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Uncertainty analysis is essential for estimating variability within specified tolerances, particularly in three-dimensional (3D) assembly tolerance analysis. This study introduces a novel analytical approach for assessing assembly deviations, integrating the Jacobian–Torsor model with the bootstrap technique. The Jacobian–Torsor model combines the efficiency of representing tolerances with the adaptability of the Jacobian matrix for their propagation. This computerized method, based on the unified Jacobian–Torsor approach, focuses on cam-clamping devices, specifically the fastening flange component. The novelty of this study lies in the application of the bootstrap technique, a Monte Carlo Simulation approach, for uncertainty analysis to estimate variability within specified tolerances. A comprehensive comparison of statistical methods—bootstrap, stratified sampling, Bayesian statistics, and analytical methods—demonstrates the advantages of the Bootstrap approach. The results emphasize its user-friendliness and precision, even with complex shapes. The primary aim is to highlight the utility of the unified Jacobian–Torsor method for tolerance analysis. An experiment involving the fastening flange assembly illustrates the practical application of this approach. The findings confirm the effectiveness of the proposed method, demonstrating its accuracy and reliability for cam-clamping devices in real-world assembly scenarios with intricate geometries. [ABSTRACT FROM AUTHOR]

Sampling-based tolerance analysis is a powerful tool for evaluating the quality of functional products, but requires realistic manufacturing distributions. However, the determination of resulting manufacturing distributions is usually associated with a high financial and time expenditure, especially for novel technologies such as Additive Manufacturing. Usually, sampling techniques are used to reproduce the original distribution of manufacturing variations based on statistical moments. In most cases, simplifying assumptions are made for this purpose, potentially leading to an inadequate representation of the correlation between machine and process parameters in the resulting distribution. In the worst case, this can lead to a falsification of the tolerance analysis results. Aiming to address this challenge, this paper presents an approach to imitate real-world manufacturing distributions using generative Machine Learning techniques based on Deep Learning with small real data sets. This enables a realistic reproduction of quasi-real manufacturing distributions and omits conventional sampling techniques. The general procedure and its applicability are shown via illustrative use cases from the tolerancing domain. [ABSTRACT FROM AUTHOR]

Accurate modeling of geometrical deviations is the premise and critical step for tolerance analysis. Traditional tolerance modeling methods usually simplify deviations to variations in degrees of freedom. Although this facilitates the uniform representation and accumulative calculation, it is not possible to consider the effects of real topography over mating interfaces on tolerance analysis in high-precision scenarios. In this regard, this paper proposed a tolerance modeling method for representing anisotropic rough surfaces information under the framework of Skin Model Shapes. Specifically, the spatial information on rough surfaces is represented by autocorrelation functions. A set of nonlinear equations are constructed according to given autocorrelation functions and then solved to obtain the desired surface topography. In case studies simulated rough surfaces with different input parameters are illustrated and the consistency of this method is verified. The proposed method provides an accurate and practical way to represent anisotropic rough surfaces for tolerance modeling and analysis. [ABSTRACT FROM AUTHOR]

This paper's goal is to give an overview to tolerance analysis. The cost and quality of a product can be significantly impacted by decisions about tolerating. Increased focus on tolerance design is required if high-precision assemblies are to be produced at cheaper costs. After a component's tolerance has been determined, tolerance analysis looks to propagate the manufacturing imprecisions (geometrical defects) and to validate the value of the functional requirements. The mathematical modelling is absolutely necessary for this validation. Models for tolerance analysis are discussed in a lot of literature. There are summaries of the current state of the art, the most recent advancements, and the upcoming trends in tolerancing research. From a mathematical perspective, this paper provides a taxonomy of mathematical concepts for tolerance analysis. [ABSTRACT FROM AUTHOR]

In sensitive mechanisms, achieving the required accuracy of the final parts at the most suitable price is a complex process. The tolerance design process is essential in design and manufacturing to achieve a quality and low-cost product. Allocation of appropriate tolerances is always time-consuming and challenging, especially for complex products, as it involves many aspects of design, manufacturing, and quality issues. In this research, a program has been written in MATLAB, in which by only one geometry model, all possible interferences of assembled parts for all tolerances and nominal sizes in different production modes have been investigated. By using this program, it is possible to add or reduce applied tolerances to nominal sizes and check the interference of parts for all tolerances. Also, temperature effects must be considered when designing a product that operates in a wide temperature range. This approach could ensure that the values of the output parameters of the mechanism remain stable with various temperature changes. The considered case study is particular clock whose structural parameter tolerances often significantly affect the accuracy of the timing output of the entire movement of the mechanism in the program; the tolerance of the parts of the delay clock mechanism has been studied. By analysing the tolerance of geometric non-interference and considering the strain of the parts due to the operating temperature of the mechanism, 24% of the examined sizes should be reduced to avoid interference and the tolerance of the axis position of the clock should be reduced to ±0.01.

