Статті в журналах: "Tolerance optimization"

1

Roubíček, Tomáš. "Constrained optimization: A general tolerance approach." Applications of Mathematics 35, no. 2 (1990): 99–128. http://dx.doi.org/10.21136/am.1990.104393.

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G V, Madhavi Reddy, and Sreenivasulu Reddy A. "Assembly Gap Tolerance Calculation Using ANFIS and Cost Function Optimization." International Journal for Research in Applied Science and Engineering Technology 10, no. 2 (February 28, 2022): 1111–17. http://dx.doi.org/10.22214/ijraset.2022.40460.

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Abstract: Tolerance plays a crucial role in the quality of a product. When different parts of an assembly are assembled, gap arises due to variation in dimensions. The tolerance for the gap is calculated using two methodologies: ANFIS and cost function optimization. In ANFIS the network is trained using mean dimensions, standard deviations as inputs and tolerances as output. The tolerances are predicted from the trained network. In cost function optimization, a cost function is formulated. The machinability of a part is calculated using Fuzzy Comprehensive Evaluation method. The tolerances are calculated by optimizing the cost function. The tolerances calculated using the two methods are compared and optimal tolerance is considered for manufacturing. Keywords: Tolerance, ANFIS, Assembly gap, Cost function, Optimization.

3

Xu, Rui, Kang Huang, Jun Guo, Lei Yang, Mingming Qiu, and Yan Ru. "Gear-tolerance optimization based on a response surface method." Transactions of the Canadian Society for Mechanical Engineering 42, no. 3 (September 1, 2018): 309–22. http://dx.doi.org/10.1139/tcsme-2018-0006.

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To address the low efficiency of gear-tolerance analysis and optimization, a gear-tolerance optimization method based on a response surface method (RSM) and optimization algorithm is presented. A gear-tolerance mathematical model, including profile deviation, pitch deviation, and geometric deviation, was developed by combining traditional profile modeling with a small displacement torsor (SDT) method. Based on this mathematical model, a tooth-contact analysis method, which takes a variety of deviations into account, and a program to compute transmission error were developed. Using the RSM and a genetic algorithm, a gear-tolerance optimization model was created to consider a variety of gear tolerances as design variables and process cost as an optimization objective. An example of gear-tolerance optimization was analyzed, and the result indicates that the method presented in this paper may help improve the efficiency of gear-tolerance optimization and is practicable for precision gear design.

4

Yang, Longbao, Yuejiao Ma, and Liheng Zhou. "Fault Tolerance Analysis and Optimization of Centralized Control Platform Based on Artificial Intelligence and Optimization Algorithm." Scalable Computing: Practice and Experience 25, no. 4 (June 16, 2024): 2621–27. http://dx.doi.org/10.12694/scpe.v25i4.2918.

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To enhance the reliability and self-healing of the system, the research on fault tolerance of the reconfigurable modular centralized control center is its development trend. Most of the previous research has focused on hardware redundancy. Improving fault tolerance performance is an essential topic in the research of centralized control platforms. Firstly, the problem of centralized fault tolerance in the working configuration of a reconfigurable manipulator is studied. The effect of each hinge on fault tolerance in the existing configuration is studied with the criterion of manoeuvrability and tolerable space. The fault module was first modelled to represent the system architecture information. A modular motion rule based on autonomous recombination technology is proposed. A self-organizing deformation algorithm with fault tolerance is studied. The fault tolerance of the motion pairs is compensated by adding a small number of motion pairs to ensure the configuration characteristics. With the addition of a failure compensation device, the joint’s range of motion was reduced, and the fault tolerance rate was enhanced. After the failure of the robot arm, the fault tolerant control method can still ensure that the robot arm can perform work in its tolerable working space. The test results show that the fault tolerance analysis method is practical and feasible. It lays a theoretical foundation for the application in aerospace, industry and other fields.

5

IRANI, S. A., R. O. MITTAL, and E. A. LEHTIHET. "Tolerance chart optimization." International Journal of Production Research 27, no. 9 (September 1989): 1531–52. http://dx.doi.org/10.1080/00207548908942638.

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6

Wang, Bingxiang, Xianzhen Huang, and Miaoxin Chang. "Reliability-based tolerance redesign of mechanical assemblies using Jacobian-Torsor model." Science Progress 104, no. 2 (April 2021): 003685042110132. http://dx.doi.org/10.1177/00368504211013227.

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The purpose of this paper is to present a new method to redesign dimensional and geometric tolerances of mechanical assemblies at a lower cost and with higher reliability. A parametric Jacobian-Torsor model is proposed to conduct tolerance analysis of mechanical assembly. A reliability-based tolerance optimization model is established. Differing from previous studies of fixed process parameters, this research determines the optimal process variances of tolerances, which provide basis for the subsequent assembly tolerance redesign. By using the Lambert W function and the Lagrange multiplier method, the analytical solution of the parametric tolerance optimization model is obtained. A numerical example is presented to demonstrate the effectiveness of the model, while the results indicate that the total cost is reduced by 10.93% and assembly reliability improves by 2.12%. This study presents an efficient reliability-based tolerance optimization model. The proposed model of tolerance redesign can be used for mechanical assembly with a better economic effect and higher reliability.

7

Gao, Yuan. "Tolerance analysis and optimization based on 3DCS." Journal of Physics: Conference Series 2137, no. 1 (December 1, 2021): 012070. http://dx.doi.org/10.1088/1742-6596/2137/1/012070.

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Abstract At present, with the increasing requirements of major enterprises on assembly accuracy, the problem of interference and excessive clearance between parts needs to be solved. In order to analyze and optimize the tolerances in the actual assembly of the parts, a three-dimensional vector ring model is proposed on the basis of the dimensional chain model, and the tolerance distribution is optimized by the “dichotomy method”. With the help of 3DCS, the virtual assembly of the automobile headlight is carried out, and the sensitivity analysis is carried out by establishing the measurement of the gap between the turn signal and headlight in the automobile headlight, and the simulation results are used to obtain a reasonable improvement in tolerance allocation that meets the design criteria and saves costs. The results are compared with the traditional method of optimizing the allocation of equal tolerances and are clearly superior, providing a method for optimizing the allocation of tolerances to parts in engineering practice.

