Introduction To Shaft types ,Design ,Materials And Applications

Introduction To Shaft types  ,Design ,Materials And Applications

Introduction 
The term shaft usually refers to a component of circular cross-section that rotates and transmits power from a driving device, such as a motor or engine, through a machine. Shafts can carry gears, pulleys, and sprockets to transmit rotary motion and power via mating gears, belts, and chains. Alternatively, a shaft may simply connect to another shaft via a coupling. A shaft can be stationary and support a rotating member, such as the short shafts that support the non driven wheels of automobiles often referred to as spindles.

Types of Shafts
The following two types of shafts are important from the subject point of view :
1. Transmission shafts. These shafts transmit power between the source and the machines absorbing power. The counter shafts, line shafts, over head shafts and all factory shafts are transmission shafts. Since these shafts carry machine parts such as pulleys, gears etc., therefore they are subjected to bending in addition to twisting.
2. Machine shafts. These shafts form an integral part of the machine itself. The crank shaft is
an example of machine shaft
Some common shaft arrangements are shown in Figure 1.

FIG 1

Shaft design considerations
Shaft design considerations include:
1. Size and spacing of components (as on a general assembly drawing), tolerances,
2. Material selection, material treatments,
3. Deflection and rigidity,
         a. Bending deflection,
         b. Torsional deflection,
         c. Slope at bearings,
         d. Shear deflection,
4. Stress and strength,
         a. Static strength,
         b. Fatigue,
         c. Reliability,
5. Frequency response,
6. Manufacturing constraints.
Shafts typically consist of a series of stepped diameters accommodating bearing mounts and providing shoulders for locating devices such as gears, sprockets, and pulleys to butt up against and keys often used to prevent rotation, relative to the shaft, of these “added” components. A typical arrangement for a transmission shaft supporting a gear and pulley wheel illustrating the use of constant diameter sections and shoulders is shown in Figure 2.
Shafts must be designed so that deflections are within acceptable levels. Too much deflection can, for example, degrade gear performance and cause noise and vibration. The maximum allowable deflection of a shaft is usually determined by limitations set on the critical speed, minimum deflections required for gear operation, and bearing requirements. In general, deflections should not cause mating gear teeth to separate more than about 0.13 mm and the slope of the gear axes should not exceed about 0.03 . The deflection of the journal section of a shaft across a plain bearing should be small in comparison with the oil film thickness. Torsional and lateral deflection both contribute to lower critical speed.

FIG 2

shaft angular deflection at rolling element bearings should not exceed 0.04⁰, with the exception being self-aligning rolling element bearings. Shafts can be subjected to a variety of combinations of axial, bending, and torsional loads (see Figure .3) which may fluctuate or vary with time. Typically, a rotating shaft transmitting power is subjected to a constant torque together with a completely reversed bending load, producing a mean torsional stress and an alternating bending stress respectively.

FIG 3

Shafts should be designed to avoid operation at, or near, critical speeds. This is usually achieved by the provision of sufficient lateral rigidity so that the lowest critical speed is significantly above the range of operation. If torsional fluctuations are present (e.g. engine crankshafts, cam-shafts, compressors) the torsional natural frequencies of the shaft must be significantly different to the torsional input frequency. This can be achieved by providing sufficient torsional stiffness so that the shaft’s lowest natural frequency is much higher than the highest torsional input frequency.
Rotating shafts must generally be supported by bearings. For simplicity of manufacture, it is desirable to use just two sets of bearings. If more bearings are required, precise alignment of the bearings is necessary. Provision for thrust load capability and axial location of the shaft is normally supplied by just one thrust bearing taking thrust in each direction. It is important that the structural members supporting the shaft bearings are sufficiently strong and rigid.
The following list outlines a shaft design procedure for a shaft experiencing constant loading. The flow charts given in (Figures 4) can be used to guide and facilitate design for shaft strength and rigidity and fluctuating load capability. 

