Analysis of shafts

Let us design the shafts construction and carry out strength analysis of the output shaft if torque at the output shaft T =400 N∙m.

9.1 Determine the minimum diameter of speed reducer shafts

,

where T is the torque at the shaft in N·mm; [τ] is the allowable tangential stress due to torsion in MPa.

In order to compensate action of bending stresses the allowable tangential stress due to torsion is assumed as down rated. For steels [τ]=15…20 MPa.

Obtained magnitude of d_min is rounded off to the greater side according to the following standard series: 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 34, 36, 38, 40, 42, 45, 48, 50, 52, 55, 58, 60, 65, 70, 75, 80, 85, 90, 95, 100,105, 110, 115, 120, 130, 140, 150.

If the speed reducer shaft is joined with the electrical motor shaft the following condition should be carried out

d_motor - d_min ≤10 mm,

where d_motor is the diameter of the electric motor shaft (table 9.1).

9.2. Design the construction of speed reducer shafts.

In general purpose speed reducers stepped shafts with solid cross-section are used as a rule.

For the input shaft d_min is the diameter of the shaft cantilever portion where such elements as a half coupling, a pulley, a sprocket or a pinion may be mounted (Fig.9.1). In order to fix above mentioned elements in the axial direction we use a shoulder which height t₁ may be ranged from 2 to 5 mm depending on the shaft diameter. Recommended values of t₁ are given in table 9.2.

The next shaft portion of diameter d ₂= d ₁+2∙ t ₁ (the value of d ₂ must correspond to standard series) is for installing a seal. Seals are used to prevent bearing assemblies from finding dust and dirt and to remain lubrication of bearings. For general purpose speed reducer lip seals are used more frequently.

In order to reduce friction at the point of contact of the seal with the shaft corresponding portion should be polished. For this purpose this portion is additionally surface hardened to hardness 45-50 HRC.