Shafts Study Notes for GATE ME Exam for Mechanical Engineering

Design of Shaft

• A shaft is a mechanical component used to transmit rotary motion or torque. Shafts transmit torque using the gears, belts, pulleys etc and provided support using bearings.
• Shafts are generally subjected to bending moment, torsion, and axial force or a combination of these three.

Axle: A stationary member used as support for rotating elements such as wheels, idler gears, etc.

Spindle: A short shaft or axle (e.g., the headstock spindle of a lathe).

Stub shaft: A shaft that is integral with a prime mover and has a geometry and projection such as to allow easy connection to other shafts.

Line shaft: A shaft having a connection with a prime mover and transmitting power, to one or many machines, is called the line shaft.

Jackshaft: A short shaft connecting a prime mover with a line shaft, is called the jackshaft.

Flexible shaft: It is a connection used for power transmission between two members having shafts axes at an angle with each other.

Shapes: Most shafts are round but they can come in many different shapes including square and octagonal. Keys and notches can also result in some unique shapes.

Hollow Shafts Vs Solid Shafts

• Hollow shafts are lighter than solid shafts of comparable strength but are more expensive to manufacture.
• Thus, hollow shafts are used primarily for applications where weight is critical. Example: rear-wheel-drive cars propeller shafts should be lightweight to handle speeds within the operating range of the vehicle.

Shaft Design: Shafts are designed based on either strength or rigidity or both.

Design based on Strength: The design in this method ensures that stresses in the shaft do not exceed the material yield stress.

Based on Rigidity: It is based on the principle that shaft deflection due to bending and maximum twist (due to torsion) is within the permissible limits.

General Principles:

• Shafts kept short and put bearings close to the external load to reduce deflections and bending moments, and to achieve higher critical speeds.
• Stress raisers should be kept away from highly stressed regions of the shafts. If it is unavoidable, then use generous radii and good surface finishes. 
• Inexpensive steels can be used for deflection-critical shafts due to the same elastic modulus of all steels.
• Early in the design of any given shaft, an estimate is usually made of whether strength or deflection will be the critical factor. A preliminary design is based on that criterion; then, the remaining factor is checked.

Shaft Equations: The following equations given below are general equations and modifying factors such as loading factors, pulsating power source factors, safety factors, and stress concentration factors can be used as per application.

Torsional shear stresses: A machine component acted upon with two equal and opposite couples acting in parallel planes is called under the torsion. The induced internal stresses to resist the twist, are called torsional shear stresses.

 The torsion equation is given as :

 Basic equations in torsion

Solid round shaft: 

Hollow round shaft:

Strength criteria: The strength criteria use the first two terms of the torsion equation and design is done on basis that stress-induced in the shaft must not exceed the strength of the material of the shaft.

Rigidity criteria: The rigidity criteria use the last two terms of the torsion equation and design is done on the basis that maximum angular twist must exceed a certain value.

Bending stresses in shafts: A beam or a member is said to be under pure bending when it is subjected to two equal and opposite couples in a plane along the longitudinal axis of the beam (i.e. bending couples) in such a way that magnitude of bending moment remains constant throughout the length of the beam.

ANALYSIS OF BENDING EQUATION

Chances of failure decrease.

• Cross-section which has higher is best suitable under bending [Bending Stress should be minimum]
• For a given area, I-section is the best section.

A.S.M.E. Code for Shaft Design

• According to the A.S.M.E. code, to consider the effect of shock and fatigue, the bending and twisting moment are need to be multiplied by factors k_b and k_t respectively.
• For a shaft operating under dynamic loading, equivalent torque and the equivalent bending moment are as follows:
  
  and
   

Values of k_b and k_t for different types of loading

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