Tolerance analysis is a well-accepted key element in industry for ensuring product quality as well as for reducing manufacturing costs. At the same time, and particularly in light of the recent ...advances in simulation technology, tolerancing decisions are also becoming increasingly important during earlier stages of design. One critical task hereby is the simulation of the “real-world” behavior of the product with minimum uncertainty, i.e. the calculation how geometrical deviations impact the mechanical behavior and/or multiple simultaneous physical phenomena in a multiphysical system. Given the short iterations in design, this usually represents a compromise between two contradictory requirements: an acceptable computation time and the accuracy of the results. The presented paper addresses this challenge by presenting a framework to assess the impact of model parameter uncertainty of the multiphysical system behavior on the accuracy of the results. The framework integrates evidence and probability theories to propagate geometrical variability and model imprecision for tolerance analysis. The information regarding geometrical variability is modelled using probability distributions; and the information regarding the model imprecision is more faithfully modelled using families of probability distributions encoded by probability-boxes (upper & lower cumulative distribution functions). Monte Carlo simulation is used for probabilistic analysis while nonlinear optimization is used for interval analysis.
This paper describes the design of a small form-factor lens for use in portraiture photography. The current general requirement of mobile cameras having good all-round performance results in a ...typical, familiar, multi-lens design. Such designs have little room for improvement, in terms of the available degrees of freedom and highly-demanding target metrics such as low F-number and wide field of view (FoV). However, the specific application of the proposed portraiture lens relaxes the requirement of an all-round high-performing lens, allowing improvement of certain aspects at the expense of others. With a main emphasis on reducing depth of field (DoF), the current design takes advantage of the simple geometrical relationship between DoF and pupil diameter. To achieve high resolution in object space, the design has a large aperture of 4 mm, for which a typical F/2 lens would have a relatively large focal length compared to z-height, requiring refractive–reflective elements; hence, FoV is reduced. The system is folded perpendicular to the optical axis using two 45∘ plane mirrors, with a 4:3 aspect ratio for the FoV maximising use of available space. Inverse sensitivity analysis was used to show that the lens has acceptable tolerancing limits. A minimalistic refocus mechanism supplements reduction of energy consumption from digital bokeh post-processing to give a low-energy, low-DoF, high-performing lens for future use in a multi-camera setup.
This paper presents a 3D formalization of manufacturing tolerancing which associates the concept of small displacements, the functional constraints, and manufacturing process capability. This ...approach would make it possible to establish relations which limit the surface variations of the production mechanism by the functional specifications. These relations have a number of requirements imposed by designer and are sufficient to evaluate the manufacturing process. The variations of the manufacturing process are defined in relation to variations measured by 3D measuring.
Tolerance analysis aims to ensure the performance of mechanical products. However, traditional analysis methods largely ignore the effects of form errors and local surface deformations, which are ...inevitably introduced during manufacturing and assembly phases. Therefore, this paper proposes a novel tolerance analysis framework integrating form errors and local surface deformations based on skin model shapes and a Boundary Element Method (BEM) for rectangular surfaces. First, it introduces a method for modeling skin model shapes considering form errors for rectangular surfaces. Next, it presents the calculation of local surface deformations based on the Conjugate Gradient-Fast Fourier Transform (CG-FFT) method, a classic BEM method for solving contact problems. Together, these can be used to obtain the relative positioning of mating surfaces considering the effects of form errors and local surface deformations. Case studies revealed the considerable effects of form errors and local surface deformations on assembly deviations, and demonstrated the efficiency of the proposed tolerance analysis process. Because the proposed tolerance analysis framework couples geometric deviations introduced during the manufacturing phase with mechanical deformations introduced during the assembly phase, it is expected to help control the geometric deviations of mechanical assemblies more accurately and also ensure product performance.
•Form errors and local surface deformations are integrated in tolerance analysis.•Skin model shapes with position, orientation, and form errors are generated.•Local surface deformations are calculated using CG-FFT method.
Reverse engineering (RE) has been widely applied in many segments of industry when digital or geometric models of existing physical objects are unavailable. This paper details components of RE ...systems and describes the needs for RE in manufacturing industries. Commonly used contact and non-contact scanning techniques are described. Possible interfaces with other manufacturing processes, especially 3D printing (3DP), are discussed. This paper also describes new trends in the field that include increased speed, accuracy, and level of automation in the future. Finally, a discussion on two major tolerance issues in terms of integrating RE and 3DP are presented.
Previous research on tolerance analysis has primarily overlooked the influence of mechanical vibration on the accuracy of motion, neglecting its significance in systems with moving components. To ...bridge this research gap, we propose an innovative tolerance analysis framework that combines the theories of skin model shapes and system dynamics. The skin model shapes are employed to represent the form deviations of the workpiece, while the principles of system dynamics are utilized to describe and analyze dynamic behavior. Then, we conduct simulation studies on cam mechanisms to show tolerance analysis outcomes with the consideration of mechanical vibration. This study also defines an index to measure the impact of internal mechanical system components on tolerance analysis. Our findings indicate that the presence of dampers reduces the effect of surface deviation of parts on kinematic accuracy, which is associated with the value of damping coefficient. Therefore, when the internal damping effect of the system is considered in the tolerance analysis, the tolerance design requirements of the parts can be appropriately relaxed, thereby reducing the cost.