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G V, Madhavi Reddy, Vani S, and Sreenivasulu Reddy A. "Selection of Optimum Assembly Gap Tolerance for Motor Assembly." International Journal for Research in Applied Science and Engineering Technology 10, no. 4 (April 30, 2022): 107–12. http://dx.doi.org/10.22214/ijraset.2022.41180.

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Abstract: The parts in the motor assembly are divided into two types: fixed and variable. The tolerances of the fixed parts cannot be changed and the tolerances of the variable parts are calculated using three methodologies such as ME boost, ANFIS, and Cost function optimization.ME boost is an Excel add in used to calculate the tolerances of the variable parts. ANFIS is a neural network based optimization tool in matlab. Cost function is formulated for the variable parts in the assembly and optimized to calculate the tolerances. Then the tolerance for the assembly gap is calculated. The tolerances for the gap from the three methodologies are compared and optimum tolerance is considered for manufacturing. Keywords: Motor assembly, Tolerance, Assembly gap, ME boost, ANFIS, Cost function Optimization.

9

Balling, Richard J., Joseph C. Free, and Alan R. Parkinson. "Consideration of Worst-Case Manufacturing Tolerances in Design Optimization." Journal of Mechanisms, Transmissions, and Automation in Design 108, no. 4 (December 1, 1986): 438–41. http://dx.doi.org/10.1115/1.3258751.

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The paper discusses the effect of manufacturing tolerances for the design variables on the solution to an optimization problem. Two formulations of the tolerance problem in an optimization context are presented. Linearization is employed to reduce the problems to quadratic and linear programming problems. The formulations and solutions of the two tolerance problems are illustrated with an example application.

10

Liu, Guanghao, Meifa Huang, and Leilei Chen. "Optimization Method of Assembly Tolerance Types Based on Degree of Freedom." Applied Sciences 13, no. 17 (August 29, 2023): 9774. http://dx.doi.org/10.3390/app13179774.

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The automatic generation of tolerance specifications is an important aspect of achieving digital product design. An obvious feature of the current automatic generation of tolerance based on rule reasoning is that all tolerance types will be inferred for the same assembly feature. However, when labelling part tolerance information, designers need to further screen based on the geometric function of the assembly, which may result in prioritizing tolerance types that do not meet the geometric requirements of the assembly. This paper presents an assembly tolerance type optimization method based on the degree of freedom (DOF) of tolerance zone for the optimization and screening problem after reasoning all possible tolerance types. Firstly, we define the DOF of tolerance zones and their representations, while also define the control parameter degrees of freedom (CPDF) of assemblies, and analyze the CPDF of typical geometric functional tolerances of assemblies; Secondly, the Boolean operation relationship between sets is used to construct a Boolean operation preference method for the CPDF. Then, an algorithm for the optimal selection of the shape and position tolerance items of the assembly is established based on the DOFs of tolerance zone. Finally, the proposed method is verified by an engineering example, and the result shows that the method can optimize and screen the geometric tolerance types of assemblies.

11

Huang, Mei Fa, Jiang Tai Huang, Xiong Cheng, Jing Zhang, and Hui Jing. "Tolerance Modeling and Optimization of XY-Table for LED Die Bonder Based on Multi-Body Systems." Advanced Materials Research 201-203 (February 2011): 2922–26. http://dx.doi.org/10.4028/www.scientific.net/amr.201-203.2922.

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High performance XY-table is commonly used in packaging equipments which needs rational tolerance to ensure its high performance requirements and low manufacturing costs. The related studies mainly focus on high speed motion control algorithms and high precision structure design. The proper tolerance is essential in the development process of new products. In this paper, a new method for tolerance optimization based on Multi-body systems is presented. The volumetric error model for XY-table is established based on Multi-body systems. And then, by identifying the basic geometric error components, the relationships between the final output precision of the XY-table and the geometry error sources are established. The tolerance optimization model of XY-table using the above relationships is presented. In this model, objective function is the total manufacturing costs and the constraints are the above relationships. By solving the optimization model, the optimal tolerances are obtained. Finally, a tolerance design example of LED die bonder is given to illustrate the proposed method.

12

Cheng, Kuo Ming, and Jhy Cherng Tsai. "Optimal Statistical Tolerance Allocation of Assemblies for Minimum Manufacturing Cost." Applied Mechanics and Materials 52-54 (March 2011): 1818–23. http://dx.doi.org/10.4028/www.scientific.net/amm.52-54.1818.

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This paper explores a systematic method for optimal statistical tolerance allocation using the Lagrange multiplier method for minimizing manufacturing cost subject to constraints on dimensional chains and machining capabilities. The reciprocal power and exponential cost-tolerance models for statistical tolerancing are investigated for employing this method. The optimization problem is solved by applying the algorithmic approach. Especially, we further derive a closed-form expression of the tolerance optimization problem for reciprocal exponential cost-tolerance model by introducing the Lambert W function. For constrained minimization problems with only equality constraints, the optimum tolerance allocation can be obtained by solving simultaneous equations without further differentiating. An example is illustrated to demonstrate this approach. The result also shows that tolerances can be allocated quickly, economically and accurately using this method.

13

Li, Hai, Hai Ping Zhu, Bo Xing Liu, and Pei Gen Li. "Tolerance Optimization for Assembly Systems Based on Quality Requirements Using State Space Model." Applied Mechanics and Materials 472 (January 2014): 985–89. http://dx.doi.org/10.4028/www.scientific.net/amm.472.985.

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The paper proposed a new systematic method to construct the functional relationship between product quality and tolerances. In the method, a unified user-defined tolerance model is designed to synthesize different kinds of tolerances using 3-D state space model; a deviation propagation model is proposed to analyze the quality-tolerance function. Particularly, the method is suitable for any kinds of tolerances and quality requirements. The method is successfully applied to the turbo-generator stator-core lamination auto-assembly project, and Monte Carlo method is used to simulate the quality performance and optimize the target tolerances.

14

Armillotta, Antonio. "Concurrent optimization of dimensions and tolerances on structures and mechanisms." International Journal of Advanced Manufacturing Technology 111, no. 11-12 (November 7, 2020): 3141–57. http://dx.doi.org/10.1007/s00170-020-06322-6.

