Experimental Verification of a Stability Theory for Periodic Cutting Operations

1993 ◽  
Vol 115 (1) ◽  
pp. 9-14 ◽  
Author(s):  
I. Minis ◽  
A. Tembo
Keyword(s):  
Stability Theory ◽  
Degrees Of Freedom ◽  
Transfer Functions ◽  
Single Point ◽  
Depth Of Cut ◽  
Work Piece ◽  
Theoretical Predictions ◽  
Critical Depth Of Cut ◽  
Linear Differential ◽  
The Stability

The stability of periodic cutting operations, the dynamics of which are described by linear differential-difference equations with periodic coefficients, is studied. A new stability theory that uses parametric transfer functions and Fourier analysis to obtain the characteristic equation of such systems is experimentally verified. The theory is applied to single-point turning of a compliant work piece with two degrees-of-freedom. The theoretical predictions of both the critical depth of cut for chatter-free turning and the corresponding chatter frequency were found to be in good agreement with the measurements obtained from actual chatter tests under various surface speeds.

Structural Dynamics in Machine-Tool Chatter: Contribution to Machine-Tool Chatter Research—2

1965 ◽  
Vol 87 (4) ◽  
pp. 455-463 ◽  
Author(s):  
G. W. Long ◽  
J. R. Lemon
Keyword(s):  
Transfer Function ◽  
Machine Tool ◽  
Stability Theory ◽  
Transfer Functions ◽  
Phase Relationship ◽  
Structure Response ◽  
Machine Tool Structure ◽  
Machine Tool Chatter ◽  
The Stability ◽  
Tool Chatter

This paper is one of four being presented simultaneously on the subject of self-excited machine-tool chatter. Transfer-function theory is applied to obtain a representation of the dynamics of a machine-tool structure. The stability theory developed to investigate self-excited machine-tool chatter requires such a representation. Transfer functions of simple symmetric systems are derived and compared with measurements. When measured frequency-response data of more complex structures are obtained, it provides a very convenient means of data interpretation and enables one to develop the significant equations of motion that define the structure response throughout a specified frequency range. The transfer function presents the phase relationship between structure response and exciting force at all frequencies in the specified range. This knowledge of phase is essential to the proper application of the stability theory and explains the “digging-in” type of instability that is often encountered in machine-tool operation. The instrumentation used throughout these tests is discussed and evaluated. The concept of developing dynamic expressions for machine-tool components and joining these together through properly defined boundary conditions, thereby building up the transfer function of the complete machine-tool structure, is suggested as an area for further study.

Single-point diamond machining of glasses

1989 ◽  
Vol 426 (1870) ◽  
pp. 19-30 ◽  
Keyword(s):  
Single Point ◽  
Soda Lime ◽  
Depth Of Cut ◽  
Soda Lime Glass ◽  
Free Surfaces ◽  
Diamond Machining ◽  
Order Of Magnitude ◽  
Critical Depth Of Cut ◽  
Crucial Part ◽  
Very High

A machine tool of very high stiffness has been constructed and used for single-point diamond grooving of blanks of soda-lime glass and optical glassy quartz. Results show that below a critical depth of cut predicted in order of magnitude by a fracture mechanics analysis, material is removed by the action of plastic flow, leaving crack-free surfaces. Subsequent observations by scanning electron microscopy indicate that a crucial part in the detachment of ribbons of swarf is played by the operation of residual stresses after the passage of the tool, particularly in the case of the amorphous ceramic.

An Experimental Study of Subcritical Bifurcations in Milling

2007 ◽  
Author(s):  
Anupam Radhakrishnan ◽  
Ben T. Edes ◽  
Brian P. Mann
Keyword(s):  
Periodic Solutions ◽  
Cutting Speed ◽  
Stable Solution ◽  
Stability Diagram ◽  
Depth Of Cut ◽  
Work Piece ◽  
Cutting Condition ◽  
Multiple Attractors ◽  
Stable Periodic ◽  
The Stability

The focus of the current paper is an experimental investigation of subcritical bifurcations in milling. Several researchers have reported results indicating that the secondary Hopf bifurcations of turning processes are subcritical. However, fewer results are available for milling — especially results that provide any substantial experimental evidence. Here, the experimental cutting tests were performed on a relatively long aluminum workpiece. The atypical length of the work piece will be used so that the depth of cut may be slowly increased or decreased during the cutting process. This provides visual evidence of hysteresis in the bifurcation diagram and the existence of multiple stable periodic solutions. The importance of this exploratory experimental effort is that multiple attractors may co-exist (stable periodic solutions) for the same cutting speed and depth of cut, but only one of these solutions would be the chatter free case. An important outcome from these results is that a small perturbation in the desirable stable solution near the borders of the stability diagram could result in a jump to the unstable cutting condition.

Effect of Offset Distance on Cutting Forces and Heat Generation in Multi-Tool Turning Process

2014 ◽  
Vol 592-594 ◽  
pp. 211-215 ◽  
Author(s):  
R. Kalidasan ◽  
M. Yatin ◽  
D.K. Sarma ◽  
S. Senthilvelan
Keyword(s):  
Cutting Tool ◽  
Gray Cast Iron ◽  
Single Point ◽  
Cutting Tools ◽  
Cutting Speed ◽  
Depth Of Cut ◽  
Work Piece ◽  
Turning Process ◽  
Additional Tool ◽  
Offset Distance

