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The gear elastomer model and vibration response analysis process the gears into a shafted elastomer. The diameter of the shaft is 2a, the diameter of the disk is 2c, and the thickness is h. A micro-body rdrdHh is taken out on the elastic disk for force analysis. Considering the normal stress and shear stress on each surface, each bend is obtained after synthesis. The moment and shear force are as follows: Mr=D5
From the calculation results, for the higher-order modes (m≥3), the theoretical analysis results are very close to the experimental test values, and the two agree well, indicating that the theoretical analysis is reasonable. However, for the lower order modes, there is a large error, and the reason for the analysis is that the main factor causing such error is caused by simplifying the inner circumference support of the gear to be rigidly fixed, especially when the mode is lower, because The plate is an elastic body, and the deformation near the inner periphery of the lower order mode is larger, the influence is larger, the error is larger, and the high order mode is hardly deformed near the inner circumference, so the error is small. Therefore, it can be concluded that the inner circumferential support condition controls the accuracy of the modality and has a large influence on it. For the low-order mode, in order to obtain a high-precision modality, it is necessary to treat the inner circumference as an elastic support. . In addition, it can be foreseen that the thicker the gear shaft and the smaller the outer diameter of the gear, the closer it is to the inner circumference, the better the results will be obtained by the above theoretical analysis method; and the thicker the gear body, the theoretical result and experiment The value error will increase and it is necessary to conduct elastic support studies. Research on this aspect will be discussed in a separate article.
Conclusion 1) During the working process of the gear body, due to the coupling of axial vibration, radial vibration and torsional vibration, especially when the width and diameter are relatively large, the coupling will be more intense. Therefore, the calculation of the natural vibration characteristics of the gear according to the thick-walled plate theory is better and more comprehensive and reasonable than the theoretical calculation of the thin-walled plate.
2) The boundary support condition controls the accuracy of the modality and has a great influence on the calculation result. In this paper, the inner circumference support is treated as rigid fixed, which is different from the actual situation. For the low-order mode, due to the large deformation near the inner circumference, the calculation result is too large, resulting in a large error. Therefore, in order to obtain a high-precision mode, it is necessary to process the inner peripheral support into an elastic support for research and analysis.