Stability and Steady-State Vibrations in a High-Speed Slider-Crank Mechanism

1970 ◽  
Vol 37 (4) ◽  
pp. 1069-1076 ◽  
Author(s):  
P. W. Jasinski ◽  
H. C. Lee ◽  
G. N. Sandor
Keyword(s):  
Steady State ◽  
Small Parameter ◽  
High Speed ◽  
Analytical Study ◽  
Elastic Stability ◽  
Connecting Rod ◽  
Concentrated Mass ◽  
Transverse Vibrations ◽  
Steady State Solutions ◽  
Crank Mechanism

The research presented in this paper is an analytical study of the vibrations associated with planar mechanical linkages. Specifically, the vibrations of a high-speed slider-crank mechanism with a uniform elastic connecting rod and a rigid crank are studied. The elastic connecting rod, with distributed mass, is taken to be externally, viscously damped with a concentrated mass present at its sliding end. The equations governing the longitudinal and transverse vibrations of the elastic connecting rod 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 of the connecting rod are obtained.

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.

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.

Member Initial Curvature Effects on the Elastic Slider-Crank Mechanism Response

1982 ◽  
Vol 104 (1) ◽  
pp. 159-167 ◽  
Author(s):  
M. Badlani ◽  
A. Midha
Keyword(s):  
Steady State ◽  
Natural Frequency ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Beam Theory ◽  
Connecting Rod ◽  
Initial Curvature ◽  
Curvature Effects ◽  
Transient Solutions ◽  
Crank Mechanism

Parametric vibration of initially curved columns loaded by axial-periodic loads has received considerable attention, concluding that regions of instability exist and that excitation frequencies less than the natural frequency of the principal resonance may occur. Recent publications have cautioned against the use of curved members in machines designed for precise operation, suggesting a detrimental coupling of the longitudinal and transverse deformations. In this work, the dynamic behavior of a slider-crank mechanism with an initially curved connecting rod is investigated. Governing equations of motion are developed using the Euler-Bernoulli beam theory. Both steady-state and transient solutions are determined, and compared with those obtained for the mechanism possessing a geometrically perfect (straight) connecting rod. A very small initial curvature is shown to cause a significantly greater steady-state response. The magnification in its transient response is shown to be even greater than that due to a straight connecting rod. Additionally, an excitation frequency less than the natural frequency is also shown to occur.

scholarly journals The Geometry of Power Systems Steady-State Equations– Part I: Power Surface

2020 ◽  
pp. 37-46
Author(s):  
B. Ayuev ◽  
V. Davydov ◽  
P. Erokhin ◽  
V. Neuymin ◽  
A. Pazderin
Keyword(s):  
Steady State ◽  
Power Systems ◽  
Power System ◽  
Power Flow ◽  
Analytical Study ◽  
State Theory ◽  
Steady States ◽  
State Equations ◽  
Feasibility Region ◽  
Steady State Solutions

Steady-state equations play a fundamental role in the theory of power systems and computation practice. These equations are directly or mediately used almost in all areas of the power system state theory, constituting its basis. This two-part study deals with a geometrical interpretation of steady-state solutions in a power space. Part I considers steady states of the power system as a surface in the power space. A power flow feasibility region is shown to be widely used in power system theories. This region is a projection of this surface along the axis of a slack bus active power onto a subspace of other buses power. The findings have revealed that the obtained power flow feasibility regions, as well as marginal states of the power system, depend on a slack bus location. Part II is devoted to an analytical study of the power surface of power system steady states.

A Variational Principle for the Hygrothermoelastodynamic Analysis of Mechanism Systems

1987 ◽  
Vol 109 (3) ◽  
pp. 294-300 ◽  
Author(s):  
C. K. Sung ◽  
B. S. Thompson
Keyword(s):  
High Speed ◽  
High Performance ◽  
Fibrous Composite ◽  
Equations Of Motion ◽  
Problem Definition ◽  
Theoretical Development ◽  
Connecting Rod ◽  
Rigid Body Motions ◽  
Crank Mechanism ◽  
Approximate Equations

A variational theorem is presented that may be employed for systematically establishing the equations governing the dynamic response of flexible planar linkage mechanisms simultaneously subjected to both mechanical and hygrothermal loadings. This theoretical development is motivated by recent research advocating that high-speed mechanisms should be fabricated in polymeric fibrous composite materials in order to achieve high-performance characteristics. The constitutive behavior of some of these materials is, however, dependent upon the ambient environmental conditions, and hence mathematical models must be developed in order to predict the response of mechanism systems fabricated with these materials. This class of mechanism systems is modeled herein as a set of continua in which elastic deformations are superimposed upon gross rigid-body motions. By permitting arbitrary independent variations of the system parameters for each link, approximate equations of motion, energy balance, mass balance, and boundary conditions may be systematically constructed. As an illustrative example, the derivation of a problem definition for the flexible connecting-rod of a slider-crank mechanism subjected to hygrothermal loading is presented.

