A Remote Temperature Sensing Technique for Estimating the Cutting Interface Temperature Distribution

1986 ◽  
Vol 108 (4) ◽  
pp. 252-263 ◽  
Author(s):  
David Wei Yen ◽  
Paul K. Wright
Keyword(s):  
Inverse Problem ◽  
Temperature Distribution ◽  
Measurement Errors ◽  
Three Dimensional ◽  
Cutting Temperature ◽  
Transformation Matrix ◽  
Dimensional Case ◽  
Interface Temperature ◽  
Unknown Boundary ◽  
Ellipsoidal Coordinates

Cutting temperature is a major factor in controlling tool wear rate. Thus, sensing and control of cutting temperature is important in achieving a desired tool performance. This paper is concerned with estimating the cutting interface temperature distribution based on remote temperature measurements. This class of problems of estimating unknown boundary conditions from known interior quantities is called the inverse problem. The inverse problem of a square insert under steady state conditions is considered in this paper. The temperature distribution in a square insert is best described in Ellipsoidal Coordinates. The mapping functional in the one-dimensional case is solved analytically. The mapping functionals in general three-dimensional cases are solved numerically using the semianalytical finite element method. The mapping functional in a three-dimensional case is represented by a transformation matrix which maps one vector representing the cutting interface temperature distribution to another vector representing the remote temperatures. The transformation matrix is then used to solve the inverse problem of estimating the interface temperature distribution with redundant remote measurements. Measurement errors and transformation matrix errors are imposed in simulation studies. The sensitivity of inverse solutions to these errors is discussed.

Reduction to the pole as an inverse problem and its application to low‐latitude anomalies

Geophysics ◽  
1986 ◽  
Vol 51 (2) ◽  
pp. 369-382 ◽  
Author(s):  
João B. C. Silva
Keyword(s):  
Inverse Problem ◽  
Geomagnetic Field ◽  
Three Dimensional ◽  
Theoretical Data ◽  
Dimensional Case ◽  
Low Latitude ◽  
Horizontal Projection ◽  
Magnetization Direction ◽  
Reduction To The Pole ◽  
Dimensional Instability

Traditionally, reduction to the pole has been accomplished either by space‐ or wavenumber‐domain filtering. In the two‐dimensional case, this procedure is stable regardless of the latitude, as long as the source strike is not parallel to the horizontal projection of the geomagnetic field. In the three‐dimensional case, however, reduction‐to‐the‐pole filtering is stable only at high magnetic latitudes. At latitudes lower than 15 degrees, it is of no practical use due to a sharply increasing instability toward the magnetic equator. The three‐dimensional instability of this filtering technique is demonstrated, and the reduction‐to‐the‐pole problem is formulated in the context of a general linear inverse problem. As a result, stable solutions are found by using well‐known stabilizing procedures developed for the inverse linear problem. The distribution of magnetization of an equivalent layer of doublets that reproduces the observed data is computed. The magnetic doublets are parallel to the magnetization direction which is assumed constant throughout the sources. The magnetic field reduced to the pole is then obtained by changing the inclinations of the geomagnetic field and the doublets to 90 degrees and recalculating the total field. The usefulness and limitations of the method at low magnetic latitudes are assessed using theoretical data. The effects of noise and anomaly truncation are also investigated for both high and low latitudes. In all cases, application of the proposed method produced meaningful results regardless of the latitude. The method is applied to field data from two different low‐latitude anomalies. The first anomaly is due to a seamount in the Gulf of Guinea with reversed magnetization. The geomagnetic field at this location is about −23 degrees. The second anomaly is an intrabasement anomaly from Parnaiba Basin, Brazil, where the magnetization is assumed to be induced by a geomagnetic field with −1.4 degree inclination. The results obtained confirm that the proposed method produces stable, meaningful, reduced‐to‐the‐pole maps.

Three-Dimensional Finite Element Analysis in Cutting Temperature for High Speed Milling of Titanium Alloys

2011 ◽  
Vol 189-193 ◽  
pp. 2259-2263
Author(s):  
You Xi Lin ◽  
Cong Ming Yan
Keyword(s):  
Finite Element ◽  
Temperature Distribution ◽  
Titanium Alloys ◽  
High Speed ◽  
Three Dimensional ◽  
Cutting Temperature ◽  
Maximum Temperature ◽  
Depth Of Cut ◽  
High Speed Milling ◽  
Radial Depth

A three dimensional fully thermal-mechanical coupled finite element model had been presented to simulate and analyze the cutting temperature for high speed milling of TiAl6V4 titanium alloy. The temperature distribution induced in the tool and the workpiece was predicted. The effects of the milling speed and radial depth of cut on the maximum cutting temperature in the tool was investigated. The results show that only a rising of temperature in the lamella of the machined surface is influenced by the milling heat. The maximum temperature in the tool increases with increasing radial depth of cut and milling speed which value is 310°C at a speed of 60 m/min and increases to 740°C at 400m/min. The maximum temperature is only effective on a concentrated area at the cutting edge and the location of the maximum temperature moves away from the tool tip for higher radial depths of milling. The predicted temperature distribution during the cutting process is consistent with the experimental results given in the literature. The results obtained from this study provide a fundamental understanding the process mechanics of HSM of titanium alloys.

