Frezeleme işlemi sırasında iş parçasındaki sıcaklık dağılımının analizi

Abstract

Talaş kaldırma işlemi sırasında üretilen ısı ve bu ısının oluşturduğu sıcaklıklar büyük önem taşımaktadır. Kesme ortamının sıcaklıklarını ölçmek için farklı deneysel yöntemler olsa bile bu yöntemlerin doğruluğu ve doğruluğu ve güvenirliği henüz istenilen seviyeye ulaşmamıştır. Bunun yanında sıcaklık dağılımları üzerine yapılan farklı çalışmalar olsa bile bu çalışmalar birbirini doğrulamamış ve deneysel olarak kanıtlanmamıştır. Bu sebeplerden dolayı hem kesme ortamının sıcaklığının ölçülmesine gerek kalmadan ortamdaki sıcaklıkları ve oluşan ısı akılarını belirleyebilecek tersine ısı geçişi yöntemi popülerlik kazanmıştır. Tersine ısı geçişi yöntemi deneysel veriler ile sayısal çözümlerden alınan sonuçları karşılaştırarak ilerleyen ve ölçümü yapılamayan değişkeni elde etmeye yaratan bir yöntemdir. Talaş kaldırma işleminde bulunmak istenilen değişken ısı akısıdır. Bu çalışmada frezeleme işlemi sırasında parçaya gelen ısı akısının ve iş parçasındaki sıcaklık dağılımının bulunması için tersine ısı geçişi yöntemi kullanılmıştır. Tersine ısı geçişi yöntemi doğrudan problem, deneysel veriler ve tersine problem olmak üzere genel olarak üç ana bölümden oluşur. Doğrudan problem bulunmak istenilen değişkeninin biliniyor olarak kabul edildiği problemdir. Deneysel veriler ise doğrudan problemin sonucunda ortaya çıkacak sonuçların deneysel olarak toplanmasıyla elde edilir. Tersine problem ise doğrudan problemin çözümü ile deneysel veriler arasında karşılaştırmalı olarak ilerleyerek, bulunmak istenilen değişkenin tahmin edilmesidir. Bu çalışmada doğrudan problem talaş kaldırma sırasında iş parçasına gelen ısı akısının bilinmesi durumunda iş parçasındaki sıcaklık dağılımının bulunmasıdır. Doğrudan problem Abaqus ve Matlab programları ile birlikte çözülmüştür. Deneysel veriler frezeleme işlemi sırasında iş parçasından iki tane termoeleman ile toplanmıştır. Tersine problem ise deneysel veriler ile sayısal çözümndeki ilgili noktaların sıcaklık farklarının toplamınının amaç fonksiyon olduğu bir optimizasyon problemidir. Bu optimizasyon probleminde amaç fonksiyonu en düşük yapacak olan ısı akısı aranmaktadır. Optimizasyon problemi de Matlab tarafından çözülmüştür.

