Radek Srb

The Process Of An Optimized Heat Radiation Intensity Calculation On A Mould Surface.

This article is focused on the optimization of heat radiation intensity across the surface of an aluminium mould. The mould is warmed by infrared heaters located above the mould surface, and in this way artificial leathers in the automotive industry are produced (e.g. the artificial leather on a car dashboard). This described model allows us to specify the location of infrared heaters over the mould to obtain approximately the same heat radiation intensity across the whole mould surface. In this way we can obtain a uniform material structure and colour tone across the whole surface of artificial leather. We used a genetic algorithm and the technique of “hill-climbing” during the optimization process. A computational procedure was programmed in the language Matlab.

Mathematical model of the metal mould surface temperature optimization

The article is focused on the problem of generating a uniform temperature field on the inner surface of shell metal moulds. Such moulds are used e.g. in the automotive industry for artificial leather production. To produce artificial leather with uniform surface structure and colour shade the temperature on the inner surface of the mould has to be as homogeneous as possible. The heating of the mould is realized by infrared heaters located above the outer mould surface. The conceived mathematical model allows us to optimize the locations of infrared heaters over the mould, so that approximately uniform heat radiation intensity is generated. A version of differential evolution algorithm programmed in Matlab development environment was created by the authors for the optimization process. For temperate calculations software system ANSYS was used. A practical example of optimization of heaters locations and calculation of the temperature of the mould is included at the end of the article.

Improving convergence properties of a differential evolution algorithm

The differential evolution is a popular and efficient way to solve complicated optimization tasks with many variables and constraints. In this article we study the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not guarantee the convergence to the global minimum. To improve this weakness we design a modification of the classic differential evolution algorithm to enrich the diversity of its populations. This modification limits the premature convergence to local minima and ensures the asymptotic global convergence. We tested the modified algorithm in numerical experiments and compared the efficiency in finding the global minimum for the classic and modified algorithm. The modified algorithm is significantly more efficient with respect to the global convergence than the classic algorithm.

Optimization Of A Heat Radiation Intensity And Temperature Field On The Mould Surface.

This article is focused on the infrared heating of shell metal moulds and optimization of temperature field on the surface of the mould. The upper part of the mould is heated by infrared heaters, and after the required temperature is attained the inner part of the mould is sprinkled with special PVC powder. The moulds are made of aluminium or nickel alloys. The described mathematical model allows us to optimize locations of heaters above the mould and thus we get an approximately uniform temperature field on the whole inner mould surface. In this way the whole surface of produced artificial leather has the same material structure and colour shade. A differential evolution algorithm is used to optimize the locations of heaters. A practical example of the optimization of the heaters locations and the calculation of the temperature field on the inner part of mould surface is included at the end of the article. The described process is one of the economical ways of artificial leathers production in the car industry.

Differential Evolution and Heat Radiation Intensity Optimization

This article focuses on heat radiation intensity optimization across the surface of an aluminium mould. The inner mould surface is sprinkled with a special PVC powder and the outer mould surface is warmed by infrared heaters located above the mould. This is an economic way of producing artificial leathers in the automotive industry (e.g. The artificial leather on a car dashboard). The article includes a description of a mathematical model that allows us to calculate the heat radiation intensity across the mould surface for every fixed location of the heaters. We also use this mathematical model to optimize the location of the heaters to provide approximately the same heat radiation intensity across the whole mould surface during the warming of the mould. In this way we obtain a uniform colour tone and material structure of the artificial leather. The problem of optimization is more complicated. Using gradient methods is not suitable because the minimized function contains many local extremes. A differential evolution algorithm is used during the process of optimization. The calculations were performed by a Mat lab code written by the authors. The article contains a practical example including graphical outputs.

The classic differential evolution algorithm and its convergence properties

Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the classic differential evolution algorithm. This modification limits the possible premature convergence to local minima and ensures the asymptotic global convergence. We also introduce concepts that are necessary for the subsequent proof of the asymptotic global convergence of the modified algorithm. We test the classic and modified algorithm by numerical experiments and compare the efficiency of finding the global minimum for both algorithms. The tests confirm that the modified algorithm is significantly more efficient with respect to the global convergence than the classic algorithm.

Optimal tool path searching and tool selection for machining of complex surfaces

This article deals with the calculation of curvature of free-surfaces for the use in processes of machining. The calculation is realized in Matlab environment. Objects with free-surfaces are mainly used in machine engineering, design, automotive and aerospace industry etc. The manufacturing of such surfaces are realized on multi-axes machining centres, where the tool path controlling is crucial process. It is necessary to ensure collisionfree states between tool and workpiece as well as between tool and peripheral shape of machined surface. It is described in this article how the surface imported into Matlab is divided into different areas. The criteria of the division is based on Gaussian curvature of a surface. Such areas of the surface are then possible to machine by an optimal tool with optimal radius that is obtained from the curvature calculation. All these calculations are done in Matlab and results are verified by practical machining on the 5-axis machining centre. The machining of the whole surface by one tool was compared to machining of divided areas by different tools. The impact on the length of tool paths during the machining process is summarized in conclusion.

Convergence rate of the modified differential evolution algorithm

Differential evolution algorithms represent an efficient framework to solve complicated optimization tasks with many variables and complex constraints. Nevertheless, the classic differential evolution algorithm does not guarantee the convergence to the global minimum of the cost function. Therefore, the authors developed a modification of this algorithm that ensures asymptotic global convergence. The article provides a comparison of the ability to identify the global minimum of the cost function for the following three algorithms: the classic differential evolution algorithm, the above mentioned modified differential evolution algorithm and an algorithm of random sampling enhanced by a hill climbing procedure. We designed a series of numerical experiments to perform this comparison. The results indicate that the classic differential evolution algorithm is in general an extremely poor global optimizer (global minimum found in 2% of cases). On the other hand the performance of the modified differential evol...

Temperature field Optimization on the Mould Surface

This article focuses on issues of uniform heating of the shell metal moulds. Infrared heaters located above the aluminium mould surface heat the mould. This is one of the economical ways of artificial leathers production in the automotive industry (e.g. the artificial leathers for car interiors). The described mathematical model allows us to specify the locations of infrared heaters over the mould to obtain approximately a uniform temperature field on the mould surface. In this way we can obtain a uniform material structure and colour shade of the artificial leather and thereby prevent the scrap production. We used a differential evolution algorithm during the optimization process. The optimization procedure was programmed in the Matlab development environment. The software package ANSYS was used for temperature calculations. A practical example of optimization of heaters locations over the mould and calculation of the temperature across the mould surface is included at the end of the article.

Heating of Mould in Manufacture of Artificial Leathers in Automotive Industry

This article focuses on a model for the creation of artificial leather production in the automotive industry. Aluminium or nickel shell moulds are used in the production of leathers. The inner mould surface is sprinkled with a special PVC powder and the outer mould surface is warmed by infrared heaters located above the mould. This is an economically advantageous way to produce artificial leathers used in car interior equipment. The article includes a description of a model that allows us to calculate the heat radiation intensity across the mould surface for every location of heaters, and to optimize the location of the heaters by using a differential evolution algorithm. The process of experimentally measuring the heat radiation intensity in the surroundings of the infrared heater by using a robot is also described in the article. The calculations were performed using a Matlab code written by the authors. The article contains a practical example including graphical outputs.