FIG 4

1. Determine the shaft rotational speed.
2. Determine the power or torque to be transmitted by the shaft.
3. Determine the dimensions of the power transmitting devices and other components mounted on the shaft and specify locations for each device.
4. Specify the locations of the bearings to support the shaft.
5. Propose a general form or scheme for the shaft geometry considering how each component will be located axially and how power transmission will take place.
6. Determine the magnitude of the torques throughout the shaft.
7. Determine the forces exerted on the shaft.
8. Produce shearing force and bending moment diagrams so that the distribution of bending
moments in the shaft can be determined.
9. Select a material for the shaft and specify any heat treatments, etc.
10. Determine an appropriate design stress taking into account the type of loading (whether
smooth, shock, repeated, reversed).
11. Analyze all the critical points on the shaft and determine the minimum acceptable diameter at each point to ensure safe design.
12. Determine the deflections of the shaft at critical locations and estimate the critical frequencies.
13. Specify the final dimensions of the shaft. This is best achieved using a detailed manufacturing drawing to a recognized standard and the drawing should include all the information required to ensure the desired quality. Typically, this will include material specifications, dimensions, and tolerances (bilateral, runout, data, etc.)surface finishes, material treatments, and inspection procedures.


Basic Equations
free-body diagram (Figure 5)

FIG 5

The various equations required to evaluate the stresses and strains in a loaded shaft and to arrive at safe operating loads are to be found in books or web . The simple equations below related to the estimating the torque resulting from a transmitted power and the surface shear stresses resulting from a transmitted torque.

where :

T : shaft torque (Nm)

𝜔 : angular velocity (Rads/sec)

n : RPM (revs /min)
P = Power transmitted (kW)

where :

σ = Direct stress (N/m²)

τ = Shear stress (N/m²)

M = Applied bending moment (N.m)

D = Shaft diameter(m)

I = Moment of Inertia (m⁴ - more normally cm⁴)

 This is very relevant to ductile metals. It is conservative and relatively easy to apply. It assumes that failure occurs when a maximum shear stress attains a certain value. This value being the value of shear strength at failure in the tensile test. In this instance it is appropriate to choose the yield point as practical failure. If the yield point = Sy and this is obtained from a tensile test and thus is the sole principal stress then the maximum shear stress Ssy is easily identified as Sy /2 .

Ssy = Sy /2

where :

Ssy = Shear yield strength (N/m²)
Sy = Tensile yield strength (N/m²)

Maximum Shear Stress = τ max = Greatest of ( σ1 - σ2 ) / 2 : ( σ2 - σ3 ) / 2 : ( σ1 - σ3 ) / 2 = ( σ1 - σ3 ) / 2

The factor of safety selected would be

FoS = Sy / ( 2 . τ max ) = Sy / ( σ1 - σ3 )

For the simple case of a tensile stress σx combined with a shear stress τ xy . with the principal stress σ3 = 0. and σy ,σz τxz , τzy = 0. .. (ref to notes on Mohrs circle) .. Mohr's Circle The two non-zero principal stresses are :

where :

σ1 ,2, 3 = Principal Stresses(N/m²)

σx ,y, z = Direct stress z ,y and z directions(N/m²)

τxy = Shear stress in xy plane (N/m²)

The resulting FoS = 

Or in terms of Torque and bending moments.

For a typical application of a shaft subject to direct stress, torque, and a bending moment the mohrs circle is as follows

where:

D = Shaft diameter(m)

Km = Shock fatigue factor. ( Moments )

Kt = Shock / fatigue factor. (Torques.)

For a rotating shaft there is a speed at which, for any small initial deflection, the centripetral force is equal to the elastic restoring force. At this point the deflection increases greatly and the shaft is said to "whirl". Below and above this speed this effect is very much reduced. This critical (whirling speed) is dependent on the shaft dimensions, the shaft material and the shaft loads . The critical speed is the same as the frequency of traverse vibrations.

