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The purpose of this paper is to present a state‐of‐the‐art review of dimensional tolerance synthesis and to demonstrate the evolution of tolerance synthesis from product to process‐oriented strategy, as well as to compare the same for single stage and multistage manufacturing systems (MMS). The main focus is in delineating the different approaches, methods and techniques used with critical appraisal of their uses, applicability and limitations, based on which future research directions and a generic methodology are proposed.

Starting with issues in tolerancing research, the review demonstrates the critical aspects of product and process‐oriented tolerance synthesis. The aspects considered are: construction of tolerance design functions; construction of optimization functions; and use of optimization methods. In describing the issues of process‐oriented tolerance synthesis, a comparative study of single and multistage manufacturing has been provided.

This study critically reviews: the relationship between the tolerance variables and the variations created through manufacturing operations; objective functions for tolerance synthesis; and suitable optimization methods based upon the nature of the tolerance variables and the design functions created.

This study is limited to dimensional tolerance synthesis problems and evolution of process‐oriented tolerance synthesis to counteract dimensional variation problems in assembly manufacturing.

The paper provides a comprehensive and step‐by‐step approach of review of dimensional tolerance synthesis.

The task of defining the parts in mechanical assembly based on their functional purpose is done by the functional dimensioning and tolerancing which tries to optimise its dimensions and tolerances. This work is very hard and complex to do. The actual development of CAD systems, which allows us to introduce intelligent help, seems to be the indicate tool to do the work easier. The international technical literature offers a number of investigation projects that contribute to establish the bases for implementing this intelligent help, in order to help the functional dimensioning in the design phase. The main aim of this study is to define and programme a computer application to aid the unidirectional dimensioning and tolerancing synthesis using graphic design (CAD).

Functional dimensioning has a clear mission: to choose the correct dimension and tolerance in order to optimise the parts in the definition of the mechanical assembly for their functional purpose. The current development of computer systems allows us to introduce intelligent help in CAD systems, which makes the complex task of functional dimensioning a lot easier. The international technical literature offers a number of investigation projects that contribute to establishing the bases for implementing intelligent help for functional dimensioning in the design phase. The main aim of this study is to define a system of computer‐aided dimensioning, using graphic design (CAD) systems and the necessary programming language.

Due to technological and financial limitations, nominal dimension may not be able achievable during manufacturing process. Therefore, tolerance allocation is of significant importance for assembly. Conventional tolerance analysis methods are limited by the assumption of the part rigidity. Every mechanical assembly consists of at least one or more flexible parts which undergo significant deformation due to gravity, temperature change, etc. The deformation has to be considered during tolerance design of the mechanical assembly, in order to ensure that the product can function as intended under a wide range of operating conditions for the duration of its life. The purpose of this paper is to determine the deformation of components under inertia effect and temperature effect.

In this paper, finite element analysis of the assembly is carried out to determine the deformation of the components under inertia effect and temperature effect. Then the deformations are suitably incorporated in the assembly functions generated from vector loop models. Finally, the tolerance design problem is optimized with an evolutionary technique.

With the presented approach, the component tolerance values found are the most robust to with stand temperature variation during the product's application. Due to this, the tolerance requirements of the given assembly are relaxed to certain extent for critical components, resulting in reduced manufacturing cost and high product reliability. These benefits make it possible to create a high‐quality and cost‐effective tolerance design, commencing at the earliest stages of product development.

With the approach presented in the paper, the component tolerance values found were the most robust to withstand temperature variation during the product's application. Due to this, the tolerance requirements of the given assembly are relaxed to a certain extent for critical components, resulting in reduced manufacturing cost and high product reliability. These benefits make it possible to create a high‐quality and cost‐effective tolerance design, commencing at the earliest stages of product development.

The traditional precision design only takes the influence of geometric tolerance of the parts and does not involve the load deformation in the assembly process. This paper aims to analyze the influence mechanism of flexible parts deformation on the geometric precision, and then to ensure the reliability and stability of the mechanical system.

Firstly, this paper adopts the N-GPS to analyze the influence mechanism of flexible parts deformation on the geometric precision and constructs a coupling 3D tolerance mathematical model of the geometric tolerance and the load deformation deviation based on the SDT theory, homogeneous coordinate transformation theory and surface authentication idea. Secondly, the least square method is used to fit the deformation surface of the mating surface under load so as to complete the conversion from the non-ideal element to the ideal element.

This paper takes the horizontal machining center as a case to obtain the deformation information of the mating surface under the self-weight load. The results show that the deformation deviation of the parts has the trend of transmission and accumulation under the load. The terminal deformation cumulative amount of the system is up to –0.0249 mm, which indicated that the influence of parts deformation on the mechanical system precision cannot be ignored.

This paper establishes a comprehensive 3D tolerance mathematical model, which comprehensively considers the effect of the dimensional tolerance, geometric tolerance and load deformation deviation. By this way, the assembly precision of mechanical system can be accurately predicted.

This study aims to develop an optimal tolerance allocation strategy involves integrating the unique transfer (UT) approach and the difficulty coefficient evaluation (DCE) routine in an interactive hybrid method. This method combines the strengths of both UT and DCE, ensuring simultaneous utilization for enhanced performance. The proposed tolerancing model manifests an integrated computer-aided design (CAD) tool.

By combining UT and DCE based on failure mode, effects and criticality analysis (FMECA) tool and the Ishikawa diagram, the proposed collaborative hybrid tool ensures an efficient and optimal tolerance allocation approach. The integration of these methodologies not only addresses specific transfer challenges through UT but also conducts a thorough evaluation of difficulty coefficients via DCE routine using reliability analysis tools as FMECA tool and the Ishikawa diagram. This comprehensive framework contributes to a robust and informed decision-making process in tolerance allocation, ultimately optimizing the design and manufacturing processes.

