# Study on Vibration Reduction Performance of Gear Pairs Made by a High-Strength Fe-Mn Damping Alloy
## 6 Transient Dynamic Analysis of Gears Made by Damping Alloy Materials  
### Numerical Simulation of Damping Alloy Materials  
As shown in Figure 14, the loading and unloading tests of the specimen, which was fabricated by two of the alloys, were completed on the tensile testing machine. During the test of material mechanical properties, the specimen was clamped between the moving beam and the base of the wa-300b universal testing machine. The structure of the specimen is shown in Figure 14c. The servo direct-current motor controlled the running speed of the motor and drove the moving beam to move up and down after being decelerated by the precision reducer. The three-way sensor transmitted the signal values of pressure, deformation and displacement to the controller and realized feedback control through one of the signal values to complete the test of the mechanical properties, such as tensile and compressive strength, of the specimen. The force measurement consisted of a force measuring sensor and data processing system. In general, the force sensor is a strain type of force sensor. Since the strain of the elastic element is proportional to the external force, the strain gauge can be connected to the measurement circuit to measure its output voltage, and then the output force can be measured. When the distance between the two chucks changes, it drives the shaft of the photoelectric encoder to rotate, and the photoelectric encoder has a pulse signal output. The pulse signal is processed by a single-chip microcomputer, and the deformation of the sample can be obtained. The load-displacement curve of the test specimen fabricated of Fe-Mn alloys during the stretching process was recorded, and the stretching speed was 0.5 mm/min until the sample was broken. To make the results more accurate, the extensometer was used to measure the small deformation during the deformation process of the specimen. The gauge length of the extensometer was set at 25 mm. When the extension meter was stretched to the limit of 1 mm of the extensometer range, the stretching was suspended, and the extensometer was unloaded. For subsequent experiments, the following steps should be followed: displacement reset, keeping the load, continuing to stretch, and recording the displacement. Finally, the acquisition system processed the load, displacement, and deformation curve recorded by the universal testing machine into a stress-strain curve. The viscoelastic constant and relaxation time parameters of the viscoelastic portion were determined according to the damping alloy material's properties. The parameters in the constitutive equation of the fitted load curve are shown in Table 3, and the parameters in the unloading curve constitutive equation are shown in Table 4. The parameter values of the nonlinear part of the damping alloy's constitutive equations were, respectively, achieved (as shown in Figure 15). Figure 13: Comparison of stress-strain relationships. We constrained the six degrees of freedom of the nodes in the left end of the canine bone test piece and applied the displacement load at the nodes in the right end. To facilitate the comparison of the experimental results with the numerical simulation results, the maximum load was 0.3 mm, the direction was along the positive direction of the \(X\)-axis, and the time interval was 0.0001 s. The load time was 0.3 s. The LS-Dyna solver obtained by the compilation was used to simulate and calculate the loading and unloading of the canine bone test piece. After the calculation, the stress-strain curve corresponding to unit 521 was extracted, and then the stress of the Fe-Mn damping alloy test piece achieved through the experiment was obtained. The strain curve was compared, as shown in Figure 15. The stress-strain curve achieved by the experiment and the stress-strain curve obtained by numerical simulation had some errors, but the trend of the curves was the same.