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.

scholarly journals Evaluation of indicators of curvilinear movement of a road train using mathematical simulation

2020 ◽  
Vol 1 (4) ◽  
pp. 2-15
Author(s):  
V.A. Gorelov ◽  
◽  
K.B. Yevseyev ◽  
O.I. Chudakov ◽  
K.S. Balkovskiy ◽  
...  
Keyword(s):  
Mathematical Model ◽  
High Accuracy ◽  
Rigid Bodies ◽  
Practical Significance ◽  
Limited Area ◽  
Supporting Surface ◽  
Systems Methodology ◽  
System Of Rigid Bodies ◽  
Wide Range ◽  
Wheeled Vehicles

Introduction: a widespread approach to the transportation of large-sized and heavy-weight indi-visible cargo on roads and terrain is the use of multi-axle wheeled transport complexes, which are road trains. At the same time, due to the significant overall dimensions, one of the most important properties of such machines is agility, that is, the ability to move along a trajectory of large curvature in a limited area, which is especially important in loading / unloading zones. Subject of research: the article presents an approach to predicting the indicators of curvilinear movement of multi-axle wheeled road trains, based on the application of the method of mathemati-cal modeling of the dynamics of body systems. Methodology and methods: the essence of the method is to create a mathematical model of the movement of a road train, represented by a system of rigid bodies, which are interconnected by kin-ematic and power connections. The simulation model developed within the framework of the study makes it possible to take into account with high accuracy the peculiarities of the interaction of the wheel propeller with the supporting surface, the redistribution of normal reactions between the sup-port modules, as well as the force factors arising in the coupling device and ensuring the interaction between the tractive vehicle and the trailer link. The mathematical description of the interaction of the propeller with the ground is based on the concept of “friction ellipse”. Using the presented mod-el, an assessment of the turnability of a wheeled road train equipped with a trailed link with swivel and non-swivel wheels was carried out. The required width along the tracks of the outer (running in) and inner (lagging) wheels was used as an assessment criterion. To assess the feasibility of using a trailed link with fully steered wheels and, accordingly, complicating the design of the machine, an additional assessment of the required power of the steering drive was carried out. Results and scientific novelty: a mathematical model of the dynamics of a road train was de-veloped. It makes possible to predict with high accuracy the indicators of curvilinear movement of wheeled vehicles, as well as to estimate the required power of the steering drive. Practical significance: a mathematical model of road train movement was developed, which al-lows a wide range of tests to be carried out to assess not only the indicators of curved-linear move-ment, but also the mobility of wheeled vehicles of any configuration as a whole.

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.

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.

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.

scholarly journals High-Speed Rotor Analytical Dynamics on Flexible Foundation Subjected to Internal and External Excitation

2016 ◽  
Vol 46 (4) ◽  
pp. 3-18
Author(s):  
Venelin S. Jivkov ◽  
Evtim V. Zahariev
Keyword(s):  
Gas Turbines ◽  
High Speed ◽  
Asymptotic Methods ◽  
Numerical Procedure ◽  
Rigid Bodies ◽  
Dynamics Simulation ◽  
Geometrical Approach ◽  
Rotating Machine ◽  
Exciting Frequency ◽  
Stiffness And Damping

Abstract The paper presents a geometrical approach to dynamics simulation of a rigid and flexible system, compiled of high speed rotating machine with eccentricity and considerable inertia and mass. The machine is mounted on a vertical flexible pillar with considerable height. The stiffness and damping of the column, as well as, of the rotor bearings and the shaft are taken into account. Non-stationary vibrations and transitional processes are analyzed. The major frequency and modal mode of the flexible column are used for analytical reduction of its mass, stiffness and damping properties. The rotor and the foundation are modelled as rigid bodies, while the flexibility of the bearings is estimated by experiments and the requirements of the manufacturer. The transition effects as a result of limited power are analyzed by asymptotic methods of averaging. Analytical expressions for the amplitudes and unstable vibrations throughout resonance are derived by quasi-static approach increasing and decreasing of the exciting frequency. Analytical functions give the possibility to analyze the influence of the design parameter of many structure applications as wind power generators, gas turbines, turbo-generators, and etc. A numerical procedure is applied to verify the effectiveness and precision of the simulation process. Nonlinear and transitional effects are analyzed and compared to the analytical results. External excitations, as wave propagation and earthquakes, are discussed. Finite elements in relative and absolute coordinates are applied to model the flexible column and the high speed rotating machine. Generalized Newton - Euler dynamics equations are used to derive the precise dynamics equations. Examples of simulation of the system vibrations and nonstationary behaviour are presented.

Dynamic Modelling and Analysis of Rectangle-Shaped Plastic-Coated Slideways in Machine Tools

2011 ◽  
Vol 50-51 ◽  
pp. 37-41
Author(s):  
Jian Fu Zhang ◽  
Zhi Jun Wu ◽  
Ping Fa Feng ◽  
Ding Wen Yu
Keyword(s):  
Mathematical Model ◽  
Machine Tools ◽  
Vibration Mode ◽  
Dynamic Modelling ◽  
Rigid Bodies ◽  
Theoretical Research ◽  
Damping Characteristics ◽  
Vibration Properties ◽  
Stiffness And Damping ◽  
The Mathematical Model

The plastic-coated slideways have been widely used for form-generating movement in machine tools. Its dynamic behavior plays an important role in the vibration properties of the whole machine. In this work, according to the situation that researches on this subject were rather insufficient, a theoretical research was analyzed concerning the stiffness and damping characteristics of rectangle-shaped plastic-coated slideways. The mathematical model was firstly suggested especially based on the assembly of the saddle and worktable. Both stiffness and damping characteristics on vertical and horizontal directions were theoretically determined. To derive the governing motion equation of the slideway system, the carriage and rail were considered as rigid bodies and connected with a series of spring and damping elements at the joint face. Moreover, through the Lagrange’s approach, the frequencies of the carriage at vertical, pitching, yawing and rolling vibration mode were identified.

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