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AbstractThe paper deals with a problem of robust optimization of mechanical assemblies, which combines the allocation of tolerances with the selection of dimensional parameters. The two tasks are carried out together with the aim of minimizing the manufacturing cost and the variation on an assembly-level functional characteristic. The problem is addressed in the specific context of planar linkages used in structures and mechanisms. The proposed solution is based on an optimality condition involving both tolerances and dimensions, which allows to define a joint optimization problem avoiding the need of two sequential optimization phases. The condition is developed with the method of Lagrange multipliers using an expanded formulation of the reciprocal power cost-tolerance function. The optimal tolerances depend on the stackup coefficients of the output characteristic, which are calculated with a tolerance analysis method based on a static analogy. The procedure is demonstrated on two examples to illustrate some application details and discuss potential advantages and limitations.

15

Hu, J., and Y. Peng. "Tolerance modelling and robust design for concurrent engineering." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221, no. 4 (April 1, 2007): 455–65. http://dx.doi.org/10.1243/0954406jmes438.

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This article presents a tolerance modelling and robust design approach to support concurrent engineering. This method allows the designer to synthetically specify dimensional and geometric tolerance, considering assembly functional requirements (AFRs) and manufacturing costs. First, features of ISO/TC 213 are used as the basis for the construction of tolerance network and tolerance model for assembly. Second, the manufacturing cost-tolerance model for cylindrical and planar features is established. This model addresses not only dimensional tolerances but also geometric tolerances and nominal parameters. Finally, the robust tolerance optimization model is established, and genetic arithmetic is used to obtain robust tolerance values. The proposed approach is consistent with the philosophy of concurrent engineering, in which AFRs are satisfied and manufacturing cost is reduced. A design instance is introduced to show the validity of this method.

16

Feng, Chang-Xue (Jack), and Andrew Kusiak. "Robust Tolerance Synthesis With the Design of Experiments Approach." Journal of Manufacturing Science and Engineering 122, no. 3 (May 1, 1999): 520–28. http://dx.doi.org/10.1115/1.1285860.

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Design of tolerances impacts quality, cost, and cycle time of a product. Most literature on deterministic tolerance design has focused on developing exact and heuristic algorithms to minimize manufacturing cost. Some research has been published on probabilistic tolerance synthesis and optimization. This paper presents the design of experiments (DOE) approach for concurrent selection of component tolerances and the corresponding manufacturing processes. The objective is to minimize the variation of tolerance stackups. Numerical examples illustrate the methodology. The Monte Carlo simulation approach is used to obtain component tolerances and tolerance stackups. Process shift, the worst case and root sum square tolerance stackup constraints, and setup reduction constraints have been incorporated into the proposed methodology. Benefits of the proposed DOE approach over exact algorithms are discussed. [S1087-1357(00)00202-1]

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Li, Hang, Songgang Xu, and John Keyser. "Optimization for statistical tolerance allocation." Computer Aided Geometric Design 75 (November 2019): 101788. http://dx.doi.org/10.1016/j.cagd.2019.101788.

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Dong, Z., W. Hu, and D. Xue. "New Production Cost-Tolerance Models for Tolerance Synthesis." Journal of Engineering for Industry 116, no. 2 (May 1, 1994): 199–206. http://dx.doi.org/10.1115/1.2901931.

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Several new production cost-tolerance models and a hybrid-model tolerance optimization formulation for tolerance synthesis are presented. These new models are introduced based upon the empirical cost-tolerance data of typical production processes, including hole producing, turning, milling, grinding and casting. The introduced models fit empirical cost-tolerance data with considerably less errors, and provide more reliable results for tolerance synthesis. In addition, the hybrid-model tolerance optimization formulation provides further modeling error reduction. The systematic evaluation of various cost-tolerance models provides model selection guidelines for tolerance synthesis. A typical tolerance design example is used to illustrate the method.

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Chen, Hua, and Xin Li. "Tolerance analysis of involute spur gear from the perspective of design." Mechanics & Industry 23 (2022): 16. http://dx.doi.org/10.1051/meca/2022013.

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The existing gears’ tolerance standards are formulated from the point of view of manufacturing and measurement. Tolerance categories are numerous. What is more, they have no correlation with each other. Tolerance analysis and optimization of gear and gear set are difficult. Module, pressure angle and center distance are the most important parameters for gears. Their variations directly affect the transmission precision of gears. Through careful research of the influence of deviations of module and pressure angle, a novel method of gear tolerance analysis is proposed in this paper from the perspective of design. For a single gear, tolerance specification and analysis only pay attention to these two tolerances. The influence of fluctuation of center distance for a gear set is also studied. Meanwhile, the calculation method of sensitivities and percent contributions about related parameters is introduced, which provides the basis for tolerance optimization. At last, a simple case is studied, which demonstrates the validity and novelty of the present work.

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Stefano, P. Di. "Tolerance analysis and synthesis using the mean shift model." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 217, no. 2 (February 1, 2003): 149–59. http://dx.doi.org/10.1243/095440603762826477.

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Tolerance design plays an important role in the modern design process by introducing quality improvements and limiting manufacturing costs. In this paper a method for statistical tolerance analysis and synthesis is presented. This method is implemented using the mean shift model of Chase and Greenwood, providing a systematic approach to evaluate the mean shift factor. This method considers all the principal factors that affect the statistical sum of a certain number of assembly dimensions. In particular, the considered factors include the mean shift ratio, the confidence level, the number of dimension of the assembly and the tolerance assortment between the component dimensions. An implementation of the mean shift model for tolerances synthesis is described. The tolerances synthesis is performed in an unusual way, taking into account in the optimization process the typical parameters that affect the product variability. For this purpose the method uses four types of condition for the dimensional tolerances: fixed tolerance value, fixed mean shift ratio, fixed mean shift and fixed natural variability. Furthermore, in the optimization process, the service variability is considered under two conditions: fixed and valuable service variability. A case study is presented and the results of some simulations are discussed.

21

Miah, Md Helal, Jianhua Zhang, and Dharmahinder Singh Chand. "Knowledge creation and application of optimal tolerance distribution method for aircraft product assembly." Aircraft Engineering and Aerospace Technology 94, no. 3 (November 23, 2021): 431–36. http://dx.doi.org/10.1108/aeat-07-2021-0193.

