# Study on Vibration Reduction Performance of Gear Pairs Made by a High-Strength Fe-Mn Damping Alloy
## 1 Introduction  
In the stage of gear design, vibration and noise depression can be achieved through the optimization of gear design parameters based on studying the gear vibration law according to gear system dynamics theory [1, 2] or adopting an active control structure output force to reduce the vibration amplitude by employing appropriate control theories in the gear meshing process. For example, by arranging the damping ring, damping plug or viscoelastic damping layer on the gear, bearing seat or gearbox, the mechanical vibration energy of the gearbox is converted into heat energy among the damping layer, the gear body or box by friction, and the heat energy can be dissipated into the surrounding environment, thereby reducing the vibration amplitude. However, the damping effect created by the damping ring and damping plug is valid only when the gear's natural frequency range is low but cannot achieve a wide range of frequency damping. For transmission systems with high precision or high-quality requirements on gears, the damping layer damping method is restricted in many application scenarios due to the limitation of additional mass or structure [3]. Compared with research about conventional vibration and noise reduction methods, the research on vibration and noise reduction by controlling the vibration source using gears and gear shafts made of a damping alloy with high strength and high damping characteristics has attracted the widespread attention of scholars. In the study of an Mn-Cu alloy, [PERSON] found that 88% Mn-Cu alloy has a high internal friction value near roomtemperature and developed the Sonoston and Incramute damping alloys of the Mn-Cu series. Sonoston is a high damping alloy specially developed for submarine propellers by the British Shi-Mn Marine Company. As a deformed heat treatment material, Incramute is mainly used to manufacture bearing structures such as frames, bases and pedestals [4; 5; 6; 7; 8] [PERSON] et al. [9] and [PERSON] et al. [10] manufactured the housing of the escalator reducer using a Fe-Mn damping alloy; they conducted vibration and noise experiments and compared it with cast iron (GC20). The results showed that the noise sound pressure level of the reducer was reduced by about 5 dB using the Fe-Mn alloy. [PERSON] [11] used Fe-12 Cr-22 Mn and Fe-12 Cr-22 Mn-2 Co, which are high-damping stainless steel alloys, to manufacture bolts, nuts, gears, shanks, and NC machine tools. The experimental results also showed that the vibration and noise were suppressed. [PERSON] [12] et al. extended the existing constitutive model to a three-dimensional state and established a relatively simple nonlinear viscoelastic constitutive model of particle-filled rubber under a three-dimensional stress state. The model was implemented in finite element software and verified through experiments. To describe the changing responses of a solid viscoelastic microstructure, [PERSON] [13] et al. integrated the multiple natural configuration theory (multi-network model) with a single integral representation for constitutive equations to construct a model, which was also confirmed by experiments. Furthermore, the effects of microstructure changes on the macroscopic deformation of polymers over time were considered in the proposed model. Based on the one-dimensional rheological model, [PERSON], [PERSON] et al. [14] set up a viscoelastic-viscoplastic constitutive model containing several springs and damper elements to represent the nonlinear and time-varying deformation behavior of polymers. [PERSON] [15] combined the damping of viscoelastic material with the pseudo-elasticity of a shape-memory alloy and deduced the time-domain model of the dynamics equation of viscoelastic material and shape memory alloy. Its damping effect was verified by a three-layer beam unit, using the shape-memory alloy steel rope symmetrically installed on both sides of the beam to control the vibration of the beam. [PERSON] et al.