Dynamic modeling of flexible multibody system using a meshing method

2013 ◽  
Vol 228 (4) ◽  
pp. 611-631 ◽  
Author(s):  
Hua-Nan Yu ◽  
Jing-Shan Zhao ◽  
Fu-Lei Chu
Keyword(s):  
Mechanical System ◽  
Multibody System ◽  
Mass Density ◽  
Rigid Bodies ◽  
The Finite Element Method ◽  
Elastic Deformations ◽  
Solid Structure ◽  
Elastic Bodies ◽  
System Of Rigid Bodies ◽  
Dynamics Problems

Multi-rigid-body system dynamics can be used to investigate the dynamics of a mechanical system of rigid bodies while the finite element method is often utilized to model the quasi-static elastic deformations of an elastic structure. However, neither of these two methods can resolve the real dynamics of a mechanical system when both rigid displacements and elastic deformations coexist. Therefore, this article proposes a meshing method to simulate the mechanical system with uniform mass point movements. To split the specified solid structure into a set of regularly distributed dynamic units, one can assume that the mass density of the structure is evenly distributed within the whole concrete volume and the elasticity and damping of the material are isotropic. Then the whole solid structure of each component can be divided into a number of tetrahedrons the vertexes of which are the points with the mass parameters. The original distances between every pair of adjacent points are supposed to be identical, and the stiffness and the damping coefficients are introduced to formulate the internal and external dynamics of the adjacent mass points. To illustrate the correction and effectiveness of the method, the dynamics problems of a number of regular elastic bodies are investigated with large rigid displacements accompanying elastic deformations. Computer simulations demonstrate that this method is especially useful for real mechanical systems where the rigid displacements and elastic deformations coexist.

scholarly journals TRACTOR DYNAMICS AS A COMPLEX MECHANICAL SYSTEM SPATIAL FRAME TYPE

2021 ◽  
Author(s):  
E. Kalinin ◽  
◽  
Y. Kolesnik ◽  
Yu. Kozlov ◽  
Keyword(s):  
Mechanical System ◽  
Complete Solution ◽  
Rigid Bodies ◽  
Coupled Systems ◽  
Support Surface ◽  
Systems Methodology ◽  
Complex Mechanical System ◽  
Spatial Frame ◽  
System Of Rigid Bodies ◽  
Stiffness And Damping

Purpose of the study is to develop a matrix method for studying the dynamics of a tractor as a multi-mass spatial system of rigid bodies with an arbitrary arrangement of elastic suspension of bodies on shock absorbers relative to a fixed support surface and the presence of elastic connections between the bodies, made in the form of beam elements. Research methods. The methodological basis of the work is the generalization and analysis of well-known scientific results regarding the dynamics of two-mass systems in resonance modes and the use of a systematic approach. The analytical method and comparative analysis were used to form a scientific problem, determine the goal and formulate the research objectives. When creating empirical models, the main provisions of the theory of stability of systems, methodology of systems analysis and research of operations were used. The results of the study. A wheeled vehicle is presented as an amortized continuous frame type structure with assemblies and assembly units located on it, as well as a methodology for calculating individual block matrices of stiffness and damping coefficients. In this case, it is assumed that a viscous damper can be connected in parallel to each elastic element. In this construction of the stiffness and damping matrix of the block matrix are formed in the same way. Damping matrices are derived from the corresponding matrices by substituting damping constants instead of stiffness constants. To determine the natural frequencies and vibration modes of an undamped system using a PC, the most effective method of diagonalization by successive rotations. This method provides a complete solution to the problem, allowing all frequencies and shapes to be determined simultaneously, and good convergence. Conclusions. The considered method for analyzing and calculating the dynamics and vibration damping of a tractor as a complex mechanical system is based on a matrix record of the problem of spatial vibrations of a system of rigid bodies with elastic bonds. Matrix equations seem to be especially useful in the study of complex tightly coupled systems with the obligatory use of a PC. The presented work provides a complete methodology for calculating a tractor as a complex mechanical system such as a spatial frame with equipment installed on it.

