Shanghai Baosight Software Co.,Ltd.,Shanghai 201900,China

Abstract: A three-dimensional electromagnetic-thermal coupled model of a 45# steel strip during longitudinal magnetic flux induction heating was established in this study.The influence of different power levels,frequencies,and electromagnetic shielding on the magnetic induction intensity and the heating of parts of different materials around the inductor was analyzed by calculating the magnetic induction intensity around the longitudinal flux induction heater under different conditions.The results show that leakage flux can be reduced up to 49% by electromagnetic shielding.The higher the frequency,the greater the electromagnetic shielding effect,and the lower the magnetic leakage around the inductor.Conversely,the higher the power,the greater the magnetic induction around the inductor.By adding electromagnetic shielding to reduce magnetic leakage of the inductor and replacing the metal part material around the inductor with stainless steel,the heat generation of the parts around the inductor can be greatly reduced.

Key words: longitudinal flux induction heating; numerical simulation; magnetic flux leakage

1 Introduction

Electromagnetic induction heating occurs when a metal workpiece is placed in an alternating magnetic field,which generates eddy currents in the workpiece through electromagnetic induction.As one of the environmentally friendly,efficient,and fast heating methods,electromagnetic induction heating is increa-singly used in the heat treatment of materials[1-2].The induced eddy currents generate Joule heating,by which the workpiece is heated[3].In regard to a thin metal strip,defined as having a thickness of 1.8-6.0 mm,it is difficult to heat to a target temperature in a short time while ensuring uniform distribution of the temperature across the strip.Previous reports[4-5]have shown that longitudinal flux induction heating is easier to achieve temperature uniformity than trans-verse flux induction heating.Therefore,longitudinal flux induction heating is typically used in the heat treatment process of metal strip material.

Leakage of flux intensity often occurs during longitudinal flux induction heating.Research has shown that the leakage of flux intensity of the longitudinal magnetic coil can be effectively reduced by using magnetic conductor technology[6-7].How-ever,the cost of magnetic conductors is high,and it is difficult to control and maintain these materials in engineering applications.Therefore,the current work primarily uses numerical simulations to investigate the influence of adding leakage shielding during the longitudinal magnetic induction heating process.

2 Induction heating finite element analysis

A schematic diagram of a longitudinal magnetic flux induction heating device without electro-magnetic shielding and with electromagnetic shield-ing is shown in Fig.1.The width and thickness of the strip are 1 200 mm and 4 mm,respectively.The coil and electromagnetic shielding materials are T2 copper.The effective coil size is 1 600 mm×200 mm.The strip passes through the center of the coil at a speed of 10 m/min.

Fig.1 Schematic diagrams of a longitudinal magnetic flux induction heating device

2.1 Maxwell equations

The following equations[8-9]list Maxwell’s equa-tions:

(1)

The heat sourceQis determined by the eddy current density and conductivity,as shown in Equa-tion (2):

(2)

And finally,heat transfer follows Equation (3):

(3)

where,ρ′ is the material density;Cpis the specific heat capacity;kis the thermal conductivity;andTis the temperature.

2.2 Material physical parameters and bound-ary conditions

The strip material selected in this work is 45#steel,whose properties are temperature-dependent.The change of material physical parameters with temperature has a great influence on induction heating[10-11].The changes in permeability,resis-tivity,thermal conductivity,and specific heat ca-pacity of 45#steel against temperature have been com-piled in Table 1.For the purposes of our simulation,material density was 7 870 kg/m3with an initial tem-perature of 298.15 K.

The electromagnetic field problem domain is defined to include the immediate airfield,coil,and slab.The induction heating numerical calculation uses the magnetic vector potential method,using magnetic potentialA(A=0),and can be used to calculate the magnetic fieldB:

(4)

The heat exchange mechanisms between the slab and surrounding air are convective heat transfer and radiant heat transfer:

(5)

This work uses multifield coupling calculations to account for magnetic field and solid heat transfer effects.First,the initial and boundary conditions were used to solve the electromagnetic field.Then,the calculated eddy current value and the initial temperature of the slab were used as the initial con-ditions to calculate the temperature field.After the preliminary temperature field results were obtained,the material properties of the slab were then updated according to the calculation results.Finally,the electromagnetic field calculation was updated to account for the coupling calculation between the magnetic and temperature fields during the move-ment of the slab.

