上海交通大学：《Design and Manufacturing》课程教学资源（参考文献）Shigley's Mechanical Engineering Design ch7 shaft and shaft components.pdf

Budynas-Nisbett:Shigley's Ill.Design of Mechanical 7.Shafts and Shaft T©The McGraw-Hill Mechanical Engineering Elements Components Companies,2008 Design,Eighth Edition 348 Mechanical Engineering Design 7-1 Introduction A shaft is a rotating member,usually of circular cross section,used to transmit power or motion.It provides the axis of rotation,or oscillation,of elements such as gears, pulleys,flywheels,cranks,sprockets,and the like and controls the geometry of their motion.An axle is a nonrotating member that carries no torque and is used to sup- port rotating wheels,pulleys,and the like.The automotive axle is not a true axle;the term is a carry-over from the horse-and-buggy era,when the wheels rotated on non- rotating members.A non-rotating axle can readily be designed and analyzed as a static beam,and will not warrant the special attention given in this chapter to the rotating shafts which are subject to fatigue loading. There is really nothing unique about a shaft that requires any special treatment beyond the basic methods already developed in previous chapters.However,because of the ubiquity of the shaft in so many machine design applications,there is some advan- tage in giving the shaft and its design a closer inspection.A complete shaft design has much interdependence on the design of the components.The design of the machine itself will dictate that certain gears,pulleys,bearings,and other elements will have at least been partially analyzed and their size and spacing tentatively determined.Chapter 18 provides a complete case study of a power transmission,focusing on the overall design process. In this chapter,details of the shaft itself will be examined,including the following: ·Material selection ·Geometric layout ·Stress and strength ·Static strength ·Fatigue strength Deflection and rigidity ·Bending deflection Torsional deflection Slope at bearings and shaft-supported elements Shear deflection due to transverse loading of short shafts Vibration due to natural frequency In deciding on an approach to shaft sizing,it is necessary to realize that a stress analy- sis at a specific point on a shaft can be made using only the shaft geometry in the vicin- ity of that point.Thus the geometry of the entire shaft is not needed.In design it is usually possible to locate the critical areas,size these to meet the strength requirements,and then size the rest of the shaft to meet the requirements of the shaft-supported elements. The deflection and slope analyses cannot be made until the geometry of the entire shaft has been defined.Thus deflection is a function of the geometry everywhere, whereas the stress at a section of interest is a function of local geometry.For this rea- son,shaft design allows a consideration of stress first.Then,after tentative values for the shaft dimensions have been established.the determination of the deflections and slopes can be made. 7-2 Shaft Materials Deflection is not affected by strength,but rather by stiffness as represented by the modulus of elasticity,which is essentially constant for all steels.For that reason,rigid- ity cannot be controlled by material decisions,but only by geometric decisions

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 7. Shafts and Shaft Components © The McGraw−Hill 351 Companies, 2008 348 Mechanical Engineering Design 7–1 Introduction A shaft is a rotating member, usually of circular cross section, used to transmit power or motion. It provides the axis of rotation, or oscillation, of elements such as gears, pulleys, flywheels, cranks, sprockets, and the like and controls the geometry of their motion. An axle is a nonrotating member that carries no torque and is used to support rotating wheels, pulleys, and the like. The automotive axle is not a true axle; the term is a carry-over from the horse-and-buggy era, when the wheels rotated on nonrotating members. A non-rotating axle can readily be designed and analyzed as a static beam, and will not warrant the special attention given in this chapter to the rotating shafts which are subject to fatigue loading. There is really nothing unique about a shaft that requires any special treatment beyond the basic methods already developed in previous chapters. However, because of the ubiquity of the shaft in so many machine design applications, there is some advantage in giving the shaft and its design a closer inspection. A complete shaft design has much interdependence on the design of the components. The design of the machine itself will dictate that certain gears, pulleys, bearings, and other elements will have at least been partially analyzed and their size and spacing tentatively determined. Chapter 18 provides a complete case study of a power transmission, focusing on the overall design process. In this chapter, details of the shaft itself will be examined, including the following: • Material selection • Geometric layout • Stress and strength • Static strength • Fatigue strength • Deflection and rigidity • Bending deflection • Torsional deflection • Slope at bearings and shaft-supported elements • Shear deflection due to transverse loading of short shafts • Vibration due to natural frequency In deciding on an approach to shaft sizing, it is necessary to realize that a stress analysis at a specific point on a shaft can be made using only the shaft geometry in the vicinity of that point. Thus the geometry of the entire shaft is not needed. In design it is usually possible to locate the critical areas, size these to meet the strength requirements, and then size the rest of the shaft to meet the requirements of the shaft-supported elements. The deflection and slope analyses cannot be made until the geometry of the entire shaft has been defined. Thus deflection is a function of the geometry everywhere, whereas the stress at a section of interest is a function of local geometry. For this reason, shaft design allows a consideration of stress first. Then, after tentative values for the shaft dimensions have been established, the determination of the deflections and slopes can be made. 7–2 Shaft Materials Deflection is not affected by strength, but rather by stiffness as represented by the modulus of elasticity, which is essentially constant for all steels. For that reason, rigidity cannot be controlled by material decisions, but only by geometric decisions

352 Budynas-Nisbett:Shigley's Ill.Design of Mechanical 7.Shafts and Shaft T©The McGraw-Hill Mechanical Engineering Elements Components Companies,2008 Design,Eighth Edition Shafts and Shaft Components 349 Necessary strength to resist loading stresses affects the choice of materials and their treatments.Many shafts are made from low carbon,cold-drawn or hot-rolled steel.such as ANSI 1020-1050 steels. Significant strengthening from heat treatment and high alloy content are often not warranted.Fatigue failure is reduced moderately by increase in strength,and then only to a certain level before adverse effects in endurance limit and notch sensitivity begin to counteract the benefits of higher strength.A good practice is to start with an inex- pensive,low or medium carbon steel for the first time through the design calculations If strength considerations turn out to dominate over deflection,then a higher strength material should be tried,allowing the shaft sizes to be reduced until excess deflection becomes an issue.The cost of the material and its processing must be weighed against the need for smaller shaft diameters.When warranted,typical alloy steels for heat treatment include ANSI1340-50.3140-50,4140.4340.5140.and8650. Shafts usually don't need to be surface hardened unless they serve as the actual joural of a bearing surface.Typical material choices for surface hardening include carburizing grades of ANSI 1020,4320,4820,and 8620. Cold drawn steel is usually used for diameters under about 3 inches.The nom- inal diameter of the bar can be left unmachined in areas that do not require fitting of components.Hot rolled steel should be machined all over.For large shafts requiring much material removal,the residual stresses may tend to cause warping. If concentricity is important,it may be necessary to rough machine,then heat treat to remove residual stresses and increase the strength,then finish machine to the final dimensions. In approaching material selection,the amount to be produced is a salient factor. For low production,turning is the usual primary shaping process.An economic view- point may require removing the least material.High production may permit a volume- conservative shaping method(hot or cold forming.casting),and minimum material in the shaft can become a design goal.Cast iron may be specified if the production quan- tity is high,and the gears are to be integrally cast with the shaft. Properties of the shaft locally depend on its history-cold work,cold forming, rolling of fillet features,heat treatment,including quenching medium,agitation,and tempering regimen. Stainless steel may be appropriate for some environments. 7-3 Shaft Layout The general layout of a shaft to accommodate shaft elements,e.g.gears,bearings,and pulleys,must be specified early in the design process in order to perform a free body force analysis and to obtain shear-moment diagrams.The geometry of a shaft is gen- erally that of a stepped cylinder.The use of shaft shoulders is an excellent means of axially locating the shaft elements and to carry any thrust loads.Figure 7-1 shows an example of a stepped shaft supporting the gear of a worm-gear speed reducer.Each shoulder in the shaft serves a specific purpose,which you should attempt to deter- mine by observation. See Joseph E.Shigley,Charles R.Mischke,and Thomas H.Brown,Jr.(eds-in-chief),Standard Handbook of Machine Design,3rd ed.,McGraw-Hill,New York,2004.For cold-worked property prediction see Chap.29,and for heat-treated property prediction see Chaps.29 and 33

