During the calculation of non-circular gear transmission error and backlash, the initial phase has a great influence on its distribution law. It is necessary to analyze the non-circular gear transmission error and backlash distribution law under different initial phases, and reduce the transmission error of the system by optimizing the initial phase.
Figure 1 shows the variation trend of bidirectional transmission error and backlash of non-circular gear under different initial phase conditions. With the increase of the initial phase, the clockwise transmission error, the counterclockwise transmission error and the tooth side clearance all show a periodic change trend. In contrast, the change of backlash is more obvious and the increase is more violent, and the transmission error under two kinds of steering shows greater difference with the increase of initial phase. When the initial phase increases to a certain extent within the range of (0, π/2), the backlash between the teeth will be greater than the transmission error (Fig. 1c, Fig. 1d). At this time, the excessive backlash between the teeth will aggravate the collision between the teeth, which is not beneficial to the stroke optimization of the reversing device of the non-circular gear pumping unit. This phenomenon should be avoided. Therefore, the phase optimization of the non-circular gear transmission error model should be carried out. Through the derivation of the initial phase in the formula, the optimal initial phases of the driving and driven wheels are obtained as follows:
In the above formula α Is the pressure angle at the node.
Figure 2 shows the distribution trend of backlash before and after phase optimization. After initial phase optimization, the fluctuation and amplitude of backlash are minimal. Figure 3 shows the distribution law of the bidirectional transmission error of the non-circular gear and the corresponding backlash after the phase optimization. The analysis shows that after the phase optimization, the transmission error of the non-circular gear under the two kinds of steering has the same distribution law, and the difference between the two is small, which shows that the phase optimization method proposed in this paper has certain effect on reducing the backlash in the process of the non-circular gear transmission.