An Analytical Study of the Dynamics of an Elastic Linkage

1966 ◽  
Vol 88 (3) ◽  
pp. 311-317 ◽  
Author(s):  
A. H. Neubauer ◽  
R. Cohen ◽  
A. S. Hall
Keyword(s):  
Physical Parameter ◽  
Analytical Study ◽  
Equations Of Motion ◽  
Connecting Rod ◽  
Numerical Techniques ◽  
Dimensionless Parameters ◽  
Vibrational Characteristics ◽  
Speed Parameter ◽  
Vibrational Activity ◽  
Crank Mechanism

The transverse vibrational characteristics of the connecting rod in a slider-crank mechanism are investigated. The equations of motion are derived, simplified, and solved. For the solution, two different numerical techniques are employed and correlation is achieved. Two dimensionless parameters, S the speed parameter and Z the physical parameter, arise during the derivation of the equations of motion. These parameters can be used by the designer as an indication of the vibrational activity of the mechanism.

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.

Dynamics of a Linkage Mechanism Using Sample Entropy

2020 ◽  
Vol 896 ◽  
pp. 67-74
Author(s):  
Dan B. Marghitu ◽  
Edmon Perkins
Keyword(s):  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Sample Entropy ◽  
Linkage Mechanism ◽  
Numerical Techniques ◽  
Motor Torque ◽  
Angular Velocities ◽  
Nonlinear Equations Of Motion ◽  
Crank Mechanism ◽  
Generalized Coordinate

The dynamics of a slider-crank mechanism is developed using Kane's equations of motion. The motor torque is a function of the derivative of the generalized coordinate. The nonlinear equations of motion are solved using MATLAB numerical techniques. The sample entropy is calculated for different angular velocities of the crank.

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.

A methodology for dynamic behavior analysis of the slider-crank mechanism considering clearance joint

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yu Chen ◽  
Jun Feng ◽  
Qiang He ◽  
Yu Wang ◽  
Yu Sun ◽  
...  
Keyword(s):  
Mechanical System ◽  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Response Analysis ◽  
Force Model ◽  
Connecting Rod ◽  
Revolute Clearance Joint ◽  
Clearance Joint ◽  
Contact Impact ◽  
Crank Mechanism

Abstract The slider-crank mechanism is used widely in modern industrial equipment whereby the contact-impact of a revolute clearance joint affects the dynamic behavior of mechanical systems. Combining multibody dynamic theory and nonlinear contact theory, the computational methodology for dynamic analysis of the slider-crank mechanism with a clearance joint is proposed. The differential equations of motion are obtained considering the revolute clearance joint between the connecting rod and slider. In the mechanical system, the contact force is evaluated using the continuous force model proposed by Lankarani and Nikravesh, which can describe the contact-impact phenomenon accurately. Then, the experimental study is performed whereby the numerical results are compared with the test data to validate the proposed model. Moreover, the dynamic response analysis is conducted with various driving velocities and clearance sizes, which also explains that the sensitive dependence of a mechanical system on the revolute clearance joint.

Kinematics of an Articulated Connecting Rod and its Effect on Simulated Compression Pressures and Port Timings

2017 ◽  
Author(s):  
Kelsey Fieseler ◽  
Timothy J. Jacobs ◽  
Mark Patterson
Keyword(s):  
Equations Of Motion ◽  
Good Method ◽  
Cylinder Pressure ◽  
Pressure Data ◽  
Connecting Rod ◽  
Piston Motion ◽  
Exhaust Port ◽  
Port Opening ◽  
Cylinder Compression ◽  
Crank Mechanism

