Physical Process Modeling


It presents the results achieved when introducing criteria for regulation of the heating process. The basic technological problem arises when, in operating electro-resistance furnaces, the heating operation mode of a detail should be carried out under certain conditions: temperature of heating, maximal admissible temperature differences and so forth. This layout emphasizes on the opportunity of receiving data for various situations of the system regulation in the process of design through the method of mathematical modeling as discussed here.
Created by Physical Process Modeling


REGULATION OF THE TEMPERATURE



    The installed power in some cases could lead to establishing of the temperature in the furnace above the admissible limits. Figure 1 shows a mode of establishing the temperature above 2100oC which is inadmissible for electro-resistance furnaces.
    The installation of power leading to such results aims to enable a regulation of the process of heating to the desired temperature within the assigned time. Figures 2 - 4 showing the processes of regulation in relation to the temperature of different nodes in the system furnace detail. Each of the heaters is 2[kW].

processes of regulation - Runge-Kutta method
Figure 1
Without regulation
Runge-Kutta regulation temperature
Figure 2
Controlled is the temperature in the first layer of the body
Runge-Kutta regulation temperature
Figure 3
Controlled is the temperature of the heater
Runge-Kutta regulation temperature
Figure 4
Controlled is the temperature of the surface of the body


    When controlling the temperature along the surface of the body, due to the thermal inertness the temperature of the heater exceeds the assigned one and reaches 1347,07oC. The reason for this is the method of regulation - the condition assigned in the performed simulation. A given temperature is being watched after it has reached a certain value and then the power of the heater is being controlled. By controlling the temperature within a few values it is possible to obtain the desired temperature with a better preciseness. Figures 5, 6 contains the graphs of regulation of the temperature in relation to the surface of the body whereby two values are used. The maximal temperature reaches 1312,28oC; there is also difference in the time for establishing of the process.
    As it has been noted, the time of heating could be influenced by the change of the installed power. The figures 5, 6 present the process of heating for the same system but with installed power of 10 [kW] per heater.

thermoregulator mathematical modeling
Figure 5
Heater and walls
thermoregulator mathematical modeling
Figure 6
Heater and body





Regulation
3D Graphics



chamber furnace regulation

chamber furnace regulation

chamber furnace regulation

chamber furnace regulation

chamber furnace regulation

chamber furnace regulation


Regulation
movie



  Simulation 1

  Simulation 2

  Simulation 3

  Simulation 4

  Simulation 5

  Simulation 6

  Simulation 7

  Simulation 8

  Simulation 9

  Simulation 10

  Simulation 11

  Simulation 12

  Simulation 13

  Simulation 14


MODEL OF REGULATION BY ASSIGNING HYSTERESIS



    The simulation has been carried out by using the Runge-Kutta method in the MatLab program at a constantly assigned step of integration dt=0.1. The question of choosing a dt with regard to the assigned hysteresis is closely linked to the frequency of the obtained commutations which determines the choice of hardware.

furnace simulation - MatLab

Figure 1
Regulation of the heater's temperature at assigned hysteresis to the regulator 1,3,4 - the heater's temperature; 2 - the body's surface

furnace simulation - MatLab

Figure 2
The process established with two-positional regulation 1,3 - the heater's temperature; 2,4 - temperature of the surface of the body

furnace simulation - MatLab

Figure 3
Three-positional regulation 1 - the heater's temperature; 2,3- the body's surface

    When assigning the range 1 = 510oC, 2=4900C (chart 3 figure 1), the process of control is carried out by two commutating impulses in a second. This necessitates using the step dt = 0,005, at which correct data are obtained. With the next assignment (chart 4) 1 = 510oC, 2 = 499oC, 10 commutating impulses per second are used which necessitates the choice of dt = 0,0001
    Figure 2 presents the temperatures of the heater (charts 1,3) and the surface of the body (2,4) after they have been established: A - regulation in relation to the temperature of the surface of the body and B - in relation to the heater.
    From the obtained results it can be concluded that the assigned hysteresis is closely linked to the step of integration, or to the frequency of discretization of the regulator in practical performance respectively.
    On the basis of the results obtained by simulation performed in various conditions it is possible to specify in advance the conditions for operating of an Electro-Resistance Furnace (ERF) and the choice of a relevant two-positional thermoregulator. Similarly, it is possible to analyze the operation of the existing complex furnace - regulator for establishing the possible limits and preciseness of regulation.
    The simulations carried out with various models of ERF show that regardless of the parameters and conditions of regulation, for the case under observation, if the capacity is bigger than zero there comes a moment 2 when the regulator loses control over the process figure 3. The operation of the furnace continues in the same way as it would operate without a regulating device, at a minimum capacity.
    The problem thus observed can easily be eliminated by attaching an additional condition in relation to the capacity status:

regulation conditions


After entering the correction, the temperature of the heater establishes as shown in chart 4 - figure 4.




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