## 3 Meshing Force Analysis
current gear set, the meshing frequency components of other gear sets only appear in part of the rotational speed, and the rotational speed of each gear set is different, indicating that the coupling relationship between the meshing forces of different gear sets is not equal. To show the waterfall in more detail, meshing force spectrums of partial rotational speeds (1000 r/min, 2000 r/min, 4500 r/min, 7000 r/min) are shown in Figures 12-14. Figure 12 shows the meshing force spectrums of the first gear set. At the speeds of 1000 r/min and 2000 r/min, in addition to meshing frequency \(f_{\rm m1}\) and frequency doubling component of the first gear set, there is also meshing frequency \(f_{\rm m3}\) and frequency doubling component of the third gear set, which is caused by the connection between the sun gear of the third gear set and the inner ring gear of the first gear set. In addition, at 1000 r/min, there is the meshing frequency \(f_{\rm m2}\) component of the second gear set, which is caused by the parallel relationship between the first gear set and the second gear set. When the rotational speed rises to 4500 r/min and 7000 r/min, the meshing frequency components of other gear sets disappear, and only the meshing frequency and frequency doubling components of the first gear set exist. Figure 12: Spectrums diagram of meshing force of the first gear set at each input speed. (a) 1000 r/min; (b) 2000 r/min; (c) 4500 r/min; (d) 7000 r/min. Figure 14: Spectrums diagram of meshing force of the third gear set at each input speed. (**a**) 1000 r/min; (**b**) 2000 r/min; (**c**) 4500 r/min; (**d**) 7000 r/min. Figure 13: Spectrums diagram of meshing force of the second gear set at each input speed. (**a**) 1000 r/min; (**b**) 2000 r/min; (**c**) 4500 r/min; (**d**) 7000 r/min. The meshing force spectrums of S2 in the second gear set is shown in Figure 13. As it has a parallel relationship with the first gear set and a series relationship with the third gear set in the overall structure, its composition is complicated. Moreover, the first and third gear set of single-fold meshing frequency components \(f_{\rm m1}\) and \(f_{\rm m3}\) and their corresponding frequency doubling components appeared, and even the first gear set of meshing frequency components \(f_{\rm m1}\) occupied the highest amplitude at 1000 r/min, indicating that the coupling effect of the parallel relation of the structure on the meshing force is more obvious at low rotational speed. When the speed increases to 4500 r/min and 7000 r/min, the meshing frequency component \(f_{\rm m3}\) of the third gear set S3 disappears, but the meshing frequency \(f_{\rm m1}\) and its frequency doubling component do not disappear with the increase in the speed. Figure 14 shows the meshing force spectrums of S3 in the third gear set. Due to the connection between S3 in the third gear set and S1 in the first gear set, except the meshing frequency \(f_{\rm m3}\) and frequency doubling component of S3 in the third gear set, the meshing frequency \(f_{\rm m1}\) and frequency doubling component of S1 in the first gear set will not disappear with the increase in the speed at different input speeds. However, the amplitude of this component will continue to decrease with the increase in rotational speed. By observing the spectrum, it can be found that due to the characteristics of the overall structure, the coupling relationship between the meshing forces of different planetary rows is not symmetric, and the coupling phenomenon is more sensitive to low speeds.