Simulation of Elastic Gears with Non-Standard Flank Profiles

2013 ◽  
Vol 60 (1) ◽  
pp. 55-73
Author(s):  
Trong Phu Do ◽  
Pascal Ziegler ◽  
Peter Eberhard
Keyword(s):  
Multibody System ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Reference Formulation ◽  
Elastic Deformations ◽  
Beveloid Gears ◽  
Elastic Multibody System ◽  
Floating Frame ◽  
Simulation Results ◽  
Gear Contact

There exist cases where precise simulations of contact forces do not allow modeling the gears as rigid bodies but a fully elastic description is needed. In this paper, a modally reduced elastic multibody system including gear contact based on a floating frame of reference formulation is proposed that allows very precise simulations of fully elastic gears with appropriately meshed gears in reasonable time even for many rotations. One advantage of this approach is that there is no assumption about the geometry of the gears and, therefore, it allows precise investigations of contacts between gears with almost arbitrary non-standard tooth geometries including flank profile corrections. This study presents simulation results that show how this modal approach can be used to efficiently investigate the interaction between elastic deformations and flank profile corrections as well as their influence on the contact forces. It is shown that the elastic approach is able to describe important phenomena like early addendum contact for insufficiently corrected profiles in dependence of the transmitted load. Furthermore, it is shown how this approach can be used for precise and efficient simulations of beveloid gears.

scholarly journals Cinemática 2D de caballos al trote mediante videometría y modelamiento matemático

2017 ◽  
Vol 26 (45) ◽  
Author(s):  
Yolanda Torres-Pérez ◽  
Edwin Yesid Gómez-Pachón ◽  
Francisco Miró-Rodriguez
Keyword(s):  
Mechanical System ◽  
Inverse Kinematics ◽  
Mathematical Optimization ◽  
Optimization Method ◽  
Rigid Bodies ◽  
The Body ◽  
Locomotor System ◽  
System Of Rigid Bodies ◽  
Observation Method ◽  
Direct Observation Method

Currently, the direct observation method is used to assess the movement of horses. However, this method is limited, totally subjective and many details of the functionality of the musculoskeletal system cannot be detected and evaluated, because they are not perceptible to the naked eye.The aim of this study was to develop a mathematical model that calculates, plots and simulates the 2D angular movement of some horse joints. The horse's locomotor system was modeled as a mechanical system of rigid bodies articulated by 15 simple joints.The mathematical solution of the mechanism was made from the standpoint of liabilities of  inverse kinematics (flat), 15 link equations were constructed associating the body segments of the system in movement with the inertial base and the mathematical optimization method based on the least squares calculation was used.The kinematic curves of the main joints were obtained in this study; trajectories (height) of the markers on fore and hind coronary band (hoofs), and a simulation of the mechanical system. This tool removes the subjectivity and enables veterinarians to observe, evaluate (qualitatively and quantitatively), diagnose and research about different phenomena of the horse’s gait.

The study of the elastic deformation of a flexible wheel by a cam wave generator

2020 ◽  
Vol 65 (1) ◽  
pp. 51-58
Author(s):  
Sava Ianici
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Elastic Deformation ◽  
Theoretical Study ◽  
Elastic Field ◽  
The Finite Element Method ◽  
Elastic Deformations ◽  
Wave Generator ◽  
Two Stages

The paper presents the results of research on the study of the elastic deformation of a flexible wheel from a double harmonic transmission, under the action of a cam wave generator. Knowing exactly how the flexible wheel is deformed is important in correctly establishing the geometric parameters of the wheels teeth, allowing a better understanding and appreciation of the specific conditions of harmonic gearings in the two stages of the transmission. The veracity of the results of this theoretical study on the calculation of elastic deformations and displacements of points located on the average fiber of the flexible wheel was subsequently verified and confirmed by numerical simulation of the flexible wheel, in the elastic field, using the finite element method from SolidWorks Simulation.

Improving Techniques in Statically Equivalent Serial Chain Modeling for Center of Mass Estimation

2014 ◽  
Author(s):  
Bingjue Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Center Of Mass ◽  
Original System ◽  
Rigid Bodies ◽  
Joint Angles ◽  
Practical Applications ◽  
Serial Chain ◽  
System Of Rigid Bodies ◽  
Final Development ◽  
Data Error ◽  
Insight Into

Any articulated system of rigid bodies defines a Statically Equivalent Serial Chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. A SESC may be generated experimentally without knowing the mass, CoM, or length of each link in the system given that its joint angles and overall CoM may be measured. This paper presents three developments toward recognizing the SESC as a practical modeling technique. Two of the three developments improve utilizing the technique in practical applications where the arrangement of the joints impacts the derivation of the SESC. The final development provides insight into the number of poses needed to create a usable SESC in the presence of data collection errors. First, modifications to a matrix necessary in computing the SESC are proposed. Second, the problem of generating a SESC experimentally when the system of bodies includes a mass fixed in the ground frame are presented and a remedy is proposed for humanoid-like systems. Third, an investigation of the error of the experimental SESC versus the number of data readings collected in the presence of errors in joint readings and CoM data is conducted. By conducting the method on three different systems with various levels of data error, a general form of the function for estimating the error of the experimental SESC is proposed.

