The Automatic Generation of a Mathematical Model for Machinery Systems

1973 ◽  
Vol 95 (2) ◽  
pp. 629-635 ◽  
Author(s):  
D. A. Smith ◽  
M. A. Chace ◽  
A. C. Rubens
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Computer Program ◽  
Mechanical System ◽  
Input Data ◽  
Automatic Generation ◽  
Electrical Networks ◽  
Lagrange’S Equation ◽  
Detailed Explanation ◽  
Independent Loops

This paper presents a detailed explanation of a technique for automatically generating a mathematical model for machinery systems. The process starts from a relatively small amount of input data and develops the information required to model a mechanical system with Lagrange’s equation. The technique uses elements of graph theory which were developed for electrical networks. The basic identifications required for mechanical systems are: paths from ground to mass centers, the independent loops of parts, if any, and paths associated with applied force effects. The techniques described in this paper have been used successfully in a generalized computer program, DAMN.

scholarly journals A Kinematical Analysis of the Flap and Wing Mechanism of a Light Sport Aircraft Using Topological Models

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1243
Author(s):  
Sorin Vlase ◽  
Ion-Marius Ghiţescu ◽  
Marius Paun
Keyword(s):  
Graph Theory ◽  
Mechanical System ◽  
Linear Systems ◽  
Kinematic Analysis ◽  
Control Mechanism ◽  
Practical Application ◽  
Dynamic Level ◽  
New Formulation ◽  
Topological Models ◽  
Independent Loops

In this, paper, we propose a method of kinematic analysis of a planar mechanism with application to the flap and wing mechanism of a light sport aircraft. A topological model is used to describe a mechanical system, which is a model that allows the study of the maneuverability of the system. The proposed algorithm is applied to determine the velocity and acceleration field of this multibody mechanical system. The graph associated with the mechanical system is generated in a new formulation and based on it, the fundamental loops of the graph are identified (corresponding to the independent loops of the mechanism), the equations for closing vectorial contours are written, and the kinematic conditions for determining velocities and accelerations and the associated linear systems are solved, which provides the field of speeds and accelerations. Graph Theory is applied at a kinematic level and not at a dynamic level, as in previous studies. A practical application for the kinematic analysis of the control mechanism of a light aircraft illustrates the proposed method.

A Study of Transient Response of Flexible Rotors in High Speed Turbomachinery

1992 ◽  
Author(s):  
V. Pavelic ◽  
R. S. Amano
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Analytical Model ◽  
High Speed ◽  
Angular Speed ◽  
Journal Bearings ◽  
Hydrodynamic Characteristics ◽  
Flexible Assembly ◽  
Lagrange’S Equation ◽  
Equations Of Motions

In many applications the design operating range of the turbomachinery may be well above the rotor first critical speed which leads to the problem of insuring that the turbomachinery performs with a stable, low-level amplitude of vibration. Under certain conditions of high speed and loading the rotor system can start orbiting in its bearing at a rate which is less than the rotor angular speed, and this phenomena is commonly known as whirling or whipping action. This whipping action may produce additional undesirable dynamic loads on the overall flexible assembly and eventually destroy the rotor. Some of this action is also transient in nature. Whirling is a self-exited vibration caused mainly by the fluid bearings and by the internal friction damping of the rotor. To understand this occurrence, a general dynamic mathematical model was derived considering also the complete viscous characteristic of hydrodynamic journal bearings. The general equations of motions of the system are obtained from Lagrange’s equation of motion. The system kinetic, potential, and dissipation functions are determined based on the generalized coordinates of the system. The journal displacements are related to the overall dynamics of the rotor using deformable bearings. The loads acting at the journals of the shaft are integrated from the fluid film pressure distribution in the journal bearings using mobility method. A unique mathematical model is formulated and solved. This model includes the elastic and inertial properties of the flexible rotor, the elastic, damping and inertial properties of supports and the hydrodynamic characteristics of the journal bearings. The equations of motions result in a system of nonlinear second order differential equations which are solved by using finite difference method. The solution of the equations of motions is used to plot maps of motion of journal centers. A computer program was implemented to aid in the solution of the system of equations and to verify analytical model. The computer program used test data available in literature and the results were compared to be very good. The analytical model and results obtained in this study can be of great help to designers of high speed turbomachinery.

scholarly journals Improved model for investigating transient stability in multimachine power systems

2019 ◽  
Vol 13 (1) ◽  
pp. 368
Author(s):  
Ali Hamzeh ◽  
Zakaria Al-Omari
Keyword(s):  
Mathematical Model ◽  
Power Systems ◽  
Computer Program ◽  
Transient Stability ◽  
Stability Study ◽  
Small Sample ◽  
General Algorithm ◽  
Electrical Networks ◽  
Protective Relays ◽  
Improved Model

<span>The determinant factor in transient stability study of electric power systems is the behavior of synchronous generators when subjected to sudden and large disturbances. The objective of this paper is to develop a mathematical model, general algorithm, and a computer program to investigate the transient stability of multi-machine power systems. The developed mathematical model is established as a first step. The new developments lie in modeling the fault occurrence and fault clearance as well as the procedure of computing the system matrices during and after the fault through only modification of the matrix before the fault. Based on the developed mathematical model, a general algorithm was built and translated into a computer program using an object-oriented and visual language called Delphi. The algorithm adopted the Runge-Kutta method for numerical solution of differential swing equations and was programmed within the program. The developed program was validated by applying it to small sample electrical networks. The program was used to analyze the transient stability of a relatively large test network and accurate results were obtained that could be relied upon for protective relays settings and optimization of control system parameters. It was found that the developed program is an effective and rapid tool for estimating transitory stability for real power systems.</span>

