A Technique for Assessing Tire Forces in a Vehicle Moving Along a Harmonic Profile and Its Application to Low-Speed Testing

2005 ◽  
Author(s):  
Alexander V. Pesterev ◽  
Lawrence A. Bergman ◽  
Chin An Tan
Keyword(s):  
Mathematical Model ◽  
Explicit Formula ◽  
Vehicle Model ◽  
Numerical Examples ◽  
Low Speed ◽  
The Matrix ◽  
Low Speeds ◽  
Tire Forces ◽  
Stiffness And Damping ◽  
The Mathematical Model

The paper is concerned with the assessment of dynamic tire forces that arise when a vehicle traverses a road with a harmonic profile. In this case, solutions of all equations are found analytically. The technique developed is not specific to a particular linear vehicle model, which is represented by its mass, stiffness, and damping matrices. A factored representation of the vector of the tire forces as the product of a matrix and a vector, where both the matrix and the vector are functions of only one variable, is derived. The matrix is constructed either by the mathematical model of the vehicle or by results of special tests on the vehicle at several values of speed. The vector is given by an explicit formula and requires knowledge of only the wheelbase distances. An application of the technique discussed to the so-called low-speed testing is discussed. It is shown that, in spite of the wheelbase filtering phenomenon, it is possible to replace testing vehicles at highway speeds by tests at artificially low speeds. The results of the latter tests can then be recalculated into those corresponding to the highway conditions. The discussions are illustrated by numerical examples.

Deep and Shallow Water Low-Speed Maneuvering Tests: Comparison Between Experimental and Simulation Results

2016 ◽  
Author(s):  
Felipe Ribolla Masetti ◽  
Pedro Cardozo de Mello ◽  
Guilherme F. Rosetti ◽  
Eduardo A. Tannuri
Keyword(s):  
Mathematical Model ◽  
Small Scale ◽  
Shallow Waters ◽  
Hydrodynamic Coefficients ◽  
Low Speed ◽  
Tunnel Model ◽  
Oceanographic Research ◽  
Simulation Results ◽  
The University ◽  
The Mathematical Model

This paper presents small-scale low-speed maneuvering tests with an oceanographic research vessel and the comparison with mathematical model using the real time maneuvering simulator developed by the University of São Paulo (USP). The tests are intended to verify the behavior of the vessel and the mathematical model under transient and low speed tests. The small-scale tests were conducted in deep and shallow waters, with a depth-draft ratio equal to 1.28, in order to verify the simulator ability to represent the vessel maneuverability on both depth conditions. The hydrodynamic coefficients used in the simulator model were obtained by CFD calculations and wind tunnel model tests carried out for this vessel. Standard turning circle and accelerating turn maneuvers were used to compare the experimental and numerical results. A fair agreement was achieved for shallow and deep water. Some differences were observed mainly in the initial phase of the accelerating turn test.

Mobile Robots Characterized by Kinematic and Dynamic Equations: Motion Planning, Trajectory Tracking, and Group Control

2008 ◽  
Author(s):  
Amit Ailon
Keyword(s):  
Mathematical Model ◽  
Motion Planning ◽  
Mobile Robots ◽  
Dynamic Equations ◽  
Kinematics And Dynamics ◽  
Control Problems ◽  
Reference Trajectory ◽  
Numerical Examples ◽  
Group Control ◽  
The Mathematical Model

The paper solves some control problems of mobile robots as both kinematics and dynamics are intertwined in the mathematical model. The problems of driving the vehicle to a desired configuration in a specified time and tracking a reference trajectory are considered. The control problems associated with motion in convoy and rigid formations of a group of vehicles are studied and some results are demonstrated by numerical examples.

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.

A Study of the Effects of Baffles on Rotating Compressible Flows

1989 ◽  
Vol 56 (3) ◽  
pp. 710-712
Author(s):  
Max D. Gunzburger ◽  
Houston G. Wood ◽  
Rosser L. Wayland
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Compressible Flows ◽  
Numerical Examples ◽  
Thermal Boundary Conditions ◽  
Gas Centrifuge ◽  
Mass Injection ◽  
Flow Domain ◽  
The Mathematical Model ◽  
Element Algorithm

Onsager’s pancake equation for the fluid dynamics of a gas centrifuge is modified for the case of centrifuges with baffles which render the flow domain doubly connected. A finite element algorithm is used for solving the mathematical model and to compute numerical examples for flow fields induced by thermal boundary conditions and by mass injection and extraction.

