Technology & Engineering
Shafts
Shafts are mechanical components used to transmit power and motion between different parts of a machine. They are typically cylindrical in shape and can be found in various types of machinery, such as engines, pumps, and conveyor systems. Shafts are designed to withstand torsional and bending forces, and they often have keyways, threads, or other features to connect them to other components.
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12 Key excerpts on "Shafts"
eBook - ePub- Wei Jiang(Author)
- 2019(Publication Date)
- Wiley(Publisher)
Shafts are important elements in virtually all types of machinery. They are supported by bearings, rotate and transmit power and thereby torque. A typical application of Shafts is input, output or intermediate Shafts supporting gears in gear reducers.Unlike standard elements, Shafts are designed for specific applications individually, considering the mounted elements, operating loads and service conditions. Power transmission elements, such as gears, belt pulleys, chain sprockets, couplings and so on are attached to the Shafts by keys, splines, pins and other devices. When Shafts rotate with power transmission elements, power and rotational motion are transmitted from one element to other rotating parts of shaft system [1 –3 ].10.1.2 Types of Shafts
A shaft is a long cylindrical element loaded torsionally, transversely and/or axially as a machine operates. Consequently, Shafts can be classified as transmission Shafts, axles and spindles according to the loads they carry [4] . Transmission Shafts carry both bending and torsional moments, and are usually stepped, as shown in Figure 10.1 a. They support gears, pulleys and so on and often transmit power. Axles carry bending moments only. They are used to support rotating wheels, pulleys and the like. An axle can turn with a wheel as a unit, like a railway car axle, as illustrated in Figure 10.1 b, or is nonrotating, like the axle of the front wheel of a bicycle. Spindles take torsional moments only, like the one in an automobile, as shown in Figure 10.1 c.Figure 10.1Types of Shafts classified by loading.According to the shapes of axis, Shafts include straight Shafts, with either different diameters or constant diameters and crankShafts. Stepped Shafts have different diameters and are usually used as transmission Shafts, while constant diameter Shafts work as axles or spindles. CrankShafts are used to convert reciprocating motion into rotary motion or vice versa. Most Shafts are solid and hollow Shafts are used to save on weight. Also, flexible Shafts are used to transmit power along a curved path when space is limited or the axes of the power source and driven machine are not aligned with each other, as shown in Figure 10.2
eBook - ePub- Sayed M. Metwalli(Author)
- 2021(Publication Date)
- Wiley(Publisher)
17 ShaftsThe shaft is one of the main power transmission elements, which connects the prime mover to other transmission elements and again retransmits power from these elements to the machine; see Chapter 13 and Figures 13.1 and 13.2 . The shaft is then a primary component of power transmission elements. Any other power transmitting element is usually connected on either or both of its input and output ends by a shaft. In addition to transmitting power, Shafts support rotating machine components and thus run in bearings. They provide a constant positioning of the axis of rotation of these components. They are, therefore, subjected to applied forces, moments, and torques and may be treated as rotating beams of bodies of revolution.Symbols
The adapted units are [in, lb, psi] or [m, kg, N, Pa], others given at each symbol definition ([k…] is 103 , [M…] is 106 and [G…] is 109 ).Symbols Quantity, units (adopted) (d1 , l2 ′), (d1 , l3 ′) Equivalent zones on equivalent shaft [r×] Cross-product matrix of r A SShaft cross-sectional area d1 Diameter of segment 1 of shaft d iDiameter of segment i of shaft d p,newNew part diameter d SShaft diameter E Elasticity modulus of the material F1 , …, F nExternal n force vectors F a, MaOperating loads at point a F x, Fy, FzComponents of the force vector F G Shear modulus of elasticity or modulus of rigidity g aGravitational acceleration Hhp Transmitted power in [hp] Symbols Quantity, units (adopted) HkW Transmitted power in [kW] I zSecond area moment of shaft cross section J iPolar second area moment of shaft section i Kconc Related to stress concentration factor KSC Kload Load factor K MMoment factor Kmiscel Miscellaneous factors Krelaib Reliability factor kSb Transverse shaft stiffness or rigidity KSC Stress concentration factor 
