3D ISO manufacturing specifications with vectorial representation of tolerance zones

In order to respect the functional drawing of a part, the process planer first has to choose the manufacturing process and then establish the manufacturing specifications to fulfill on the part after each phase. This paper introduces the tolerance zone transfer method, which is based on a vectorial representation of tolerance zones. For each functional requirement, it consists in analyzing the tolerance zone mobilities and the datum function. The transfer determines by iteration manufacturing specifications for each phase. Operations on degrees of freedom allow us to specify the right need using the ISO standards of tolerancing.     

Dimensioning of the intermediate states of the machined phases “DISMP” approach

In manufacturing practice for each machining operation, transfer techniques are extensively used for the allocation of manufacturing specification tolerance type and value. This paper focuses more on tolerance type which is the basis for a coherent and complete tolerancing process. We developed an algorithmic method called “DISMP” in order to generate the necessary types of manufacturing specifications that guarantee the respect of the functional requirements. A geometric variation model, based on the invariants degrees of freedom (DOFs) of the datum reference frames (DRF) and the toleranced surfaces serves to specify the two extremities of the tolerance chain. The identification of the controlled DOFs (Cont-DOFs) of the positioning reference frames in each machining phases and also the constrained DOFs (Cons-DOFs) of each machined surface contributes to the development of the way linking between the functional toleranced surface and its functional DRF. To generate the appropriate manufacturing geometric specifications, our method can be divided in five steps. We started by the translation of the ISO functional specification using the topologically and technologically related surfaces rules “TTRS” (Step 1: M1). Mapping the manufacturing process (Step 2: M2 and M3) requires the identification of the Cons-DOFs of the machined surfaces and those controlled by the positioning surfaces “Cont-DOFs” in each phase. The search of all chain links, which constitute the tolerance chain, is realized on Step3 (M4 and M5). Then, in step 4 (M6), we generate ISO standardized manufacturing specification. The fifth step (M7) draft technological constraints related to the manufacturing process, i.e., the case where there are inversion in the order between the toleranced surfaces and its DRF. Finally, we present the manufacturing process phases with ISO standards requirements.     

3D manufacturing tolerancing with probing of a local work coordinate system

The safety and performance requirements for mechanisms are such that the necessary accuracy of part geometry is difficult to reach using classical manufacturing processes. This paper proposes a manufacturing tolerance stack-up method based on the analysis line method. This technique enables both the analysis and the synthesis of ISO manufacturing specifications through a new approach which relies on production specifications, adjustment specifications, and their analysis to stack up the 3D resultant. The originality of the method resides in the 3D calculation for location requirements, which takes into account angular effects and probing operations on numerical-control machine-tools in order to define a local work coordinate system (WCS). For achieving tolerance analysis, deviations are modeled using small-displacement torsor. This tolerance analysis method enables one to determine explicit three-dimensional linear relations between manufacturing tolerances and functional requirements. These relations can be used as constraints for tolerance optimization.     

新一代产品几何量技术规范(GPS)标准体系研究

新成立的国际尺寸与产品几何技术委员会(ISO/TC213)提出了新一代GPS标准体系,该标准体系由基础、全局、通用和补充GPS标准组成。新一代GPS标准为产品的设计、制造、检验与评估提供了一套完整的技术规范。分析了新一代产品几何量技术规范(GPS)的系统模型、标准体系、关键技术、目前的研究方向与内容,以及我国新一代GPS标准体系的建立途径。     

基于宽容分层序列法的飞机装配公差稳健设计技术

飞机制造中由于工序能力指数和公差等设计变量存在变差,可能导致无法满足飞机装配质量要求以及制造成本波动较大的问题。运用稳健设计方法建立了飞机装配公差的可行稳健性和敏感稳健性两类设计模型。可行稳健设计考虑了公差等设计变量对装配可行性的影响,使其变差不影响装配功能的实现;敏感稳健性设计则考虑了公差等设计变量对制造成本和装配质量的影响,在目标成本较小的前提下使得目标成本和装配质量受设计变量变差的影响最小。提出了针对飞机装配公差可行敏感稳健设计的多目标优化问题的宽容分层序列求解算法。将公差设计中制造成本、装配质量波动、制造成本波动多个设计目标按照重要性依次排序。首先求解成本最小情况下的公差一般优化解,然后在成本最小值的宽容约束下,求得具有装配质量波动最小值的公差,最后在上述两个优化目标的宽容约束下,求得成本波动最小的最优公差。应用实例和分析结果表明了方法的有效性。       

Three-dimensional modelling of manufacturing tolerancing using the ascendant approach

This paper proposes a three-dimensional approach towards manufacturing tolerancing that uses a strategy to strictly consider the definition of a datum system imposed by ISO standards. This approach, called three-dimensional manufacturing tolerancing (TMT), is based on the small displacement torsor, which describes the possible deviations between machined surfaces and nominal surfaces of the part model. Every requirement of the definition drawing is treated separately with its own calculation model. The iterative ascending analysis allows one to establish the influence of the most recent phase and determine the influential parameters from previous phases. The nominal part model is defined on the datum systems of the requirement, and deviations are expressed with respect to both the machining process and the chosen machine adjustment method. The result takes the form of a formula that yields the variation in characteristics specified in the requirement based on quantifiable parameters identified on the machine.     

