NONLINEAR MODELING OF COMPLEX MECHANICAL SYSTEMS

1994 ◽  
Vol 04 (03) ◽  
pp. 521-551 ◽  
Author(s):  
MARTIN LESSER
Keyword(s):  
Nonlinear Models ◽  
Nonlinear Modeling ◽  
Mechanical Systems ◽  
Computer Software ◽  
Nonholonomic Systems ◽  
Reference List ◽  
Spacecraft Design ◽  
Vehicle Technology ◽  
Configuration Manifold ◽  
Complex Mechanical Systems

This article provides an introduction to a technique for formulating nonlinear models of mechanical systems composed of interconnected and constrained rigid body systems such as those encountered in vehicle technology, biomechanics, spacecraft design and robotics. The approach is based on an algorithm developed by Kane to treat nonholonomic systems, for example systems with rolling constraints. The algorithm is interpreted geometrically in terms of tangent vectors to the instantaneous configuration manifold embedded in the space of nonconstrained motions for the system. The level and style of the presentation is intended to be understood by scientifically literate readers with minimal knowledge in mechanics beyond the introductory level. Examples also show how computer algebra can be used to reduce the effort required for treating complex systems. An annotated reference list, which includes a discussion of computer software, is also provided.

Energy Method for Determining Dynamic Characteristics of Mechanisms

1949 ◽  
Vol 16 (3) ◽  
pp. 283-288
Author(s):  
B. E. Quinn
Keyword(s):  
Dynamic Characteristics ◽  
Energy Method ◽  
Mechanical Systems ◽  
Direct Approach ◽  
Graphical Methods ◽  
Applied Forces ◽  
Complex Mechanical Systems

Abstract Two types of problems are dealt with in the paper which are involved in the design of mechanisms required to have specified dynamic characteristics: (1) Determination of applied forces required to produce specified dynamic characteristics. (2) Determination of the dynamic characteristics which will result from the application of known forces. While graphical methods may be used in the solution of type (1) problems involving more or less complex mechanical systems, they do not afford a direct approach to type (2) problems. The energy method which will be outlined can be applied in either case, although this paper will be primarily concerned with the determination of the dynamic characteristics which result when a known force is applied to a given mechanism.

A Form Verification System for the Conceptual Design of Complex Mechanical Systems

1993 ◽  
Author(s):  
Jonathan S. Colton ◽  
Mark P. Ouellette
Keyword(s):  
Conceptual Design ◽  
Process Model ◽  
Mechanical Systems ◽  
Data Representation ◽  
Design System ◽  
Complex Data ◽  
Graphical Display ◽  
Design Environment ◽  
Blackboard System ◽  
Complex Mechanical Systems

Abstract This paper presents a summary of research into the development and implementation of a domain independent, computer-based model for the conceptual design of complex mechanical systems (Ouellette, 1992). The creation of such a design model includes the integration of four major concepts: (1) The use of a graphical display for visualizing the conceptual design attributes; (2) The proper representation of the complex data and diverse knowledge required to design the system; (3) The integration of quality design methods into the conceptual design; and (4) The modeling of the conceptual design process as a mapping between functions and forms. Using the design of an automobile as a case study, a design environment was created which consisted of a distributed problem solving paradigm and a parametric graphical display. The requirements of the design problem with respect to data representation and design processing were evaluated and a process model was specified. The resulting vehicle design system consists of a tight integration between a blackboard system and a parametric design system. The completed system allows a designer to view graphical representations of the candidate conceptual designs that the blackboard system generates.

