Modeling and Theory of Intermittent Motions in a Machine Tool With a Friction Boundary

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Brandon C. Gegg ◽  
Steve C. S. Suh ◽  
Albert C. J. Luo
Keyword(s):  
Machine Tool ◽  
Systems Theory ◽  
Frictional Force ◽  
Periodic Motion ◽  
Mechanical Model ◽  
The State ◽  
Discontinuous Systems ◽  
Intermittent Cutting ◽  
Boundary Mapping ◽  
Simplified Mechanical Model

In this paper the simplified mechanical model for a machine-tool system is presented. The state and domains are defined with respect to the (contact and frictional force) boundaries in this system. The switching sets for this machine-tool will be defined for all the boundaries considered herein. The forces and force product components at the switching points are determined according to discontinuous systems theory. The forces and force product govern the passability of the machine-tool through the respective boundary. Mapping definitions and notations are developed through the switching sets for the boundaries. A mapping structure and notation for one type of intermittent cutting periodic motion is defined as an example.

Effects of Chip Seizure on Steady State Motion of a Machine-Tool

2009 ◽  
Author(s):  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Machine Tool ◽  
Systems Theory ◽  
Degree Of Freedom ◽  
Continuous Systems ◽  
Discontinuous Systems ◽  
Mechanical Analogy ◽  
Steady State Motion ◽  
Two Degree Of Freedom

The steady state motion of a machine-tool is numerically predicted with interaction of the chip/tool friction boundary. The chip/tool friction boundary is modeled via a discontinuous systems theory in effort to validate the passage of motion through such a boundary. The mechanical analogy of the machine-tool is shown and the continuous systems of such a model are governed by a linear two degree of freedom set of differential equations. The domains describing the span of the continuous systems are defined such that the discontinuous systems theory can be applied to this machine-tool analogy. Specifically, the numerical prediction of eccentricity amplitude and frequency attribute the chip seizure motion to the onset or route to unstable interrupted cutting.

Analytical Prediction of Periodic Motions in a Machine Tool With Loss of Effective Chip Contact

2008 ◽  
Author(s):  
Brandon C. Gegg ◽  
Steven C. S. Suh ◽  
Albert C. J. Luo
Keyword(s):  
Machine Tool ◽  
Closed Form ◽  
Systems Theory ◽  
Phase Trajectory ◽  
Degree Of Freedom ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Discontinuous Systems ◽  
Closed Form Solutions ◽  
Two Degree Of Freedom

This study applies a discontinuous systems theory by Luo (2005) to an approximate machine-tool model. The machine-tool is modeled by a two-degree of freedom forced switching oscillator. The switching of the model emulates the various types of dynamics in a machine-tool system. The main focus of this study is the loss of effective chip contact and boundaries of this motion. The periodic motions will be studied through the mappings developed for this machine-tool. The periodic motions will be numerically and analytically predicted via closed form solutions. The phase trajectory, velocity, and force responses are presented.

Sensitivity of Steady State Intermittent Cutting Motion to Work-Piece Characteristics

2010 ◽  
Author(s):  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Steady State ◽  
Dynamical Systems ◽  
Machine Tool ◽  
General Model ◽  
Solution Structure ◽  
Work Piece ◽  
Periodic Motions ◽  
Discontinuous Systems ◽  
Intermittent Cutting

The tool and work-piece interactions will be modeled via discontinuous systems to study the effects of work-piece characteristics the on sensitivity of steady state motions. The general model will be presented through the domains of continuous dynamical systems for this machine-tool. The periodic motions of intermittent cutting will be developed and implemented to describe the solution structure. The switching components at the chip/tool friction boundary will be discussed in regard to work-piece characteristics.

Characteristics and Effects on a Machine-Tool Due to Grazing Motions of a Friction Boundary

2010 ◽  
Author(s):  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Machine Tool ◽  
Systems Theory ◽  
Rake Face ◽  
Discontinuous Systems ◽  
Transient Motion ◽  
System Parameters ◽  
Definition Of

The machine-tool interactions are studied with respect to the chip/tool friction boundary on the tool-piece rake face. The grazing motions with this chip/tool friction boundary are the focus of the study and how the effects are identified quantitatively. This study considers the transient motion of the machine-tool and will provide a framework for prediction of such grazing motions. The proposed study will include prediction through a range of excitation and system parameters. The significance of this lay within the application and the general approach to the definition of grazing via discontinuous systems theory.

