Case Studies
Uncertainty Analysis of Longitudinal Vehicle Dynamics with OptiY® and MapleSim®
For a simulation of vehicle dynamic performance, the longitudinal vehicle dynamics and the tire/wheel dynamics with a controller must be both considered. These can be captured by a linear two-wheel version model for acceleration analysis. The longitudinal vehicle model is created in MapleSim®. It simulates the acceleration performance up to a motorway with an angle. Design specifications for a required performance are given by the parameter space, design, process and environment uncertainties as well as design constraints. The dynamical simulation in MapleSim shows the nominal behavior of the longitudinal vehicle dynamics fulfilled all given design specifications. Because of the design, process and environment uncertainties, a probabilistic simulation in OptiY based on the vehicle model in MapleSim must be performed considering these uncertainties as stochastic distributions. It reveals however a failure probability of 5.21% related to the design specifications. The global variance-based sensitivity study shows the most important model parameters and its interactions in order to reduce the design complexity.
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Probabilistic Fatigue Life Prediction of Microelectronic Components on the Example of a Chip Resistor
Fatigue
life prediction is a difficult task related to the accurate and
applicable results. First of all, many theoretical parameters for
the life time model have to be validated by measurement data.
Physical experiments for one prototype should be carried out to get
realistic fatigue life data. Based on these data, relative fatigue
life prediction can be made for other design variants. The second
problem is that the fatigue life especially for microelectronic
components depends on many different environment, manufacturing and
design parameters, which are very randomly and should be considered
all by the theoretical lifetime model. The predicted results by
classical nominal simulation are therefore very poor to the reality.
Probabilistic fatigue prediction using meta-modeling technology is
the best methodology to solve these problems. The uncertainties of
design, manufacturing and environment parameters are considered as
stochastic distributions for prediction modeling. Thus, an accurate fatigue life prediction can be made by theoretical models. As result, we have
got a stochastic distribution of the fatigue life with min and max value of the lifetime.
In the case of a chip resistor, the probabilistic analysis can predict the realistic fatigue life characterized by a distribution.
To maximize the life time, some design parameters are changed using
numerical optimization. Although the achieved nominal fatigue life is greater than than initial design, the probabilistic
fatigue life prediction reveals a very bad minimal value of the life time for this design,
thus worse than the initial design.
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Design Optimization of a Electromagnetic Valve Actuator
As a world market leader for gas springs and
hydraulic vibration dampers, Stabilus GmbH is currently developing gas springs with an
electromagnetically operated valve for automotive applications. Such a valve actuator is a
complex mechatronic system. During system design the
several subsystems are modeled separately first and
coupled to each other in the next step. This makes complexity and the
numerous interactions between the subsystems manageable. Steady state magnetic fields
and force-stroke-current characteristics are determined by the finite element
software FEMM. The dynamic behavior is modeled in SimulationX. Furthermore, the finite
element program COMSOL Multiphysics calculates the transient temperature distribution. This
approach is suitable for an in-depth design of the subsystems and their interactions. The
multidisciplinary analysis and optimization tool OptiY is used to integrate and automate the
several simulation steps. Thus the fundamentals for an automated system design are
accomplished. Defining system parameters, given boundary conditions and objective
functions in
terms of constraints and criteria, the characteristics of the actuator are improved
systematically using numerical optimization regarding magnetic forces, power
losses and and dynamic behavior.
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Numerical Optimization of the Distribution of Damping Layers
In this work, a method
for the numerical optimization of the distribution of damping layers
in a shells structure is presented. The structure intensity of body
acoustic noise, that describes the flow of energy from a source to a sink, can be used to determine how much
energy being dissipated in a control volume. Also the input power for a control volume
is calculated. Based on the results of the previous tests, the FE model
is created. This is the floor assembly of a car, on which floor
metal sheet six damping rubbers are applied. The thickness of these
sheets is the design optimization variable. As objective function, the
reciprocal value of the relation from loss to input power is minimized. Both performances are
integrated over the frequency range before they are used to each other in the ratio. This work has shown that the structure intensity can be used to determine a optimal
damping distribution. The structural behavior should be investigated in a
next step, but closer to get more detailed information, what happens
in transition zone between bottom sheet and cushioning surfaces. A more accurate
investigation of cutting forces and the speed in this field can be so the thinner cushioning covering significantly more energy dissipated than thicker coating. Also the observation of divergence of structure intensity can
provide further result , because it indicates how the amount and the direction of the structure intensity change. The consideration of the structure intensity in the damping rubbers even
is also very revealing.