The critical speed Nc  of a shaft is simply

Where

 m = the mass of the shaft assumed concentrated at single point .
k  =the stiffness of the shaft to traverse vibrations

For a horizontal shaft this can be expressed as

Where

y = the static deflection at the location of the concentrated mass

g = acceleration due to gravity (m.s-² )
Shaft Deflection

Maximum deflection is an important parameter when considering functionality of the shaft. Its maximum permitted value depends on the type of shaft, its function and structural features. The following recommendations can be applied for its size (shaft with toothed wheel):

At the point of seating of the toothed wheel
for spur gearing y = 0.01 * m
for bevel and worm wheels y = 0.005 * m
[m...module of toothed wheel]

Or recommended maximum deflection (not at points of seating of wheels) is for:
General engineering y = 0.0003 * L
Construction of machine tools y = 0.0002 * L
[L...distance between bearings]
The angular deflection of the shaft at points of seating of the toothed wheel should not exceed a value between 0.05° and 0.12° (3' - 7').
The angular deflection at bearing points depends on the type and inner structure of the bearing. Generally applicable:

forces on shafts examples

Indicative Transmittable Torque Values
This table is provided to allow comparison between shafts and is based on very simplistic assumptions with no allowance for fatigue, additional stresses to Bending Moments

Shaft materials And Applications 

The choice of steel for a particular application can sometimes be a bewildering experience. Within the current British Standard alone for steels (BS970), there are several hundred steel specifications. In practice, relatively few steels are used for the majority of applications, and some of the popular specifications are listed below.

Steels can be divided into seven principal groupings.

1. Low carbon free cutting steels. These are the most popular types of steel for the production of turned components, where machinability and surface finish are important. Applications include automotive and general engineering. The principal specification is 230M07.

2. Low carbon steels or mild steels. These are used for lightly stressed components, welding, bending, forming, and general engineering applications. Some of the popular specifications are 040A10, 045M10, 070M20, 080A15, and 080M15.

3. Carbon and carbon manganese case hardening steels. These steels are suitable for components that require a wear resisting surface and tough core. Specifications include 045A10, 045M10, 080M15, 210M15, and 214M15.

4. Medium carbon and carbon manganese steels. These offer greater strength than mild steels and respond to heat treatment. Tensile strengths in the range of 700e1000 MPa can be attained. Applications include gears, racks, pinions, shafts, rollers, bolts, and nuts. Specifications include 080M30, 080M40, 080A42, 080M50, 070M55, and 150M36.

5. Alloy case-hardening steels. These are used when a hard wear resisting surface is required but, because of the alloying elements, superior mechanical properties can be attained in comparison with carbon and carbon manganese case-hardening steels. Typical applications include gears, cams, rolled, and transmission components. Types include 635M15,

655M13, 665M17, 805M20, and 832M13.

6. Alloy direct hardening steels. These steels include alloying elements such as Ni, Cr, Mo, and Vand are used for applications where high strength and shock resistance are important. Types include 605M36, 708M40, 709M40, 817M40, and 826M40.

7. Stainless steels. There are three types of stainless steels: martensitic, ferritic, and austenitic.

Martensitic stainless steels can be hardened and tempered to give tensile strengths in the range from 550 to 1000 MN/m2. Applications include fasteners, valves, shafts, spindles, cutlery, and surgical instruments. Specifications include 410S21, 420S29, 420S45, 431S29, 416S21, 416S41, 416S37, and 441S49.

Ferritic stainless steels are common in strip and sheet form, and applications include domestic and automotive trim, catering equipment, and exhaust systems. They have good ductility and are easily formed. Specifications include 403S17 and 430S17. Austenitic stainless steels offer the highest resistance to corrosion, and applications are affiliated with the food, chemical, gas, and oil industries, as well as medical equipment and domestic appliances. Specifications include 302S31, 304S15, 316S11, 316S31, 320S31, 321S31, 303S31, 325S31, 303S42, and 326S36.

  some steel types and typical material property values.