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Purpose This paper aims to illustrate the tolerance optimization method based on the assembly accuracy constrain, precession constrain and the cost of production of the assembly product. Design/methodology/approach A tolerance optimization method is an excellent way to perform product assembly performance. The tolerance optimization method is adapted to the process analysis of the hatch and skin of an aircraft. In this paper, the tolerance optimization techniques are applied to the tolerance allocation for step difference analysis (example: step difference between aircraft cabin door and fuselage outer skin). First, a mathematical model is described to understand the relationship between manufacturing cost and tolerance cost. Second, the penalty function method is applied to form a new equation for tolerance optimization. Finally, MATLAB software is used to calculate 170 loops iteration to understand the efficiency of the new equation for tolerance optimization. Findings The tolerance optimization method is based on the assembly accuracy constrain, machinery constrain and the cost of production of the assembly product. The main finding of this paper is the lowest assembly and lowest production costs that met the product tolerance specification. Research limitations/implications This paper illustrated an efficient method of tolerance allocation for products assembly. After 170 loops iterations, it founds that the results very close to the original required tolerance. But it can easily say that the different number of loops iterations may have a different result. But optimization result must be approximate to the original tolerance requirements. Practical implications It is evident from Table 4 that the tolerance of the closed loop is 1.3999 after the tolerance distribution is completed, which is less than and very close to the original tolerance of 1.40; the machining precision constraint of the outer skin of the cabin door and the fuselage is satisfied, and the assembly precision constraint of the closed loop is satisfied. Originality/value The research may support further research studies to minimize cost tolerance allocation using tolerance cost optimization techniques, which must meet the given constrain accuracy for assembly products.

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Sing, P. K., S. C. Jain, and P. K. Jain. "Comparative study of genetic algorithm and simulated annealing for optimal tolerance design formulated with discrete and continuous variables." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 219, no. 10 (October 1, 2005): 735–58. http://dx.doi.org/10.1243/095440505x32643.

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Optimal tolerance design has been the focus of extensive research for a few decades. This has resulted in several formulations and solution algorithms for systematic tolerance design considering various aspects. Availability of different alternative manufacturing processes or machines for realization of a dimension is frequently encountered. In such cases optimal tolerance design must also consider optimal selection of a set of manufacturing processes or machines as appropriate. Such a non-linear multivariate optimal tolerance design problem results in a combinatorial and multi-modal solution space. Optimal solution of this advanced tolerance design problem is difficult using traditional optimization techniques. The problem formulation becomes more complex with simultaneous selection of design and manufacturing tolerances. The focus of the current research is on the optimal solution of this advanced and complex tolerance design problem. Genetic algorithm and simulated annealing as non-traditional global optimization techniques have been used to obtain the solution. Application of the solution techniques has been demonstrated with the help of appropriate examples. Comparison of the results establishes that the genetic algorithm is the superior of the two approaches.

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Kusiak, A., and Chang-Xue Feng. "Robust Tolerance Design for Quality." Journal of Engineering for Industry 118, no. 1 (February 1, 1996): 166–69. http://dx.doi.org/10.1115/1.2803639.

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Design of a product (process) includes system design, parameter design, and tolerance design. Robust design is closely applicable to parameter design and tolerance design. The current literature on robust design has focused on parameter design while the problem of tolerance design has not been adequately covered. The tolerance design literature emphasizes the use of optimization to minimize cost while little attention has been paid to minimizing the sensitivity of tolerances to the variation of manufacturing processes. This paper discusses the application of the design of experiments (DOE) approach to tolerance synthesis to minimize manufacturing variations in a probabilistic case. The DOE approach is illustrated with an example.

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Li, Chun Yan, Cong Dong Ji, and Kai Ding. "The Tolerance Optimization Design of Displacement Pump." Advanced Materials Research 605-607 (December 2012): 376–79. http://dx.doi.org/10.4028/www.scientific.net/amr.605-607.376.

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The paper provided an overview of computer aided tolerance design and described the research methods of tolerance design. An example of a displacement pump was employed to analyze the angle and linear tolerance. With the application of tolerance optimization design of CAD assemblies combined with tolerance annotation and tolerance accumulation validation, the product design can be optimized and the cost can be reduced effectively.

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Yang, Kaili, Yi Gan, Yanlong Cao, Jiangxin Yang, and Zijian Wu. "Optimization of 3D Tolerance Design Based on Cost–Quality–Sensitivity Analysis to the Deviation Domain." Automation 4, no. 2 (April 21, 2023): 123–50. http://dx.doi.org/10.3390/automation4020009.

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Under the new geometric product specification (GPS), a two-dimensional chain cannot completely guarantee quality of the product. To optimize the allocation of three-dimensional tolerances in the conceptual design stage, the geometric variations of the tolerance zone to the deviation domain will be mapped in this paper. The deviation-processing cost, deviation-quality loss cost, and deviation-sensitivity cost function relationships combined with the tolerance zone described by the small displacement torsor theory are discussed. Then, synchronous constraint of the function structure and tolerance is realized. Finally, an improved bat algorithm is used to solve the established three-dimensional tolerance mathematical model. A case study in the optimization of three-part tolerance design is used to illustrate the proposed model and algorithms. The performance and advantage of the proposed method are discussed in the end.

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Lee, W. J., and T. C. Woo. "Optimum Selection of Discrete Tolerances." Journal of Mechanisms, Transmissions, and Automation in Design 111, no. 2 (June 1, 1989): 243–51. http://dx.doi.org/10.1115/1.3258990.

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Tolerancing involves considerations from all phases of the life cycle of a product including design, manufacturing, assembly, and inspection. Along with minimum cost and maximum functionality and interchangeability, the practice of tolerancing urges a designer to choose an appropriate manufacturing (or inspection) process as well. This situation is formalized as a discrete optimization problem. For an optimum selection of tolerances from a given discrete model involving various manufacturing processes, minimization of manufacturing cost is achieved under the constraint of tolerance stack-up. A random variable and its standard deviation are associated with a dimension and its tolerance. This probabilistic approach enables a trade-off between performance and tolerance (cost). But it also suggests probabilistic optimization. With the aid of a notion called the reliability index [8], tolerance selection is formulated as an integer programming problem. A branch and bound algorithm for ensuring optimum selection is developed by exploiting the special structure of the constraints. To make the enumeration tree small, monotonic relations among the reliability index, cost, and tolerance are examined. The algorithm is tested with examples.