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Robust Design of a Hydraulic Cylinder Drive
Controlled
hydraulic cylinder drive works already stable. It performs a
specified displacement curve for a mass using hydraulic drive
system. For a good quality of the drive system, high design
specifications are required as damped oscillation of the piston
velocity and valve pressure. They are normally satisfied by a
nominal design by classical dynamical system. However, process and
environment uncertainties cause frequently a bad satisfying of the
design specifications leading to a bad product quality. Although a
nominal design shows reliable working of the drive, probabilistic
simulation reveals however violations of design
specifications caused by the parameter und process uncertainties. The robust design optimization can reduce the failure
probability from 82.1% by nominal design to 59.4% by robust design. This is the best design for the manufacturing.
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Robust Design of a Cohn Filter Circuit
The design specification of
a Cohn filter circuit is the frequency range between 15-17 MHz for
the output signal.
First of all, a nominal optimization process is carried out to get the optimal design parameters satisfying the specification.
Because of manufacturing inaccuracy, process uncertainty and environment influences,
all design parameters have to be considered as stochastic distributions. Although the nominal simulation of the circuit
fulfill all design constraints, the probabilistic simulation with the uncertainty design parameters show its violation.
The failure probability of the nominal design is fixed about 76% which is inacceptable for the manufacturing.
With the variance based sensitivity analysis, the most non-important design parameters are found to reduce the design complexity.
Thus, only 6 important design parameters are required for further research. To reduce the failure probability,
we perform a robust design optimization considering these 6 stochastic design parameter. As result, a failure probability about 53% is achieved
by other nominal values of the design parameters with the same tolerances for the design specification.
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Robust Design of MEMS on the Example of a Thermal Actuator
The
thermal actuator works on the basis of a differential thermal
expansion between the thin arm and blade. The nominal FE-analysis is
a coupled-field multi-physics analysis that accounts for the
interaction between thermal, electric, and structural fields. A
potential difference applied across the electrical connection pads
induces a current to flow through the arm and blade. The current
flow and the resistivity of the silicon produce Joule heating in the
arm blade. The Joule heating causes the arm and the blade to heat
up. The operating temperature of 750 °C is generated. It produce
thermal strain and thermally induced deflections. The resistance in
the thin arm is greater than the resistance in the blade. Therefore,
the thin arm heats up more than the blade, which causes the actuator
to bend towards the blade. The maximum deformation occurs at the
actuator tip. The amount of tip deflection is a direct function of
the applied potential difference. Therefore, the amount of tip
deflection can be accurately calibrated as a function of applied
voltage. For the functional requirement, this deformation is
specified in the range of [0.2,0.24] μm. The equivalent stress
should be minimal as possible and the first resonance frequency
maximal as possible. At the first design step, a nominal design
optimization is performed. Because of geometry tolerances and
uncertainty material and process parameters, the nominal design
yields a failure probability of 6,69% for the manufacturing. At the
last design step, a robust design optimization carried out to obtain
the robust design with zero failure probability. The sensitivity
study identifies the most important design and process parameters.
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Six Sigma Design of a Solenoid Actuator
The
solenoid actuator consists of a armature, coil and back-iron. The armature is the moving component of the
actuator. The back-iron is the stationary iron component of the
actuator that completes the magnetic circuit around the coil. The
stranded, wound coil supplies the
predefined current. The air-gap is
the thin rectangular region of air between the armature and the pole
faces of the back-iron. For the functional requirement, the force on
the armature is specified in the range [-15, -10] N. The coil flux
linkage should be minimal as possible. As the result of the nominal
design optimization, the nominal design yields a failure probability
of 78,93% for the manufacturing caused by the geometry tolerances
and uncertainty process and material parameters. Until the robust
design yields a minimal failure probability of 5,48% obtained by a
robust design optimization with the Taguchi quality loss function.
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Thick Film Accelerometers in LTCC Technology
State of the art in mechanical elements of MEMS in LTCC-technology are diaphragms and beams, e.g. for force
and pressure sensors. These elements perform small strains and small deformations under loads. However a lot
of sensor and actuator applications require movable elements that allow higher deformations whereas the local
strains are still low. Such applications are e.g. springs, accelerometers, actuators, positioners, and valves. For an
accelerometer we developed an approach for the fabrication of leaf springs integrated into the LTCC technology.
The working principle of the accelerometer is based on a seismic mass disposed on two parallel leaf springs
which carry piezoresistors connected to form a measuring bridge. In a first design optimization step, we used a
FEA model for finding an optimized design conforming to our sensitivity requirements, inclusive of resonance
frequency. In a second step, we performed a tolerance analysis that calculates the probability distributions of
functional variables from the probability distributions of the design parameters. This enables the probability of a
system failure to be deduced. In a final design step, a design of the ceramic thick film accelerometer was
calculated that minimizes the system failure probability. As a result we obtained a design optimized with concern
to a set of functional requirements and design tolerances. The results of the computations using the FEA
models were compared to results of measurement data acquired from prototypes of the accelerometer.
