Showing papers in "Journal of Mechanical Design in 1991"

A Global Performance Index for the Kinematic Optimization of Robotic Manipulators

Abstract: In this paper, a novel performance index for the kinematic optimization of robotic manipulators is presented. The index is based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the kinematic and static transformations between the joint and Cartesian spaces. Moreover, the index proposed here, termed global conditioning index (CGI), is meant to assess the distribution of the aforementioned condition number over the whole workspace. Furthermore, the concept of a global index is applicable to other local kinematic or dynamic indices. The index introduced here is applied to a simple serial two-link manipulator, to a spherical three-degree-of-freedom serial wrist, and to three-degree-of-freedom parallel planar and spherical manipulators. Results of the optimization of these manipulators, based on the GCI, are included.

Experimental micro mechanics methods for conventional and negative Poisson's ratio cellular solids as Cosserat continua

Abstract: Continuum representations of micromechanical phenomena in structured materials are described, with emphasis on cellular solids. These phenomena are interpreted in light of Cosserat elasticity, a generalized continuum theory which admits degrees of freedom not present in classical elasticity. These are the rotation of points in the material, and a couple per unit area or couple stress. Experimental work in this area is reviewed, and other interpretation schemes are discussed. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. New experimental results are presented for foam materials with negative Poisson's ratios.

Extensions to the Taguchi method of product design

Abstract: The Taguchi method of product design is an experimental approximation to minimizing the expected value of target variance for certain classes of problems. Taguchi’s method is extended to designs which involve variables each of which has a range of values all of which must be satisfied (^necessity), and designs which involve variables each of which has a range of values any of which might be used (^possibility). Tuning parameters, as a part of the design process, are also introduced into Taguchi’s method. The method is also extended to solve design problems with constraints, invoking the methods of constrained optimization. Finally, the Taguchi method uses a factorial method to search the design space, with a confined definition of an optimal solution. This is compared with other methods of searching the design space and their definition of an optimal solution.

Similarity analysis of compressor tip clearance flow structure

Abstract: A new approach is presented for analyzing compressor tip clearance flow. The basic idea is that the clearance velocity field can be (approximately) decomposed into independent throughflow and crossflow, since chordwise pressure gradients are much smaller than normal pressure gradients in the clearance region. As in the slender body approximation in external aerodynamics, this description implies that the three-dimensional steady clearance flow can be viewed as a two-dimensional, unsteady flow. Using this approach, a similarity scaling for the crossflow in the clearance region is developed and a generalized description of the clearance vortex is derived. Calculations based on the similarity scaling agree well with a wide range of experimental data in regard to flow features such as crossflow velocity field, static pressure field, and tip clearance vortex trajectory.

A Modified Game Theory Approach to Multiobjective Optimization

Abstract: Many mechanical and structural design problems encountered in practice require solutions which balance several conflicting objectives. The vector, scalarization, and trade-off-curve methods have been developed to achieve multiobjective solutions. One of the best known methods for generating a compromise solution, based on the concept of Pareto minimum solution, is the cooperative game theory method since it uses a scalarized approach and has a numerical measure of compromise. However, game theory is hard to automate due to a two step optimization process involved. Hence, in this work, a modification to the game theory is introduced in which the two optimization steps are combined and an algorithm for its implementation is developed. The algorithm is tested on two numerical examples, including one dealing with the probabilistic design of an eighteen speed machine tool gear train. The probabilistic theory necessary for the design of the gear train is also introduced. The examples validate the modified game theory.

A Sequential Linearization Approach for Solving Mixed-Discrete Nonlinear Design Optimization Problems

Abstract: Design optimization models of often contain variables that must take only discrete values, such as standard sizes. Nonlinear optimization problems with a mixture of discrete and continuous variables are very difficult, and existing algorithms are either computationally intensive or applicable to models with special structure. A new approach for solving nonlinear mixed-discrete problems with no particular structure is presented here, motivated by its efficiency for models with extensive monotonicities of the problem’s objective and constraint functions with respect to the design variables. It involves solving a sequence of mixed-discrete linear approximations of the original nonlinear model. In this article, a review of previous approaches is followed by description of the resulting algorithm, its convergence properties and limitations. Several illustrative examples are given. A sequel article presents a detailed algorithmic implementation and extensive computational results.

The Determination of the Probabilistic Properties of Velocities and Accelerations in Kinematic Chains With Uncertainty

Abstract: A probabilistic model and methods to determine the means and variances of the velocity and acceleration within stochastically-defined planar pin jointed kinematic chains are presented. The presented model considers the effect of tolerances on link length and radial clearance and uncertainty of pin location as a net effect on the link’s effective length. The determination of the mean values and variances of the output variables requires the calculation of sensitivities of secondary variables with respect to the random variables. It is shown that this computation is straightforward and can be accomplished by a conventional kinematic analysis package. Thus, the concepts of tolerance and clearance have been captured by the model and analysis. The only input data is the nominal linkage model and statistical information. The “effective link length” model is shown to be applicable to both analytical solution and Monte Carlo simulation. The results from both methods are compared. This paper solves the higher-order kinematics problem for the probabilistic design analysis of stochastically defined mechanisms.

