Robust design of assembly and machining tolerance allocations

Tolerancing is one of the most important tasks in product and manufacturing process design. The allocation of design tolerances between the components of a mechanical assembly and manufacturing tolerances in the intermediate machining steps of component fabrication can significantly affect a product's quality and its robustness. This paper presents a methodology to maximize a product's robustness by appropriately allocating assembly and machining tolerances. The robust tolerance design problem is formulated as a mixed nonlinear optimization model. A simulated annealing algorithm is employed to solve the model and an example is presented to illustrate the methodology.     

Tolerance analysis and synthesis for cam mechanisms

Tolerance is one of the most important parameters in product and process design, so tolerancing plays a key role in design and manufacturing. Tolerance synthesis is in a period of extensive study due both to increased demands for quality products and to increasing automation of machining and assembly. Optimum tolerance design and synthesis ensures good quality product at low cost. This paper presents an analytical methodology for tolerance analysis and synthesis for a disk cam-translating follower system. Both dimensional ( size) and geometric tolerances ( position and profile ) on the components are considered. Tolerance analysis is performed on individual tolerances as well as on total tolerance accumulation. With the lowest manufacturing cost as its objective function a nonlinear optimization model is formulated for tolerance synthesis and solved by a sequential quadratic programming ( SQP) algorithm. An example is provided to illustrate the optimization model and solution procedure.     

Quality design of tolerance allocation for sheet metal assembly with resistance spot weld

Tolerance directly influences the functionality of the products and the related manufacturing costs, and tolerance allocation is of great importance for improving the assembly quality. However, the information required to allocate tolerances for complex 3D assemblies is generally not available at the initial design stage. In this paper, a new quality design methodology is developed, which makes use of both original design data obtained by the response surface methodology and the extra interpolation data obtained by the Kriging method. The finite element modelling is presented for the sheet metal assembly process as no explicit relationship of the variations for key characteristic points are available. The robust tolerances can be allocated based on the quality design model. A case study with the typical assembly process of the rear compartment pan and the wheelhouse is carried out in the paper, the tolerance allocation results show that the developed quality design methodology is capable of determining the robust manufacturing tolerance before assembly, which satisfies the product requirements. This method enables a robust tolerancing scheme to be used in the sheet metal assembly process.     

Optimization of machining datum selection and machining tolerance allocation with genetic algorithms

In machining process planning, selection of machining datum and allocation of machining tolerances are crucial as they directly affect the part quality and machining efficiency. This study explores the feasibility to build a mathematical model for computer aided process planning (CAPP) to find the optimal machining datum set and machining tolerances simultaneously for rotational parts. Tolerance chart and an efficient dimension chain tracing method are utilized to establish the relationship between machining datums and tolerances. A mixed-discrete nonlinear optimization model is formulated with the manufacturing cost as the objective function and blueprint tolerances and machine tool capabilities as constraints. A directed random search method, genetic algorithm (GA), is used to find optimum solutions. The computational results indicate that the proposed methodology is capable and robust in finding the optimal machining datum set and tolerances. The proposed model and solution procedure can be used as a building block for computer automated process planning.     

Concurrent optimization of assembly tolerances for quality with position control using scatter search approach

Tolerance allocation to individual parts in any assembly should be a vital design function with which both the design and manufacturing engineers are concerned. Generally design engineers prefer to have tighter tolerances to ensure the quality of their design, whereas manufacturing engineers prefer loose tolerances for ease of production and the need to be economical. This paper introduces a concurrent tolerance approach, which determines optimal product tolerances and minimizes combined manufacturing and quality related costs in the early stages of design. A non-linear multivariable optimization model is formulated here for assembly. A combinatorial optimization problem by treating cost minimization as the objective function and stack-up conditions as the constraints are solved using scatter search algorithm. In order to further explore the influence of geometric tolerances in quality as well as in the manufacturing cost, position control is included in the model. The results show how position control enhances quality and reduces cost.     

