# A Tolerance Specification Automatic Design Method for Screening Geometric Tolerance Types

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Application of Ontology in the Field of Product Design Tolerance Design

#### 2.2. Screening of Automatically Generating AT-Types

## 3. Constructing an AT Representation Model Containing Tolerance-Zone DOF Layers

#### 3.1. Tolerance-Zone Layer

**M**

_{T}

_{,21×6}, as indicated in Equation (1).

**M**

_{T}

_{,21×6}represent the tolerance types and the columns correspond to the AFE types, and the values of the elements

**C**

_{i,j}are related to the correspondence between the tolerance types and the AFEs, and if the tolerance type of the ith row has a mapping relationship with the type of AFE of the jth row, the value will be the tolerance zone type designation in Table 1, otherwise it will be “0”.

#### 3.2. Tolerance-Zone DOF Layer

**V**. If the coordinate system of the assembly is different from the coordinate system marked by each tolerance zone in Table 1, the element values in vector

**V**will change. The mapping relationship between the DOFs of each tolerance zone and the coordinate direction is represented by the adjacency matrix shown in Equation (2):

**M**

_{v}

_{i}

_{,3×6}, i {i = X, Y, Z} represent the tolerance-zone DOF vectors for the principal orientation of the coordinate system (usually the normal orientation of the tolerance feature), such as

**X_DOF**for the X axis,

**Y_DOF**for the Y axis and

**Z_DOF**for the Z axis. As shown in Table 1, for tolerance band TS5, if the principal direction of the tolerance band is the Z axis, the DOF vector

**V**=

**Z_DOF**is (1 1 0 1 1 0). (Note: when the coordinate system is changed, if the Z-axis direction is converted to the X-axis direction, the X axis is the main direction; if the Z-axis direction is converted to the Y-axis direction, the Y axis is the main direction).

## 4. Construction of an Ontology Framework for Assembly Tolerance Domain Oriented to Tolerance-Zone DOFs

#### 4.1. Semantic Modelling of Geometric Tolerance Information with Tolerance-Zone DOFs

#### 4.2. Construction of an AT Information Meta-Ontology Model Based on Tolerance-Zone DOFs

#### 4.3. Constructing the Class of AT Information Ontology Knowledge Base

#### 4.4. Defining Class Properties

**a**

_{u}and

**a**

_{v}are the individuals of the parts; if u ≠

**v**and there is an attribute hasACR between

**a**and

_{u}**a**, then there is an assertion that Part(

_{v}**a**

_{u}) and Part(

**a**

_{v}) and hasACR(

**a**

_{u},

**a**

_{v}) hold.

#### 4.5. OWL/SWRL Representation for AT Information Based on Tolerance-Zone DOFs

#### 4.5.1. SWRL Representation of Generation Rules for AT Specifications

- SWRL representation of rules for generating shape tolerance types. The form tolerance type is related to the target feature element type. SWRL rules are constructed according to the correspondence between the type of the target feature element and the form tolerance [3], and the automatically generated SWRL rule base for form tolerance items can be obtained [5,23,31]. For example, the commonly used shape tolerance types for cylinders are cylindricity, centre element axis straightness, cross-section roundness and rotation bus straightness; the inference rules are as follows: RCyindrical(?x) ∧ ICyindrical(?y) ∧ hasNON(?x,?y) → hasCylindricity(?x,?y) ∧ HasRoundness(?x,?y) ∧ hasStraihtness(?x,?y).
- SWRL representation of rules for generating orientation–position tolerance types. The orientation–position tolerance type of the target feature element is closely related to the orientation and position of the constrained feature element. The mapping relationship between the assembly tolerance type and the spatial relationship is expressed as the corresponding SWRL inference rule, and the SWRL rule base for the automatic generation of the orientation–position tolerance type can be established. For example, if the target feature plane and the constraint feature plane are perpendicular to each other, the tolerance types that can be selected for the target feature elements are positional and perpendicular. The inference rules are expressed as follows: TPlane(?x) ∧ CPlane(?y) ∧ hasPER(?x,?y)→ hasPerpendicularity(?x,?y) ∧ hasPostion(?x,?y).

