An Analytical Design Method for Milling Cutters With Non-Constant Pitch to Increase Stability

2000 ◽  
Author(s):  
Erhan Budak
Keyword(s):  
Surface Finish ◽  
Design Method ◽  
Stability Limit ◽  
Analytical Stability ◽  
Chatter Vibrations ◽  
Constant Pitch ◽  
Improved Stability ◽  
Limited Frequency ◽  
The Stability ◽  
Explicit Relation

Abstract Chatter vibrations result in reduced productivity, poor surface finish and decreased cutting tool life. Milling cutters with non-constant pitch angles can be very effective in improving the stability of the process against chatter. In this paper, an analytical stability model and a design method are presented for non-constant pitch cutters. An explicit relation is obtained between the stability limit and the pitch variation which leads to a simple equation for optimal pitch angles. A certain pitch variation is effective for limited frequency and speed ranges which are also predicted by the model. The improved stability, productivity and surface finish are demonstrated by several examples.

An Analytical Design Method for Milling Cutters With Nonconstant Pitch to Increase Stability, Part I: Theory

2003 ◽  
Vol 125 (1) ◽  
pp. 29-34 ◽  
Author(s):  
E. Budak
Keyword(s):  
Surface Finish ◽  
Design Method ◽  
Stability Limit ◽  
Analytical Stability ◽  
Chatter Vibrations ◽  
Improved Stability ◽  
Limited Frequency ◽  
The Stability ◽  
Explicit Relation

Chatter vibrations result in reduced productivity, poor surface finish and decreased cutting tool life. Milling cutters with nonconstant pitch angles can be very effective in improving stability against chatter. In this paper, an analytical stability model and a design method are presented for nonconstant pitch cutters. An explicit relation is obtained between the stability limit and the pitch variation which leads to a simple equation for determination of optimal pitch angles. A certain pitch variation is effective for limited frequency and speed ranges which are also predicted by the model. The improved stability, productivity and surface finish are demonstrated by several examples in the second part of the paper.

scholarly journals A dynamic model of cylindrical plunge grinding process for chatter phenomena investigation

2018 ◽  
Vol 148 ◽  
pp. 09004
Author(s):  
Paweł Lajmert ◽  
Małgorzata Sikora ◽  
Dariusz Ostrowski
Keyword(s):  
Degrees Of Freedom ◽  
Stability Limit ◽  
Element Model ◽  
Grinding Wheel ◽  
Grinding Process ◽  
Plunge Grinding ◽  
Chatter Vibrations ◽  
Grinding Conditions ◽  
The Stability ◽  
Improved Model

In the paper, chatter vibrations in the cylindrical plunge grinding process are investigated. An improved model of the grinding process was developed which is able to simulate self-excited vibrations due to a regenerative effect on the workpiece and the grinding wheel surface. The model includes a finite-element model of the workpiece, two degrees of freedom model of the grinding wheel headstock and a model of wheel-workpiece geometrical interferences. The model allows to studying the influence of different factors, i.e. workpiece and machine parameters as well as grinding conditions on the stability limit and a chatter vibration growth rate. At the end, simulation results are shown and compared with exemplified real grinding results.

scholarly journals Chatter Investigation on Machining of Gray Cast Iron Considering the Damping Effect

2019 ◽  
Vol 7 (3) ◽  
pp. 64
Author(s):  
Everton Ruggeri Silva Araujo ◽  
Giovanni De Souza Pinheiro ◽  
João Álvaro Belo Pantoja Junior ◽  
Salomão Levy Neto
Keyword(s):  
Cast Iron ◽  
Surface Finish ◽  
Gray Cast Iron ◽  
Machining Process ◽  
System Stability ◽  
Gray Cast ◽  
Stability Lobes ◽  
Chatter Vibrations ◽  
Roughness Analysis ◽  
The Stability

In recent years, the study of chatter vibrations has been intensifying in the machining of materials. In this paper an investigation of this phenomena was conducted for gray cast iron (CGI). The chatter vibrations in machining process can considerably compromise the workpiece surface finish, tool wear and in some cases provide severe damage to the machine-tool. Thus there is an imminent need to expand the theory of chatter vibrations for the class of brittle materials. To analyze the vibrations of the process of machining and zones where the process is stable, and where it is unstable, the stability lobes diagram was used. This diagram is constructed at low speed cutting, where the phenomenon of damping arises. The damping is a crucial factor in the process, it increases system stability. This effect was considered in the formulation of chatter vibrations using the indentation model of Wu. For experimental validations the signals of cutting force were acquired and analysis was conducted in frequency domain to identify where the vibrations emerged allied with a roughness analysis of the workpiece. The results demonstrated perfectly the consequences of chatter vibrations in surface finish of grey cast iron and proved that the stability lobes diagram provides good results to detect these vibrations, determining the areas where the material removal should be avoid.

