Validation of New Mathematical Model of Flank Wear by Different Methods

2012 ◽  
Vol 729 ◽  
pp. 169-174 ◽  
Author(s):  
Zoltán Pálmai ◽  
Márton Takács ◽  
Balázs Zsolt Farkas
Keyword(s):  
Activation Energy ◽  
Mathematical Model ◽  
Flank Wear ◽  
Technological Parameters ◽  
Wear Process ◽  
Oxidation Processes ◽  
Industrial Manufacturing ◽  
Thermally Activated ◽  
Optical Electron ◽  
The Mean

Having reviewed the literature on cutting and based on the optical, electron-optical and morphological examinations of wear processes we have reached the conclusion that it is possible to describe the abrasive, adhesive and thermally activated diffusion, oxidation processes in a single mathematical model. The model is a non-linear autonomous differential equation, which can be solved by simple numerical methods. The complex wear equation was validated by the results of the cutting tests performed with P20 carbide on C45 carbon steel. If we have this data, we can calculate the activation energy of the process determining the nature of the wear process. The apparent activation energy of wear is Q=151,7kJ/mol. The model can even be used with changing technological parameters, and the data necessary for the constants of the wear equation may as well be determined even by measurements performed on the tool during industrial manufacturing. By the mean of this data, we can calculate the activation energy determining the nature of the wear process.

Flank Wear Model of Cutting Tools Using Control Theory

1978 ◽  
Vol 100 (1) ◽  
pp. 103-109 ◽  
Author(s):  
Y. Koren
Keyword(s):  
Control Theory ◽  
Tool Life ◽  
Flank Wear ◽  
Cutting Tools ◽  
Mathematical Expression ◽  
Wear Coefficient ◽  
Wear Model ◽  
Wear Process ◽  
Thermally Activated ◽  
Linear Control Theory

A model of the flank wear of cutting tools is developed by using linear control theory. The flank wear is assumed to consist of a mechanically activated and a thermally activated component. The wear process is mathematically treated as a feedback process, whereby the progressive wear raises the cutting forces and temperature thereby increasing the thermally activated wear-rate, and contributes to the mechanically activated wear. A mathematical expression for the flank wear growth is derived and shown to be consistent with experimental results. The experimental data is fitted to the wear model for calculating the mechanical wear coefficient and activation energy for the thermally activated wear. The model yielded a new tool-life equation which is valid over a wider range of speed than Taylor tool-life equation.

The Effect of Annealing on the Internal Friction in ECAP-Modified Ultrafine Grained Copper

2012 ◽  
Vol 184 ◽  
pp. 289-294 ◽  
Author(s):  
Igor S. Golovin ◽  
P.P. Pal-Val ◽  
L.N. Pal-Val ◽  
E.N. Vatazhuk ◽  
Yuri Estrin
Keyword(s):  
Activation Energy ◽  
Activation Parameters ◽  
Coarse Grained ◽  
Relaxation Processes ◽  
Exponential Factor ◽  
Mean Values ◽  
Thermally Activated ◽  
Ultrafine Grained ◽  
Relaxation Loss ◽  
The Mean

A detailed study of anelastic effects in submicrocrystalline copper using resonance (~70 kHz, 2 K to 320 K) and sub-resonance (0.05-100 Hz, 300 K to 675 K) techniques was carried out. Several relaxation processes were found in the temperature range of 2 K - 675 K: the relaxation loss peaks (Q-1) near 35 (P1) and 90K (P2) with the activation energy and the pre-exponential factor (H1≈ 0.02 eV,το1≈ 10-9s andH2≈ 0.09 eV,το2≈ 10-11s) similar to those of the Bordoni and the Niblett-Wilks peaks in coarse-grained Cu. This suggests that the peaks are due to the thermally activated motion of dislocation kinks in the primary and secondary Peierls relief. The mean values of activation parameters (H3≈1.4-1.6 eV,το3≈10-17s) of a third thermally activated peak (P3), which was significantly broadened, can be interpreted as a grain boundary peak with uncoupled activation parametersH3*≈0.45 eV andτο3*≈10-14s. A pseudo peak PRis associated with irreversible recrystallization processes. The influence of annealing on the observed effects is also discussed.