—In state of the art high-precision motion systems, which utilize magnetic levitation, a quasi-zero stiffness gravity compensation is one of the essentials to improve dynamic performance, eliminate position dependency and thus simplify controller design. Special configurations of permanent magnets, such as Halbach magnet arrays, can realize magnetic levitation as a form of magnetic spring. However, unlike conventional permanent magnet machines with large stiffness, the quasi-zero stiffness magnetic spring requires higher modeling accuracy for force estimation, which is affected by the nonlinear reluctance effect of permanent magnets. In this study, we propose an accurate magnetic modeling method for the quasi-zero stiffness magnetic spring. By correcting the reluctance effect of magnets, the proposed magnetic model achieves superior accuracy estimating levitation force and stiffness to the conventional surface current model. Using the reluctance-corrected magnetic model, tolerance analysis was performed to identify dominant geometric parameters affecting the uncertainty of the Halbach array magnetic spring performance. A Monte-Carlo simulation was used to estimate the overall tolerance of magnetic forces and stiffness. The experimental results fit in the tolerances. • Accurate analytical model for Halbach array linear magnetic spring (HMS) considering magnet's reluctance. • The model estimates the level of quasi-zero stiffness of the HMS accurately. • Performance variations were quantitatively estimated with some dominant tolerances identified. • Overall uncertainties were evaluated using the Monte-Carlo method. [ABSTRACT FROM AUTHOR]

The contact quality between geometric features significantly affects the assembly accuracy and dynamic performance of mechanical products. However, accurate and efficient contact problem solving is currently a common challenge in the fields of tolerance analysis and tooth contact analysis (TCA). In this paper, a tolerance analysis method for gear mechanisms considering form deviations and elastic-plastic contact behaviors is proposed. Specifically, tolerance modeling of systematic and random deviations on tooth surfaces is represented by skin model shapes (SMS). Elastic-plastic contact behaviors including contact deformation, status, and stress distribution are modeled and calculated by a modified boundary element method (BEM). The accuracy and efficiency of this BEM algorithm are verified by comparing with the finite element method (FEM), indicating that the BEM can greatly improve the computational efficiency while maintaining high solution accuracy. A case study for a pair of spur gears demonstrates the significant effects of contact behaviors on transmission performance. This research provides an effective method to introduce mechanical contact behaviors in tolerance analysis of gear mechanisms. In addition, the contact simulation results can also be adopted in the analysis of vibration, reliability, and other aspects. • An accurate and efficient tolerance analysis method for gear mechanisms is proposed. • Real tooth surface topography and elastic-plastic contact behaviors are considered. • Systematic and random tooth surface deviations are represented by skin model shapes. • Elastic-plastic contact behaviors are modeled by a modified boundary element method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In sensitive mechanisms, achieving the required accuracy of the final parts at the most suitable price is a complex process. The tolerance design process is essential in design and manufacturing to achieve a quality and low-cost product. Allocation of appropriate tolerances is always time-consuming and challenging, especially for complex products, as it involves many aspects of design, manufacturing, and quality issues. In this research, a program has been written in MATLAB, in which by only one geometry model, all possible interferences of assembled parts for all tolerances and nominal sizes in different production modes have been investigated. By using this program, it is possible to add or reduce applied tolerances to nominal sizes and check the interference of parts for all tolerances. Also, temperature effects must be considered when designing a product that operates in a wide temperature range. This approach could ensure that the values of the output parameters of the mechanism remain stable with various temperature changes. The considered case study is particular clock whose structural parameter tolerances often significantly affect the accuracy of the timing output of the entire movement of the mechanism in the program; the tolerance of the parts of the delay clock mechanism has been studied. By analysing the tolerance of geometric non-interference and considering the strain of the parts due to the operating temperature of the mechanism, 24% of the examined sizes should be reduced to avoid interference and the tolerance of the axis position of the clock should be reduced to ±0.01. [ABSTRACT FROM AUTHOR]

Uncertainties in manufacturing can have a significant effect on the outcomes of a process and pose difficulties for the management of the processes. Although many models that consider uncertainties in the manufacturing process focus on differences in the processing time and availability of resources, this article reflects on a new aspect of the Stochastic Job Shop Scheduling Problem, evaluating the probability of success (or failure) of a manufacturing job and the effect of a job failure on the other jobs in the process, in particular the rework costs. The article presents a Markovian approach to model a set of manufacturing jobs based on the cost and the probabilistic distribution for success. A failure causes either rework of the failed job, or repetition of some or all previous jobs. The article presents a brief analysis for optimal tolerance assignment using the proposed model and includes a discussion on how this approach can be augmented with machine-learning tools. The article also presents an artificial intelligence–assisted methodology through online scheduling of production processes coupled with online and adaptive tolerance redesign for better management of machining assets. [ABSTRACT FROM AUTHOR]

Addressing the prevalent issues of low accuracy, low efficiency, and poor image quality in online diameter measurement of large-sized stepped shafts, this study introduces a novel method based on a symmetrical dual-telecentric optical path utilizing dual CCDs, specifically designed for step shafts with diameters ranging from 600 mm to 800 mm. By developing and optimizing an imaging system grounded in the object-image dual-telecentric optical path principle and employing Zemax software for comprehensive analysis and optimization, this research achieves significant findings. The system's Airy disk radius is calculated at 3.204 μm; the modulation transfer function (MTF) remains above 0.6 across various fields of view at a spatial cutoff frequency of 71.4 lp/mm, with smooth MTF curves; the field curvature is confined within 0.1 μm; and the distortion is maintained below 0.1%, fulfilling high-quality imaging requirements. Additionally, a tolerance analysis is conducted to ensure the system's stability and reliability. Applied to an experimental setup for measuring the diameter of large-sized step shafts, the system demonstrates an improved measurement precision of 0.02 mm. This research offers a robust technical solution for the high-precision online measurement of large stepped shaft diameters, presenting significant practical implications for enhancing productivity and product quality. [ABSTRACT FROM AUTHOR]

