Study of the Influence of the Revolute Joint Model on the Dynamic Behavior of Multibody Mechanical Systems: Modeling and Simulation

2007 ◽  
Author(s):  
P. Flores ◽  
J. Ambro´sio ◽  
J. C. P. Claro ◽  
H. M. Lankarani
Keyword(s):  
Mechanical System ◽  
Dynamic Behavior ◽  
Multibody Systems ◽  
Numerical Models ◽  
Equations Of Motion ◽  
Joint Model ◽  
Hydrodynamic Forces ◽  
Contact Forces ◽  
Revolute Joint ◽  
Revolute Joints

The influence of the revolute joint model on the dynamic behavior of multibody systems is investigated throughout this work. In the process, under the framework of the multibody systems formulation, a general methodology for modeling revolute joints with clearance is presented. The numerical models for normal and tangential contact forces are reviewed. The contact-impact forces developed during the contact are evaluated and introduced into the equations of motion of the multibody mechanical system. Moreover, the main kinematic and dynamic aspects of the modeling lubricated revolute joints are presented and discussed in this work in order to compare them with the dry revolute joint. The hydrodynamic forces are obtained by integrating the pressure distribution evaluated with the aid of Reynolds’ equation written for the dynamic regime. The hydrodynamic forces are nonlinear functions of the journal centre position and of its velocity with reference to the bearing center. The hydrodynamic forces built up by the lubricant fluid are evaluated from the state of variable of the system and included into the equations of motion of the mechanical system. The main assumptions and procedures adopted in this work are demonstrated through simulations of a slider-crank mechanism, which includes a revolute joint with clearance.

An Overview of Several Formulations for Dry and Lubricated Revolute Joint Clearances in Planar Rigid-Multi-Body Mechanical Systems

2014 ◽  
Author(s):  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Numerical Models ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Revolute Joint ◽  
Coulomb’S Friction ◽  
Revolute Joints ◽  
Joint Clearances ◽  
Multi Body

The influence of the revolute joint model on the dynamic response of planar multibody mechanical systems is studied in this work. In the sequel of this process, under the framework of the multibody formalisms, a general methodology for modeling the main kinematic aspects of dry revolute joint clearances is revisited. The numerical models for normal and tangential contact forces developed at the clearance joints are also discussed, which are based on the Hertzian contact theory and dry Coulomb’s friction law, respectively. The fundamental kinematic and dynamic issues of the modeling lubricated revolute joints are presented in this work in order to compare them with the dry revolute joint approach. In a simple manner, the lubrication forces are obtained by integrating the pressure distribution evaluated with the aid of Reynolds’ equation corresponding to the dynamic regime. The intra-joint forces developed for both dry and lubricated cases are evaluated based on the state of variable of the system and subsequently included into the dynamic equations of motion of the multibody system as external generalized forces. The main assumptions and procedures adopted throughout this work are demonstrated through simulations of a planar slider-crank mechanism, which includes dry and lubricated revolute joint with clearance. Finally, some experimental data is also presented and analyzed.

Dynamics of a Multibody Mechanical System With Lubricated Long Journal Bearings

2004 ◽  
Vol 127 (3) ◽  
pp. 493-498 ◽  
Author(s):  
B. J. Alshaer ◽  
H. Nagarajan ◽  
H. K. Beheshti ◽  
H. M. Lankarani ◽  
S. Shivaswamy
Keyword(s):  
Dynamic Response ◽  
Mechanical System ◽  
Journal Bearing ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Journal Bearings ◽  
Connecting Rod ◽  
Revolute Joint ◽  
Order Of Magnitude

Clearances exist in different kinds of joints in multibody mechanical systems, which could drastically affect the dynamic behavior of the system. If the joint is dry with no lubricant, impact occurs, resulting in wear and tear of the joint. In practical engineering design of machines, joints are usually designed to operate with some lubricant. Lubricated journal bearings are designed so that even when the maximum load is applied, the joint surfaces do not come into contact with each other. In this paper, a general methodology for modeling lubricated long journal bearings in multibody mechanical systems is presented. This modeling utilizes a method of solving for the forces produced by the lubricant in a dynamically loaded long journal bearing. A perfect revolute joint in a multibody mechanical system imposes kinematic constraints, while a lubricated journal bearing joint imposes force constraints. As an application, the dynamic response of a slider-crank mechanism including a lubricated journal bearing joint between the connecting rod and the slider is considered and analyzed. The dynamic response is obtained by numerically solving the constraint equations and the forces produced by the lubricant simultaneously with the differential equations of motion and a set of initial conditions numerically. The results are compared with the previous studies performed on the same mechanism as well a dry clearance joint. It is shown that in a multibody mechanical system, the journal bearing lubricant introduces damping and stiffness to the system. The earlier studies predict that the order of magnitude of the reaction moment is twice that of a perfect revolute joint. The proposed model predicts that the reaction moment is within the same order of magnitude of the perfect joint simulation case.