Table 1 Material property parameters of 45# steel

3 Calculation results and analysis

A point 100 mm away from the edge of the coil was selected for magnetic induction intensity analysis.This point,marked asA,was used to analyze the influence of power and frequency on the intensity of the magnetic field around the inductor.PointAis outside the coil，and is 100 mm away from the edge of the coil.Fig.2 shows the selected pointAin a cross-sectional plane along the model.

3.1 Magnetic induction intensity around the inductor

Figs.3 and 4 show the magnetic induction inten-sity without and with electromagnetic shielding,re-spectively.For this simulation,the longitudinal magnetic flux induction heating power was 1 000 kW,

Fig.2 Schematic diagram of the relative position of point A and the coil

and the frequency was 8 kHz.As shown in the magnetic flux leakage heatmaps,there is a strong magnetic field around the inductor.As the distance increases,the magnetic induction intensity gradually decreases.The maximum magnetic induction inten-sity around the inductor occurs at pointA,the midpoint of the inductor length,and is 67×10-4T without electromagnetic shielding.With electro-magnetic shielding,the magnetic leakage intensity is significantly reduced to 34×10-4T at pointA.The overall flux leakage intensity could be reduced up to 49% by electromagnetic shielding.

Fig.3 Magnetic flux leakage of the inductor without electro-magnetic shielding

Fig.4 Magnetic flux leakage of the inductor with electro-magnetic shielding

3.2 Influence of power and frequency on the intensity of magnetic field around the inductor

Figs.5 and 6 show the magnetic induction inten-sity at pointAunder different frequencies and power levels,respectively.As shown in Fig.5,when the in-duction coil power is 1 000 kW,the magnetic induc-tion intensity at pointAdecreases from 34×10-4T to 24×10-4T as the power frequency increases from 8 to 50 kHz.Magnetic field penetrating power decreases with increasing frequency with the electromagnetic shielding.The higher the power frequency,the greater the electromagnetic shielding effect and the smaller the magnetic leakage around the inductor.As shown in Fig.6,when the inductor frequency is 8 kHz,as the induction heating power increases from 1 000 to 3 000 kW,the magnetic induction intensity at pointAincreases from 34×10-4T to 58×10-4T.When the frequency is held constant,an increase in power generates greater magnetic induction intensity around the inductor.

Fig.5 Magnetic induction intensity at point A under dif-ferent frequencies at a fixed induction coil power of 1 000 kW

Fig.6 Magnetic induction intensity at point A under different powers at a fixed induction coil frequency of 8 kHz

3.3 The influence of magnetic flux leakage on surrounding parts

As shown in Fig.7,a small,100 mm×40 mm×40 mm metal part was placed outside the coil to measure the influence of magnetic flux leakage around the strip.The simulation was repeated with different part materials,45#steel and stainless steel.This work assumes that the relative permeability of the stainless steel material is 1.Specific heat capa-city,thermal conductivity,resistivity,and density of stainless steel are the same as 45#steel.At an in-duction heating power of 1 000 kW and a frequency of 8 kHz,the influence of part material and electro-magnetic shielding on the heat of the part is cal-culated.

Fig.7 Schematic diagram of an external part around the longitudinal flux induction heater

As shown in Fig.8,the 45#steel part is heated from 298.15 K to 472.15 K,and the temperature rises by 174 K when there is no electromagnetic shielding.After electromagnetic shielding,the tem-perature rise is only 47 K.If the temperature rises too high,the parts must be cooled by water.This greatly increases the complexity of the inductor design when the material of this part is changed to stainless steel.It is heated to 306.45 K,the stainless steel part only experiences a temperature rise of 8.3 K;thus,it does not require water cooling.

Fig.8 Schematic diagram of the magnetic induction intensity,induced current density,and heated temperature distribution of the part under different conditions

4 Conclusions

(1) Longitudinal flux induction heating exhibits high leakage flux intensity,which can be reduced up to 49% by electromagnetic shielding.

(2) The higher the frequency,the better the electromagnetic shielding effect and the lower the magnetic leakage intensity around the inductor.

(3) The higher the power,the greater the magnetic induction intensity around the inductor.

(4) In the engineering design,the heat gener-ation of the parts around the inductor can be greatly reduced by increasing the electromagnetic shield-ing,which reduces the magnetic leakage of the inductor.Replacing the material of the parts sur-rounding the inductor with stainless steel will also dramatically reduce heat generation.