Fingerprint recognition is a widely used biometric authentication method in LED-backlight smartphones. Due to the increasing demand for full-screen smartphones, under-display fingerprint recognition has become a popular trend. In this paper, we propose a design of an optical fingerprint recognition lens for under-display smartphones. The lens is composed of three plastic aspheric lenses, with an effective focal length (EFL) of 0.61 mm, a field of view (FOV) of 126°, and a total track length (TTL) of 2.54 mm. The image quality of the lens meets the target specifications, with MTF over 80% in the center FOV and over 70% in the 0.7 FOV, distortion less than 8% at an image height of 1.0 mm, and relative illumination (RI) greater than 25% at an image height of 1.0 mm. The lens also meets the current industry standards in terms of tolerance sensitivity and Monte Carlo analysis. [ABSTRACT FROM AUTHOR]

This study proposes a parabolic off-axis reflective optical system design method to reduce the wave aberration of the optical system of a large aperture single star simulator and improve the optical system's imaging quality. Firstly, we determined the design indexes of the optical system of the large aperture single star simulator by analyzing the technical indexes of the star sensitizer and the development status of the single star simulator; secondly, the initial structural parameters of the optical system were calculated based on the theory of primary aberration; then, we carried out the design optimization of the optical system, the image quality evaluation, and the tolerance analysis using Zemax software; finally, the study tested the wave aberration of the optical system by using the four-dimensional interferometer and the standard mirror together. The simulation results of the optical system are as follows: in the entire field of view, the aberration of the optical system is far less than 0.002%, the modulation transfer function (MTF) reaches the diffraction limit, and the maximum wave aberration is 0.0324 λ. The experimental results are as follows: the maximum wave aberration of the optical system is 0.0337 λ, which is less than 1/25 λ, and it meets the requirements of the index. The simulation and experimental results show that the optical system of the large aperture single star simulator designed by this method has good imaging quality and a simple system structure. [ABSTRACT FROM AUTHOR]

The requirements for the quality, reliability, and cost-effectiveness of engineering products and engineering production itself are constantly improving. As a result, there is an increasing demand for the quality of design and technological preparation of production, which includes classical dimensional analysis as its foundation. The Classical Method of dimensional analysis calculation represents a comprehensive set of computational and analytical actions carried out during the development and analysis of projects and technological processes, including: the construction of specialized dimensional diagrams for projects and technological processes, the identification and recording of interconnections between all dimensional parameters, the identification of dimensional chains, verification, and the establishment of rational sizing methods in drawings. Dimensional analysis involves a significant number of procedures and actions. The time required for dimensional analysis is substantial, ranging from 10 to 50 hours for a single technical drawing or technological process. At the same time, the use of Modern Methods for calculating dimensional chains will allow us to determine, after a thorough evaluation of manufacturing conditions at each production stage (operation), leading to a reduction in the manufacturing cost of parts. The increased workload of the evaluation process can be compensated by using databases and appropriate software that operates interactively with the user. This will also lead to a reduction in the labor intensity of dimensional analysis of projects and technological processes through automation.

The tolerance of reconfigurable monopulse linear arrays on the uncertainties of the excitation amplitudes is analyzed with a method based on the rules of the interval arithmetic (IA) and analytic bounds for the sum and the difference power patterns are computed. Thanks to the reliability and the computational efficiency of such an IA-based formulation in deriving conservative and narrow pattern bounds, which include all possible pattern deviations, an innovative strategy is proposed for the worst-case performance analysis when dealing with tolerances on different parts of the beam forming network. Representative numerical examples both validate the formulation at hand and prove the effectiveness of the arising worst-case tool. [ABSTRACT FROM AUTHOR]

Addressing the prevalent issues of low accuracy, low efficiency, and poor image quality in online diameter measurement of large-sized stepped shafts, this study introduces a novel method based on a symmetrical dual-telecentric optical path utilizing dual CCDs, specifically designed for step shafts with diameters ranging from 600 mm to 800 mm. By developing and optimizing an imaging system grounded in the object-image dual-telecentric optical path principle and employing Zemax software for comprehensive analysis and optimization, this research achieves significant findings. The system’s Airy disk radius is calculated at 3.204 μm; the modulation transfer function (MTF) remains above 0.6 across various fields of view at a spatial cutoff frequency of 71.4 lp/mm, with smooth MTF curves; the field curvature is confined within 0.1 μm; and the distortion is maintained below 0.1%, fulfilling high-quality imaging requirements. Additionally, a tolerance analysis is conducted to ensure the system’s stability and reliability. Applied to an experimental setup for measuring the diameter of large-sized step shafts, the system demonstrates an improved measurement precision of 0.02 mm. This research offers a robust technical solution for the high-precision online measurement of large stepped shaft diameters, presenting significant practical implications for enhancing productivity and product quality.

