1 Introduction
2 Power loss calculation
2.1 Load-dependent gear power losses
2.2 No-load gear power losses
2.3 Bearing power losses
2.4 Seal power losses
3 Temperature calculation
3.1 Steady state operation conditions
3.2 Transient operation conditions
4 Implementation in calculation program
4.1 Preprocessing gear data
4.2 Efficiency calculation
4.3 Heat balance calculation
5 Object of investigation and data
5.1 Object of investigation
Parameter | Gear | Symbol | Unit | C | LL | SH |
---|---|---|---|---|---|---|
Centre distance | – | a | mm | 91.5 | ||
Number of teeth | Pinion/wheel | z1/z2 | – | 16/24 | 35/43 | 29/36 |
Normal module | Pinion/wheel | mn | mm | 4.5 | 2 | 2.44 |
Normal pressure angle | Pinion/wheel | \(\alpha _{n}\) | ° | 20 | 24.67 | 17.5 |
Helix angle at pitch circle | Pinion/wheel | \(\beta\) | ° | 0 | 31.0 | 29.5 |
Face width | Pinion/wheel | b | mm | 14 | 25.7 | 17.2 |
Addendum modification coefficient | Pinion | x1 | – | 0.182 | 0.1500 | 0.1523 |
Wheel | x2 | – | 0.172 | 0.1035 | 0.009 | |
Flank surface roughness | Pinion/wheel | Ra | µm | 0.174/0.157 | 0.357/0.203 | 0.152/0.150 |
Material | Pinion/wheel | – | – | 16MnCr5 |
5.2 Experimental data
Name | Oil type | Kin. viscosity ν in \(mm^{2}/s\) | Viscosity index | Density \(\rho (15^{\circ}C)\) in \(kg/m^{3}\) | |
---|---|---|---|---|---|
\(\nu (40^{\circ}C)\) | \(\nu (100^{\circ}C)\) | ||||
FVA2A | Mineral oil | 32.63 | 5.45 | 104 | 876.8 |
Wheel shaft torque T2 | Nm | 0 | 141 | 453 | |
---|---|---|---|---|---|
Hertzian pressure at pitch point pH,C | C | N/mm2 | 0 | 940 | 1660 |
LL | 0 | 660 | 1150 | ||
SH | 0 | 920 | 1590 |
Circumferential speed at pitch circle vt | m/s | 1 | 2 | 5 | 8.3 | 15 | 20 | |
---|---|---|---|---|---|---|---|---|
Rotational speed wheel shaft n2 | C | min−1 | 174 | 348 | 870 | 1444 | 2609 | 3479 |
LL | 189 | 379 | 947 | 1571 | 2840 | 3786 | ||
SH | 188 | 377 | 942 | 1564 | 2827 | 3769 |
5.3 Calculation models and data
Load-dependent gear power loss | |
No-load gear power loss | Mauz [25] |
Bearing power loss | SKF04 [39] |
Seal power loss | ISO/TR14179‑2 [15] |
\(\mu _{\mathrm{mz}| \mathrm{ref}}\) | \(p_{\mathrm{ref}}\) in \(\mathrm{N}/\mathrm{m}m^{2}\) | \(v_{\mathrm{ref}}\) in \(\mathrm{m}/\mathrm{s}\) | \(\eta _{\mathrm{ref}}\) in mPas | \(\alpha\) | \(\beta\) | \(\gamma\) | |
---|---|---|---|---|---|---|---|
Solid (s) | 0.0863 | 1000 | 0.2 | – | 0.00 | −0.13 | – |
Fluid (f) | 0.0500 | 1000 | 8.3 | 20 | 0.07 | 0.07 | 0.29 |
Time step size | 360 s | |
Heat dissipation via the housing | ||
Gearbox surface outside (without bottom) | 0.214 m2 | |
Gearbox surface inside | 0.149 m2 | |
Gearbox height | 0.215 m | |
Wall thickness | 0.024 m | |
Emission factor | 0.8 | |
Heat transfer coefficient between oil and housing | 950 \(W/(m^{2}\cdot K)\) | |
Thermal conductivity of housing | 40 \(W/(m\cdot K)\) | |
Velocity of cooling aira | 2 \(m/s\) | |
Temperature of cooling airb | [25, 29] °C | |
Contact surface of forced cooling airc | 0.214 m2 | |
Flow length of cooling airc | 0.054 m | |
Heat capacity to consider foundationd | 1336 \(J/(kg\cdot K)\) | |
Heat dissipation via the foundation | ||
Length/Width/Height | 1.200 m/0.420 m/0.030 m | |
Surface housing bottom | 0.052 m2 | |
Surface housing feet | 0.052 m2 | |
Heat transfer coeff. between foundation and air | 40 \(W/(m^{2}\cdot K)\) | |
Thermal conductivity of foundation | 42 \(W/(m\cdot K)\) | |
Direction of heat dissipation | Top | |
Heat dissipation via couplings | ||
Shaft | Pinion shaft | Wheel shaft |
Length of shaft/flange | 0.223 m/0.040 m | 0.090 m/0.156 m |
Diameter of shaft/flange | 0.024 m/0.088 m | 0.055 m/0.023 m |
Thermal conductivity of shaft and flange | 46 \(W/(m\cdot K)\) | 46 \(W/(m\cdot K)\) |