#### 4.5.2. SWRL Representation of Inference Rules for Screening Tolerance Types

**M**

_{vi}

_{,3×6}for the tolerance-zone DOF layer and the mapping matrix

**M**

_{T}

_{,21×6}for the tolerance zone type layer. The tolerance type selection algorithm using the tolerance-zone DOFs proposed in reference [14] is shown in Figure 7. The protege 5.5 tool is used to complete the instantiation of different tolerance-zone DOF vectors for different tolerance types of the same AFE. Based on this, the SWRL rule language is used to describe the tolerance type selection algorithm using tolerance-zone DOFs, and the SWRL representation of the intelligent tolerance type selection rules is constructed.

- Reasoning rules for common DOF vector
**V**_{c}. In the coordinate system, if the normal direction of the target feature element is the Y-axis direction, the vector V_{t}is an instance of the class Y_DOF. The measurement reference feature DOF vector**V**_{f}is an instance of class DOFs. Then, the values of the elements in the vector**V**_{C}are the Boolean values between**V**_{t}and**V**_{f}. Based on the adjacency matrix**M**_{vi}_{,3×6}, which represents the tolerance-zone DOF vectors, the inference rule for finding the values of the six data attributes of the vector**V**_{c}is constructed. For example, the SWRL of the inference rule for finding the value of translational DOFs in the Y-axis direction for the vector**V**_{c}is expressed as: hasDOF_Y(**V**_{t},?x) ∧ hasDOF_Y(**V**_{f},?y) ∧ swrlb:notEqual(?x, ?y) -> hasDOF_Y(**V**_{c}, false); hasDOF_Y(**V**_{t},?x) ∧ hasDOF_Y(**V**_{f},?y) ∧ swrlb:Equal(?x, ?y) -> hasDOF_Y(**V**_{c}, ture).Similarly, the inference rules can be constructed for the other five data attribute values in the common DOF vector**V**_{c}. - Reasoning rules for the control parameter DOF vector
**V**_{0}. If**V**_{p}is the auxiliary DOF vector, the control parameter DOF vector V_{0}is the result of the Boolean of the auxiliary DOF vector**V**_{P}and the common DOF vector**V**_{C}. With reference to the method of determining the inference rule for the common DOF vector, the inference rule for determining the six data values in the control parameter DOF vector**V**_{0}is constructed. As an example, the SWRL of the inference rule for finding the rotational DOF value of the DOF vector**V**_{0}around the Y axis is expressed as follows: hasDOF_aroundY(**V**_{c},?x) ∧ hasDOF_aroundY(**V**_{p},?y) ∧ swrlb:notEqual(?x, ?y) -> hasDOF_aroundY(**V**_{0}, false); hasDOF_aroundY(**V**_{c},?x) ∧ hasDOF_aroundY(**V**_{p},?y) ∧ swrlb:Equal(?x, ?y) -> hasDOF_aroundY(**V**_{0}, true).Similarly, the inference rules can be constructed for the other five data values in the vector of control parameter DOFs V_{0}. - Inference rules for determining the comparative DOFs
**V**’_{ij_k}If_{.}**V**_{ij_k}is a vector of DOFs for the different tolerance types of an AFE (subscript**i**is the part number, j is the contact surface number, and k is the tolerance mark sequence number) and**V**_{0}is a vector of control parameter DOFs, then the comparative DOFs vector**V’**is the result of a Boolean operation between_{ij_k}**V**and_{ij_k}**V**_{0}. With reference to the method of determining the inference rule for the common DOF vector, the inference rule for determining the values of the six data attributes in the comparative DOF vector**V’**is constructed. As an example, the SWRL of the inference rule for determining the value of the translational DOF in the Y axis of the comparative DOF vector_{ij_k}**V**’_{ij_k}is expressed as follows: hasDOF_Y(**V**_{ij_k},?x) ∧ hasDOF_Y(**V**_{0},?y) ∧ swrlb:notEqual(?x, ?y) -> hasDOF_Y(V’_{ij_k}, false); hasDOF_Y(V_{ij_k},?x) ∧ hasDOF_Y(V_{0},?y) ∧ swrlb:Equal(?x, ?y) -> hasDOF_Y(V’_{ij_k}, true). - Reasoning rules for screening tolerance types. If the comparison DOF vector
**V’**and the control parameter DOF vector_{ij_k}**V**_{0}are equal, then**V**’is the comparison DOF for the preferred tolerance type. For this purpose, the SWRL rule for filtering the tolerance type is obtained and described as follows: hasDOF_X(_{ij_k}**V**_{’ij_k},?b) ∧ hasDOF_X(**V**_{0},?c) ∧ swrlb:Equal(?b, ?c) ∧ hasDOF_Y(**V**’_{ij_k},?d) ∧ hasDOF_Y(**V**_{0},?e) ∧ swrlb:Equal(?d, ?e) ∧ hasDOF_Z (**V**’_{ij_k},?f)∧ hasDOF_Y(**V**_{0},?g) ∧ swrlb:Equal(?f, ?g) ∧ hasDOF_aroundX(**V**’_{ij_k},?k) ∧ hasDOF_aroundX(**V**_{0},?l) ∧ swrlb:Equal(?k,?l) ∧ hasDOF_aroundY(**V**’_{ij_k},?m) ∧ hasDOF_aroundY(V_{0},?n) ∧ swrlb:Equal(?m,?n) ∧ hasDOF_aroundZ(**V**’_{ij_k},?j) ∧ hasDOF_aroundZ(**V**_{0},?k) ∧ swrlb:Equal(?j, ?k)->Select_of_effectiveness(**V**’_{ij_k},ture).