Fingerprint recognition is a widely used biometric authentication method in LED-backlight smartphones. Due to the increasing demand for full-screen smartphones, under-display fingerprint recognition has become a popular trend. In this paper, we propose a design of an optical fingerprint recognition lens for under-display smartphones. The lens is composed of three plastic aspheric lenses, with an effective focal length (EFL) of 0.61 mm, a field of view (FOV) of 126°, and a total track length (TTL) of 2.54 mm. The image quality of the lens meets the target specifications, with MTF over 80% in the center FOV and over 70% in the 0.7 FOV, distortion less than 8% at an image height of 1.0 mm, and relative illumination (RI) greater than 25% at an image height of 1.0 mm. The lens also meets the current industry standards in terms of tolerance sensitivity and Monte Carlo analysis.

Industry is facing the management of geometrical deviations along the entire lifecycle of the product. It is helped by digital twin tools that may minimise the geometrical deviations from nominal of products. The new digital twin tools allow to manage geometrical variations through a set of steps fully related by modern information and communication technologies that establish a continuous and unambiguous flow of information among the different steps of this digital process along the whole product lifecycle. They are based on data coming from manufacturing, assembly and inspection. The available large data sets from manufacturing and inspection allow to develop new and more accurate simulation models that realistically consider form deviations and process signature, i.e. the pattern left by the manufacturing process on the produced part surfaces. The present work introduces a digital twin tool to support the lightweight design of assemblies in composite material. It establishes a continuous and unambiguous flow of variation information from the part design to assembly, passing through manufacturing by considering the manufacturing signature. It was applied to a case study and the obtained results agree with the experimental ones. [ABSTRACT FROM AUTHOR]

Industrial requirements to design high quality products in shorter and shorter times impose the use of numerical models to estimate the geometrical deviations of these products, which are assemblies, starting from the geometrical deviations of their components. Numerical models may support this estimation activity, thus reducing the time to market and the design costs. The free-body model is an interesting numerical method to translate the tolerance chain into a static problem solved by algebraic or graphical procedures by using the free-body diagrams of force analysis. This work presents a free-body model that is able to deal with dimensional and geometrical tolerances that involve translations of the features to which the tolerances are applied. Moreover, it validates the free-body model for tolerance analysis of rigid parts by defining and solving a case study through numerical and experimental activities. The present work uses a case study to demonstrate the effectiveness of the free-body model by underlining that the experimental results obtained are very close to those from the numerical model. [ABSTRACT FROM AUTHOR]

The size of the optical zoom system is important in smartphone camera design, especially as it governs the thickness of the smartphone. We present the optical design of a miniaturized 10× periscope zoom lens for smartphones. To achieve the desired level of miniaturization, the conventional zoom lens can be replaced with a periscope zoom lens. In addition to this change in the optical design, the quality of the optical glass, which also affects the performance of the lens, must be considered. With advancements in the optical glass manufacturing process, aspheric lenses are becoming more widely used. In this study, aspheric lenses are incorporated into a design for a 10× optical zoom lens with a lens thickness of less than 6.5 mm and an eight-megapixel image sensor. Furthermore, tolerance analysis is carried out to prove its manufacturability. [ABSTRACT FROM AUTHOR]

Acousto-optic interaction geometry determines the spectral and spatial response of an acousto-optic tunable filter (AOTF). The precise calibration of the acousto-optic interaction geometry of the device is a necessary process before designing and optimizing optical systems. In this paper, we develop a novel calibration method based on the polar angular performance of an AOTF. A commercial AOTF device with unknown geometry parameters was experimentally calibrated. The experimental results show high precision, in some cases falling within 0.01°. In addition, we analyzed the parameter sensitivity and Monte Carlo tolerance of the calibration method. The results of the parameter sensitivity analysis show that the principal refractive index has a large influence on the calibration results, while other factors have little influence. The results of the Monte Carlo tolerance analysis show that the probability of the results falling 0.1° using this method is greater than 99.7%. This work provides an accurate and easy-to-perform method for AOTF crystal calibration and can contribute to the characteristic analysis of AOTFs and the optical design of spectral imaging systems. [ABSTRACT FROM AUTHOR]

Free-form surfaces have good aberration correction capability and balance capability for nonrotationally symmetric imaging systems. In this study, we analyzed the quantitative relationship between X–Y polynomial combination and aberration for the efficient design of X–Y free-form optical systems. The purpose of this study was to provide an exhaustive design method for off-axis triple inverse optical systems with X–Y free-form surfaces. Finally, we designed a free-form off-axis optical system with a large field of view (FOV) and low distortion based on the off-axis triple inverse optical system without an intermediate image plane. The primary mirror (PM) of the system adopted an X–Y polynomial free-form surface to correct the aberration of different FOVs of the system and improve the image width and quality. The optical system had a focal length of 1000 mm, an F-value of 9.5, an FOV angle of 23° × 1°, a maximum distortion grid in the FOV less than or equal to −0.05%, and a full-field average wave aberration better than 0.055 λ (λ/18.2, λ = 632.8 nm). The analysis of the design results showed that the system had high-quality imaging and a compact structure. This design method can provide a technical reference for the study of such free-form off-axis systems. [ABSTRACT FROM AUTHOR]