THERMALLY ACTIVATED FLUX CREEP AND CURRENT CONDUCTION IN YBCO + BZO COMPOSITES

2011 ◽  
Vol 25 (03) ◽  
pp. 387-398
Author(s):  
A. MOHANTA ◽  
S. DASH ◽  
D. BEHERA
Keyword(s):  
Magnetic Field ◽  
Activation Energy ◽  
Doping Concentration ◽  
Powder Size ◽  
Chemical Route ◽  
Thermally Activated ◽  
Grain Sizes ◽  
The Mean ◽  
Activated Flux ◽  
Submicron Powder

BaZrO 3 submicron powder obtained from chemical route was added to YBCO for preparation of YBCO + xBZO (x = 0, 1, 2.5, 5, 10 rm wt%) composites samples. The X-ray peak profile analyses and the scanning electron microscopy have indicated that the mean powder size for BZO ranges from 500 to 800 nm. In fact, the presence of BZO brings about a significant modification in the microstructure of the composites. The resistive transition in presence of magnetic field (0–8 T) was investigated. With application of magnetic field, Tc0 decreases significantly, suggesting that grain boundaries (Josephson junctions) are affected more than the grains (Abrikosov junctions). Activation energy is found dependent not only on the particle size, but also on penetration depth and decreases with increasing doping concentration of BZO submicron size particles in contrast to what has been recently observed by M. Safonchik et al. with grain sizes of 40 nm BZO. It has also been observed by H. Shakeripour, M. Akhavan [Supercond. Sci. Technol.14, 234 (2001)] and Gamchi et al. [Phys. Rev. B50, 12950 (1994)] that the activation energy depends not only on the temperature and magnetic field, but also on the doping concentration.

Mathematical model for combined extrusion of bar stock into cylindrical die by fl at working surface punch

2020 ◽  
pp. 309-312
Author(s):  
S.N. Larin S.N. ◽  
V.I. Tregubov ◽  
A.N. Isaeva
Keyword(s):  
Mathematical Model ◽  
Extrusion Force ◽  
Technological Parameters ◽  
Thin Walls ◽  
Working Surface ◽  
Industrial Implementation ◽  
Pressure Estimation

Combined extrusion processes can be in demand in the production of body products with jumper in the central part and thin walls. Often, their industrial implementation requires theoretical justifi cation of power regimes. Mathematical model of combined extrusion created on the basis of the upper estimates method is presented. The effect of technological parameters on extrusion force is established based on the obtained expressions for pressure estimation.

Batch Crystallization with Crystals Attrition

1993 ◽  
Vol 58 (8) ◽  
pp. 1855-1860 ◽  
Author(s):  
Jaroslav Nývlt ◽  
Stanislav Žáček
Keyword(s):  
Mathematical Model ◽  
Calcium Sulfate ◽  
Crystal Size ◽  
Theoretical Description ◽  
Secondary Nucleation ◽  
Batch Crystallization ◽  
Batch Time ◽  
The Mean

The dependence of the mean crystal size of the products from batch crystallizers on the batch time occasionally exhibits a maximum, which can be explained by secondary nucleation due to the attrition of crystals. A kinetic equatation of nucleation, comprising a term for crystal attrition, can be used for the theoretical description of such behaviour. A mathematical model of a batch crystallizer with crystal attrition has been verified on the calcium sulfate precipitation.

scholarly journals The Performance of Polycrystalline Diamond (PCD) Tools Machined by Abrasive Grinding and Electrical Discharge Grinding (EDG) in High-Speed Turning

2021 ◽  
Vol 5 (2) ◽  
pp. 34
Author(s):  
Guangxian Li ◽  
Ge Wu ◽  
Wencheng Pan ◽  
Rizwan Abdul Rahman Rashid ◽  
Suresh Palanisamy ◽  
...  
Keyword(s):  
Electrical Discharge ◽  
High Speed ◽  
Flank Wear ◽  
Polycrystalline Diamond ◽  
Machining Efficiency ◽  
Crater Wear ◽  
Wear Process ◽  
High Speed Turning ◽  
Tools Wear ◽  
Pcd Tools

