UDK 621.77.014.2 Original scientific article/Izvirni znanstveni članek ISSN 1580-2949 MTAEC9, 47(1)85(2013) HEAT-FLUX COMPUTATION FROM MEASURED-TEMPERATURE HISTORIES DURING HOT ROLLING RAČUNANJE TOPLOTNEGA TOKA NA OSNOVI PRETEKLIH MERITEV TEMPERATURE MED VROČIM VALJANJEM Jana Ondrouskova1, Michal Pohanka1, Bart Vervaet2 JHeat Transfer and Fluid Flow Laboratory, Faculty of Mechanical Engineering, Brno University of Technology, Technicka 2, 616 69 Brno, Czech Republic 2Centre for Research in Metallurgy, Technologiepark 903c, 9052 Zwijnaarde, Belgium ondrouskova@lptap.fme.vutbr.cz Prejem rokopisa — received: 2012-08-31; sprejem za objavo - accepted for publication: 2012-09-18 Due to the long service life of work rolls it is very important to follow the thermal load, but it is very difficult to measure it. One option for computing this thermal load is to measure the temperature and to study the thermal load through the heat flux. A unique work roll was made for testing different process conditions, such as rolling velocity, roll cooling, skin cooling and reduction. This work roll was tested on a real, hot-rolling, continuous pilot line. Two types of temperature sensors were embedded in the work roll in order to measure the temperature and these gave very detailed information about the development of the temperature inside the work roll. A time-dependent heat flux was computed using an inverse heat-conduction task with a detailed numerical model. The surface-temperature history was also obtained from this computational model. These boundary conditions give detailed information about the influence of different process conditions and allow a computation of the temperature field in the work roll. The paper describes the measuring equipment, details of the used temperature sensors, the inverse heat-conduction task for computing the thermal-surface boundary conditions and the results obtained from hot-rolling conditions. Keywords: heat flux, hot rolling, roll cooling, inverse heat-conduction problem, surface temperature Zaradi dolge dobe trajanja delovnih valjev je pomembno sledenje njihovih toplotnih obremenitev, ki jih je težko izmeriti. Ena od opcij izračuna termičnih obremenitev je merjenje temperature in študij toplotne obremenitve s toplotnim tokom. Izdelan je bil valj za preizkušanje različnih procesnih pogojev, kot so hitrost valja, ohlajanje valja, ohlajanje skorje valja in odvzem. Ta delovni valj je bil preizkušen na realni kontinuirni vroči valjarniški pilotni liniji. V delovni valj sta bili vgrajeni dve vrsti temperaturnih senzorjev, da bi izmerili temperature, in obe sta dali zelo podrobno informacijo o poteku temperature v njem. Izračunana je bila časovna odvisnost toplotnega toka z natančnim matematičnim modelom inverznega toka toplote. Iz tega računskega modela je bila dobljena tudi zgodovina temperature površine. Ti mejni pogoji so dali natančno informacijo o učinku različnih parametrov procesa in omogočili izračun temperaturnega polja v delovnem valju. V članku je predstavljena merilna oprema, detajli uporabljenih senzorjev temperature, inverzno prevajanje toplote za izračun mejnih termičnih razmer na površini in rezultati, dobljeni pri valjanju. Ključne besede: toplotni tok, vroče valjanje, hlajenje valja, problem inverznega prevajanja toplote, temperatura površine 1 INTRODUCTION The work roll is repeatedly heated and cooled during the hot-rolling process. A good knowledge of the temperature field of the work roll and a stress-strain analysis help us improve the cooling of the work roll and, thus, to extend its service life. The measurement of temperature histories inside the work roll during a hot-rolling trial was reported by Raudensky et al.1 This article describes the results of the measurements in the pilot mill of CRM, Gent. The temperature sensors were embedded into the roll using inserts (as seen on the top of Figure 1). There were five thermocouples in each roll. An example of the data from the real measurement is on the bottom of Figure 1. The thermocouples were placed at two different depths. Two thermocouples were soldered at a depth of 0.4 mm (Figure 1) and three were drilled at a depth of 0.8 mm. A detailed description of the plug with a drilled shielded thermocouple and the discretization used for the computational model is given in2. 2 INVERSE HEAT-CONDUCTION PROBLEM A complex 2D-axis symmetric model was used for the numerical computation. The model includes the shielded thermocouple with all its parts and the used solder. The thermocouple must be taken into account because the homogeneity of the material is disturbed by the inserted thermocouple, and, thus, the temperature profile is also disturbed. One-dimensional sequential Beck's approach3 is used for the computing of the heat fluxes and the surface temperatures. The main feature of this method is the sequential estimation of the time-varying heat fluxes and surface temperatures using the future time-step data to stabilize an ill-posed problem. The measured temperature history is used as input T* to minimize the equation: m+f SSE = X (T* - T )2 (1) i=m +1 Figure 1: Cross-section of the rolls with the inserts from HiCr and HSS materials and the holes for the thermocouple wires; a detail of the plug with a soldered shielded thermocouple; temperature data of the two roll cycles (depth of 0.4 mm, speed of 0.1 m/s, reduction of 10 %) Slika 1: Prečni prerez valja z vložki iz materialov HiCr in HSS in luknje za žico termoelementov; detajl čepa s prispajkanim termo-elementom; podatki o temperaturah pri dveh ciklih valjanja (globina 0,4 mm, hitrost 0,1 m/s, odvzem 10-odstoten) Figure 2: Comparison of the results obtained from the drilled and soldered thermocouple Slika 2: Primerjava rezultatov, dobljenih iz izvrtanega oziroma pri-spajkanega termoelementa where m is the current time, f is the number of future time steps and T indicates the computed temperatures from the forward solver4. SSE denotes the sum of square errors. The value of surface heat flux q at time m is: m + f X (T* - t\ =m +1 ,)ši m + f š, = X( š,)2 d