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Design Robustness Demonstration by
DOE and Montecarlo Methods.
Application to automotive Fuses
MTA - Ricardo González Luna
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This work was originally Published in the Meet Minitab 2015 (Milan)
http://www.gmsl.it/materiale-e-presentazioni-meet-minitab-2015
/
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MTA USA
MTA BRASIL
MTA MEXICO MTA INDIA MTA CHINA
MTA POLAND
MTA SLOVAKIA
HEADQUARTERS CODOGNOELECTRONICS ROLO
FRONT OFFICE FRANCEFRONT OFFICE GERMANY
FRONT OFFICE TURKEY
Production
R & D
SalesMTA is an Italian automotive
company with more than 1100 employees worldwide
(2015)RGL 3
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MTA Electromechanic and Electronic Components
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AGCO Group ARGO Group CNH GEHL JCB John Deere SDF Group
Cargotec Elgin Sweeper Freightliner Iveco Navistar Smith Electric
Aston Martin BMW Ferrari-Maserati FCA Ford GM Lamborghini Lotus Mahindra PSA Peugeot Citröen Renault – Nissan TATA Tesla Volvo Car Corporation Volkswagen
Aprilia BMW Motorrad Brammo Cagiva Ducati Derby Harley Davidson Husqvarna MBK Moto Guzzi MV Agusta Piaggio Yamaha
MTA Tier 1 Customers
MTA PRODUCES AUTOMOTIVE FUSES SINCE
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FUNCIONALITY OF AN AUTOMOTIVE FUSE
1. Is the weakest link in the chain, to be able to protect the entire electrical system and specifically the wire
2. There are two kind of anomalies1. Short circuit2. Overload
3. Must also reliably supply the electrical current, flowing through himself, therefore causing heating and as a consequence, materials degradation.
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FUNCIONALITY OF AN AUTOMOTIVE FUSE
Conditions of functionality:
1. If there is an anomaly, the fuse must act before the wire can be damaged, but….
2. The fuse never must blown if there is no anomaly and…..
3. Should heat as less as possible, under normal operating conditions
Statistical guarantee for functional characteristics is :• Demonstrate CpK>1,67,
OR• Test 100%.
But fuses test is destructive!!!
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FUNCIONALITY OF AN AUTOMOTIVE FUSE
Joule EffectPIN=I2xR = I x Voltage drop
Conv
ectio
n
i
Rad
iatio
n
i
Conduction
Conduction
The physics of the fuse is the interaction among the thermal effects: Joule Heating, Heat dissipation, phase changes and resitivity variation with temperature.
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WHY THIS WORK?
Customers wants the probability to
find a defective part well below 5ppm, and that Defect
Free does not rely just on End-of-Line
test
The Direction of the Company requires
that product quality is
guaranteed and does not incurs in
high costs of control and scrap
at End-of-Line test.
Therefore require a Capability Index
greater than 1,67!!
FAIL!!
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SINTHESYS: Statistical Content of the Robustness Demonstration Method
Determine Transfer
Functions
DOE
Identify parameter distribution
Data Analysis
Evaluate design robustness
Capabi-lity
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TRANSFER FUNCTION DETERMINATION
We want to understand the relationship between the values of the physical components that built the fuse
Width
BLOW TIMEFiThickn.
Length
Melting °CResistivity HEAT
Then Predict the effect of the natural variability of the physical characteristics
And his behavior:
The Transfer
Functions «Fi»
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Transfer Function Determination
Use Engineering functions and solve mathematically
Design of Experiments (DOE)
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OR
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Select appropriate combination of parameters and find the functional results for those combinations. The results will serve to define mathematical functions through regression methods. Results can be obtained:
Experimentally By Numerical Methods
DOE obtains the effect of each single parameter, but also the effect of the combination of two or more of this parameters («interactions»)
Design Of Experiments (DOE):
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X-Y Interaction means that effect of X is modified by the presence of YDOE
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X-Y Interactions example
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Define the variables that influences the system and their range of variation according to the goal of the DOE:◦ Identification of the influent parameters and interactions◦ Design optimization by selection of parameter’s values◦ Efect of the natural variation of the parameters
This requires a good technical knowledge about the system itself and must be carried out by system experts helped by DOE practitioners.
It is important to reduce the number of parameters to reduce time and cost. Also interesting from a practical view to choose those parameters that can be easily varied in an experimental method.
