PSI - Issue 81

Taras Dubyniak et al. / Procedia Structural Integrity 81 (2026) 562–569

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displacement on it. On the left side, the end surface of the drive half-coupling 1 is made with a toothed profile 4, and on the right side, the drive half-coupling 1 contacts the compression spring 5. The compression spring 5 rests with its other end against the left side of the drive cup-shaped bushing 6, which on the right side enters into a hexagonal engagement 7 with a self-locking nut 8, with a stop 15, which is screwed onto the drive shaft 2. The clamping force of the compression spring 5 is adjusted by nuts 9. On the left side, on the inner surface of the cup-shaped sleeve 6, there are longitudinal projections 10 evenly spaced around the circumference, which fit into the corresponding recesses between the end projections 11 of the cylindrical ring 12. The cylindrical ring 12 is rigidly connected to the driven half-coupling 13, which is mounted on the drive shaft 2 with the possibility of circular rotation. The end surface of the driven half-coupling 13, which is located between the centre of the coupling and the cylindrical ring 12, is made with a toothed profile 14, which engages with a similar toothed profile 4 made on the end surface of the driving half-coupling 1 [1]. 3. Calculation and analysis of the gear coupling model At the beginning of slippage, corresponding forces will act on the drive half-coupling (Fig. 2).

Fig. 2. Schematic diagram of forces acting in the gear engagement of the coupling

The condition for equilibrium of the movable half-coupling due to the action of torque moment T Q will be   sin cos 0, Q s s v v Q f N P f P f        (1) where β - is the angle of inclination of the contact tooth profile; f Q , f S , f V – friction coefficients in gear meshing, splines, on the cam and in the bushing; P S – normal force in splines; N – spring force; Q – normal pressure on cams. The circumferential effort on bushings is equal to 2 . Q V V T D P      cos sin 0, 2 2 2 Q p s Q s D D d Q f P N tg          (2) where D s , D Q – diameters of force application on splines and cams; d p – thread diameter;  – angle of rise of the screw line in the thread;  – friction angle in a screw pair. Determine the forces in splines Ps from equation (2) and, substituting into equation (1), we find the normal pressure on the cams