A MULTIPLE-CHOICE KNAPSACK MODEL FOR TOLERANCE ALLOCATION IN MECHANICAL ASSEMBLIES

Geometric and dimensional tolerances must be determined not only to ensure proper achievement of design function but also for manufacturability and assemblability of mechanical assemblies. We are investigating the degree to which it is possible to automate tolerance assignment on mechanical assemblies received only as STEP AP 203 (nominal) geometry files. In a previous paper, we reported on the preprocessing steps required: assembly feature recognition, pattern recognition, and extraction of both constraints and directions of control (DoC) for assembly. In this paper, we discuss first-order tolerance schema development, based purely on assemblability conditions. This includes selecting features to be toleranced, tolerance types, datums, and datum reference frames (DRFs), and tolerance value allocation. The approach described here is a combination of geometric analysis and heuristics. The assumption is that this initial geometric dimensioning and tolerancing (GD&T) specification will be sent to a stack analysis module and iterated upon until satisfactory results, such as desired acceptance rates, are reached. The paper also touches upon issues related to second-order schema development, one that takes intended design function into account.

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A Kinematic Based Analysis for Tolerances Within Mechanical Assemblies

20th Design Automation Conference: Volume 1 — Dynamic Mechanical Systems; Geometric Modeling and Features; Concurrent Engineering ◽

10.1115/detc1994-0066 ◽

1994 ◽

Author(s):

M. M. Ogot ◽

B. J. Gilmore

Keyword(s):

Sensitivity Analysis ◽

Design Tool ◽

Tolerance Allocation ◽

Analytical Sensitivity ◽

Mechanical Assemblies ◽

Analytical Sensitivity Analysis ◽

Design Function ◽

Minimum Sensitivity ◽

The Individual ◽

The Cost

Abstract Variation of dimensions within assemblies can unexpectedly displace parts from their intended location and therefore degrade the assembly’s performance. This paper presents a design tool based on the principles of kinematics to analyze nonlinear tolerance stackup, increase the reliability of the assembly without decreasing tolerances and where necessary, judiciously allocate tolerances such that the critical parts fit relative to each other with the specified precision. Through an analytical sensitivity analysis, the procedure outlined in this paper alters the orientations of the parts to yield an assembly with the highest positional reliability. If the desired level of reliability is not met by the minimum sensitivity approach, a tolerance allocation method incorporating the above sensitivity analysis and the cost of manufacturing each dimension as a function of tolerance is applied. In addition, this approach allows the individual tolerances within the assembly to assume any distribution. The method shown by this paper allows the design engineer to consider manufacturing effects and provides an analytical basis to evaluate design function.

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A framework for tolerance design considering systematic and random uncertainties due to operating conditions

Assembly Automation ◽

10.1108/aa-10-2018-0160 ◽

2019 ◽

Vol 39 (5) ◽

pp. 854-871

Author(s):

S. Khodaygan

Keyword(s):

Operating Conditions ◽

Tolerance Allocation ◽

Manufacturing Cost ◽

Tolerance Design ◽

Element Analysis ◽

Content Type ◽

Multi Objective ◽

Mechanical Assemblies ◽

Conflicting Objectives ◽

Random Uncertainties

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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