eBook - ePub- Ansel C. Ugural(Author)
- 2022(Publication Date)
- CRC Press(Publisher)
Shafts and Associated PartsDOI: 10.1201/9781003251378-129.1 Introduction
Shafts are used in a variety of ways in all types of mechanical equipment. A shaft, usually a slender member of round cross-section, rotates and transmits power or motion. However, a shaft can have a noncircular cross-section and need not be rotating. An axle, a nonrotating member that carries no torque, is used to support rotating members. A spindle designates a short shaft. A flexible shaft transmits motion between two points (e.g., motor and machine), where the rotational axes are at an angle with respect to one another. The customary shaft types are straight Shafts of constant or stepped cross-section and crankShafts (Figure 9.1 ). The former two carry rotating members such as gears, pulleys, grooved pulleys (sheaves), or other wheels. The latter are used to convert reciprocating motion into rotary motion or vice versa.FIGURE 9.1 Common shaft types: (a) constant diameter, (b) stepped, and (c) crankshaft.Most Shafts are under fluctuating loads of combined bending and torsion with various degrees of stress concentration. Many Shafts are not subjected to shock or impact loading; however, some applications arise where such load takes place (Section 9.5 ). Thus, the associated considerations of static strength, fatigue strength, and reliability play a significant role in shaft design. A shaft designed from the preceding viewpoint satisfies strength requirements. Usually, the shaft geometry is such that the diameter will be the variable used to satisfy the design. Of equal importance in design is the consideration of shaft deflection and rigidity requirements. Excessive lateral shaft deflection can cause bearing wear or failure and objectionable noise. The operating speed of a shaft should not be close to a critical speed (Section 9.7 ), or large vibrations are likely to develop.In addition to the shaft itself, the design usually must include calculation of the necessary keys and couplings. Keys, pins, snap rings, and clamp collars are used on Shafts to secure rotating elements. The use of a shaft shoulder is an excellent means of axially positioning the shaft elements. Figure 9.2 shows a stepped shaft supporting a gear, a crowned pulley, and a sheave. The mounting parts, discussed in Section 9.8 , as well as shaft shoulders, are a source of stress raisers, and they must be properly selected and located to minimize the resulting stress concentrations. Press and shrink fits (Section 9.6 ) are also used for mounting. Shafts are earned in bearings, in a simply supported form, cantilevered or overhang, depending on the machine configuration. Couplings connect a shaft to a shaft of power source or load. Parameters that must be considered in the selection of a coupling to connect two Shafts include the angle between the Shafts, transmitted power, vibrations, and shock loads. The websites www.pddnet.com , www.powertransmission.com , and www.grainger.com
eBook - PDF- P.R.N. Childs, T.H.C. Childs(Authors)
- 2003(Publication Date)
- Butterworth-Heinemann(Publisher)
d 79 5 Shafts The objective of this chapter is to introduce the concepts of shaft design. An overall shaft design procedure is presented, including consideration of bearing and component mounting and shaft dynamics. At the end of the chapter the reader should be able to scheme out a general shaft arrangement, determine deflections and critical speeds, and specify shaft dimensions for strength and fluctuating load integrity. LEARNING OBJECTIVES At the end of this chapter you should be able to: • select appropriate methods for mounting and locating components on Shafts; • produce a scheme for a shaft design to locate and mount standard machine elements; • determine the deflection of a shaft; • calculate the first two critical frequencies of a shaft; • determine the minimum diameter of a shaft to avoid fatigue failure. 5.1 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.Alterna-tively, a shaft may simply connect to another 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. Some common shaft arrangements are illustrated in Figure 5.1. Shaft design considerations include: 1. size and spacing of components (as on a gen-eral assembly drawing), tolerances 2. material selection, material treatments 3. deflection and rigidity – bending deflection – torsional deflection – slope at bearings – shear deflection 4. stress and strength – static strength – fatigue – reliability 5.