Synthesis and Steady State Analysis of High-Speed Elastic Cam-Follower Linkages With Concentrated Masses: Part I — Theory

1991 ◽  
Author(s):  
Hsin-Ting J. Liu ◽  
Donald R. Flugrad
Keyword(s):  
Steady State ◽  
Iterative Procedure ◽  
High Speed ◽  
Linear Ordinary Differential Equations ◽  
Periodic Linear ◽  
Cam Follower ◽  
Cam Profile ◽  
Concentrated Masses ◽  
Design Speed ◽  
Steady State Solutions

Abstract A cam driving a lumped inertia through a massless, elastic, slider-crank follower linkage with two concent rated masses located at the pin joints is considered. An iterative procedure taking the elasticity, damping, and changing geometry of the linkage into account is developed for synthesizing the cam profile to produce a desired output motion at a given design speed. The steady state solutions for the inhomogeneous, periodic, linear, ordinary differential equations are solved numerically by Hsu’s method.

Dynamic Response of a High-Speed Slider-Crank Mechanism With an Elastic Connecting Rod

1975 ◽  
Vol 97 (2) ◽  
pp. 542-550 ◽  
Author(s):  
S.-C. Chu ◽  
K. C. Pan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Response ◽  
Ordinary Differential Equations ◽  
High Speed ◽  
Polynomial Method ◽  
Connecting Rod ◽  
Partial Differential ◽  
Weighted Residuals ◽  
Crank Mechanism

To achieve the performance of a mechanism to a higher degree of accuracy requires that the elastic deformations of a member in a mechanism under dynamic loading conditions be taken into account. Coupled nonlinear governing partial differential equations have been derived for transverse and longitudinal vibrations of an elastic connecting rod in a slider-crank mechanism operating at high speed conditions. The derived coupled governing nonlinear partial differential equations of motion were transformed into ordinary differential equations by use of the Kantorovich method and the method of weighted residuals. The resulting coupled ordinary differential equations were solved numerically by use of the piecewise polynomial method and the fourth-order Runge-Kutta method. The dynamic response of the system has been investigated on the basis of natural frequencies of the first mode free vibrations, the ratios of the length of crank to the length of connecting rod, viscous damping, and rotating speeds of crank. These parameters can be used by the designer to predict the vibrations of an elastic mechanism under high-speed conditions.

Effect of Internal Material Damping on the Dynamics of a Slider-Crank Mechanism

1983 ◽  
Vol 105 (3) ◽  
pp. 452-459 ◽  
Author(s):  
M. Badlani ◽  
A. Midha
Keyword(s):  
Steady State ◽  
Transverse Vibration ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Mathieu Equation ◽  
Perturbation Approach ◽  
Material Damping ◽  
Connecting Rod ◽  
The Stability ◽  
Crank Mechanism

A study of the effect of internal material damping on the dynamic response behavior of a slider-crank mechanism is presented in this paper. In developing the governing equations of motion, an assumption of a linear viscoelastic model for the connecting rod is made. A perturbation approach is utilized for reducing these coupled axial and transverse nonlinear equations to a nonhomogeneous damped Mathieu equation, describing the transverse vibration of the connecting rod. Both steady-state and transient solutions are determined and compared to those obtained from the use of an undamped connecting rod. It is demonstrated that the viscoelastic material damping can have significant influence, both favorable and adverse, in attempting to attenuate the steady-state and transient response of the connecting rod. The response is computed for several combinations of the excitation parameter and the frequency ratio. The stability of the transverse vibration of the connecting rod is also investigated in this paper.

Conventional Versus Self-Steering Radial Trucks for High-Speed Passenger Trains

1982 ◽  
Vol 104 (4) ◽  
pp. 290-296 ◽  
Author(s):  
G. R. Doyle
Keyword(s):  
Steady State ◽  
High Speed ◽  
Analytical Study ◽  
The Self ◽  
Lateral Stability ◽  
Rail Head ◽  
Passenger Trains ◽  
Design Speed ◽  
Wear Index

The performance of self-steering, articulated, and nonarticulated trucks for high-speed passenger trains was compared to a conventional passenger truck. Lateral stability and steady state curving analyses were used to evaluate a design speed of 200 km/h (125 mi/h), and a wheel tread/rail head wear index in curves. Based on the results of this analytical study, the self-steering articulated truck would reduce the wear index in curves by a factor of two. However, the use of a “relaxation” device in the secondary yaw suspension of the conventional nonarticulated truck would reduce the wear index in curves by a factor of four.

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