Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies

The goal of this article is to develop a tolerance representation for assemblies compatible with tolerance analysis based on a closed-form algorithm used in robotic applications. A methodology is described that represents standard Y14.5M-1982 tolerances using homogeneous 4×4 matrix transforms. Transforms represent both the nominal relations between parts and the variations caused by geometric deviations allowed by the tolerances. The analysis calculates a statistical estimate of the location of theNth part in an assembly starting from the first part or a fixture. Except forform tolerances, most types of tolerance specifications are compatible with the proposed representation. This approach is well suited to integration with CAD systems and feature-based design. Since assembly apparatus errors can be calculated using the same methodology, one can predict the relative position and angle errors between two parts about to be mated. This permits useful evaluation of assembly equipment errors, comparison of different product tolerance assignments, and calculations of assembly process capability.     

Mathematical model and boundary conditions in stress analysis relating to steam turbine rotors,under transient operating conditions

An appropriate mathematical model for calculation of thermoelastic stress in steam turbine rotors, under transient operating conditions, is developed in the framework of so called uncoupled quasi-static theory. The numerical analysis has been carried out by means of the finite element code ANGUS, the accuracy of which has been evaluated by comparing it with an analytical solution given by one of the authors in Reference 2. It has been shown that, with an appropriate choice of thermal and elastic boundary conditions, it is possible to carry out stress transient analysis considering only a segment of the hottest zone of high or intermediate pressure body of rotors. The paper includes a comparison study of the influence of two types of thermal boundary conditions in the labyrinth glands.     

Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments

The direct linearization method (DLM) for tolerance analysis of 3-D mechanical assemblies is presented. Vector assembly models are used, based on 3-D vector loops which represent the dimensional chains that produce tolerance stackup in an assembly. Tolerance analysis procedures are formulated for both open and closed loop assembly models. The method generalizes assembly variation models to include small kinematic adjustments between mating parts. Open vector loops describe critical assembly features. Closed vector loops describe kinematic constraints for an assembly. They result in a set of algebraic equations which are implicit functions of the resultant assembly dimensions. A general linearization procedure is outlined, by which the variation of assembly parameters may be estimated explicitly by matrix algebra. Solutions to an over-determined system or a system having more equations than unknowns are included. A detailed example is presented to demonstrate the procedures of applying the DLM to a 3-D mechanical assembly.     

An analytical computation method for statistical tolerance analysis of assemblies with truncated normal mean shift

This paper proposes an analytical solution for fast tolerance analysis of the assembly of components with a mean shift or drift in the form of a doubly-truncated normal distribution. The assembly of components with a mean shift or drift in the form of a uniform distribution (the Gladman model) can be calculated by this method as well since the uniform distribution is a special form of the doubly-truncated normal distribution. Integration formulae of the first four moments of the truncated normal distribution are first derived. The first four moments of the resultant tolerance distribution are then calculated. As a result, the resultant tolerance specification is represented as a function of the standard deviation and the coefficient of kurtosis of the resultant distribution. Based on this method, the calculated resultant tolerance specification is more accurate than that predicted by the Gladman's model or the simplified truncated normal model. The difference between this model and the Monte Carlo method with 1,000,000 simulation samples is less than 0.5%. The merit of the proposed method is that it is fast and accurate which is crucial for engineering applications in tolerance analysis.     

Equivalent histories,states and a variational problem for a rigid linear heat conductor with memory

The model of a rigid linear heat conductor which exhibits a constitutive equation with memory for the heat flux can be characterized by processes and states. The equivalence between histories is introduced in order to consider minimal states. The inversion of the constitutive equation, in which the heat flux appears as a linear functional of the history of the temperature gradient, allows to consider states expressed in terms of the heat flux vector instead of the temperature gradient. A variational formulation of an evolution problem with mixed initial boundary conditions is also given.     

Monitoring and analysis of the operating conditions of heat sources

Data-analysis systems for monitoring and analyzing the operating conditions of heat sources are described. The functional capabilities of systems are considered as part of a retrospective analysis of measurement results. Translated from Izmeritel'naya Tekhnika, No. 11, pp. 51–55, November, 2008.     

