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.

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.

Modeling and simulation of planar flexible link manipulators with rigid tip connections to revolute joints

Robotica ◽  
2004 ◽  
Vol 22 (3) ◽  
pp. 285-300 ◽  
Author(s):  
S. M. Megahed ◽  
K. T. Hamza
Keyword(s):  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Link ◽  
Link Length ◽  
Finite Segment ◽  
Revolute Joints ◽  
Body Dynamics ◽  
Lumped Masses ◽  
Multi Body ◽  
Rigid Zones

This paper presents the basis of a mathematical model for simulation of planar flexible-link manipulators, taking into consideration the effect of higher stiffness zones at the link tips. The proposed formulation is a variation of the finite segment multi-body dynamics approach. The formulation employs a consistent mass matrix in order to provide better approximation than the traditional lumped masses often encountered in the finite segment approach. The formulation is implemented into a computational code and tested through three examples; cantilever beam, rotating beam and three-link manipulator. In these examples, the length of the rigid tips at both sides of each link ranges from 0% to 6.25% of the whole link length. The zones of higher stiffness at the link tips are treated as short rigid zones. The effect of the rigid zones is averaged along with some portions of the flexible links, thereby allowing further simplification of the dynamic equations of motion. The simulation results demonstrate the effectiveness of the proposed modeling technique and show the importance of not ignoring the effect of the rigid tips.

Explicit Poincaré equations of motion for general constrained systems. Part I. Analytical results

2007 ◽  
Vol 463 (2082) ◽  
pp. 1421-1434 ◽  
Author(s):  
Firdaus E Udwadia ◽  
Phailaung Phohomsiri
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Constrained Systems ◽  
Analytical Results ◽  
Multi Body ◽  
D'alembert's Principle

This paper gives the general constrained Poincaré equations of motion for mechanical systems subjected to holonomic and/or nonholonomic constraints that may or may not satisfy d'Alembert's principle at each instant of time. It also extends Gauss's principle of least constraint to include quasi-accelerations when the constraints are ideal, thereby expanding the compass of this principle considerably. The new equations provide deeper insights into the dynamics of multi-body systems and point to new ways for controlling them.

A Recursive Formulation for Real-Time Dynamic Simulation of Mechanical Systems

1991 ◽  
Vol 113 (2) ◽  
pp. 158-166 ◽  
Author(s):  
Dae-Sung Bae ◽  
Ruoh-Shih Hwang ◽  
Edward J. Haug
Keyword(s):  
Real Time ◽  
Dynamic Simulation ◽  
Recursive Algorithm ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Dynamic ◽  
Time Simulation ◽  
Kinematic Loops ◽  
Multi Body ◽  
Recursive Equations

A new recursive algorithm for real-time dynamic simulation of mechanical systems with closed kinematic loops is presented. State vector kinematic relations that represent translational and rotational motion are defined to simplify the formulation and to relieve computational burden. Recursive equations of motion are first derived for a single loop multi-body system. Faster than real-time performance is demonstrated for a closed loop manipulator, using an Alliant FX/8 multiprocessor. The algorithm is extended to multi-loop, multi-body systems for parallel processing real-time simulation in companion papers [1, 2] where performance of the algorithm on a shared memory multi-processor is compared with that achieved with other dynamic simulation algorithms.

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.

scholarly journals Dynamic Responses of Planar Multilink Mechanism considering Mixed Clearances

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Xiulong Chen ◽  
Shuai Jiang ◽  
Yu Deng
Keyword(s):  
Great Influence ◽  
Friction Model ◽  
Contact Forces ◽  
Dynamic Responses ◽  
Prototype Model ◽  
Planar Mechanisms ◽  
Coulomb’S Friction ◽  
Revolute Joints ◽  
Friction Models ◽  
Coulomb Friction Model

Translational and revolute joints are the main kinds of joints in planar multilink mechanisms. Translational and revolute clearance joints have great influence on dynamical responses of planar mechanisms. Most research studies mainly focused upon revolute clearance of planar mechanisms based upon the modified Coulomb friction model, some studies investigated clearance of the pin-slot joint, and few studies researched mixed clearances (considering both translational clearance and revolute clearance) based on the LuGre friction model. Dynamic response of the 2-DOF nine-bar mechanism considering mixed clearances based on the LuGre model is investigated in this work. The dynamic model with mixed clearances is built by the Lagrange multipliers. Dynamic responses including motion output of the slider, driving torques, contact forces, shaft center trajectories at revolute clearance pairs, and slider trajectory inside the guide are analyzed, respectively. Influences of different friction models on dynamic responses are studied, such as LuGre and modified Coulomb’s friction models. Effects of different clearance values and different driving speeds on dynamic responses with mixed clearances are both analyzed. Virtual prototype model considering mixed clearances is carried out through ADAMS to verify correctness.

Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics

2006 ◽  
Vol 462 (2071) ◽  
pp. 2097-2117 ◽  
Author(s):  
Firdaus E Udwadia ◽  
Phailaung Phohomsiri
Keyword(s):  
Explicit Form ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Constrained Motion ◽  
Holonomic Constraints ◽  
Constrained Mechanical Systems ◽  
Mass Matrices ◽  
Body Dynamics ◽  
Multi Body ◽  
Explicit Equations Of Motion

We present the new, general, explicit form of the equations of motion for constrained mechanical systems applicable to systems with singular mass matrices. The systems may have holonomic and/or non-holonomic constraints, which may or may not satisfy D'Alembert's principle at each instant of time. The equation provides new insights into the behaviour of constrained motion and opens up new ways of modelling complex multi-body systems. Examples are provided and applications of the equation to such systems are illustrated.

Computational and Experimental Analysis of Mechanical Systems With Revolute Clearance Joints

2013 ◽  
Author(s):  
Sony Cheriyan ◽  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Contact Force ◽  
Computational Models ◽  
Mechanical Systems ◽  
Contact Forces ◽  
Force Model ◽  
Connecting Rod ◽  
Normal Contact ◽  
Clearance Joints ◽  
Coulomb’S Friction ◽  
Experimental Apparatus

The main objective of this work is to present a computational and experimental study on the contact forces developed in revolute clearance joints. For this purpose, a well-known slider-crank mechanism with a revolute clearance joint between the connecting rod and slider is utilized. The intra-joint contact forces that generated at this clearance joints are computed by considered several different elastic and dissipative approaches, namely those based on the Hertz contact theory and the ESDU tribology-based for cylindrical contacts, along with a hysteresis-type dissipative damping. The normal contact force is augmented with the dry Coulomb’s friction force. An experimental apparatus is use to obtained some experimental data in order to verify and validate the computational models. From the outcomes reported in this paper, it is concluded that the selection of the appropriate contact force model with proper dissipative damping plays a significant role in the dynamic response of mechanical systems involving contact events at low or moderate impact velocities.

Effects of Non-Hertzian Contact Models on Derailment Simulation

2020 ◽  
Author(s):  
Qinghua Guan ◽  
Binbin Liu ◽  
Stefano Bruni
Keyword(s):  
State Of The Art ◽  
Contact Forces ◽  
Contact Model ◽  
Hertzian Contact ◽  
Contact Modeling ◽  
Derailment Coefficient ◽  
Contact Models ◽  
Creep Force ◽  
Multi Body ◽  
Different Levels

Abstract The derailment of trains is a complex phenomenon that requires an elaborate contact model in simulation to better understand its mechanism. The CONTACT program is a well-known reference for wheel-rail contact modeling due to its high accuracy. However, its low computational efficiency restricts its applications especially in the context of a multi-body simulation. Therefore, a high computational efficient, simplified and approximate non-Hertzian contact is preferred in derailment simulation. The aim of this research is to verify the efficiency of a recently developed non-Hertzian wheel-rail contact model in derailment simulation, which is a combination of the Kik-Piotrowski model and the KBTNH that is a fast creep force solver for non-Hertzian contacts. To assess the performance of the non-Hertzian model in derailment simulation, the derailment coefficient for steady-state and quasi-steady conditions, the wheel/rail contact forces during flange contact, and the dynamics behaviors of the wheelset prior to the derailment are compared with the state of the art contact methods representing different levels of modeling complexity, accuracy and efficiency, namely the classical approach (Hertz theory+FASTSIM algorithm) and the ‘exact’ solver CONTACT.

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