In a recent work, a technique was proposed to recover the absolute phase maps of fringe patterns with two or three selected fringe wavelengths with the aim to improve anti-error capability. To further increase the anti-error capability associated with the phase unwrapping operation, multiple fringe patterns with different wavelengths may also be used. In this paper, we present a general rule to select the wavelengths and the strategy to increase phase error tolerance bound. Based on this rule, it is concluded that to maximize the error tolerance, four-wavelength method should be selected, where the maximum upper bound of the tolerable phase error is π/6. To minimize the required number of fringe patterns, three-wavelength method with three-step PSP should be selected, that is exactly the case the previous paper has demonstrated. These theoretical conclusions are verified by experimental results. [ABSTRACT FROM AUTHOR]

Tolerance analysis is a key engineering task that is usually supported by domain-specific analysis models and tools that are generally not connected to the system functionality. The model-based system engineering (MBSE) approach is a potential solution to this limitation, but it has not yet been deeply explored in this type of mechanical analysis, for which some problems need to be explored. One of these issues is the capacity of languages such as SysML to describe solution principles based on active surfaces that participate in functionality and are present for tolerance analysis. Thus, this study explored the possibilities that enable SysML to represent these geometries and their mathematical relationships based on Topologically and Technologically Related Surfaces (TTRS) theory and aligned with Geometric Dimensioning and Tolerancing (GD&T) standards. Additionally, the capacity of SysML to assure the consistency of tolerance analysis models is also explored, due to the limitations identified in analysis languages like Modelica. In this context, this paper presents a SysML profile for tolerance analysis modeling (SysML4TA), containing domain-specific semantics (concepts and constraints) to assure the completeness of the analysis models and consistency between the different models considered in the integrated model of the system. Finally, a case study applied to a manufacturing context is presented to validate the capacity of SysML to solve the identified problems. [ABSTRACT FROM AUTHOR]

Featured Application: The results of this work can be included in the design stage of modular permanent magnet synchronous machines for fault-tolerant applications. Addressing stator-rotor misalignment, usually called eccentricity, is critical in permanent magnet (PM) machines since significantly high radial forces can be developed on the bearings, which can trigger a major fault and compromise the structural integrity of the machine. In this regard, this paper aims to provide insight into the unaddressed identification and analysis of the impact of eccentric tolerances on relevant performance indices of permanent magnet synchronous machines (PMSMs) with modular stator core. Static and dynamic eccentricity are assessed for different slot/pole combinations through the finite element method (FEM), and the results are compared with those of PMSMs with a conventional stator core. The unbalanced magnetic forces (UMF), cogging torque, back-emf, and mean torque variations are described and related to the eccentricity magnitude and classification. The main findings indicate that severe radial forces and significant additional cogging torque harmonics are generated because of eccentricity. Additionally, it is found that the main differences between modular PMSMs and conventional PMSMs rely on the value of slots per pole per phase. [ABSTRACT FROM AUTHOR]

In order to meet the requirements of target detection at different distances in infrared polarization detection, a transmission-type long-wave infrared polarization zoom optical system is designed, can zoom in 18–90 mm and the wavelength range is 8–14 μm. The spatial resolution is 0.18–0.9 mrad, and the machining and assembly errors are analyzed. Based on BRDF and Stokes vector model, aluminum is spontaneous emission, and reflected emission characteristics under specific conditions are simulated and analyzed. Infrared polarization imaging and island imaging experiments verify the unique advantages of infrared polarization technology in distinguishing natural and manufactured objects, metal and non-metal, and high-temperature object recognition. The changing trend of contrast between infrared intensity image and polarization image with solar altitude angle is explored, providing theoretical support for developing an infrared photoelectric detection field.

This study proposes a parabolic off-axis reflective optical system design method to reduce the wave aberration of the optical system of a large aperture single star simulator and improve the optical system’s imaging quality. Firstly, we determined the design indexes of the optical system of the large aperture single star simulator by analyzing the technical indexes of the star sensitizer and the development status of the single star simulator; secondly, the initial structural parameters of the optical system were calculated based on the theory of primary aberration; then, we carried out the design optimization of the optical system, the image quality evaluation, and the tolerance analysis using Zemax software; finally, the study tested the wave aberration of the optical system by using the four-dimensional interferometer and the standard mirror together. The simulation results of the optical system are as follows: in the entire field of view, the aberration of the optical system is far less than 0.002%, the modulation transfer function (MTF) reaches the diffraction limit, and the maximum wave aberration is 0.0324 λ. The experimental results are as follows: the maximum wave aberration of the optical system is 0.0337 λ, which is less than 1/25 λ, and it meets the requirements of the index. The simulation and experimental results show that the optical system of the large aperture single star simulator designed by this method has good imaging quality and a simple system structure.

