Behrooz Fallahi

A unified approach to form error evaluation

Abstract Evaluation of form error is a critical aspect of many manufacturing processes. Machines such as the coordinate measuring machine (CMM) often employ the technique of the least squares form fitting algorithms. While based on sound mathematical principles, it is well known that the method of least squares often overestimates the tolerance zone, causing good parts to be rejected. Many methods have been proposed in efforts to improve upon results obtained via least squares, including those, which result in the minimum zone tolerance value. However, these methods are mathematically complex and often computationally slow for cases where a large number of data points are to be evaluated. Extensive amount of data is generated where measurement equipment such as laser scanners are used for inspection, as well as in reverse engineering applications. In this report, a unified linear approximation technique is introduced for use in evaluating the forms of straightness, flatness, circularity, and cylindricity. Non-linear equation for each form is linearized using Taylor expansion, then solved as a linear program using software written in C++ language. Examples are taken from the literature as well as from data collected on a coordinate measuring machine for comparison with least squares and minimum zone results. For all examples, the new formulations are found to equal or better than the least squares results and provide a good approximation to the minimum zone tolerance.

Automatic segmentation of digitized data for reverse engineering applications

Reverse engineering is the process of developing a Computer Aided Design (CAD) model and a manufacturing database for an existing part. This process is used in CAD modeling of part prototypes, in designing molds, and in automated inspection of parts with complex surfaces. The work reported in this paper is on the automatic segmentation of 3-Dimensional (3-D) digitized data captured by a laser scanner or a Coordinate Measuring Machine (CMM) for reverse engineering applications. Automatic surface segmentation of digitized data is achieved using a combination of region and edge based approaches. It is assumed that the part surface contains planar as well as curved surfaces that are embedded in a base surface. The part surface should be visible to a single scanning probe (21/2D object). Neural network algorithms are developed for surface segmentation and edge detection. A back propagation network is used to segment part surfaces into surface primitives which are homogenous in their intrinsic differential geometric properties. The method is based on the computation of Gaussian and mean curvatures of the surface. They are obtained by locally approximating the object surface using quadratic polynomials. The Gaussian and mean curvatures are used as input to the neural network which outputs an initial region-based segmentation in the form of a curvature sign map. An edge based segmentation is also performed using the partial derivatives of depth values. Here, the output of the Laplacian operator and the unit surface normal are computed and used as input to a Self-Organized Mapping (SOM) network. This network is used to find the edge points on the digitized data. The combination of the region based and the edge based approaches, segment the data into primitive surface regions. The uniqueness of our approach is in automatic calculation of the threshold level for segmentation, and on the adaptability of the method to various noise levels in the digitized data. The developed algorithms and sample results are described in the paper.

Computer-aided manufacturing of implants for the repair of large cranial defects: an improvement of the stereolithography technique.

The objective of this study is to demonstrate the utility of geometric modeling in cranioplasty; in other words, to use geometric modeling to generate a prototype that will be used as the base structure of a composite prosthesis for covering cranial defects. This geometric model is easy to manipulate and can be modified. To achieve this goal, the top surface of a cranial bone flap is digitized using a portable coordinate measurement machine. Intentionally, a sub-surface of the bone flap, representing the skull defect, was not digitized. A geometric model of the bone flap is generated that includes the undigitized region. With the technique described in this paper the authors generated the geometric model of the undigitized region (the skull defect). The geometric model of the bone flap is further manipulated and a series of conical cavities are introduced. Prototypes of the geometric models are manufactured using stereolithography. The clinical implications of this technique are discussed.

A new approach to semi-active vibration suppression using adjustable inertia absorbers

Abstract Detuning is a common occurrence, which is widely seen in industry and brings sub par vibration suppression performance. This study introduces a semi-active retuning methodology that imparts optimum absorber features without the danger of inviting instability. The proposed scheme uses an adjustable effective inertia mechanism and a piezoelectric actuation. It consists of periodic system identification to detect variations in both the absorber and the primary system and⁄or excitation frequency, a concurrent in situ adjustment of a secondary mass position, and a variable rate-damping coefficient to comply with the desired optimality criterion. Although various mechanisms can be used, the example presented in this paper demonstrates the novelty of the concept. The absorber retuning is optimal; hence, it is effective for a wide band excitation. The feasibility of the proposed methodology is demonstrated through simulations. Results indicate that the retuned absorber delivers considerable vibration suppression improvement over the detuned absorber.

