# Current status and challenges of using geometric tolerance information in intelligent manufacturing systems

- 2.2k Downloads
- 5 Citations

## Abstract

Recent development in computer-based manufacturing and inspection has necessitated extended knowledge and usage of geometric tolerances as carriers of design intent. The aim of applying geometrical tolerances in design is to provide function-oriented precise description of part geometry where the conventional size tolerance system fails to address. In view of the current development of computer-aided systems, applying geometric tolerances opens a new research front. This article examines the challenges in applying geometric tolerance information to carry the design intent to other downstream manufacturing processes and intelligently integrate the whole system. Based on the observed practical capabilities and literature studies, it is concluded that the current computer-aided design (CAD) systems cannot effectively provide the appropriate use of geometric tolerances. This article highlights the existing challenges and proposes a scheme of algorithm development for appropriate use of tolerance symbols and conditions at the design specification stage. This, in the long run, enables the CAD model to carry the design intent and opens a window of opportunity for intelligently integrating manufacturing systems.

## Keywords

Geometric tolerance ISO 1101 ASME Y14.5M Intelligent manufacturing Coordinate measuring machine Computer-aided tolerating## 1 Introduction

Mechanical design is by nature a synthesis work intended to give precise description of the part on engineering drawings using pictures, texts, numbers and symbols. The design specifications transfer the design intent stated as the geometrical and material characteristics, the critical function relationships among features in part and the assembly requirements. The design specifications are not unique in nature, but valid within permissible ranges that should not come in conflict with the functional requirements. In order to guarantee the intended functions and assembly relationships, tolerances are specified, which define the permissible variations from the ideal part given in the drawing. This is because it is almost impossible to produce a part with perfect size and form as indicated in the drawing. Size variations are given by the size tolerances that are traditionally accepted to be sufficient to guarantee fulfilment of functional requirements. Taguchi [1] came up with another view indicating that any deviation from the ideal geometry was a loss of functionality. Thus, by specifying dimensions and size tolerances on drawings, designers convey the design intent concerning the shape requirements for manufacturing and inspection. Similarly, geometric tolerances convey the design intent concerning form and functional requirements.

Nowadays manufacturing industries are under intense pressure from the ever-increasing competition demanding products to be produced within tighter tolerances, shorter time to market and more accurate communication with design intent [2]. This has made many companies to recognize the importance of having competence in tolerating their drawings with geometric tolerances. The existing manufacturing practice on the workshop floor indicates that there are two main challenges to make smooth flow of design intent. Primarily, the practical use of the rules, symbols and concepts of geometric tolerances is not well established. In view of the extended use of computers in almost every activity involved in a product’s life cycle, the ability to represent a design model that is complete, consistent, meaningful and unambiguous is absolutely necessary. As the interpretation of the standards is not easy, companies are doing significant investment on training their engineers and technicians so that the geometric tolerance concepts given by the standards are well understood and applied. Secondly, computer representation of geometric tolerances, i.e., the symbols and textual rules, demands development of complex algorithms. It is crucial that the design representations including the tolerance information allow easy modification and design optimization. The ability to transfer both the dimensional model data and the associated tolerances including the providing functional requirements from computer-aided design (CAD) model is important for future progress of computer-aided inspection systems. In the process of developing common neutral files for data transfer, recent development in the standard for the exchange of product model data is widely expected as the most promising tool to solve the constraints on transfer of design data.

The objective of this article is to highlight the research and application challenges of using geometric tolerance information as a carrier of design intent to intelligently integrate the activities in the manufacturing process. On the one hand, the article addresses the concern in the possible misunderstanding of the relatively complicated international standards of geometric tolerances when implemented in the industry. On the other hand, as a result of the dynamic situation due to regular updates of the standards and the wider room for different interpretations of the geometric tolerance parameters, it is clearly observed that the established codes of measurement practice of geometric tolerances are insufficient. Variation in inspection techniques obviously leads to different results. Thus parts to be rejected may be accepted or parts to be accepted can not pass the quality control. The lack of unified and consistent measurement practice is more of concern when software-based inspection tools is used and mainly driven by commercial interests that dominate their availability and the frequency of software and hardware updates.