A method based on an interval arithmetic is proposed to analyze uncertain factors such as the curvature radii, excitation amplitude, and excitation phase of a spherical conformal array antenna. An interval description of element factors under different curvature radii of spherical substrates is established using the surrogate model based on the data obtained through a full-wave analysis method. The interval formula of the spherical curvature radius and array element position error is derived and the effects of the spherical radius tolerance, excitation amplitude tolerance, and excitation phase tolerance on the antenna power pattern are studied. To evaluate the effectiveness and reliability of the proposed method, a set of representative numerical results are reported and discussed and a comparison with the Monte Carlo methods and full-wave simulation is described. This method can be widely used during the antenna design and before the antenna prototyping/manufacturing to predict the effects, on the radiation performance, of possible errors/tolerances in the antenna structure to guarantee the antenna working 'in operation'. [ABSTRACT FROM AUTHOR]

Sheet metal assemblies are widely used in the automobile, aerospace, and shipbuilding industries. Sheet metals deform during the manufacturing and assembly process due to their high flexibility. Traditional tolerance analysis approaches were developed for rigid assemblies; however, new approaches of tolerance analysis and variation simulations have been proposed for flexible (compliant) assemblies using FEM. In this paper, a new method called Interactive Worst Case (IWC) is introduced for tolerance analysis of flexible assemblies, which demands a few FEM simulations and is based on traditional Worst Case (WC) method. IWC method guarantees that all the parts will assemble accurately and have proper function. The case study of this paper is two flexible sheets in the form of quarter cylinders, joined together by six spot welding to form a half-cylinder assembly. The accuracy of IWC is verified by comparing the results to uniform MIC. The results of MIC are also compared to the results of the Monte-Carlo simulation (MCS).

[Display omitted] • Achieving Six Sigma Quality for robust analytical method. • Utilizing design of Experiments techniques and tolerance analysis. • Stability indicating method for quantification of Impurities in Vonoprazan Fumarate. • Our Method Adheres to SFSTP guidelines for method validation. • Greenness, blueness and whiteness assessment for the proposed method. Vonoprazan fumarate (VPZ), a potent potassium-competitive acid blocker, holds great promise as a therapeutic option for addressing acid-related disorders. This study introduces a refined reversed phase liquid chromatography methodology tailored for the comprehensive analysis of eight related substances, including starting materials, byproducts, and degradants within VPZ. Our approach integrates response surface methodology and tolerance analysis to achieve six sigma quality standards in chromatographic performance. By embedding specifications into the optimization process, we ensure robustness during method development. Chromatographic separation was executed using an XSelect CSH Phenyl-Hexyl column under stepped gradient conditions, employing a mobile phase comprising 0.1 % trifluoroacetic acid aqueous solution and acetonitrile. The flow rate was maintained at 1.3 mL/min, with UV absorbance at 252 nm, and a column temperature set at 25 °C. To evaluate the stability indicating ability of the method, forced degradation studies were conducted. Importantly, identified degradants did not interfere with the accurate quantification of VPZ and its associated impurities. Validation of the method was achieved through accuracy profiles. A greenness assessment was conducted using National Environmental Methods Index (NEMI), carbon footprint analysis, Analytical Greenness Calculator (AGREE), and Complementary Green Analytical Procedure Index (Complex GAPI). Additionally, blueness and whiteness assessments were conducted using the Blue Applicability Grade Index (BAGI) and Red-Green-Blue 12 (RGB 12) algorithms, respectively. The proposed method exhibited a green profile in NEMI and Complex GAPI. The carbon footprint was calculated at 0.055 kg CO 2 equivalent per sample. The AGREE score was 0.67, BAGI was 80.0, and the whiteness score from the RGB12 algorithm was 83.5.This methodological framework holds promise for utilization in process development and quality assurance of VPZ in bulk drug manufacturing, particularly in the absence of official monographs within recognized compendia. [ABSTRACT FROM AUTHOR]

A new methodology for realizing fabrication-tolerant planar directional couplers is proposed and experimentally demonstrated. Performance of power splitting and WDM couplers can be made highly tolerant to typical process errors when an appropriate center-to-center spacing is chosen due to changes in the mode area compensating waveguide edge to edge variation along a very specific design locus. Using this approach, 2–3% index contrast waveguide couplers were fabricated and tested, demonstrating the predicted improved fabrication tolerances. High index contrast silicon-on-insulator systems are also shown to exhibit the same mechanism. The high fabrication tolerance demonstrated is of particular importance for vertically stacked hybrid integration of different materials platforms, where achieving tight critical dimension control over significant physical topology is problematic. Additionally the method will be of utility in circumstances where tight tolerances are required on coupling ratios such as coupled resonator filter devices etc.

The radar jamming technology has been studied in this paper mainly, which uses the antenna synthetic wave to generate phase distortion at the signal reception to carry out angle measuring jamming, such as traditional cross-eye jamming. However, cross-eye jamming has strict parameter tolerance. To improve the tolerance range of the phase parameters, a multiple antennas synthetic false target electromagnetic jamming technique is proposed in this paper, which has a wider phase parameter tolerance and jamming range. The jamming method can be regarded as an improved cross eye jamming method. We can conclude that this method can generate a “false target” in space and far away from the carrier which has jamming system, which mislead the radar to point to “false target” rather than to real targets. A jamming system with three jamming antennas was considered as the research object. The position of “false target” can be controlled casually by adjusting the feed amplitude and phase of the three antennas simultaneously. The jamming mathematical model of synthetic false target with three antenna emitters is constructed under the sum and difference channel transceiver mechanism of radar in this paper. The error angle and synthetic gain of the three jamming antennas were derived. The phase parameter tolerance of the proposed method was obtained- and compared with cross-eye jamming. A rigorous mathematical derivation is proposed in this paper, and the superiority of the multiple antennas synthetic false target jamming method is verified.

