Mathematical simulation of the temperature field in hardening gears by induction heating under a layer of water

2000 ◽  
Vol 73 (2) ◽  
pp. 420-427
Author(s):  
P. S. Gurchenko ◽  
M. L. German
Keyword(s):  
Temperature Field ◽  
Mathematical Simulation ◽  
Induction Heating

The Numerical Analysis of Temperature Field During Moveable Induction Heating of Steel Plate

2012 ◽  
Vol 28 (02) ◽  
pp. 73-81
Author(s):  
Xue-biao Zhang ◽  
Yu-long Yang ◽  
Yu-jun Liu
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Numerical Model ◽  
Induction Heating ◽  
Temperature Difference ◽  
Steel Plate ◽  
Heating Process ◽  
Quasi Steady State ◽  
Initial State ◽  
Plate Temperature

In shipyards, hull curved plate formation is an important stage with respect to productivity and accuracy control of curved plates. Because the power and its distribution of induction heat source are easier to control and reproduce, induction heating is expected to be applied in the line heating process. This paper studies the moveable induction heating process of steel plate and develops a numerical model of electromagneticthermal coupling analysis and the numerical results consistent with the experimental results. The numerical model is used to analyze the temperature changing rules and the influences on plate temperature field of heating speed of moveable induction heating of steel plate, and the following conclusions are drawn. First, the process of moveable induction heating of steel plate can be divided into three phases of initial state, quasi-steady state, and end state. The temperature difference between the top and bottom surfaces of the steel plate at the initial state is the biggest; it remains unchanged at the quasi-steady state and it is the smallest at the end state. Second, obvious end effect occurs when the edges of the steel plate are heated by the inductor, which causes a decrease in temperature difference between the top and bottom surfaces of the steel plate that is unfavorable for formation of pillow shape plates. Third, with the increase of heating speed, the temperature difference between the top and bottom surfaces of the steel plate increases gradually.

scholarly journals Experimental and numerical study of the effect of coil structure on induction nitriding temperature field

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402093848
Author(s):  
Kangjie Song ◽  
Jing Guan ◽  
Kunmao Li ◽  
Jing Liu
Keyword(s):  
Temperature Field ◽  
Temperature Distribution ◽  
Induction Heating ◽  
Current Density ◽  
Numerical Study ◽  
Radial Temperature ◽  
Current Frequency ◽  
Variable Pitch ◽  
Variable Radius ◽  
Heating Efficiency

The axial and radial temperature distributions of an induction heating workpiece considerably impact the subsequent nitriding process. To obtain a satisfactory temperature distribution, an equal pitch coil, a variable pitch coil, and a variable radius coil were designed. Furthermore, an induction heating model that exhibits electromagnetic and temperature field coupling was established; thus, the effects of the current density and frequency on the heating efficiency and temperature distribution of the workpiece were analyzed and compared. In addition, an induction heating experiment was conducted to verify the model. According to the numerical results, the variable radius coil can reduce the axial temperature difference in comparison with equal pitch coil and variable pitch coil. Hence, the workpiece heated using the variable radius coil can achieve a better temperature distribution when compared with those heated by the equal pitch coil and variable pitch coil, with appropriate current density and current frequency values.

scholarly journals Two-channel time-optimal control of induction heating process with maximum temperature constraint

2020 ◽  
Vol 28 (2) ◽  
pp. 41-58
Author(s):  
Natalya A. Il`ina
Keyword(s):  
Optimal Control ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Induction Heating ◽  
Time Optimal Control ◽  
Maximum Temperature ◽  
Heating Process ◽  
Problem Of Time ◽  
Control Actions ◽  
Time Optimal

The formulation and method of solution of the problem of time-optimal control of induction heating process of an unlimited plate with two control actions on the value of internal heat sources with technological constraint in relation to a one-dimensional model of the temperature field are proposed. The problem is solved under the conditions of a given accuracy of uniform approximation of the final temperature distribution over the thickness of the plate to the required. The method of finite integral transformations is used to search for the input-output characteristics of an object with distributed parameters with two control actions. The preliminary parameterization of control actions based on analytical optimality conditions in the form of the Pontryagin maximum principle is used. At the next stage reduction is performed to the problem of semi-infinite optimization, the solution of which is found using the alternance method. The alternance properties of the final resulting temperature state at the end of the optimal process lead to a basic system of relations, which, if there is additional information about the shape of the temperature distribution curve, is reduced to a system of equations that can be solved. An example of solving the problem of time-optimal control of temperature field of an unlimited plate with two offices is carried out in two stages. At first stage the case of induction heating without maximum temperature constraints is considered, at the second stage is carried out on the basis of the results of the first stage to obtain the solution subject to the limitation on the maximum temperature of the heated billet.

scholarly journals A Simplified Calculation Method of Heat Source Model for Induction Heating

Materials ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 2938 ◽  
Author(s):  
Hongbao Dong ◽  
Yao Zhao ◽  
Hua Yuan ◽  
Xiaocai Hu ◽  
Zhen Yang
Keyword(s):  
Heat Flux ◽  
Temperature Field ◽  
Heat Source ◽  
Heat Generation ◽  
Induction Heating ◽  
Generation Rate ◽  
Heat Generation Rate ◽  
Line Heating ◽  
Computation Efficiency ◽  
Computation Process

Line heating is used in forming the complex curve plates of ships, and this process is becoming integrated into automated tools. Induction heating equipment has become commonly used in automatic line heating. When applying automated equipment, it is necessary to calculate the relationship between the heating parameters and the temperature field. Numerical methods are primarily used to accomplish the calculations for induction heating. This computation process requires repeated iterations to obtain a stable heat generation rate. Once the heat generation rate changes significantly, a recalculation takes place. Due to the relative position of the coil and plate changes during heating, the grid needs to be frequently re-divided during computation, which dramatically increases the total computation time. In this paper, through an analysis of the computation process for induction heating, the root node that restricts the computation efficiency in the conventional electromagnetic-thermal computation process was found. A method that uses a Gaussian function to represent the heat flux was proposed to replace the electromagnetic computation. The heat flux is the input for calculating the temperature field, thus avoiding the calculation of the electromagnetic analysis during induction heating. Besides, an equivalence relationship for multi-coil was proposed in this paper. By comparing the results of the experiment and the numerical method, the proposed heat source model’s effectiveness was verified.

scholarly journals Induction heating of a shape memory alloy beam

2018 ◽  
Vol 83 (3) ◽  
pp. 30905 ◽  
Author(s):  
S. Dufour ◽  
G. Vinsard
Keyword(s):  
Temperature Field ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Induction Heating ◽  
Mechanical Model ◽  
Eddy Currents ◽  
Shape Change ◽  
Nickel Titanium ◽  
Thin Shells ◽  
Induced Currents

The shape memory alloy heating by eddy currents is a quick solution for the shape change. Then, the analysis of the temperature field as a function of the shape is important to build a mechanical model in large deformation. Even if the temperature can be obtained by experiment, a computational model is useful. The computation of the induced currents in a nickel–titanium shape memory alloy beam is here considered with a T − Ω model adapted to thin shells with the help of a change of coordinates. It allows us to take into account the shape change, without the need of remeshing, as a function of the temperature. Experiments are carried out to validate the model.

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