Rosenau's adaptive behaviour approach – a critique

1981 ◽  
Vol 7 (2) ◽  
pp. 107-126 ◽  
Author(s):  
Steve Smith
Keyword(s):  
Political Science ◽  
Systems Theory ◽  
Systems Analysis ◽  
Political System ◽  
State Level ◽  
The State ◽  
Adaptive Behaviour ◽  
Systemic Level ◽  
The Individual ◽  
Level Of Analysis

With the widespread usage of systems analysis in political science over the last twenty years it is axiomatic that the problem of adaptation has been a recurring theme in the literature. At the level of the individual political system this concern has been germane to the work of Easton, the structural functionalists and the developmental/modernization writers. In International Politics writing, the problem of adaptation is central to both the applications of systems theory, at whatever level of analysis (for example Kaplan, Rosecrance at the systemic level, and Hanrieder and Modelski at the state level) and the less overtly theoretical works which still emphasize the importance of a state adapting to its environment.

The Prediction of Size Effect on J-R Curve for Eurofer97 Steel by Simplified Mechanical Model

2015 ◽  
Author(s):  
Ludek Stratil ◽  
Filip Siska ◽  
Hynek Hadraba ◽  
Ivo Dlouhy
Keyword(s):  
Fracture Toughness ◽  
Size Effect ◽  
Mechanical Model ◽  
Scale Up ◽  
Test Characteristics ◽  
Toughness Testing ◽  
Point Bend ◽  
Definition Of ◽  
Shelf Region ◽  
Simplified Mechanical Model

The possibilities to derive fracture toughness from small specimens are naturally limited due to constraint requirements which are especially restrictive in toughness testing. The loss of constraint at the crack tip is more likely to occur as specimen size decreases. Application of miniature specimens in fracture toughness testing thus requires a suitable methodology or correction procedure to deal with phenomenon of the constraint loss. Schindler et al. have proposed a simplified mechanical model that can be used to scale-up the key test characteristics from miniature specimen to the larger one. The model is applied to the miniature bending specimens to describe size effect on J-R curve of the Eurofer97 steel. The examined steel exhibits quite high toughness values at upper shelf region of fracture toughness. As a result, experimentally determined J-R curves of three different sizes of pre-cracked bending specimens showed high values of J-integral, which were significantly different each other. Using semi-empirical definition of the exponent of the power law function of J-R curve the performance of the Schindler’s model was quite successful. It was shown that the model is able to handle with size effect of tested pre-cracked three-point-bend specimens.

Drag Force Analysis of Spheres Penetrating Gelatin Based on Surface Integral

2011 ◽  
Vol 105-107 ◽  
pp. 561-565
Author(s):  
Gen Lin Mo ◽  
Zhi Lin Wu ◽  
Kun Liu
Keyword(s):  
Frictional Force ◽  
Mechanical Model ◽  
High Speed ◽  
Dynamic Force ◽  
Force Analysis ◽  
Surface Integral ◽  
Area Element ◽  
Position Data ◽  
Calculation Results ◽  
Wetted Area

A new method based on surface integral is presented in the research of mechanical mechanism of spheres penetrating gelatin. On the assumption that each wetted area element is applied with dynamic force perpendicular to the surface, frictional force parallel to the surface and material resistance which is a constant, the resultant force applied on spheres was integrated containing three unknown coefficients. Transparent gelatin was used in the experiments and steel spheres were fired at speed around 800m/s. High speed cameras got the position data of the penetrating spheres. The uncertain coefficients in the movement equations were determined with these data. The equations were solved in analytical forms. Experiments show that the coefficients are constant for spheres with different radiuses. Calculation results demonstrate that the mechanical model is good to predict the movement of spheres in gelatin.

The state space in systems theory

1969 ◽  
Vol 1 (4) ◽  
pp. 335-342 ◽  
Author(s):  
R.B. Banerji
Keyword(s):  
State Space ◽  
Systems Theory ◽  
The State
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