The independent variables of the orthogonal test and the natural frequency values of the double circular arc constraint mode solved by workbench software are summarized. The orthogonal test is carried out by SPSS software to analyze the variance of the first-order natural frequency of the double circular arc gear constraint mode. The results are shown in the table. According to the F value in the table, it can be determined that the importance of the variables affecting the natural frequency of the constrained mode of double circular arc gear is B, a, C and D from large to small, that is, the modulus has the greatest influence on the natural frequency of the constrained mode, followed by the number of teeth, then the helix angle and tooth width. Significance probability of factor B P = 0.05 017, significance probability of factor A, P = 0 029, all less than 0 05, the significance probabilities of factors C and D are greater than 0.05 05, indicating that factor A and factor B have a significant impact on the test results, while factors C and d have no significant impact on the test results.
| Source of variation | Sum of squares | Freedom | Mean square | F | Significance probability p |
| Number of teeth | 15 902 290． 49 | 3 | 5 300 763． 50 | 14． 032 | 0． 029 |
| Modulus | 22 809 386． 35 | 3 | 7 603 128． 78 | 20． 127 | 0． 017 |
| Helix angle | 3 317 203． 84 | 3 | 1 105 734． 61 | 2． 927 | 0． 201 |
| Tooth width | 1 185 038． 64 | 3 | 395 012． 88 | 1． 046 | 0． 486 |
| Error | 1 133 264． 03 | 3 | 377 754． 68 | / | / |
| Total | 44 347 183． 35 | 15 | / | / | / |
The first-order natural frequency trend of different double circular arc gear parameter combinations is shown in the figure. It can be seen that the natural frequency is the highest when the number of teeth is 41 and the lowest when the number of teeth is 71. With the increase of the number of teeth, the downward trend of natural frequency slows down; With the increase of modulus, the natural frequency decreases; Helix angle from 16 263 ° to 22 At 263 °, the natural frequency shows a downward trend as a whole, but the frequency variation range is smaller than that of different number of teeth and modulus; When the tooth width increases from 50 mm to 60 mm, the natural frequency decreases obviously, but when it increases from 60 mm to 70 mm, the natural frequency does not decrease but increases. When it increases from 70 mm to 80 mm, the natural frequency shows a downward trend. To sum up, the first-order natural frequency of constrained mode of double circular arc gear shows a downward trend with the increase of independent variables as a whole.