## 2 Literature review

Intelligent integration of design intent to manufacturing, assembly and inspection implies that the tolerance information is computer readable. This has not been an easy task as geometric tolerance information is expressed by a symbolic language using various symbols and texts. Driven by the industrial need and the computerization progresses, current research focuses on modeling and representation of the tolerance information to make the geometric tolerances readable by computer. For instance, Zhao et al. [3] reported that research in modeling and representation of geometric tolerances could be classified as system dependent and system independent. This classification is based on whether the tolerance modeling takes place within or out of the geometric modeling environment. Accordingly, the representation technique used will depend on the geometric modeling and representation. The solid models can be based on the implicit (unevaluated) form such as constructive solid geometry (CSG) representation or boundary representation (B-rep). While the CSG expresses the solid object symbolically using some basic primitives and Boolean operations, the B-rep uses topology and structure of vertices, edges and faces to represent a solid surface. The algorithms for these techniques are mainly developed to express the mathematical representation of the solid models, and they are less applicable to represent the functional requirements that geometric tolerances stand for. However, some researchers have attempted to incorporate geometric tolerance information into the geometry representations using CSG [4], B-rep solid model representation [5] and hybrid B-rep/CSG representation [6]. B-rep models represent the object explicitly and thus offer good visualization of the geometry. On the other hand, CSG models contain information about the model in unevaluated form, thus good visualization requires evaluated forms into explicit vertices, edges and surfaces. Hybrid B-rep/CSG representation is favoured in modern CAD systems in order to benefit from both representations.

- (i)
be compatible with current solid modeling system;

- (ii)
represent standard tolerance practices;

- (iii)
support automated tolerance analysis and synthesis.

This study highlights that the variational representation is more appropriate with respect to current solid modeling systems. It allows variation of the boundary surface of the surface model within specified tolerance zone. On the other hand, as discussed later in this article, the existing CAD systems have no capability to make automated tolerance analysis at least at the level of advising the designer on correct use of the tolerance symbols and application conditions.

## 3 Overview of geometric tolerancing principles

According to ISO 1101 [12] and ASME 14.5 [13], geometric tolerance is defined as “···an international language of symbols placed on technical drawings to adequately describe the allowable variation of part geometry.” In other words, the purpose of geometric tolerances is to establish smooth communication between the users of the standard. Accordingly, the geometric tolerance language uses well-defined set of symbols, rules, definitions and conventions to enable the required smooth communication.

*S*), i.e., one of the symbols in Fig. 1, and the tolerance value (

*t*) are given in a rectangular tolerance frame with at least two compartments (for single features) and up to five compartments (for related features). A typical tolerance frame with examples of modifying parameters is illustrated in Fig. 2.

Two major principles, the maximum material condition (MMC) principle and the independence principle (ISO 8015), lay the foundation of modern tolerating principle using geometric tolerances. While the MMC principle attempts to contain the form variations within the worst case boundary, the independence principle provides clear distinction between size and form tolerances unless a specific relationship is defined.

## 4 Standardization of geometric tolerances

Terminology difference between ASME 14.5M: 2009 and ISO 1101: 2004

ASME 14.5M | ISO 1101 |
---|---|

Basic dimension | Theoretical exact dimension (TED) |

Feature control frames | Tolerance frame |

Variation | Deviation |

True position (TP) | Theoretical exact position |

Reference dimension | Auxiliary dimension |

Symbols specified in ASME 14.5M: 2009 (not in ISO 1101: 2004)

Symbol | Designation | Interpretation |
---|---|---|

All round | Tolerance applicable all round to the bounded line shown by the tolerance specification | |

ALL OVER | All over | Applicable everywhere (to all surfaces) |

AVG | Average | Arithmetic mean (specially for flexible parts) |

CR | Controlled radius | Radii at all points within tolerance |

Between | Tolerance applicable to a limited segment | |

Tangent | Applicable to the tangent (contacting) element | |

Statistical tolerating | Statistical tolerance control (STC) required |

## 5 Tolerance zone

Tolerance zone formulation is one of the early attempts to achieve computer-based representation of geometric tolerances. Requicha [16] indicated the challenges of incorporating tolerance information, which are essential for design analysis, process planning, assembly planning and other applications into modern solid modeling systems.