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Heo, Seongku, Jaeyoo Choi, Yooseong Park, Neil Vaz, and Hyunchul Ju. "Reliability-Based Design Optimization of the PEMFC Flow Field with Consideration of Statistical Uncertainty of Design Variables." Energies 17, no. 8 (April 15, 2024): 1882. http://dx.doi.org/10.3390/en17081882.

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Recently, with the fourth industrial revolution, the research cases that search for optimal design points based on neural networks or machine learning have rapidly increased. In addition, research on optimization is continuously reported in the field of fuel cell research using hydrogen as fuel. However, in the case of optimization research, it often requires a large amount of training data, which means that it is more suitable for numerical research such as CFD simulation rather than time-consuming research such as actual experiments. As is well known, the design range of fuel cell flow channels is extremely small, ranging from hundreds of microns to several millimeters, which means the small tolerance could cause fatal performance loss. In this study, the general optimization study was further improved in terms of reliability by considering stochastic tolerances that may occur in actual industry. The optimization problem was defined to maximize stack power, which is employed as objective function, under the constraints such as pressure drop and current density standard deviation; the performance of the optimal point through general optimization was about 3.252 kW/L. In the reliability-based optimization problem, the boundary condition for tolerance was set to 0.1 mm and tolerance was assumed to occur along a normal distribution. The optimal point to secure 99% reliability for the given constraints was 2.918 kW/L, showing significantly lower performance than the general optimal point.

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Sun, Wei, Xiaokai Mu, Qingchao Sun, Zhiyong Sun, and Xiaobang Wang. "Analysis and optimization of assembly precision-cost model based on 3D tolerance expression." Assembly Automation 38, no. 4 (September 3, 2018): 497–510. http://dx.doi.org/10.1108/aa-10-2017-137.

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PurposeThis paper aims to comprehensively achieve the requirements of high assembly precision and low cost, a precision-cost model of assembly based on three-dimensional (3D) tolerance is established in this paper.Design/methodology/approachThe assembly precision is related to the tolerance of parts and the deformation of matching surfaces under load. In this paper, the small displacement torsor (SDT) theory is first utilized to analyze the manufacturing tolerances of parts and the assembly deformation deviation of matching surface. In the meanwhile, the extracting method of SDT parameters is proposed and the assembly precision calculation model based on the 3D tolerance is established. Second, an integrated optimization model based on the machining cost, assembly cost (mapping the deviation domain to the SDT domain) and quality loss cost is built. Finally, the practicability of the precision-cost model is verified by optimizing the horizontal machining center.FindingsThe assembly deviation has a great influence on cost fluctuation. By setting the optimization objective to maximize the assembly precision, the optimal total cost is CNY 72.77, decreasing by 16.83 per cent from the initial value, which meets economical requirements. Meanwhile, the upper bound of each processing tolerance is close to the maximum value of 0.01 mm, indicating that the load deformation can be offset by appropriately increasing the upper bound of the tolerance, but it is necessary to strictly restrict the manufacturing tolerances of lower parts in a reasonable range.Originality/valueIn this paper, a 3D deviation precision-cost model of assembly is established, which can describe the assembly precision more accurately and achieve a lower cost compared with the assembly precision model based on rigid parts.

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Zhou Wei, W., M. Moore, and F. Kussener. "Visual tolerance analysis for engineering optimization." International Journal of Metrology and Quality Engineering 4, no. 3 (2013): 153–62. http://dx.doi.org/10.1051/ijmqe/2013056.

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KHAIRY, PAUL, MARIO TALAJIC, MANUEL DOMINGUEZ, JEAN-CLAUDE TARDIF, MARTIN JUNEAU, LINDA LAVOIE, DENIS ROY, and MARC DUBUC. "Atrioventricular Interval Optimization and Exercise Tolerance." Pacing and Clinical Electrophysiology 24, no. 10 (October 2001): 1534–40. http://dx.doi.org/10.1046/j.1460-9592.2001.01534.x.

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Hallmann, Martin, Benjamin Schleich, and Sandro Wartzack. "From tolerance allocation to tolerance-cost optimization: a comprehensive literature review." International Journal of Advanced Manufacturing Technology 107, no. 11-12 (April 2020): 4859–912. http://dx.doi.org/10.1007/s00170-020-05254-5.

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阮, 天昊. "Motor Tolerance Optimization Design Based on Particle Swarm Optimization Algorithm." Modeling and Simulation 12, no. 02 (2023): 1107–16. http://dx.doi.org/10.12677/mos.2023.122105.

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Khodaygan, S. "A framework for tolerance design considering systematic and random uncertainties due to operating conditions." Assembly Automation 39, no. 5 (November 4, 2019): 854–71. http://dx.doi.org/10.1108/aa-10-2018-0160.

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Purpose The purpose of this paper is to present a novel Kriging meta-model assisted method for multi-objective optimal tolerance design of the mechanical assemblies based on the operating conditions under both systematic and random uncertainties. Design/methodology/approach In the proposed method, the performance, the quality loss and the manufacturing cost issues are formulated as the main criteria in terms of systematic and random uncertainties. To investigate the mechanical assembly under the operating conditions, the behavior of the assembly can be simulated based on the finite element analysis (FEA). The objective functions in terms of uncertainties at the operating conditions can be modeled through the Kriging-based metamodeling based on the obtained results from the FEA simulations. Then, the optimal tolerance allocation procedure is formulated as a multi-objective optimization framework. For solving the multi conflicting objectives optimization problem, the multi-objective particle swarm optimization method is used. Then, a Shannon’s entropy-based TOPSIS is used for selection of the best tolerances from the optimal Pareto solutions. Findings The proposed method can be used for optimal tolerance design of mechanical assemblies in the operating conditions with including both random and systematic uncertainties. To reach an accurate model of the design function at the operating conditions, the Kriging meta-modeling is used. The efficiency of the proposed method by considering a case study is illustrated and the method is verified by comparison to a conventional tolerance allocation method. The obtained results show that using the proposed method can lead to the product with a more robust efficiency in the performance and a higher quality in comparing to the conventional results. Research limitations/implications The proposed method is limited to the dimensional tolerances of components with the normal distribution. Practical implications The proposed method is practically easy to be automated for computer-aided tolerance design in industrial applications. Originality/value In conventional approaches, regardless of systematic and random uncertainties due to operating conditions, tolerances are allocated based on the assembly conditions. As uncertainties can significantly affect the system’s performance at operating conditions, tolerance allocation without including these effects may be inefficient. This paper aims to fill this gap in the literature by considering both systematic and random uncertainties for multi-objective optimal tolerance design of mechanical assemblies under operating conditions.

