3D Tolerance Analysis Research Articles

Solid modelling approach for 3D tolerance analysis of linear dimension applied to planar faces in an assembly

ABSTRACT This paper presents a 3D tolerance analysis approach for linear dimensions applied to planar faces in an assembly. The assembly variations are generated and visualized as an explicit geometrical stack-up of the component variations using the solid modeller Solidworks®. The feature variations are obtained by adapting the geometric solid model of each component, either by offsetting the target planar face or by tilting it within the tolerance zone. A concept of Oriented Minimum Bounding Box (OMBB) is introduced to generate individual component variations with any generalized shape of the target planar face. The analysis of the OMBB extents, the tilting angles and the corresponding pivot points has revealed symmetry in these data. Rigorous mathematical formulations have been implemented in this study to handle the general case of large and small displacements. An approach is suggested to evaluate the functional dimensions, the target face’s centroid and normal for each assembly variation. Functional dimensions of the assembly variations obtained by the software ‘3DCS Variation Analyst’ are found to deviate from those obtained by the proposed approach by up to 40% of the assembly tolerance size. 3DCS tool has also failed to detect out-of-specification assembly variations, which were identified by the proposed approach.

A statistical method of distinguishing and quantifying tolerances in assemblies

Distinguishing and quantifying the roles of tolerances in assemblies are very important to tolerance allocation and optimization. Some of geometric tolerances, such as orientation tolerances and form tolerances, are difficult to be considered in tolerance analysis and allocation processes. Three dimensional (3D) tolerance analysis methods explore a new way to deal with these tolerances. However, existing 3D models lack of effective methods to distinguish and quantify these tolerances in a statistical way. In this paper, based on a unified Jacobian-Torsor model, a statistical method of distinguishing and quantifying tolerances in assemblies is presented. The internal relation of tolerances inside a combinational tolerance is established by data fitting methods, and a calculating scheme used for percent contributions and their subdivisions is proposed. This method improves the utility of the unified Jacobian-Torsor model and has reference meaning to other 3D models. At last, this method has been illustrated on a simple two-block assembly. Sufficient comparison and discussion were made for the results, which demonstrated the effectiveness of the method.

Implementation of dimensional management methodology and optimisation algorithms for pre-drilled hinge line interfaces of critical aero assemblies – A case study

A dimensional management procedure is developed and implemented in this work to deal with the identification of the optimum hole diameter that needs to be pre-drilled in order to successfully join two subassemblies in a common hinge line interface when most of the degrees of freedom of each subassembly have already been constrained. Therefore, an appropriate measure is suggested that considers the assembly process and permits the application of optimisation algorithms for the identification of the optimum hole diameter. The complexity of the mechanical subassemblies requires advanced 3D tolerance analysis techniques to be implemented and the matrix method was adopted. The methodology was demonstrated for an industrial, aerospace engineering problem, that is, the assembly of the joined wing configuration of the RACER compound rotorcraft of AIRBUS Helicopter and the necessary tooling needed to build the assembly. The results indicated that hinge line interfaces can be pre-opened at a sufficiently large size and thus, accelerate the assembly process whilst the suggested methodology can be used as a decision-making tool at the design stage of this type of mechanical assembly.

3D tolerance analysis of the 1/32 CFETR vacuum vessel

Researchers began exploring methods for selecting tolerances at design level to ensure competitive products since the late 1980. Reliability of mechanical product depends greatly on different performance parameters among which tolerance optimization design is one of the most important activities. Application of the tolerance design to mechanical assemblies has benefits for obtaining valuable information regarding manufacturing process. This paper proposes methods for tolerance design of China Fusion Engineering Test Reactor (CFETR) vacuum vessel using the CETOL code based on the CATIA platform. Depending on the three-dimensional solid model, the tolerance analysis model of the vacuum vessel is simplified and then subdivided. Tolerances are allocated according to the overall assembly requirements of the vacuum vessel. The theoretical basis for tolerance analysis has been given as well as two proposed analyzing methods. Then the tolerance analysis model was established. The sensitivity and contribution analysis by CETOL were addressed to draw conclusions about the critical dimensions which could affect the target tolerances. Based on the results, the unreasonable tolerances have been redistributed to meet the tolerance requirements, which is very beneficial to ensure the assembly quality of the vacuum vessel.