eBook - ePub- Ansel C. Ugural(Author)
- 2020(Publication Date)
- CRC Press(Publisher)
9 Shafts and Associated Parts9.1 Introduction
Shafts are used in a variety of ways in all types of mechanical equipment. A shaft , usually a slender member of round cross-section, rotates and transmits power or motion. However, a shaft can have a noncircular cross-section and need not be rotating. An axle , a nonrotating member that carries no torque, is used to support rotating members. A spindle designates a short shaft. A flexible shaft transmits motion between two points (e.g., motor and machine), where the rotational axes are at an angle with respect to one another. The customary shaft types are straight Shafts of constant or stepped cross-section and crankShafts (Figure 9.1 ). The former two carry rotating members such as gears, pulleys, grooved pulleys (sheaves), or other wheels. The latter are used to convert reciprocating motion into rotary motion or vice versa.FIGURE 9.1 Common shaft types: (a) constant diameter, (b) stepped, and (c) crankshaft.Most Shafts are under fluctuating loads of combined bending and torsion with various degrees of stress concentration. Many Shafts are not subjected to shock or impact loading; however, some applications arise where such load takes place (Section 9.5). Thus, the associated considerations of static strength, fatigue strength, and reliability play a significant role in shaft design. A shaft designed from the preceding viewpoint satisfies strength requirements. Usually, the shaft geometry is such that the diameter will be the variable used to satisfy the design. Of equal importance in design is the consideration of shaft deflection and rigidity requirements. Excessive lateral shaft deflection can cause bearing wear or failure and objectionable noise. The operating speed of a shaft should not be close to a critical speed (Section 9.7), or large vibrations are likely to develop.In addition to the shaft itself, the design usually must include calculation of the necessary keys and couplings. Keys, pins, snap rings, and clamp collars are used on Shafts to secure rotating elements. The use of a shaft shoulder is an excellent means of axially positioning the shaft elements. Figure 9.2 shows a stepped shaft supporting a gear, a crowned pulley, and a sheave. The mounting parts, discussed in Section 9.8, as well as shaft shoulders, are a source of stress raisers, and they must be properly selected and located to minimize the resulting stress concentrations. Press and shrink fits (Section 9.6) are also used for mounting. Shafts are earned in bearings, in a simply supported form, cantilevered or overhang, depending on the machine configuration. Couplings connect a shaft to a shaft of power source or load. Parameters that must be considered in the selection of a coupling to connect two Shafts include the angle between the Shafts, transmitted power, vibrations, and shock loads. The websites www.pddnet.com , www.powertransmission.com , and www.grainger.com
eBook - ePubDesign of Mechanical Elements
A Concise Introduction to Mechanical Design Considerations and Calculations
- Bart Raeymaekers(Author)
- 2022(Publication Date)
- Wiley(Publisher)
7 Shafts7.1 Introduction
In this chapter, we will use the knowledge of Chapters 5 and 6 , and apply it directly to the design of Shafts. We define a shaft as a rotating mechanical element that transmits power or motion. This is different than an axle, which is a nonrotating member that does not transmit torque and only supports, e.g. rotating wheels or pulleys. Nothing is unique about the design of Shafts. However, it is perhaps the most common machine element and, therefore, we pay extra attention to it.7.1.1 Practical Considerations Related to Shaft Design
Shaft design involves both local stress and deflection calculations. Local stress in the shaft depends on the local geometry and dimensions of the shaft. In contrast, deflection of the shaft depends on the entire (global) geometry of the shaft. Hence, we first calculate the local stress in the shaft to determine the dimensions of the shaft geometry and, afterwards, we calculate the deflection of the shaft. We design the shaft dimensions to achieve the required design factor and account for the material we select through its yield stress. Alternatively, we select a material with yield stress that provides the required safety (design) factor for a given shaft geometry. Thus, the material choice primarily depends on the local stress in the shaft.Deflection depends on the stiffness of the shaft, which in turn depends on the length of the shaft , the area moment of inertia of the cross‐section of the shaft (which might vary along the shaft if the shaft dimensions change), and the Young's modulus of the shaft material . For instance, if we consider a shaft supported on both ends and subject to a transverse load in the middle between both ends, then the maximum deflection occurs in the middle of the shaft and is (considering small elastic deformations)(see Appendix B ). Hence, the (bending) stiffness of the shaft or, . The stiffness of the shaft is proportional to the Young's modulus of the shaft material and the area moment of inertia of the shaft cross‐section and inverse proportional to