Shafts and Axles: Fundamental Components in Mechanical Engineering

Shafts and Axles: Fundamental Components in Mechanical Engineering

Shafts and Axles

shafts

Shafts are cylindrical components that transmit rotational speed and driving or resisting torques. Mechanical parts such as gears, pulleys, and brakes are mounted on them

The stresses present in a shaft are torsion, bending, and shear

brakes

gear

pulley

Types of Shafts and Axles

Shafts are classified into straight-axis shafts, which can be circular (solid or hollow) or profiled (square section, splined profile, etc.), as well as crankshafts

In shafts and axles, specific cylindrical sections called journals are identified. These are in contact with bearings, which are mounted inside the supports that sustain the thrusts transmitted to the shaft. If the direction of the acting forces is normal to the axis of rotation of the shaft, the journals and bearings are called supporting or radial, and they can be end journals or intermediate journals

X Fig. 1.3 Representation of two shafts: a) Straight splined shaft; b) Crankshaft

Shafts and Axles

axles

Axles are cylindrical mechanical components, also known simply as axles. They do not transmit torsional moments but are limited to maintaining the position of mechanical components, such as the axles of trailers and railway carriages

The stresses present in axles are bending and shear

axles of railway carriages

axles of trailers

dimensioning of shafts and axles

Load = Constant → Induced Stress (Static) is compared against the Static Allowable Stress

Fixed Axle Sizing

Load = Variable → Induced Stress (Pulsating) is compared against the Pulsating Fatigue Allowable Stress

dimensioning of shafts

If the axle rotates with the components placed on it → Alternating Fatigue Normal Stress is applied.

Rotating Axle Sizing

When bending moments are negligible compared to the transmitted torque (torsion only)→ Shear Stress is compared against the Allowable Shear Stress

Shaft Sizing

Constant Torque → Generates Constant Shear Stress →Checked against Static Allowable Shear Stress .

Torsional Stress

Variable Torque → Generates Pulsating Shear Stress → Checked against Pulsating Fatigue Allowable Shear Stress

dimensioning of axles

Pulsating Bending Stress

Rotating AxleVariable Alternating Stress → Rotating Bending Sizing (Dimensioning)

Rotating Axle Sizing

dimensioning of axles

Fixed Axle (Circular or Hollow Section) Simple Bending Sizing (Dimensioning) = Static Bending Stress.

Fixed Axle Sizing

Flexural section modulus (or section modulus for bending) of a solid circular axle section

Flexural section modulus (or section modulus for bending) of a hollow circular section

dimensioning of shafts

Solid Circular Section Shaft →Static Torsional Stress (Sizing/Dimensioning)

Solid Circular Shaft Sizing

Hollow Circular Section Shaft →Pulsating Torsional Stress (Sizing/Dimensioning)

Hollow Circular Shaft Sizing

Flexo-Torsion Case → It is necessary to consider the Ideal Bending Moment or Equivalent Bending Moment

Combined Bending and Torsion (Flexo-Torsion)