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 7. Shafts and Shaft Components 352 © The McGraw−Hill Companies, 2008 Shafts and Shaft Components 349 Necessary strength to resist loading stresses affects the choice of materials and their treatments. Many shafts are made from low carbon, cold-drawn or hot-rolled steel, such as ANSI 1020-1050 steels. Significant strengthening from heat treatment and high alloy content are often not warranted. Fatigue failure is reduced moderately by increase in strength, and then only to a certain level before adverse effects in endurance limit and notch sensitivity begin to counteract the benefits of higher strength. A good practice is to start with an inexpensive, low or medium carbon steel for the first time through the design calculations. If strength considerations turn out to dominate over deflection, then a higher strength material should be tried, allowing the shaft sizes to be reduced until excess deflection becomes an issue. The cost of the material and its processing must be weighed against the need for smaller shaft diameters. When warranted, typical alloy steels for heat treatment include ANSI 1340-50, 3140-50, 4140, 4340, 5140, and 8650. Shafts usually don’t need to be surface hardened unless they serve as the actual journal of a bearing surface. Typical material choices for surface hardening include carburizing grades of ANSI 1020, 4320, 4820, and 8620. Cold drawn steel is usually used for diameters under about 3 inches. The nominal diameter of the bar can be left unmachined in areas that do not require fitting of components. Hot rolled steel should be machined all over. For large shafts requiring much material removal, the residual stresses may tend to cause warping. If concentricity is important, it may be necessary to rough machine, then heat treat to remove residual stresses and increase the strength, then finish machine to the final dimensions. In approaching material selection, the amount to be produced is a salient factor. For low production, turning is the usual primary shaping process. An economic viewpoint may require removing the least material. High production may permit a volumeconservative shaping method (hot or cold forming, casting), and minimum material in the shaft can become a design goal. Cast iron may be specified if the production quantity is high, and the gears are to be integrally cast with the shaft. Properties of the shaft locally depend on its history—cold work, cold forming, rolling of fillet features, heat treatment, including quenching medium, agitation, and tempering regimen.1 Stainless steel may be appropriate for some environments. 7–3 Shaft Layout The general layout of a shaft to accommodate shaft elements, e.g. gears, bearings, and pulleys, must be specified early in the design process in order to perform a free body force analysis and to obtain shear-moment diagrams. The geometry of a shaft is generally that of a stepped cylinder. The use of shaft shoulders is an excellent means of axially locating the shaft elements and to carry any thrust loads. Figure 7–1 shows an example of a stepped shaft supporting the gear of a worm-gear speed reducer. Each shoulder in the shaft serves a specific purpose, which you should attempt to determine by observation. 1 See Joseph E. Shigley, Charles R. Mischke, and Thomas H. Brown, Jr. (eds-in-chief), Standard Handbook of Machine Design, 3rd ed., McGraw-Hill, New York, 2004. For cold-worked property prediction see Chap. 29, and for heat-treated property prediction see Chaps. 29 and 33

354 Budynas-Nisbett:Shigley's Ill.Design of Mechanical 7.Shafts and Shaft ©The McGraw-Hil Mechanical Engineering Elements Components Companies,2008 Design,Eighth Edition Shafts and Shaft Components 351 Axial Layout of Components The axial positioning of components is often dictated by the layout of the housing and other meshing components.In general,it is best to support load-carrying com- ponents between bearings,such as in Fig.7-2a,rather than cantilevered outboard of the bearings,such as in Fig.7-2c.Pulleys and sprockets often need to be mounted outboard for ease of installation of the belt or chain.The length of the cantilever should be kept short to minimize the deflection. Only two bearings should be used in most cases.For extremely long shafts carrying several load-bearing components,it may be necessary to provide more than two bearing supports.In this case,particular care must be given to the alignment of the bearings. Shafts should be kept short to minimize bending moments and deflections.Some axial space between components is desirable to allow for lubricant flow and to pro- vide access space for disassembly of components with a puller.Load bearing com- ponents should be placed near the bearings,again to minimize the bending moment at the locations that will likely have stress concentrations,and to minimize the deflec- tion at the load-carrying components. The components must be accurately located on the shaft to line up with other mating components,and provision must be made to securely hold the components in position.The primary means of locating the components is to position them against a shoulder of the shaft.A shoulder also provides a solid support to minimize deflec- tion and vibration of the component.Sometimes when the magnitudes of the forces are reasonably low,shoulders