Concurrent design and process tolerances determination may ensure the manufacturability of products, improve the design efficiency, lower the overall production cost, reduce the quantity of unqualified products, and shorten product development cycle. Yet most of the current concurrent tolerancing models focus on the concurrent design of dimensional tolerances without taking into consideration geometrical tolerances. The objective of this study is to extend the concurrent tolerancing model to consider geometrical tolerance requirements. Firstly, the geometrical tolerances are either converted into equivalent dimensional tolerances or only treated as additional machining constraints based on their respective characteristics. Then, a concurrent tolerancing model is established based on ensuring the fulfillment of the product's functional requirements, taking the combination of expected quality loss and manufacturing cost as target function, and taking the functional constraints, geometrical tolerance constraints and process bound constraints as the constraint conditions. After having established the concurrent tolerancing model, the nonlinear programming technique is employed to solve this model to gain the optimal design and process tolerances. Finally, an example of wheel assembly is given to illustrate the validity of the suggested method.

This paper focuses on exploring an iterative method of statistical tolerance design to guide designers to select tolerances more economically and effectively. After having identified the assembly functional requirement (FR) and the functional elements (FEs) of corresponding tolerance chain, the expression of a unified Jacobian–Torsor model can be derived. Monte Carlo simulation is employed to generate random variables simulating the variations of small displacement torsor associated with the FE pairs with all the generated random values being within the intervals constrained by the corresponding tolerance zones. Then, the real multiplication operations are repeatedly executed to this model, a large number of real torsor component values of FR will be obtained and we can perform statistical analysis for these simulated data to get the statistical limits of the assembly FR in the desired direction. The tolerances of critical FEs may need to be adjusted to satisfy the assembly FR imposed by the designer, and the percentage contribution of each FE to the assembly FR can help determine these critical tolerances that need to be tightened or loosened. Once the calculated FR is in close agreement with the imposed FR, the iterative process can be stopped, and the statistical tolerance redesign is achieved. The effectiveness of the proposed method is illustrated with a case study. Compared with the deterministic tolerancing method, the results show that the proposed method is more economical and that can relax significantly the precision required, manufacturing and inspection costs can then be reduced considerably.

No abstract

The aim of this paper is to study the modeling method of the geometric variations which occur at the successive set-ups of the machining process by relying on the small displacement torsor (SDT) and its transfer formula, and to develop the machining process evaluation method based on the limitation of functional tolerances. The proposed method firstly considers the machining process of the mechanical part as a mechanism mainly consisted of machine-tool, part-holders, machined part, and cutting tools; Then, the SDT parameters are employed to represent the geometrical variations of the part caused by the positioning errors and machining operations during successive machining set-ups; the SDT chains are used to model the deviation propagation between different set-ups. During the whole modeling, there are three kinds of torsors need to be defined which are the global SDT of the part-holder, machined part or machining operation relative to their respective nominal positions, the gap torsor between two contact surfaces, and the deviation torsor of the associated surface relative to their respective nominal positions on the part-holder, machined part or machining operation. After obtaining all SDT chains based on the process planning of the part, an evaluation method is developed to verify the effectiveness of machining process by cumulating the impacts of various manufacturing variations on the respect of functional tolerances. Finally, an example is given to illustrate how to use the proposed method to model the manufacturing variations and evaluate the machining process of the part in the field of CNC milling machining.

No abstract