The presented methodology is implemented with the aim of generating allocated tolerances that align with specific difficulty requirements, facilitating the creation of a mechanical assembly characterized by high quality and low cost. To substantiate and validate the conceptual framework and methods, an integrated tool has been developed, featuring a graphical user interface (GUI) designed in MATLAB. This interface serves as a platform to showcase various interactive and integrated tolerance allocation approaches that adhere to both functional and manufacturing prerequisites. The proposed integrated tool, designed with a GUI in MATLAB, offers the capability to execute various examples that effectively demonstrate the benefits of the developed tolerance transfer and allocation methodology.

The originality of the proposed approach is the twining between the UT and DCE simultaneous in an integrated and concurrent tolerance transfer and allocation model. Therefore, the proposed approach is named an integrated CAD/tolerance model based on the manufacturing difficulty tool. The obtained results underscore the tangible advantages stemming from the integration of this innovative tolerance transfer and allocation approach. These benefits include a notable reduction in total cost and a concurrent enhancement in product quality.

The purpose of this paper is to apply the statistical tolerancing technique to analyze the dual responses of APFA arm height deviation with respect to next stage of disk assembly process and simultaneously optimize and allocate the required tolerance of the responses onto its components at minimum cost of manufacturing and the quality loss.

The relationships between the dual responses of APFA heights and the geometric dimensions and tolerances of APFA components, and orientation of the assembled part with respect to disk assembly were first defined. The effects of the APFA orientation, and the component tolerances on the distributions and variations of the responses were derived and investigated in terms of resultant product/process performance, quality loss, and the cost of assembly. The tolerance cost-based objective function is then formulated as the combined manufacturing/assembly cost and the quality loss. Direct search method was used to find the best feasible tolerance solutions satisfying the required product performance at minimum cost.

The constructed relationship or transfer functions of the dual responses were probabilistic depending on the orientation of part with respect to the next assembly process. The Monte Carlo simulation is empirically suitable for the computation of the conditional distributions of the responses against the first-order linear approximation of component variances. The proposed solution of tolerance control plan increases the product performances, C _pm , from 0.6 to be at least 1. The proposed tolerance allocation plans will reduce the amount of rework currently as high as 5 percent to at most 0.01 percent with minimally increased assembly cost.

This proposed methodology to design and allocate component tolerances is suitable and applicable to the APFA assembly process. The derived assembly functions of probabilistic type relating the responses to the process and component characteristics can represent the actual dynamic of assembled part better than a traditional single deterministic function developed under static concept. This presented methodology can be applied to other assembly cases where quality characteristic depends on the part dynamic.

This research simultaneously optimized the dual APFA height deviation responses with minimum cost of tolerance and quality loss using two different conditional distributions and transfer functions of the resultant deviations generated from dynamic of APFA with respect to disk.

The purpose of this paper is to provide an optimal tolerance allocation model for assemblies with consideration of the manufacturing cost, the quality loss, the design reliability index with various distributions to enhance existing models. Results of two case studies are presented.

The paper develops a model with consideration of the manufacturing cost, the Taguchi's asymmetric quadratic quality loss and the design reliability index for the optimal tolerance allocation of assemblies. The dimensional variables in normal distributions are initially used as testing and compared with the data from the prior researches. Then, the dimensional variables in lognormal distributions with the mean shift and the correlation are applied and investigated.

The results obtained based on a lognormal distribution and a normal distribution of the dimension are similar, but the tolerance with a lognormal distribution is little smaller than that with a normal distribution. The result of the reliability with the lognormal distribution obtained by the Monte‐Carlo is higher than that with a normal distribution. This paper shows that effects of the mean shift, the correlation coefficient and the replacement cost on the cost are significant and designers should pay attention to them during the tolerance optimization. The optimum tolerances of components of a compressor are recommended.

The model is limited to the dimensions of components with the normal distribution and lognormal distributions. The implication should be enhanced with more data of dimension distributions and cost of assembly components.

Two case studies are presented. One is an assembly of two pieces and another is a compressor with many components.

This model provides an optimal tolerance allocation method for assemblies with the lowest manufacturing cost, the minimum quality loss, and the required reliability index for the normal distribution and lognormal distribution.

The purpose of this paper is to present an experimental approach to measure and quantify the three‐dimensional geometrical manufacturing errors on a mass production of parts.

A methodology is developed to model and analyse the combined effect of these errors on a machined feature. Deviation of a machined feature due to the combined errors is expressed in terms of the small displacement torsor (SDT) parameters. Given a tolerance on the machined feature, constraints are specified for that feature to establish a relationship between the tolerance zone of the feature and the torsor parameters. These constraints provide boundaries within which the machined feature must lie. This is used for tolerance analysis of the machined feature. An experimental approach is proposed to measure and quantify the three‐dimensional manufacturing variations as torsors. The results are used to verify the analytical model.

Results show that it is possible to quantify manufacturing dispersions. The paper proposes a measuring method which can be done during the production. In the context of process planning, these experimental data allow us to perform realistic geometrical simulation of manufacturing. The results of this method are torsor components dispersions. Analysis and synthesis of the geometrical simulation of manufacturing are viable with reliable numerical data in order to predict the defects.

To perform realistic geometrical simulation of manufacturing, an experimental approach to measure and quantify the three‐dimensional geometrical manufacturing errors is proposed which is based on the SDT concept.

Proposes a new formulation for allocating process tolerances. The major contribution of the model is to assign tolerances with maximization of the conformance rate of the entire process. The cumulative standard normal probability is used to estimate the scrap rate of each operation with respect to the machining accuracy of equipment, therefore, the design engineers are able to predict the failure rate before production. Results of comparison with other methods indicate that the proposed model can cost‐effectively assign tolerances.