Simultaneous optimal selection of design and manufacturing tolerances with different stack-up conditions using genetic algorithms

Tolerance design is one of the most critical aspects of product design and development process as it affects both the product's functional requirements and manufacturing cost. Unnecessarily tight tolerances lead to increased manufacturing cost, while loose tolerances may lead to malfunctioning of the product. Traditionally, this important phase of product development is accomplished intuitively to satisfy design constraints, based on handbooks' data and/or skill and experience of the designers. Tolerance design carried out in this manner does not necessarily lead to an optimum design. Research in this area indicates that, in general, tolerance design is carried out sequentially in two steps; (1) tolerance design in CAD to obtain design or functional tolerances and (2) tolerance design in CAPP to obtain manufacturing tolerances. Such a sequential approach to tolerance design suffers from several drawbacks, such as more time consumption, suboptimality and unhealthy working atmosphere. This paper reports on an integrated approach for simultaneous selection of design and manufacturing tolerances based on the minimization of the total manufacturing cost. The nonlinear multivariable optimization problem formulated in this manner may result in a noisy solution surface, which can effectively be solved with the help of a global optimization technique. A solution methodology using genetic algorithms and applying penalty function approach with proper normalization of the penalty terms for handling the constraints is proposed. The application of the proposed methodology is demonstrated on a simple mechanical assembly with different tolerance stack-up conditions.     

Concurrent optimal allocation of design and process tolerances for mechanical assemblies with interrelated dimension chains

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.     

Tolerance optimization of a mobile phone camera lens system

In the manufacturing process for the lens system of a mobile phone camera, various types of assembly and manufacturing tolerances, such as tilt and decenter, should be appropriately allocated. Because these tolerances affect manufacturing cost and the expected optical performance, it is necessary to choose a systematic design methodology for determining optimal tolerances. In order to determine the tolerances that minimize production cost while satisfying the reliability constraints on important optical performance indices, we propose a tolerance design procedure for a lens system. A tolerance analysis is carried out using Latin hypercube sampling for evaluating the expected optical performance. The tolerance optimization is carried out using a function-based sequential approximate optimization technique that can reduce the computational burden and smooth numerical noise occurring in the optimization process. Using the proposed design approach, the optimal production cost was decreased by 28.3% compared to the initial cost while satisfying all the constraints on the expected optical performance. We believe that the tolerance analysis and design procedure presented in this study can be applied to the tolerance optimization of other systems.     

Process-oriented tolerancing for multi-station assembly systems

In multi-station manufacturing systems, the quality of final products is significantly affected by both product design as well as process variables. Historically, however, tolerance research has primarily focused on allocating tolerances based on the product design characteristics of each component. Currently, there are no analytical approaches to optimally allocate tolerances to integrate product and process variables in multi-station manufacturing processes at minimum costs. The concept of process-oriented tolerancing expands the current tolerancing practices, which bound errors related to product variables, to explicitly include process variables. The resulting methodology extends the concept of “part interchangeability” into “process interchangeability,” which is critical due to increasing requirements related to the selection of suppliers and benchmarking. The proposed methodology is based on the development and integration of three models: (i) the tolerance-variation relation; (ii) variation propagation; and (iii) process degradation. The tolerance-variation model is based on a pin-hole fixture mechanism in multi-station assembly processes. The variation propagation model utilizes a state space representation but uses a station index instead of a time index. Dynamic process effects such as tool wear are also incorporated into the framework of process-oriented tolerancing, which provides the capability to design tolerances for the whole life-cycle of a production system. The tolerances of process variables are optimally allocated through solving a nonlinear constrained optimization problem. An industry case study is used to illustrate the proposed approach.     

Simultaneous tolerancing for design and manufacturing

This paper presents a new tolerance design theory—simultaneous tolerancing— which works in the concurrent engineering context. After stating the need to develop a simultaneous tolerancing theory by showing the shortcomings of conventional tolerancing technique, the concept of simultaneous tolerancing is given, and its elements are briefly presented. Then we focus our attention on the development of a general mathematical model of optimal tolerancing supporting concurrent engineering. Two commonly used models, worst-case and statistical, are discussed in detail. Next, a method of ‘interim tolerances’, which help to determine an appropriate machining process without using functional tolerances, is proposed. The simultaneous tolerancing theory presented in this paper permits of determining directly optimal machining tolerances in product design, reducing the manufacturing cost and improving the quality of products. Finally, an example is given, showing that the proposed theory is feasible in practice.     

