Solution
It is usual to start with a small module and firstly select teeth numbers for speed reduction - full geometric information can then be obtained for each gear. To acheive the desired speed reduction choose a pinion of 12 teeth and a wheel of 60 teeth from the list of preferred standard numbers of gear teeth. The gear facewidths in this example are taken from Hinchcliffe Precision Components Catalogue. Values of velocity and maximum bending stress can then be calculated for a range of values of the module.
Pitch line velocity can be calculated from known speeds and pitch circle diameters. The pitch line velocity is calculated from, v = pi m Tpnp / 60 or v = pi m Twnw / 60
Bending stress may be determined for each gear using Lewis equation. The Lewis form factors, from the table, are 0.230 and 0.410 respectively.
The maximum tooth bending stresses are calculated from
stp = P / (m f Yp v K) and stw = P / (m f Yw v K)
The following table shows the results:
| Module, m | 2 | 2.5 | 3 | 4 | ||||
| Facewidth, F(mm) | 25 | 30 | 35 | 45 | ||||
| - | Pinion | Wheel | Pinion | Wheel | Pinion | Wheel | Pinion | Wheel |
| Pitch Dia, D(mm) | 24 | 120 | 30 | 150 | 36 | 180 | 48 | 240 |
| Centre dist, C(mm) | 72 | 90 | 108 | 144 | ||||
| Velocity, V(m/s) | .628 | .785 | .943 | 1.26 | ||||
| Velocity ok? | Yes | Yes | Yes | Yes | Velocity factor, K | .905 | .884 | .864 | .827 |
| - | Pinion | Wheel | Pinion | Wheel | Pinion | Wheel | Pinion | Wheel |
| Max. bending stress, st(MPa) | 307 | 171 | 167 | 57 | 102 | 93 | 47 | 26 |
| Stress ok? | None | Some | Some | All | All | All | All | All |
| Material (Allowable stress) | Gear suitability and (Relative cost) based on £5 units at June 1991. | |||||||
| EN8 (131 MPa) | No (1) | No (3.8) | No (1.5) | Yes (5.3) | Yes (1.8) | Yes (10.9) | Yes (2.5) | Yes (19.8) |
| EN8 InH (117 MPa) | No (1) | No (3.8) | No (1.5) | Yes (5.3) | Yes (1.8) | Yes (10.9) | Yes (2.5) | Yes (19.8) |
| EN24 (221 MPa) | No (1.2) | Yes (4.5) | Yes (1.7) | Yes (6.2) | Yes (2.1) | Yes (12.7) | Yes (2.9) | Yes (23) |
| EN24 InH (183 MPa) | No (1.2) | Yes (4.5) | Yes (1.7) | Yes (6.2) | Yes (2.1) | Yes (12.7) | Yes (2.9) | Yes (23) |
| EN32 (217 MPa) | No (1.2) | No (4.5) | No (1.7) | Yes (6.2) | Yes (2.1) | Yes (12.7) | Yes (2.9) | Yes (23) |
| EN32 InH (276 MPa) | No (1.2) | No (4.5) | No (1.7) | Yes (6.2) | Yes (2.1) | Yes (12.7) | Yes (2.9) | Yes (23) |
| Gear-pair suitability | None | Some | All | All | ||||
The calculations show that 2 Mod is unsuitable as the pinion is overstressed for all materials. 2.5 Mod may be used with stronger pinion material and any material may be used at 3 Mod and 4 Mod.
The least expensive alternative is at 2..5 Mod, using EN24 for the pinion and EN8 for the wheel.