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.

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.

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 Analytical Solution for the Deformation and Support Parameters of Coal Roadway in Layered Roof Strata

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Kai Wang ◽  
Bao-gui Yang ◽  
Zhong-kui Wang ◽  
Xiao-long Wang
Keyword(s):  
High Efficiency ◽  
Design Method ◽  
Beam Theory ◽  
High Strength ◽  
Failure Criteria ◽  
Key Stratum ◽  
Coal Roadway ◽  
The Stability ◽  
Roof Strata

In order to meet the security and high-efficiency production needs, high-strength bolt (cable) reinforcement technology is usually used to maintain the stability of roadways. However, due to the great variability of lithology and mechanical properties, the failure form and stability of the layered roof in coal roadways are significant differences. The traditional supporting design method of the layered roof support in coal roadways is the engineering analogy method, which depends on experiences rather than theoretical analysis. Based on the theory of the elastic foundation beam and key stratum, this paper establishes a simplified analytical model of layered roof strata in coal roadways. Based on the Mohr-Coulomb theory, this paper gives the failure criteria of the layered roof strata, and the failure range of the layered roof strata is obtained. The length and pretightening force of bolt (cables) of the layered roof strata can be calculated based on the suspension theory and composite beam theory, which providing a quantitative theoretical basis for the determination of supporting parameters. Finally, as a case, the layered roof strata failure range and supporting parameters of the S1301 auxiliary transportation roadway in Gucheng coal mine are calculated.

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.

On the stability limit of charged droplets

1989 ◽  
Vol 422 (1863) ◽  
pp. 319-328 ◽  
Keyword(s):  
Surface Tension ◽  
Particle Size ◽  
Light Scattering ◽  
Stability Limit ◽  
Prolate Spheroid ◽  
Charged Droplets ◽  
Electric Stress ◽  
The Stability ◽  
Stability Limits

Single, highly charged droplets of dioctylphthalate and sulphuric acid of radius between 1 and 10 μm are suspended in vacuum in a quadrupol trap. As the droplets evaporate their radius is monitored continuously by light scattering and their charge is determined periodically by weight balancing. The droplets break when the electric stress exceeds that of surface tension. The largest fragment remains trapped allowing a determination of the change in volume and charge. The fraction of volume and charge lost is found to be independent of particle size and sign of charge and is variable. The oil drops lose (15.0 ± 3.9)% of their charge on breakup and (2.25 ± 0.96)% of their mass. The acid droplets lose (49.4 ± 8.3)% of their charge and less than 0.1% of their mass. The acid results are compared with those from a model of field emission based upon prolate spheroid deformation and the formation of Taylor cones. For both oil and acid droplets the stability limits are in agreement with those predicted by Lord Rayleigh.

Determining the Norton’s Equivalent Model of Distribution System with Distributed Generation (DG) for Stability Analysis

2019 ◽  
Vol 12 (2) ◽  
pp. 190-198
Author(s):  
Sunny Katyara ◽  
Lukasz Staszewski ◽  
Faheem Akhtar Chachar
Keyword(s):  
Distributed Generation ◽  
Normal Condition ◽  
Distribution System ◽  
Distribution Networks ◽  
Equivalent Model ◽  
Stability Factor ◽  
Matlab Simulation ◽  
The Stability ◽  
Stability Issues

Background: Since the distribution networks are passive until Distributed Generation (DG) is not being installed into them, the stability issues occur in the distribution system after the integration of DG. Methods: In order to assure the simplicity during the calculations, many approximations have been proposed for finding the system’s parameters i.e. Voltage, active and reactive powers and load angle, more efficiently and accurately. This research presents an algorithm for finding the Norton’s equivalent model of distribution system with DG, considering from receiving end. Norton’s model of distribution system can be determined either from its complete configuration or through an algorithm using system’s voltage and current profiles. The algorithm involves the determination of derivative of apparent power against the current (dS/dIL) of the system. Results: This work also verifies the accuracy of proposed algorithm according to the relative variations in the phase angle of system’s impedance. This research also considers the varying states of distribution system due to switching in and out of DG and therefore Norton’s model needs to be updated accordingly. Conclusion: The efficacy of the proposed algorithm is verified through MATLAB simulation results under two scenarios, (i) normal condition and (ii) faulty condition. During normal condition, the stability factor near to 1 and change in dS/dIL was near to 0 while during fault condition, the stability factor was higher than 1 and the value of dS/dIL was away from 0.

