By deflecting the moment in the joint, the additional moment M_Z acts on the fork. For the joint shown in Fig. 21, M₂ and M_Z are calculated by dividing the moments vectors:

Fig. 21:

Position 0° and 180°
M₂ = M₁ · cos ß
M_Z = M₁ · sin ß

Position 90° and 270°
M₂ = M₁ · 1/cos ß
M_Z = M₁ · tan ß

7.1 Bearing Forces in Z-Arrangement

The additional moment M_Z 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.

Fig. 22:

side view
top view
Position at 1= 0° = 180° Propeller shaft centre under bending stress.	Position at 1= 90° = 270° Input and output shaft under bending stress
A = B = C = D = 0

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:

Fig. 23:

side view
top view
Position 1= 0° = 180° Propeller shaft centre and input and output shafts under bending stress.	Position 1= 90° = 270° Input and output shafts under bending stress.

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:

where

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)

Table

Profile to DIN 5480	dt·cos [m]	Cmin [m]
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	0,0310 0,0427 0,0452 0,0503 0,0539 0,0626 0,0758 0,0789	0,072 0,100 0,105 0,075 0,125 0,145 0,175 0,085

This gives the bearing forces:

Usually only axial forces are significant.