Question 11.8: Maximum Load Transmitted by a Gear Based on Wear Strength an...
Maximum Load Transmitted by a Gear Based on Wear Strength and Using the Buckingham Formula
The pinion of Example 11.6 is to be mated with a gear. Determine
a. The allowable load for wear for the gearset using the Buckingham formula
b. The maximum load that can be transmitted
Given: N_{p} = 25, d_{p} = 50mm, b = 45mm, N_{g} = 60.
Design Decision: The mating gear is made of 60-tooth cast iron.
a. Using Equation 11.40,
Q=\frac{2 N_g}{N_p+N_g}=\frac{120}{85}=\frac{24}{17}
By Table 11.9,
K = 1.014 MPa for 200 Bhn
Applying Equation 11.38,
F_w=d_p b Q K=(50)(45)\left(\frac{24}{17}\right)(1.014)=3.221 kN
b. The dynamic load, from Example 11.6, is 1.77F_{t} The wear-limiting value of the transmitted load, using Equation 11.41, is then
F_w \geq F_d (11.41)
3.221=1.77 F_t \quad \text { or } \quad F_t=1.82 kN
| Table 11.9 Surface Endurance Limit S_{e} and Wear Load Factor K for Use in the Buckingham Equation |
||||||
| K | ||||||
| S_{e} | \phi=20^{\circ} | \phi=25^{\circ} | ||||
| Materials in Pinion and Gear | ksi | (MPa) | psi | (MPa) | psi | (MPa) |
| Both steel gears, with average | ||||||
| Bhn of pinion and gear | ||||||
| 150 | 50 | (345) | 41 | (0.283) | 51 | (0.352) |
| 200 | 70 | (483) | 79 | (0.545) | 98 | (0.676) |
| 250 | 90 | (621) | 131 | (0.903) | 162 | (1.117) |
| 300 | 110 | (758) | 196 | (1.352) | 242 | (1.669) |
| 350 | 130 | (896) | 270 | (1.862) | 333 | (2.297) |
| 400 | 150 | (1034) | 366 | (2.524) | 453 | (3.124) |
| Steel (150 Bhn) and cast iron | 50 | (354) | 60 | (0.414) | 74 | (0.510) |
| Steel (200 Bhn) and cast iron | 70 | (483) | 119 | (0.821) | 147 | (1.014) |
| Steel (250 Bhn) and cast iron | 90 | (621) | 196 | (1.352) | 242 | (1.669) |
| Steel (150 Bhn) and phosphor bronze | 59 | (407) | 62 | (0.428) | 77 | (0.531) |
| Steel (200 Bhn) and phosphor bronze | 65 | (448) | 100 | (0.690) | 123 | (0.848) |
| Steel (250 Bhn) and phosphor bronze | 85 | (586) | 184 | (1.269) | 228 | (1.572) |
| Cast iron and cast iron | 90 | (621) | 264 | (1.821) | 327 | (2.555) |
| Cast iron and phosphor bronze | 83 | (572) | 234 | (1.614) | 288 | (1.986) |