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. Read full article.
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. Read full article.
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. Read full article
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. Read full article.
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. Read full article.
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. Read full article.
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. Read full article.
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. Read full article.
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. Read full article.
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. Read full article.
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. Read full article.
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. Read full article.
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. Read full article.
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. Read full article.
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. Read full article.