This document discusses induction heating of bars and billets. It covers choosing frequency and power based on material properties, batch and continuous heating processes, and typical industrial heater configurations. Fast through heating induction processes and innovative heating with permanent magnets for aluminum billets are also presented. Formulas for calculating heating time, power requirements and temperature distribution are provided for both non-magnetic and magnetic materials.

1. EPM webinar n.7
Induction Heating of
Bars and Billets
Michele Forzan
Laboratory of Electroheat Padova LEP
Università di Padova – Dipartimento di Ingegneria industriale
LEP

2. 2
LEP
LEP since 1967

3. 3
LEP
outline
• Choice of frequency, power and heating time for
non magnetic and magnetic materials
• Batch and continuous through heating
• Fast through heating processes
• Typical configurations of industrial heater
• Innovative induction heating with permanent
magnets also for taper heating of aluminum billets
Michele.forzan@unipd.it
Laboratory of Electroheat of Padova
University of Padova

4. 4
LEP INDUCTION THROUGH HEATING
OF BILLETS AND BARS
MASS heating
prior to metal hot working
(forging, forming,extrusion)
GOAL -> UNIFORM TEMPERATURE
Carbon
Steel
Stainless
steel
Copper Aluminium Titanium
Extrusion 1230 1300 870 480 950
Lamination 1230 1260 760-870 480-540 930
Forging 1180-1300 1200-1320 870 450 930

5. 5
LEP
INDUCTION HEATING HAS
ADVANTAGES :
• Repeatability of heating cycle: OPTIMAL production
• Small size (in comparison with fossil fuel furnaces)
• FAST HEATING Power intensive process with high throughputs
• less oxidation and decarburization (for steel) longer working life of
forging dies
• Rapid start of the production
• Better working ambient
• Possible taper heating
DISADVANTAGES:
• Cost of the installation/electricity in some countries
• Difficulty of homogeneous heating complex shape workpieces
• Necessity of changing inductors for different billet dimensions

6. 6
LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
R22HP 2
eload



P(m)
• The square value of the magnetic field intensity on
the surface
• The resistivity of the metal, function of temperature
• The skin depth, function of magnetic permeability,
electric resistivity, frequency (so it depends on T)
• m, the ratio between the billet radius and the skin
depth
The power induced in a cylindrical billet depends on:

7. 7
LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
m= 2 R/  ≥ 2.5Dimensioneless radius ‚m‘
0
0.1
Q
P
A
B
m
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0
1 2 3 4 5 6 7 8 9 10
R22HP 2
0load



P(m)

8. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
The electrical efficiency,
the ratio between the USEFUL power and the TOTAL power at the inductor ends,
depends on the resistance of inductor (copper):
I
V
r’load
rinductor
xe
'
loadind
'
loadind
'
load
inductorlossuseful
useful
e
rr1
1
)m(r)m(r
)m(r
PP
P









9. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
The series equivalent
resistance of the
inductor
depends on the
copper thickness s:
ii
ii
i
i
2
2
i
i kA
R2
N
I
P
r





3,0
mi=1
2 
2,52,01,51,00,50
Q2Bi 
i
A
6

s2
m 
0
1
2
3
4
0.25 0.50 0.75 1.00 1.25 1.50 1.57 1.75 2.00 3.00 5.00 10.0
Ai 4.00 2.01 1.37 1.086 0.959 0.920 0.918 0.925 0.950 0.999 1.00 1.00
Bi 0.167 0.333 0.490 0.632 0.781 0.893 0.918 0.965 1.004 1.006 1.00 1.00
s i  2 157,
A SIMPLE RULE TO
CALCULATE THE COPPER
THICKNESS

10. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
i
a
s
@ 50 Hz
i= 10 mm → si = 15 mm
@ 1000 Hz
i= 2,3 mm → si = 3-4 mm
COPPER FOR INDUCTORS

11. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
P2
kA
1
1
iii
i
e












i
maxe
1
1


0
A)
C)
B)
E)
D)
=2.2
m
e
2.2
1.8
2 4 6 8 10 12 14
0
0.2
0.4
0.6
1.0
2.2
=1.4
2.2
1.8
=1.4
2.2
[A) Magnetic steel heated to 800°C B) Steel from 800 to 1200°C C) Steel from 0 to 1200°C
D) Alluminium and its alloys heated to 500°C and copper to 800°C E) Brass heated to 800°C]
load
induc
R
R


12. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
6
1
3
4
5
2
6
1
3
4
5
2
6
1
3
4
5
2
1 - billet or bar;
2 - rails;
3 - thermal insulation; 4-
inductor;
5 - refractory concrete;
6 - external box
Inductor cross-section
50
 = Di/D
20
1,0
100 150
D[mm]
200
1,5
2,0
2,5

13. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
)t,r( 
z
r
dr
Fourier’s equation in
cylindrical c.s.


















c
w
rr
1
r
k
t 2
2
Thermal transient in a cylindrical workpiece depends on:
TEMPERATURE FIELD
w INDUCED POWER DENSITY [W/m3]
c specific heat [J/°C/kg]
 material density [kg/m3]
l thermal conductivity [W/m/°C]
𝑘 =
𝜆
𝑐 𝛾
thermal diffusivity [m2/s]

14. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
The solution of Fourier’s equation is quite complex
I thermal equalization with an imposed surface temperature B.C.
S
2
R
tk
R
r







DIMENSIONLESS
QUANTITIES.
AFTER  = 0,3, THAT IS t = 0.3 R2/k, TEMPERATURE DIFFERENCE BETWEEN SURFACE AND
CORE IS ABOUT 30%

15. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
II thermal transient with constant surface heating power
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5









 
 





1n n0
2
n
n02 2
n
e
)m(J
)m(J
2
4
1
2
1
2 



t
R
k
RP
R
r
2
o





l

DIMENSIONLESS
QUANTITIES.
AFTER
 ≈ 0,2
   2
1
2
1
4
2
 

16. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
Heating Time and Power for non magnetic billets – linear
properties
ENERGY BALANCE
Per unit lenght








(m)]F"-[1
P
c
Rt
)m(F
4P
s
u
2
0
su




l
M
mF
4
c
M
R
t
2
0
l

)(


s
as





1197531
0
0.2
0.3
0.5
0.7
1.0


2
D
m
F’(m
)
F’’(m)
F(m)
s
2
0u cRtP 

17. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
Heating Time and Power for magnetic billets
at constant frequency and surface magnetic field
0
250
500
750
1000
1250
0 t0
 [°C]
 s
 s  a
t
surface
axis

Heating in a single inductor

18. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
HEATING TIMES WITH STEEL
PuB
0
PuA
A
B
PuB
tA tB
t0
*
*
53.047.0
t
t
;36.020.0
t
t
;20.015.0
P
P
;2010
m
m
*
0
0
B
A
uA
uB
B
A

37.1
1
P
P
f
f
H
H
P
P
f
f
m
m
A
B
AA
B
A
B
2
A0
B0
uA
uB
AB
A
A
B
A
B























 



uB
ABB
uA
AA2
BA0
P
)(c
P
c
Rttt
uA
uB
AB
A
B
A
B
AB
uA
uB
A
uB
BB
uB
ABB
uA
AA
*
0
0
P
P
t
t
)(
P
P
P
c
P
)(c
P
c
t
t












19. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
PREVIOUS FORMULA GIVES POWER AND TIME FOR ‘STANDARD’
STATIC HEATING.
•
Without soaking period With soaking period
k
R
1500750t
2
0 )..( 
Soaking time for reducing the temperature
difference to 30% and 10% of the initial value
HEATING OF ALUMINIUM BILLET
D=150 mm; θs=520 C; ε=0.075; f=50 Hz

20. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
‘STANDARD’ AND ‘FAST’ HEATING FOR STEEL BILLETS
D = 40 mm;
f =2 kHz
%.256
s
as 





s
a
s-a
s
a
s-a

21. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
THERMAL LOSSES!!!!
W/cm2
t [s]
W/cm2
t [s]
W/cm2
t [s]
W/cm2
t [s]

22. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
Choice of Frequency
0 50 100 150 200 250
0,1
0,2
D[mm]
0,3
0,5
1,0
2,0
3,0
5,0
10
f[kHz]
a) c)
b)
a), b) - minimum and maximum values;
c) - optimum frequency
m < 2 - low electrical efficiency
m = 2.5 - optimum frequency
2 < m < 5 - satisfactory efficiency
m > 7 - low thermal efficiency
For steel heated
from ambient temperature to
1200 °C
22
63
D
f
D
 (D in m)
Michele.forzan@unipd.it
Laboratory of Electroheat of Padova
University of Padova

