Theoretical analysis of noncircular gears

Analyze each tooth of the meshing diagram of the driving wheel and driven wheel, number each tooth, as shown in Figure 1, measure the distance from the rotation center of the driving wheel and driven wheel to each tooth, and the angular velocity of the driven wheel is ω 2 = ω 1 / i12, the results are shown in the table. The angular velocity of the driving wheel is the same as that of the test, which is 30 ° / s. here, for the sake of table simplicity, only the data of some teeth are listed. Note: here, the unit of the angular velocity of the driving wheel and the driven wheel is ° / s. Draw the corresponding relationship between the transmission ratio and the angular velocity of the driven wheel in the table and the driven gear teeth. The results are shown in Fig. 2 and Fig. 3.

Meshing toothDriving wheel / mmDriven wheel / mmTransmission ratioDriving wheel angular speedAngular velocity of driven wheel
Slave 8 master 124.10324.0410.9973030.077
Slave 6 master 327.56420.5930.7473040.155
Slave 4 master 529.60018.5730.6273047.811
Slave 2 master 729.27918.9130.6463046.443
Slave 19 master 926.74921.4440.8023037.422
Slave 17 master 1123.13925.0411.0823027.721
Slave 15 master 1319.92128.2631.4183021.145
Slave 13 master 1518.42129.7551.6153018.573
Slave 11 master 1719.35828.8051.4883020.161
Slave 9 master 1922.28425.8751.1613025.837

It can be seen from Fig. 2 that the theoretical transmission ratio of non-circular gear is compared with the transmission ratio i12 to be realized( φ 1 ) = 1. 118 + 0. 5sin( φ 1) through comparison, it is found that the graphics are basically consistent. By observing Fig. 3, it can be concluded that the theoretical angular velocity of the driven wheel is basically consistent with the angular velocity curve of the driven wheel obtained by ADAMS simulation. Through the analysis of Figure 2 and figure 3, it is well proved that the method of designing non-circular gear in this paper is correct.

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