1 Introduction
2 Determination of extreme values
2.1 Gearbox Model
Name | Abb. | Unit | Value |
---|---|---|---|
Stationary gear ratio | \(i_{0}\) | – | \(-3\) |
Gear ratio sun to carrier | \(i_{\text{1s}}\) | – | 4 |
Number of planets | \(N_{\text{P}}\) | – | 3 |
Input torque | \(T_{\text{in}}\) | Nm | 900 |
Output torque | \(T_{\text{out}}\) | Nm | 3,600 |
Normal module | \(m_{n}\) | mm | 4.500 |
Helix angle | \(\beta\) | \({}^{\circ}\) | 0 |
Contact ratio | \(\epsilon_{\alpha}\) | – | 1.247 |
Center distance | \(a\) | mm | 135.0 |
Common face width | \(b\) | mm | 40 |
2.2 Characteristics of contact pattern movement
2.3 Derivation of a substitute sine curve
3 Validation of the approach
Designation | Feature |
---|---|
a | Radially displaced sun shaft |
b | Radially displaced planet carrier |
c | Tilted planet carrier |
d | Tilted ring gear |
Mesh | Variant | \(c_{\text{CPM,A}}\) | Mean \(c_{\text{CPM,B}}\) | Difference between \(c_{\text{CPM,A}}\) and the mean \(c_{\text{CPM,B}}\) in percent | Max. deviation from \(c_{\text{CPM,A}}\) in percent |
---|---|---|---|---|---|
Sun – planet | a | 0.395 | 0.407 | 3.04 | 8.00 |
b | 0.582 | 0.637 | 9.45 | 14.94 | |
c | 0.541 | 0.585 | 8.13 | 12.14 | |
d | 0.065 | 0.074 | 13.85 | 23.53 | |
Planet – ring gear | a | 0.055 | 0.062 | 12.27 | 25.27 |
b | 0.077 | 0.093 | 20.78 | 33.51 | |
c | 0.271 | 0.271 | 0.00 | 14.10 | |
d | 0.449 | 0.469 | 4.45 | 6.90 |