Developing of an Active Hydraulic Bushing for Multi-Displacement Engines

2006 ◽  
Author(s):  
S. Arzanpour ◽  
M. F. Golnaraghi
Keyword(s):  
Mathematical Model ◽  
Research Effort ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Feedback Signal ◽  
Frequency Range ◽  
Engine Mount ◽  
Isolation Requirements ◽  
Stiffness And Damping ◽  
The Mathematical Model

This paper outlines the development of an active hydraulic bushing system for the Multi Displacement System (MDS) Engine isolation problems. The prior art research effort on engine mounts and bushings has so far focused on the improvement of the mount dynamic stiffness properties. The optimum dynamic stiffness and damping of the engine bushings is both frequency and amplitude dependent. While these systems are available commercially, they have many limitations, particularly for new vehicle models and new engine generations such as MDS engines. A suitable isolator for an MDS engine should be half as stiff in the operating frequency range of the engine (5-70 Hz) in MDS mode, while showing the same performance as conventional hydraulic bushings in normal engine operations. Passive hydraulic bushings are not capable of meeting the isolation requirements discussed for the MDS engines because they are not adjustable. There are different parameters which contribute to the dynamic stiffness response of a hydraulic bushing. Some of those parameters are defined by passive components such as rubber stiffness and damping. However, other parameters such as the pressure inside the bushing can be altered actively. The mathematical model of a conventional hydraulic bushing is given in this paper. The model suggests that the pressure inside the bushing has a significant role in the dynamic stiffness response of the bushing. As a result, an additional pumping chamber is introduced as a solution. The pump is utilized to adjust the pressure inside the bushing based on the engine excitation frequency. This pump can be driven by proper actuators which can produce pressure differences in the frequency range of interest. The mechanical and mathematical model of such a system is derived using a simplified linear model. This technique enables the engine mount to adjust to the dynamic stiffness characteristics by applying a feedback signal to the actuator. The feedback signal to the actuator is also obtained using the mathematical model for many required cases yet adjustable for others. The response of the system is discussed in frequency domains. The simulation results prove that the additional pumping chamber can effectively be used to control the stiffness of the conventional hydraulic bushings.

scholarly journals Full 16-parametric model of calibration processes and direct measurement of parameters of four-poles

2019 ◽  
Vol 55 (1) ◽  
pp. 69-76
Author(s):  
A. V. Gusinski ◽  
V. A. Bogush
Keyword(s):  
Mathematical Model ◽  
Direct Measurement ◽  
Scattering Matrix ◽  
Parametric Model ◽  
Matrix Form ◽  
Matrix Analysis ◽  
The Matrix ◽  
Measurement Object ◽  
Cellular Matrices ◽  
The Mathematical Model

A complete mathematical model for measuring the parameters of the scattering matrix for a measurement object [Sx] in the form of a four-port network is developed, in which the mathematical model of the eight-port error is described by 16 parameters of the scattering matrix [E]. In addition, in comparison with the 12-parameter model of the eight-port error network, four parameters are included, which allow taking into account leaks, parasitic transmissions of microwave modules under study (microwave microassemblies). Due to the use of matrix analysis methods, the equations in matrix form are obtained that connect the matrices of the measurement object [Sи] and the actual values of the matrix parameters [Sx], with the aim of enabling the solution of these equations instead of the scattering matrix [E] to use a transmition matrix [T] in the form of cellular matrices [Taa], [Tab], [Tba], [Tbb].

scholarly journals The use of Lambert function method for analysis of a multidimensional control system with delays and with structure of the complete graph

2012 ◽  
Vol 53 ◽  
Author(s):  
Irma Ivanovienė ◽  
Jonas Rimas
Keyword(s):  
Mathematical Model ◽  
Complete Graph ◽  
Function Method ◽  
Lambert Function ◽  
Mutual Synchronization ◽  
Delayed Argument ◽  
The Matrix ◽  
Matrix Differential ◽  
The Mathematical Model ◽  
Step Responses

The mathematical model of the mutual synchronization system with structure having form of the complete graph and composed of n  oscillators, is investigated. The mathematical model of the system is the matrix differential equation with delayed argument. The step responses matrix of the system is obtained applying the Lambert function method. The transition processes are investigated using obtained step responses of the system.