Productivity enhancement assumes a paramount importance in today’s competitive industrial world. The aim of this work is to improve productivity in a conventional lathe with two single point cutting tools machining a workpiece simultaneously. An additional tool holding fixture is fabricated and integrated so that distance between the two cutting tools can be varied and has a provision to provide individual depth of cut. Experiments were performed on gray cast iron workpiece at different offset distances between the cutting tools, at a particular cutting speed, feed rate and depth of cut. In the multi-tool turning process, lagging rear cutting tool experiences lesser cutting force than leading front cutting tool. This behaviour is due to the machining of front cutting tool preheat as well as reduction of effective cutting speed while machining with rear cutting tool. With increase in offset distance, moment acting on the work piece contributes to increase in resistance against machining and hence front tool experiences higher force than rear cutting tool.

scholarly journals Features of Loss of Stability of the Work of Two-Link Mechanisms That Have an Infinite Number of Degrees of Freedom

2018 ◽  
Vol 3 (4) ◽  
Author(s):  
Leonid Kondratenko ◽  
Lubov Mironova
Keyword(s):  
Real Time ◽  
Infinite Number ◽  
Degrees Of Freedom ◽  
Transfer Functions ◽  
Hydraulic Drive ◽  
Loss Of Stability ◽  
Hydraulic Systems ◽  
The Stability ◽  
Executive Body ◽  
Lines Of Force

Mechanisms consisting of two links, a leading (engine) and a slave (executive body), which are connected by long lines of force, are considered. With the use of the new method, general equations are derived in Laplace images describing the oscillations of the velocities of motion and stresses in mechanical and hydraulic systems. Obtained transfer functions. The functional coefficients in these equations take into account the properties of the mechanisms and the distribution of the parameters of the lines of force. As a result of the transition from equations in images to equations in the originals, expressions are obtained that describe in real-time oscillations of the velocities of motion. The criterion for the stability of the work is derived on the basis of Lyapunov's first method. As an example, a volumetric hydraulic drive with long hydraulic lines is considered. With the loss of stability in this mechanism, self-oscillations appeared. Areas of stable and unstable work are defined.

scholarly journals Stability analysis for the virtual element method

2017 ◽  
Vol 27 (13) ◽  
pp. 2557-2594 ◽  
Author(s):  
Lourenço Beirão da Veiga ◽  
Carlo Lovadina ◽  
Alessandro Russo
Keyword(s):  
Degrees Of Freedom ◽  
Stability And Convergence ◽  
Virtual Element Method ◽  
Theoretical Predictions ◽  
Elliptic Model ◽  
Virtual Element Methods ◽  
Virtual Element ◽  
The Stability ◽  
The One ◽  
General Meshes

We analyze the virtual element methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to the parent element diameter) can be dealt with. Our general approach applies to different choices of the stability form, including, for example, the “classical” one introduced in Ref. 4, and a recent one presented in Ref. 34. Finally, we show that the stabilization term can be simplified by dropping the contribution of the internal-to-the-element degrees of freedom. The resulting stabilization form, involving only the boundary degrees of freedom, can be used in the VEM scheme without affecting the stability and convergence properties. The numerical tests are in accordance with the theoretical predictions.

Single Point Diamond Turning of CVD Coated Silicon Carbide

2006 ◽  
Author(s):  
Biswarup Bhattacharya ◽  
John A. Patten ◽  
Jerry Jacob
Keyword(s):  
Silicon Carbide ◽  
Single Point ◽  
Diamond Turning ◽  
Depth Of Cut ◽  
Critical Depth ◽  
Machined Surface ◽  
Brittle Transition ◽  
Ductile Regime Machining ◽  
Critical Depth Of Cut ◽  
Ductile To Brittle Transition

Scratching experiments, using diamond styli and single point diamond tools, were performed to simulate Single Point Diamond Turning (SPDT). The results of these experiments were used to determine if a ductile response is possible, and then to determine the critical depth of cut or penetration depth for the ductile to brittle transition (DBT). The depths of the scratches produced at different loads were measured and correlated to the ductile and brittle response of the material. The DBT depth for Chemically Vapor Deposited (CVD) coated Silicon Carbide (SiC) samples was determined. The analysis for the critical depth (DBT) did confirm the possibility for SPDT of CVD coated SiC in the ductile regime. These results were further used for SPDT of CVD SiC. Post experimental analysis of the machined surface did reveal a final surface roughness of 8–20nm, successfully demonstrating ductile regime machining of CVD coated SiC.

Analytical Prediction of Stability Lobes for Passively Damped Boring Bars

2017 ◽  
Vol 33 (5) ◽  
pp. 641-654 ◽  
Author(s):  
M. Fallah ◽  
B. Moetakef-Imani
Keyword(s):  
Closed Form ◽  
Superior Performance ◽  
Depth Of Cut ◽  
Analytical Prediction ◽  
Critical Depth ◽  
Boring Bar ◽  
Stability Lobes ◽  
Wide Range ◽  
Critical Depth Of Cut ◽  
The Stability

AbstractThe present article proposes the closed-form solution for analytical prediction of stability lobes in internal turning process. The passively damped boring bar is modeled as a cantilevered Euler-Bernoulli beam with constant cross sectional properties in which a Tuned Mass Damper (TMD) is embedded for the purpose of chatter suppression. The non-dimensional equations of motion are derived, assuming that the boring bar dynamics is well-represented by the fundamental mode of vibration. The stability of equivalent two-DOF dynamic model, i.e. boring bar with TMD, is analyzed in frequency domain. The closed- form expressions for critical depth of cut and spindle speed are presented in terms of boring bar and TMD characteristics. The proposed solution considers the effects of boring bar's structural damping and cutting geometry of insert on the stability behavior of passively damped cutting tool. An unconstrained optimization method is utilized to compute the most optimal set of tuning parameters for anti-chatter TMD. In order to improve the boundary of stability in a global sense, maximization of minimum critical depth of cut is selected as the objective of optimization. The superior performance of anti-chatter TMD is compared to H∞and H2TMDs for a wide range of applications. Moreover, the achieved results show a remarkable improvement of stability boundary compared to recent research works.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

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