Tuning parameters in engineering design

Abstract: In the design and manufacture of mechanical devices, there are parameters whose values are determined by the manufacturing process in response to errors introduced in the device’s manufacture or operating environment. Such parameters are termed tuning parameters, and are distinct from design parameterswhich the designer selects values for as a part of the design process. This paper introduces tuning parameters into the design methods of: optimization, Taguchi’s method, and the method of imprecision [8]. The details of the mathematical formulation, along with a design example, are presented and discussed. Including tuning parameters in the design process can result in designs that are more tolerant of variational noise.

Computation of Member Stiffness in Bolted Connections

Abstract: The member stiffness in a bolted connection has a direct influence upon safe design with regard to both static and fatigue loading, as well as in the prevention of separation in the connection This work provides a simple technique for computing the member stiffness in many types of bolted connections Finite element analyses are performed for joints having a range of materials and geometries, and the results are generalized by nondimensionalization An exponential expression for the stiffness is determined, and the results are compared with those of some of the techniques currently used

Modeling of plane strain fatigue crack closure

Abstract: A mechanism based on out-of-plane plastic strain component, e z p , in plane strain is shown not to be adequate in explaining closure. In the second model, partial relief of compressive stresses in front of the crack tip upon crack advance is forwarded as responsible for crack closure in plane strain. A third model based on compressive strain accumulation in the x-direction, e x p , is studied. Stress-strain history and material displacements as crack advances are presented for plane strain conditions that lend further support to the third model

Friction models for metal forming in the boundary lubrication regime

Abstract: Wilson and Shen's semi-empirical equation for the effective hardness of a plastically deforming workpiece is used to develop models for tool-workpiece friction in metalforming processes operating in the boundary lubrification regime

Influence of Linear Profile Modification and Loading Conditions on The Dynamic Tooth Load and Stress of High-Contact-Ratio Spur Gears

Abstract: This paper presents a computer simulation for the dynamic response of high-contact-ratio spur gear transmissions.High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented in this paper examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. This paper shows that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High contact ratio gears were found to require less modification than standard low-contact-ratio gears.

A Procedure Using Manufacturing Variance to Design Gears With Minimum Transmission Error

Abstract: This paper deals with the design of spur gears that have minimum transmission error and are insensitive to manufacturing variance. We address two stages of design: (1) generation of candidate designs (selection of number of teeth, pressure angle, etc.), and (2) tooth profile modification. The first stage involves a search of discrete combinations of design variables, while the second stage utilizes numerical optimization techniques. The key research issue is finding a candidate design and its profile modification that not only has low transmission error, but is insensitive to variations in the design values caused by the manufacturing process. To achieve this goal, the procedure applies Taguchi’s concept of parameter design. In this paper, we consider a design problem with a set specification: fixed center distance, speed ratio, and transmission torque. We seek to find a limited number of candidate designs by applying conventional design generation techniques and some design heuristics. For each candidate design, the procedure determines the optimum profile modification (linear tip relief) by linking the Load Distribution Program (LDP) for gears with an optimization program package (OPTPAK). From the resulting peak optimum, we further seek the statistical optimum using an algorithm developed in this paper. The statistical optimum shows a nominal increase in the transmission error, but is quite insensitive to typical process error associated with gear manufacturing. The developed algorithm readily applies to other gear designs as well as other types of machine elements. In particular, we foresee our procedure to be particularly effective for helical gears. We hope to further our method by developing a means to add statistical heuristics to the discrete design generation stage.

Measuring residual stresses by hole-drilling and coherent optics techniques: a numerical calibration

Abstract: This paper reports the displacement calibration constants derived from the results of an extensive numerical analysis. The constants proposed enable a uniform residual stress field to be determined, whatever the displacement component detected

Computational Implementation and Tests of a Sequential Linearization Algorithm for Mixed-Discrete Nonlinear Design Optimization

Abstract: A previous article gave the theoretical background and motivation for a new sequential linearization approach to the solution of mixed-discrete nonlinear optimal design problems. The present sequel article gives the implementation details of program MINSLIP based on this approach. Illustrative examples, modeling issues, and program parameter selection are discussed. A report on extensive computational results with test problems, as well as comparisons with other methods, shows advantages in both robustness and efficiency. Sample design applications are included.

Single crystal modeling for structural calculations. I, Model presentation

Abstract: A micro-macro model derived from slip theory is shown. It is applied to the modeling of nickel base single crystal superalloys. The experimental data include monotonic and cyclic solicitations at 950°C. The general agreement between tests and numerical simulations is good for all the studied orientations: , , , and . The model is simple enough to be implemented in a finite element code as shown in a future part of the paper