Evaluating the manufacturability of machined parts and their setup plans

Design-for-manufacturability is an approach that requires product designers to consider the manufacturing issues of a product concurrently with the geometrical and design aspects. This paper presents a manufacturability evaluation methodology that incorporates design, machining and work-holding issues. The evaluation is carried out in two parts. The first part is related to the machinability of the features of the part, whereas the second part is concerned about the fixturability of the part with regards to its planar faces. The methodology uses the fuzzy sets theory and the analytical hierarchy process method to evaluate the accessibility, orientation, dimensional tolerances, and surface finish specifications of a part. The former is used to model the various ill-defined boundaries of the criteria, while the latter allows for differences in opinions from designers/machinists to be incorporated into the evaluation process. The quantitative machinability and fixturability indices found can be used to evaluate designs and generate redesign suggestions. A setup plans evaluation module has been developed to determine the merit indices of setup plans for machining a part using these machinability and fixturability indices.     

Tolerance allocation for compliant beam structure assemblies

This paper presents a tolerance allocation methodology for compliant beam structures in automotive and aerospace assembly processes. The compliant beam structure model of the product does not require detailed knowledge of product geometry and thus can be applied during the early design phase to develop cost-effective product specifications. The proposed method minimizes manufacturing costs associated with tolerances of product functional requirements (key product characteristics, KPCs) under the constraint(s) of satisfying process requirements (key control characteristics, KCCs). Misalignment and fabrication error of compliant parts, two critical causes of product dimensional variation, are discussed and considered in the model. The proposed methodology is developed for stochastic and deterministic interpretations of optimally allocated manufacturing tolerances. An optimization procedure for the proposed tolerance allocation method is developed using projection theory to considerably simplify the solution. The non-linear constraints, that ellipsoid defined by τ(stochastic case) or rectangle defined by T x (deterministic case) lie within the KCC region, are transformed into a set of constraints that are linear in σ(or T x )-coordinates. Experimental results verify the proposed tolerance allocation method.     

Tolerance chart optimization for quality and cost

This paper introduces a mathematical model for tolerance chart balancing during machining process planning. The criteria considered in this study are based on the combined effects of manufacturing cost and quality loss, under the constraints of process capability limits, design functionality restrictions, and product quality requirements. Manufacturing cost is expressed in geometrical decreasing functions, which represent tolerances to be assigned. Process variability is expressed in quadratic loss functions, which represent the deviation between part measurement and the target value. Application of this model minimizes the total cost of manufacturing activities and quality issues relating to machining process planning, particularly in the early stages of planning.     

Modelling and analysis of selective assembly using Taguchi's loss function

An assembly is the integrative process of joining components to make a completed product. It brings together the upstream process of design, engineering and manufacturing processes. The functional performance of an assembled product and its manufacturing cost are directly affected by the individual component tolerances. But, the selective assembly method can achieve tight assembly tolerance through the components manufactured with wider tolerances. The components are segregated by the selective groups (bins) and mated according to a purposeful strategy rather than being at random, so that small clearances are obtained at the assembly level at lower manufacturing cost. In this paper, the effect of mean shift in the manufacturing of the mating components and the selection of number of groups for selective assembly are analysed. A new model is proposed based on their effect to obtain the minimum assembly clearance within the specification range. However, according to Taguchi's concept, manufacturing a product within the specification may not be sufficient. Rather, it must be manufactured to the target dimension. The concept of Taguchi's loss function is applied into the selective assembly method to evaluate the deviation from the mean. Subsequently, a genetic algorithm is used to obtain the best combination of selective groups with minimum clearance and least loss value within the clearance specification. The effect of the ratio between the mating part quality characteristic's dimensional distributions is also analysed in this paper.     

Functional tolerancing: A design for manufacturing methodology

The problem addressed in this paper is the development of a physico-mathematical basis for mechanical tolerances. The lack of such a basis has fostered a decoupling of design (function) and manufacturing. The groundwork for a tolerancing methodology is laid by a model of profile errors, whose components are justified by physical reasoning and estimated using mathematical tools. The methodology is then presented as an evolutionary procedure that harnesses the various tools, as required, toanalyze profiles in terms of a minimum set of profile parameters and tore-generate them from the parameters. This equips the designer with a rational means for estimating performance prior to manufacturing, hence integrating design and manufacturing. The utility of thefunctional tolerancing methodology is demonstrated with performance simulations of a lathe-head-stock design, focusing on gear transmission with synthesized errors.     

