Upload
others
View
56
Download
0
Embed Size (px)
Citation preview
Parametric Sensitivity Characteristics of Numerical Simulations on EMF Free Bulging of Circular Sheet Metal
1 2 3 3 4Evandro Paese , Martin Geier , Roberto P. Homrich , Rodrigo Rossi , Pedro A. R. C. Rosa1. Universidade de Caxias do Sul, Campus Universitário da Região dos Vinhedos, Bento Gonçalves, RS 95700-000, Brazil2. Universidade do Vale do Rio dos Sinos, São Leopoldo, RS 93.022-750, Brazil,3. Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 90035-190, Brazil4. Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal Mon-Mo-Po1.02-01 [13]
I. INTRODUCTION An electromagnetic forming (EMF) can be considered essentially like primary and secondary electrical circuits coupled by mutual inductances, composed of an actuator coil and a conductive workpiece. The EMF system geometry and parameters of pulse unit are very important to reach a high, optimum rise time, and adequate distribution of electromagnetic pressure, aming a higher or adequate workpiece displacement. This study focuses on carrying out a parametric analysis by performing numerical simulations of free bulging of circular sheet metal by the EMF system using a spiral actuator coil with a single layer.
II. OBJECTIVES� Demonstrate the influence of EMF system parameters on the electromagnetic pressure, and consequently achieving higher or
adequate workpiece displacement;‚ Use a numerical method to solve the fully coupled electric-magnetic problems applying an in-house script developed in the Matlab.
This aproach can predict the reflected inductances from secondary(workpiece) circuits to a primary one(machine);ƒ Solve the uncoupled mechanical problem using the ABAQUS/Explicit Finite Element Software;„ Show comparative numerically predicted deflections versus experimental measurements to verify the calculation method;… Outline desing principles for EMF systems of sheet metals.
III. BASIC METHODOLOGY OF ANALYSIS The calculations of the electromagnetic problem use a method based on discretization of the actuator spiral coil into concentric (N) elements and the workpiece into multilayered concentric elements. The RLC primary circuit is fully coupled with several secondary RLs circuits and can be modeled using a set of ODEs applying Kirchhoff’s law. The inductances couple the electric-magnetic phenomena.
This system of ODEs is solved by employing the explicit Runge–Kutta method inside Matlab 2015b (ODE45 function). The Biot-Savart’s law is applied to calculate the magnetic field B and B , which are used to calculate the self z r
and mutual inductances, and the electromagnetic force in the axial direction, respectively. Both B , and B use numerical z r
methods to solve the equations. The total electromagnetic force and consequent pressure along of the r-axis is calculated using
The skin effect in the workpiece is an important electrical parameter to be evaluated, aiming the efficiency of the EMF process. In the present numerical method, the skin effect is implicitly considered in the performance of the EMF system, as it uses fully coupled electric-magnetic method, and multilayer discretization.