In this work, the tolerance zone is used as a means of defining a minimum region of space so that the feature is said to be produced according to the design intent when all points of the tolerance feature are constrained within the limits of the tolerance zone. The diversity of parameters and application conditions cause difficulties to define a universal representation technique. This has forced researchers to focus on a particular geometric tolerance or a few of them with certain common characteristics. For instance, Teck et al. [17] developed a general method to define tolerance zones of form deviation using three parameters corresponding to the three degrees of freedom of a planar surface (one translation and two rotations). The method is not only limited to form deviations but also applied only to planar/flat surfaces. Others [18, 19, 20, 21] focused on representation of circularity error.

According to the technical note of Moroni and Petró [22], the minimum zone criterion can essentially be formulated as a non-linear optimization that mostly leads to local minima or even non-convergence. Using this criterion, many optimal theories are proposed [23] including combinatorial optimization approaches.

## 6 Geometric tolerances and assembly requirements

As stated earlier, geometric tolerance information is given in a drawing primarily to fulfill functional requirement. Additional purposes include assembly requirement (e.g., interchangeability of products), manufacturing requirement and inspection requirement are conveyed by geometric tolerance specification.

Functional requirement cannot be seen isolated from other requirements, particularly assembly. This is because the assembly condition influences the product’s functionality. A tight tolerance may be good for some parts but the assembly process can be difficult. Relaxed tolerance can also influence both function and ease of assembly. This is particularly true when the tolerance of a component exceeds its permissible designed value that leads to either difficulty of assembly work or ease of assembly but poor performance. Cost is directly related with either side of the conditions.

Assembly process of a part is affected by dimension and geometric tolerances. Location and orientation tolerances in particular are carriers of design intent on how a feature on the part is located and oriented both in the manufacturing process and the assembly. Dimensions of features with location and orientation tolerances are indicated in the drawing using data that are given partly with respect to assembly requirements and partly to indicate how the feature is constrained in space. Considering that producing the exact feature is impossible and in order to ease the assembly requirement, geometric tolerances are often given with material conditions that fall into three categories: MMC designated by Open image in new window , least material condition (LMC) designated by Open image in new window , and regardless of material condition that serves as a default value when the other two material conditions are not specified.

## 7 Coordinate measuring machines for inspection of geometric tolerances

- (i)
developing suitable and easy way to use measuring techniques and enabling the measured set of data to accurately represent the part to be inspected;

- (ii)
developing tolerance verification algorithms that are consistent with the existing standards of geometric tolerances like ISO 1101 and ASME 14.5M.

The advantage of CMM as a tool of product inspection is not only the fact that it improves inspection quality, but also enables control of complex geometries such as free form surfaces and reduces the inspection time. The last mentioned is attributed to the elimination of complex jigs and fixtures’ setup that are common problems in the traditional inspection method.

Though CMM is a precise machine being used as a standard inspection tool now, the application is hampered by problems related to issues like sampling scheme, probing strategies and identifying systematic errors and random noises in the measured data [24]. The sampling and probing work is mostly done by experience that leads to variations in the inspection quality and reliability. Correct sampling techniques highly influence the reference substitute geometry generated in order to estimate the error in the tolerance zone. To tackle the second problem, two types of algorithms are widely mentioned as suitable algorithms for CMM based inspections: (i) least-square type algorithms [25, 26] that compute the sum of squared errors; (ii) the minimum zone type algorithms [22]. The least-square type algorithm is widely used in commercial CMM-based inspections and claimed to be efficient, but inconsistent with the ASME 14.5M standard. Thus, inspections based on such algorithms can result in rejection of good parts or acceptance of poor parts. The minimum zone algorithm, on the other hand, is claimed to be better consistent with standards, but previous studies [27, 28] show that the algorithm is more computationally demanding specially for complex geometries.

