## 2 Details of Anti-Loosening Bolted Connections  
A plain washer is a kind of gasket with an annular shape that has become an international standard due to its widespread use in engineering. In the standard, the sizes, materials, surface treatment technologies and other parameters are provided. Plain washers were originally designed to protect the surfaces of clamped components instead of preventing bolted joints from loosening. Whether plain washers contribute to anti-loosening performance is controversial. A wedge washer consists of a pair of locking washers with a cam on one side and radial teeth on the other side, as shown in Figure 3. The anti-loosening mechanism is based on negative feedback adjustment, i.e., loosening leads to relative misalignment of upper and lower washers and, in turn, causes tensile elongation of the bolt and an increase in preload.  
Figure 2: Three types of anti-loosening bolted connections.  
In the second type of anti-loosening bolted connections, a wedge-locking nut has a wedge ramp at the root of the thread, as shown in Figure 4a. During tightening of the wedge-locking nut, the bolt tips are pushed against the wedge ramps, and linear contact is formed between the internal and external threads, which gives a wedge-locking nut a greater locking force than a regular nut. The tips of external threads are easily deformed, resulting in a large frictional force and uniform load distribution on the wedge thread. A variable-diameter nut is another type of anti-loosening bolted connection, as shown in Figure 4b. This nut is similar to conventional prevailing torque nuts, which essentially change the size of the internal thread in a normal nut to generate interference between the internal thread in the nut and the standard external thread in a bolt.  
Double nuts consist of two identical regular nuts, as shown in Figure 2e, where the lower nut is called the power nut and the upper nut is called the locking nut. The power nut is first tightened, followed by the locking nut. After the tightening process of regular double nuts, the thread of the lower nut may come into contact with the surface opposite that it is in contact with during the standard tightening process. A locking force is generated to prevent loosening. An eccentric double nut is composed of an eccentric convex nut and a concentric concave nut. When the convex nut and the concentric nut are combined, a powerful locking effect can be produced via the wedge principle, as shown in Figure 5a. The interference between convex and concave nuts generates a strong frictional force after tightening, achieving the aim of loosening resistance. Double-thread bolts, which engage with two nuts with different rotational thread directions, were invented for anti-loosening. The nut with right-hand thread is the power nut, and the one with left-hand thread is the locking nut, as shown in Figure 5b. The power nut is tightened first, followed by the locking nut. In vibration or impact environments, the power nut tends to loosen first, causing the locking nut to rotate in the tightening direction; thus, the loosening of the power nut is prevented.  
Figure 4: Schematic representation of the second type of anti-loosening bolted connections: (**a**) wedge-locking nut; (**b**) variable-diameter nut.  
Figure 3: Image of a wedge washer.