DESIGN OF SHAFTSINTRODUCTION

Shaft is a rotating machine element, which is used to transmit power from one place to another usually having a circular cross-section much smaller in diameter than the shaft length.

Power transmitting elements such as gears, pulleys, belts, fly wheels, etc are mounted on the shafts.

Loading on the shaft can be various combinations of bending, torsion, shock,

axial, normal or transverse shear. Shafts have a variety of uses. Some of them are listed below:

AXLE is a shaft that supports rotating elements like wheel hoisting drum & is fitted to the housing by means of bearings. An axle may rotate with a wheel or simply supports a rotating wheel.EG: Automobile & Railway axle

A SPINDLE is a short rotating shaft but the word often is used to refer to the entire rotary unit. EG: On a lathe, the spindle is the main component of head stock

A LINE SHAFT consists of number of shafts that are connected in axial direction by means of couplings. Numbers of pulleys are mounted on line shaft & power is transmitted to individual machines by different belts.

COUNTER SHAFT is a secondary shaft that is driven by the main shaft from which power is supplied to machine component. Often it is obtained with the help of spur or helical gears.

TYPES OF SHAFTS

TRANSMISSION SHAFTS which transmit power between source and machine absorbing power like the counter shafts, line shafts, etc….

MACHINE SHAFTS which are integral part of the machine itself like the crank shaft….

FLEXIBLE SHAFTS which transmit rotary motion to any desired place like used in the speedometer of an automobile.

MANUFACTURING OF SHAFTS

Shafts are generally manufactured by following methods:

COLD ROLLING in which steel bars are passed through proper rollers until reduced to required size.

COLD DRAWING in which shafts are made by drawing through dies of required size.

Turning & Grinding of rough bars to accurate size.

Properties of shaft materials:-

Sufficient high strength

Low sensitivity to stress concentration.

Good machinability.

Ability to withstand heat.

Materials used in manufacture of shafts:-

Steel

Low-priced standard

High load capacity

Application in dry area

Hard chrome-plated also available

Lower coefficient of friction against plastic bearing

Ordinary transmission shafts are made of medium carbon steels with carbon content from 0.15% to 0.40% EG 30C8, 40C8.

For higher strength high carbon steels are used. Ex 45C8, 50C8.

Steel alloys:

Alloys such as nickel, nickel-chromium & molybdenum steels are using. Ex- 16Mn5Cr4, 40Cr4Mo2, 16Ni3Cr2, 40Ni6Cr4Mo2

Alloy steels are costly compared with plain carbon steels.

Alloy steels have higher strength, hardness & toughness.

Alloy steels possess higher resistance to corrosion compared with plain

Carbon steels

DESIGN METHODOLOGY Execute a preliminary design. Based on the preliminary design of the minimum diameter and

technological and functional requirements, make a design of the shaft shape.

Define all notches, necking-down and holes which may cause stress concentration.

Define all external loading forces. Consider the parameters of rotating masses (wheels, pulleys, clutches)

connected to the shaft (for calculation of critical speed). Choose the material of the shaft depending upon the type of loading

(static, repeated, reverse). Start the "Shaft calculation". Check results of the calculation (deflection, position of the shaft in

bearings, stress, safety coefficients...). If the shaft is under dimensioned (or over dimensioned), modify the

dimensions (material) and repeat the calculation.

SHAFT DESIGN ON STRENGTH BASIS

Transmission shafts are subjected to axial tensile force, bending moment or torsion or any possible combination of the three.

The Design of shaft consists of determining the correct shaft diameter from its strength and rigidity considerations, after selecting suitable material.

When tensile force acts, the axial Tensile Stress is given by:

When shaft such as axel is subjected to pure bending moment, bending stress is given by:

When the shaft is subjected to pure torsional moment, Torsional Shear is given by:

When the shaft is subjected to any combination of loads, the Principal stress and Principal shear stress are obtained by the following methods:

1) Max. Principal stress theory2) Max. Shear stress theory

MOHR’S CIRCLE METHOD

Max. Principal Stress,

Max. Shear Stress,

However for designing the shaft, simple equations can be developed by using the above equations and apply them for shaft subjected to combined loading.

MAX. PRINCIPAL STRESS THEORY

The Max. Principal stress is for a shaft subjected to bending and torsional

moments without any axial force,

OR

The permissible value is given by:

The above two equations help in determining the shaft diameter. Experimentally this gives good predictions for BRITTLE materials, but shafts are

generally made of ductile materials.

MAX. SHEAR STRESS THEORYAccording to this theory,

The permissible value is given by:

The above two equations help in determining the shaft diameter. Experimentally this gives good predictions for DUCTILE materials and hence is

logical to apply for Shaft Design.

DEDUCTIONS FROM THE ABOVE THEORIES:

1) From Max. Principal Stress Theory:

Is called EQUIVALENT BENDING MOMENT

It is defined as:

Bending moment which when acting alone will produce same bending stresses in a shaft as under the combined action of Bending Moment(M) and Torsional

Moment(T).

2) From Max. Shear Stress Theory:

Is called EQUIVALENT TORSIONAL MOMENT

It is defined as:

Torsional moment which when acting alone will produce same torsional stresses in a shaft as under the combined action of Bending Moment(M) and

Torsional Moment(T).

This concept of EQUIVALENT TORSIONAL MOMENT is generally used in Design of Shafts.

SHAFT DESIGN ON BASIS OF TORSIONAL RIGIDITY

In certain applications like Machine Tool spindles, it is necessary to design shafts on basis of

TORSIONAL RIGIDITY (G): Angle of twist per meter length of shaft.

We have,

Therefore,

Θ= rad

OR

Θ= deg

ASME Code for Shaft DesignFor shafts without keyways:

OR Whichever is minimum.

For shafts with keyways:

The above values are reduced by 25%.

If there are shocks and fatigue in operating condition of the shaft,

Accordingly the bending and torsional moments are to be multiplied by:

=Combined Shock and fatigue factor for Bending Moment.

=Combined Shock and fatigue factor for Torsional Moment.

Therefore we get:

The values of Shock & fatigue factors are taken as follows:

ApplicationGradual loading 1.5 1.0

Sudden loading(MINOR SHOCK) 1.5-2.0 1.0-1.5Sudden loading(MAJOR SHOCK) 2.0-3.0 1.5-3.0

Accordingly:

Is EQUIVALENT BENDING MOMENT

Is EQUIVALENT TORSIONAL MOMENT