THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

This paper describes a general formulation for free, steady-state and transient vibration analyses of functionally graded shells of revolution subjected to arbitrary boundary conditions. The formulation is derived by means of a modified variational principle in conjunction with a multi-segment partitioning procedure on the basis of the first-order shear deformation shell theory. The material properties of the shells are assumed to vary continuously in the thickness direction according to general four-parameter power-law distributions in terms of volume fractions of the constituents. Fourier series and polynomials are applied to expand the displacements and rotations of each shell segment. The versatility of the formulation is demonstrated through the application of the following polynomials: Chebyshev orthogonal polynomials, Legendre orthogonal polynomials, Hermite orthogonal polynomials and power polynomials. Numerical examples are given for the free vibrations of functionally graded cylindrical, conical and spherical shells with different combinations of free, shear-diaphragm, simply-supported, clamped and elastic-supported boundary conditions. Validity and accuracy of the present formulation are confirmed by comparing the present solutions with the existing results and those obtained from finite element analyses. As to the steady-state and transient vibration analyses, functionally graded conical shells subjected to axisymmetric line force and distributed surface pressure are investigated. The effects of the material power-law distribution, boundary condition and duration of blast loading on the transient responses of the conical shells are also examined.

A unified formulation for vibration analysis of functionally graded shells of revolution with arbitrary boundary conditions

Recent trends in piezoelectric actuators for precision motion and their applications: a review

Industrial robot provides an optimistic alternative of traditional CNC machine tool due to its advantages of large workspace, low cost and great flexibility However, the low posture-dependent stiffness deteriorates the machining accuracy in robotic milling tasks To increase the stiffness, this paper introduces a pose optimization method for the milling robot when converting a five-axis CNC tool path to a commercial six-axis industrial robot trajectory, taking advantage of a redundant degree of freedom First, considering the displacements of at least three points on the end effector of the robot, a new frame-invariant performance index is proposed to evaluate the stiffness of the robot at a certain posture Then, by maximizing this index, a one-dimensional posture optimization problem is formulated in consideration of the constraints of joint limits, singularity avoidance and trajectory smoothness The problem is solved by a simple discretization search algorithm Finally, the performance index and the robot trajectory optimization algorithm are validated by simulations and experiments on an industrial robot, showing that the machining accuracy can be efficiently improved by the proposed method

Stiffness-based pose optimization of an industrial robot for five-axis milling

The Haar wavelet method for free vibration analysis of functionally graded cylindrical shells based on the shear deformation theory

Optimum structural design of a two-limb Schönflies motion generator

Piezoelectric bending actuators have been widely used in a variety of micro- and nano-applications, including atomic force microscopy, micro assembly, cell manipulation, and in general, micro elect...

High-frequency robust position control of a nonlinear piezoelectric bending actuator:

The present study deals with the nonlinear free vibration analysis of sandwich plates containing electrorheological (ER) fluid as the core layer. Since yield stress of the ER fluid is relatively lo...

Post-Yield characteristics of electrorheological fluids in nonlinear vibration analysis of smart sandwich panels

The elastodynamic analysis of a two-limb Schonflies motion generators is the subject of this paper. This analysis calls for the calculation of the stiffness and mass matrices. By resorting to the generalized spring concept, the posture-dependent stiffness matrix of the robot is computed. With the motors locked, the motion caused by the flexible components leads to the robot mass matrix. The generalized springs help to simplify the model. Although this simplification filters out the higher natural frequencies, it eases the computation of the posture-dependent stiffness and mass matrices. This provides a valuable tool to simplify the evaluation of the robot performance from an elastodynamic point of view, while the robot executes a given task. Finally, the modal analysis of the McGill Schonflies motion generator, while executing a pick-and-place operation, is conducted; under these conditions, the evolution of the first six natural frequencies is obtained. The elastodynamic performance of the robot for the ...

Elastodynamics of a two-limb Schönflies motion generator

This paper aims at the kinematic reliability analysis of the 3-PSS parallel robot. Parallel manipulators bear many advantages like higher stiffness, more accuracy, and speed compared to the serial counterparts. Because of several uncertainty factors such as actuators error, links flexibility, etc. a robot moving platform cannot follow the desired trajectory without an error. In this study, at first, eight, and next twelve uncertainties that seem to affect the kinematics of robot are selected. Next, the probability distribution of the moving platform position is conducted using the closed-form kinematic relation of a robot and the Monte Carlo Simulation, then, the kinematic reliability is calculated for different levels of accuracy. As the closed-form kinematic relation between the actuators rate and the moving platform position cannot be obtained, a polynomial algebraic equation is fitted via the design of experiments method. Using fitted polynomial kinematic equation at hand, the reliability analysis is conducted and evaluated for different levels of accuracy. Also, an experimental reliability analysis is performed to evaluate the results which are obtained numerically. The results show that the difference between the reliability values obtained by the design of experiments and the Monte Carlo Simulation methods is %4.7, and between the design of experiments method and experimental data is %7.7. In the end, a sensitivity analysis is conducted to determine the influence of each uncertainty on the accuracy.

https://ajme.aut.ac.ir/article_3640_e93fa8d4c463653a81e9317e6d1fc4fb.pdf

Afshin Taghvaeipour

Papers

Optimum structural design of a two-limb Schönflies motion generator

High-frequency robust position control of a nonlinear piezoelectric bending actuator:

Post-Yield characteristics of electrorheological fluids in nonlinear vibration analysis of smart sandwich panels

Elastodynamics of a two-limb Schönflies motion generator

Kinematic Reliability Analysis of 3-PSS manipulator based on the explicit solution and design of experiment method