Research on tolerance modeling method and 3D tolerance analysis technology based on STD

The description methods of various tolerance zones and kinematic links based on SDT are discussed. The surfacemodels are applied to describe an assembly, and SDT is used to express the relative position between any two surfaces of anassembly; According to the effect of each functional element on the whole functional requirements of products, the 3-1; dimension-chain is created, and 3-D dimensional and geometrical tolerance analysis for assembly is realized. The engineering example involving 3-D tolerance analysis is given to test the proposed method.

A variational model for 3D tolerance analysis with manufacturing signature and operating conditions

PurposeThe purpose of this work is to present a variational model able to deal with form tolerances and assembly conditions. The variational model is one of the methods proposed in literature for tolerance analysis, but it cannot deal with form tolerances and assembly conditions that may influence the functional requirements of mechanical assemblies.Design/methodology/approachThis work shows how to manage the actual surfaces generated by the manufacturing process and the operating conditions inside the variational model that has been modified to integrate the manufacturing signature left on the surfaces of the parts and the operating conditions that arise during an actual assembly, such as gravity and friction. Moreover, a geometrical model was developed to numerically simulate what happens in a real assembly process and to give a reference value.FindingsThe new variational model was applied to a three-dimensional case study. The obtained results were compared to those of the geometrical model and to those of the variational model to validate the new model and to show the improvements.Research limitations/implicationsThe proposed approach may be extended to other models of literature. However, its limitation is that it is able to deal with a sphere–plane contact.Practical implicationsTolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly before getting the physical assembly. It involves a decrease in the manufacturing costs.Originality/valueThe main contributions of the study are the insertion of a systematic pattern characterizing the features manufactured by a process, assembly operating conditions and development of a geometrical model to reproduce what happens in a real assembly process.

3DAモデルの3次元公差解析ツールへの活用

3DAモデルの3次元公差解析ツールへの活用

3D Tolerance Analysis with Manufacturing Signature and Operating Conditions

The present work shows a method to integrate the manufacturing signature and the operating conditions into a model for 3D tolerance analysis of rigid parts. The paper presents an easy way to manage the actual surfaces due to a manufacturing process and the operating conditions, such as gravity and friction, inside the variational model for a 3D tolerance analysis. The used 3D case study is deliberately simple in order to develop a conceptual demonstration.The obtained results have been compared with those due to a geometrical model that reproduces what happens during assembly. It has been considered as reference case.

A solution of partial parallel connections for the unified Jacobian–Torsor model

The unified Jacobian–Torsor model is an innovative three dimensional (3D) tolerance analysis method which uses the torsor model for tolerance representation and the Jacobian matrix for tolerance propagation. It is very suitable for complex assemblies which contain a large number of joints and geometric tolerances. However, previous studies about this model only considered serial connections in assemblies. Two reasons may account for this problem. One hand, the Jacobian matrix for parallel structures is complex. On the other hand, the torsor model which represents tolerance of assembly containing parallel connections is not presented. Ignoring these partial parallel connections would result in a loss of accuracy and reliability of the unified Jacobian–Torsor model. In this paper, a solution of partial parallel connections for the unified Jacobian–Torsor model is presented. A new torsor model representing partial parallel connections caused by joints of cylindrical and planar surfaces is obtained by a composition operation of screw parameters between torsors. Meanwhile, variations of this new torsor are achieved by an intersection or composition operation between participated torsors. A calculation scheme is proposed for this solution with a deterministic way and statistical way. An example is also presented to illustrate this solution.