The lake ecosystem simulation program

1995 ◽  
Vol 31 (8) ◽  
pp. 367-370
Author(s):  
J. Heringa ◽  
H. Hylkema ◽  
M. Kroes ◽  
E. Ludden ◽  
P. G. van Schaick Zillesen
Keyword(s):  
Mathematical Model ◽  
Water Resources ◽  
Computer Program ◽  
Water Resources Management ◽  
Lake Ecosystem ◽  
Original Research ◽  
Ecological Processes ◽  
Resources Management ◽  
Lake Ecology ◽  
Ecosystem Simulation

The computer program LAKE simulates a shallow lake ecosystem. The program is based on a mathematical model. In the model the most important aspects of several models for water resources management are integrated (Collins and Wlosinski, 1988; Jørgensen, 1976; Jørgensen et al., 1978; Scheffer, 1988). Furthermore, the model describes several ecological processes that have not yet been described by lake-ecosystem models so far. In the computer program, the mathematical model and an advanced, object oriented, user interface are combined. Following this approach the use of the original research models was extended to a use for the purpose of teaching lake ecology. We suggest that the same approach may be followed to open research models to other groups concerned with water resources management, such as management authorities, industry, agricultural extension, nature conservation and recreation.

scholarly journals Optimal feeder reconfiguration in distributed generation environment under time-varying loading condition

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Yanrenthung Odyuo ◽  
Dipu Sarkar ◽  
Lilika Sumi
Keyword(s):  
Graph Theory ◽  
Distributed Generation ◽  
Spanning Tree ◽  
Voltage Stability ◽  
Electrical Network ◽  
List Type ◽  
Network Reconfiguration ◽  
Time Varying ◽  
Electrical Networks ◽  
Tree Algorithm

Abstract The development and planning of optimal network reconfiguration strategies for electrical networks is greatly improved with proper application of graph theory techniques. This paper investigates the application of Kruskal's maximal spanning tree algorithm in finding the optimal radial networks for different loading scenarios from an interconnected meshed electrical network integrated with distributed generation (DG). The work is done with an objective to assess the prowess of Kruskal's algorithm to compute, obtain or derive an optimal radial network (optimal maximal spanning tree) that gives improved voltage stability and highest loss minimization from among all the possible radial networks obtainable from the DG-integrated mesh network for different time-varying loading scenarios. The proposed technique has been demonstrated on a multiple test systems considering time-varying load levels to investigate the performance and effectiveness of the suggested method. For interconnected electrical networks with the presence of distributed generation, it was found that application of Kruskal's algorithm quickly computes optimal radial configurations that gives the least amount of power losses and better voltage stability even under varying load conditions. Article Highlights Investigated network reconfiguration strategies for electrical networks with the presence of Distributed Generation for time-varying loading conditions. Investigated the application of graph theory techniques in electrical networks for developing and planning reconfiguration strategies. Applied Kruskal’s maximal spanning tree algorithm to obtain the optimal radial electrical networks for different loading scenarios from DG-integrated meshed electrical network.

The Control of Vibration Transmissibility Using an Electrodynamic Actuator –Close-Loop Solution

2013 ◽  
Vol 436 ◽  
pp. 166-173
Author(s):  
A. Mihaela Mîţiu ◽  
Daniel Constantin Comeagă ◽  
Octavian G. Donţu
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Mechanical System ◽  
Closed Loop ◽  
Mechanical Systems ◽  
Vibration Transmissibility ◽  
Technical Solutions ◽  
The Mathematical Model

In this paper are presented some aspects of transmissibility control of mechanical systems with 1 DOF so that the effects of vibration on their action to be minimized. Some technical solutions that can be used for this purpose is analyzed. Starting from the mathematical model of an electro-mechanical system with 1 DOF, are identified the parameters which influence the effectiveness of the transmissibility control system using an electrodynamic actuator who work in "closed loop".

Nonlinear Dynamics of an Oilless Reciprocating Compressor

1993 ◽  
Author(s):  
Constantinos Minas
Keyword(s):  
Mathematical Model ◽  
Mechanical System ◽  
Input Voltage ◽  
Amplitude Dependence ◽  
Integration Step ◽  
Damped System ◽  
Steady State Operation ◽  
Pressure Term ◽  
Sinusoidal Input ◽  
Mass Flow Rates

Abstract Two modeling methodologies of the dynamics of a motor-compressor system are presented. The first approach considered only the mechanical system subjected to a sinusoidal input force with the pressure term in the equation of motion treated as a nonlinear stiffness term. The second methodology consisted of a mathematical model that couples the electromagnetic and thermodynamic equations to the dynamic equations that describe the motion of the piston. The mathematical model which consisted of a set of four first order simultaneous nonlinear time varying differential equations, was solved by numerical integration routines that use the Adams-Moulton method with an adaptive integration step. The two methodologies are illustrated through an example. Steady-state operation was shown to be reached rapidly after a 0.13s transient. An analysis at various amplitudes and frequencies of the input voltage in the driver-coil of the motor, showed the amplitude dependence of the resonant frequency of the mechanical system, and a heavily damped system when operating at the design amplitude. The most efficient frequency of operation was also determined for a variety of required mass flow rates.

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