## 5. Implementation and Examples

#### 5.1. Constructing an Automatic Generation Algorithm for Screening AT Types Based on Tolerance-Zone DOF Ontology

#### 5.2. Example Verification

_{4}, which performs linear up and down motion, is actively connected to a hydraulic cylinder drive device. In this section, the workpiece Part

_{3}of the product model was selected as the research object to verify the feasibility of the tolerance specification design process shown in Figure 8.

#### 5.2.1. Pre-Processing of Product Modelling Information

- Acquisition of 3D models of products. The CAD 3D assembly model of the product was constructed, as shown in Figure 9a.
- The measurement target and reference object of the assembly and the global coordinate system were defined. The geometric functional requirement of the assembly was perpendicularity, as shown in Figure 9a. Then, the part Part
_{4}was defined as the target part of the assembly, and Part1 was defined the measurement datum part. According to the measurement elements and datum elements, the global coordinate system was established, as shown in Figure 9b. - According to the method introduced in reference [27], we extracted the assembly constraint information of the simple stamping model from the product assembly design data structure in the CAD system, such as the assembly constraint relationship between parts shown in Figure 10. In the figure,
**M**_{i(Pu,Pv)}indicates the assembly relationship between the assembled workpieces, subscript**i**indicates the assembly number, P**u**,P**v**indicates the assembled part number, respectively, and**u**is not equal to**v**. APJ_{k,l-n}indicates the localisation constraint connection between the assembled feature surfaces of the parts, subscript**k**indicates the assembly number of the parts and**l,m**indicates the feature surface number of the different parts, respectively; we extracted the assembly feature surfaces (AFSs) information of each part, such as the geometric and coordinate feature information of these AFSs and the geometric spatial relationship between each AFE of the part.

#### 5.2.2. Automatically Generate Tolerance Items for Parts of the Assembly

- Building the axiom set of the OWL assertions ABox. The OWL assertion axiom set ABox was established, which represents the assembly constraint relationships between the geometric product components based on these AFSs of each component and these constraint relationships between features. Taking Part
_{3}in Figure 10 as an example, the constraint relationship assertion AP between the parts was obtained, and AP can be expressed as per Equation (5).

_{P}= {Part

_{2}, Part

_{3}, Part

_{4}, hasMAT(Part

_{2}, Part

_{3},), hasMAT(Part

_{3}, Part

_{4})}

_{F}can be expressed as Equation (6).

