Dynamic Stability of the Flexible Connecting Rod of a Slider Crank Mechanism

1986 ◽  
Vol 108 (4) ◽  
pp. 487-496 ◽  
Author(s):  
Iradj G. Tadjbakhsh ◽  
Christos J. Younis
Keyword(s):  
Material Properties ◽  
Floquet Theory ◽  
Equation Of Motion ◽  
Connecting Rod ◽  
Linear Ordinary Differential Equations ◽  
Stability And Instability ◽  
Regions Of Stability ◽  
Modal Coordinates ◽  
Crank Mechanism ◽  
Input Torque

The partial differential equation of motion of the flexible connecting rod of a slider crank is derived, under the assumption of small deflections. Application of the Galerkin procedure, leads to a system of linear ordinary differential equations, with respect to the modal coordinates of vibration of the rod. For periodic solutions, the foregoing system reduces to a system of coupled Hill equations. Application of Floquet theory, determines those values of the parameters: speed, input torque, geometry, and material properties that constitute the boundaries between the regions of stability and instability.

Dynamic Analysis of a Slider-Crank Mechanism With Flexible Connecting Rod and Viscous Friction

2001 ◽  
Author(s):  
Jinfu Zhang ◽  
Qingyu Xu ◽  
Ling Zhang
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Elastic Deformation ◽  
Coupling Effect ◽  
Lagrange Equation ◽  
Viscous Friction ◽  
Equation Of Motion ◽  
Body Motion ◽  
Connecting Rod ◽  
Crank Mechanism

Abstract The equation of motion for the slider-crank mechanism with flexible connecting rod and viscous friction are formulated using Lagrange equation. Viscous friction and coupling effect between rigid body motion and elastic deformation are considered in the formulation. Numerical results show that viscous friction and flexibility of connecting rod have effects on motion of the mechanism.

scholarly journals The Rabi problem with elliptical polarization

2020 ◽  
Vol 75 (11) ◽  
pp. 937-962
Author(s):  
Heinz-Jürgen Schmidt
Keyword(s):  
Floquet Theory ◽  
Equation Of Motion ◽  
Quantum Spin ◽  
Heun Equation ◽  
Elliptical Polarization ◽  
Third Order ◽  
Polynomial Coefficients ◽  
Resonance Frequencies ◽  
Classical Quantum ◽  
Elliptically Polarized

AbstractWe consider the solution of the equation of motion of a classical/quantum spin subject to a monochromatical, elliptically polarized external field. The classical Rabi problem can be reduced to third-order differential equations with polynomial coefficients and hence solved in terms of power series in close analogy to the confluent Heun equation occurring for linear polarization. Application of Floquet theory yields physically interesting quantities like the quasienergy as a function of the problem’s parameters and expressions for the Bloch–Siegert shift of resonance frequencies. Various limit cases are thoroughly investigated.

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yan-Shin Shih ◽  
Chen-Yuan Chung
Keyword(s):  
Governing Equation ◽  
Moving Boundary ◽  
Beam Theory ◽  
Crack Model ◽  
Breathing Crack ◽  
Connecting Rod ◽  
Bernoulli Beam ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Crank Mechanism

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

scholarly journals THREE-DIMENSIONAL STABILITY ANALYSIS OF OPEN CHANNEL FLOW OVER AN ERODIBLE BED

1971 ◽  
Vol 2 (2) ◽  
pp. 93-108 ◽  
Author(s):  
FRANK ENGELUND ◽  
JØRGEN FREDSØE
Keyword(s):  
Open Channel ◽  
Three Dimensional ◽  
Open Channel Flow ◽  
Present Theory ◽  
Bed Load ◽  
Lower Range ◽  
First Order ◽  
Stability And Instability ◽  
Regions Of Stability ◽  
Bed Waves

The formation of ripples and dunes (lower range bed waves) is assumed to be related to the transport of sediment as bed load. From the present theory it is concluded that the formation of the upper range bed configurations (standing waves, antidunes) may be explained on the assumption that the predominant part of the sediment transport is in suspension. The paper presents a mathematical model of the formation of double-periodic antidunes, first-order potential flow theory being applied. It differs from previous models in taking account of the non-uniform distribution of the suspended load. The theory predicts regions of stability and instability. Results are compared with measurements made by different observers.