the third power of the length of the shaft. Therefore, the material choice of the shaft, which enters the stiffness equation through the Young's modulus , has a limited effect on and, thus, on the deflection of the shaft. Indeed, the Young's modulus is almost constant for most steels (approximately GPa), independent of its alloying elements. On the other hand, changing the length of the shaft has a significant influence on the stiffness of the shaft, i.e. shortening the shaft increases its stiffness by a cubic factor. However, the length of the shaft might not necessarily be a design variable because it is likely defined by the dimensions of a machine, or an application in which it must transmit power or motion. Finally, the geometry and dimensions of the cross‐section of the shaft have a substantial influence on the stiffness on the shaft. For instance, the area moment of inertia of a shaft with a circular cross‐section changes with the fourth power of the diameter (see Eq. (5.12) ) and, increasing the diameter of the shaft (even a circular tube, see Eq. (5.11)
eBook - PDFStrength of Materials & Structures N5
TVET FIRST
- P du Toit, A Knott(Authors)
- 2022(Publication Date)
- Macmillan(Publisher)
These loads can either act separately or in combination. transverse: forces that act perpendicularly (at a 90° angle) to the axis running lengthwise along a member Module 7 239 Shafts TVET FIRST Starter activity Discuss the following in class: 1. Name the most common Shafts in a motor car. 2. Discuss possible reasons why a shaft would break. 3. Based on what you have learnt about stress, what would happen to a shaft that is overstressed? Unit 7.1: Introduction to limits in shaft design Important definitions The following are definitions of Shafts used for a specific purpose: shaft: a rotating member used for transmitting power axle: a member that does not rotate itself, but is used as a support for rotating elements, such as wheels, idler gears and so on spindle: a short shaft or axle stub: a shaft that is necessary to complete an engine or motor and of which the size, shape and how far it protrudes allow for easy connection to other Shafts line shaft: a shaft that is directly connected to a prime mover and is used to transmit power to a machine flexible shaft: a shaft that allows motion between two points where the axes around which they rotate are at an angle to each other 7.1.1 Twisting of solid and hollow Shafts Shafts support and rotate machine elements, such as gears, pulleys and flywheels. The torque that drives the shaft comes from an engine or a motor. If a reduction gearbox is used, the torque in the Shafts is multiplied. The twisting motion or torque leads to high shearing and bending stresses in Shafts. Most Shafts are solid elements, but to save weight, hollow Shafts are also used. An example of a hollow shaft is the propshaft in a rear-wheel-drive vehicle. When too much torque acts on a shaft, the shaft will fail. For this reason, Shafts should be designed against possible failure modes. There are three different kinds of ductile and brittle failures for Shafts depending on the type of loading, namely tensile, torsional and bending.
eBook - PDFStrength of Materials & Structures N5 SB
TVET FIRST
- L Maraschin, VH Dookhi A Knott(Authors)
- 2021(Publication Date)
- Macmillan(Publisher)
Starter activity Discuss the following with your fellow students: 1. Name the most common Shafts in a motor car. 2. Discuss possible reasons why a shaft would break. 3. Based on what you have learnt about stress, what would happen to a shaft that is overstressed? transverse: forces that act perpendicularly (at a 90° angle) to the axis running lengthwise along a member 200 TVET FIRST Module 8 Important definitions The following are definitions of Shafts used for a specific purpose: shaft: a rotating member used for transmitting power axle: a member that does not rotate itself, but is used as a support for rotating elements, such as wheels, idler gears , and so on spindle: a short shaft or axle stub: a shaft that is necessary to complete an engine or motor and of which the size, shape and how far it protrudes allow for easy connection to other Shafts line shaft: a shaft that is directly connected to a prime mover and is used to transmit power to a machine flexible shaft: a shaft that allows motion between two points where the axes around which they rotate are at an angle to each other Unit 8.1: Twisting of solid and hollow Shafts Shafts support and rotate machine elements, such as gears, pulleys and flywheels . The torque that drives the shaft comes from an engine or a motor. If a reduction gearbox is used, the torque in the Shafts is multiplied. The twisting motion or torque leads to high shearing and bending stresses in Shafts. Most Shafts are solid elements, but to save weight, hollow Shafts are also used. An example of a hollow shaft is the propshaft in a rear-wheel-drive vehicle. 8.1.1 Power transmitted by Shafts Formula for calculating the power transmitted by a shaft To calculate the power that a shaft transmits, use the formula: P = 2 × π × N × T MEAN ____________ 60 . . . . . . . . . . W where: P is the power transmitted in watts (W). N is the speed of the shaft in revolutions per minute (r/min).