Optimization of operating conditions for a double-row tapered roller bearing

This paper proposes a methodology that combines the Finite Element Method and multiple response surface optimization to search for the optimal operating conditions of a double-row Tapered Roller Bearing (TRB) that has a Preload (P), radial load (F_r), axial load (F_a) and torque (T). Initially, FE models based on a double-row TRB are built and validated in the basis of experimental data and theoretical models. Three of the most important parameters used in the design of TRB were obtained from a simulation of the FE models with a combination of several operating conditions that were previously selected in accordance with a design of experiments. The design parameters are: contact stress radio for both rows of rollers (S₁ and S₂), maximum deformation of the outer raceway (α_max), and the difference between the gaps of the inner raceways (Δδ) or misalignment. Based on the results of the FE simulations, quadratic regressions models are generated that use the response surface method to predict the design parameters when new operating condition are applied. Then, a multi-response optimization study based on these models and using desirability functions is conducted. It is concluded that the accuracy of the results demonstrates that this methodology may be used to search for the optimal operating condition in a double-row TRB.     

Online variational learning of finite inverted Beta-Liouville mixture model for biomedical analysis

Image segmentation is widely applied for biomedical image analysis. However, segmentation of medical images is challenging due to many image modalities, such as, CT, X-ray, MRI, microscopy among others. An additional challenge to this is the high variability, inconsistent regions with missing edges, absence of texture contrast, and high noise in the background of biomedical images. Thus, many segmentation approaches have been investigated to address these issues and to transform medical images into meaningful information. During the past decade, finite mixture models have been revealed to be one of the most flexible and popular approaches in data clustering. In this article, we propose a statistical framework for online variational learning of finite inverted Beta-Liouville mixture model for clustering medical images. The online variational learning framework is used to estimate the parameters and the number of mixture components simultaneously, thus decreasing the computational complexity of the model. To this end, we evaluated our proposed algorithm on five different biomedical image data sets including optic disc detection and localization in diabetic retinopathy, digital imaging in melanoma lesion detection and segmentation, brain tumor detection, colon cancer detection and computer aid detection (CAD) of Malaria. Furthermore, we compared the proposed algorithm with three other popular algorithms. In our results, we analyze that the proposed online variational learning of finite IBL mixture model algorithm performs accurately on multiple modalities of medical images. It detects the disease patterns with high confidence. Computational and statistical approaches like the one presented in this article hold a significant impact on medical image analysis and interpretation in both clinical applications and scientific research. We believe that the proposed algorithm has the capacity to address multi modal biomedical image data sets and can be further applied by researchers to analyze correct disease patterns.     

A variational formulation based contact algorithm for rigid boundaries in two-dimensional SPH applications

Smooth particle Hydrodynamics (SPH) is one of the most effective meshless techniques used in computational mechanics. SPH approximations are simple and allow greater flexibility in various engineering applications. However, modelling of particle-boundary interactions in SPH computations has always been considered an aspect that requires further research. A number of techniques have been developed to model particle-boundary interactions in SPH and allied methods. In this paper, an innovative approach is introduced to handle the contact between Lagrangian SPH particles and rigid solid boundaries. The formulation of boundary contact forces are derived based on a variational formulation, thus directly ensuring the conservativeness of the governing equations. In addition, the new elegant boundary contact force terms maintain the simplicity of the SPH governing equations.     

A survey of research in the application of tolerance analysis to the design of mechanical assemblies

Tolerance analysis is receiving renewed emphasis as industry recognizes that tolerance management is a key element in their programs for improving quality, reducing overall costs, and retaining market share. The specification of tolerances is being elevated from a menial task to a legitimate engineering design function. New engineering models and sophisticated analysis tools are being developed to assist design engineers in specifying tolerances on the basis of performance requirements and manufacturing considerations. This paper presents an overview of tolerance analysis applications to design with emphasis on recent research that is advancing the state of the art. Major topics covered are (1) new models for tolerance accumulation in mechanical assemblies, including the Motorola Six Sigma model; (2) algorithms for allocating the specified assembly tolerance among the components of an assembly; (3) the development of 2-D and 3-D tolerance analysis models; (4) methods which account for non-normal statistical distributions and nonlinear effects; and (5) several strategies for improving designs through the application of modern analytical tools.     