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Yang, Zhaohui, Wenrong Yang, Tianshi Gao, and Yu Zhang. "Tolerance analysis method considering multifactor coupling based on the Jacobian–torsor model." Advances in Mechanical Engineering 14, no. 12 (December 2022): 168781322211402. http://dx.doi.org/10.1177/16878132221140215.

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Assembly quality affects the performance of mechanical products and reasonable tolerance designs are central to assembly quality. Unreasonable tolerance design leads to the mechanical equipment performance degradation under complex operating conditions. This study developed a novel tolerance analysis method that considers the influence of temperature, load, and other environmental factors based on the Jacobian–torsor and skin models. First, the deformation caused by multifactor coupling was analyzed using the finite element method, and the feature surface of deformation is extracted. Second, the deformation extraction and tolerance conversion based on the new generation geometrical product specification theory was used to convert the deformation of the feature into the dimension, orientation, and form tolerance. Third, the modified Jacobian–torsor model considering multifactor coupling was constructed by superimposing the converted tolerance with the design tolerances. Finally, the abrasion problem of the airborne actuator was considered as an example to verify the effectiveness and accuracy of the novel method. Through the accurate calculation of tolerances, it accurately analyzes the assembly state of the product under the influence of environmental factors, and provides more accurate guidance for the design and optimization of product tolerance in complex working conditions.

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El Hraiech, Safa, Ahmed H. Chebbi, Zouhaier Affi, and Lotfi Romdhane. "Genetic Algorithm Coupled with the Krawczyk Method for Multi-Objective Design Parameters Optimization of the 3-UPU Manipulator." Robotica 38, no. 6 (August 27, 2019): 1138–54. http://dx.doi.org/10.1017/s0263574719001292.

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SUMMARYIn this paper, a multi-objective design optimization of the 3-UPU translational parallel manipulator is presented. Based on a new algorithm, which combines the genetic algorithms and the Krawczyk operator, the robot position error is minimized and the robot design parameters tolerances are maximized, simultaneously. The results show that the designer can maintain the manipulator accuracy by using a specific size of the base, and can restrict its tolerance even by enlarging the actuators’ tolerance intervals. This algorithm is also used to determine the maximum design parameters tolerances for an allowable robot position error. The proposed algorithm can be extended to optimize other types of robots.

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Wu, Di, Xiaofei Ma, Jinbao Chen, Chuanzhi Chen, Jiang Zhao, and Kunyang Lin. "Multiobjective Optimization Design of Truss Antenna." International Journal of Aerospace Engineering 2022 (December 5, 2022): 1–8. http://dx.doi.org/10.1155/2022/6125831.

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During the design and manufacturing process of the truss antenna, the surface accuracy of the truss antenna is inherently affected by tolerance. An appropriate optimal design of the truss antenna structure is important to improve surface accuracy. In order to receive the optimal design of the truss structure, this paper adopts the multiobjective optimization algorithm based on an approximate model to optimize the tolerance model with random error. Firstly, considering the influence of the processing and assembly errors of the members on the surface accuracy of the structure, the equilibrium state equation of the truss is established by the principle of minimum potential energy. Then, the relationship between the tolerance and the surface accuracy is obtained by the Monte Carlo method. For improving the computing efficiency of the Monte Carlo method, an approximate model of the truss antenna unit is established, where the rod length tolerance is set as the design variable, and the truss surface accuracy and processing cost are set as the objective functions. Finally, tolerance optimization is carried out by using the multiobjective genetic algorithm. The results indicate that the Pareto solution is obtained with an error less than 10%. Moreover, a set of solutions of the tolerance are obtained which can meet different antenna design requirements. And the results show that the influence of the web rod is significantly greater than that of the bottom rod on the surface accuracy of the structure.

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Wang, Ping, Xiang Liu, Zhe Luo, and Yi Zhang. "Research on Tolerance Optimization of High Precision Equipment Assembly Based on Error Transfer Prediction Model." Journal of Physics: Conference Series 2650, no. 1 (November 1, 2023): 012012. http://dx.doi.org/10.1088/1742-6596/2650/1/012012.

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Abstract In this paper, the assembly error transfer prediction model was established based on the error transfer attribute and the error transfer path of the assembly process. The assembly accuracy prediction was realized by combining error variation inequality, constraint inequality and mathematical statistics method. Aiming at the lowest processing cost of high-precision equipment assembly, the assembly accuracy required the reliability of index, the value interval of tolerance item and the principle of tolerance selection as constraints, the tolerance optimization model was established. The tolerance optimization of high-precision equipment assembly was carried out by combining the penalty function method and the improved genetic algorithm. Finally, taking gear oil pump assembly as an example, according to the reliability calculation formula of assembly accuracy, the reliability is 97.35%. Compared with the processing cost before and after optimization, the processing cost decreased by 12.13% after optimization, and the assembly accuracy reliability increased by 1.65%. The correctness and effectiveness of assembly accuracy prediction and tolerance optimization are verified.

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Zeng, Wenhui, Jin Yi, Rongfu Lin, and Wenlong Lu. "Statistical tolerance–cost–service life optimization of blade bearing of controllable pitch propeller considering the marine environment conditions through meta-heuristic algorithm." Journal of Computational Design and Engineering 9, no. 2 (April 2022): 689–705. http://dx.doi.org/10.1093/jcde/qwac023.