Mechanical tolerance is something that should be carefully taken into consideration and cannot be avoided in a product for manufacturing and assembly needs, especially in the design stage, to avoid excessive dimensional and geometric deviations of the components made. This paper discusses how to determine and allocate dimensional and geometric tolerances in the design of a 10 kW, 500 rpm radial flux permanent magnet generator prototype components. The electrical and mechanical design results in the form of the detailed nominal dimensions of the generator components, and the allowable air gap range are used as input parameters for tolerance analysis. The values of tolerance allocation and re-allocation process are carried out by considering the capability of the production machine and the ease level of the manufacturing process. The tolerance stack-up analysis method based on the worst case (WC) scenario is used to determine the cumulative effect on the air gap distance due to the allocated tolerance and to ensure that the cumulative effect is acceptable so as to guarantee the generator's functionality. The calculations and simulations results show that with an air gap of 1 ± 0.2 mm, the maximum air gap value obtained is 1.1785 mm, and the minimum is 0.8 mm. The smallest tolerance value allocation is 1 µm on the shaft precisely on the FSBS/SRBS feature and the rotor on the RPMS feature. In addition, the manufacturing process required to achieve the smallest tolerance allocation value is grinding, lapping, and polishing processes.

The CEPC Plasma Injector is designed as the beam energy multiplier for avoiding the dipole magnet issue of the Circular Electron Positron Collider (CEPC) booster. Besides the final energy, other requirements including the energy stability, bunch charge and energy spread all make the injector design very challenging. With respect to the electron acceleration, a high transformer ratio plasma wakefield acceleration stage is necessary if we constrain the beam energy at the end of the linac and the plasma injector are 10 GeV and 45.5 GeV, respectively. In this work, we use the particle-in-cell code QuickPIC to design the electron acceleration stage. Based on the current conceptual design, a comprehensive analysis of single-parameter tolerance is performed. Through the tolerance studies, we obtain some useful guidance for the further optimization of the injector. [ABSTRACT FROM AUTHOR]

This work presents a simple grouping method for efficient power pattern tolerance analysis of antennas/radomes using the Monte Carlo method. The discrete elements, as antenna array elements or antenna/radome discretized meshes, are grouped into a limited number of clusters to reduce the number of independent random variables. Three grouping strategies based on Cartesian coordinates, polar coordinates, and random case are presented to group the discrete elements into eight types. A method combining two sets of results with pattern main-lobe-region and sidelobe-region optimal grouping numbers is proposed to improve the tolerance analysis precision. A 60 $\times $ 60 uniformly excited rectangular array antenna with excitation errors and its variants with amplitude taper or circular aperture, and a spherical radome with more than 1100 discrete meshes are considered. The results show that the proposed method can yield desirable electromagnetic (EM) performance variation ranges using 103–2 $\times \,\,10^{3}$ random samplings. Through grouping, the obtained EM performance interval percentages with respect to the interval analysis results are improved from 3%–6% to 47%–88% for the antenna cases and from 1%–2% to 19%–30% for the radome cases, respectively. [ABSTRACT FROM AUTHOR]

The design and performance of a high-efficiency broadband and polarization-independent reflective grating is reported. The physical mechanism of the gratings can be described by the modal method. By using rigorous coupled wave analysis (RCWA) and simulated annealing (SA) algorithms, the parameters of grating were optimized. The calculated diffraction efficiencies of −1st order for TE and TM polarizations in Littrow mounting exceeded 95%, from 988 nm to 1122 nm, and by over 98% in the bandwidth ranging from 1015 nm to 1085 nm, with the value of polarization-dependent loss (PDL) lower than 0.06 dB. Moreover, the electric field distribution of the grating was simulated by the finite element method (FEM), which demonstrated that most of the energy of the incident light was diffracted to the −1st order and the electric field was distributed almost outside the grating. In addition, the great fabrication tolerances and incident angle tolerance ensured high performance of the designed grating in manufacture and application. With its properties of high efficiency, broadband, and polarization-independence, the designed grating should be of great interest for lots of practical applications, including chirped pulse amplification (CPA), interferometers, and spectrometers. [ABSTRACT FROM AUTHOR]

The size of the optical zoom system is important in smartphone camera design, especially as it governs the thickness of the smartphone. We present the optical design of a miniaturized 10× periscope zoom lens for smartphones. To achieve the desired level of miniaturization, the conventional zoom lens can be replaced with a periscope zoom lens. In addition to this change in the optical design, the quality of the optical glass, which also affects the performance of the lens, must be considered. With advancements in the optical glass manufacturing process, aspheric lenses are becoming more widely used. In this study, aspheric lenses are incorporated into a design for a 10× optical zoom lens with a lens thickness of less than 6.5 mm and an eight-megapixel image sensor. Furthermore, tolerance analysis is carried out to prove its manufacturability.