Adaptive 3D Imaging and Tolerance Analysis of Prefabricated Components for Accelerated Construction

Tolerance analysis of prefabricated components poses challenges to effective quality control of accelerated construction projects in urban areas. In busy urban environments, accelerated construction methods quickly assemble prefabricated components to achieve workflows that are more efficient and reduce impacts of construction on urban traffic and business. Accelerated constructions also bring challenges of “fit-up:” misalignments between components can occur due to less detailed tolerance assessments of components. Conventional tolerance checking approaches, such as manual mock-up, cannot provide detailed geometric assessments in a timely manner. This paper proposes the integration of an adaptive 3D imaging and spatial pattern analysis methods to achieve detailed and frequent “fit-up” analysis of prefabricated components. The adaptive 3D imaging methods progressively adjust imaging parameters of a laser scanner according to the geometric complexities of prefabricated components captured in data collected so far. The spatial pattern analysis methods automatically analyze deviations of prefabricated components from as-designed models to derive tolerance networks that capture relationships between tolerances of components and identify risks of misalignments.

A small displacement torsor model for 3D tolerance analysis of conical structures

The small displacement torsor model is a classic three-dimensional tolerance analysis method. It uses three translational vectors and three rotational vectors to represent tolerance information in three-dimensional Euclidean space. However, the target features of this model mainly focused on planes and cylinders in previous studies. Little attention is invested to conical features and their joints which are used widely and more complex than the planar and cylindrical features. The objective of this article is to present a three-dimensional mathematical method of tolerance representation about conical surfaces and their joints based on the small displacement torsor model, and propose a mathematical model of variations and constraint relations of components of the small displacement torsor for conical surfaces caused by geometric tolerances limited by its tolerance zone. In addition, a simple example involving conical structures is used to demonstrate three-dimensional conical tolerance propagation. Both deterministic and statistical results are obtained by this model.

A Comparison Study of Mathematical Models for Tolerance Analysis

This paper reviews two major models (Small Displacement Torsor, Deviation and Clearance Domain) for 3D functional tolerance analysis and compares them. The underlying mathematical representation of geometric tolerances can be classified as inequalities and multi-variate region. The corresponding algebraic or geometric tolerance propagation mechanism of each model is briefly introduced for worst-case and statistical tolerancing. Through a comprehensive comparison of these models, this paper gives some suggestions for choosing the appropriate method for a given tolerancing problem.

Statistical Tolerancing based on Variation of Point-set

Functional tolerancing of mechanisms has now been well accepted in industry and become a major concern for academia. After a brief comparison of existing 3D functional tolerance analysis models, a statistical tolerancing approach based on variation of point- set is proposed in this paper. The toleranced surface is represented by a point-set which is consistent with its parametric equations, the semantics of geometrical tolerances are parameterized with respect to variation of point-set and associated mathematical interpretations of tolerance zone are formalized. Three methods are presented to extract individual points from point-set: characteristic points of MGRE, characteristic points of geometrical surface and discrete points of geometrical surface. The tolerance chains through key assembly features are analyzed and represented by homogenous transform matrix. The over-constrained degrees of freedom of a complex junction with multiple mating features are taken into account in accordance with datum precedence. The approach is applied to statistical tolerance analysis of a coordinate measuring machine to analyze deviation distribution of a geometrical functional requirement on the ending geometric feature.

Comparison of Spatial Math Models for Tolerance Analysis: Tolerance-Maps, Deviation Domain, and TTRS

This paper presents a comparison of degree of freedom (DOF) based math models, viz., tolerance-maps, deviation domain, and TTRS, which have shown most potential for retrofitting the nuances of the ASME/ISO tolerance standards. Tolerances specify allowable uncertainty in dimensions and geometry of manufactured products. Due to these characteristics and application of tolerances, it is necessary to create a math model of tolerances in order to build a computer application to assist a designer in performing full 3D tolerance analysis. Many of the current efforts in modeling tolerances are lacking, as they either do not completely model all the aspects of the ASME/ISO tolerance standards or are lacking the requisite full 3-D tolerance analysis. Some tolerance math models were developed to suit CAD applications used by the designers while others were developed to retrofit the ASME/ISO tolerance standard. Three math models developed to retrofit the ASME/ISO standard, tolerance-maps, deviation domain, and TTRS are the main focus of this paper. Basic concepts of these math models are summarized in this paper, followed by their advantages and future issues. Although these three math models represent all aspects of the ASME/ISO tolerance standard, they are still lacking in one or two minor aspects.