Polycrystalline diamond (PCD) tools are widely used in industry due to their outstanding physical properties. However, the ultra-high hardness of PCD significantly limits the machining efficiency of conventional abrasive grinding processes, which are utilized to manufacture PCD tools. In contrast, electrical discharge grinding (EDG) has significantly higher machining efficiency because of its unique material removal mechanism. In this study, the quality and performance of PCD tools machined by abrasive grinding and EDG were investigated. The performance of cutting tools consisted of different PCD materials was tested by high-speed turning of titanium alloy Ti6Al4V. Flank wear and crater wear were investigated by analyzing the worn profile, micro morphology, chemical decomposition, and cutting forces. The results showed that an adhesive-abrasive process dominated the processes of flank wear and crater wear. Tool material loss in the wear process was caused by the development of thermal cracks. The development of PCD tools’ wear made of small-sized diamond grains was a steady adhesion-abrasion process without any catastrophic damage. In contrast, a large-scale fracture happened in the wear process of PCD tools made of large-sized diamond grains. Adhesive wear was more severe on the PCD tools machined by EDG.

Non-invasive determination of the systolic peak-to-peak gradient in children with aortic stenosis: validation of a mathematical model

2000 ◽  
Vol 10 (2) ◽  
pp. 115-119 ◽  
Author(s):  
Valter C. Lima ◽  
Evan Zahn ◽  
Christine Houde ◽  
Jeffrey Smallhorn ◽  
Robert M. Freedom ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Pulse Pressure ◽  
Linear Regression Analysis ◽  
Systolic Pressure ◽  
Pressure Gradients ◽  
Non Invasive ◽  
The Mean ◽  
Congenital Aortic Valvar Stenosis ◽  
Peak Gradient

AbstractDoppler derived systolic pressure gradients have become widely applied as noninvasively obtained estimates of the severity of aortic valvar stenosis. There is little correlation, however, between the Doppler derived peak instantaneous gradient and the peak-to-peak gradient obtained at catheterisation, the latter being the most applied variable to determine severity in children. The purpose of this study was to validate a mathematical model based on data from catheterisation which estimates the peak-to-peak gradient from variables which can be obtained by noninvasive means (Doppler derived mean gradient and pulse pressure), according to the formula: peak-to-peak systolic gradient=6.02+1.49*(mean gradient)−0.44*(pulse pressure). Simultaneous cardiac catheterization and Doppler studies were performed on 10 patients with congenital aortic valvar stenosis. Correlations between the gradients measured at catheter measured, and those derived by Doppler, were performed using linear regression analysis. The mean gradients correlated well (y=0.67 × + 11.11, r=0.87, SEE=6 mm Hg, p=0.001). The gradients predicted by the formula also correlated well with the peak-to-peak gradients measured at catheter (y=0.66 × + 14.44, r=0.84, SEE=9 mm Hg, p=O.002). The data support the application of the model, allowing noninvasive prediction of the peak-to-peak gradient across the aortic valvar stenosis.

scholarly journals Generalization of research results on the dynamics of continuous wide-strip hot-rolling mills

2018 ◽  
pp. 275-289
Author(s):  
V.V. Verenev
Keyword(s):  
Mathematical Model ◽  
Hot Rolling ◽  
Large Data ◽  
Dynamic Processes ◽  
Technological Parameters ◽  
Rolling Moment ◽  
Rolling Mills ◽  
Wide Strip ◽  
The Impact ◽  
First Time