eBook - PDFFundamentals of Machine Elements
SI Version
- Steven R. Schmid, Bernard J. Hamrock, Bo. O. Jacobson(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
The torque as a function of slip can be modified through use of a stator design in torque converters, or through delay chambers as shown. Gear couplings , shown in Fig. 11.27, consist of two geared hubs connected by a sleeve with two internally geared sections. The in-line misalignment that can be tolerated de-pends on the width of the internal gear teeth. Further, some angular misalignment can be accommodated through the use of contoured teeth. These couplings have high torque capac-ity, but must be well lubricated to prevent wear. 11.10 Summary A shaft is usually a circular cross-section rotating member that has such power-transmitting elements as gears, pulleys, flywheels, sprockets, and rolling-element bearings mounted on it. The loading on the shaft can be one or various combi-nations of bending, torsion, or axial or transverse shear. Fur-thermore, these types of loading can be either static or cyclic. A design procedure was presented that established the ap-propriate shaft diameter for specific conditions. If the shaft diameter is known, the safety factor (or the smallest diameter where failure first occurs) is often an important considera-tion. Three failure prediction theories considering important combinations of loading were presented. These theories are Summary of Equations 289 Input shaft hub (section removed for clarity) Driven shaft hub Hub Internal gear Figure 11.27: A gear coupling. Source: Courtesy of Rexnord, Inc. by no means all-inclusive but should provide the essential understanding from which any other considerations can be easily obtained. Shaft dynamics and in particular the first critical speed are important to design, since the rotating shaft becomes dy-namically unstable and large vibrations are likely to develop at this speed. Both the Rayleigh and the Dunkerley equations for determining the first critical speed of a multiple-mass sys-tem were presented.
eBook - PDF- Ajeet Singh(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
The power is transmitted through pulleys and belts, gears, or chains and sprockets. These components are fixed on the shaft, such that they Shafts and Keys 685 do not slip while transmitting torque. A key is used to prevent the relative rotation of a shaft and the rotating member mounted on the shaft. A key forms a temporary joint to transmit power from the shaft to the connected member or vice versa. A key is very widely used because of its simple construction, operation, and convenience while assembling or dissembling. It offers the following advantages over other types of joints: • Low cost • Simple construction and • Ease of operation. It has the following disadvantages also: • It weakens the shaft, because the cross sectional area decreases due to keyway • Stress concentration at the keyway • Causes eccentricity to rotor, if the clearance is more between shaft and rotor over it • Can not transmit large powers • Causes slight unbalance due to its weight projecting outside the rotor and • Not suitable for high speeds. Keys are made of mild steel to withstand both shear and compressive stresses, which act during power transmission. A key is inserted between the shaft and hub of the rotor as shown in Figure 19.4. A keyway is the groove made on the shaft and its mating part. A key is inserted in these grooves after aligning them. Keys are designed more or less by empirical proportions and then checked for shear and compressive stresses. 19.18.1 Key materials and allowable stresses Small keys are made of steel and large size keys can be of cast iron. The FOS for fixed keys can be between 1.5 and 2 and for sliding keys between 3 and 4. Table 19.5 lists the materials and used to make the keys, along with their allowable stresses.
eBook - ePubThe Economy of Workshop Manipulation
A logical method of learning constructive mechanics. Arranged with questions for the use of apprentice engineers and students.
- John Richards(Author)
- 2018(Publication Date)
- Perlego(Publisher)
In the case of line shafting for manufactories, if the speed varies so much from that of the first movers on machines as to require one or more intermediate or counterShafts, the expense would be very great; on the contrary, if counterShafts can be avoided, there is a great saving of belts, bearings, machinery, and obstruction. The practical limit of speed for line Shafts is in a great measure dependent upon the nature of the bearings, a subject that will be treated of in another place.
