Billet Temperature Field Research Articles

Solving the heat transfer boundary condition of billet in reheating furnace by combining “black box” test with mathematic model

Comprehensive radiant heat transfer coefficient, convective heat transfer coefficient and furnace temperature are the key parameters constituting the boundary conditions of the billet heat transfer model. This paper presents a novel method to obtain these parameters by combining "black box" test with mathematical model. Average relative errors of the calculated surface temperature and centre temperature of the case reheating furnace compared with the measured values are 2.34% and 3.51%, which verifies the method's feasibility. Influence law of furnace temperature characteristic parameters on billet temperature is analyzed. When the intercept, slope and amplitude change, the regions where the billet temperature field changes significantly is in or near the HEⅠsection, which are the key section to adjust the billet temperature field through single characteristic parameter. The longer the period is, the smoother the change of billet temperature in the same spatial region is, which is conducive to the uniform heating of billet. However, if only increasing the period, there may be a situation that the billet discharging temperature exceeds the target. Change of single characteristic parameter has its limitations. In order to achieve the accurate control of billet temperature, the collaborative change of each characteristic parameter is required.

An improved sequential function specification coupled with Broyden combined method for determination of transient temperature field of the steel billet

Accurate knowledge of the steel billet temperature field in the reheating furnace is of crucial importance to improvement of product quality and energy conservation. For this purpose, the determination of the transient temperature field of the steel billet during reheating is investigated based on the inverse heat conduction problem. The transient two-dimensional heat transfer model of the billet in the furnace is established and used as the direct problem. The sequential function specification coupled with the Broyden combined method (BC-SFSM) is developed to obtain the temperature field of steel billet. A real measurement experiment is conducted for validation of the inverse model, which indicates that the BC-SFSM can accurately determine the billet temperature field from the temperatures measured at three points inside the billet. A series of numerical experiments are implemented to analyze the performance of the BC-SFSM and study the effects of the measurement point locations and of the number of future time steps on inverse results. The results illustrate that the BC-SFSM can take only 49.0% of the computing time of the sequential function specification method to estimate the billet temperatures, and the relative root-mean-square error of estimated temperatures is generally less than 1.5% when the reasonable number of future time steps and suitable measurement point locations are adopted. Therefore, the BC-SFSM in this work is a promising algorithm to determine the billet temperature field in the reheating furnace with high accuracy and efficiency.

Three-dimensional analysis of medium-frequency induction heating of steel pipes subject to motion factor

As hydrocarbon resource exploration will extend towards deep sea and alpine cold areas in future, the corresponding welded pipes for oilfield use will face increasingly adverse operating environment. Acquisition of more precise heat source for medium-frequency heat treatment of welded pipes is fundamental to postweld residual stress analysis, weld microstructure improvement and performance research. However, as a pipe billet is subjected to movement factor, it is very tough to solve for a three-dimensional heat source closer to real pattern with complex process parameters. In this paper, the authors utilized a computing method of sequential coupling combining electromagnetic-thermal coupling and relative motion between steel pipe and coils, and designed the corresponding computation flowchart, and by computing pipe billet heat treatment process, they found that the steady-state temperature field formed around a weld appears double ellipsoidal. Further analysis shows that the root cause of the double ellipsoidal temperature field is asymmetric distribution of magnetic flux density and induction current, generated in the weld zone due to electromagnetic effect, within the steel pipe in axial direction. Moreover, stability and hysteresis of pipe billet temperature field were studied. It’s found that there is a certain hysteresis between the maximum temperature of inner surface and that of outer surface, because of two different heat sources undergone by the inner and outer surfaces of the weld, as well as relative motion between induction coil and welded pipe. The unique heat transfer process and temperature distribution pattern in wall-thickness direction is the immediate cause of the double ellipsoidal three-dimensional temperature field. This study offers a referenceable analysis method for further exploring steel pipe induction heating process under complex process parameters and optimization of the process parameters.

Temperature Field and Extrusion Load in Needle Piercing Extrusion Process Based on Ingot Billet for Large 7075 Aluminum Alloy Tube

Abstract. The change rules of the billet temperature field and extrusion load are the significant basis for the optimal design of the needle piercing extrusion process based on ingot billet for the manufacture of large-diameter thick-walled tube. Taking the needle piercing extrusion process of a 7075 aluminum alloy tube with sizes of Φ500mmx400mm/6000mm as study object, we developed a precise FE model for the process under DEFORM-2D environment, then numerically revealed the distributions and evolution rules of the billet temperature field, and obtained the effects of the extrusion speed and initial billet temperature on the billet temperature filed and extrusion load. The results show that the peak extrusion load decreases linearly with the increase of initial billet temperature but is insensitive to the extrusion speed, and that the peak temperature rises with the increase of the extrusion speed and initial billet temperature, and always locates on the surface of the initially extruded tube close to the exit of the cavity die.

Research of Billet Heating Optimal Strategy Oriented to Energy Saving

The character of billet heating is studied, in order to improve the billet heating quality and save energy, the prediction model within a billet temperature field is established. The billet heating process is carried on the modeling successful used finite element analysis. Based on analysis of billet heating model and ANSYS software, the temperature field in billet and the temperature setting of reheating furnace are combined, two methods are put forward of temperature optimal setting, the heat transfer situation and temperature field distribution within billet has been reappeared in the billet heating process, the optimal energy saving strategy of billet heating has got.

The Simplified Method to Calculate Two-Dimensional Heat Conduction Equations of Heating Slab

The most effective way of determining the whole billet temperature field is to use a simulation model. Large amount of calculation as well as computational time is consumed to employ two-dimensional finite difference method since the heating process is extremely complex, then it’s necessary to simplify the calculation process. In this paper, a simplified method in one-dimension format was presented to calculate two-dimensional heat conduction equations of heating slab. The billet simulated was placed in a changeable thermal flux boundary environment, in which the thermal flux was proportional to fourth power of temperature. During the heating process, the changeable parameters were taken into account: i. e different billet dimensions, different billet thermal conduction, different specific heat, etc. The comparision between results of two-dimensional finite difference method and the simplified method verified that the simplified method can satisfy accuracy requirement as well as calculation time saving, which enable the simplified method online using.