CYLINDRICAL INVOLUTE GEARS | |
---|---|

CALCULATION REPORT | |

Order | Niemann-Winter |

Project | Planetary Gear Train |

Sub project | Calculation Example |

Item | Band II Edition 2 page 364 |

ID Gear1 | z1=17 |

ID Gear2 | z2=49 |

Calculated by | André Dewispelaere |

Company | Dware - Belgium |

Date | 09/06/2023 |

1 | 1. Plan gear train verification ca | Symbol | Unit | Data | |
---|---|---|---|---|---|

2 | Planetary gear type | -- | -- | idler | |

3 | 2. Motion state | Symbol | Unit | Rot speed | State |

4 | Rotation speed sun gear | n_{1} |
rpm | 100.000 | imposed |

5 | Rotation speed ring gear | n_{4} |
rpm | 0.000 | imposed |

6 | Rotation speed planet carrier | n_{c} |
rpm | 12.800 | dependent |

7 | Transmission is speed | -- | -- | reducing | |

8 | Modulus | m_{n} |
mm | 5.500 | |

9 | Face width | b | mm | 73.4 | |

10 | Helix angle | β | °.dec | 0.00000 | |

11 | Number of planets | p | -- | 3 | |

12 | Desired fixed carrier ratio | i_{14} |
-- | -6.8000 | |

13 | 3. Input pair1: sun-planet gear | Symbol | Unit | Sun gear1 | Planet gr2 |

14 | Number of teeth | z_{1,2} |
-- | 17 | 49 |

15 | Center distance | a_{12} |
mm | 183.000 | |

16 | Sum profile shift coefficients | (x_{1} + x_{2}) |
-- | 0.0000 | |

17 | Profile shift coefficient | x_{1,2} |
-- | 0.2570 | 0.0000 |

18 | 4. Input pair2: planet-ring gear | Symbol | Unit | Planet gr3 | Ring gear4 |

19 | Number of teeth | z_{3,4} |
-- | 49 | -115 |

20 | Profile shift coefficient | x_{3} |
-- | 0.0240 | -- |

21 | 5. Calcul pair1: sun-planet gear | Symbol | Unit | Sun gear1 | Planet gr2 |

22 | Center distance | a_{12} |
mm | 183.000 | |

23 | Sum profile shift coefficients | (x_{1} + x_{2}) |
-- | 0.2810 | |

24 | Good balanced gearing P4 | P-Cl | -- | P4 | |

25 | Profile shift coefficient | x_{1,2} |
-- | 0.2570 | 0.0240 |

26 | Reference diameter | d_{1,2} |
mm | 93.500 | 269.500 |

27 | Tip diameter | d_{a1,2} |
mm | 107.327 | 280.764 |

28 | 6. Calcul pair2: planet-ring gear | Symbol | Unit | Planet gr3 | Ring gear4 |

29 | Center distance | a_{34} |
mm | -183.000 | |

30 | Sum profile shift coefficients | (x_{3} + x_{4}) |
-- | -0.2810 | |

31 | Profile shift coefficient | x_{3,4} |
-- | 0.0240 | -0.3050 |

32 | Reference diameter | d_{3,4} |
mm | 269.500 | -632.500 |

33 | Tip diameter | d_{a3,4} |
mm | 280.764 | -624.855 |

34 | 7. Conditions | Symbol | Unit | Data | |

35 | Planets insert condition satisfied | -- | -- | yes | |

36 | Condition (x3 + x4) <= 0 satisfied | -- | -- | yes | |

37 | Condition x4 <= 0 satisfied | -- | -- | yes | |

38 | Face width/reference diamet ratio | b/d_{1} |
-- | 0.79 | |

39 | 8. Transmission ratio | Symbol | Unit | Data | |

40 | Fixed carrier transm ratio | i_{14} |
-- | -6.7647 | |

41 | Transm ratio sun gear-planet carr | i_{1c} |
-- | 7.7647 | |

42 | Transm ratio sun gear-planet gear | i_{12} |
-- | 2.8824 | |

43 | Transm ratio planet gear-ring gear | i_{34} |
-- | -2.3469 | |

44 | 9. Rotation speeds | Symbol | Unit | Data | |

45 | Rotation speed sun gear shaft | n_{1} |
rpm | 100.000 | |

46 | Rotation speed ring gear shaft | n_{4} |
rpm | 0.000 | |

47 | Rotation speed planet carr shaft | n_{c} |
rpm | 12.879 | |

48 | 10. Relative rotation speeds | Symbol | Unit | Data | |

49 | Relative rotation speed sun gear | n_{1r} |
rpm | 87.121 | |

50 | Relative rotation speed planet gr | n_{2r} |
rpm | -30.226 | |

51 | Relative rotation speed ring gear | n_{4r} |
rpm | -12.879 | |

52 | 11. Torques | Symbol | Unit | Data | |

53 | Torque on sun gear shaft | T_{1} |
Nm | 6875.492 | |

54 | Torque on ring gear shaft | T_{4} |
Nm | 46510.641 | |

55 | Torque on planet carrier shaft | T_{c} |
Nm | -53386.133 | |

56 | 12. Forces | Symbol | Unit | Data | |

57 | Transverse tangent force sun gr 1 | F_{t1} |
N | -49023.12 | |

58 | Transverse tangent force plan gr 2 | F_{t2} |
N | 49023.12 | |

59 | Transverse tangent force plan gr 3 | F_{t3} |
N | 49023.12 | |

60 | Transverse tangent force ring gear | F_{t4} |
N | -49023.12 | |

61 | Transv force planet bearing pivot | F_{c} |
N | 98046.24 |