Reduction of Hamiltonian Mechanical Systems With Affine Constraints: A Geometric Unification

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Robin Chhabra ◽  
M. Reza Emami ◽  
Yael Karshon
Keyword(s):  
Symmetry Group ◽  
Mechanical Systems ◽  
Hamiltonian Formalism ◽  
Geometrical Approach ◽  
Constraint Forces ◽  
Dynamical Equations ◽  
Relative Configuration ◽  
D’Alembert Equation ◽  
Dynamical Reduction ◽  
Configuration Manifold

This paper presents a geometrical approach to the dynamical reduction of a class of constrained mechanical systems. The mechanical systems considered are with affine nonholonomic constraints plus a symmetry group. The dynamical equations are formulated in a Hamiltonian formalism using the Hamilton–d'Alembert equation, and constraint forces determine an affine distribution on the configuration manifold. The proposed reduction approach consists of three main steps: (1) restricting to the constrained submanifold of the phase space, (2) quotienting the constrained submanifold, and (3) identifying the quotient manifold with a cotangent bundle. Finally, as a case study, the dynamical reduction of a two-wheeled rover on a rotating disk is detailed. The symmetry group for this example is the relative configuration manifold of the rover with respect to the inertial space. The proposed approach in this paper unifies the existing reduction procedures for symmetric Hamiltonian systems with conserved momentum, and for Chaplygin systems, which are normally treated separately in the literature. Another characteristic of this approach is that although it tracks the structure of the equations in each reduction step, it does not insist on preserving the properties of the system. For example, the resulting dynamical equations may no longer correspond to a Hamiltonian system. As a result, the invariance condition of the Hamiltonian under a group action that lies at the heart of almost every reduction procedure is relaxed.

scholarly journals Degrading systems availability analysis: analytical semi-Markov approach

2021 ◽  
Vol 23 (1) ◽  
pp. 195-208
Author(s):  
Varun Kumar ◽  
Girish Kumar ◽  
Rajesh Kumar Singh ◽  
Umang Soni
Keyword(s):  
Steady State ◽  
Degradation Mechanism ◽  
Continuous Process ◽  
Mechanical Systems ◽  
Embedded Markov Chain ◽  
Steady State Probability ◽  
Opportunistic Maintenance ◽  
System Availability ◽  
Availability Analysis ◽  
Complex Mechanical Systems

This paper deals with modeling and analysis of complex mechanical systems that deteriorate with age. As systems age, the questions on their availability and reliability start to surface. The system is believed to suffer from internal stochastic degradation mechanism that is described as a gradual and continuous process of performance deterioration. Therefore, it becomes difficult for maintenance engineer to model such system. Semi-Markov approach is proposed to analyze the degradation of complex mechanical systems. It involves constructing states corresponding to the system functionality status and constructing kernel matrix between the states. The construction of the transition matrix takes the failure rate and repair rate into account. Once the steady-state probability of the embedded Markov chain is computed, one can compute the steady-state solution and finally, the system availability. System models based on perfect repair without opportunistic and with opportunistic maintenance have been developed and the benefits of opportunistic maintenance are quantified in terms of increased system availability. The proposed methodology is demonstrated for a two-stage reciprocating air compressor with intercooler in between, system in series configuration.

Nonlinear Modeling of a Rigid Rotor Supported on Rolling Element Bearings With Localized Defects

2010 ◽  
Author(s):  
Karthik Kappaganthu ◽  
C. Nataraj
Keyword(s):  
Nonlinear Model ◽  
Nonlinear Models ◽  
Nonlinear Modeling ◽  
Rolling Element Bearings ◽  
Rigid Rotor ◽  
Rolling Element ◽  
Localized Defects ◽  
Bearing Race ◽  
Overall Performance ◽  
Bearing System

In this paper a nonlinear model for defects in rolling element bearings is developed. Detailed nonlinear models are useful to detect, estimate and predict failure in rotating machines. Also, accurate modeling of the defect provides parameters that can be estimated to determine the health of the machine. In this paper the rotor-bearing system is modeled as a rigid rotor and the defects are modeled as pits in the bearing race. Unlike the previous models, the motion of the rolling element thorough the defect is not modeled as a predetermined function; instead, it is dynamically determined since it depends on the clearance and the position of the shaft. Using this nonlinear model, the motion of the shaft is simulated and the effect of the rolling element passing through the defect is studied. The effect of shaft parameters and the defect parameters on the precision of the shaft and the overall performance of the system is studied. Finally, suitable measures for health monitoring and defect tracking are suggested.

Sign in / Sign up

Export Citation Format

Share Document