Non-Normal Statistical Tolerance Analysis Using Analytical Convolution Method

Liu, S. G.; Wang, P.; Li, Z. G.

doi:10.1142/s0219686708001218

Cited by 3 publications

(4 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was also demonstrated how the process can be used to determine if existing part tolerances in an assembly make it impossible to achieve the desired KPC dimension tolerances. Furthermore, the approach is deterministic and welldefined compared to a statistical approach that may differ in its results at different manufacturing sites [39], [40], [41] and [42].…”

Section: Discussionmentioning

confidence: 99%

Using CAD parameter sensitivities for stack-up tolerance allocation

Din

Robinson

Armstrong

et al. 2014

Int J Interact Des Manuf

View full text Add to dashboard Cite

Tolerance allocation is an important step in the design process. It is necessary to produce high quality components cost effectively. However, the process of allocating tolerances can be time consuming and difficult, especially for complex models. This work demonstrates a novel CAD based approach, where the sensitivities of product dimensions to changes in the values of the feature parameters in the CAD model are computed. These are used to automatically establish the assembly response function for the product. This information has been used to automatically allocate tolerances to individual part dimensions to achieve specified tolerances on the assembly dimensions, even for tolerance allocation in more than one direction simultaneously. It is also shown how pre-existing constraints on some of the part dimensions can be represented and how situations can be identified where the required tolerance allocation is not achievable. A methodology is also presented that uses the same information to model a component with different amounts of dimensional variation to simulate the effects of tolerance stack-up.

show abstract

Section: Discussionmentioning

confidence: 99%

Using CAD parameter sensitivities for stack-up tolerance allocation

Din

Robinson

Armstrong

et al. 2014

Int J Interact Des Manuf

View full text Add to dashboard Cite

show abstract

“…Chase [5] transformed the tolerance interval of the product into a constraint condition, and used the Lagrange multiplier method to solve the inequality, thereby completing the optimization of the tolerance value. Liu [8] put forward the calculation method of optimal tolerance under different conditions based on the validity of assembly accuracy constraint and machining accuracy constraint, and solved the tolerance optimization model by using analytical method, and obtained the analytical solution of optimal tolerance of each composing ring. Bjorke [9] used linear programming to obtain the optimal solution of tolerance by solving the objective function linearly with the constraint condition of tolerance value as the feasible region.…”

Section: Tolerance-cost Modelmentioning

confidence: 99%

Research on antenna installation tolerance design based on genetic algorithm

Hua

Kang

Tan

2023

Third International Conference on Mechanical, Electronics, and Electrical and Automation Control (METMS 2023)

View full text Add to dashboard Cite

In modern manufacturing industry, the impact of tolerance cost is increasing fast, and reasonable tolerance design plays an important role. Product manufacturing cost was taken as the research object in this paper, the appropriate cost tolerance model was selected, and the tolerance optimization model was established by combining genetic algorithm. Taking antenna window installation as an example, the closed loop dimension chain analysis was carried out first. Then the power exponential tolerance model was used to obtain the cost parameters through the empirical method. Finally, the tolerance optimization problem was transformed into a multi-objective optimization mathematical model. The tolerance values were obtained by genetic algorithm and compared with the equal tolerance method. The results were shown that the manufacturing cost can be effectively reduced by the minimum cost method.

show abstract

“…Varghese [14] utilized the probability distribution function for manufacturing data, together with a numerical method, to perform rapid statistical tolerance stack-up analyses. Similarly, Liu [15] used convolution to compute probability density functions to describe closed-loop components analytically. Tsai [16] proposed a moment-based method to compute the resultant tolerance to deal with non-normal error distributions with variance, skewness, and kurtosis.…”

Section: Literature Reviewmentioning

confidence: 99%

“…(14), (15), (17), and (18), the variances of all displacements of the rectangular plane can be expressed as…”

Section: Variation In a Planementioning

confidence: 99%

Efficient statistical analysis of geometric tolerances using unified error distribution and an analytical variation model

Chongying

Liu

Jiang

2015

Int J Adv Manuf Technol

View full text Add to dashboard Cite

Inaccuracies in conventional tolerance characterization methods, which are based on worst-case and rootsquare-error methods, as well as inefficiencies in Monte Carlo computational methods of statistical tolerance analysis, require an accurate and efficient method of statistical analysis of geometric tolerances. Here, we describe a unified error distribution model for various types of geometric tolerance to obtain the distribution of the deviations in different directions. The displacement distributions of planes, straight lines, and points are analyzed based on distributions within tolerance zones. The distribution of the displacements of clearance fits is then determined according to the precedence of the assembly constraints. We consider the accumulated assembly variations and displacement distributions, and an analytical model is constructed to calculate the distribution of the deviations of the control points and the process capability index to validate the functional requirements. The efficiency of the method is shown by applying it to the assembly of a singlerod piston cylinder. The results are compared with other statistical methods of tolerance analysis. We find an improvement of approximately 20 % in tolerance analysis, and the process capability index of the assembly procedure was reduced by 10 %.

show abstract

Non-Normal Statistical Tolerance Analysis Using Analytical Convolution Method

Cited by 3 publications

References 2 publications

Using CAD parameter sensitivities for stack-up tolerance allocation

Using CAD parameter sensitivities for stack-up tolerance allocation

Research on antenna installation tolerance design based on genetic algorithm

Efficient statistical analysis of geometric tolerances using unified error distribution and an analytical variation model

Contact Info

Product

Resources

About