Driven by the steadily increasing digitization of design and manufacturing, digital twins, which describe the tight connection of models from design with data streams from manufacturing and product operation, are becoming more and more important. Particularly in geometrical variations management, digital twins can be used beneficially, for example, to identify joining partners that fit together ideally despite geometrical deviations, thereby reducing manufacturing costs and increasing product quality. Motivated by the increasing importance of these approaches with a simultaneous lack of training offers for this, a teaching unit was developed, which aims at students acquiring competencies for the independent development of a digital twin and its exemplary use in geometrical variations management. The paper describes the conceptualization and elaboration of this teaching unit on digital twins in geometrical variations management and carves out opportunities for its further improvement. [ABSTRACT FROM AUTHOR]

Besides manufacturing-induced part deviations, operational wear in persistent moving assemblies leads to time-dependent deviations of part geometries and the functionality of the mechanism. This article presents an approach based on the Archard wear model to predict the lifetime-functionality of an assembly by carrying out a tolerance analysis, considering both, time-dependent variations in wear activity due to volume loss and the impact of process-induced geometrical variation on the wear. The novelty of this approach lies in the consideration of time-varying operational wear effects in tolerance analysis and non-conformance rate estimation. To prove its applicability, the approach is applied to a oneway-clutch. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic theory based tolerance analysis method for wedge assembly. Wedge is a class of contact features with a small contact angle such as cone and triangle. The impact usually applied in wedge assembly to tighten the structure. The force and times of the impact could affect the assembly dimension and must be considered in tolerance analysis. The wedge contact is formulated as the dynamic model, which the model could be solved to obtain the variation length. Then the variation could be compensated to the tolerance model or dimension chain. The proposed method is used in a case of wedge belt assembly for verification. [ABSTRACT FROM AUTHOR]

During the manufacturing process of a product, variability in its parts is unavoidable. Tolerance analysis allows estimating the consequences of the component's deviation of a mechanism on its functionality. Nowadays, it is possible to determine the contribution of each surface and/or contact on the final result in isostatic mechanisms by using the tools already presented in the literature; however, it is still a challenge to do so in over-constrained mechanisms. In previous works, we introduced a method based on prismatic polyhedra to model over-constrained mechanisms. In this paper, several simulations based on the previous approach are performed, varying the tolerances of the surfaces and contacts of the mechanism. The use of statistical methods to analyze the previous simulations' data is proposed to quantify the contribution of local deviations with respect to the total variation of the mechanism. This analysis determines the most relevant contacts, hence the most critical parts of the mechanism. The process is applied to a pump as an over-constrained case study and uses the prismatic polyhedra method for tolerance analysis. [ABSTRACT FROM AUTHOR]

This paper proposes a mechanics-based method for calculating the elastic-plastic contact behaviors in tolerance analysis. Specifically, form deviations of geometric features are modeled based on the concept of Skin Model Shapes (SMS). Elastic-plastic contact behaviors are calculated by an improved Boundary Element Method (BEM). The calculation accuracy and efficiency are compared with the Finite Element Method (FEM). The simulation results indicate that the proposed method has good calculation accuracy and significantly improves the calculation efficiency at the same time, which provides a feasible method to consider the effects of elastic-plastic contact behaviors in tolerance analysis. [ABSTRACT FROM AUTHOR]

Tolerance analysis, as an effective tool for predicting the effects of geometrical and dimensional deviations on the key characteristics, plays an essential role in increasing the functionality and quality of mechanical products. The conventional methods in the literature have been developed based on this main assumption that the assembly function is available in an explicit form. However, in most industrial applications, deriving an assembly function in an explicit form may be difficult if not impossible. On the other hand, one of the major weaknesses of the conventional tolerance analysis methods in the literature is that all effective dimensions should be varied under the normality assumption. To overcome these weaknesses, in this paper, a new tolerance analysis approach is developed based on the univariate DRM and Pearson system concepts. The proposed method can analyze directly without the need to define any assembly function and also the rejected product rate can be easily predicted using evaluations of the assembly dimension at the limited number of special points. Finally, for verification of the proposed method, some illustrative case studies are considered and results are compared to obtained results of the Monte-Carlo Simulations and the improved Hassofer-Lind and Rack-Fizzler reliability index methods. [ABSTRACT FROM AUTHOR]

Improving productivity and performance of products require professional tolerance analysis and variation control and, in this context, to make sure the final product will achieve the aimed function, analysing the cumulative effects of component tolerances in an assembly is necessary. Such tolerance analysis generally involves complex and tedious calculations which take time and are susceptible to human error; therefore, for automating this process, computer-aided tolerance (CAT) systems have been used extensively. They are, however, complicated and also require relatively detailed definitions of an assembly (CAD models) before they can be used. In this paper, system topology with highly abstracted geometrical information is translated into an analytical vector model based on a semantic tool in the manner of an 'idea algebra'. Tolerances may be defined at any level of the system (ranging from the component level to the system-level function), to more readily realise the design intent. This lightweight 3D-capable representation is possible already at an early concept stage, prior to CAD, and persists and is updated throughout the design process. Using a comparative numerical simulation-based study, it was demonstrated that the presented method provides quicker computation with equally accurate output as CAT, while requiring substantially lower complexity of input. [ABSTRACT FROM AUTHOR]

The large-diameter diffractive telescope has the advantage of observing space debris. Some of the key issues are the design and tolerance analysis of the telescope with the segmented primary lens. In this paper, we design a space large-diameter sub-aperture stitching diffractive telescope that can achieve a large diameter of 1438 mm, a long focal length of 2000 mm, and a full field of view (FOV) of 0.34°. Considering the manufacturing and stitching errors of the sub-aperture can affect the telescope's image quality, we provide a tolerance analysis method based on Monte Carlo analysis, which makes the consequence of the tolerance analysis nearly reality. The tolerance ranges are proposed not only for the segmented primary lens but also for the whole telescope system. [ABSTRACT FROM AUTHOR]