# A Tolerance Type Screening Method Based on Similarity Evaluation
## 3 Similarity Assessment Strategies
### Tolerance Specification Scheme
\(\mathbf{E}_{\text{t}}\) is the tolerance element, \(\mathbf{P}\) represents the part containing assembly feature elements, \(\mathbf{R}_{\text{t}}\) represents the spatial topological relationship, \(\mathbf{A}_{\text{c}}\) represents the constituent elements of the part, and \(\mathbf{F}_{\text{t}}\) represents the functional characteristics. The problem description of determining the tolerance type is composed of five tuples: \(\mathbf{E}_{\text{t}}\), \(\mathbf{P}\), \(\mathbf{R}_{\text{t}}\), \(\mathbf{A}_{\text{c}}\), and \(\mathbf{F}_{\text{t}}\). \(\mathbf{T}_{\text{dt}}\), \(\mathbf{T}_{\text{ds}}\), \(\mathbf{A}\), and \(\mathbf{T}_{\text{dt}}\) description of the solution to the problem consists of four tuples including \(\mathbf{T}_{\text{t}}\). Based on the perspective of similarity reasoning, the above-mentioned \(\mathbf{T}_{\text{df}}\), \(\mathbf{T}_{\text{ds}}\), \(\mathbf{T}_{\text{dt}}\), \(\mathbf{E}_{\text{t}}\), \(\mathbf{P}\), \(\mathbf{R}_{\text{t}}\), \(\mathbf{A}_{\text{c}}\), and \(\mathbf{F}_{\text{t}}\) can be used to represent the target case; previous resource cases can be represented by \(\mathbf{T}_{\text{df}}\), \(\mathbf{T}_{\text{ds}}\), \(\mathbf{T}_{\text{dt}}\), \(\mathbf{F}_{\text{t}}\), \(\mathbf{E}_{\text{t}}\), \(\mathbf{P}\), \(\mathbf{R}_{\text{t}}\), \(\mathbf{A}_{\text{c}}\), and \(\mathbf{F}_{\text{t}}\). Therefore, the formal representations of geometric tolerance project resource cases and target cases are defined as follows:  
Define tolerance resource case. A tolerance resource case is defined as an eleven tuple \(\mathbf{T}_{\text{c}}=(\mathbf{N},\mathbf{D},\mathbf{T}_{\text{df}},\mathbf{T}_{\text{ds}}, \mathbf{T}_{\text{dt}},\mathbf{T}_{\text{t}},\mathbf{T}_{\text{t}},\mathbf{E}_{ \text{t}},\mathbf{P},\mathbf{R}_{\text{t}},\mathbf{A}_{\text{c}},\mathbf{F}_{\text{t}})\). Figure 2: Tolerance element model diagram for pushing. Where \(T_{t}\) denotes the type of tolerance, \(R_{t}\) denotes the spatial topological relationship between the tolerance element and the datum element, and \(A_{c}\) denotes the component element of the part; \(F_{t}\) denotes the working characteristics of the part, \(E_{t}\) denotes the tolerance element, \(N\) is the case number, \(D\) is the designer, and \(T_{dt}\), \(T_{ds}\), and \(T_{dt}\) denote the first, second and third datums of the tolerance element, respectively. \(E_{t}\) is the tolerance element, and \(P\) denotes the element of the assembly feature. \(P\) is the part that contains the assembly feature element. From the case representation, it can be seen that the case is an 11-tuple data structure: \(E_{t}\), \(P\), \(R_{t}\), \(A_{c}\), and \(F_{t}\), and the other five tuples constitute the tolerance specification case \(T_{c}\) on the characteristics of the tolerance design problem description; \(T_{dt}\), \(T_{ds}\), \(T_{dt}\), and \(T_{t}\) and other four tuples constitute the problem-solving programmer description. Define two target cases. The target case can be defined as an 8-tuple of \(T_{o}\) = (\(T_{dt}\), \(T_{ds}\), \(T_{dt}\), \(E_{t}\), \(P\), \(R_{t}\), \(A_{c}\), \(F_{t}\)). The meaning of each tuple in \(T_{o}\) is consistent with the meaning in resource case \(T_{c}\). After the benchmark is determined, factors such as \(E_{t}\), \(R_{t}\), \(A_{c}\), and \(F_{t}\) are the key factors determining the tolerance scheme. Figure 2 shows an example of a resource case. Assuming the resource case number is \"HC0001\" and the designer is \"Liugh\". According to Definition 1, the resource cases in Figure 1 can be described as follows:  
\(T_{c}\) = (HC0001, Liugh, \(A\), Verticality, \(\mathbf{g}_{3}\), \(P\), [Vertical, Parallel, Vertical, Parallel], Vertical, Parallel]), [\(\mathbf{g}_{1}\), \(\mathbf{g}_{2}\), \(\mathbf{g}_{3}\), \(\mathbf{g}_{4}\), \(\mathbf{g}_{5}\), \(\mathbf{g}_{6}\)], \(F_{t}\)), Rotating motion, medium speed rotation.