Post on 14-Dec-2015
Lightning Effects and Structure Analysis Tool (LESAT)
Steve Peters410-273-7722steve.peters@survice.comwww.survice.com
What Is LESAT?
• LESAT - Lightning Effects Structure Analysis Tool– Computational methodology implemented in MATLAB
to analytically predict actual transient current levels and voltages on aircraft wiring and structural elements.
– Assists designers in protecting aircraft against the indirect effects of lightning strikes.
– Implements the methodology used successfully for MH-47 lightning analysis.
Motivation
• Lightning is a severe threat (up to 200 kA peak).• More reliance on electronic systems.• Technology evolution from metallic aircraft
structure to composite structure.• High cost aircraft-level testing and hazardous
aspect of experiments in laboratories.
Objectives
• Input system geometry in a CAD format.• Circuit analysis approach - apply Kirchhoff’s
laws to obtain linear equations that can be solved in matrix form.
• Predict induced currents and voltage drops on wiring and structural elements.
Lightning Indirect Effects Waveform• MIL-STD-464C Severe Stroke in both Time and Frequency Domains
1
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Why Kirchhoff Rather Than Maxwell?• Since the source frequency is very low, we have a
Quasi-static (near steady state) situation.• Dimensions of the conducting network are much
smaller than the wavelength.• Tool gives good results for aircraft dimensions up to ¼
the wavelength of the maximum frequency.
mMHz
smx
f
c
fc
3001
/103 8
Drawing not to scale
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1
Code Analysis MethodologyRead Geometry
& Electrical Characteristics
From Mesh Files
Break UpStructure Into
Linear Segments
Compute System of
LinearEquations
CalculateFrequency DomainImpulse
Response forEach Branch
Calculate Time-DomainSolutions (Induced
Currents and Voltages)
Plot Results
ComputeResistances
CalculateSelf & MutualInductances
ComputeImpedance
Matrix
Calculate Laplace
Responses
Input Geometry
• Input system CAD geometry as a series of mesh files used to represent skins, pylons, and other routed cabling and electrical equipment inside the aircraft.
Example Mesh Geometry Input for a Structure
BULK RESISTIVITY Ω-m
LENGTH (L), WIDTH (W), THICKNESS (H)
Fundamental Resistance Data
SKIN RESISTIVITY Ω/□
LENGTH
RADIUS
Line/CableResistivity Ω/m
1. Lines/Cable Resistivity is measured in Ohms per meter ρ – to get Ohms use: Rc = ρL
2. Skin/Mesh Resistivity is measured in Ohms per square ρ – to get Ohms use: Rskin = ρL/W
3. Bulk Resistivity is measured in Ohm-meters ρ – to get Ohms use: Rbulk = ρL/(WH)
4. Equivalent resistance for a branch use:
R = Rbulk X Rskin/(Rbulk + Rskin)
Model• Circuit Approach: The airframe is represented by an
equivalent R,L circuit network.
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R2
R3
L2
L3
L4
L1 R1
R4
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connected b
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Kirchhoff’s Laws are enforced:
Piece of the meshhas 5 nodes and 4 branches.
x
B
y
I1 I2
A C
DM12
z 3D representation
Each branch is a resistive, mutually inductive circuit element.
Code calculates mutual inductances
Five-Branch Four-Node Circuit Example
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System of linear equations
Matrix Notation
Topology
TopologyT
0
Z I
=
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0
I s
Input
Output
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0topology
topology Ax = b
Physics(squarematrix)
Number ofBranches
Number ofNodes
Number ofBranches
Number ofNodes
A x b
bxA
1
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0
0
0
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0
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00000001
000
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100
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Z Z Z Z Z
Z Z Z Z Z
Z Z Z Z Z
Z Z Z Z Z
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Is
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Is
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0
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1100
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1001
4
3
2
1
5
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ZZZZZ
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E
E
E
I
I
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Reduction To Transformed Currents
System reduces to:
branches – (nodes – 1)
transformed currents.
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34
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4544
Z
Z
Z Z
Z Z
5
4
I
I
Solution for Multiple Frequencies
Solution for a specific branchcurrent at each frequency.
Branch Current Laplace Transform – represents the frequency-domain Transfer function between the Injected lightning current and the current of the “victim” component.
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currentsbranch of # 1 n
241 k kkf 2
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nm
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s
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s
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m
nm
nm
n sc
sbs
1a )(S
o
)(SI Jn
sssn
Lightning Time Dependence
Lightning Laplace Transform
Frequency Domain Transfer Function
Branch Current Laplace Response
1
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sc
sb
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Isss
Time-Domain Solution
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b
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Note the addition of the purely resistive part ao
Branch Current Time Dependence
Cable Inside A Conducting Box• Rectangular
volume of material with dimensions (13.6m x 2.5m x 2.5m).
• Skin Thickness: 1.6mm
• Bulk Resistivity: 2.65x10-8 Ohm-meters
• Skin Parallel Mesh Resistivity: 1.35x10-4 Ohms/sq
• Skin Perpendicular Mesh Resistivity: 1.35x10-4 Ohms/sq
• Cable Resistivity: 1.728x10-15 Ohms/meter
• Cable Radius: 2.54cm
Results for Aluminum Conducting Box
• Blue curve represents cable current and voltage drop on cable for blue bolt strike location.• Magenta curve represents cable current and voltage drop on cable for magenta bolt strike location.
DrivingWaveform
Conclusions and Future Work
• Validation: compare calculated results to experimental data.
• Apply methodology to:– Ground systems– Buildings– Electromagnetic Pulse (EMP) excitation
• Relate predicted Lightning Effects to structural damage.