A New Method for Identification and Modeling of Process Damping in Machining

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
E. Budak ◽  
L. T. Tunc
Keyword(s):  
Stability Limit ◽  
Damping Coefficient ◽  
Test Results ◽  
Limited Data ◽  
Damping Force ◽  
Process Damping ◽  
Analytical Stability ◽  
Practical Model ◽  
The Stability ◽  
Stability Limits

Although process damping has a strong effect on cutting dynamics and stability, it has been mostly ignored in chatter analysis as there is no practical model for estimation of the damping coefficient and very limited data are available. This is mainly because of the fact that complicated test setups were used in order to measure the damping force in the past. In this study, a practical identification and modeling method for the process damping is presented. In this approach, the process damping is identified directly from the chatter tests using experimental and analytical stability limits. Once the process damping coefficient is identified, it is related to the instantaneous indentation volume by a coefficient which can be used for different cutting conditions and tool geometries. In determining the indentation coefficient, chatter test results, energy, and tool indentation geometry analyses are used. The determined coefficients are then used for the stability limit and process damping prediction in different cases, and verified using time-domain simulations and experimental results. The presented method can be used to determine chatter-free cutting depths under the influence of process damping for increased productivity.

scholarly journals Suboptimal Disturbance Observer Design Using All Stabilizing Q Filter for Precise Tracking Control

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1434 ◽  
Author(s):  
Wonhee Kim ◽  
Sangmin Suh
Keyword(s):  
Design Method ◽  
Industrial Applications ◽  
Point Of View ◽  
Observer Design ◽  
Linear Matrix ◽  
External Disturbances ◽  
Closed Loop Systems ◽  
Control Target ◽  
The Stability ◽  
Unified Index

For several decades, disturbance observers (DOs) have been widely utilized to enhance tracking performance by reducing external disturbances in different industrial applications. However, although a DO is a verified control structure, a conventional DO does not guarantee stability. This paper proposes a stability-guaranteed design method, while maintaining the DO structure. The proposed design method uses a linear matrix inequality (LMI)-based H∞ control because the LMI-based control guarantees the stability of closed loop systems. However, applying the DO design to the LMI framework is not trivial because there are two control targets, whereas the standard LMI stabilizes a single control target. In this study, the problem is first resolved by building a single fictitious model because the two models are serial and can be considered as a single model from the Q-filter point of view. Using the proposed design framework, all-stabilizing Q filters are calculated. In addition, for the stability and robustness of the DO, two metrics are proposed to quantify the stability and robustness and combined into a single unified index to satisfy both metrics. Based on an application example, it is verified that the proposed method is effective, with a performance improvement of 10.8%.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

scholarly journals Actuator Saturated Fuzzy Controller Design for Interval Type-2 Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 823
Author(s):  
Wen-Jer Chang ◽  
Yu-Wei Lin ◽  
Yann-Horng Lin ◽  
Chin-Lin Pen ◽  
Ming-Hsuan Tsai
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Fuzzy Model ◽  
The Stability ◽  
Interval Type ◽  
Takagi Sugeno

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

Parallel-Process (Simultaneous) Machining and its Stability

1999 ◽  
Author(s):  
O. Burak Ozdoganlar ◽  
William J. Endres
Keyword(s):  
Initial Conditions ◽  
General System ◽  
Parallel Process ◽  
Analytical Stability ◽  
Multiple Processes ◽  
Or Practice ◽  
Machining System ◽  
Eigenvector Analysis ◽  
The Stability ◽  
Machining Operations

Abstract This paper presents a mathematical perspective, to complement the intuitive or practice-oriented perspective, to classifying machining operations as parallel-process (simultaneous) or single-process in nature. Illustrative scenarios are provided to demonstrate how these two perspectives may lead in different situations to the same or different conclusions regarding process parallelism. A model representation of a general parallel-process machining system is presented, based on which the general parallel-process stability eigenvalue problem is formulated. For a special simplified case of the general system, analytical methods are employed to derive a fully analytical stability solution. Thorough study of this solution through eigenvector analysis sheds light on some fundamental phenomena of parallel-process machining stability, such as dependence of the stability solution on phasing of the initial conditions (disturbances). This establishes the importance, when employing numerical time-domain simulation for such analyses, of specifying initial conditions for the multiple processes to be arbitrarily phased so that correct results are achieved across all spindle speeds.

scholarly journals Stabilizing immature breathing patterns of preterm infants using stochastic mechanosensory stimulation

2009 ◽  
Vol 107 (4) ◽  
pp. 1017-1027 ◽  
Author(s):  
Elisabeth Bloch-Salisbury ◽  
Premananda Indic ◽  
Frank Bednarek ◽  
David Paydarfar
Keyword(s):  
Preterm Infants ◽  
Respiratory Control ◽  
Behavioral State ◽  
Mean Square ◽  
Breathing Patterns ◽  
Nonlinear Properties ◽  
Improved Stability ◽  
Postconceptional Age ◽  
The Stability ◽  
Large Improvement

Breathing patterns in preterm infants consist of highly variable interbreath intervals (IBIs) that might originate from nonlinear properties of the respiratory oscillator and its input-output responses to peripheral and central signals. Here, we explore a property of nonlinear control, the potential for large improvement in the stability of breathing using low-level exogenous stochastic stimulation. Stimulation was administered to 10 preterm infants (postconceptional age: mean 33.3 wk, SD 1.7) using a mattress with embedded actuators that delivered small stochastic displacements (0.021 mm root mean square, 0.090 mm maximum, 30–60 Hz); this stimulus was subthreshold for causing arousal from sleep to wakefulness or other detectable changes in the behavioral state evaluated with polysomnography. We used a test-retest protocol with multiple 10-min intervals of stimulation, each paired with 10-min intervals of no stimulation. Stimulation induced an ∼50% reduction ( P = 0.003) in the variance of IBIs and an ∼50% reduction ( P = 0.002) in the incidence of IBIs > 5 s. The improved stability of eupneic breathing was associated with an ∼65% reduction ( P = 0.04) in the duration of O2 desaturation. Our findings suggest that nonlinear properties of the immature respiratory control system can be harnessed using afferent stimuli to stabilize eupneic breathing, thereby potentially reducing the incidence of apnea and hypoxia.

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