Co-Simulation Procedure for Multibody Reeving Systems

2018 ◽  
Author(s):  
Grzegorz Orzechowski ◽  
Aki M. Mikkola ◽  
José L. Escalona
Keyword(s):  
Multibody System ◽  
Wire Rope ◽  
Rigid Bodies ◽  
Arbitrary Lagrangian Eulerian ◽  
Transverse Deformation ◽  
Absolute Position ◽  
Eulerian Approach ◽  
Wire Ropes ◽  
Simulation Procedure ◽  
Flexible Wire

In this paper, co-simulation procedure for a multibody system that includes reeving mechanism will be introduced. The multibody system under investigation is assumed to have a set of rigid bodies connected by flexible wire ropes using a set of sheaves and reels. In the co-simulation procedure, a wire rope is described using a combination of absolute position coordinates, relative transverse deformation coordinates and longitudinal material coordinates. Accordingly, each wire rope span is modeled using a single two-noded element by employing an Arbitrary Lagrangian-Eulerian approach.

scholarly journals Method of Equivalent Strength Conditions in Composite Structures Evaluations

2021 ◽  
pp. 106-115
Author(s):  
A.D. Matveev
Keyword(s):  
Composite Structures ◽  
High Efficiency ◽  
Approximation Error ◽  
Regular Structure ◽  
Approximate Solutions ◽  
Discrete Models ◽  
The Finite Element Method ◽  
Elastic Bodies ◽  
Equivalent Strength ◽  
Computer Resources

It is important to know the error or the approximate solution when calculating the strength of elastic composite structures (bodies) using the finite element method (FEM). To construct a sequence of solutions according to the FEM is necessary for the evaluation of the approximation error. It involves the grinding procedure for discrete models. The implementation of the grinding procedure for basic models that take into account the inhomogeneous, micro-homogeneous structures of bodies within the microapproach requires ample computer resources. This paper proposes a method of equivalent strength conditions (MESC) to calculate the static strength of elastic bodies with a non-uniform, microuniform regular structure. The calculation of composite bodies strength according to the MESC is reduced to the calculation of isotropic homogeneous bodies strength using equivalent strength conditions. Adjusted equivalent strength conditions are used in the numerical implementation of the MESC. They take into account the error of the approximate solutions. If a set of loads is specified for a composite body, then generalized equivalent strength conditions are applied. The FEM-based calculation of composite bodies strength that follows the MESC using multigrid finite elements requires 103 ÷ 105 times less computer memory than a similar calculation using ground basic models of composite bodies. The provided example of strength calculation for a beam with an inhomogeneous regular fiber structure using the MESC shows its high efficiency. The main MESC implementation procedures are outlined.

scholarly journals Ternary Logic of Motion to Resolve Kinematic Frictional Paradoxes

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 620 ◽  
Author(s):  
Michael Nosonovsky ◽  
Alexander D. Breki
Keyword(s):  
Dry Friction ◽  
Sliding Friction ◽  
Rigid Bodies ◽  
Newtonian Mechanics ◽  
Stability Criteria ◽  
Ternary Logic ◽  
Elastic Bodies ◽  
Logic Approach ◽  
Frictional System ◽  
Painlevé Paradoxes

Paradoxes of dry friction were discovered by Painlevé in 1895 and caused a controversy on whether the Coulomb–Amontons laws of dry friction are compatible with the Newtonian mechanics of the rigid bodies. Various resolutions of the paradoxes have been suggested including the abandonment of the model of rigid bodies and modifications of the law of friction. For compliant (elastic) bodies, the Painlevé paradoxes may correspond to the friction-induced instabilities. Here we investigate another possibility to resolve the paradoxes: the introduction of the three-value logic. We interpret the three states of a frictional system as either rest-motion-paradox or as rest-stable motion-unstable motion depending on whether a rigid or compliant system is investigated. We further relate the ternary logic approach with the entropic stability criteria for a frictional system and with the study of ultraslow sliding friction (intermediate between the rest and motion or between stick and slip).

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