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.

Dynamic Absorption by Passive and Active Control1

2000 ◽  
Vol 122 (4) ◽  
pp. 429-433 ◽  
Author(s):  
Kumar Vikram Singh ◽  
Yitshak M. Ram
Keyword(s):  
Steady State ◽  
Active Control ◽  
Conservative System ◽  
Degree Of Freedom ◽  
Loss Of Stability ◽  
Steady State Motion ◽  
Damped System ◽  
Single Sensor ◽  
Dynamic Absorber

The motion of a particular degree-of-freedom in a harmonically excited conservative system can be vanished by attaching an appropriate dynamic absorber to it. It is shown here that under certain conditions, which are characterized in the paper, the steady state motion of a damped system may be completely absorbed, without loss of stability, by active control implementing a single sensor and an actuator. The results are established theoretically and they are demonstrated by means of analytical examples. [S0739-3717(00)02104-8]

The Galloping Response of a Two-Degree-of-Freedom System

1974 ◽  
Vol 41 (4) ◽  
pp. 1113-1118 ◽  
Author(s):  
R. D. Blevins ◽  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Natural Frequencies ◽  
Analytic Solutions ◽  
Degree Of Freedom ◽  
Approximate Analysis ◽  
Stability Criteria ◽  
Integer Multiple ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

The galloping response of a two-degree-of-freedom system is investigated using asymptotic techniques to generate approximate steady-state solutions. Simple closed-form analytic solutions and stability criteria are presented for the case where the two structural natural frequencies are harmonically separated. Examples of the nature of the galloping response of a particular section are presented for the case where the frequencies are harmonically separated as well as for the case where the two natural frequencies are near an integer multiple of each other. The results of the approximate analysis are compared with experimental and numerical results.

Period-1 Motions in a Periodically Forced, Nonlinear, Machine-Tool System

2019 ◽  
Author(s):  
Siyuan Xing ◽  
Albert C. J. Luo
Keyword(s):  
Machine Tool ◽  
Numerical Simulations ◽  
Analytical Method ◽  
Degree Of Freedom ◽  
Eigenvalue Analysis ◽  
Tool Vibrations ◽  
Stability And Bifurcations ◽  
The Stability ◽  
Two Degree Of Freedom

Abstract In this paper, period-1 motions in a two-degree-of-freedom, nonlinear, machine-tool system are investigated by a semi-analytical method. The stability and bifurcations of the period-1 motions are discussed from the eigenvalue analysis. A condition is presented for the tool-and-workpiece separation in period-1 motions. Machine-tool vibrations varying with displacement disturbance from a workpiece are discussed. Numerical simulations of period-1 motions are completed from analytical predictions.

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.

The Steady-State Response of a Two-Degree-of-Freedom Bilinear Hysteretic System

1965 ◽  
Vol 32 (1) ◽  
pp. 151-156 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Degree Of Freedom ◽  
Finite Limit ◽  
Steady State Response ◽  
Varying Parameters ◽  
Hysteretic System ◽  
State Response ◽  
The Stability ◽  
Two Degree Of Freedom

The method of slowly varying parameters is used to obtain an approximate solution for the steady-state response of a two-degree-of-freedom bilinear hysteretic system. The stability of the system is investigated and it is shown that such a system exhibits unbounded amplitude resonance when the level of excitation is increased beyond a certain finite limit.

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.

D-partition Stability Analysis of a Two-Degree-of-Freedom System with Delayed Restoring Force

1967 ◽  
Vol 9 (3) ◽  
pp. 190-197 ◽  
Author(s):  
B. Porter
Keyword(s):  
Stability Analysis ◽  
Machine Tool ◽  
Algebraic Equation ◽  
Characteristic Equation ◽  
Normal Modes ◽  
Degree Of Freedom ◽  
Central Feature ◽  
Restoring Force ◽  
The Stability ◽  
Two Degree Of Freedom

The method of D-partition is used to analyse the stability of a two-degree-of-freedom system subjected to a delayed restoring force of the kind which causes chatter in certain types of machine tool. The central feature of the analysis is the reduction of a stabliity problem involving a transcendental characteristic equation to a much simpler problem concerning the roots of a related algebraic equation. The results of the exact analysis are compared with approximate results obtained by assuming that the normal modes of the two-degree-of-freedom system can be decoupled.

Asymptotic Analysis of the Torsional Vibrations in Reciprocating Machinery

1996 ◽  
Vol 118 (3) ◽  
pp. 485-490 ◽  
Author(s):  
H. Ashrafiuon ◽  
A. M. Whitman
Keyword(s):  
Numerical Modeling ◽  
Steady State ◽  
Asymptotic Analysis ◽  
Degree Of Freedom ◽  
Torsional Vibrations ◽  
Transient Vibration ◽  
Asymptotic Expressions ◽  
Parameter Values ◽  
Two Degree Of Freedom ◽  
Good Agreement

A class of two degree of freedom reciprocating machines is analyzed and simple asymptotic expressions for both the steady state and transient vibration levels are obtained. The results are compared with those of a standard numerical modeling package, and are found to be in good agreement for parameter values typical of real machines. This happens because real machines are designed so that the vibration levels are small, thereby satisfying the conditions for the validity of the approximation.

Asymptotic Analysis of the Torsional Vibrations in Reciprocating Machinery

1995 ◽  
Author(s):  
Hashem Ashrafiuon ◽  
Alan M. Whitman
Keyword(s):  
Numerical Modeling ◽  
Steady State ◽  
Asymptotic Analysis ◽  
Degree Of Freedom ◽  
Torsional Vibrations ◽  
Transient Vibration ◽  
Asymptotic Expressions ◽  
Parameter Values ◽  
Two Degree Of Freedom ◽  
Good Agreement

Abstract A class of two degree of freedom reciprocating machines is analysed and simple asymptotic expressions for both the steady state and transient vibration levels are obtained. The results are compared with those of a standard numerical modeling package, and are found to be in good agreement for parameter values typical of real machines. This happens because real machines are designed so that the vibration levels are small, thereby satisfying the conditions for the validity of the approximation.

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