational properties of the fan and its compliance with the standards and regulations for vibrations’ impact on the human body. Calculations and results of the forced spatial vibrations are provided for specific parameters of the mechanical system.

scholarly journals Numerical simulation of oscillations of a nonlinear mechanical system with a spring-loaded viscous friction damper

2019 ◽  
Vol 265 ◽  
pp. 05030
Author(s):  
Viktor Nekhaev ◽  
Viktor Nikolaev ◽  
Marina Safronova
Keyword(s):  
Differential Equations ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
External Disturbance ◽  
Viscous Friction ◽  
Force Characteristic ◽  
Friction Damper ◽  
System Of Differential Equations ◽  
Nonlinear Force ◽  
Linear Spring

The dynamics of a mechanical system consisting of a parallel-connected main elastic element, an external disturbance compensator having a nonlinear force characteristic, and a viscous friction damper sprung by a linear spring are studied. The resulting system of differential equations describing the behavior of the system has one and a half degrees of freedom and has specific properties depending on the ratio of stiffness of the main spring and the spring suspension of a viscous friction damper. It is established that a single nonlinear system with one and a half degrees of freedom has either one or two harmonics. In the general solution of the system of differential equations, there are always two harmonics in the above-resonance zone, one of which is always equal to the disturbance frequency, and the second one is sufficiently close to the frequency k0. In the linear conservative case and the absence of suspension of the viscous friction damper, the natural frequency of the displacement of the system k0 =14.046 s-1.

scholarly journals MATHEMATICAL MODEL OF SPATIAL OSCILLATIONS OF A RAILWAY FOUR-AXLE AUTONOMOUS TRACTION MODULE

2021 ◽  
pp. 55-68
Author(s):  
František Bures
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Mechanical System ◽  
Traffic Safety ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Railway Track ◽  
Theoretical Studies ◽  
System Of Differential Equations ◽  
Spatial Oscillations

A description of the original mathematical model of spatial oscillations of a four-axle autonomous traction module during its movement along straight and curved sections of the railway track is proposed. In this case, the design of a four-axle autonomous traction module is presented as a complex mechanical system, and the track is considered as an elastic-viscous inertial system. The equations of motion were compiled using the Lagrange method of the ІІ kind. For each of the solids, the kinetic energy is determined by the Koenig theorem. The potential energy component is obtained by the Clapeyron theorem, as the sum of the energies accumulated in the elastic elements of the system during their deformations. The dissipative energy was also taken into account when compiling the equations of motion. Generalized forces that have no potential, in this case, include the forces of interaction between wheels and rails, which are determined using the creep hypothesis. It is important to note that the model takes into account the forces in the bonds between the bodies of the system and the spatial displacements of the rigid bodies of the mechanical system, taking into account possible restrictions. Moreover, the mathematical model developed by the author is a system of differential equations of the 100th order. This mathematical model is the base for further theoretical studies of the dynamics of railway four-axle autonomous traction modules in single motion or when moving as part of a train. To solve the resulting system of differential equations, the author develops special software that allows for complex theoretical studies of spatial oscillations of a four-axle autonomous tractionmodule to determine the indicators of its dynamic loading and traffic safety. 

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

scholarly journals An Efficient Contact Model for the Simulation of Cargo Airdrop Extraction Phase

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Leiming Ning ◽  
Jichang Chen ◽  
Mingbo Tong
Keyword(s):  
Degrees Of Freedom ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Dynamics ◽  
Moving Frame ◽  
Contact Friction ◽  
Practical Implementation ◽  
Contact Formulation ◽  
Efficient Code ◽  
Extraction Phase

A high-fidelity cargo airdrop simulation requires the accurate modeling of the contact dynamics between an aircraft and its cargo. This paper presents a general and efficient contact-friction model for the simulation of aircraft-cargo coupling dynamics during an airdrop extraction phase. The proposed approach has the same essence as the finite element node-to-segment contact formulation, which leads to a flexible, straightforward, and efficient code implementation. The formulation is developed under an arbitrary moving frame with both aircraft and cargo treated as general six degrees-of-freedom rigid bodies, thus eliminating the restrictions of lateral symmetric assumptions in most existing methods. Moreover, the aircraft-cargo coupling algorithm is discussed in detail, and some practical implementation details are presented. The accuracy and capability of the present method are demonstrated through four numerical examples with increasing complexity and fidelity.

