## 2 Construction of Assembly Multidimensional Evaluation Index
### Evaluation Index of Assembly Ontology Dimension
#### 2.2.1 Individual Indicators of Assembly Base Unit Parts
\(d_{min}\) and \(d_{max}\) denote the minimum and maximum sizes of the base unit parts that can be assembled in the small assembly space of reducers, and they are determined empirically. The fuzzy evaluation value \(w(x)\) is 0 if the maximum size is exceeded or the minimum size is lower, which means that the assembly process is not suitable. When the size of the assembly base unit is in the intervals [\(d_{min}\), \(d_{1}\)] and [\(d_{2}\), \(d_{max}\)], the fuzzy evaluation value \(w(x)\) is in the interval [0, 1], and the assembly base unit needs to be assembled using auxiliary tools. Therefore, the smaller the fuzzy evaluation value of the assembly base unit, the poorer the operability, and the assembly should be prioritized. \(3\) Symmetry of individual base units  
Typically, the individual base units of aerospace reducers have a complex structure, and many components are symmetrical. Base units are assembled according to whether the symmetry of their structure is good or bad. Assembly base units with poor symmetry in their structure are given priority. In the assembly process of an aviation reducer, the better the symmetry of the base unit body, the fewer adjustments to the assembly direction are required and the greater the operability of the assembly. Generally, the symmetry of an assembly base unit is determined according to the distance between the center of mass of the unit and the ideal symmetry center of mass. Thus, the basic idea of an enclosed box is introduced to calculate the symmetry index of individual base units, and the center of the enclosed box is taken as the ideal symmetry center of mass; the calculation method is shown in Equation (7):  
\[d(x)= \begin{cases}1-\frac{|x-u|}{l_{u}}\\ 1-\frac{|y-v|}{l_{v}}\\ 1-\frac{|z-v|}{l_{w}}\end{cases}  \tag{7}\]  
\(x,y,\) and \(z\) denote the coordinates of the center of mass of the assembly base unit. \(u,v,\) and \(w\) denote the coordinates of the center of the enclosed box of the assembly base unit. \(l_{u},l_{v},\) and \(l_{w}\) denote the maximum values of the side lengths of the enclosed box of the assembly base unit in the u, v, and w directions. In Equation (7), the closer the center of mass of the assembly unit is to the ideal symmetric center of mass, the better the symmetry. \(x,\)\(y,\) and \(z\) represent the symmetry of any three dimensions of the assembly unit, assuming that the distance between the two centers in a certain direction is zero, which means that the unit is symmetrical in that direction. As the distance between the two centers increases, the individual symmetry value \(d(x)\) of the base unit becomes smaller, which means that the symmetry of the base unit in that direction is worse, and, thus, it should be given priority. The fit relationship between individual base units mainly includes a gap fit, a transition fit, and an interference fit, resulting in three types of fit couplings. In an aviation reducer base unit, some individual units have more than one fit; that is, there are a variety of fit relationships. The higher the fit relationship value of the individual base unit, the more it should be prioritized for assembly. The evaluation value of the fit relationship between base unit individuals is determined according to the experience of the craftsman, as shown in Table 1. If the individual base unit has both a gap fit and an interference fit or a transition fit in the assembly process, then the lowest evaluation value is selected. From the assembly base unit fit relationship index value table, it can be seen that base units with a lower value should be assembled first.