Frezeleme işlemi sırasında iş parçasındaki sıcaklık dağılımının analizi
Thermal analysis of work piece during milling process
Yazar: TAYGUN RECEP GÜNGÖR
Danışman: PROF. DR. MUSTAFA ÖZDEMİR
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Isı-Akışkan Bilim Dalı
Derece: Yüksek Lisans, 2014
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: CNC frezeleme = CNC milling

Özet:
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.

Abstract:
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. Espically 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. Direct solution is solution of the direct problem which is the problem while the unknown is estimated. Generally direct problem is solved by numerical methods. In this problem direct solution is the solution of heat transfer problem of milling operation with a random heat flux, in other words thermal analysis of milling operation. A 100 x 100 x 2 milimeters work piece is choosen for this study. Due to its very small thickness, the temperature gradient in z direction is assumed as zero. 
Thermal analysis of milling operation is a 3-D transient heat transfer problem which involves a moving heat source and chip disposal process. In milling process heat is  generated by cutting of metal and due to this fact location of the tool can be considered as location of the heat source. For this reason, heat source is modelled as a moving heat source and its motion is modelled based on motion of the tool. In real situtation heat flux applied to work piece might increase and decrease, but in this study heat flux is assumed as constant during the operation to simplify model. Besides this heat source in real is a half circle because of shape of the tool, however, in this study heat source is modelled as linear since tool has high angular and linear velocity of tool. Another important subject of this problem is chip disposal. Due to the chip disposal process, there has to be a mass extraction from system based on motion of tool or another word heat source. Top, bottom and side surfaces of work piece, there is a natural convection boundary condition and heat is convected to ambient air. Shortly, therma analysis of work piece 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 motion of heat source and chip disposal process, two different software packages, which are Abaqus (uses finite element method to solve heat transfer problems) and Matlab, are used to solve this problem. Motion of heat source is not modelled as continous, instead of it, it is modelled discretely. There are different ways to model a moving heat source in a commercial code, but chip disposal process cannot be done by conventional methods. To model milling process with motion of heat source and chip disposal process, thermal analysis is divided into 125 steps. In every step, specific meshes are discarded from problem for chip disposal and heat source is replaced for motion of it. Temperature distribution of work piece at the end of a step is used as intial condition of next step. After mesh are discarded, heat source is relocated. Hence, heat source does not move continously, it moves discretely step by step. Basically, thermal analysis of milling process is not a one analysis, it is a sum of 125 analysis.  Mesh discarding process and replacement of heat source for every step is done by Matlab. Thermal analysis is done by Abaqus but 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 motion of heat source and chip disposal could be modeled. 
Next step of inverse heat transfer method is collecting experimenta data. Experimental results are temperature data which is collected from spesicific points in work piece during milling. Experimental data for inverse heat transfer method is collected from milling test. Work piece, dimension of which are specified, are milled with specific cutting parameter by a CNC machine. Temperature data is collected from specific points of work pieces by two thermocouples. Thermocouples has approximately 0.1 milimeter diameter and they are located to holes that has diameter of 1 milimeter. They are located in the middle of work piece in z direction. Also to eliminate side effects they are located 45 milimeter and 55 milimeter to front face. Thermocouples distance to cutting surfaces is 2 milimeter. They should be close to cutting surface to increase accuracy of inverse heat transfer method. On the other hand, if thermocouples are located more close to cutting surface, temperature rise might be too rapid for dynamic response of thermocouples and measurement errors can occur. To prevent those errors and increase accuracy, they are located to 2 milimeter to cutting surface.
Last step of inverse heat transfer method is the solution of the inverse problem. In this part, result of direct solution and experimental temperature data are compared. Heat flux value of direct solution is altered respectively those comparison and the heat flux makes differences between minimum is determined as solution of the problem. In other words, this step is an optimization problem which aims to minimize objective function which is sum of differences between temperature of specified points in work piece in solution of direct problem and experimental temperature data. Simplex method is used for optimization of 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 work piece is obtained by the last step of inverse heat transfer method. After estimation of heat flux, temperature of specific points are determined to analyze accuracy of method. Experimental temperature data and estimated temperature values are compared and 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 inverse heat transfer method is applied succesfully to milling operation. 
During milling operation, forces that applied to work piece to mil work piece are measured by a force measurement system. Forces are collected for three directions. Total work to remove metal from work piece are calculated by analytical methods for milling. To calculate total work done by tool, firstly shear and friction forces are calculated based on force data what are collected during test. Then work are done by shear and friction forces are obtained based on friction, shear forces and cutting velocity and chip velocity. Sum of those works is total work  done by machining process. 
After determination of the heat flux which is generated by machining process and applied to work piece, temperature distribution of work piece is obtained from numerical solution. Therefore temperature of different regions of the work piece for whole milling operation is obtained. Also temperature varitaion in time and space for specific points is determined. Effects of milling operation is observed and heating and cooling trends is investigated during and after milling process. Avarage chip temperatures are estimetad from numerical solution of milling process. Temperature determination of work piece and chip temperature during milling process are important for milling operations. 
Total heat energy which flows to work piece and total work done by machinin process are calculated. Therefore energy rate or in another world energy partition rate is obtained.