## 4 Verification of Model  
The leaf spring torsional vibration damper used in marine diesel engines is sizable and heavy, demanding considerable resources for testing. The extensively employed finite element analysis method has matured and proven reliable in theoretical research, commercial software, and simulation of contact surfaces. This paper utilizes Ansys 2022R1 software to validate the established mechanical model governing the damper's torsional stiffness. The key aspects encompass the following: (1) The leaf spring group exhibits typical plane strain characteristics, with the four-node quadrilateral plane strain element chosen for the finite element analysis. (2) There are degrees of freedom of the coupled Y-axis at the end of the red copper gasket (at \(T_{2}\) in Figure 2). (3) The thicker edge of the leaf spring group is fixed by the positioning block, treating the finite element model as  
Figure 4: Kinematic parameter model of leaf spring torsional vibration damper. a fixed constraint. (4) As observed in Section 2, both the hub and leaf spring are crafted from chrome alloy. Nonetheless, due to the considerable discrepancy in contact area sizes between the hub clamping groove and the leaf spring length, and the greater stiffness of the clamping groove compared to the leaf spring, the clamping groove's deformation is disregarded and treated as a rigid body. (5) Classify the contact region between the leaf spring and the clamping groove as frictional contact, with a friction coefficient of 0.1. (6) Rotate the hub clockwise around the damper center shaft in 0.1\({}^{\circ}\) steps to reach 1.8\({}^{\circ}\). The geometry of the damper is interconnected with the structure, size, power, and other factors of the diesel engine. The geometric dimensions of various parts in different dampers vary significantly. While ensuring optimal performance, researchers are tasked with designing parameters and sizes in a manner that aligns reasonably with the diesel engine's space constraints. In general, the maximum diameter of the damper body typically falls within a range of 500 to 1500 mm. Using the leaf spring torsional vibration damper structure (depicted in Figure 5) as an example, the specific parameters include a thick edge leaf spring thickness of 0.016 m, thin edge thickness of 0.006 m, red copper gasket's bending part length of 0.14 m, arc radius of 0.16 m, leaf spring bending part length of 0.22 m, leaf spring width of 0.15 m, \(O_{1}O_{2}\) center distance of 0.261 m, rotation center horizontal distance of 0.426 m, angle between \(O_{1}O_{2}\) line and horizontal direction at 39.48\({}^{\circ}\), leaf spring elastic modulus of 2.1 \(\times\) 10\({}^{5}\) MPa, and Poisson's ratio of 0.3, with 20 leaf spring groups. Typically, the damper's torsion angle remains below 2\({}^{\circ}\), with this example's maximum torsion angle capped at 1.8\({}^{\circ}\). Figure 6 demonstrates grid independence, confirming the upper limit criterion for the maximum hub torque with the specified parameters at a 1.8\({}^{\circ}\) torsion angle. Findings reveal that when the element count surpasses 1485, the maximum hub torque variation remains within 1%. Given the minimal influence of heightened mesh density on the outcomes, a meshing strategy with 1485 elements is employed. Validation outcomes for additional parameters are depicted in Figures 7-9. The numerical outcomes for transverse force F, horizontal distance L, and hub torque \(M_{2}\) align well with the finite element simulation's results in this mechanical model. At a torsion angle of 1.8\({}^{\circ}\), the maximum error of these parameters remains within 3%. At a torsion angle of 1.8\({}^{\circ}\), the mentioned parameters exhibit their maximum error but remain within 3%. The damper's torsional stiffness is determined based on its natural frequency. During the design process, the torsional stiffness is calculated under various torsion angles, based on the required natural frequency of the damper. This difference is substantial, and the range is extensive.