On the Field of Temperatures in Lubricating Films

1967 ◽  
Vol 89 (4) ◽  
pp. 483-491 ◽  
Author(s):  
N. Tipei ◽  
Al. Nica
Keyword(s):  
Temperature Distribution ◽  
Pressure Distribution ◽  
Energy Equation ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Dimensional Case ◽  
Experimental Measurements ◽  
Lubricating Film ◽  
Good Agreement

The temperature distribution in the lubricating film of journal bearings for the three-dimensional case is obtained by using the results already known regarding the pressure distribution in the film and by integrating the energy equation. Relations for the divergent and convergent zones of the bearing are established by taking into account the viscosity and the side leakage; the distribution of the temperature along the bearing width is also considered. Comparisons between the theoretical values and experimental measurements are also performed, resulting in good agreement.

Analytical Prediction of Three Dimensional Cutting Process—Part 3: Cutting Temperature and Crater Wear of Carbide Tool

1978 ◽  
Vol 100 (2) ◽  
pp. 236-243 ◽  
Author(s):  
E. Usui ◽  
T. Shirakashi ◽  
T. Kitagawa
Keyword(s):  
Computer Simulation ◽  
Temperature Distribution ◽  
Characteristic Equation ◽  
Single Point ◽  
Three Dimensional ◽  
Cutting Temperature ◽  
Analytical Prediction ◽  
Carbide Tool ◽  
Arbitrary Geometry ◽  
Crater Wear

Through the energy method proposed in the previous parts of this study, it is possible to predict chip formation and cutting force for a single point tool of arbitrary geometry. By using the predicted results together with an assumption made on the stress distribution on the tool face, the temperature distribution within chip and tool is obtained through a numerical analysis. A characteristic equation of crater wear of carbide tool is derived theoretically and verified experimentally. Computer simulation of crater wear development is then carried out by using the characteristic equation, and the predicted distributions of the stress and the temperature.

Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature Using Inverse Formulation

2004 ◽  
Vol 126 (3) ◽  
pp. 619-626 ◽  
Author(s):  
Hakan Ertu¨rk ◽  
Ofodike A. Ezekoye ◽  
John R. Howell
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Design Problem ◽  
Manufacturing Industry ◽  
Three Dimensional ◽  
Chemical Deposition ◽  
Iterative Solution ◽  
Conveyor Belt ◽  
Temperature History ◽  
Transient Temperature

The boundary condition design of a three-dimensional furnace that heats an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as industrial baking, curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history. The spatial temperature distribution on the object is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is transient where a series of inverse problems are solved. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located on the top and the design object moves along the bottom. The inverse design approach is used for the solution, which is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem is ill-posed and involves a set of Fredholm equations of the first kind. The use of advanced solvers that are able to regularize the resulting system is essential. These include the conjugate gradient method, the truncated singular value decomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination.

scholarly journals Simulation of Thermal and Electric Field Distribution in Packaged Sausages Heated in a Stationary Versus a Rotating Microwave Oven

Foods ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1622
Author(s):  
Wipawee Tepnatim ◽  
Witchuda Daud ◽  
Pitiya Kamonpatana
Keyword(s):  
Temperature Distribution ◽  
Electric Field ◽  
Three Dimensional ◽  
Development Stage ◽  
Microwave Oven ◽  
Computational Time ◽  
Plastic Package ◽  
Heating Uniformity ◽  
The Cost ◽  
Good Agreement

The microwave oven has become a standard appliance to reheat or cook meals in households and convenience stores. However, the main problem of microwave heating is the non-uniform temperature distribution, which may affect food quality and health safety. A three-dimensional mathematical model was developed to simulate the temperature distribution of four ready-to-eat sausages in a plastic package in a stationary versus a rotating microwave oven, and the model was validated experimentally. COMSOL software was applied to predict sausage temperatures at different orientations for the stationary microwave model, whereas COMSOL and COMSOL in combination with MATLAB software were used for a rotating microwave model. A sausage orientation at 135° with the waveguide was similar to that using the rotating microwave model regarding uniform thermal and electric field distributions. Both rotating models provided good agreement between the predicted and actual values and had greater precision than the stationary model. In addition, the computational time using COMSOL in combination with MATLAB was reduced by 60% compared to COMSOL alone. Consequently, the models could assist food producers and associations in designing packaging materials to prevent leakage of the packaging compound, developing new products and applications to improve product heating uniformity, and reducing the cost and time of the research and development stage.

Process Modeling in Laser Deposition of Multilayer SS410 Steel

2007 ◽  
Vol 129 (6) ◽  
pp. 1028-1034 ◽  
Author(s):  
Liang Wang ◽  
Sergio Felicelli
Keyword(s):  
Phase Transformation ◽  
Temperature Distribution ◽  
Three Dimensional ◽  
Element Model ◽  
Traverse Speed ◽  
Processing Parameters ◽  
Dimensional Finite Element ◽  
Net Shaping ◽  
Three Dimensional Finite Element ◽  
Continuous Cooling Transformation Diagram

A three-dimensional finite element model was developed to predict the temperature distribution and phase transformation in deposited stainless steel 410 (SS410) during the Laser Engineered Net Shaping (LENS™) rapid fabrication process. The development of the model was carried out using the SYSWELD software package. The model calculates the evolution of temperature in the part during the fabrication of a SS410 plate. The metallurgical transformations are taken into account using the temperature-dependent material properties and the continuous cooling transformation diagram. The ferritic and martensitic transformation as well as austenitization and tempering of martensite are considered. The influence of processing parameters such as laser power and traverse speed on the phase transformation and the consequent hardness are analyzed. The potential presence of porosity due to lack of fusion is also discussed. The results show that the temperature distribution, the microstructure, and hardness in the final part depend significantly on the processing parameters.

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