Bernhard Bettig

Derivation of a standard set of geometric constraints for parametric modeling and data exchange

This paper describes the derivation of a consistent and comprehensive set of geometrical constraints for shape definition in CAD. Such a set is needed to enable compatibility in parametric data exchange and to promote both standard capabilities and predictable solutions from constraint solving software kernels. The paper looks at the mathematical basis for constraints present in the literature and elaborates about all types of constraints that can be described by the same mathematical basis. Exhaustive combinations of distance and angle constraints, on one point or all points of curves and surfaces, as well as transformations and mappings that are required in mechanical design are included in the proposed taxonomy and representation. Consistency is promoted by distinguishing necessary constraint types from redundant constraint types. Comprehensiveness is promoted by including all constraint types from the literature that are within the scope and considering combinatorial variations of them.

Topology Optimization of Smart Structures Using a Homogenization Approach

Engineers are often required to design mechanical structures to meet specific loading conditions. Topology optimization automates the process of finding an optimal structural design, allowing for size, shape, and topology variations. For a given set of boundary conditions and design specifications, an optimal structure is computed, based on a formulated cost function. In this paper, the optimization considers not only the distribution of conventional material, but also simultaneously the distribution of active piezoelectric material within the domain. In the formulation of the topology optimization problem, a microstructure consisting of smart as well as conventional material is used. Instances of the microstructure occur in a rectangular grid and cover the design domain. Since the microstructure is defined parametrically, the density of each material can be controlled individually at each point. This enables us to formulate the problem of finding an optimal material distribution as a parameter optimization problem. A homogenization approach is used to find and use effective material properties for the limiting case of an infinitely small microstructure. Several numerical examples are provided to demonstrate the application of the method to find structures that maximize the deflection at a point when the piezoelectric material is activated.

Towards Sustainable "Product and Material Flow" Cycles: Identifying Barriers to Achieving Product Multi-Use and Zero Waste

Material and energy resource consumption is on the rise in both the industrialized and developing world (e.g., countries like India and China). In order to sustain this growth and provide resources for future generations, there is a need to design products that are easy to recover and recondition, thus enabling multiple use cycles. Processes are needed that can achieve this multiuse while producing zero (or very near zero) waste. There exist a number of barriers and challenges to achieving this vision of multi-use with zero waste; one such challenge is the development of a product recovery infrastructure that will minimize short-term impacts due to existing products and will be robust enough to recover products of the future. This paper identifies the barriers to developing such a recovery and reuse infrastructure. The aim is to achieve product multi-use and zero waste.

Optimal sensor design and control of piezoelectric laminate beams

In this paper, a new smart structure optimal design strategy is introduced and applied to robust vibration control of a piezoelectric laminate beam. The optimization of the smart material layout and the control law are performed simultaneously to extract maximum performance from the system. A homogenization approach is used to allocate sensor material, while a linear quadratic regulator (LQR) is used for the control law. The method is applied to a pinned-pinned beam where two cost functions are considered, both focusing on increasing the stability margin of the closed-loop system. The first is based on the observability gramian and the second on the control weighting parameter of the LQR cost function. Both cost functions yield optimal sensor distributions that improve the closed-loop performance as compared with uniform density distributions. In addition to investigating the effect of the cost function on the design, two different sensor design domains are considered. The first consists of five isolated patches of sensor material (a discrete sensor domain), while the second assumes the five patches cover the entire beam, but are electrically isolated (segmented distributed sensor domain). In all cases considered, the cost function based on the LQR control weighting parameter generates smoother sensor distributions that are always positively polled, an important fabrication consideration. The segmented distributed sensor approach yields the overall best performance.

Solution Selectors: A User-Oriented Answer to the Multiple Solution Problem in Constraint Solving

The development of solid modeling to represent the geometry of designed parts and the development of parametric modeling to control the size and shape have had significant impacts on the efficiency and speed of the design process. Designers now rely on parametric solid modeling, but often are frustrated by a problem that unpredictably causes their sketches to become twisted, contorted, or take an unexpected shape. Mathematically, this problem, known as the multiple solution problem occurs because the dimensions and geometric constraints yield a set of non-linear equations with many roots. In practice, this situation occurs because the dimensioning and geometric constraint information given in a CAD model is not sufficient to unambiguously and flexibly specify which configuration the user desires. This paper first establishes that only explicit, independent solution selection declarations can provide a flexible mechanism that is sufficient for all situations. The paper then describes the systematic derivation of a set of solution selector types by considering the occurrences of multiple solutions in combinations of mutually constrained geometric entities. The result is a set of eleven basic solution selector types and two derived types that incorporate topological information. In particular, one derived type concave/convex is user-oriented and may prove to be particularly useful.