23. LEP Choice of frequency, power and heating time for non magnetic and magnetic materials
NUMERICAL MODELS FOR OPTIMAL
PERFORMANCE
Process constraints:
Temperature difference in the cross-section
Distribution and control of induced power along line
-200
0
200
400
600
800
1000
0 50 100 150 200 250 300 350 400
time
Temperature
1
2
3
Limitation of radial thermal
stresses for certain steel
grades
Holding time above specified
temperature for metallurgical
transformations
1D, 2D CODES coupled with
optimisation procedure

24. LEP Batch and continuous through heating
mA
mB mBBBATCH PROCESS IN A SINGLE INDUCTOR
STEP BATCH PROCESS IN TWO – THREE INDUCTORS

25. LEP Batch and continuous through heating
CONTINUOUS THROUGH HEATING OF BILLETS

26. LEP CONCLUSION OF THE FIRST PART
ANALYTICAL SOLUTIONS OF THE THROUGH HEATING PROCESS ARE REALLY
CUMBERSOME (solution of II order differential equations in cylindrical configurations).
THE ANALYTICAL SOLUTION GIVES SOME FUNDAMENTAL DIRECTIONS FOR THE DESIGN
OF THIS CLASS OF INDUCTION HEATERS.
m= 2 R/  ≥ 2.5
m= 2 R/  ≤ 7
ELECTRICAL EFFICIENCY
THERMAL EFFICIENCY
s i  2 157, CORRECT COPPER THICKNESS

27. LEP CONCLUSION OF THE FIRST PART
INNOVATIVE INDUCTION HEATING WITH
PERMANENT MAGNETS ALSO FOR TAPER
HEATING OF ALUMINUM BILLETS

28. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
Principle of rotating billet
superconducting induction heating
Principle of PMH
Permanent Magnet Heating
MECHANICAL ENERGY THERMAL ENERGY

29. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
• Uniform external D.C.
magnetic field
• Billet rotating at constant
angular velocity  [radiant/s]



0
1
diffusion length [m];


R
m ;
R
r
 ; 1j  ;
R =
2
2 R
m 






 - magnetic Reynolds number
R – radius of cylindrical workpiece [m]
 - electrical conductivity [ohm-1
m-1
]
7
0 104  - vacuum magnetic permeability [H/m]
. – relative permeability
)602(n  - angular velocity of shaft
B0 – external magnetic field [T]

30. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
2
ri n
60
R2
B),(w 





 


n - revolutions per minute
Bri – radial component of induction
 - electrical conductivity












)jm(J
e)jm(JR)1(B
eB
1
j
1
2
0
ri



















 

j
2
2
0e e1BjeB
)jm(Jjm)jm(J)1(
)jm(Jjm)jm(J)1(
01
012




31. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
11
Average induced power distribution
as a function of m and 
1.0
m=1

W/W0
0.8
0.6
0.4
0.2
0
0.20 0.4 0.6 0.8 1.0
2.5
3.5
5
7.5 10
15
)m('bei)m('ber
)m('bei)m('ber
w
w
22
22
ms
m




These distribution are the same
as in the induction heating of a
static cylinder with longitudinal
A.C. exciting flux

32. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
ALUMINUM BILLET HEATER (PMH) PROPOSED BY UNIPD
 achievement of high efficiency without using expensive superconductors
 a robust solution: rotating magnets installed on a steel rotor and keeping fixedthe billet
 small footprint (smaller than traditional Induction Heating and gas furnaces)
 no water cooling
 Possibility to modify the rotational velocity by varying the number of magnetic poles
An industrial scale prototype for 200 mm diameter, 500 mm length aluminum billet has been
realized with rated power of 55 kW.

33. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
The process – Taper Heating of Al Billets
EXTRUSION OF ALUMINIUM
BILLET
Images from: http://machinedesign.com/archive/smart-ways-design-aluminum-extrusions,
http://www.otto-junker.de/go/en/products-technologies/furnaces-plants-for-aluminium-and-aluminium-based-alloys/extrusion-plant/heating_induction.html
𝜂 =
1
1 + 𝛼
𝜌𝑖
𝜌 𝜇
Induction heating is the only technology that
allows a precise control of temperature but
electrical efficiency is poor for high
conductive metals.

34. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
SPECIFICATION OF PMH FOR FIRST INDUSTRIAL PROTOTYPE
Aluminum alloys 6060-6063-6005-6082-3103
Billet diameter 203 [mm]
min. billet length 350 [mm] Input temperature 400 [°C]
max. billet length 1100 [mm] PRESCRISBED TEMPERATURE DISTRIBUTION
min. billet weight 30.6 [kg] Output temp. zone 1 500 [°C]
max. billet weight 96.1 [kg] Output temp. zone 2 470 [°C]
Max. productivity 45 Bill/h Output temp. zone 3 450 [°C]
Cycle time 80 [s] Output temp. zone 4 430 [°C]

35. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
THE ACTIVE PART IS COMPOSED BY 4 ROTORS, INDEPENDENTLY CONTROLLED.
THE INDUCED POWER IS CONTROLLED BY VARYING THE SPEED,
THE NET TORQUE ACTING ON THE BILLET IS STRONGLY REDUCED OR CANCELLED BY
ROTATING THE MAGNETS IN OPPOSITE DIRECTIONS

36. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
45 s
n rotor rpm f Al P_Al Cem heating Time T
- [rpm] [Hz] [kW] [Nm] [s] [s]
1 1500 150.0 40.0 245.0 45.0
2 1200 120.0 36.0 -256.0 45.0
3 1000 100.0 30.1 265.0 45.0
4 800 80.0 22.1 -256.0 45.0
1 800 80.0 20.2 256.0 13.0
2 600 60.0 15.5 -235.0 13.0
3 0 0.0 0.0 0.0 13.0
4 0 0.0 0.0 0.0 13.0
1 0 0.0 0.0 0.0 22.0
2 0 0.0 0.0 0.0 22.0
3 0 0.0 0.0 0.0 22.0
4 0 0.0 0.0 0.0 22.0
45.0
58.0
80.0
Michele.forzan@unipd.it
Laboratory of Electroheat of Padova
University of Padova

37. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
58 s
n rotor rpm f Al P_Al Cem heating Time T
- [rpm] [Hz] [kW] [Nm] [s] [s]
1 1500 150.0 40.0 245.0 45.0
2 1200 120.0 36.0 -256.0 45.0
3 1000 100.0 30.1 265.0 45.0
4 800 80.0 22.1 -256.0 45.0
1 800 80.0 20.2 256.0 13.0
2 600 60.0 15.5 -235.0 13.0
3 0 0.0 0.0 0.0 13.0
4 0 0.0 0.0 0.0 13.0
1 0 0.0 0.0 0.0 22.0
2 0 0.0 0.0 0.0 22.0
3 0 0.0 0.0 0.0 22.0
4 0 0.0 0.0 0.0 22.0
45.0
58.0
80.0
Michele.forzan@unipd.it
Laboratory of Electroheat of Padova
University of Padova

38. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
80 s
n rotor rpm f Al P_Al Cem heating Time T
- [rpm] [Hz] [kW] [Nm] [s] [s]
1 1500 150.0 40.0 245.0 45.0
2 1200 120.0 36.0 -256.0 45.0
3 1000 100.0 30.1 265.0 45.0
4 800 80.0 22.1 -256.0 45.0
1 800 80.0 20.2 256.0 13.0
2 600 60.0 15.5 -235.0 13.0
3 0 0.0 0.0 0.0 13.0
4 0 0.0 0.0 0.0 13.0
1 0 0.0 0.0 0.0 22.0
2 0 0.0 0.0 0.0 22.0
3 0 0.0 0.0 0.0 22.0
4 0 0.0 0.0 0.0 22.0
45.0
58.0
80.0
Michele.forzan@unipd.it
Laboratory of Electroheat of Padova
University of Padova

39. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
80 s
n rotor rpm f Al P_Al Cem heating Time T
- [rpm] [Hz] [kW] [Nm] [s] [s]
1 1500 150.0 40.0 245.0 45.0
2 1200 120.0 36.0 -256.0 45.0
3 1000 100.0 30.1 265.0 45.0
4 800 80.0 22.1 -256.0 45.0
1 800 80.0 20.2 256.0 13.0
2 600 60.0 15.5 -235.0 13.0
3 0 0.0 0.0 0.0 13.0
4 0 0.0 0.0 0.0 13.0
1 0 0.0 0.0 0.0 22.0
2 0 0.0 0.0 0.0 22.0
3 0 0.0 0.0 0.0 22.0
4 0 0.0 0.0 0.0 22.0
45.0
58.0
80.0
Temperature profile required: 500-470-450-430 °C
Michele.forzan@unipd.it
Laboratory of Electroheat of Padova
University of Padova

40. LEP Innovative induction heating with permanent magnets also for taper heating of aluminum billets
Industrial system @240 kW for taper heating
 82%
overall
efficiency
i.e. the ratio between
Thermal Energy
AND
Electric Energy

41. LEP
Thank you for attention,
now Q&A
Michele.forzan@unipd.it
Laboratory of Electroheat of
Padova
University of Padova