Passage contains an image (1.) What kind of strains are Shafts subjected to?—(2.) What determines the strength of Shafts in resisting transverse strain?—(3.) Why are Shafts often more convenient than belts for transmitting power?—(4.) What is the difference between the strains to which Shafts and belts are subjected?—(5.) What is gained by constructing a line shaft of sections diminishing in size from the first mover?—(6.) What is gained by constructing line Shafts of uniform diameter?CHAPTER XII. BELTS FOR TRANSMITTING POWER.
The traction of belts upon pulleys, like that of locomotive wheels upon railways, being incapable of demonstration except by actual experience, for a long time hindered the introduction of belts as a means of transmitting motion and power except in cases when gearing or Shafts could not be employed. Motion is named separately, because with many kinds of machinery that are driven at high speed—such as wood machines—the transmission of rapid movement must be considered as well as power, and in ordinary practice it is only by means of belts that such high speeds may be communicated from one shaft to another.The first principle to be pointed out in regard to belts, to distinguish them from Shafts as a means of transmitting power, is that power is communicated by means of tensile instead of torsional strain, the power during transmission being represented in the difference of tension between the driving and the slack side of belts. In the case of Shafts, their length, or the distance to which they may be extended in transmitting power, is limited by torsional resistance; and as belts are not liable to this condition, we may conclude that unless there are other difficulties to be contended with, belts are more suitable than Shafts for transmitting power throughout long distances. Belts suffer resistance from the air and from friction in the bearings of supporting pulleys, which are necessary in long horizontal belts; with these exceptions they are capable of moving at a very high rate of speed, and transmitting power without appreciable loss.
eBook - ePub- Peter Childs, Peter R. N. Childs(Authors)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
Shaft design involves consideration of the layout of features and components to be mounted on the shaft, specific dimensions and allowable tolerances, materials, deflection, frequency response, life, and manufacturing constraints. This chapter has introduced the use of steps and shoulders and miscellaneous devices to locate components. It has also presented methods to calculate the deflection of a shaft and its critical speeds and to determine the minimum safe diameter for shaft experiencing torque and bending for a given life.References
Books and Papers
1. Beswarick J. Shaft for strength and rigidity. In: Hurst K, ed. Rotary Power Transmission Design . McGraw Hill 1994a;135–141.2. Beswarick J. Shaft with fluctuating load. In: Hurst K, ed. Rotary Power Transmission Design . McGraw Hill 1994b;142–148.3. Childs PRN. Mechanical design. In: 2nd edition Butterworth Heinemann 2004.4. Fuchs HO, Stephens RI. Metal Fatigue in Engineering . Wiley 1980.5. Hurst K. Shaft/hub connections. In: Hurst K, ed. Rotary Power Transmission Design . McGraw Hill 1994;55–65.6. Juvinall RC. Engineering Considerations of Stress, Strain and Strength . McGraw Hill 1967.7. Kuguel R. A relation between theoretical stress concentration factor and fatigue notch factor deduced from the concept of highly stressed volume. Proc ASTM . 1961;61:732–748.8. Kuhn P, Hardrath HF. An Engineering Method for Estimating Notch Size Effect on Fatigue Tests of Steel . National Advisory Committee for Aeronautics, NACA 1952; TN2805.9. Marin J. Mechanical Behaviour of Engineering Materials . Prentice Hall 1962.10. Mischke CR. Shafts. In: Shigley JE, Mischke CR, eds. Standard Handbook of Machine Design . McGraw Hill 1996.11. Neale MJ, Needham P, Horrell R. Couplings and Shaft Alignment . Professional Engineering Publishing 1998.12. Noll CG, Lipson C. Allowable working stresses . Society for Experimental Stress Analysis . vol. 3 1946.13. Peterson RE. Stress Concentration Factors . Wiley 1974.14. Piotrowski J. Shaft Alignment Handbook . third ed. CRC Press 2006.15. Pyrhonen J, Jokinen T, Hrabovcova V. Design of Rotating Electrical Machines . Wiley-Blackwell 2008.16. Reshetov DN. Machine Design . Mir Publishers 1978.17. Sclater N. Mechanisms and Mechanical Devices Sourcebook
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