Paper 3: An Analysis of the Dynamics of Automobiles during Simultaneous Cornering and Ride Motions

Author(s):  
R. R. McHenry

A mathematical model of an automobile is described, which permits the study of simultaneous cornering and ride motions on irregular terrain. A major departure from previous analytical treatments of vehicles is abandonment of the concept of a vehicle-fixed ‘hinge’ to approximate the changing virtual axis about which roll takes place. Eleven degrees of freedom and all major non-linearities are included in the equations of motion, which are programmed for time-history solutions on a digital computer. Empirical relationships used to generate tyre forces over extreme ranges of operating conditions are presented in detail. To ease the task of interpretation of the extensive output information, a computer-graphics display technique has been developed to produce detailed perspective drawings of the vehicle and terrain at selected intervals of time during a simulated manoeuvre. Comparisons are presented of analytically predicted vehicle responses and test results. Future applications of the described mathematical model, in research related to highway safety, are briefly discussed.

2011 ◽  
Vol 97-98 ◽  
pp. 787-793 ◽  
Author(s):  
Shen Hua Yang ◽  
Guo Quan Chen ◽  
Xing Hua Wang ◽  
Yue Bin Yang

Due to the target ship in the traditional ship handling simulator have not the ability to give way to other ships automatically to avoid collision, this paper put forward a new idea that bringing the hydraulic servo platform, six degrees of freedom ship mathematical model, the actual traffic flow, researching achievement of automatic anti-collision in research of the new pattern ship handling simulator, and successfully develop the Intelligent Ship Handling Simulator(ISHS for short). The paper focuse on the research on the network communication model of ISHS. We took the entire simulator system as three relatively independent networks, proposed a framework of communication network that combined IOCP model based on TCP with blocking model based on UDP, and gave the communication process and protocols of system. Test results indicate that this is an effective way to improve the ownship capacity of ship handling simulator and meet the need of multi-ownship configuration of desktop system of ship handling simulator.


Author(s):  
Darina Hroncová

Urgency of the research. Computer models mean new quality in the knowledge process. Using a computer model, the properties of the subject under investigation can be tested under different operating conditions. By experimenting with a com-puter model, we learn about the modelled object. We can test different machine variants without having to produce and edit prototypes. Target setting. The development of computer technology has expanded the possibility of solving mathematical models and allowed to gradually automate the calculation of mathematical model equations. It is necessary to insert appropriate inputs of the mathematical model and monitor and evaluate the output results through the computer output device The target was to describe the mathematical apparatus required for mathematical modeling and subsequently to compile a model for computer modeling. Actual scientific researches and issues analysis. When formulating a mathematical model for a computer, the laws and the theory we use are always valid under more or less idealized conditions, and operate with fictitious concepts such as, material point, ideal gas, intangible spring, and the like. However, with these simplifications, we describe a realistic phenomenon where the initial assumptions are only met to a certain extent. In order for the results not to be different from the modeled reality, it is to be assumed that a good computer model arises gradually, by verifying and modifying it, which is one of the advantages of MSC Adams. Uninvestigated parts of general matters defining. The question of building a real manipulator model. Based on the above simulation, it is possible to build a real model. The research objective. Using MSC Adams to simulate multiple body systems and verify its suitability for simulating ma-nipulator and robot models. In various versions of the assembled model we can monitor its behavior under different operating conditions. The statement of basic materials. In computer simulation, MSC Adams-View is used to simulate mechanical systems. It has an interactive environment for automated dynamic analysis of parameterized mechanical systems with an arbitrary struc-ture of rigid and flexible bodies with geometric or force joints, in which act gravity, inertia, experimentally designed contact, friction, aerodynamic, hydrodynamic or electromechanical forces and have integrated control, hydraulic, pneumatic or elec-tromechanical circuits. Conclusions. Working with a mathematical model on a computer opens space for specific synthesis of empirical and ana-lytical method of scientific knowledge. Working with the computer model carries the characteristic features of classical experi-mentation. It represents a qualitatively new way of solving tasks that can not be experimented with on a real object. The result is the equivalence of the computer model and the object being investigated with the features and expressions chosen as essen-tial, with accuracy sufficient to the exact purpose.


2011 ◽  
Vol 11 (06) ◽  
pp. 1201-1228 ◽  
Author(s):  
AJAY SHARMA ◽  
R. S. JANGID

The influence of high initial isolator stiffness on the response of a base-isolated benchmark building is investigated. The base-isolated building is modeled as a three-dimensional linear-elastic structure having three degrees-of-freedom at each floor level. The time-history analysis of this building is carried out by solving the governing equations of motion using Newmark-beta method along with an iterative predictor–corrector approach. The force–deformation behavior of the isolation system is modeled by a bilinear law, which can be effectively used to model all isolation systems in practice. Three near-field earthquakes with bidirectional ground motions are considered. Structural response parameters such as absolute top floor acceleration, base shear, and base displacement are chosen for investigating the effects of high initial isolator stiffness. It was observed that the high initial isolator stiffness of the isolation system excites the higher modes in the base-isolated building and increases the top floor acceleration. Such a phenomenon can be detrimental to the sensitive instruments placed in the isolated structure. On the other hand, both the base displacement and base shear reduce marginally due to increase in the initial isolator stiffness. Further, the influences of high initial isolator stiffness are found to dependent on the period and characteristic strengths of the base isolation system.