_{F}= {Cylindrical (P

_{2}SF

_{4}), Planar (P

_{2}SF

_{3}), Planar (P

_{3}SF

_{4}), Cylindrical (P

_{3}SF

_{3}), Cylindrical (P

_{3}SF

_{2}), Cylindrical (P

_{3}SF

_{1}), Cylindrical (P

_{4}SF

_{2})}

- 2.
- A knowledge ontology library for the automatic generation of tolerance types was built. Following 4.5.3 and 4.5.4, the input of TBox, a set of terms for the tolerance specification design concepts, was realised using the protege5.5 ontology editor application, as shown in Figure 11. Taking part Part
_{3}as an example, the A_{P}A_{F}and A_{FR}assertion sets were input into the ontology editing tool software Protege 5.5 to realise the establishment of the OWL assertion axiom set ABox, and the tolerance type auto-generation knowledge base was finally obtained. The object property assertion of the assembly feature face P_{3}SF_{1}of part P3 is shown in Figure 12. - 3.
- Inference generation for tolerance types. The SWRL inference rules [35] were input to automatically recommend tolerance items for each part of the assembly. Taking part Part
_{3}as an example, the inference result of feature surface P_{3}SF_{1}was obtained, as shown in Figure 13. The tolerance types for other assembly feature surfaces are shown in Table 4.

#### 5.2.3. Automatic Screening of AT Types

- Constructing the set of tolerance type assertions TABOX for each assembly face of Part
_{3}. According to the reasoning in Section 5.2.2, the tolerance types of each AFS P_{3}SF_{1}, P_{3}SF_{2}, P_{3}SF_{3}, and P_{3}SF_{4}of part Part_{3}were obtained. The selection tolerance type assertion set As was constructed, as represented by Equation (8).

- 2.
- Setting of the control parameters DOF vector
**V**_{0}. Based on the geometric functional requirements of the assembly and the coordinate system determined in step 2 of Section 5.2.1, we instantiated tolerance-zone DOFs under the DOF class in the tolerance specification design knowledge ontology library. Based on this, the common parameter DOF determination rule and the control parameter DOF determination rule proposed in Section 4.5.2 were combined to infer the control parameter DOF vector**V**_{0}(the instantiation name is represented by CPDF). The data properties of instance CPDF are shown in Figure 14. The control parameter DOF vector**V**_{0}= (0 0 0 1 1 0) can be obtained from the data attributes of CPDF. - 3.
- Determination of comparative DOFs for different tolerance types. Using the comparative DOF calculation inference rule proposed in Section 4.5.2, the comparative DOFs for the different tolerance types on the AFSs of the work piece Part
_{3}were inferred. The AFS P_{3}S_{1}of the work piece Part_{3}had multiple recommended tolerance types, and coaxiality tolerance was one of them. Example B_ Coa3 is the comparative DOF for instance Coa3. After reasoning through the SWRL rule for comparing DOFs, the attribute values of the B_Coa3_1 instance were obtained, as shown in Figure 15. - 4.
- Screening of tolerance types. Using the screening rules proposed in Section 4.5.2, the screening of inferred tolerances for all the feature faces of part Part
_{3}was completed, and the results are shown in Table 5.

#### 5.2.4. Detailed Design of Tolerance Specifications

_{3}, further manual screening of tolerance types, adding tolerance material condition symbols and tolerance domain feature symbols were required [23,32]. The benchmark conditions for the directional positional tolerances were simultaneously selected. The marked tolerance of the final part Part

_{3}is shown in Figure 16.

## 6. Discussion

_{3}using the Qin [35] method are shown in Table 6. For example, the cylindrical assembly feature elements P

_{3}S

_{2}and P

_{3}S

_{3}of part Part

_{3}are recommended to obtain 10 kinds of shape and position tolerances, and through the design method of the automatic screening of tolerance types proposed by us, 6 kinds of tolerances were obtained; the planar assembly feature element P

