Concurrent tolerance allocation has been the focus of extensive research, yet very few researchers have considered how to concurrently allocate design and process tolerances for mechanical assemblies with interrelated dimension chains. To address this question, this paper presents a new tolerance allocation method that applies the concept of concurrent engineering. The proposed method allocates the required functional assembly tolerances to the design and process tolerances by formulating the tolerance allocation problem into a comprehensive model and solving the model using a non-linear programming software package. A multivariate quality loss function of interrelated critical dimensions is first derived, each component design tolerance is formulated as the function of its related process tolerances according to the given process planning, both manufacturing cost and quality loss are further expressed as functions of process tolerances. And then, the objective function of the model, which is to minimize the sum of manufacturing cost and expected quality loss, is established and the constraints are formulated based on the assembly requirements and process constraints. The purpose of the model is to balance manufacturing cost and quality loss so that concurrent optimal allocation of design and process tolerances is realized and quality improvement and product cost reduction is achieved. The proposed method is tested on a practical example.

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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.

The quality loss function developed by Taguchi provides a monetary measure for the deviation of the product quality characteristic from the target value. Product use causes degradation on its quality characteristic, and since such a deviation can be changing over time, so can the quality loss. However, most studies on concurrent tolerancing theory do not consider the quality loss caused by the degradation. In this paper, the present worth of expected quality loss expressed as the function of the pertinent process tolerances in a concurrent tolerancing environment is derived to capture the quality loss due to product degradation over time as a continuous cash flow function under continuous compounding. A new tolerance optimization model, which is to minimize the summation of manufacturing cost and the present worth of expected quality loss, is established to realize the concurrent tolerance allocation for products with multiple quality characteristics. An example of the bevel gear assembly involving concurrent allocation of design and process tolerances is given, demonstrating that the proposed model is feasible in practice.

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.