Orthogonal test of double circular arc gear is an important mathematical statistical method to study multi factor test. The orthogonal table can quickly find out the best level combination of test factors, understand the importance and interaction of test factors, realize the reasonable and effective arrangement of test factors, and minimize the test error. It has the remarkable characteristics of high efficiency, speed and economy. It is widely used in various fields of chemical industry and national production.
1. Test design
The experiment adopts the orthogonal experimental design of 4 factors and 4 levels, and uses the model option in workbench to solve the constrained mode of double circular arc gear. The number of teeth, modulus, helix angle and tooth width of double circular arc gear are selected as the research object. Each independent variable is composed of four levels. The test sequence is Latin square to avoid sequence effect. According to the above modal shapes and frequencies of double circular arc gear, it can be seen that the difference between the second-order and third-order, fifth-order and sixth-order vibration shapes and frequencies is small. The lower the natural frequency, the easier it is to be excited by the outside world. Therefore, the influencing factors of the low-order natural frequency of double circular arc gear should be analyzed in the modal analysis. Therefore, the regression analysis of the first-order natural frequency is carried out in the later stage.
2. Test scheme
The orthogonal test table of L16 (45) is adopted, in which l is the orthogonal symbol, 16 is the number of rows in the orthogonal table, 4 is the number of factor levels, and 5 is the number of columns in the orthogonal table. Each factor of the independent variable is arranged in the corresponding position of the orthogonal table. Generally, one factor accounts for one column and different factors account for different columns.
| Test number | A | B | C | D | E | First order natural frequency / Hz |
| 1 | 1( 41) | 1( 3 mm) | 1( 16． 263°) | 1( 50 mm) | 1 | 7 177． 5 |
| 2 | 1 | 2( 4 mm) | 2( 18． 263°) | 2( 60 mm) | 2 | 4 019． 1 |
| 3 | 1 | 3( 5 mm) | 3( 20． 263°) | 3( 70 mm) | 3 | 2 432． 9 |
| 4 | 1 | 4( 6 mm) | 4( 22． 263°) | 4( 80 mm) | 4 | 1 615． 1 |
| 5 | 2( 51) | 1 | 2 | 3 | 4 | 4 379． 2 |
| 6 | 2 | 2 | 1 | 4 | 3 | 2 592． 1 |
| 7 | 2 | 3 | 4 | 1 | 2 | 1 529． 3 |
| 8 | 2 | 4 | 3 | 2 | 1 | 1 075． 2 |
| 9 | 3( 61) | 1 | 3 | 4 | 2 | 2 863． 4 |
| 10 | 3 | 2 | 4 | 3 | 1 | 1 670． 5 |
| 11 | 3 | 3 | 1 | 2 | 4 | 1 141． 6 |
| 12 | 3 | 4 | 2 | 1 | 3 | 774． 93 |
| 13 | 4( 71) | 1 | 4 | 2 | 3 | 2 119． 8 |
| 14 | 4 | 2 | 3 | 1 | 4 | 1 272． 5 |
| 15 | 4 | 3 | 2 | 4 | 1 | 813． 66 |
| 16 | 4 | 4 | 1 | 3 | 2 | 577． 05 |
As shown in the table, a represents the number of teeth, B represents the modulus, C represents the helix angle, D represents the tooth width, and e represents the empty column. 1 ~ 4 in the table are regarded as the horizontal number of each factor respectively. Each line corresponding to the orthogonal table has one test scheme, that is, the horizontal combination of each factor. The empty column has no influence on the test, mainly to investigate the test error.