Yassı çelik mamüllerin sıcak haddelenmesinde haddeleme yükünün hesaplanmasında kullanılan metodların incelenmesi

Abstract

Yassı mamullerin sıcak haddelenmesinde haddeleme yükünün hesaplanmasında kullanılan literatürde önerilen metodlarla hesaplanan yükler ile ölçülen yükler arasın da az yada çok daima bir sapma bulunmaktadır. Zire yükü etkileyen faktörlerin (mukavemet, sürtünme katsayısı, ezme hızı ve miktarı gibi) kompleks oluşu ve değerlerinin tam olarak tesbitinin zor olması ölçülen ile hesaplanan yükler arasında farklılıklara yol açmaktadır. Her had de tezgahının kendine has özellikleri bulunması nedeniyle ezme bölgesinin geometrisi hadde tezgahının özelliklerine göre değişmektedir. Bu çalışmada yassı çelik mamullerin sıcak haddelenmesinde haddeleme yüküne etki eden faktörler incelenmiş dokuz ayrı metodla hesaplanan haddeleme yüklerinin ölçülen yüklerle karşılaştırması yapılmıştır. Bu amaçla dörtlü tersinir haddeden Fe-33, Fe-37 veFe-44 kalite çeliklerin haddelenmesi sırasında alman veriler bir bilgisayar programı yardımı ile her metod için yük ve deformasyon direnci, akma ve dinamik akma gerilmeleri deformasyon hızı ve ezme oranları, farklı kalite çelik deformasyon hızı ve sıcaklık değerleri için hesaplattırılmıştır. Haddeleme yükünü etkileyen sürtünme katsayısı ve kuvveti, akma ve dinamik akma gerilmesi, ezme bölgesi geometrisi ve bunlara etki eden faktörler incelenip, literatürde önerilen farklı matematik modeller kullanılarak, haddeleme yükleri hesaplatılıp ölçülen yüklerle karşılaştırılmıştır. Hazırlanan bir bilgisayar programı yardımı ile teorik yükler hesaplatılmış, teorik yükler ile ölçülen yükler arasındaki korelasyon ve korelasyon sabitleri "en küçük kareler" metodu ile bulunarak her metodun ölçülen yükle olan bağıntısı elde edilmiştir. Geometrik faktör, karbon miktarı, sıcaklık ve de formasyon hızının deformasyon direnci üzerindeki etkileri incelenmiştir. Ölçülen haddeleme yükü ve motor akımı arasındaki doğrusal ilişkiyi veren bir bağıntı elde edilmiştir.