Simple models for piston-type micromirror behavior

Parallel-plate electrostatic actuators are a simple way to achieve piston motion for large numbers of mirrors in spatial light modulators. However, selection of design parameters is made difficult by their nonlinear behavior. This paper presents simple models for predicting static and dynamic behaviors of fixed–fixed parallel-plate electrostatic actuators. Static deflection equations are derived based on minimization of the total potential energy of the beam. Beam bending, residual stress, beam stretch and applied electrostatic force are included in the potential energy formulation. Computation time is reduced by working with assumed mode shapes. The problem of predicting midpoint beam deflection has been reduced to finding the roots of a third-order equation. Model results are compared to finite-element analysis results. In the dynamic analysis, Lagranges method is used to derive the nonlinear equation of motion. An equation for predicting natural frequency, assuming small midpoint deflections about a dc setpoint, is presented. In addition, the effect of gas pressure on the damped natural frequency of a rigid actuator is analyzed. Experimental measurements of static deflection and frequency response are compared to model predictions. The actual micromirrors exhibit less strain stiffening than the model predicts.

Modeling the Lateral Vibration of Hydraulic Turbine-Generator Rotors

An extensive hydro-generator rotordynamic model is presented along with a technique for determining imbalances and shaft misalignments using the model and mechanical run vibration measurements. The hydro-generator model combines a finite element rotor model with a finite difference guide bearing model, generator magnetic forces and turbine hydraulic forces to calculate natural frequencies, stability and steadystate response. The complete model allows a great number of inputs including imbalances, rotation speed, guide bearing misalignments, coupling misalignments, bearing clearances, bearing temperatures, generator stator and rotor center misalignments, generator average air gap, generator power output and turbine blade tip clearance, all of which are described in this paper. Finally, the numerical results are compared with vibration data from the mechanical run and load test of an actual hydro generator unit.

Predictive Maintenance Using the Rotordynamic Model of a Hydraulic Turbine-Generator Rotor

A use of rotordynamic models in predictive maintenance is described in which variables characterizing the state of a deterioration mechanism are determined from online measurements. These variables are trended to determine the rate of deterioration and to perform a simulation to predict either the machine life or the maintenance period. Some useful terms for using models in predictive maintenance are defined and the prediction procedure is described. The procedure is demonstrated with a simple two degree-of-freedom example and the numerical model of an actual hydraulic turbine-generator rotor. Some benefits and problems associated with the implementation of the procedure are then discussed. It is considered that this procedure brings the possibility of a better understanding of deterioration processes and a resulting better life prediction.

The representation of module interfaces

Modular design issues are receiving increased attention from companies interested in reducing the costs from carrying large numbers of components while, at the same time, increasing product quality and providing customers with greater product variety. Existing research has focused mainly on optimising product platforms and product offerings, with little attention being given to the interfaces between modules. This research presents an investigation into how module interfaces are best represented in a Computer-Aided Design/Product Data Management (CAD/PDM) environment. The representation decisions are identified and the advantages and limitations for each option are presented. Representation decisions revolve around issues such as the use of higher abstraction models, the use of ports, and referencing interface components in interface definitions. We conclude that higher abstraction models are necessary, ports should be represented explicitly and interface hardware should not be included directly with the interfaces. The research considers a large number of components from representative products offered by a home appliance manufacturer.

Limitations of Parametric Operators for Supporting Systematic Design

Computers are being used extensively in the manufacturing industry to design and analyze products. In spite of the power of existing CAD systems and potential power of current Design Automation systems, we believe that they possess an inherent limitation that keeps them from aligning with and fully supporting the design process. Specifically, all of these systems are based on using parametric operators to generate valid designs. This paper examines the limitations of parametric operators for CAD and design automation and shows how “variational” methods could be used. An approach using variational methods is compared with traditional CAD and design automation methods. The paper also proposes a language of objects and relationships to represent design requirements. This work is a step towards realizing an interactive design synthesis system that can represent and satisfy design requirements.Copyright