_{3}S

_{4}is recommended to obtain 6 kinds of tolerance types, and after the automatic screening, 4 kinds of tolerances were obtained.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Armillotta, A. A method for computer-aided specification of geometric tolerances. Comput. Des.
**2013**, 45, 1604–1616. [Google Scholar] [CrossRef] - Zhao, Q.; Li, T.; Cao, Y.; Yang, J.; Jiang, X. A computer-aided tolerance specification method based on multiple attributes decision-making. Int. J. Adv. Manuf. Technol.
**2020**, 111, 1735–1750. [Google Scholar] [CrossRef] - Zhang, Y.; Li, Z.; Gao, J.; Hong, J. New reasoning algorithm for assembly tolerance specifications and corresponding tolerance zone types. Comput. Des.
**2011**, 43, 1606–1628. [Google Scholar] [CrossRef] - Zhang, Y.; Li, Z.; Wang, J. Hierarchical Reasoning Model of Tolerance Information and Its Using in Reasoning Technique of Geometric Tolerance Types. In Intelligent Robotics and Applications: First International Conference, ICIRA 2008 Wuhan, China, 15–17 October 2008 Proceedings, Part II, Wuhan, China, 2008; Springer: Berlin/Heidelberg, Germany, 2008; pp. 858–868. [Google Scholar]
- Qie, Y.; Qiao, L.; Cui, Y.; Anwer, N. A Doman Ontology for Assembly Tolerance Design. In Proceedings of the 2017 ASME International Mechanical Engineering Conference and Exhibition, Tampa, FL, USA, 3–9 November 2017; Volume 2. [Google Scholar]
- Luo, C.; Franciosa, P.; Mo, Z.; Ceglarek, D. A Framework for Tolerance Modeling based on Parametric Space Envelope. J. Manuf. Sci. Eng.
**2020**, 142, 061007. [Google Scholar] [CrossRef] - Johannesson, H.; Söderberg, R. Structure and Matrix Models for Tolerance Analysis from Configuration to Detail Design. Res. Eng. Des.
**2000**, 12, 112–125. [Google Scholar] [CrossRef] - Hong, Y.S.; Chang, T.C. A comprehensive review of tolerancing research. Int. J. Prod. Res.
**2002**, 40, 2425–2459. [Google Scholar] [CrossRef] - Mao, J.; Zong, Y. Assembly Tolerance Modeling Based on Generalized Directed Graph. Procedia CIRP
**2015**, 27, 318–323. [Google Scholar] [CrossRef] - Zhang, X.; Xiao, G.; Lin, Z.; Van den Bussche, J. Inconsistency-tolerant reasoning with OWL DL. Int. J. Approx. Reason
**2014**, 55, 557–584. [Google Scholar] [CrossRef] - Moguillansky, M.O. Ontology reasoning and evolution with inconsistency tolerance. AI Commun.
**2016**, 29, 405–407. [Google Scholar] [CrossRef] - Zhong, Y.; Qin, Y.; Huang, M.; Lu, W.; Gao, W.; Du, Y. Automatically generating assembly tolerance types with an ontology-based approach. Comput. Des.
**2013**, 45, 1253–1275. [Google Scholar] [CrossRef] - Shi, X.; Tian, X.; Wang, G. Screening Product Tolerances Considering Semantic Variation Propagation and Fusion for Assembly Precision Analysis. Int. J. Precis. Eng. Man.
**2020**, 21, 1259–1278. [Google Scholar] [CrossRef] - Liu, G.; Huang, M.; Chen, L. Optimization Method of Assembly Tolerance Types Based on Degree of Freedom. Appl. Sci.
**2023**, 13, 9774. [Google Scholar] [CrossRef] - Khodaygan, S.; Movahhedy, M.R.; Saadat Fomani, M. Tolerance analysis of mechanical assemblies based on modal interval and small degrees of freedom (MI-SDOF) concepts. Int. J. Adv. Manuf. Technol.
**2010**, 50, 1041–1061. [Google Scholar] [CrossRef] - Yang, L.; Cormican, K.; Yu, M. Ontology Learning for Systems Engineering Body of Knowledge. IEEE Trans. Ind. Informatics
**2021**, 17, 1039–1047. [Google Scholar] [CrossRef] - Gupta, R.K.; Gurumoorthy, B. Feature-based ontological framework for semantic interoperability in product development. Adv. Eng. Inform.
**2021**, 48, 101260. [Google Scholar] [CrossRef] - Chhim, P.; Chinnam, R.B.; Sadawi, N. Product design and manufacturing process based ontology for manufacturing knowledge reuse. J. Intell. Manuf.
