Areal surface texture data extraction from X-ray computed tomography reconstructions of metal additively manufactured parts

Many applications that exploit the manufacturing flexibility of additive manufacturing (AM) produce surfaces, primarily internal features, which cannot be measured using conventional contact or line-of-sight optical methods. This paper evaluates the capability of a novel technique to extract areal surface data from micro-focus X-ray computed tomography (XCT) from AM components and then generate surface parameter data per ISO 25178-2. This non-destructive evaluation of internal features has potential advantages during AM product research and commercial production. The data extracted from XCT is compared with data extracted using a focus variation instrument. A reference dimensional artefact is included in all XCT measurements to evaluate XCT surface determination performance and dimensional scaling accuracy. Selected areal parameters generated using the extraction technique are compared, including Sa, for which the nominal difference between the value obtained using XCT and used the focus variation method was less than 2.5%.     

尺寸公差与形位公差混合优化分配

为解决尺寸公差与形位公差混合优化分配问题,提出了一种公差优化分配方法.根据成本-公差函数和尺寸公差与形位公差的关系,建立了以最小制造总成本为目标的非线性公差混合优化分配模型.该模型的约束包括装配尺寸链的功能要求和加工能力.求解该模型能同时得到优化的尺寸公差和形位公差.最后,分别用公差混合优化分配法和传统方法对一个实例进行公差分配,结果表明所提方法比传统方法更优越.     

Fuzzy-small degrees of freedom representation of linear and angular variations in mechanical assemblies for tolerance analysis and allocation

Tolerances naturally generate an uncertain environment for design and manufacturing. In this paper, a novel fuzzy based tolerance representation approach for modeling the variations of geometric features due to dimensional tolerances is presented. The two concepts of fuzzy theory and small degrees of freedom are combined to introduce the fuzzy-small degrees of freedom model (F-SDOF). This model is suitable for tolerance analysis of mechanical assemblies with linear and angular tolerances. Based on the fuzzy concept, a new index (called the assemblability index) is introduced which signifies the fitting quality of parts in the assembly. Graphical and numerical representations of tolerance allocation by this method are presented. The goal of tolerance allocation is to adjust the tolerances assigned at the design stage so as to meet a functional requirement at the assembly stage. The presented method is compatible with the current dimensioning and tolerancing standards. The application of the proposed methodology is illustrated through presenting an example problem.     

CAD系统中并行公差的建模方法

提出一种基于产品设计与制造、支持公差工程语义和并行公差的几何公差计算机辅助建模表示新方法。在CAD系统中，进行装配公差和零件制造公差建模，利用特征的几何公差结构块，求出各种公差带的空间表示函数，计算有关公差带在三维空间中相应自由度的允许变动量，为公差分析和综合提供实用的模型。用工程实例验证了所提出的方法。     

Using tolerance maps to validate machining tolerances for transfer of cylindrical datum in manufacturing process

Process planers typically utilize different datum features than designers use when specifying tolerances. Datum features used in process plans are chosen to simplify setups and achieve desired geometric accuracy. Meanwhile, proper machining tolerances are required to be reassigned to satisfy design requirements. However, existing methods to transfer geometric tolerances directly and accurately are still missing due to incompatible mathematical models of tolerances. Also, the affection of material conditions on datum and partial constraint situations have not been deeply considered yet. Since cylindrical features are often used as datum features, this paper describes the use of tolerance maps (T-Maps) (patent no. 6963824) and manufacturing maps (M-maps) to establish analytical relationship among all relevant design and machining tolerances for transfer of cylindrical datum. Firstly, a parametric model of datum transfer is proposed to describe factors involving the process. Next, based on spatial and geometric parameters, as well as tolerances information, variation analysis among features is implemented to formulate transformed T-Maps, sum of which constructs M-Map. Then, distinct bounding boxes of cross-sections in M-Map are extracted through computing vertex coordinates of their boundaries due to complete and partial constraint scenarios. Thereafter, by virtue of bounding boxes, relationship among design and machining tolerances are obtained through fitting M-Maps into T-Maps. Finally, an example is introduced to verify feasibility of the proposed model and method.     

新一代GPS中平面度公差域的研究

在现代制造行业中,技术标准的发展成为影响制造业的重要因素,目前推行的为新一代产品几何技术规范(geometrical product specification and verification,简称GPS)。如何根据新一代GPS的要求,制定一系列标准规范已成为很多国家的重要课题。本文根据新一代GPS的要求,利用尺寸公差和几何公差的独立原则,通过对平面度相关自由度变量的确定来规范所要求的平面,并分析平面度公差域的范围;通过实例分析求解平面度公差域的变化范围,得出一种求平面度公差域范围的方法。     

A variational geometric constraints network for a tolerance types specification

A geometric tolerance specification includes specifying the tolerance types and values for nominal geometry parts. In current computer-aided tolerancing practices, designers have to specify manually both tolerance types and values in a CAD system, usually starting out from single components. The paper presents a framework and computer implementation that provides automated methods for the specification of geometric tolerance types. Based on the ISO/TC 213 geometric product specification, a new concept of a variational geometric constraints network is presented. The generation and application of the network to specify geometric tolerance types is studied. An example is analysed to show the scheme to be effective, and the model for a tolerance specification, including the types and values specification, is presented.     