## 8 Indications for future research

Geometric tolerances have been implemented in engineering drawings as carriers of design intent for over half a century. They can ease the communication between design to manufacturing and inspection. The geometric tolerances are symbolic languages involving many parameters and application conditions, and that this language is still under dynamic change in the standardization front, which makes it less understood in the industry—at least requires regular updating.

The symbolic representation and the regular changes being undertaken by standardization organizations have also created certain level of challenges on research to develop consistent algorithms that contribute to smooth transfer of design intent with less human intervention. As most of the geometric tolerance parameters have mutual interdependence, the algorithm development can be eased by studying the common characteristics.

- (i)
identifying the tolerance type in regard to the functional and assembly requirements;

- (ii)
identifying how the specifications are indicated in the drawing according to accepted/established language given by the standards;

- (iii)
specifying the legal conditions and determining the value of the tolerance that is achievable by the existing competence.

## 9 Conclusions

This paper assessed current status and application challenges of geometric tolerance information in mechanical drawing of parts from the view point of intelligently transferring design intent to manufacturing and inspection. The article focuses on highlighting both the application challenges of the existing international standards (ISO/ASME) on the workshop floor and the research challenges to develop efficient, unambiguous and consistent algorithms that facilitate the transfer of design intent to the downstream processes with no or minor human interference.

The computer-aided tools in the future of design engineering are expected to establish a system that operates intelligently and performs better than before. However, the existing machines and operations in the area are still unable to mimic some basic human capabilities such as adjusting appropriately to the dynamic environment, understanding some of the human readable symbols and texts, etc. It is only when such human actions and other natural reactions are “learned” that the system is said to be intelligent. This requires both hardware and software used in the area that have the ability to adapt to the dynamic changes. Investigating the extent of the use of geometric tolerance information to realize the required manufacturing system intelligence and the accompanying challenges is the main goal of the study reported in this article.

The challenges are observed both on the upstream and downstream side. On the upstream side, i.e., at the design specification phase, the design tools fall short of giving conceptual support to the designer when inappropriate geometric tolerance symbols and conditions are used. On the downstream side, CMM tools are providing formidable support to the inspection work by allowing inspection of complex geometries and reducing the inspection time. However, interpretation of the output results still depends, to a certain extent, on the competence of the inspector. Future research should particularly focus on the upstream side of the manufacturing system to further develop algorithms and find how the developed results can be incorporated into future CAD systems.

