Jaroslav Mlynek

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.

Mathematical model of composite manufacture and calculation of robot trajectory

This paper discusses the problem of calculating the trajectory in a 3D environment of an industrial robot in the production of composites for the automotive industry. The used technology is based on a winding of a carbon (or a glass) filament rovings on a non-bearing polyurethane core which is a frame shape with a circular cross section. The polyurethane frame is fastened to the end-effector of the robot arm (robot-end-effector) and during the winding process goes through a fibre-processing head on the basis of the suitably determined robot-end-effector trajectory. The fibre-processing head is fixed and is composed of three guide lines (two outer lines are rotary and the middle is static) with coils of carbon rovings. The fibre-processing head winds on the frame three layers of filaments at angles of 45°, 0° and -45°. The model of a non-bearing polyurethane frame passing through the fibre-processing head is described in Euclidean space E3 of the robot. The non-bearing polyurethane frame is specified in the local Euclidean coordinate system E3, the origin of this system is in the robot-end-effector. The location of the local system of the robot-end-effector in the basic coordinate system of the robot is specified using the “tool-center-point” of the robot. We use the described mathematical model and matrix calculus to calculate the trajectory of the robot-end-effector to determine the desired passage of the frame through the fibre-processing head. The required translation and rotation matrices of the local coordinate system (of the robot-end-effector) relative to the base coordinate system of the robot are gradually calculated. Subsequently, the Euler angles of rotations are determined corresponding to the transformation matrices. The sequence of “tool-center-point” values which allows us to define the desired trajectory of the robot-end-effector and thereby the passage of the frame through the fibre-processing head is determined in this manner. The calculation of the trajectory was programmed in the Delphi development environment. A practical example of the passage of a polyurethane non-bearing frame through fibre-processing head is dealt with in the article. The calculation of the robot-end-effector trajectory was used as input values for a graphics software simulator of robot activities. We can accurately determine the trajectory of the robot-end-effector during required work activities of the robot. This approach of determining the exact trajectory is qualitatively different from the application of the principle of programming a robot by teach-in. The advantages of the described approach will be significantly enforced, for example, when we need to solve the problem of the robot-end-effector trajectory optimization. The determining calculation of the trajectory can of course be used in other applications of industrial robot use. Moreover, the described procedure for determining the trajectory brings the manufacturer almost no additional costs.

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.