Alternative tolerance allocations for machining parts represented with multiple sets of features

In a feature-based model, if feature interactions occur, there may exist multiple sets of features that can be used to represent the same part. The multiple sets of features represent different ways for machining the same part. In tolerance charting, the different sets of features represent alternative ways that the working dimensions and working tolerances can be allocated to achieve the specified blueprint dimensions and tolerances. This paper presents a feature-based tolerance charting approach to evaluate the multiple sets of features from the tolerance allocating point of view. A feature-based tolerance charting methodology is developed for automatically allocating the working dimensions and tolerances for 3D prismatic parts represented in boundary representation data. The tolerance charting methodology is used as a basis for evaluating the multiple sets of features. The objective is to find the set of features that is capable of maximizing the cumulative sum of working tolerances and minimizing the cost functions. Under a consistent tolerance charting methodology, different sets of features are analysed and evaluated. The set of features that fully utilizes the blueprint tolerances to achieve the objective functions is considered 'better' for machining. The developed method is implemented on a personal computer. Example parts are tested and discussed.     

Integrating assembly and machining planning using graph-based representation models

Traditionally, assembly planning and machining planning are considered as two independent tasks. In assembly planning, the components to be sequenced are considered as machined and finished. In machining planning, the focus has been on machining each individual component. In previous research, machining and assembly planning are analysed separately. However, in order to achieve some design specifications, the assembly and machining operations may need to be mixed in an integrated sequence. For example, a machining operation may need to be performed on a subassembly formed by a group of components in order to complete certain geometric features. In other cases, an assembly operation cannot be performed unless certain geometric features are completely machined. Therefore, the assembly and machining operations need to be planned in a combined sequence. In this research, new graph-based representation models were developed to integrate assembly and machining planning. First, an assembly-machining operation graph was developed to represent the spatial relationships between the components as well as to express the operational precedence of the machining and assembly operations. Next, the integrated assembly and machining sequences were generated using a tree structure called the assemblymachining sequence tree. Using the graph-based methodology, all the feasible integrated assembly and machining sequences can be generated and evaluated. The main objective is to provide a complete model for integrating assembly and machining sequences. A combined evaluation can be performed to find the best sequence based on certain time and cost objectives. The presented methodology is implemented on a personal computer and several example parts are discussed.     

Simultaneous tolerance synthesis for manufacturing and quality

Tolerance allocation affects product design, manufacturing, and quality. No existing technique has been found by the authors that takes product design, manufacturing, and quality into account simultaneously. This paper introduces a new concurrent engineering method for tolerance allocation. A nonlinear optimization model was constructed to implement the method. The model minimizes the combination of quality loss and manufacturing cost simultaneously in a single objective function by setting both process tolerances and design tolerances simultaneously. The purpose of the model is to balance manufacturing cost and quality loss to achieve near-optimal design and process tolerances simultaneously for minimum combined manufacturing cost and quality loss over the life of the product. Compared to other models, this model shows significant improvements. Electronic Publication     

Complex assembly variant design in agile manufacturing. Part I: System architecture and assembly modeling methodology

In the distributed and horizontally integrated manufacturing environment found in agile manufacturing, there is a great demand for new product development methods that are capable of generating new customized assembly designs based on mature component designs that might be dispersed at geographically distributed partner sites. To cater for this demand, this paper addresses the methodology for complex assembly variant design in agile manufacturing. It consists in fundamental research in two parts: (i) assembly modeling; and (ii) assembly variant design methodology. This paper, the first of a two-part series, presents the assembly variant design system architecture and the assembly modeling methodology. First, a complementary assembly modeling concept is proposed with two kinds of assembly models, the hierarchical assembly model and the relational assembly model. The first explicitly captures the hierarchical and functional relationships between constituent components whereas the second explicitly captures the mating relationships at the form-feature-level. These models are complementary in the sense that each of them models only a specific aspect of assembly-related information but together they include the required assembly-related information. They are further specialized to accommodate the features of assembly variant design. As a result, two kinds of assembly models, the assembly variants model and the assembly mating graph are generated. These assembly models serve as the basis for assembly variant design which is discussed in the companion paper.