DOE
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For example in our case the effect of the variation of Width and Thickness can be considered two similar ways to vary the of cross-section, therefore we choose to vary only the width, than can be more easily done using CAM samples made with numerically controlled instruments.
DOE PARAMETERS CHOICE
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W
Th
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We can also exclude interactions between the geometrical characteristics and the quantity of low melting temperature material add to the fuse (tin in this case).
To have a lower experimental uncertainty in the practical samples preparation method, we decided to investigate this effect with a regression to be add to the DOE.
The effect is within the experimental error, then it is reppresented as a Uniform Noise.
DOE PARAMETERS CHOICE
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For example in our case the effect of the variation of Width and Thickness can be considered two ways to vary the of cross-Section, therefore we choose to vary only the width, than can be more easily done using CAM samples made with numerically controlled instruments.
Transfer Function Determination
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Inserting the experimental results in the Minitab ® Software, we obtain easily which parameters and interactions have statistical significance in the results, and therefore must be used in the regression model.
Transfer Function Determination
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Pareto Chart of Standardized Effects: For Blow Time, Width and Resistivity are significative with more than 95% Confidence. Length is also significative but less evident because experimental error mask somewhere it’s smaller effect
These are the parameters and interactions that influence measurable Resistance changes for the expected variation in production.
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Residuals are the measured variation NOT explained by the significant parameters
The conclusions given by the DOE model are acceptable if the residuals are normally distributed, and have equal variance across all the regression range, and are independent from the experimental order◦ Normally Distributed◦ Do not show a trend versus the fitted value◦ Do not show a trend versus the order of measure
Transfer Function Determination
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5002500-250-500
9990
50
10
1
Residual
Perc
ent
1600140012001000800
500
2500
-250
-500
Fitted Value
Resid
ual
6004002000-200-400
10,0
7,5
5,0
2,5
0,0
Residual
Freq
uenc
y
30282624222018161412108642
500250
0-250-500
Observation Order
Resid
ual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for t-150% [sec]
You can verify these hypothesis with the Residual Plots.
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Transfer Function Determination
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Minitab model supply also the coefficients for the transfer functions in form of Linear Combination (LC), then:
Blow time = LC [WxTh; L;Resistivity ; Normal_Noise]
Resistance = LC[WxTh;Resistivity; Uniform_Noise]
1,2851,215
1400
1300
1200
1100
1000
900
80015,31014,660 1,016740,97516
W
Mea
n of
t-15
0% [s
ec]
L resistività
Effetti principali tempo fusione 150%Fitted Means
Graphical reppresentation for parameter’s effect: for example increasing width implies a strong increase in Blow time.
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Identify the practical distribution for all the construction parameters
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Identify what are the distribution type closest to the historical values for each construction parameter
Minitab© and other software have applications to find the most suitable distributions
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How is the resulting distribution for the functional values??
MONTE CARLO METHOD
Extract Randomly the values of each parameters and calculate the operating characteristics with the Transfer Functions
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MONTE CARLO METHOD
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𝑌 𝑗=F [ 𝑋 𝑖 ]
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36003000250020001500100050090
Pp 4,70PPL 2,77PPU 6,62Ppk 2,77Cpm *
Cp 5,58CPL 3,29CPU 7,86Cpk 3,29
Potential (Within) Capability
Overall Capability
PPM < LSL 0,00 0,00 0,00PPM > USL 0,00 0,00 0,00PPM Total 0,00 0,00 0,00
Observed Expected Overall ExpectedDifetti
LSL USL
OverallWithin
Distribuzione del Tempo di Fusione e relativa Capability
DESIGN ROBUSTNESS
A simple Robustness analysis allow us to predict the number of defective parts, if the input parameters respect the distribution used in the simulation
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By repeating the process hundreds thousands of times we obtain the distribution of the operating characteristics.
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CONCLUSIONS
We want to demonstrate that if some geometrical and material parameters are under control, the whole production of an automotive fuse will respect the functional specifications
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CONCLUSIONS1° Use DOE to obtain the mathematical relationship between construction parameters and operating results.2° Determine parameters distribution according to historical values3° Extract random values from the distributions and calculate the operating value that would be obtained for such fuse. Repeat the process till a suitable distribution is obtained (Monte Carlo simulation).4° Analyce this distribution Robustness against the operating limits and predict the number of defects
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https://it.linkedin.com/in/ricardogonzalezluna
https://ricardogonzalezluna.wordpress.com
Ricardo Gonzalez Luna
Thank You!!