2018 ◽  
Vol 79 (2) ◽  
pp. 15-31
Author(s):  
Wafi A. Mabrouk ◽  
M. F. L. Abdullah

Designing a new monorail suspension system for an existing monorail bogie to accommodate larger cars, locomotives and more passengers is a difficult and complicated problem to solve. This paper introduces a simulation of a mathematical model for a monorail suspension system that can be used as an analytical tool to investigate and predict the behavior of the model under different speeds and track conditions. In this paper, the simulation is performed to predict some dynamic characteristics monorail suspension system. This research work concentrates on the simulation of 15 degrees of freedom full-car Monorail suspension system. The model features the Monorail body, Front bogie, and rear bogie geometries, adopted equations of motion of the monorail suspension system and system matrices. Numerical Central Difference method was used to obtain the system responses subject to sinusoidal Track excitations. Three Track scenarios that have different loads and different driving speeds were conducted to investigate the monorail suspension system. The system results are analysed in terms of their dynamic responses. Fourier Fast transforms was used to calculate the frequency ranges of dynamic responses. As a result, some very important characteristics of the Monorail suspension system were revealed, with indicators that help to understand the effects of driving speeds and different loads, which can be used to better understand the system dynamic performance, to improve Monorail suspension system designs flaws detection.


Author(s):  
Giuseppe Catania ◽  
Alessandro Zanarini

An analytical-experimental approach is followed to obtain the dynamic model of a car vehicle, taking into account the full dynamic contribution due to tires. Linearized and condensed vehicle equations of motion are first introduced. The experimental modal model of a car tire, consisting of limited sets of eigenfrequencies and eigenshapes is then experimentally estimated in the frequency range Δftire=0÷300 Hz, starting from a restricted set of experimental degrees of freedom (d.o.f.). The tire is locally loaded to simulate the displacements due to gravitational loads and road contact occurring in operating conditions. Elastic coupling between the car structural model and the tire modal model is thus obtained; a linear, complex eigenproblem is thus formulated, and eigenfrequencies related to the full system are obtained as well. Results are reported and discussed in detail.


1970 ◽  
Vol 10 (03) ◽  
pp. 311-320 ◽  
Author(s):  
Ben G. Burke

Abstract A mathematical model was developed to compute the motions of semisubmersible drilling vessels in waves for a wide variety of semisubmersible configurations. The model was derived from a linear representation of motions, ocean waves, and forces. The semisubmersible is represented as a rigid space frame composed of a number of cylindrical members with arbitrary diameters, lengths and orientations. Forces on the semisubmersible are derived from anchorline properties, and hydrostatic hydrodynamic principles. A solution is obtained for motions in six degrees of freedom for a sinusoidal wave train of arbitrary height, period, direction and water depth. Results from the analysis of three semisubmersibles are compared with results from available model test data to verily the mathematical model. Introduction An accurate and complete representation of the response of a drilling vessel to waves is a valuable engineering tool for predicting vessel performance and designing drilling equipment. The performance and designing drilling equipment. The wave response for a floating vessel may be obtained to various degrees of accuracy from model tests or analytical means, as described by Barkley and Korvin-Kroukovsky and as applied by Bain. A review of the works cited shows that the evaluation of the wave response for a particular vessel requires considerable time and effort, either in model construction and testing or in computer programming and calculations. In order to reduce programming and calculations. In order to reduce the amount of time and effort required to evaluate a particular vessel, means were investigated to generalize and automate, on a digital computer, methods for evaluating wave response for vessels of arbitrary configuration. The mathematical model described in this paper is the result of such an investigation for semisubmersible-type drilling vessels. The paper presents a general description of the mathematical model and the basic principles and assumptions from which it was derived. The validity of the model is evaluated by comparing results of the analysis of three semisubmersibles with available model test data. MATHEMATICAL MODEL The mathematical model for calculating the motions of a semisubmersible in waves is derived from basic principles and empirical relationships in classical mechanics. All equations are derived for "small amplitude" waves and motions. The nonlinear equations that appear in the problem are replaced by "equivalent" linear equations in order to conform to the linear analysis method used in obtaining a solution. The model is implemented in a computer program that computes vessel response in all six degrees of freedom for a broad range of semisubmersible configurations and wave parameters. The basic elements in the theoretical model are outlined, with a more detailed discussion of the principles and derivations used to obtain the model principles and derivations used to obtain the model presented in the Appendix. presented in the Appendix. SEMISUBMERSIBLE DESCRIPTION AND EQUATIONS OF MOTION The semisubmersible is characterized as a space-frame of cylindrical members and is described geometrically by specifying end-coordinates and diameters for all of the members. Specification of the mass, moments of inertia, center of gravity and floating position are required to complete the description. The six equations of motion for the semisubmersible derive from Newton's second law for a rigid body. These differential equations, when written in matrix form, equate the product of the six-component acceleration vector, {x}, and the inertia matrix, I, to a six-component, force-moment vector, {FT}. SPEJ P. 311