•A skin model-based framework for tolerance analysis is proposed to achieve enhanced accuracy in analysis results.•Integrating mechanical vibration in tolerance analysis improves real-time error prediction.•The effectiveness of the framework is demonstrated through its application to a snail cam mechanism.
We present an intraocular lens (IOL) design that renders it more compliant to actual conditions where tilt may be present in the fabricated lens or the implanted locus. When an IOL is implanted in ...the eye some degree of tilt is commonly observed, negatively affecting the retinal image (Eppig et al., 2009). The distinguishing feature of the proposed design method is the use of a tilted lens as reference, with a genetic algorithm (NSGA-II) applied and followed by a Damped Least Square (DLS) optimization. It is compared to the classical IOL optimization based on the DLS applied to a perfectly aligned lens. The optimized IOL was evaluated considering the specifications of ISO and Liou and Brennan eye models. The image resolution (MTF curves) of the resulting IOL is analyzed for both to compare performance. It is demonstrated that in the Liou and Brennan eye model the visual acuity is comparable for both design methods when the lens is aligned to the optical axis, however, when tilt is present the proposed method presents a significant benefit in relation to the classical method. This approach can be used for a more robust design of any lens system at no additional cost.
•Our method for lens design is more robust to tolerance in fabrication and deployment.•Case study presented for IOLs, but method can be applied to any optical element.•Proposed method presents better results for scenarios where some tilt play a role.•Tolerance analysis comparing classical and proposed results is done.•There is no additional production cost or clinical procedure added by our method.
ISO standards on geometrical product specifications and verification (GPS) categorize the geometrical features partitioned from shapes based on their kinematic invariance classes. As a key issue to ...achieve predictable and interchangeable shape, geometrical tolerancing defines the tolerance zone within which the partitioned features shall be contained for dimensional and geometrical accuracy. However, most of the current research activities consider the geometrical features as orientation and position deviations of substitute ideal surfaces and neglect form errors within the developed models. In order to enhance the tolerance analysis and simulation, the concept of Skin Model Shapes (SMS) is therefore proposed to represent surface deviations in accordance with random nature of geometric deviations. In this paper, a new approach based on spectral analysis is proposed for SMS generation on mechanical parts. The Eigen-system of Laplace-Beltrami Operator (LBO) enables shape analysis with an unambiguous mathematical language due to its invariance of the position and orientation. The SMS generation process is completed with LBO by developing a modeling methodology for geometric deviation representation and generation on single surfaces in the design process. The obtained spatial frequency LBO decomposition on the single surface of invariant class is used to represent the statistical characteristics of the deviations and further used to reproduce deviations with similar distributions. A comparison is presented in the paper to illustrate the difference between a conventional Discrete Cosine Transform (DCT) based method and the proposed LBO-based method. Another case study is investigated to explain the implementation of the proposed method on different types of single surfaces of invariant class generation based on SMS.
Even though they are weakly noticed, geometric part deviations accompany our everyday life. These geometric deviations affect the assemblability and functional compliance of products, since small ...part variations accumulate through large-scale assemblies and lead to malfunction as well as decreased product reliability and safety. However, the consideration of part deviations in the virtual modelling of mechanical assemblies is an ongoing challenge in computer-aided tolerancing research. This is because the resulting assembly configurations for variant parts are far more complicated than for nominal assemblies. In this contribution, two approaches for the relative positioning of point based models are highlighted and adapted to the assembly simulation of Skin Model Shapes, which are specific workpiece representatives considering geometric deviations. The first approach employs constrained registration techniques to determine the position of variant parts in an assembly considering multiple assembly steps simultaneously, whereas the second utilizes the difference surface to solve the positioning problem sequentially. The application of these approaches to computer-aided tolerancing is demonstrated, though their applicability reaches various fields of industrial geometry.
•Skin Model Shapes are digital part representatives comprising geometric deviations.•Approaches for the relative positioning of point-based Skin Model Shapes are proposed.•The approaches ground on algorithms from computational geometry and computer graphics.•Applications for the assembly simulation in tolerancing are given.
As technology increases and performance requirements continually tighten, the cost and required precision of assemblies increase as well. There exists a strong need for increased attention to ...tolerance design to enable high-precision assemblies to be manufactured at lower cost. For automotive and aircraft industries, the tolerancing process has become an important issue in product and process design. There is an important question that would need to be looked into: “How to define a coherent expression of Geometrical Product Specification during the tolerancing process along life cycle?”. There is a necessity for developing a complete answer representing standard tolerance practices. This paper proposes a model to allow a complete and coherent tolerancing process. The description of GeoSpelling, the model proposed to ISO for rebuilding standards in the fields of tolerancing and metrology, allows a unified description of geometrical specification. This model takes into account, not only the specification on isolated parts, but also on assemblies with the integration of the quantifier concept.
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