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.     

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.     

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.     

Tolerancing algebra: A building block for handling tolerance interactions in design and manufacturing Part 1: Concept and representation

As a fundamental building block for 3D tolerance transfer analysis, tolerancing algebra on a deviation space has been proposed and elaborated. Based on the investigation of the spatial characteristic and the propagation mechanism of geometric tolerances and manufacturing process dispersions, a set of primitives and operations has been defined, which forms the algebraic structure of tolerancing algebra. Some important algebraic properties have been derived that will be extensively used to establish a tolerance transfer technique for process planning. Companion papers present the idea of tolerancing algebra in two parts. Part 1 presents some important concepts and their representations. Part 2 endeavours to show the interactions between product tolerances and process dispersions by way of the basic algebraic operations on deviation volumes.     

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.     

Tolerancing techniques: the state-of-the-art

The intense global competition to produce quality products at a low cost has led many industrial nations to consider mechanical tolerances as a key factor to bring about cost saving as well as to remain competitive. In the last two decades, some work has been done in the area of tolerance techniques. In this paper a comprehensive summary of the state-of-the-art and the projection of future trends in tolerancing techniques is presented to describe improved techniques available today and to aid in guiding research for the future. This paper reviews the status of theory and practice of how manufacturing and assembly processes are characterized for relating tolerancing to process or production cost. The specification of tolerancing on the dimension of the manufactured part has a significant impact on the final production cost. Tight tolerances can result in excessive process cost, while loose tolerances may lead to increased waste and assembly problems. This paper systematically reviews the state-of-the-art by classifying more than 50 papers written so far into five categories. They are, the dimensional tolerances chain technique, geometrical modelling in tolerances, statistical and probabilistic methods in tolerancing, tolerances based on analysis and synthesis, tolerances based on cost-tolerance algorithms and design methods. Future areas of research and the unresolved issues have been presented that will serve as a springboard for researchers to investigate and produce solutions for the end of this century. The present problems and issues once resolved, will revolutionize the manufacturing industry as the year 2000 approaches!     

Tolerancing of board-level-free-space optical interconnects

For optical interconnects to become a mature technology they must be amenable to electronic packaging technology. Two main obstacles to including free-space optical interconnects are alignment and heat-dissipation issues. Here we study the issues of alignment tolerancing that are due to assembly and manufacturing variations (passive-element tolerancing) over long board-level distances (>10 cm) for free-space optical interconnects. We also combine these variations with active optoelectronic device variations (active-element tolerancing). We demonstrate a computer-aided analysis procedure that permits one to determine both active- and passive-element tolerances needed to achieve some system-level specification, such as yield or cost. The procedure that we employ relies on developing a detailed design of the system to be studied in a standard optical design program, such as code v. Using information from this model, we can determine the integrated power falling on the detector, which we term optical throughput, by performing Gaussian propagation or general Fresnel propagation (if significant vignetting occurs). This optical throughput can be used to determine system-level performance criteria, such as bit-error rate. With this computer-aided analysis technique, a sensitivity analysis of all the variations under study is made on a system with realistic board-level interconnect distances to find each perturbation's relative effects (with other perturbations set to 0) on the power falling on the detector. This information is used to set initial tolerances for subsequent tolerancing analysis and design runs. A tolerancing analysis by Monte Carlo techniques is applied to determine if the yield or cost (yield is denned as the percentage of systems that have acceptable system performance) is acceptable. With a technique called parametric sampling, a subsequent tolerancing design run can be applied to optimize this yield or cost with little increase in computation. We study a design example and show that most of the tolerances can be achieved with current technology.     

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.     

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.     

Tolerancing for manufacturing: A three-dimensional model

This paper proposes a three-dimensional (3D) model on manufacturing tolerancing for mechanical parts. The work presented relies on research conducted at the LURPA on the computation of 3D tolerance chains for mechanisms. Starting from these works, the authors propose a formalization of the problem within the more specific context of manufacturing tolerances. Models of the workpiece, the set-ups and the machining operations are provided. The main originality is to model the machining set-up as a mechanism. The concept of the small displacements torsor (SDT) is used to model the process planning. It opens up the way for the 3D integration product/process because of the similarities between the concepts used in both points of view. The first part recalls the principle of the modelling of surface variations with SDT as well as its application to the modelling of mechanisms. The second part introduces the use of the concept in the case of manufacturing tolerancing. A third part shows the modelling of the problem with the help of an example. At last, a detailed computer implementation is described.     

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.     

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     

Generalization and evaluation of vectorial tolerances

In recent years, vectorial tolerancing has emerged as a new alternative for representing workpiece tolerances. In contrast to conventional geometric tolerances which originated from hard gauging practices, vectorial tolerancing follows the working principle of coordinate measuring machines and CAD/ CAM systems. Moreover it provides feedback from measurement directly to manufacturing process control. Many believe it is a better tolerancing method to tie design, manufacuturing, and measurement together. However, the current proposal of vectorial tolerancing has some limitations. First, the currently adopted orientation vector is not sufficient for representing true 3D orientations. As a result, the orientation of a free form surface cannot be properly established. Second, there is lacking a unified and consistent method for the evaluation of vectorial tolerances. This paper proposes a new orientation vector which provides a more general mathematical basis for representing vectorial tolerances. It enables true 3D orientation representation and relates tolerances to the functional requirement. With the improved mathematical definition, a systematic tolerance evaluation approach becomes possible for both analytical geometric elements and free-form surfaces. Computer simulations and real-world applications are studied to validate this new approach.     