A Comprehensive Tolerancing System for 3D Mechanical Assemblies

A comprehensive tolerancing system is presented with its design principle, system architecture and key functions. The following functional modules, automatic generation of dimension chain, equivalent variational mechanism (EVM) modeling and visualized 3D tolerance analysis, are described in detail. Design intent is expressed by assembly tolerance specifications, which may be added to the model and used in computing predicted quality levels. A comprehensive method, based on equivalent replacement, has been developed for modeling variations in 3D mechanical assemblies. The models are constructed of common engineering elements: dimension chain, kinematic joints, assembly datums, dimensional and geometric feature tolerances, and assembly tolerance limits. The method is consistent with engineering design practice and is well suited for integration with commercial CAD systems. To make the tolerancing system robust and efficient, new functionalities are added to well-known CAD software and simulation environment. Tested by many samples, this system shows good robustness and practicability.

3DTS: A 3D tolerancing system based on mathematical definition

Tolerance is almost ubiquitous during the whole product lift cycle and is imperative for seamless integration of CAD and CAM. Based on the mathematical definition of tolerance, a 3D tolerancing system, 3DTS, is presented with its design principle, system architecture and key functions. The following functional modules, tolerance modeling, semantics interpretation, 3D tolerance analysis, are described in detail. To make the tolerancing system robust and efficient, many techniques such as hierarchical tolerance representation, rule-based evaluation and non-intersection determination of tolerance zone have been devised. Tested by many samples, this system shows good robustness and practicability.

3D tolerance analysis in PC manufacture

Describes Toshiba’s assembly of notebook PCs and the need to use simulation to verify assembly sequences which have tight 3D tolerances.

Computer-aided 3D tolerance analysis of disk drives

Disk drives are multicomponent products in which product build variations directly affect quality. Dimensional management, an engineering methodology combined with software tools, was implemented in disk drive development engineering at IBM in San Jose to predict and optimize critical parameters in disk drives. It applies statistical simulation techniques to predict the amount of variation that can occur in the disk drive due to the specified design tolerances, fixturing tolerances, and assembly variations. This paper presents statistics describing the measurement values produced during simulations, a histogram showing the measurement values graphically, and an analysis of the process capability, C pk , to ensure robust designs. Additionally, it describes how modeling can determine the location(s) of the predicted variation, the contributing factors, and their percent of contribution. Although a complete 2.5-in. disk drive was modeled and all critical variations such as suspension-to-disk gaps, disk-stack envelope, and merge clearances were analyzed, this paper presents for illustration only one critical disk real estate parameter. The example shows the capability of this methodology. VSA®-3D software by Variation Systems Analysis was used.

Tolerancing a solid model with a kinematic formulation

The 3D analysis of tolerances is one of the critical functional requirements of solid-modelling systems which is most lacking at the present time. 3D tolerance analysis is most difficult to carry out by hand when it involves geometrical tolerances. A computerized 3D tolerance analysis is therefore needed, and an appropriate tolerancing model must be devised. The paper first acknowledges the kinematic nature of tolerance-chain analysis. A kinematic formulation of full 3D dimensional and geometrical tolerances is then proposed. The scheme represents all tolerances within a kinematic model, which is compatible with existing standards such as ansi y14.5m. The semantics of tolerances is respected, as tolerances are automatically interpreted to yield tolerance zones and datum reference frames. A tolerance chain is modelled as a kinematic chain, thus enabling multiple tolerances to be manipulated to solve 3D tolerance-chain analysis problems. The implementation of the modelling concept on an exact solid modeller is described. An application of the tolerancing model to the visualization of tolerance zones is also shown.