## 3 Structural Analysis of Fish-Bellied Swing Arm Torsion Bar Suspension
### Kinematic Analysis of Fish-Bellied Swing Arm Torsion Bar  
Having reviewed the reasons for track derailment outlined in the introduction, except for damage to the parts, there are two main reasons for track derailment; the action force of the track tensioning mechanism is not sufficient and the track is not taut enough, which causes the supporting wheel to slip out of the track plate when crossing obstacles; and the structure of the track chassis and the swing arm structure of the supporting wheel is inefficient, and the supporting wheel is subjected to a considerable impact load when the track vehicle is climbing over a gully, resulting in the deformation of the supporting wheel shaft and track derailment [23]. Over the past few decades, there has been significant research on track tensioning systems. [PERSON] et al. [24] put forward a method to calculate the perimeter of the track. [PERSON] et al. [25] selected system parameters by using the numerical model based on the multi-body dynamics method, and used the numerical analysis results to determine the parameter setting of the track tensioning control system. The primary purpose of the current research was to improve the track derailment caused by the unreasonable structure of the tracked chassis. Based on the torsion bar suspension of the military-tracked armored vehicle, the swing arm structure of the axle sleeve was changed into a fish-bellied swing arm structure, which is rigidly linked to one end of the torsion bar through a short keyway. When impacted by the road surface, the swing arm itself will deflect and drive the torsion bar spring to produce torsion force. When the suspension was subjected to different impact loads, the change in torsion bar torsion force was analyzed. The intuitive swing diagram of the torsion bar suspension was established, as shown in Figure 3a,b. The relationship between the torsion angle, torsion bar material property, and torsion force can be obtained according to Formula (11). Formula (11) provides a theoretical basis for simulating and analyzing the stiffness characteristics of the torsion bar suspension in Section 4. \[\varphi=\frac{M\times D}{G\times J}\times\frac{180}{\pi} \tag{11}\]where \(\varphi\) is the torsion angle of the torsion bar under the torsion force \(M\), \({}^{\circ}\); \(M\) is the torsion force, N; \(D\) is the length of torsion bar, m; \(G\) is the shear modulus, Pa; \(J\) is the anti-torsional stiffness of torsion bar, N/m\({}^{2}\), of which:  
\[G=\frac{E}{2\times(1+v)} \tag{12}\]  
\[J=\frac{\pi\times D^{4}}{32} \tag{13}\]  
where \(E\) is [PERSON]'s modulus, Pa; \(v\) is [PERSON]'s ratio; \(D\) is the diameter of torsion bar, m.  
The torsion bar material used in the test was 60 Si\({}_{2}\)Mn, combined with Formulas (12) and (13) to obtain the material properties of the torsion bar; as shown in Table 1.  
When the supporting wheel point \(C\) encounters the impact load, the torsion bar \(OA\) twists, the swing arm \(AB\) rotates around point \(A\), the supporting wheel point \(C\) moves to the C', and the swing arm \(AB\) moves to the \(AB\)'. The position relationship of the swing arm suspension is shown in Figure 3c. The initial coordinates of points \(B\) and \(C\) are \((X_{1}Y_{1}Z_{1})_{,}(X_{2}Y_{2}Z_{2})\), and the angle \(\alpha\) between the initial position of the swing arm \(AB\) and the horizontal direction is \(38^{\circ}\)