Dynamics of a Multibody Mechanical System With Lubricated Long Journal Bearings

2001 ◽  
Author(s):  
B. J. Alshaer ◽  
H. M. Lankarani ◽  
S. Shivaswamy
Keyword(s):  
Dynamic Response ◽  
Mechanical System ◽  
Journal Bearing ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Journal Bearings ◽  
Connecting Rod ◽  
Revolute Joint ◽  
Order Of Magnitude

Abstract Clearances exist in different kinds of joints in multibody mechanical systems, which could drastically affect the dynamic behavior of the system. If the joint is dry with no lubricant, impact occurs, resulting in wear and tear of the joint. In practical engineering design of machines, joints are usually designed to operate with some lubricant. Lubricated journal bearings are designed so that even when the maximum load is applied, the joint surfaces do not come into contact with each other. In this paper, a general methodology for modeling lubricated long journal bearings in multibody mechanical systems is presented. This modeling utilizes a new method of solving for the forces produced by the lubricant in a dynamically loaded long journal bearing. A perfect revolute joint in a multibody mechanical system imposes kinematic constraints, while a lubricated journal bearing joint imposes force constraints. As an application, the dynamic response of a crank-slider mechanism including a lubricated journal bearing joint between the connecting rod and the slider is considered and analyzed. The dynamic response is obtained by numerically solving the constraint equations and the forces produced by the lubricant simultaneously with the differential equations of motion and a set of initial conditions numerically. The results are compared with the previous studies performed on the same mechanism as well a dry clearance joint. It is shown that in a multibody mechanical system, the journal bearing lubricant introduces damping and stiffness to the system. The earlier studies previous predict that the order of magnitude of the reaction moment is twice that of a perfect revolute joint. The proposed model predicts that the reaction moment is within the same order of magnitude of the perfect joint simulation case.

Dynamic Behavior of the Band/Wheel Mechanical System of Industrial Band Saws

1995 ◽  
Author(s):  
Y. Y. Chung ◽  
C. K. Sung
Keyword(s):  
Mechanical System ◽  
Dynamic Behavior ◽  
Tilt Angle ◽  
Metal Cutting ◽  
Equations Of Motion ◽  
Continuity Condition ◽  
Dynamic Responses ◽  
Moving Beam ◽  
Band Saw ◽  
The Mathematical Model

Abstract This paper presents an analytical and experimental investigation on the dynamic behavior of the band/wheel mechanical system of an industrial metal-cutting band saws. In practice, as a result of the existence of the wheel tilt angle, a pair of roller bearings in which one of them is movable must be employed to twist the saw band perpendicular to the workpiece. Therefore, the saw band is modelled as a finite moving beam span that composes of three consecutive segments, in which the middle segment, that is, the cutting span, and the neighboring two segments may be assumed to be a straight and a twisted beams, respectively. The deformation of the band must satisfy the continuity condition at the connections between segments. The equations of motion governing the dynamic behavior of the beam span in axial, torsional and transverse directions are derived using mixed variational principle. The axial motion of the beam span couples linearly with its torsional motion. The dynamic responses and the natural frequencies of the beam are computed when parameters vary, such as the transport velocity of the saw band, band tension, wheel tilt angle, and the length of the cutting span. Finally, an experimental study is performed on an industrial band saw for the verification of the mathematical model and the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.

scholarly journals Dynamic Response of Multibody Systems With Multiple Clearance Joints

2011 ◽  
Author(s):  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Contact Force ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Physical And Mechanical Properties ◽  
Contact Forces ◽  
Force Model ◽  
Modeling And Analysis ◽  
Clearance Joints ◽  
Continuous Contact ◽  
Dissipative Term

A general methodology for the dynamic modeling and analysis of planar multibody systems with multiple clearance joints is presented. The inter-connecting body components that constitute a real joint are modeled as colliding bodies, which dynamic behaviors are influenced by geometric, physical and mechanical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory, together with a dissipative term, is used to evaluate the intra-joint contact forces. The incorporation of the friction, based on the classical Coulomb’s friction law, is also included. The suitable contact force models are embedded into the dynamic equations of motion for the multibody system. A simple mechanical system with multiple clearance joints is used to demonstrate the accuracy and efficiency of the presented approach and to discuss the main assumptions and procedures adopted. The effects of single versus multiple clearance joints are discussed.