in the present uıork, nine different load colcula- tion methads far the höt rolling of flat products are investigated. The factors used in these methods that affact ralling load are studied. These factors are the defor- mation zone geometry, external friction in the deforma- tion zane and the factors affecting vstrenght of -tbe" rnaterial. Standart terms used in theories of flat rolling are: average uork piece thickness, draft, relative reduction, roll bite angle and roll contact length. Many factors affect rolling load, öne of them is aspect ratio of the rolling deformation zone uhich is described in öne of the folloujing three terms; 1- Arithmetic average aspect ratio, Z. 3 2- Parabolle average aspect ratio, Z. 3- Geometric mean aspect ration, Z. A number of solutions have been proposed för type and magnitude of coefficient of friction and distribu- tion of frictional force in the roll bite of höt mili. Although distribution of frictional force is different at the roll-strip interfaces according to different theories, there are tuo typgg of friction. These are slippi.ng and sticking friction. ıx It is well known that friction between the rolls and the workpiece is necessary to transmit deformation energy from the rolls to the strip. Excessive friction however, tends to restrain the deformation and results in undesirably high rolling force and spindle torques. On the other hand, too little friction results in either roll slippage or the failure of workpiece to enter the roll bite. The value of the friction coefficient depends on temperature, scale condition of workpiece surface type of roll, surface condition and state of lubricant. The values of the effective coefficient of friction in the roll bite of a hot mill changes from 0.2 to 0.5. in the roll bite. In order to compute the rolling force in a particu lar stand ot a hot strip mill, it is necessary to know the flow stress at the temperature and strain rate associated with the deformation at that stand. A number of expressions have been developed empirically relating the flow stress (or dynamic constrained flow stess) to the temperature and the average strain rate for stell. Turakh and Seredynski developed an expression using Sims' method based on sticking friction. They also proposed another equation based on sliding priction in the temperature range 1500 to 2300 F for flow stress. ?îkelund drived an equation for yield stress of the rolled material corresponding to a given temperature and chemical composition. Geleji proposed an equation to calculate yield stress Df the rolled material based on rolling temperature. The most important factor affecting flow stress or yield stress of rolled material is temperature. The temperature distribution within a coil at any instant during the rolling process is determined by a number of factors which may be classified into two groups; those that impart heat to the workpiece and those that cool it. The piece may acquire heat by (1) its deformation (2) frictional effects in the roll bites, (3) oxidation or scaling of the workpiece surfaces, (4) physical and metallurgical changes accorring in the piece, and (5) heating such as may be introduced into heat-shields located on crop shear tables. Heat may be lost by the piece by (1 ) direct conduction of the work rolls and table rolls (2) radiation, (3) air cooling, and (5)heat conduction within the piece. The rate of deformation of an element of a work- piece as it passes through a roll bite decreases as the elements moves from the entry to the exit end of the bite. For computational purposes, however, it is desirable, for reasons of mathematical simplicity, tD use an effecttive average value of the strain rate. Five solutions are proposed for mean strain rate. These are: a)- Ford and Alexander's solution b)- Simsv solution c)- Drowan and Pascoe's solution d)- klusatowski ' s solution Although a number of equation were drived tD calculate strain rate, they were expressed as a function of the roll speed and the reduction divided by the length of the contact area. Many matematical methods have been proposed to calculate rollingload for hot rolling of steel. Nine of these methods are studied and used in this study for rolling load calculation of steel flat products. These methods are: 1 - Sims' method 2- Cook-McCrum' s method 3- Ford-Alexander's method k- Denton-Crane's method 5- Green-Wallace ' s method 6- Ekelund's method xi 7- Ride's method B- Geleji's method 9- Tselikov's method Another restriction about yield stress used in Geleji 's method is that yield strees value is valid for carbon steels of a tensile strength üd to 60 kg/mm2 and in a temperature range of BOD to 1 300 C. Ride has utilized a statictical analysis of the rolling mill data in order to derive an empirical formula for the calculation the roll separating force. In this formula, each of the parameters affecting the roll separating force was included as a parabolic function. These parameters are roll peripheral speed, strip temperature, per cent reduction and roll contact length The resulting equation is obtained from a. correlation by the method of least squares. Data used in this uork uere collected from the 1 676- mm reversible hot strip mill in Ereğli Iron an steel works consists of a 4-high powered by two 25D0- hp drive motor. Tests with different rolling conditions on plai'n carbon steels (Fe-33, Fe-37,Fe kk) were performed and data is evaluated by a computer program in order to find adequate rolling load calculation method or met hods for hot flat rolling of steel strip which gives satisfactory results when compared with measured loads. The fallowing rolling parameters were measured; i)- Incoming temperature and thickness of bar Xll Ü-) Roll gap-set Hi-) Rolling load and motor current iv_) Outgoing temperature and thickness v-) Strip width after last pass. Data collected from hot strip mill were stored in a computer Appendix-1. To calculate -foiling load; ı entry and exit thicknesses and temperatures for each pass were calculated by a subprogram presented at Appendix-2. Rolling load for each of the nine methods used in this work was calculated by a computer program and compared with measured load. - Strain rate and deformation resistance were cal culated according to the equations given in each of these methods. At the same time, the deformation resistances are also calculated by using measured load and compared with calculated deformation resistance values of the methods. The first objective of this study was to compare calculated and measured rolling loads in order to find adequate method or methods for calculation of rolling load wich can be used to obtain optimum rolling conditions such as rolling speed, number of pass, draft and rolling temperature. Comparetive curves drawn fDr measured and calculated rolling load showed that there is always some deviation between calculated and mesaured.rolling loads for each of these methods because of the difficulties to determine accurately ' the factors affecting rolling load such as flow stress, drift, coefficient of friction and geometry of deformation zone in the hot rolling of steel flat products. The results of this study showed that Geleji's method gave the best result for calculation of rolling load when its calculated values compared to measured load values. Xlll Some load values calculated by Ride's method gave large scatter according to measured loads. This scatter may be related to the high sensitivity to per cent reduction of Ride's'-mBt'hod. Measurement error in thickness for each reduction wnich is less than 0.22 mm affects the load value obtained from Ride's method especially at small drafts. If the true per cent reduction value is determined, Ride's method gives adequate load values. The rolling load values obtained by Ekelund's method gave 30-40% standart error against measured load. Sims, Ford-Alexander,_ Cook-McCrum, Denton-Craen Green Wallace and Tselikov's methods gave approxmately 60-70 % standart error against measured rolling load. These results are probably due to inadequate geometric factor of deformation zone and improper rolling speed effect used in these methods. The deformation resistance of Fe-kk steel increased with increasing geometric factor. It also increased with increasing deformation rate at a constant temperature and reduction and decreased with increasing temperature at a constant deformation rate and reduction. A linear relation between measured rolling load and motor current was found. The motor current increased linearly with increasing rolling load.