The aim of the work is to summarize the results of experimental-industrial and theoretical studies of dynamic processes in wide-strip hot rolling mills 1680, 1700, 2000 and 2500. We describe the methods of collecting, storing, identifying, visualizing and mathematical processing of large data arrays, which made it possible to establish new laws and correlations of technological parameters. New results related to the peculiarities of transient processes, their patterns and the use of the latter for the purpose of diagnosing technology and equipment condition are presented. Vibrodynamic processes are described when the strip is captured by the rollers. For the first time, a correlation between the maximum peak moment when the strip is captured and the static rolling moment on the 1680 mill is obtained and substantiated by measuring and statistical modeling. A new mathematical model of the roll line is developed, incorporating the equations of dynamic processes in gears and axles of the gearbox. For the first time, the dynamics of the formation of intercellular tensions in the process of sequential filling and release with a 6-cell band is shown. A complete mathematical model and a computer program for the dynamic interaction of six-group stands of a rolling strip have been developed. A new line of research has been proposed, which includes the search, substantiation and testing of new methods and methods for diagnosing the technical condition of rolling mills based on the use of transients and their parameters in various modes of equipment operation. Proposed and tested in industrial conditions at the mills 1680 and 1700-M are effective ways to reduce the impact loads during the period of the strip capture by the rollers.

Evaluation of a method for noninvasive intracranial pressure assessment during infusion studies in patients with hydrocephalus

2000 ◽  
Vol 92 (5) ◽  
pp. 793-800 ◽  
Author(s):  
Bernhard Schmidt ◽  
Marek Czosnyka ◽  
Jens Jürgen Schwarze ◽  
Dirk Sander ◽  
Werner Gerstner ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Intracranial Pressure ◽  
Time Course ◽  
Cerebral Blood Flow Velocity ◽  
Absolute Error ◽  
Content Type ◽  
Arterial Blood ◽  
Potential Clinical Benefit ◽  
The Mean ◽  
Fine Print

Object. A mathematical model previously introduced by the authors allowed noninvasive intracranial pressure (nICP) assessment. In the present study the authors investigated this model as an aid in predicting the time course of raised ICP during infusion tests in patients with hydrocephalus and its suitability for estimating the resistance to outflow of cerebrospinal fluid (Rcsf).Methods. Twenty-one patients with hydrocephalus were studied. The nICP was calculated from the arterial blood pressure (ABP) waveform by using a linear signal transformation, which was dynamically modified by the relationship between ABP and cerebral blood flow velocity. This model was verified by comparison of nICP with “real” ICP measured during lumbar infusion tests. In all simulations, parallel increases in real ICP and nICP were evident. The simulated Rcsf was computed using nICP and then compared with Rcsf computed from real ICP. The mean absolute error between real and simulated Rcsf was 4.1 ± 2.2 mm Hg minute/ml. By the construction of simulations specific to different subtypes of hydrocephalus arising from various causes, the mean error decreased to 2.7 ± 1.7 mm Hg minute/ml, whereas the correlation between real and simulated Rcsf increased from R = 0.73 to R = 0.89 (p < 0.001).Conclusions. The validity of the mathematical model was confirmed in this study. The creation of type-specific simulations resulted in substantial improvements in the accuracy of ICP assessment. Improvement strategies could be important because of a potential clinical benefit from this method.

Static Recovery Activation Energy of Pure Aluminum at Room Temperature

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Yeh An-Chou ◽  
Chuang Ho-Chieh ◽  
Kuo Chen-Ming
Keyword(s):  
Activation Energy ◽  
Room Temperature ◽  
Pure Aluminum ◽  
Pure Copper ◽  
Tensile Tests ◽  
Engineering Strain ◽  
Static Recovery ◽  
Thermally Activated ◽  
Recovered Strain ◽  
Dislocation Annihilation

Thermally activated energy, which varies linearly with static recovered strain, is calculated from static recovery experiments of pure aluminum initially plastically deformed by strain-rate-controlled tensile tests up to 10% engineering strain at room temperature. The activation energy at the initial static recovery is 20 kJ mol−1, which is much less than that of pure copper and attributed to the dislocation annihilation by glide or cross-slip as well as higher stacking fault energy. Once dislocation annihilation processes are exhausted, more energy is required for subgrains to form and then grow. Eventually the recovered strain is slowed down and gradually saturated.

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