## References

- 1.Taguchi G (1986) Introduction to quality engineering: designing quality into products and processes. Asian Productivity Organization, TokyoGoogle Scholar
- 2.Cogorno GR (2006) Geometric dimensioning and tolerancing for mechanical design. McGraw-Hill Professional, New YorkGoogle Scholar
- 3.Zhao X, Pasupathy TM, Wilhelm RG (2006) Modelling and representation of geometric tolerances information in integrated measurement processes. Comput Ind 57:319–330CrossRefGoogle Scholar
- 4.Requicha AAG, Chan SC (1986) Representation of geometric features tolerances and attributes in solid models based on constructive geometry. IEEE J Robot Autom RA-2(3):156–166CrossRefGoogle Scholar
- 5.Guilfor J, Turner JD (1993) Representational primitives for geometric tolerancing. Comput Aided Des 25(9):577–586CrossRefGoogle Scholar
- 6.Turner JU (1990) Relative positioning of parts in assembly using mathematical programming. Comput Aided Des 22(7):394–400CrossRefGoogle Scholar
- 7.Samuel GL, Shunmugam MS (2000) Evaluation of circularity from coordinate and form data using computational geometric techniques. Precis Eng 24(3):251–263CrossRefGoogle Scholar
- 8.Samuel GL, Shunmugam MS (1999) Evaluation of straightness and flatness error using computational geometric techniques. Comput Aided Des 31(13):829–843CrossRefzbMATHGoogle Scholar
- 9.Gupta S, Turner JU (1991) Variational solid modelling for tolerance analysis. In: Proceedings of ASME International Conference on Computer Engineering, CA, USA, pp 487–494Google Scholar
- 10.Tsai J-C, Cutkosky MR (1997) Representation and reasoning of geometric tolerances in design. Artif Intell Eng Des Anal Manuf 11:325–341.Google Scholar
- 11.Roy U, Li B (1999) Representation and interpretation of polyhedral objects II. Comput Aided Des 31:273–285CrossRefzbMATHGoogle Scholar
- 12.ISO 1101 (2004) Geometrical product specification (GPS)—tolerance of form, orientation, location and runout, 2nd edn. International Organization for Standardization, GenevaGoogle Scholar
- 13.ASME (2009) Dimensioning and tolerancing. ASME Standard Y14(5M):2009Google Scholar
- 14.Krulikowski A (1998) Fundamentals of geometric dimensioning and tolerancing, 2nd edn. Division of Thomas Learning Inc., DelmarGoogle Scholar
- 15.Green P (2005) The geometrical tolerancing desk reference: creating and interpreting ISO standard technical drawings. Elsevier Ltd, OxfordGoogle Scholar
- 16.Requicha AAG (1983) Toward a theory of geometric tolerancing. Int J Robot Res 2(4):45–60.Google Scholar
- 17.Teck TB, Kumar AS, Subramanian V (2001) A CAD integrated analysis of flatness in a form tolerance zone. Comput Aided Des 33:853–865CrossRefGoogle Scholar
- 18.Zhu LM, Ding H, Xiong YL (2003) A steepest descent algorithm for circularity evaluation. Comput Aided Des 35(3):255–265CrossRefGoogle Scholar
- 19.Dhanish PB (2002) A simple algorithm for evaluation of minimum zone circularity error from coordinate data. Int J Mach Tool Manu 42(14):1589–1594CrossRefGoogle Scholar
- 20.Wen X, Xia Q, Zhao Y (2007) An effective genetic algorithm for circularity error unified evaluation. Int J Mach Tool Manu 46:1770–1777CrossRefGoogle Scholar
- 21.Venkaiah N, Shunmugam MS (2007) Evaluation of form data using computational geometric techniques—part I: circularity error. Int J Mach Tool Manu 47:1229–1236CrossRefGoogle Scholar
- 22.Moroni G, Petró S (2008) Geometric tolerance evaluation: a discussion on minimum zone fitting algorithms. Precis Eng 32:232–237CrossRefGoogle Scholar
- 23.Anthony GT, Anthony HM et al (1996) Reference software for finding Chebyshev best-fit geometric elements. Precis Eng 19(1):28–36CrossRefGoogle Scholar
- 24.Gou JB (1999) A geometric theory of form, profile and orientation tolerances. Precis Eng 23:79–93CrossRefGoogle Scholar
- 25.Forbes AB (1989) Least-square best fit geometric elements. Technical report of National Physical Laboratory, Middlesex, UKGoogle Scholar
- 26.Gou JB, Chu YX, Li ZX (1998) On the symmetry localization problem. IEEE Trans Robot Autom 14(4):540–553Google Scholar
- 27.Wang Y (1992) Minimum zone evaluation of form tolerances. ASME Manuf Rev 5(3):213–220Google Scholar
- 28.Kanada T, Suzuki S (1993) Application of several computing techniques for minimum zone straightness. Precis Eng 15(4):274–280CrossRefGoogle Scholar
- 29.Makelainen E, Heilala J (2001) Assembly process level tolerance analysis for electromechanical products. In: Proceedings of the IEEE international symposium on assembly and task planning, 2001, pp 405–410Google Scholar