By deflecting the moment in the joint, the additional moment MZ acts on the fork. For the joint shown in Fig. 21, M2 and MZ are calculated by dividing the moments vectors:
Position 0° and 180°
M2 = M1 · cos ß
MZ = M1 · sin ß
Position 90° and 270°
M2 = M1 · 1/cos ß
MZ = M1 · tan ß
7.1 Bearing Forces in Z-Arrangement
The additional moment MZ exerts forces on the bearing which apply bending stresses to the shaft. Fig. 22 shows the additional moments and bearing forces in the 0° and 90° position.
The bearing forces swing between zero and maximum twice per rotation.
7.2 Bearing Forces in W-Arrangement
According to Fig. 23, in this arrangement the following additional moments and bearing forces apply:
The bearing forces swing between minimum and maximum twice per rotation.
7.3 Displacement Force on Propeller Shafts with Length Extension
To displace the sliding piece under the effect of torque, a displacement force L is required which must be supported by the bearing A, B, C, D.
The maximum displacement force is:
|µ ||= ||Coefficient of friction. For hardened, nitrated and/or phosphatized parts, µ = 0,1 can be assumed; for rilsan-coated parts, µ = 0,06 |
|M1 ||= ||drive torque |
|dt ||= ||reference diameter of sliding profile (see table) |
| ||= ||angle between tooth flank and centre point beam (see table) |
|C ||= ||profile overlap (tooth engagement length, see table) |
|Profile to DIN 5480 ||dt·cos |
|38 x 2 |
52 x 2,5
55 x 2,5
62 x 2
65 x 2,5
75 x 2,5
90 x 2,5
95 x 2
This gives the bearing forces:
Usually only axial forces are significant.