Dynamic Behavior of the Band/Wheel Mechanical System of Industrial Band Saws

1998 ◽  
Vol 120 (4) ◽  
pp. 842-847 ◽  
Author(s):  
Y. Y. Chung ◽  
C. K. Sung
Keyword(s):  
Mechanical System ◽  
Dynamic Behavior ◽  
Tilt Angle ◽  
Metal Cutting ◽  
Equations Of Motion ◽  
Continuity Condition ◽  
Dynamic Responses ◽  
Initial Tension ◽  
Saw Blade ◽  
Band Saw

This paper presents an analytical and experimental investigation on the dynamic behavior of the band/wheel mechanical system of an industrial metal-cutting band saws. In practice, this machine is equipped with two pairs of roller bearings to twist the saw blade perpendicularly to the surface of the workpiece. This results in the existence of the wheel tilt angle. The saw band is modeled as a finite moving beam span that composes three consecutive segments: the middle straight segment, that is, the cutting span, and the neighboring two segments that are considered as twisted beams. The deformation of the band must satisfy the continuity condition at the connections between segments. The equations of motion governing the dynamic behavior of the saw band in axial, torsional and transverse directions are derived using mixed variational principle. The axial motion of the span couples linearly with its torsional motion. The dynamic responses and the natural frequencies of the beam are computed when parameters vary, such as the transport velocity of the saw band, initial tension, wheel tilt angle, and the length of the cutting span. Finally, an experimental study is performed on an industrial band saw for the verification of the mathematical model and the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.

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.

scholarly journals Finite Element Method-Based Elastic Analysis of Multibody Systems. A Review

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 257
Author(s):  
Sorin Vlase ◽  
Marin Marin ◽  
Negrean Iuliu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mechanical System ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Methods ◽  
Engineering Applications ◽  
Lagrange’S Equations ◽  
Lagrange's Equations ◽  
Element Method

This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered.

scholarly journals Dynamic Response of Multibody Systems with Multiple Clearance Joints

2012 ◽  
Vol 7 (3) ◽  
Author(s):  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Contact Force ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Physical And Mechanical Properties ◽  
Contact Forces ◽  
Force Model ◽  
Normal Contact ◽  
Clearance Joints ◽  
Continuous Contact ◽  
Dissipative Term

A general methodology for the dynamic modeling and analysis of planar multibody systems with multiple clearance joints is presented. The inter-connecting bodies that constitute a real physical mechanical joint are modeled as colliding components, whose dynamic behavior is influenced by the geometric, physical and mechanical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory, together with a dissipative term associated with the internal damping, is utilized to evaluate the intra-joint normal contact forces. The incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also included in this study. The suitable contact force models are embedded into the dynamic equations of motion for the multibody systems. In the sequel of this process, the fundamental methods to deal with contact-impact events in mechanical systems are presented. Finally, two planar mechanisms with multiple revolute clearance joints are used to demonstrate the accuracy and efficiency of the presented approach and to discuss the main assumptions and procedures adopted. The effects of single versus multiple clearance revolute joints are discussed.

Vibrations of Square and Hexagonal Cylinders in a Liquid

1981 ◽  
Vol 103 (3) ◽  
pp. 233-239 ◽  
Author(s):  
Y. Shinohara ◽  
T. Shimogo
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fuel Assembly ◽  
Dynamic Behavior ◽  
Nuclear Fuel ◽  
Equations Of Motion ◽  
Hydrodynamic Forces ◽  
Partial Differential ◽  
Nuclear Fuel Assembly

A mathematical model is proposed to describe the dynamic behavior of square and hexagonal cylinder bundles immersed in a liquid. First, the hydrodynamic forces associated with cylinder motions are examined, and then equations of motion of the spring-mounted cylinders including liquid coupling are derived. When the number of cylinders is very large, these equations are replaced by partial differential equations on the assumption that the cylinder bundles form a continuum. The results of this study have application in the modeling of vibration of a nuclear fuel assembly under the excitation of earthquakes.

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