[ ]( ) [ ]( ) ( ) [ ]( ) ( )[ ]( )( )1
1 1 1 1 1 1mn mn x mn mn x mn mni M R
d
di
t
-
+ + + + + += -
0ca
dvi C
dt=+
DISCRETIZATION OF EMF SYSTEM
SYSTEM PARAMETERS USED FOR EXPERIMENTAL RESULTS
2,5
8
5,5
67,5
110
t = t0
La Raia
C
V0 Primary Circuit (RLC)
RiLi
DiscretizedWorkpiece(L to L )11 mn
Rij
Lij iqij
r
z
i
mj
n
Secundary Circuits(m x n RLs Circuitsof the Discretized
Workpiece)
iaia
iaiaiaia
N - Windingsof the Discretized
Actuator Coil
Parameter
Value
Single-layer copper spiral coil
Number of windings (N)
6
Outer diameter (D0)
67.5mm
Inner diameter (Di)
7.5mm Pitch (P)
5.5mm
Cross section (Aa) 20mm2
Self-inductance (La) 0.9mH (calculated)
EMF machine Capacitance (C)
60mF
Maximum energy (U)
1.5kJ
Workpiece
Material
AA1050
(annealed)
Diameter
110 mm
Thickness
1mm
I. IV. EXPERIMENTAL RESULTS
Radial Point of Workpiece (mm)
Axi
al D
efle
ctio
n of
Wor
kpie
ce (
mm
)
5
10
15
20
25
30
35
40
00 5 10 15 20 25 30 35 40 45 50 55
5.5
13
20.5
700J
50ms
125ms
210ms
0 50 100 150 200 250 300 3500
10
20Sensor at z = 4.5mm
0 50 100 150 200 250 300 350Am
plit
ude
(V)
0
10
20Sensor at z = 12mm
t (ms)0 50 100 150 200 250 300 350
0
10
20Sensor at z = 19.5mm
EXPERIMENTAL APPARATUS
(a)
(b)
Holder
Die
Workpiece
rz
( c )
Springs
Die
Electrical Connections
Actuator CoilHolder
Out
RL
VRIF
OPV302 OP 906
Laser OPV302Photodiode OP906
VI. CONCLUSIONS� There exists an optimum time for the maximum
electromagnetic pressure to happen, producing higher sheet displacements and this optimum time is related to the spiral coil geometry, and mainly with pulse unit parameters;
‚ The greatest electromagnetic pressure is obtained for the highest number of coil windings along with the lowest capacitance, but the best EMF system configuration (geometry/machine) is observed for the capacitance value of 210µF;
ƒ The experimental results for N=6 and 60µF have good correlation with the calculated workpiece movements, demonstrating the effectiveness of this solution methodology;
„ The EMF process is analyzed using a fully coupled electric-magnetic, and uncoupled mechanical solution method, as a result the method can predict the reflected impedances from secondary circuits to a primary one;
… Finally, this methodology can outline optimum geometry and machine parameters aiding in the design of the EMF equipment.
36033030027024021018015012090603034
56
7
0.45
0.4
0.3
0.35
0.25
0.55
0.5
8
Skin Effect
Capacitance (mF)
Number of Windings
Ski
n D
epth
(m
m)
36033030027024021018015012090603034
56
7
0
20
40
60
80
100
8
Capacitance (mF)
Number of Windings
2E
lect
rom
agne
tic
Pre
ssur
e (M
N/m
)
Maximum Electromagnetic Pressure
700Jr
z
N=3
Radial Point of Workpiece (mm)
Axi
al D
efle
ctio
n of
Wor
kpie
ce (
mm
)
5
10
15
20
25
30
35
40
00 5 10 15 20 25 30 35 40 45 50 55
N=4N=5N=6N=7
N=8
N=8(210mF)
60mF
2E
lect
rom
agne
tic
Pre
ssure
(M
N/m
)
Distribution of Electromagnetic Pressure
5 10.5 16 21.5 27 32.5 38 43.5 49 54.50
10
20
30
40
50
60
70
80
N=3N=4N=5N=6N=7N=8
60mF
N=8(210mF)
r (mm)
V. PARAMETRIC RESULTS
Calculated Self-Inductance as Function of the Number of Coil Windings Number of Windings
3 4 5 6 7 8
0.30.6
0.91.2
1.5
Indu
ctan
ce (m
H)
360330
270210
15090
3034
56
7
65
60
50
45
55
408
Pea
k of
Dis
char
ge C
urre
nt (
kA)
Number of Windings Capacitance (mF)
360330
270210
15090
3034
56
7
0
5
10
15
20
8
Ris
e T
ime
of t
he D
isch
arge
Cur
rent
(m
s)
Capacitance (mF)Number of Windings
Maximum Discharge Currentas Function of the Number of
Coil Windings and Capacitance
The Peak of Electromagnetic PressureHappens at the Same Moment of the
Maximum Discharge Current
-1/2d=(pf �km)f
( )2 21
zj
zj
j j
fP
r rp +
=-
1
m
zj rij ij ijif B i lq=
=å
f ��is based onf
Fourier analysis
Martin Geier would like to acknowledge the financial support of the National Council for Scientific and Technological Development CNPq - Brazil, process n. 430725/2016-7