Fuzzy Analysis of Geometric Tolerances Using Interval Method

2006 ◽  
Vol 220 (4) ◽  
pp. 489-497 ◽  
Author(s):  
W Wu ◽  
S S Rao
Keyword(s):  
Mechanical System ◽  
Current Approach ◽  
Distribution Functions ◽  
Manufacturing Cost ◽  
Mechanical Assembly ◽  
Geometric Dimensioning And Tolerancing ◽  
Analysis And Synthesis ◽  
Linear Interval ◽  
Linear Interval Equations ◽  
And Performance

The quality and performance of any mechanical system are greatly influenced by the GD&T (geometric dimensioning and tolerancing) used in its design. A proper consideration of the various types of tolerances associated with different components could not only satisfy the assembly requirements, but also minimize the manufacturing cost. To satisfy the design and functional specifications, one has to know how various tolerance patterns affect the manufacturability and assemblability of the designed parts. Therefore, a thorough understanding of how different forms of mechanical tolerances interact with each other becomes a must for designers and manufacturers. The effects of form, orientation, and position tolerances on the kinematic features and dimensions of mechanical systems are analysed using a new approach, based on fuzzy logic, in this article. In this approach, the α-cut method is used with the mechanical tolerances concerned as intervals. The proposed approach represents a more natural and realistic way of dealing with uncertain properties like geometric dimensions. A typical mechanical assembly system involving form, orientation, and position tolerances is used as an illustrative example. As the fuzzy approach leads to systems of non-linear interval equations, a modified Newton-Raphson method is developed for the solution of these equations. The current approach is found to be effective, simple, and accurate and can be extended to the analysis and synthesis of any uncertain mechanical system where the probability distribution functions of the uncertain parameters are unknown.

scholarly journals An Asymptotically Optimal NMPC Core for Multi Degrees of Freedom Rigid Bodies

2012 ◽  
Vol 45 (17) ◽  
pp. 207-212
Author(s):  
Chyon Hae Kim ◽  
Shimon Sugawara ◽  
Shigeki Sugano
Keyword(s):  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Asymptotically Optimal

A Novel 4D Chaotic System Based on Two Degrees of Freedom Nonlinear Mechanical System

2018 ◽  
Vol 73 (7) ◽  
pp. 595-607 ◽  
Author(s):  
Sezgin Kacar ◽  
Zhouchao Wei ◽  
Akif Akgul ◽  
Burak Aricioglu
Keyword(s):  
Mechanical System ◽  
Chaotic System ◽  
Degrees Of Freedom ◽  
Electronic Circuit ◽  
Chaotic Behaviour ◽  
Two Degrees Of Freedom ◽  
Nonlinear Mechanical System ◽  
Linear Mechanical System ◽  
Low Amplitude ◽  
The Mathematical Model

AbstractIn this study, a non-linear mechanical system with two degrees of freedom is considered in terms of chaos phenomena and chaotic behaviour. The mathematical model of the system was moved to the state space and presented as a four dimensional (4D) chaotic system. The system’s chaotic behaviour was investigated by performing dynamic analyses of the system such as equilibria, Lyapunov exponents, bifurcation analyses, etc. Also, the electronic circuit realisation is implemented as a real-time application. This system exhibited vibration along with noise-like behaviour because of its very low amplitude values. Thus, the system is scaled to increase the amplitude values. As a result, the electronic circuit implementation of the 4D chaotic system derived from the model of a physical system is realised.

Generalized Abbe Principle: Position Error Propagation in Machine Elements

1996 ◽  
Author(s):  
Joseph Pegna
Keyword(s):  
Error Propagation ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Statistical Characterization ◽  
Physical Limit ◽  
Potential Applications ◽  
Machine Elements ◽  
Tolerance Verification ◽  
Precision Machines

Abstract In the quest for ever finer levels of technology integration, mechanical linkages reach their precision limits at about 5micrometers per meter of workspace. Beyond this physical limit, all six dimensional degrees of freedom need to be precisely ascertained to account for mechanical imperfections. This paper substantiates Wu’s vision of “precision machines without precision machinery.” A formulation and statistical characterization of position and orientation error propagation in rigid bodies are presented for two extreme models of measurement. It is shown that error distribution is uniquely dependent upon the design of the measurement plan. The theoretical foundations presented were evolved in the course of designing precision machinery. Other potential applications include: fixture design, metrology, and geometric tolerance verification.

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