In order to explore the potential relationship between non-circular gear transmission error and backlash, the corresponding relationship between non-circular gear transmission error and backlash shown in Figure 1 is obtained through numerical calculation. In Figure 1, the distribution rules of clockwise transmission error and counterclockwise transmission error are basically the same, with only certain differences in numerical value.
Further analysis shows that the difference of bidirectional transmission error is consistent with the distribution law of backlash in the figure. In order to verify the correctness of the above analysis, the corresponding relationship between transmission error and backlash is obtained by changing the initial phase, as shown in Figure 2.
The distribution law of backlash in Figure 2 is also consistent with the difference of bidirectional transmission error under the same parameters. The above analysis results are consistent with the conclusion that the backlash of the elliptical gear pair can be obtained by the transmission error under two-way no-load, which indicates that the backlash of the non-circular gear can be obtained by the difference of the two-way transmission error.