written 5.7 years ago by |
A cast steel pinion running at 960 rpm transmit a maximum power of 20 kW to a cast iron gear running at 144 rpm. Design a spur gear drive having a standard 20° stub tooth of involute profile. Check the design for dynamic load & wear. Take static safe stress a 103MPa & 55MPa for cast steel pinion & cast iron gear respectively. Assume [σc]=1000mPa
Solution:
Steps | Particular | Details |
---|---|---|
Step 1 | Given data | Spur gear, Power(Pm)=20kW, N1 =960rpm, N2 =144rpm, α=20∘ design criteria- Lewis dynamic load, checking criteria- wear strength, pinion-cast steel [σb1]=103MPa, gear-cast iron [σb2]=55MPa |
Step 2 | Assumptions | '1' or 'p'-driver (pinion) and 2 or 'g'-driven (gear), external meshing, closed structure, carefully cut gears, service factor=1.3(light shock), module-m, face width (b) = 10m |
Further steps are explained as below
3) Gear pair dynamics
Design Power, ( P ), P = Pm x Service Factor, P = 20 x 1.3 = 26kW
Gear Ratio, ( i )
i=NpNG=N1N2=960144=6.67
Selection number of teeth on pinion and gear
Z1=Zp=14 to 17=14
Z2=Zg=i×Z1=6.67×14=93.38≅93
Lewis form factor PSG 8.50
Y=π[0.175−0.95Z] for 20∘ Stub teeth a) Yp=π[0.175−0.95Zp]=π[0.175−0.9514]=0.3365 b) Yg=π[0.175−0.95Zg]=π[0.175−0.9593]=0.5176
4) Strength factor calculation to find weaker element
(SF)P=(σb)P×Yp=103×0.3365=34.66
(SF)g=(σb)g×Yg=55×0.5176=28.47
5) Comparing both, gear is weaker hence designing the gear.