Synthesis and solvatochromic studies of 2- amino-3-phenolazo1-(4-sulfophenyl)-3-methyi-5-pyrozolone and use it for the determination of trace amount of Nickel (II) in blood samples

2016 ◽  
Vol 5 (10) ◽  
pp. 4920
Author(s):  
Amar M. Ali ◽  
Hussain. J. Mohammed*
Keyword(s):  
Stability Constant ◽  
Trace Amount ◽  
Benzenesulfonic Acid ◽  
Determination Method ◽  
Blood Samples ◽  
Determination Of Nickel ◽  
Normal Human ◽  
The Stability ◽  
Normal Human Blood

A new, simple, sensitive and rapid spectrophotometric method is proposed for the determination of trace amount of Nickel (II). The method is based on the formation of a 1:2 complex with 4-(4-((2-hydroxy-6-nitrophenyl) diazenyl) -3-methyl-5-oxo-2, 5-dihydro-1H-pyrazol-1-yl) benzenesulfonic acid (2-ANASP) as a new reagent is developed. The complex has a maximum absorption at 516 nm and εmax of 1. 84 X 105 L. mol-1. cm-1. A linear correlation (0. 25 – 4. 0μg. ml-1) was found between absorbance at λmax and concentration. The accuracy and reproducibility of the determination method for various known amounts of Nickel (II) were tested. The results obtained are both precise (RSD was 1. 2 %) and accurate (relative error was 0. 787 %). The effect of diverse ions on the determination of Nickel (II) to investigate the selectivity of the method were also studied. The stability constant of the product was 0. 399 X 106 L. mol-1. The proposed method was successfully applied to the analysis of diabetes blood and normal human blood. 

scholarly journals Determination of Objective Weights Using a New Method Based on the Removal Effects of Criteria (MEREC)

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 525 ◽  
Author(s):  
Mehdi Keshavarz-Ghorabaee ◽  
Maghsoud Amiri ◽  
Edmundas Kazimieras Zavadskas ◽  
Zenonas Turskis ◽  
Jurgita Antucheviciene
Keyword(s):  
Essential Elements ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Analysis Of Means ◽  
Simulation Based ◽  
Criteria Weights ◽  
The Stability ◽  
Computational Analyses ◽  
Weighting Methods

The weights of criteria in multi-criteria decision-making (MCDM) problems are essential elements that can significantly affect the results. Accordingly, researchers developed and presented several methods to determine criteria weights. Weighting methods could be objective, subjective, and integrated. This study introduces a new method, called MEREC (MEthod based on the Removal Effects of Criteria), to determine criteria’ objective weights. This method uses a novel idea for weighting criteria. After systematically introducing the method, we present some computational analyses to confirm the efficiency of the MEREC. Firstly, an illustrative example demonstrates the procedure of the MEREC for calculation of the weights of criteria. Secondly, a comparative analysis is presented through an example for validation of the introduced method’s results. Additionally, we perform a simulation-based analysis to verify the reliability of MEREC and the stability of its results. The data of the MCDM problems generated for making this analysis follow a prevalent symmetric distribution (normal distribution). We compare the results of the MEREC with some other objective weighting methods in this analysis, and the analysis of means (ANOM) for variances shows the stability of its results. The conducted analyses demonstrate that the MEREC is efficient to determine objective weights of criteria.

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