A Mathematical Framework for the Key Characteristic Process

To maximize product quality, a product design team selects concepts and dimensions to minimize a product’s sensitivity to variation. However, even for the most robust products, it is rarely possible to transition a product into production without encountering any variation-related problems. In a complex product, it is not economically or logistically feasible to control and/or monitor the thousands of tolerances specified in a product’s drawing set. To address this problem, many organizations are using Key Characteristic (KCs) methods to identify where excess variation will most significantly affect product quality, and what product features and tolerances require special attention from manufacturing. As simple as this principle seems, most companies struggle to effectively implement KC methods because no quantitative methods to prioritize KCs exist. This paper develops a mathematical definition of a KC based on a variation propagation model. In addition, it develops a quantitative effectiveness measure used to prioritize where verification, variation reduction, and on-going monitoring should be applied. The effectiveness measure incorporates the cost of control, the benefit of control, and the expected change in process capability. The methods are illustrated using an automotive door assembly.     

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.     

Statistical Analysis of Geometrical Tolerances: A Case Study

Tolerancing is one of the most important but complex activities in design. Tolerance information takes place at every phase of design activity. It represents the fundamental link between the theoretical model of the mechanical product and the actual one. During the two previous decades, engineering projects and scientific researches demonstrated that ongoing miniaturization increased the influence of geometric tolerances. They also admit that mass production is mainly based on statistical techniques. On the other hand, the decomposition of the global tolerancing process into functional-level, assembly-level, part-level, and manufacturing-level, reduces dramatically the domain of the solution. In this paper, the global tolerancing process is described and a novel method for statistical analysis of geometrical tolerances is discussed. Then the statistical approach is introduced and its performance is evaluated on a best case study. The analysis of the technical drawing of a part is given in order to highlight the advantages of the statistical approach.     

Variation propagation modelling for multi-station machining processes with fixtures based on locating surfaces

Modelling the dimensional variation propagation in multi-station machining processes (MMPs) has been studied intensively in the past decade to understand and reduce the variation of product quality characteristics. Among others, the Stream-of-Variation (SoV) model has been successfully applied in a variety of applications, such as fault diagnosis, process planning and process-oriented tolerancing. However, the current SoV model is limited to the MMPs where only fixtures with punctual locators are applied. Other types of fixtures, such as those based on locating surfaces, have not been investigated. In this paper, the derivation of the SoV model is extended to model the effect of fixture- and datum-induced variations when fixtures with locating surfaces are applied. Due to the hyperstatic nature of these fixtures, different workholding configurations can be adopted. This will increase the dimension of the SoV model exponentially and thus may make the model-based part quality prediction extremely complex. This paper presents a method of reducing the complexity of the SoV model when fixtures based on locating surfaces are applied and evaluates the worst-case approach of the resulting part quality.     

设计与制造中的统计几何公差建模及应用

几何与尺寸公差(形位公差GD&T)广泛用于机械工程设计与制造中重要几何特征的偏差控制.相对较成熟和简单的尺度公差建模与分析,几何公差统计建模与分析更具挑战性,是当前CAD技术中尚未但亟待解决的课题之一.现提出采用统计几何模态模型(SMA)方法解决这一问题.SMA可识别刻划与解释测量数据中的几何特征信号模式及其变化,从而服务于制造中的(公差)质量检验、诊断及变化模式的统计建模.在设计中SMA可进行模态重组综合,从而再现或仿真几何特征偏差的随机变化进行统计几何公差分析.     

A systematic approach to preliminary polymer process development: modeling and design

A general and complete methodology is presented to facilitate systematic modeling and design of polymer processes during the early development period. To capture and handle the subjective type of uncertainty, embedded in the preliminary process development, fuzzy theories are used as a basis to model and design the process in the presence of ambiguity and vagueness. Physical membership functions are developed for mapping the relation between process variables and the associated fuzzy uncertainties. Based on the qualitative results generated using our previously proposed “linguistic based preliminary design method,” the process modeling can be followed even in the absence of any process governing equations. The modeling is carried out by establishing an appropriate fuzzy reasoning system which provides a specific functional mapping that relates input process variables to one (or more than one) output performance parameter(s). A reduced yet feasible domain is generated by our qualitative design scheme to constrain the process variables. Now, any optimization routine can then be employed to search for a proper process design. We demonstrate the effectiveness of the proposed methodology by its application to a typical compression molding process.     

CAE FOR THE MANUFACTURING ENGINEER: THE ROLE OF PROCESS SIMULATION IN CONCURRENT ENGINEERING

As America refocuses its attention on the factory, design and manufacturing engineers must work together closely to design the appropriate products, and matching production process in a team effort. By building off the designer's CAE tools that predict product performance, the manufacturing engineer is today able to simulate the proposed production process. Process simulations for the following manufacturing processes are available or being developed:

▪Forging, ▪Machining, ▪Injection Molding, ▪Die Casting, ▪Investment Casting, ▪Metal Forming, ▪Heat Treating, ▪Assembly Tolerancing

By utilizing the same 3-D solid model and finite element modeling tools used by the designer, coupled to powerful analysis simulation tools to predict the transient nonlinear heat transfer and plastic material flow found in many manufacturing processes, the manufacturing engineer is able to explore alternative processing plans, evaluate trade-offs and even influence the design to produce superior products.

Process simulation brings a science to support the manufacturing engineers experience for reduced lead time, lower cost, increase product quality and better understanding of the process. The next step will be to directly link the process simulation to an expert system.

This paper describes the current state of technology in the area of manufacturing process computer simulation for a number of manufacturing operations and suggests how these tools can be used “up-front” and lead to concurrent engineering.