Applying the Coordinate Tolerance System to Tolerance Stack Analysis Involving Position Tolerance

Geometric dimensioning and tolerancing (GDT) has been playing an important role in specifying the geometry of part features during the product design stage. Tolerance stack analysis is then used to study the conformity of the parts to the tolerance zone. Performing stack analysis is time consuming because geometric tolerances are complex to compute. This paper presents a technique to formulate the bonus and shift tolerances (due to positional callout) and convert them to equal bilateral expressions as in a coordinate tolerance system. An example is used to demonstrate the effectiveness of the expressions. The usage of the expressions is less conceptual and this makes the application simple and direct. Most importantly, the results are shown to be accurate and reliable.     

基于特征的公差表示方法与实现

公差的存储表示是公差分析和公差综合的基础 ,提出一种几何公差的计算机辅助表示方法。利用特征的几何公差结构块 ,建立各种公差带的空间表示函数 ,并计算其三维空间中相应自由度的允许变动量。通过图论方法给出公差图的形式化定义 ,设计公差图的数据结构 ,可实现零件公差的计算机存储表示。最后给出零件实例来验证所提出的方法。     

Flexible tools for specifying design variation

This paper describes flexible tools for specifying design variations that are based on non-uniform profile tolerance definitions. These tools specify bounds of design performance that can be used for negotiation among engineers in a collaborative design process. These specification methods allow for the capture of many different design functions that are not easily described with current tool designs. In addition, these specification methods lend themselves to efficient verification methods. Profile tolerance definitions provide the most general variation controls for complex mechanical surfaces. Common design practices and engineering standards for profile tolerances exhibit many weaknesses and limitations. We present a rationale for a complete specification approach using B-splines [1, 2] for profile tolerances, and illustrate the approach with examples. B-splines can be used to specify both uniform and non-uniform profile tolerance boundaries. Subsequently, algorithms for the evaluation of actual feature deviations and reporting methodologies for such tolerance zones are presented.     

Dimensional and geometrical tolerance balancing in concurrent design

In conventional design, tolerancing is divided into two separated sequential stages, i.e., product tolerancing and process tolerancing. In product tolerancing stage, the assembly functional tolerances are allocated to BP component tolerances. In the process tolerancing stage, the obtained BP tolerances are further allocated to the process tolerances in terms of the given process planning. As a result, tolerance design often results in conflict and redesign. An optimal design methodology for both dimensional and geometrical tolerances (DGTs) is presented and validated in a concurrent design environment. We directly allocate the required functional assembly DGTs to the pertinent process DGTs by using the given process planning of the related components. Geometrical tolerances are treated as the equivalent bilateral dimensional tolerances or the additional tolerance constraints according to their functional roles and engineering semantics in manufacturing. When the process sequences of the related components have been determined in the assembly structure design stage, we formulate the concurrent tolerance chains to express the relations between the assembly DGTs and the related component process DGTs by using the integrated tolerance charts. Concurrent tolerancing which simultaneously optimizes the process tolerance based on the constraints of concurrent DGTs and the process accuracy is implemented by a linear programming approach. In the optimization model the objective is to maximize the total weight process DGTs while weight factor is used to evaluate the different manufacturing costs between different means of manufacturing operations corresponding to the same tolerance value. Economical tolerance bounds of related operations are given as constraints. Finally, an example is included to demonstrate the proposed methodology.     

基于工序加工能力的并行公差优化设计

提出一种基于工序加工能力的并行工序公差优化设计方法。在产品的初步结构设计阶段，通过相配零件的加工工艺规划把装配功能公差表示为零件的工序公差，建立以加权制造总成本最小为目标，以并行公差链、标准化的工序公差系数、机床最大经济极限公差为约束的非线性并行公差优化设计模型，求解该模型得到最佳的工序公差。最后给出了并行公差优化设计的一个工程实例，结果表明，所提的方法具有比传统串行等精度方法更合理、工序公差数值更大的优点。     

Compatibility of tolerancing

Tolerances are assigned to a mechanical engineering design either on the basis of functional and/or manufacturing requirements (toleranced dimensions, geometrical tolerances) or on the basis of the general categories—fine, medium, coarse—of the international standards or the designer's knowledge and experience (untoleranced dimensions). Conventional dimensions of the currently applicable dimensioning rules and implicit dimensions, including those attributed to geometrical tolerances, thus create four groups of tolerances which may or may not be compatible. In addition, any tolerance compromise, however tedious and difficult, not achieved systematically may well lead to accuracies which cannot be produced by the available machine tools. In the paper, a systematic approach to the above problems is presented. A methodology is demonstrated for the verification of the tolerance compatibility and for the assignment of compatible, producible and cost optimum tolerances.     