scholarly journals Design of a prototype of an engine mechanism with rotating cylinders

2020 ◽  
Vol 318 ◽  
pp. 01004
Author(s):  
Miroslav Blatnický ◽  
Ján Dižo
Keyword(s):  
High Speed ◽  
Cooling System ◽  
Ambient Air ◽  
Combustion Engines ◽  
Connecting Rod ◽  
Rotating Cylinders ◽  
Liquid Cooling ◽  
Working Cycle ◽  
Liquid Cooling System ◽  
Crank Mechanism

In this article, authors focus on the design and construction of a real prototype of an engine mechanism with rotating cylinders and its using mainly in piston combustion engines. It is assumed, that the normal force of a piston will be completely eliminated, because the swing angle of a connecting rod will equal to zero during the whole working cycle, since the connecting arm of the piston moves just the cylinder axis. It will by allowed by the conceptual design of the mechanism presented in this article. As rotating blocks of cylinders concurrently act as a flywheel, it is proposed, that in this way there is possible to save the mass of additional flywheels. Moreover, liquid cooling system is not necessary, because the rotating cylinders sufficiently transfer heat to ambient air. In addition, the output of torque will be reached without necessity of gear transmission, which results to decreasing of needs of mechanism lubrication. Other advance of the designed mechanism are two outputs. The first output is low-speed and it goes out from rotating cylinders, i. e. from the slider-crank mechanism with revolutions n1. The other output is high-speed, from the crankshaft with revolutions n2. Because of more favourable properties of the mechanism, authors have decided to create a real device to confirm all mentioned advantages of the mechanism by the suitable way.

Vibrations of Elastic Connecting Rod of a High-Speed Slider-Crank Mechanism

1971 ◽  
Vol 93 (2) ◽  
pp. 636-644 ◽  
Author(s):  
Peter W. Jasinski ◽  
Ho Chong Lee ◽  
George N. Sandor
Keyword(s):  
Small Parameter ◽  
High Speed ◽  
Elastic Stability ◽  
Method Of Averaging ◽  
Connecting Rod ◽  
Transverse Vibrations ◽  
Elastic Bar ◽  
The Moment ◽  
Steady State Solutions ◽  
Crank Mechanism

The research involved in this paper falls into the area of analytical vibrations applied to planar mechanical linkages. Specifically, a study of the vibrations, associated with an elastic connecting-bar for a high-speed slider-crank mechanism, is made. To simplify the mathematical analysis, the vibrations of an externally viscously damped uniform elastic connecting bar is taken to be hinged at each end (i.e., the moment and displacement are assumed to vanish at each end). The equations governing the vibrations of the elastic bar are derived, a small parameter is found, and the solution is developed as an asymptotic expansion in terms of this small parameter with the aid of the Krylov-Bogoliubov method of averaging. The elastic stability is studied and the steady-state solutions for both the longitudinal and transverse vibrations are found.

Failure Process and Mechanism Analysis for the Connecting Rod of Diesel Engine

2012 ◽  
Vol 463-464 ◽  
pp. 1597-1600
Author(s):  
Ying Kui Gu ◽  
Kang Hu ◽  
Jing Li
Keyword(s):  
Diesel Engine ◽  
Material Properties ◽  
Treatment Process ◽  
Failure Process ◽  
Organization Structure ◽  
Scientific Basis ◽  
Mechanism Analysis ◽  
Connecting Rod ◽  
Fault Mechanism ◽  
Physical And Chemical

The operational fault of diesel engine caused by losing the required function in running is a random phenomenon. It needs to collect a large number of fault samples and reliability data to reveal the fault occurrence rule and describe it with mathematical method. In this paper, the fault law and mechanism of the engine connecting rod were researched by the physical and chemical analysis of the fault samples. The fault reasons and the fault mechanism can be found through the analysis of the organization structure, material properties, process features, heat treatment process and other reliability information of the fault sample. It can provide scientific basis for the failure exclusion as well as the optimization and improvement of connecting rod structure.

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