Mathematical Simulation of Thermomechanics in an Impermeable Porous Medium

2020 ◽  
pp. 4-23
Author(s):  
M.V. Alekseev ◽  
N.G. Sudobin ◽  
A.A. Kuleshov ◽  
E.B. Savenkov
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Chemical Reactions ◽  
Three Dimensional ◽  
Element Model ◽  
Lumped Element ◽  
The Matrix ◽  
Thermochemical Processes ◽  
Lumped Element Model ◽  
The Mathematical Model

The paper reports on mathematically simulating behaviour of a porous medium featuring isolated interstices filled with a chemically active substance by using a mathematical model of thermomechanics in the matrix and thermochemical processes inside the pores. We used three-dimensional thermomechanical equations to describe the behaviour of the medium. A lumped-element model accounting for chemical reactions and phase equilibrium describes the processes in pores. We outline the mathematical model of the medium and the respective computational algorithm. We provide parametric computation results using realistic thermophysical and thermodynamical parameters, composition of the organic substance found inside pores (products of thermal decomposition of kerogen) and chemical reactions, which show that it is necessary to employ complex, interconnected models to simulate the process class under consideration

Investigation of Influence of Geometrical and Adjusting Parameters on the Rotor Engine Power.

2015 ◽  
Vol 2015 (1) ◽  
pp. 10-13
Author(s):  
Евгений Дмитриевский ◽  
Evgeniy Dmitrievskiy
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Polynomial Model ◽  
Matrix Approach ◽  
Piston Engine ◽  
The Matrix ◽  
The Mathematical Model ◽  
Engine Power ◽  
Regressive Analysis ◽  
Diagnostic Variables

It has been determined that diagnostic variables which have an effect on the rotor-piston engine power Ne are the geometrical one (coefficient of inflation ηv) and the adjusting one (coefficient of air excess α). According to the mathematical model of the rotor engine, by the method of multiple regressive analysis, based on the use of the method of the least squares and on the matrix approach to the calculation of coefficients of the polynomial model, an equation has been obtained which properly describes the dependence of its power Ne on the combination of two independent diagnostic variables: ηv and α.

scholarly journals Coordinating a three level supply chain with multiple retailers

2021 ◽  
Author(s):  
Shahzad Naqvi
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Supply Chain Coordination ◽  
Research Work ◽  
The Other ◽  
Total Cost ◽  
Numerical Examples ◽  
Conflicting Interests ◽  
Order Quantities ◽  
The Mathematical Model

The objective of this research is to highlight the factors that can optimize the total cost of a centralized supply chain through coordination of order quantities amongst the players in a supply chain. Survey of earlier research reveals that players in a supply chain usually have conflicting interests, such as reducing inventories and increasing profitability. Thus, to make coordination feasible, it is essential to provide proper incentives to individual players. Munson and Rosenblatt (2001) were the first to discuss coordination in a three level supply chain with a single player at each level. On the other hand, Viswanathan and Piplani (2001) are believed to be the first to consider cooordination in a two level supply chain with a single vendor and multiple retailers. This research extends upon these works by investigating coordination in a three level supply chain with multiple retailers. This is done by incorporating the model of Viswanathan and Piplani (2001) into that of Munson and Rosenblatt (2001). A new mathematical model is developed, with numerical examples presented and results discussed. When players in a supply chain agree to coordinate, it is possible to have some of the players benefiting more than others in the chain, if not losing. The mathematical model developed in this research work guarantees that the local costs for the players either remain the same as before coordination, or decrease as a result of coordination. Furthermore, this research work assumes that savings generated from coordination should be distributed among the players of the chain. This led to developing a scheme to fairly distribute savings amongst the players of the supply chain. Results indicate that even though players may have conflicting interests in the supply chain, coordination is recommended and should be pursued.

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