# Optimization Method of Assembly Tolerance Types Based on Degree of Freedom
## 1 Introduction  
Product precision design is an important task in mechanical product design [1, 2, 3, 4, 5], and product precision affects the quality and performance of mechanical products [2, 3, 4]. Reasonable and accurate tolerance specifications for parts can help improve product quality and reduce manufacturing costs [3, 4, 5, 6, 7]. At present, with the development of digital and intelligent product design, the automatic generation of tolerance specifications has become an important research content and made an important breakthrough. The multi-color set method [8, 9], hierarchical tolerance information model method [10, 11, 12, 13, 14], adjacency matrix method [15, 16] and other methods [17] are combined with the computer to realize automatic reasoning of tolerance types of assembly parts. With the above method of automatic generation of tolerance types, the assembly features of the part are analyzed in order to obtain all the tolerance terms matching the assembly features. However, it generates a large number of tolerance terms, and designers need further manual screening and processing when marking part tolerance information. In the screening process, the designers mainly rely on their own experience in tolerance application to select the dimensioned tolerance type [13]. Because the designers are not thoughtful, the selected tolerance types may not meet the geometric tolerance functional requirements of mechanical products. Therefore, it is necessary to study a method that can realize screening optimization of the automatically recommended tolerance items under the circumstance of meeting the demand of the geometrical function tolerance of assemblies. The tolerance zone is usually used to limit the allowable variation range of the geometric shape, geometric position and geometric dimension of the geometric entity [18; 19]. To determine different tolerance zones, the tolerance zones can be determined and distinguished by the control parameters of the shape, size, direction, and position of the different tolerance zones [19]. The DOF can effectively represent the position and possible motion of assembly feature elements in three-dimensional space [20; 21]. In an assembly, the different directions of the tolerance zones of the assembly feature elements and their positional variations are ultimately transferred to the target parts of the assembly [7; 21; 22; 23]. [PERSON] [21] constructed a cumulative error transfer equation between contact displacement variations and assembly geometric-functional tolerances using small tolerance band displacement degrees of freedom to enable assembly tolerance analysis. In the ideal assembly connection without considering contact deformation, the position variation of the assembly connection mainly comes from the errors in the four dimensions of shape, size, direction, and position of the assembly feature surfaces. Assembly feature elements marked with different shape and position tolerances will have different tolerance zones. Different tolerance zones will constrain different variation characteristics of assembly feature surfaces, and the degree of influence on the geometric function of the assembly will be different [18; 19; 21]. Logically, using the DOF to describe the change direction of the tolerance zone and the change direction that affects the geometric functional error of the assembly, and studying the influence relationship between the above two types of change displacement is helpful to optimize the tolerance type of the assembly feature elements. Therefore, by introducing the concept of DOF to define the change direction of tolerance zone, the DOFs of tolerance zones with different shapes are obtained. By analyzing the level of influence of the variation displacement of typical assembly joint feature surfaces on the geometric function of typical assemblies, the mapping relationship between the geometric function requirements of typical assemblies and the control parameter freedom degrees (CPDFs) is constructed.