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Abstract Blade bearing is the key mechanism of the controllable pitch propellers (CPPs) to adjust the pitch to change the thrust. In the marine environment, wear and deformation of the contact surface of the blade bearing are quite large, which may result in leakage to reduce the service life of CPP. However, most studies on tolerance optimization of blade bearing disregard deformations and wear, and it could result in unreasonable tolerances and impair the CPP’s service life. In this paper, to establish the statistical tolerance–cost–service life optimization model of the blade bearing of the CPP considering the marine environment effects in propellers, a prediction model about the relationship between the thrust and rotation speed of the CPP considering environment conditions of wind, wave, and ocean currents is constructed. Based on this, the wear and deformation are simulated according to the predicted rotation speed in the marine environment. Considering the deformation and wear in the marine environment, a tolerance analysis model of the assembly deviations of the blade bearing is introduced, and the assembly characteristics and functional requirements are established and converted into probability constraints to establish the service-life model based on statistical tolerance analysis and Monte Carlo simulation methods. Afterward, a statistical tolerance–cost–service life optimization model is established and transformed into a single-objective optimization problem through the normalization method and the weighted sum method, and solved by a meta-heuristic algorithm named cuckoo search. Finally, the application of the proposed model is demonstrated through a case involving the blade bearing of a CPP, and the optimized results show that the manufacturing cost of the blade bearing is reduced and its service life is extended.

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Hamasuna, Yukihiro, Yasunori Endo, and Sadaaki Miyamoto. "On Tolerant Fuzzyc-Means Clustering." Journal of Advanced Computational Intelligence and Intelligent Informatics 13, no. 4 (July 20, 2009): 421–28. http://dx.doi.org/10.20965/jaciii.2009.p0421.

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This paper presents a new type of clustering algorithms by using a tolerance vector called tolerant fuzzyc-means clustering (TFCM). In the proposed algorithms, the new concept of tolerance vector plays very important role. In the original concept of tolerance, a tolerance vector attributes to each data. This concept is developed to handle data flexibly, that is, a tolerance vector attributes not only to each data but also each cluster. Using the new concept, we can consider the influence of clusters to each data by the tolerance. First, the new concept of tolerance is introduced into optimization problems based on conventional fuzzyc-means clustering (FCM). Second, the optimization problems with tolerance are solved by using Karush-Kuhn-Tucker conditions. Third, new clustering algorithms are constructed based on the explicit optimal solutions of the optimization problems. Finally, the effectiveness of the proposed algorithms is verified through numerical examples by fuzzy classification function.

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Yu, Chunxia, and Yuru Liu. "A Personalized Mean-CVaR Portfolio Optimization Model for Individual Investment." Mathematical Problems in Engineering 2021 (March 8, 2021): 1–12. http://dx.doi.org/10.1155/2021/8863597.

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Investment as an important issue in daily life is accompanied by the occurrence of various financial assets, such as stocks, bonds, and mutual funds. However, risk tolerances vary across individuals. Individual investors have to select corresponding personalized investment portfolios to satisfy their own needs. Moreover, it is difficult for ordinary people to select a personalized investment portfolio by themselves, and it is too expensive and inefficient to look for professional consultation. Therefore, the objective of this research is to propose a personalized portfolio recommendation model, which can build the personalized portfolio based on investors’ risk tolerances. In this research, investors’ risk tolerance is determined by the fuzzy comprehensive evaluation method based on investors’ demographic characteristics. The CVaR is used as the risk measurement of financial assets. The dynamics of the distribution of returns are described in the combined Copula-GARCH model, and the future scenarios of returns are generated by the Monte Carlo simulation based on the combined Copula-GARCH model to estimate CVaR. The mean-CVaR portfolio optimization model is used to find out the best personalized portfolio. Finally, experiments are conducted to validate the applicability and feasibility of the personalized investment portfolio optimization model. Results show that the proposed investment portfolio optimization model can recommend personalized investment portfolio according to investor’s risk tolerance.

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Ayadi, Badreddine, Lotfi Ben Said, Mohamed Boujelbene, and Sid Ali Betrouni. "Three-Dimensional Synthesis of Manufacturing Tolerances Based on Analysis Using the Ascending Approach." Mathematics 10, no. 2 (January 10, 2022): 203. http://dx.doi.org/10.3390/math10020203.

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The present paper develops a new approach for manufacturing tolerances synthesis to allow the distribution of these tolerances over the different phases concerned in machining processes using relationships written in the tolerance analysis phase that have been well developed in our previous works. The novelty of the proposed approach is that the treatment of non-conventional surfaces does not pose a particular problem, since the toleranced surface is discretized. Thus, it is possible to study the feasibility of a single critical requirement as an example. During the present approach, we only look for variables that influence the requirements and the others are noted F (Free). These variables can be perfectly identified on the machine, which can be applied for known and unknown machining fixtures; this can be the base for proposing a normalized ISO specification used in the different machining phases of a mechanical part. The synthesis of machining tolerances takes place in three steps: (1) Analysis of the relationship’s terms, which include the influence of three main defects; the deviation on the machined surface, defects in the machining set-up, and the influence of positioning dispersions; then (2) optimization of machining tolerance through a precise evaluation of these effects; and finally (3) the optimization of the precision of the workpiece fixture, which will give the dimensioning of the machining assembly for the tooling and will allow the machining assembly to be qualified. The approach used proved its efficiency in the end by presenting the optimal machining process drawing that explains the ordered phases needed to process the workpiece object of the case study.

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Shi, Xiaolin, Xitian Tian, Gangfeng Wang, and Dongping Zhao. "Semantic-Based Assembly Precision Optimization Strategy Considering Assembly Process Capacity." Machines 9, no. 11 (November 4, 2021): 269. http://dx.doi.org/10.3390/machines9110269.

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Assembly precision optimization is an important means to ensure product accuracy, including two aspects: on the one hand, the relevant deviations of out-of-tolerance key characteristics are reduced to the design tolerance range; on the other hand, the deviation fluctuation range of key characteristics with a large process capability index (Cp) can be extended to achieve the balance between accuracy, process capacity, and production cost. By virtue of the accumulated experience, a fast solution can be provided for the out-of-tolerance problem. Therefore, a semantic-based assembly precision optimization method considering process capacity is proposed in this paper. By constructing an ontology model between Cp and optimization strategy, a reasonable assembly precision optimization strategy can be pushed based on product accuracy analysis results. Firstly, an assembly precision optimization semantic model is established by association between analysis results, out-of-tolerance key characteristics, assembly process, and tolerance adjustment defined with Web Ontology Language (OWL) assertions. Furtherly, according to different Cp corresponding to different assembly success rates, Semantics Web Rule Language (SWRL) rules based on Cp are constructed to the push optimization strategy. Finally, the effectiveness of the model is illustrated by an aircraft inner flap.