**2019**, 30, 905–916. [Google Scholar] [CrossRef] - Anjum, N.; Harding, J.A.; Young, R.I.; Case, K. Manufacturability verification through feature-based ontological product models. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf.
**2012**, 226, 1086–1098. [Google Scholar] [CrossRef] - Qin, Y.; Qi, Q.; Lu, W.; Liu, X.; Scott, P.J.; Jiang, X. A review of representation models of tolerance information. Int. J. Adv. Manuf. Technol.
**2018**, 95, 2193–2206. [Google Scholar] [CrossRef] - Hagedorn, T.J.; Smith, B.; Krishnamurty, S.; Grosse, I. Interoperability of disparate engineering domain ontologies using basic formal ontology. J. Eng. Des.
**2019**, 30, 625–654. [Google Scholar] [CrossRef] - Su, S.; Wang, Y.; Chen, C.; Li, P.; Zhang, D.; Chen, G. Research on the knowledge representation and retrieval for mechanical product design based on ontology. Int. J. Wirel. Mob. Comput.
**2019**, 16, 340–349. [Google Scholar] [CrossRef] - Zhu, D.; Zhang, Z.; Shi, L.; Qian, J.; Qimuge, S.; Song, D. A hierarchical assembly knowledge representation framework and microdevice assembly ontology. Adv. Eng. Inform.
**2022**, 53, 101705. [Google Scholar] [CrossRef] - Li, Z.; Huang, M.; Zhong, Y.; Qin, Y. A Description Logic Based Ontology for Knowledge Representation in Process Planning for Laser Powder Bed Fusion. Appl. Sci.
**2022**, 12, 4612. [Google Scholar] [CrossRef] - Roh, B.; Kumara, S.R.T.; Witherell, P.; Simpson, T.W. Ontology-based Process Map for Metal Additive Manufacturing. J. Mater. Eng. Perform.
**2021**, 30, 8784–8797. [Google Scholar] [CrossRef] - Chen, R.; Lu, Y.; Witherell, P.; Simpson, T.W.; Kumara, S.; Yang, H. Ontology-Driven Learning of Bayesian Network for Causal Inference and Quality Assurance in Additive Manufacturing. IEEE Robot. Autom. Lett.
**2021**, 6, 6032–6038. [Google Scholar] [CrossRef] - Zhong, Y.; Qin, Y.; Huang, M.; Lu, W.; Chang, L. Constructing a meta-model for assembly tolerance types with a description logic based approach. Comput. Des.
**2014**, 48, 1–16. [Google Scholar] [CrossRef] - Peng, Z.; Huang, M.; Zhong, Y.; Tang, Z. Construction of ontology for auto-interpretable tolerance semantics in skin model. J. Amb. Intel. Hum. Comp.
**2020**, 11, 3545–3558. [Google Scholar] [CrossRef] - Sarigecili, M.I.; Roy, U.; Rachuri, S. Interpreting the semantics of GD&T specifications of a product for tolerance analysis. Comput. Des.
**2014**, 47, 72–84. [Google Scholar] [CrossRef] - Shah, J.J.; Yan, Y.; Zhang, B. Dimension and tolerance modeling and transformations in feature based design and manufacturing. J. Intell. Manuf.
**1998**, 9, 475–488. [Google Scholar] [CrossRef] - Desrochers, A.; Clément, A. A dimensioning and tolerancing assistance model for CAD/CAM systems. Int. J. Adv. Manuf. Technol.
**1994**, 9, 352–361. [Google Scholar] [CrossRef] - Anselmetti, B. Generation of functional tolerancing based on positioning features. Comput. Des.
**2006**, 38, 902–919. [Google Scholar] [CrossRef] - Cao, Y.; Zhang, H.; Li, B.; Wu, Z.; Yang, J. Study on functional specification scheme on interface based on positioning features. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf.
**2013**, 227, 745–753. [Google Scholar] [CrossRef] - Ma, N.; Yang, B.; Li, J.; Liu, Y.; Wang, D.; Gao, C. Transfer method of geometric tolerance items based on assembly joints. Int. J. Adv. Manuf. Technol.
**2021**, 117, 1689–1708. [Google Scholar] [CrossRef] - Qin, Y.; Zhong, Y.; Huang, M.; Liu, F. An assembly tolerance representation model based on spatial relations for generating assembly tolerance types. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**2013**, 228, 1005–1020. [Google Scholar] [CrossRef] - ISO 1101:2012; Geometrical Product Specifications (GPS)—Geometrical Tolerancing—Tolerances of Form, Orientation, Location and Run-Out. International Organization for Standardization: Geneva, Switzerland, 2012.

