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A mechanical system inherently affected by the conditions, factors, and parameters of uncertainties. Without including the uncertainty effects in the design procedure, the designs may not be robust and reliable. Robust design optimization (RDO) method is a procedure to find the insensitive design with respect to the variations. On the other hand, reliability is measured by the probability of satisfying a specific design criterion. Therefore, a reliable design is a design that satisfies the specified criteria even with some uncertainties in variables and parameters. Reliability-based design optimization (RBDO) is an optimization procedure that incorporates reliability requirements to find the proper design. Since RDO and RBDO are usually the expensive computational approaches, the Reliability-Based Robust Design Optimization (RBRDO) may be difficult to apply. In this paper, a new model for the reliability based robust design optimization is introduced.

Tolerance allocation is a key tool to reach a product with the minimum cost and the maximum performance. Since the thermal effects can cause the dimensional and geometrical variations in the components of mechanical assemblies, the tolerance allocation may be inefficient in the optimal tolerance design at the nominal conditions without including the thermal impacts. In this paper, a new optimal tolerance design of mechanical assemblies with the thermal effects is proposed. According to the proposed method, the tolerance allocation procedure is modeled as a multi-objective optimization problem. The functional objective, the manufacturing cost, and the quality loss function are considered as the corresponding objectives multi-objective optimal tolerance design problem. Using the computational results from the finite element simulations and based on the Artificial Neural Network (ANN) method, the design function as functional objective can be modeled.

Operational modal analysis based on power spectral density transmissibility functions (PSDT) is a powerful tool to identify the modal parameters with low sensitivity to excitations. The rotor systems may have the asymmetric damping or stiffness matrices which can lead to increase the difficulties of the identification procedure. In this paper, a new method is proposed to identify the modal parameters of the asymmetric rotary systems by the operational modal analysis based on the power spectral density transmissibility functions. For pole extraction from the PSDT function, a proper parametric identification method such as the Poly-reference Least Squares Complex Frequency-domain method (PLSCF) or poly-Max method can be used. Then, the rotary system poles can be identified from a Stabilization Diagram (SD) with overestimating the system model order. The proposed algorithm is validated by a computer simulation.

Fixtures play a key role in locating workpieces to manufacture high quality products within many processes of the product lifecycle. Inaccuracies in workpiece location lead to errors in position and orientation of machined features on the workpiece, and strongly affect the assemblability and the final quality of the product. The accurate positioning of workpiece on a fixture is influenced by rigid body displacements and rotations of the workpiece. In this paper, a systematic approach is introduced to investigate the located workpiece position errors. A new mathematical formulation of fixture locators modeling is proposed to establish the relationship between the workpiece position error and its sources. Based on the proposed method, the final locating errors of the workpiece can be accurately estimated by relating them to the specific dimensional and geometric errors or tolerances of the workpiece and the related locators.

One of the most important characteristics of industrial products, especially mechanical set-ups, is considering the tolerances of production and assembly of these set-ups, which directly influences the products’ operations. In sheet metal structures, due to the high flexibility of the sheets, the errors appeared while assembly will be as highly influential as the errors due to the production tolerance of the sheets. As a result, having a comprehensive model which could analyze the assembly process of these structures and also clarifies the relation between the tolerance of the parts and the ultimate changes of the set-up will be of considerable importance. During the assembly process, the contact effect between the components is inevitable. If such effect is not considered, the contact surfaces will permeate. The purpose of this paper is to present a method to analyze the tolerance of flexible sheet structures, considering the contact effect between surfaces.

Kinematic accuracy of the robot end-effector is decreased by many uncertainties. In order to design and manufacture robots with high accuracy, it is essential to know the effects of these uncertainties on the motion of robots. Uncertainty analysis is a useful method which can estimate deviations from desired path in robots caused by uncertainties. This paper presents an applied formulation based on Direct Linearization Method (DLM), for 3D statistical uncertainty analysis of open- loop mechanisms and robots. The maximum normal and parallel components of the position error on the end-effector path are introduced. In this paper, uncertainty effects of both linear and angular variations in performance of spatial open-loop mechanisms and robots are considered.

The design process always has some known or unknown uncertainties in the design variables and parameters. The aim of robust design is minimization of performance sensitivity to uncertainties. Tolerance allocation process can significantly affect quality and robustness of the product. In this paper, a methodology to minimize a product's sensitivity to uncertainties by allocating manufacturing tolerances is presented. The robust tolerance design problem is formulated as a multi-objective optimization based on the combined function-uncertainty-cost model. Genetic algorithm is utilized to solve the multi-objective optimization and a case study is presented to illustrate the methodology.

Inaccuracies in workpiece location lead to errors in position and orientation of machined features on the workpiece, and strongly affect the assemblability and the final quality of the product. The accurate positioning of workpiece on a fixture is influenced by rigid body displacements and rotations of the workpiece due to locator errors. In this paper, a new mathematical modeling of a fixture - workpiece system is proposed to establish the relationship between the workpiece location error and its sources. For the purpose of eliminating the locator errors of the fixtured workpiece, the resultant errors due to several sources are modeled in the locator error. Then the displacement and rotation errors of the located workpiece can be compensated by adjusting the length of locators. The proposed method is proper for error analysis based on both worst case and statistical approaches.

The process capability indices are widely used to measure the capability of the process to manufacture objects within the required tolerance. Fit quality is mainly dominated by the distribution of fit dimensions, i.e., a gap dimension. As the fit dimensions are very difficult to be measured in mass production, they are not to be considered as a direct inspection objective. The quality inspection and evaluation relative to fit quality are focused on whether the processes of assembly requirements are conformed with their specification limits respectively. Fit quality specification can be indicated by the process capability indices of mating parts. In this paper, the statistical-based process capability analysis method is presented to estimate ability of manufacturing process for considering of assembly requirements and fit quality in a mechanical assembly with asymmetric tolerances.