1 Introduction
2 State of the art
3 Models used for calculation
Steel | Plastic | |
---|---|---|
Young’s modulus at 20 °C in N/mm2 | 210,000 | 3100 |
Poisson’s ratio | 0.3 | 0.4 |
Permissible bending stress σFP in N/mm2 | 1650 | 35 |
kst‑A | kst‑C | kst-CS | ||||
---|---|---|---|---|---|---|
Pinion | Wheel | Pinion | Wheel | Pinion | Wheel | |
mn in mm | 1.00 | 3.00 | 2.75 | |||
z | 72 | 108 | 24 | 36 | 24 | 36 |
b in mm | 22 | 20 | 22 | 20 | 22 | 20 |
a in mm | 91.5 | |||||
α in ° | 20.0 | |||||
β in ° | 0 | 0 | −25.6 | 25.6 | ||
df in mm | 70.4 | 106.9 | 65.3 | 101.8 | 66.3 | 101.4 |
da in mm | 74.7 | 111.1 | 78.3 | 114.7 | 78.8 | 114.7 |
εα | 1.209 | 1.198 | 1.369 | |||
εβ | 0 | 0 | 1.000 | |||
\({\mathrm{h}}_{\mathrm{aP}0}^{\mathrm{*}}\) | 1.25 | |||||
\({\uprho }_{\mathrm{aP}0}^{\mathrm{*}}\) | 0.30 | 0.46 | 0.25 | 0.33 | 0.25 | 0.25 |
Material | Steel | Plastic | Steel | Plastic | Steel | Plastic |
4 Comparison of calculation results
4.1 Total contact ratio under load
4.2 Tooth root bending stress
4.3 Contact stress
5 Conclusion
6 Nomenclature
Symbol | Entity | Description |
---|---|---|
a | mm | Center distance |
b | mm | Tooth width |
da | mm | Tip diameter |
df | mm | Root diameter |
h*aP0 | – | Addendum factor rack |
kϑ,Fla | K ⋅ (m/s)0.75 ⋅ mm1.75/W | Heat transfer coefficient of the plastic gear |
mn | mm | Normal module |
u | – | Gear ratio |
vt | m/s | Tangential velocity |
z | – | Number of teeth |
AG | m2 | Heat-dissipation surface of the mechanism housing |
ED | – | Relative tooth-engagement time with respect to ten minutes |
Ft | N | Nominal tangential load |
HV | – | Degree of tooth loss |
KF | – | Tooth root load factor |
KH | – | Tooth flank load factor |
Rλ,G | K ⋅ m2/W | Heat transfer resistance of the mechanism housing |
P | W | Nominal output |
YFa | – | Form factor |
YSa | – | Stress correction factor |
Yβ | – | Helix angle factor |
Yε | – | Contact ratio factor |
ZE | – | Elasticity factor |
ZH | – | Zone factor |
Zε | – | Contact ratio factor |
Zβ | – | Spiral angle factor |
α | ° | Pressure angle |
β | ° | Helix angle |
εα | – | Contact ratio |
εβ | – | Overlap ratio |
ϑ0 | °C | Ambient temperature |
ϑFla | °C | Flank temperature characteristic |
µ | – | Coefficient of friction |
ρ*aP0 | – | Tip radius coefficient |