**Figure 1.**Assembly tolerance information representation model. A denotes the assembly, P denotes the part, PS denotes the part assembly feature surface (AFS), SPL denotes the assembly feature element (AFE) spatial relationship, TYP denotes the assembly tolerance type, TZ denotes the tolerance domain and TZDF denotes the tolerance-zone DOFs.

**Figure 7.**Tolerance type screening process [14].

Tolerance Code | TS_{1} | TS_{2} | TS_{3} | TS_{4} | TS_{5} | TS_{6} | TS_{7} | TS_{8} | TS_{9} |
---|---|---|---|---|---|---|---|---|---|

TZ form | |||||||||

DOI ^{1} | T_{Z} | T_{X}, T_{Y} | T_{X}, T_{Y} | T_{Z} | T_{Z} | T_{Z} | T_{Y} | ||

R_{X}, R_{Y}, R_{Z} | R_{X}, R_{Z} | R_{Z} | R_{X}, R_{Y}, R_{Z} | R_{Z} | R_{Z} | R_{X}, R_{Y}, R_{Z} | R_{X}, R_{Z} | ||

DOFs | T_{X}, T_{Y} | T_{Z}, | T_{Z}, | T_{X}, T_{Y}, | T_{X}, T_{Y}, | T_{X}, T_{Y} | T_{X}, T_{Y}, T_{Z} | T_{X}, T_{Z} | T_{X}, T_{Y}, T_{Z} |

R_{Y} | R_{X}, R_{Y} | R_{X}, R_{Y}, | R_{X}, R_{Y} | R_{Y}, | R_{X}, R_{Y}, R_{Z} | ||||

Representation | Ti (1,1,0) | Ti (0,0,1) | Ti (0,0,1) | Ti (1,1,0) | Ti (1,1,0) | Ti (1,1,0) | Ti (1,1,1) | Ti (1,1,1) | Ti (1,1,1) |

Ri (0,0,0) | Ri (0,1,0) | Ri (1,1,0) | Ri (0,0,0) | Ri (1,1,0) | Ri (1,1,0) | Ri (0,0,0) | Ri (0,1,0) | Ri (1,1,1) |

^{1}DOI represents degree of invariance.

**Table 2.**Mapping matrix of tolerance zone type relationship between assembly features and tolerance types.

Tolerance Number | Tolerance Type | Common Typical Assembly Feature Features (Exported Features) | |||||
---|---|---|---|---|---|---|---|

Cylindrical Surface (Line) | Plane (Plane) | Free-form Surface (Point, Line, Surface) | Sphere (Point) | Circular Countertop (Point, Line) | Prismatic Surface (Line, Surface) | ||