This master thesis is about heat generation phenomena and determination of work piece temperature during milling process. Heat generation in milling, more generally in machining is a highly complex process due to complex nature of machining. Heat is generated in three different zones which are called primary zone or shear zone, secondary zone or rake face zone and lastly tool clearance face or work surface zone. In primary zone heat is generated because of the plastic deformation of the work piece. Most of heat is generated during the machinin operation is generated in this region. In secondary zone the heat is generated because of the fricton between tool and chip. Heat generated in primary zone generally flows to work piece and chip, on the other hand, heat is generated in secondary zone generally flows chip and tool. Heat is generated in work surface zone is generated due to fricton between tool and work surface, usually unsharpened tools cause this heat generation and heat flows work piece and tool. As it mentioned basically there are three different heat generation mechanism in machining. During machining heat have to be carried away from cutting medium, work piece, tool and chip behave as heat sink. Besides that in many applications coolant liqiuds is used to carry heat from cutting medium. Temperature of cutting medium is a very important subject about machining because of its effects on productivity, efficiency and quality of manufacturing process. However, any analytical solution or empirical formula which is verified by tests for heat generation in milling has not been derived yet. Many analytical or numerical solutions or techniques have been developed since middle of 20th century, but still there is no verified general solution about heat generation or formula / tehcnique about determination of cutting medium temperature. Due to this, heat generation cannot be controled by cutting parameters. Apart from these cutting medium temperatures cannot be measured by any technique. There are many measurement technique such as tool-work piece thermocouples, embedded thermocouples, single-wire thermocouples, infared based measurement methods, thermal cameras. Every measurment technique has its advantages and disadvantages, and all of them are used in different applications. However, these methods are not accurate or reliable enoguh to determine exact temperature of a exact place in cutting medium. Due to the reason that there is no verified approach for heat generation and measurement techniques for cutting medium temperature; inverse heat transfer method is employed to estimate them. Inverse heat transfer method is used for estimation an unknown such as a thermo- psychical property or a heat flux. In this method unknown is determined iteratively between based on experimental results. In this study, it is used for estimating heat flux generated by machining process. Inverse heat transfer method is used to estimate an unkown function or variable in different problems where direct measurement techniques cannot be applied. This method is used first time n the middle of 20th centruy, however, because of the mathematical problems of this method it had not been used effectively since numerical and optimization methods were developed. Especially in last decade of 20th century, after computer powers increase, inverse heat transfer method gained popularity and its applications increased. Mainly inverse heat transfer method has three different parts namely direct solution, experimental results, and optimization. The direct solution is the solution of the direct problem which is the problem while the unknown is estimated. Generally, a direct problem is solved by numerical methods. In this problem, the direct solution is the solution of the heat transfer problem of milling operation with random heat flux, in other words, thermal analysis of milling operation. A 100 x 100 x 2 millimeters workpiece is chosen for this study. Due to its very small thickness, the temperature gradient in the z-direction is assumed as zero. Thermal analysis of milling operation is a 3-D transient heat transfer problem that involves a moving heat source and chip disposal process. In the milling process heat is generated by cutting of metal and due to this fact location of the tool can be considered as the location of the heat source. For this reason, the heat source is modeled as a moving heat source and its motion is modeled based on the motion of the tool. In a real situation heat flux applied to the workpiece might increase and decrease, but in this study heat flux is assumed as constant during the operation to simplify the model. Besides this heat source in real is a half-circle because of the shape of the tool, however, in this study heat source is modeled as linear since the tool has high angular and linear velocity of the tool. Another important subject of this problem is chip disposal. Due to the chip disposal process, there has to be a mass extraction from a system based on the motion of the tool or other words heat source. Top, bottom, and side surfaces of the workpiece, there is a natural convection boundary condition and heat is convected to ambient air. Shortly, therma analysis of the workpiece is a 3 D transient heat transfer problem with a heat flux boundary condition that has a motion, a mass extraction process, and natural convection boundary condition. To model the motion of heat source and chip disposal process, two different software packages, which are Abaqus (which uses finite element method to solve heat transfer problems) and Matlab, are used to solve this problem. The motion of the heat source is not modeled as continuous, instead of it, it is modeled discretely. There are different ways to model a moving heat source in a commercial code, but the chip disposal process cannot be done by conventional methods. To model the milling process with the motion of heat source and chip disposal process, thermal analysis is divided into 125 steps. In every step, specific meshes are discarded from the problem for chip disposal and the heat source is replaced for the motion of it. Temperature distribution of workpiece at the end of a step is used as the initial condition of the next step. After the mesh is discarded, the heat source is relocated. Hence, the heat source does not move continuously, it moves discretely step by step. Basically, thermal analysis of the milling process is not one analysis, it is a sum of 125 analyses. Mesh discarding process and replacement of heat source for every step is done by Matlab. Thermal analysis is done by Abaqus but the analysis is prepared by Matlab. Meshes that need to be discarded are determined for every step, so relevant Abaqus files are rewritten for every step to prepare a new analysis, and Abaqus is executed via Matlab. Therefore the motion of heat source and chip disposal could be modeled. The next step of the inverse heat transfer method is collecting experimental data. Experimental results are temperature data which is collected from specific points in the workpiece during milling. Experimental data for the inverse heat transfer method is collected from the milling test. The workpiece, dimensions of which are specified, are milled with specific cutting parameters by a CNC machine. Temperature data is collected from specific points of workpieces by two thermocouples. Thermocouples have approximately 0.1-millimeter diameter and they are located in holes that have a diameter of 1 millimeter. They are located in the middle of the workpiece in the z-direction. Also to eliminate side effects they are located 45 millimeters and 55 millimeters to the front face. Thermocouples' distance to cutting surfaces is 2 millimeters. They should be close to the cutting surface to increase the accuracy of the inverse heat transfer method. On the other hand, if thermocouples are located close to the cutting surface, temperature rise might be too rapid for the dynamic response of thermocouples, and measurement errors can occur. To prevent those errors and increase accuracy, they are located to 2 millimeters from the cutting surface. The last step of the inverse heat transfer method is the solution of the inverse problem. In this part, the results of the direct solution and experimental temperature data are compared. Heat flux value of the direct solution is altered respectively that comparison and the heat flux makes differences between minimum is determined as the solution of the problem. In other words, this step is an optimization problem that aims to minimize objective function which is the sum of differences between the temperature of specified points in the workpiece in a solution of the direct problem and experimental temperature data. The simplex method is used for the optimization of the inverse heat transfer method. In this step of inverse heat transfer method Optimization Toolbox of Matlab is used. Heat flux generated by milling operation and applied to the workpiece is obtained by the last step of the inverse heat transfer method. After estimation of heat flux, the temperature of specific points is determined to analyze the accuracy of the method. Experimental temperature data and estimated temperature values are compared and the sum of errors for a single thermocouple varies from 3% to 5%. Also, similar heating and cooling trends are observed in both experimental and numerical results. Therefore it can be assumed that the inverse heat transfer method is applied successfully to milling operations. During milling operation, forces that are applied to the workpiece to the mil workpiece are measured by a force measurement system. Forces are collected for three directions. Total work to remove metal from the workpiece is calculated by analytical methods for milling. To calculate total work done by tool, firstly shear and friction forces are calculated based on force data that are collected during the test. Then work is done by shear and friction forces are obtained based on friction, shear forces and cutting velocity, and chip velocity. Some of those works are the total work done by the machining process. After determination of the heat flux which is generated by the machining process and applied to the workpiece, the temperature distribution of the workpiece is obtained from the numerical solution. Therefore the temperature of different regions of the workpiece for the whole milling operation is obtained. Also, temperature variation in time and space for specific points is determined. Effects of a milling operation are observed and heating and cooling trends are investigated during and after the milling process. Average chip temperatures are estimated from numerical solutions of the milling process. Temperature determination of workpiece and chip temperature during the milling process is important for milling operations. Total heat energy which flows to the workpiece and total work done by the machining process are calculated. Therefore energy rate or in another world energy partition rate is obtained.