Rigorous Application of Tolerance Analysis in Setup Planning

Decades of computer-aided process planning research has resulted in techniques that automate portions of the process planning task such as operation sequencing and cutter path optimisation. Nonetheless, solutions to other areas such as setup planning and fixturing remain elusive. Setup planning research has received increased attention in recent years. The importance of tolerance analysis in setup planning has been recognised. However, due to the lack of a common measure for different types of tolerances, the analysis is carried out in an ad hoc fashion and often results in suboptimal setup plans. In this paper, a tolerance normalisation approach is presented to provide an accurate means for direct comparison of different types of geometric tolerances and dimensional tolerances. A normalised tolerance is an angle representing the maximum permissible rotation error when locating a component. It is calculated based on rigorous analysis of manufacturing errors involved in component setups. The formulae for tolerance normalisation are derived and the use of normalised tolerance in setup planning is illustrated.     

Tolerance design optimization of machine elements using genetic algorithm

An important problem that faces design engineers is how to assign tolerance limits. In practical applications, tolerances are most often assigned as an informal compromise between functionality, quality and manufacturing cost. Frequently, the compromise is obtained iteratively by trial and error. A more scientific approach is often desirable for better performance. In this paper, a genetic algorithm (GA) is used for the design of tolerances of machine elements to obtain the global optimal solution. The objective is to design the optimum tolerances of the individual components to achieve the required assembly tolerance, zero percentage rejection of the components and minimum cost of manufacturing. The proposed procedure using GA is described in this paper for two tolerance design optimization problems: gear train and overrunning clutch assemblies. Results are compared with conventional techniques and the performances are analyzed.     

推荐采用跳动公差评定凸轮

在建立了形位公差国家标准之后,一般仍用尺寸公差或者用线轮廓度公差评定凸轮.用径向圆跳动公差评定凸轮的方法优于前两者,径向圆跳动公差更适合于凸轮的评定.径向圆跳动公差评定时,凸轮的误差(测量)值和公差(评定)值都要是径向值,便于测量、处理、评定,方法简便、直观.     

尺寸链中形位公差的判别与解算

从零件形位公差要素所采用的公差原则入手,讨论了在尺寸链计算中,是否应该考虑形位公差的影响以及形位公差组成环性质的判别方法,并通过实例加以说明。     

Optimal tolerance design of assembly for minimum quality loss and manufacturing cost using metaheuristic algorithms

Tolerance allocation is a design tool for reducing overall cost of manufacturing while meeting target levels for quality. An important consideration in product design is the assignment of design and manufacturing tolerances to individual component dimensions so that the product can be produced economically and functions properly. The allocation of tolerances among the components of a mechanical assembly can significantly affect the resulting manufacturing costs. In this work, the tolerance allocation problem is formulated as a non-linear integer model by considering both the manufacturing cost of each component by alternate processes and the quality loss of assemblies so as to minimise the manufacturing cost. Metaheuristics techniques such as genetic algorithm and particle swarm optimisation are used to solve the model and obtain the global optimal solution for tolerance design. An example for illustrating the optimisation model and the solution procedure is provided. Results are compared with conventional technique and the performances are analysed.     

形位公差的计算机描述

公差信息是产品设计、制造和检测等过程中所必需的重要信息,在计算机集成制造环境中它为产品提供了设计的功能要求和工艺要求,是构成信息流自动化中的主要组成部分。本文着重研究常规和形位公差的计算机描述方法。提出了一套描述公差的数据结构,它可以与实体模型的CAD软件相连接,成为CAD软件中的一个功能模块。此数据结构已在IBM CATIA CAD/CAM软件上实现。     

Particle swarm optimization (PSO) algorithm for optimal machining allocation of clutch assembly

Nowadays tolerance optimization is increasingly becoming an important tool for manufacturing and mechanical design. This seemingly, arbitrary task of assigning dimension tolerance can have a large effect on the cost and performance of manufactured products. With the increase in competition in today’s market place, small savings in cost or small increase in performance may determine the success of a product. In practical applications, tolerances are most often assigned as informal compromises between functional quality and manufacturing cost. Frequently the compromise is obtained interactively by trial and error. A more scientific approach is often desirable for better performance. In this paper particle swarm optimization (PSO) is used for the optimal machining tolerance allocation of over running clutch assembly to obtain the global optimal solution. The objective is to obtain optimum tolerances of the individual components for the minimum cost of manufacturing. The result obtained by PSO is compared with the geometric programming (GP) and genetic algorithm (GA) and the performance of the result are analyzed .