lewis_factor

property HelicalGear.lewis_factor: float | None

Factor used to compute stresses on the gear tooth.

It is a tabular value that in general depends on the number of gear teeth, the pressure angle and the helix angle. In this case, the considered pressure angle is always 20 degrees, so the Lewis factor depends only on the number of gear teeth n_teeth and the helix_angle.

Returns

float

Factor used to compute stresses on the gear tooth.

Notes

The Lewis factor is a tabular value that depends on the helical gear virtual number of teeth, which can be computed as:

\[z_v = \frac{z}{\cos^2 \beta_b \, \cos \beta}\]

where:

  • \(z\) is the gear number of teeth n_teeth,

  • \(\beta\) is the gear helix_angle,

  • \(\beta_b\) is the gear base helix angle.

The gear base helix angle \(\beta_b\) can be computed as:

\[\beta_b = \tan^{-1} \left( \cos \alpha_t \, \cos \beta \right)\]

where the \(\alpha_t\) is the gear transverse pressure angle, which can be computed as:

\[\alpha_t = \tan^{-1} \frac{\tan \alpha}{\cos \beta}\]

where \(\alpha\) is the pressure angle of the gear, always equal to 20 degrees.

Lewis Factor Table

Number of teeth

Lewis Factor

10

0.201

11

0.226

12

0.245

13

0.264

14

0.276

15

0.289

16

0.295

17

0.302

18

0.308

19

0.314

20

0.320

21

0.325

22

0.330

24

0.337

26

0.344

28

0.352

30

0.358

32

0.364

34

0.370

36

0.377

38

0.383

40

0.389

43

0.394

45

0.399

50

0.408

55

0.415

60

0.421

65

0.425

70

0.429

75

0.433

80

0.436

90

0.442

100

0.446

150

0.458

200

0.463

300

0.471

400

0.478

500

0.484