A continuous tolerance system

This paper analyzes the current ISO tolerance systems (ISO 286-1¹ and ISO 286-22) and presents new formulas that allow the aggregation of the tolerance system in a simple way. The approach used makes it possible to compute the tolerances in a continuous manner with respect to both dimension and grade of tolerance (quality). The results are always within the tolerances tabulated in the ISO 286-1' and 286-22 Standards. This continuous approach is suitable for optimization in design and automation in tolerancing on computer-assisted design (CAD) systems. The paper proposes a tolerancing approach closer to the modern tolerancing philosophy as given by the Taguchi methods.     

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.     

一种基于制造环境的统计公差分析方法

在并行公差设计理论的基础上,提出基于制造环境的面向装配的统计公差分析方法,使得在公差设计中,考虑实际加工环境的加工状况,即各种加工方法的工序能力。在此基础上,建立基于工序能力的统计公差分析模型。在假定过程平均漂移为均匀分布和正态分布两种情况下,计算出制造偏差的概率密度函数,进而推导出线性装配相应函数的概率统计特性值,为统计公差优化设计奠定了基础．     

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.     

棱柱公差一致性验证技术的研究

分别按照国际中的包容要求、最大实体要求及最小实体要求 ,分析了棱柱形零件尺寸公差和形位公差一致性准则 ,给出了判别一致性的数学等效式 ,举例说明了棱柱公差一致性验证的过程 ,为棱柱形零件计算机辅助公差设计的一致性验证提供了理论方法。     

面向公差技术的几何要素自由度表示与操作及其应用

描述了几何要素的本征方向和本征自由度概念、几何要素自由度的表示方法和约束自由度的计算规则。根据基本几何元素的几何特征以及与基准要素的位置关系确定了几何要素的本征方向,根据几何量测量原理,提出了基准要素约束自由度的计算方法,建立了基准体系约束自由度的计算规则。根据公差类型与基准要素和目标要素的关系,建立了公差设计正确性、完整性验证的具体规则,提出了基于自由度分析的公差标注正确性验证方法。     

Evaluation of machining process by integrating 3D manufacturing dispersions,functional constraints,and the concept of small displacement torsors

This paper presents a 3D formalization of manufacturing tolerancing which associates the concept of small displacements, the functional constraints, and manufacturing process capability. This approach would make it possible to establish relations which limit the surface variations of the production mechanism by the functional specifications. These relations have a number of requirements imposed by designer and are sufficient to evaluate the manufacturing process. The variations of the manufacturing process are defined in relation to variations measured by 3D measuring.     

A solution of worst-case tolerance analysis for partial parallel chains based on the Unified Jacobian-Torsor model

The Unified Jacobian-Torsor model is highly suitable for tolerance analysis of complex assemblies that are constituted by a large number of rigid parts. However, partial parallel chains with leverage effect of geometrical structures widely exist in these assemblies, especially in a transmission device, such as gear-box; but this model only considers the serial kinematic chains in the assemblies. If this type of partial parallel chains was ignored, it would lead to a large loss in accuracy and reliability; few previous studies have focused on it. In this paper, a solution of worst-case tolerance analysis based on Unified Jacobian-Torsor model is proposed to solve this type of partial parallel chains. First, the parallel joints that form parallel chains in the assembly are determined. Second, the contact points originated in the CLIC (localization tolerancing with contact influence) method are used to determine the boundary position of the parallel joints, and the analysis points from the analysis line method are determined to calculate their deviations at each joint. Third, these deviations are used together to calculate the torsor parameter of the parallel joints according to their torsor features and geometric structure. Fourth, the partial parallel chains are replaced by a new serial chains with the obtained torsor parameters to calculate the final deviations of the functional requirements based on the Unified Jacobian-Torsor model. An industrial application of the spiral bevel gear-box is given to demonstrate this solution.     

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.     

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。     

公差分析中的统计公差方法综述

公差分析是公差设计中的重要问题,公差分析方法分为极值法和统计公差方法两类,其中大多数方法是以概率统计原理为基础的统计公差方法。本文介绍了常用的公差分析方法,包括极值法、方和根法、修正的方和根法、蒙特卡洛模拟法、田口试验法和卷积方法等,并对这些方法进行了比较,阐述了统计公差方法的适用性。     

A new algorithm for optimum tolerance allocation of complex assemblies with alternative processes selection

Allocating tolerance to sub-components of a complex assembly with alternative processes selection by using Lagrange’s multiplier method is tedious as well as difficult. The present work is aims to solve the problem with simple effort in three stages. In the first stage, the maximum of two processes are selected from the alternative processes of each component and these two processes correspond to the smaller sum of difference in manufacturing cost. A hybrid optimum tolerance allocation method is developed in a second and third stage by combining Tabu search (TS) and heuristic approach. Application of the proposed algorithm is demonstrated on complex tolerancing products like knuckle joint and wheel mounting assembly. For the same manufacturing conditions, compared with tolerance synthesis by Singh method, the proposed method saved nearly $74,880 and $479,520, respectively, per year in manufacturing costs of knuckle joint and wheel mounting assembly.     

An industrial implementation of computer-aided tolerance charting

This paper argues that tolerance charting is not relevant for design tolerancing, but that it is an effective tool for process planning. It also argues that the tolerance charting algorithm based on rooted tree graphs, developed by the authors, provides a very general and powerful representation technique for tolerance charting. The technique is explained in detail to show how it can encompass all practical manufacturing processes that affect dimensions. A computer-based implementation of this technique, called CATCH, has been developed and is currently being used by a company in Singapore for process planning.