A Finite Element Formulation of a Flexible Slider Crank Mechanism Using Local Coordinates

The need for higher manufacturing throughput has lead to the design of machines operating at higher speeds. At higher speeds, the rigid body assumption is no longer valid and the links should be considered flexible. In this work, a method based on the Modified Lagrange Equation for modeling a flexible slider-crank mechanism is presented. This method possesses the characteristic of not requiring the transformation from the local coordinate system to the global coordinate system. An approach using the homogeneous coordinate for element matrices generation is also presented. This approach leads to a formalism in which the displacement vector is expressed as a product of two matrices and a vector. The first matrix is a function of rigid body motion. The second matrix is a function of rigid body configuration. The vector is a function of the elastic displacement. This formal separation helps to facilitate the generation of element matrices using symbolic manipulators.

A nonlinear finite element approach to kineto-static analysis of elastic beams

Recently the demand for higher speed in design of mechanical systems has led to an intensive research in the formulation of the elastic mechanisms. In this study it is shown that the kineto-static solution is close to full dynamic solution for typical dimensions of the links. The formulation presented here uses the Timoshenko Beam Model with geometric stiffening. The element matrices and nodal forces are reported as integral of product of shape functions. This gives a more generic form and can be easily applied to other shape functions. A new formalism is introduced for the nonlinear effect (geometric stiffening). Fundamental to this approach is the introduction of a tensor and its assembly which plays a similar role as element matrices of the linear terms. Several numerical simulations are conducted to quantify the effect of geometric stiffening, tip mass, and normal and tangential acceleration on the nodal displacements.

Tonal Tuning of a Variable Inertia Vibration Absorber: A Feasibility Study

The primary goal of this study is to investigate the dynamics of a new class of adaptive Tuned Vibration Absorber (TVA): A variable effective inertia absorber. In particular, the accuracy of linearization of the dynamic equations, the effect of the moving mass on the dynamics of the absorber, and steady state vibration of the primary system are investigated. It is shown that the linearized model is accurate. Two simulations using the nonlinear model are reported. These simulations show effectiveness of the absorber on reducing the displacement and acceleration of the primary system. In a third simulation, the block is moved from a detuned position to a tuned position and nonlinear differential equation of the motion is solved. The results show a significant decrease of the vibration of the primary system.Copyright

New constitutive model for vibrations of a beam with a piezoceramic patch actuator

Piezoceramic wafer (patch) actuators have been used for the excitation and control of vibrations of beam and plate-like structures. Accurate constitutive modeling of the beam or plate with a piezo-patch actuator adhered to it is an important aspect to understanding this problem. In this paper, a multi-layered beam model is presented that predicts natural frequencies of the open-circuited beam-patch system. Both the beam and the patch actuator are modeled as Timoshenko beams. Constraints are introduced to ensure continuity of the axial and transverse displacements at the interface of the two Timoshenko beams. The cross section of each layer is allowed to take different values, which adds an additional degree of freedom to the system. The displacement equation of each Timoshenko beam is represented in a factored matrix form. This factored matrix form is utilized to develop a procedure for derivation of element mass and stiffness matrices using a symbolic manipulation program (MAPLE). MAPLE is used to form the global mass and stiffness matrices. An eigenvalue analysis is conducted and natural frequencies of the layered beam are calculated. To verify the model, experimental studies are performed to determine cantilevered beam-patch system natural frequencies. Better agreement between the theoretical and experimental results is observed than could be obtained using Eulers (thin) beam theory.

Three-Point Contact Study of a Wheelset and Rails

Three-point contact occurs in curving and transfer of a wheelset over switches and turnouts. In this study, an approach is presented that enforces three-point contact between a wheelset and a rail. This is accomplished by placing the wheelset over the track by setting the wheelset position parameters. Then, the location of all common normal are computed. Next, three common normal with shortest length are used to set up the non-penetrating constraint equations in track coordinate system. This led to nine algebraic equations whose Jacobean can be represented by block matrices. A Newton iterate based on these block matrices are used to compute the location of the three contact points. Several numerical examples are presented to verify the accuracy of the approach.Copyright

Computation of Common Normal Between Wheelset and Rail as an Optimization Problem

Computation of Common Normal between a wheelset and rail is a key problem in simulation of wheel/rail interaction. Such an algorithm must be robust and efficient. In this work, computation of location of the common normal is formulated as an optimization problem. This framework has the advantage of being able to use optimization techniques for determination of location of common normal as an alternative Newton method. The numerical results obtained using Trust-Region Method are presented.Copyright