This study discusses the motion of the articulated connecting rod of an integral-engine compressor and the effect of the kinematics on in-cylinder pressure and port timings. A piston position modeling technique based on kinematics and engine geometry is proposed in order to improve the accuracy of simulated in-cylinder compression pressures. Many integral-engine compressors operate with an articulated connecting rod. For this type of engine-driven compressor, two power pistons share a crank throw with the compressor. The hinge pins that attach the power piston connecting rods to the crank are offset, causing the piston locations for each cylinder to be out of phase with each other. This causes top dead center to occur at different crank angles, alters the geometric compression ratio, and also changes the port timings for each cylinder. In this study, the equations of motion for the pistons of the four possible compressor/piston configurations of a Cooper-Bessemer GMW are developed. With the piston profiles, the intake and exhaust port timings were determined and compared to those of a slider-crank mechanism. The piston profile was then inputted into GT-POWER, an engine modeling software developed by Gamma Technologies, in order to obtain an accurate simulation match to the experimental in-cylinder pressure data collected from a Cooper-Bessemer GMWH-10C. Assuming the piston motion of an engine with an articulated connecting rod is similar to a slider-crank mechanism can create a difference in port timings. The hinge pin offset creates asymmetrical motion about 180°aTDC, causing the port timings to also be asymmetrical about this location. The largest differences are shown in the intake port opening of about 10° and a difference in exhaust port opening of about 7° when comparing the motion of the correct configuration to the motion of a slider-crank mechanism. It is shown that properly calculating the piston motion profiles according to the crank articulation and engine geometry provides a good method of simulating in-cylinder pressure data during the compression stroke.

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.

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.

Kinematics of an Articulated Connecting Rod and Its Effect on Simulated Compression Pressures and Port Timings

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Kelsey Fieseler ◽  
Timothy J. Jacobs ◽  
Mark Patterson
Keyword(s):  
Equations Of Motion ◽  
Good Method ◽  
Cylinder Pressure ◽  
Pressure Data ◽  
Connecting Rod ◽  
Piston Motion ◽  
Exhaust Port ◽  
Port Opening ◽  
Cylinder Compression ◽  
Crank Mechanism

This study discusses the motion of the articulated connecting rod of an integral-engine compressor and the effect of the kinematics on in-cylinder pressure and port timings. A piston position modeling technique based on kinematics and engine geometry is proposed in order to improve the accuracy of simulated in-cylinder compression pressures. Many integral-engine compressors operate with an articulated connecting rod. For this type of engine-driven compressor, two power pistons share a crank throw with the compressor. The hinge pins that attach the power piston connecting rods to the crank are offset, causing the piston locations for each cylinder to be out of phase with each other. This causes top dead center (TDC) to occur at different crank angles, alters the geometric compression ratio, and also changes the port timings for each cylinder. In this study, the equations of motion for the pistons of the four possible compressor/piston configurations of a Cooper-Bessemer GMW are developed. With the piston profiles, the intake and exhaust port timings were determined and compared to those of a slider-crank mechanism. The piston profile was then inputted into GT-POWER, an engine modeling software developed by Gamma Technologies, in order to obtain an accurate simulation match to the experimental in-cylinder pressure data collected from a Cooper-Bessemer GMWH-10C. Assuming the piston motion of an engine with an articulated connecting rod is similar to a slider-crank mechanism can create a difference in port timings. The hinge pin offset creates asymmetrical motion about 180°aTDC, causing the port timings to also be asymmetrical about this location. The largest differences are shown in the intake port opening of about 10 deg and a difference in exhaust port opening of about 7 deg when comparing the motion of the correct configuration to the motion of a slider-crank mechanism. It is shown that properly calculating the piston motion profiles according to the crank articulation and engine geometry provides a good method of simulating in-cylinder pressure data during the compression stroke.

Nonlinear Dynamic Response of Elastic Slider-Crank Mechanism

1971 ◽  
Vol 93 (1) ◽  
pp. 251-262 ◽  
Author(s):  
B. V. Viscomi ◽  
R. S. Ayre
Keyword(s):  
Dynamic Response ◽  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Connecting Rod ◽  
Nonlinear Dynamic Response ◽  
Dimensionless Parameters ◽  
Crank Angle ◽  
Crank Mechanism ◽  
Bending Response

An investigation of the vibratory bending response of the elastic connecting rod of a slider-crank mechanism is presented. The response of the system is found to be dependent upon five dimensionless parameters. These are classified as the length, mass, damping, external piston force, and frequency parameters; and the effects of these parameters on the response of the system are investigated. The dynamic behavior is described as graphs of nondimensionalized deflection versus crank angle. Solutions of the linear as well as the nonlinear forms of the equations are included.

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.

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