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Robust Design of a Butterfly Valve
The
butterfly valve controls the water fluid and sand particles. For the
outlet flow rate, the adjustable angel and the surface radius are
important for the design process. Satisfying all design
specifications, the tolerances and uncertainty process or
environment parameters are included in design stage. Robust design
is a powerful tool for design of reliable and quality valves. The
failure probability can be reduced from 56,12% to 0.36% for the
manufacturing.
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Robust Design Optimization of Static Mixer
The
nominal simulation of the static mixer is carried out by different
specialized CAD/CAE-software CATIA, ICEM and CFX. The advantages are
fast modeling process and more accurate and detailed system
component behavior. The process workflow is build once time in OptiY.
For the meta-modeling, the adaptive Gaussian process is applied
which needs only 88 number of original model calculations for 8
design parameters and 1 design goal. The global sensitivity study
indentifies most important parameters and its interactions. The
robust design optimization using the Taguchi quality loss function
for the outlet temperature leads to a robust design with a minimal
variance of its probability distribution.
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Design Space Visualization of Waveguide Hybrid Junction
The structure
of the waveguide hybrid junction contains a coupling section with a small metallic disk and an external cavity resonator connected to the waveguides by a coupling hole.
The definition of S-parameter symmetries enables the reduction of performed solver runs.
The nominal FE-simulation is carried out by the CST Microwave
Studio. The design goals are the transmission and the reflection at
the operating point of 8 GHz. Using the adaptive Gaussian process,
the design space can archived and visualized in 2D- and 3D-graphics.
The global nonlinear and quantitative sensitivity analysis explains
the cause-effect-chain for the design goals and it identifies most
important parameters and its interactions. The robust design
optimization with the Taguchi quality loss function leads to the
robust design point with minimal stochastic variance of the
transmission. Read full article.
Sensitivity Study and Design Optimization of a Car Suspension
The performance index is the
first rotational yaw-pitch-roll of
the tire. The performance and comfort
of the car is characterized by
minimal range between min. and
max. yaw-pitch-roll. There are 27 design
parameters of joint coordinates. The nominal simulation is carried out by the
software RecurDyn. First of all, a global sensitivity using
Latin-Hypercube-sampling is performed to identify the most important
design parameters and to reduce the complexity. Only 10 important
design parameters are used for the design optimization process to
improve the performance and the comfort of the car suspension.
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Sensitivity Study, Design Optimization and Probabilistic Analysis of a Rotor Brake System
The
brake system consists of a moveable pad and a revolving rotor, which
is welded with the blade. The pressure of 4000 MPa is put on the pad
to brake the revolution of the rotor. For the braking system, the
contact between the rotor and the pad is important be simulated to
gain the maximal braking force. It is characterized by the maximal
contact pressure. On the first step, the global sensitivity study is
carried out based on the nonlinear meta model. On the next step, the
nominal design optimization also based on the meta model yields the
best nominal design point, which contains the maximal contact
pressure between the pad and the rotor. Because of uncertainty
process and environment parameters as well as tolerances, the
unavoidable variability of the design goals is obtained by a
probabilistic analysis. A design sensitivity shows the
cause-effect-chain for this variability of the design goals.
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Failure and Lifetime Assessment of Welded Stainless Steel Structures
For
the failure and lifetime assessment of welded stainless steel
structures, it is important to identify the most influenced design
parameters to explain the cause-effect-chain. The nominal simulation
is carried out by ANSYS. some model parameters are validated by
measurement data. The global variance-based sensitivity study is
performed in OptiY. Some important recommendations are derive for
the design process to minimize the failure and to improve the
lifetime of welded steel structures.
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Design Optimization of a Braille Printer
For an exemplary electromagnetic actuator used to drive a Braille printer, a design optimization was performed. The optimization involves stochastic variables and comprises nominal optimization, robustness analysis and robust design optimization. A heterogeneous model simulates the static and the dynamic behavior of the actuator and its non-linear load. It consists of a network model in SimulationX and a static magnetic FEA model in COMSOL Multiphysics. The network model utilizes look-up tables of the magnetic force and the flux linkage computed by the FEA model. The optimization tool OptiY controls the design variables of the models during the optimization and the stochastic analysis. In order to reduce the computational effort we used response surfaces instead of the system model in all stochastic analysis and optimization steps. This allows Monte-Carlo simulations to be applied. The optimization itself uses gradient-based algorithms.
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full article.