can be constructed with retaining rings in grooves, sleeves between components,or clamp-on collars.In cases where axial loads are very small,it may be feasible to do without the shoulders entirely,and rely on press fits. pins,or collars with setscrews to maintain an axial location.See Fig.7-2b and 7-2d for examples of some of these means of axial location. Supporting Axial Loads In cases where axial loads are not trivial,it is necessary to provide a means to trans- fer the axial loads into the shaft,then through a bearing to the ground.This will be particularly necessary with helical or bevel gears,or tapered roller bearings,as each of these produces axial force components.Often,the same means of providing axial location,e.g..shoulders,retaining rings,and pins,will be used to also transmit the axial load into the shaft. It is generally best to have only one bearing carry the axial load,to allow greater tolerances on shaft length dimensions,and to prevent binding if the shaft expands due to temperature changes.This is particularly important for long shafts. Figures 7-3 and 7-4 show examples of shafts with only one bearing carrying the axial load against a shoulder,while the other bearing is simply press-fit onto the shaft with no shoulder. Providing for Torque Transmission Most shafts serve to transmit torque from an input gear or pulley,through the shaft,to an output gear or pulley.Of course,the shaft itself must be sized to support the torsional stress and torsional deflection.It is also necessary to provide a means of transmitting the torque between the shaft and the gears.Common torque-transfer elements are: ·Keys ·Splines ·Setscrews

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 7. Shafts and Shaft Components 354 © The McGraw−Hill Companies, 2008 Shafts and Shaft Components 351 Axial Layout of Components The axial positioning of components is often dictated by the layout of the housing and other meshing components. In general, it is best to support load-carrying components between bearings, such as in Fig. 7–2a, rather than cantilevered outboard of the bearings, such as in Fig. 7–2c. Pulleys and sprockets often need to be mounted outboard for ease of installation of the belt or chain. The length of the cantilever should be kept short to minimize the deflection. Only two bearings should be used in most cases. For extremely long shafts carrying several load-bearing components, it may be necessary to provide more than two bearing supports. In this case, particular care must be given to the alignment of the bearings. Shafts should be kept short to minimize bending moments and deflections. Some axial space between components is desirable to allow for lubricant flow and to provide access space for disassembly of components with a puller. Load bearing components should be placed near the bearings, again to minimize the bending moment at the locations that will likely have stress concentrations, and to minimize the deflection at the load-carrying components. The components must be accurately located on the shaft to line up with other mating components, and provision must be made to securely hold the components in position. The primary means of locating the components is to position them against a shoulder of the shaft. A shoulder also provides a solid support to minimize deflection and vibration of the component. Sometimes when the magnitudes of the forces are reasonably low, shoulders can be constructed with retaining rings in grooves, sleeves between components, or clamp-on collars. In cases where axial loads are very small, it may be feasible to do without the shoulders entirely, and rely on press fits, pins, or collars with setscrews to maintain an axial location. See Fig. 7–2b and 7–2d for examples of some of these means of axial location. Supporting Axial Loads In cases where axial loads are not trivial, it is necessary to provide a means to transfer the axial loads into the shaft, then through a bearing to the ground. This will be particularly necessary with helical or bevel gears, or tapered roller bearings, as each of these produces axial force components. Often, the same means of providing axial location, e.g., shoulders, retaining rings, and pins, will be used to also transmit the axial load into the shaft. It is generally best to have only one bearing carry the axial load, to allow greater tolerances on shaft length dimensions, and to prevent binding if the shaft expands due to temperature changes. This is particularly important for long shafts. Figures 7–3 and 7–4 show examples of shafts with only one bearing carrying the axial load against a shoulder, while the other bearing is simply press-fit onto the shaft with no shoulder. Providing for Torque Transmission Most shafts serve to transmit torque from an input gear or pulley, through the shaft, to an output gear or pulley. Of course, the shaft itself must be sized to support the torsional stress and torsional deflection. It is also necessary to provide a means of transmitting the torque between the shaft and the gears. Common torque-transfer elements are: • Keys • Splines • Setscrews