TT01 | TS_{4} | TS_{4} | TS_{4} | ||||

TT02 | Single direction | TS_{2} | TS_{2} | TS_{2} | TS_{2} | ||

TT03 | In any direction | TS_{5} | |||||

TT04 | TS_{3} | ||||||

TT05 | TS_{6} | ||||||

TT06 | TS_{8} | TS_{8} | |||||

TT07 | TS_{9} | TS_{9} | |||||

TT08 | Single direction | TS_{3} | |||||

TT09 | In any direction | TS_{5} | TS_{3} | ||||

TT10 | Single direction | TS_{3} | |||||

TT11 | In any direction | TS_{5} | TS_{3} | ||||

TT12 | In any direction | TS_{5} | TS_{3} | ||||

TT13 | Single directional | TS_{3} | TS_{2} | ||||

TT14 | TS_{3} | ||||||

TT15 | TS_{3} | ||||||

TT16 | TS_{1} | TS_{1} | |||||

TT17 | In any direction | TS_{5} | TS_{3} | TS_{7} | |||

TT18 | Radial circular | TS_{4} | |||||

TT19 | Axial circular | TS_{2} | |||||

TT20 | Total radial | TS_{6} | |||||

TT21 | Total axial | TS_{3} |

_{1}, TS

_{2}…TS

_{9}—see Table 1 for tolerance-zone marking codes. Symbol indicates parallelism, symbol indicates perpendicularity, symbol indicates coaxiality, t, symbol indicates straightness, symbol indicates positionality, symbol indicates cylindricity, symbol indicates roundness, symbol indicates flatness, symbol indicates line profile, symbol indicates surface profile, symbol indicates symmetry, symbol indicates run-out, symbol indicates inclination and symbol indicates total run-out.

Serial Number | Object Properties | Domain | Range |
---|---|---|---|

1 | hasZone | RealFeature | ToleranceZone |

2 | hasSpatialRelations | ConstainedFeature/RealFeature | TargetFeature/RealFeature |

3 | hasDOFs | ToleranceType | DOFs |

4 | hasToleranceType | TargetFeature/RealFeature | TolerranceType |

5 | hasADF | ConstainedFeature | TargetFeature |

6 | HasACR | RealFeature | RealFeature |

7 | hasFuncRequirement | Assembly | FuncRequirement |

Data Properties | Domain | Data Types | |

8 | hasDOF_AroundX | DOFs | Boolean |

9 | hasDOF_AroundY | DOFs | Boolean |

10 | hasDOF_AroundZ | DOFs | Boolean |

11 | hasDOF_X | DOFs | Boolean |

12 | hasDOF_Y | DOFs | Boolean |

13 | hasDOF_Z | DOFs | Boolean |

14 | hasDirection | ToleranceZone | String |

15 | Select_of_effectiveness | TolerranceType | Boolean |

ASF ^{1} | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

In the Plan | In Any Direction | |||||||||||

Recommended tolerances | P_{3}S_{1} | √ | √ | √ | √ | √ | √ | √ | ||||

P_{3}S_{2} | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ | ||

P_{3}S_{3} | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ | ||

P_{3}S_{4} | √ | √ | √ | √ | √ | √ |

^{1}AFS represents assembly feature surface.

ASF ^{1} | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

In the Plan | In Any Direction | |||||||||||

Selected tolerances | P_{3}S_{1} | √ | √ | √ | √ | √ | √ | |||||

P_{3}S_{2} | √ | √ | √ | √ | √ | √ | ||||||

P_{3}S_{3} | √ | √ | √ | √ | √ | √ | ||||||

P_{3}S_{4} | √ | √ | √ | √ |

ASF ^{1} | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

In the Plan | In Any Direction | |||||||||||

Qin [35] method | P_{3}S_{1} | √ | √ | √ | √ | √ | √ | √ | ||||

P_{3}S_{2} | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ | ||

P_{3}S_{3} | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ | ||

P_{3}S_{4} | √ | √ | √ | √ | √ | √ | ||||||

Our method | P_{3}S_{1} | √ | √ | √ | √ | √ | √ | |||||

P_{3}S_{2} | √ | √ | √ | √ | √ | √ | ||||||

P_{3}S_{3} | √ | √ | √ | √ | √ | √ | ||||||

P_{3}S_{4} | √ | √ | √ | √ |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, G.; Huang, M.; Su, W.
A Tolerance Specification Automatic Design Method for Screening Geometric Tolerance Types. *Appl. Sci.* **2024**, *14*, 1302.
https://doi.org/10.3390/app14031302

**AMA Style**

Liu G, Huang M, Su W.
A Tolerance Specification Automatic Design Method for Screening Geometric Tolerance Types. *Applied Sciences*. 2024; 14(3):1302.
https://doi.org/10.3390/app14031302

**Chicago/Turabian Style**

Liu, Guanghao, Meifa Huang, and Wenbo Su.
2024. "A Tolerance Specification Automatic Design Method for Screening Geometric Tolerance Types" *Applied Sciences* 14, no. 3: 1302.
https://doi.org/10.3390/app14031302