2019 ◽  
Vol 13 (4) ◽  
pp. 226-232
Author(s):  
Arkadiusz Trąbka

Abstract Forging hammers are machines whose operation causes negative effects both at the place of their foundation (the soil settlement) and in their surroundings (e.g., vibrations propagating to the other devices, noise, etc.). Knowledge of the parameters characterizing the time history of the force that arises as a result of impact of a ram on a shaped material is of fundamental importance for the correct analysis of both the structure of the hammer and its impact on the surroundings. In the paper, the effect of the shape and duration of a pulse load on the dynamic response of a hammer-foundation forging system was assessed. An analytical method of description of the forces that arise as a result of impact of the ram on the forged material, using different forms of pulses was presented. The forces defined in this way as loads in a mathematical model of three degrees of freedom forging system were used. The equations of motion derived from d’Alembert’s principle were solved numerically in the Matlab program. The analyses for eight forms of the pulse loads with the same pulse sizes but different durations were performed. The results in the graphs were presented. It was found, among other things, that a greater impact on the maximum displacement, velocity and acceleration of each component of the hammer-foundation system as well as on the maximum forces transmitted to the soil has the duration of a pulse than its shape.


2013 ◽  
Vol 61 (2) ◽  
pp. 475-484 ◽  
Author(s):  
L. Baranowski

Abstract In the paper the three different mathematical models of motion of a spin-stabilized, conventional artillery projectile, possessing at least trigonal symmetry, have been introduced. The vector six-degrees-of-freedom (6-DOF) differential equations of motion are an updated edition of those published by Lieske and McCoy and are consistent with STANAG 4355 (Ed. 3). The mathematical models have been used to developing software for simulating the flight of the Denel 155mm Assegai M2000 series artillery projectile and to conduct comprehensive research of the influence of the applied model and integration step on the accuracy and time of computation of projectile trajectory.


2012 ◽  
Vol 445 ◽  
pp. 1082-1087 ◽  
Author(s):  
Ahmet Sagirli ◽  
C. Oktay Azeloglu

This paper is concerned with investigation of the dynamic behaviors of cranes under seismic effects. For this purpose, firstly we have performed experiment on a 1/20 scale crane model on the shake table with real earthquake data, then a multi degree-of-freedom non-linear mathematical model is developed including behavior of the container cranes under earthquakes and simulated. The simulation system has a five degrees-of-freedom and modeled system was simulated for the ground motion of the El Centro earthquake in USA, 1940. Finally, the time history of the crane bridge displacement and acceleration responses of the both theoretical and experimental cases are presented. Theoretical and experimental results exhibit that the mathematical model is accurate. This study also shows the destructive effects of high accelerations which occur during the earthquake. These effects cannot be omitted in the design of cranes. The result of this study which is an accurate mathematical model can be inspiring for the engineers in terms of design parameters.


2019 ◽  
Vol 16 (33) ◽  
pp. 668-680
Author(s):  
L. A. KONDRATENKO ◽  
L. I. MIRONOVA ◽  
V. G. DMITRIEV ◽  
O. V. EGOROVA ◽  
A. O. SHEMIAKOV

Many of the mechanisms used in industry contain input and output links connected by long lines of force. Increasing the efficiency and service life of mechanical systems with long lines is of great importance for the country's economy. For a more rational use of these devices, it is important to maintain these operating modes with maximum accuracy, usually including the required speed of the actuator and the voltage in the lines. Such parameters can spontaneously change depending on the operating conditions of the system. In the presence of various influences, similar tasks to determine the marked regimes and parameters indicating the need for their change can be solved only with the help of the corresponding theory and research methods. The article presents the problems and the method of studying two-tier mechanical systems with an infinite number of degrees of freedom on the basis of the equations of momentum and moment of momentum in differential form. Transformations with the use of well-known wave equations are proposed, which made it possible to explicitly take into account the oscillations of the speeds of motion and stresses in the force lines of mechanical systems when describing dynamic processes. The solution of systems of partial differential equations is given using the Laplace transform, which made it possible to obtain general equations of motion and, after some simplifications, proceed to ordinary differential equations that take into account the dynamic features of systems with distributed parameters. The modernized Runge-Kutta method obtained solutions and carried out numerical simulation of transient processes in the hydraulic drive, the results of which have good convergence with full-scale experiments.


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