刚性颗粒模型下粉体层最大应力理论分析

以朗夫力学分析为基础,将粉体视作为均匀球形颗粒的随机堆积体,按照公理化逻辑体系要求,对粉体受力后,粉体层内某个切面上的应力进行分析研究,以揭示粉体受力后特有的内在规律性,改善了半理论半经验的粉体应力分析的推理过程,为进一步揭示粉体的摩擦规律和抗拉强度提供了参考。     

Numerical analysis and experiments on transferred plasma torches for finding appropriate operating conditions and electrode configuration for a waste melting process

Thermal plasma characteristics of transferred plasma torches are numerically and experimentally investigated under atmospheric conditions to find the effects of operating variables and electrode arrangements on them. A control volume method and a modified SIMPLER algorithm are used for numerical analysis, and the temperature distributions of argon plasma are calculated in different torch operating conditions of a typical transferred arc torch. Transferred plasma torches are designed and fabricated, which have six different electrode arrangements, respectively, consisting of a conical rod cathode and a nozzle in the torch, and a distant anode material. The dynamic behaviors of arc voltage are measured to obtain stable arc conditions, and a similarity criterion is determined to analyze static behaviors of arc voltage. For predicting the heat transfer rate to melted material from arc column, measurements are made for the heat loss at the anode material and fractions of input power transferred to the anode. Furthermore, thermal plasma temperatures are measured by the optical emission spectroscopy of an Ar I line. As a result of the present work, an appropriate electrode configuration and operating conditions for waste melting process are presented for the optimization of transferred plasma torches.     

Finite element analysis for a class of nonlinear variational inequalities

In this paper, we prove that the error estimates for the finite element approximation of a class of variational inequalities arising in elastostatics is of order h in the energy norm. In fact, our estimates improve all of the previously known error estimates for elliptic variational inequalities.     

Optimum operating conditions for scanning devices in photoelectric recording

Conclusions Scanned phototransducers with a small scanning amplitude can be used under the same conditions as similar transducers based on the measurement of the duration of adjacent pulses, since the parameters of the former do not depend in a zero measuring method on the amplitude of vibrations or the width of the graduation image. The sensitivity of such a circuit can be determined from (10) and its maximum from (15).     

Multicriteria materials selection for extreme operating conditions based on a multiobjective analysis of irradiation embrittlement and hot cracking prediction models

A methodology for evaluating different combinations of materials specifications for extreme environment applications is presented. This new approach addresses the materials selection problem using a multicriteria stringency level methodology that defines several thresholds obtained by analyzing different prediction models of irradiation embrittlement and hot cracking. To solve the conflicts among thresholds as provided by the different prediction models, a multiobjective approach is carried out. Materials for reactor pressure vessels have been considered as case study. It has been concluded that the best option to manufacture a pressure vessel for a pressurized water modern reactor is the selection of German manufacturing standards. Finally, a sensitivity analysis of the proposed methodology has been performed to evaluate the divergences between the single stringency level methodology and the new proposal including multicriteria decision making aspects.     

The dynamic vectorial model for assemblies of acicular particles

We use the Landau-Lifshitz equations to construct a dynamic model for describing a system of interacting particles. The dynamic model will produce results different from the static model for a finite line of particles with weak interaction strength and parallel anisotropy axes at a large angle to the line. Small two and three dimensional clusters of particles are also discussed. All the results indicate that increasing the angular distribution of the particles will reduce the difference between the static and dynamic simulations. The dynamic switching model is necessary for perpendicular recording because of the alignment of the switching units in the perpendicular media.     

Choice of operating conditions and plasma parameters of a magnetoplasma compressor

B. I. Stepanov Institute of Physics, Academy of Sciences of Belorussia, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 62, No. 3, pp. 386–390, March, 1992.