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Walter, Michael S. J., Christina Klein, Björn Heling, and Sandro Wartzack. "Statistical Tolerance Analysis—A Survey on Awareness, Use and Need in German Industry." Applied Sciences 11, no. 6 (March 16, 2021): 2622. http://dx.doi.org/10.3390/app11062622.

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The importance of geometric deviations of components for the aesthetic and functional quality of products has been undisputed for decades. So, it is not surprising that not only have numerous researchers devoted themselves to this field, but also commercial software tools for the analysis and optimization of tolerance specifications (currently already fully integrated in 3D-CAD systems) have been available for around 30 years. However, it is even more surprising that the well-founded specification of tolerances and their analysis using a so-called statistical tolerance analysis are only established in a few companies. There is thus a contradiction between the proclaimed relevance of tolerances and their actual consideration in everyday business life. Thus, the question of the significance of geometric deviations and tolerances as well as the use of statistical tolerance analysis arises. Therefore, a survey among 102 German companies was carried out. The results are presented and discussed in this paper.

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Jeang, A. "Tolerance chart optimization for quality and cost." International Journal of Production Research 36, no. 11 (November 1998): 2969–83. http://dx.doi.org/10.1080/002075498192238.

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Xu, Songgang, and John Keyser. "Geometric computation and optimization on tolerance dimensioning." Computer-Aided Design 46 (January 2014): 129–37. http://dx.doi.org/10.1016/j.cad.2013.08.025.

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Ray, Subhasis, and David Lowther. "Tolerance and multiobjective optimization in electromagnetic devices." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 28, no. 4 (July 10, 2009): 1020–32. http://dx.doi.org/10.1108/03321640910959071.

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Mao, J., Y. L. Cao, S. Q. Liu, and J. X. Yang. "Manufacturing environment-oriented robust tolerance optimization method." International Journal of Advanced Manufacturing Technology 41, no. 1-2 (April 3, 2008): 57–65. http://dx.doi.org/10.1007/s00170-008-1460-2.

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Vihola, Matti, and Jordan Franks. "On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction." Biometrika 107, no. 2 (February 3, 2020): 381–95. http://dx.doi.org/10.1093/biomet/asz078.

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Summary Approximate Bayesian computation enables inference for complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often sensitive to the tolerance parameter: low tolerance leads to poor mixing and large tolerance entails excess bias. We propose an approach that involves using a relatively large tolerance for the Markov chain Monte Carlo sampler to ensure sufficient mixing and post-processing the output, leading to estimators for a range of finer tolerances. We introduce an approximate confidence interval for the related post-corrected estimators and propose an adaptive approximate Bayesian computation Markov chain Monte Carlo algorithm, which finds a balanced tolerance level automatically based on acceptance rate optimization. Our experiments show that post-processing-based estimators can perform better than direct Markov chain Monte Carlo targeting a fine tolerance, that our confidence intervals are reliable, and that our adaptive algorithm leads to reliable inference with little user specification.

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Li, Li-li, Kun Chen, Jian-min Gao, Jun-kong Liu, Zhi-yong Gao, and Man-xian Wang. "Multiobjective Optimization Method and Application of Tolerance Allocation for the Steam Turbine Based on Cooperative Game Theory." Shock and Vibration 2021 (November 16, 2021): 1–13. http://dx.doi.org/10.1155/2021/9244389.

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Aiming at the optimization problem of multiple objectives with contradictions and conflicts in the process of allocating the tolerance for complex products, taking advantage of the features of coordinating, and balancing contradictions and conflicts of cooperative game theory, this paper uses cooperative game theory to solve the multiobjective optimization problem of tolerance allocation. The quality requirements and cost requirements of assembly products are used as the game decision parties, and the fuzzy clustering method is used to group the design variables of tolerance allocation problem of the steam turbine to form the strategic space of game parties. Take the quality level and cost level of the assembly product as the optimization goals, complete the calculation of the utilities of the two game parties, and establish the multiobjective optimization model of tolerance allocation based on cooperative game theory. Finally, the Shapley value method based on cooperative game theory, the Nash equilibrium method based on noncooperative game theory, and the traditional single-objective optimization method with the quality as the constraint and the cost as the optimization objective are used to solve the tolerance allocation problem of steam turbine. The solution results show that the method of cooperative game realized the balance, coordination, and comprehensive optimization of the quality and cost from the perspective of collective interests, overcame the shortcomings of the traditional single-objective optimization method, and obtained better result than the Nash equilibrium method.

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Orosz, Tamás, Krisztián Gadó, Mihály Katona, and Anton Rassõlkin. "Automatic Tolerance Analysis of Permanent Magnet Machines with Encapsuled FEM Models Using Digital-Twin-Distiller." Processes 9, no. 11 (November 19, 2021): 2077. http://dx.doi.org/10.3390/pr9112077.

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Tolerance analysis is crucial in every manufacturing process, such as electrical machine design, because tight tolerances lead to high manufacturing costs. A FEM-based solution of the tolerance analysis of an electrical machine can easily lead to a computationally expensive problem. Many papers have proposed the design of experiments, surrogate-model-based methodologies, to reduce the computational demand of this problem. However, these papers did not focus on the information loss and the limitations of the applied methodologies. Regardless, the absolute value of the calculated tolerance and the numerical error of the applied numerical methods can be in the same order of magnitude. In this paper, the tolerance and the sensitivity of BLDC machines’ cogging torque are analysed using different methodologies. The results show that the manufacturing tolerances can have a significant effect on the calculated parameters, and that the mean value of the calculated cogging torque increases. The design of the experiment-based methodologies significantly reduced the calculation time, and shows that the encapsulated FEM model can be invoked from an external system-level optimization to examine the design from different aspects.

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