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CHAPTER 15 SHAFTS A shaft is one of the most important components in machines. Shafts are used to support rotating elements. And transmit rotational motion and power. 15.1 INTRODUCTION TO SHAFTS The types of shafts According to the shapes, there are crank shaft, the axis is not at a horizontal line; straight shaft: The axis is at a horizontal line; flexible shaft, convoluted by groups of steel wire ,goodflexibility. According to the straight shafts, there are plain shaft, no-diameter-change shafts, simple, is prone to machining, inconvenient to install the components on the shafts; stepped shaft: inconvenient to install the components on the shafts; hollow shaft and solid shaft To machining technics, straight shafts are the best, but difficult to fixed. To the forces on the shafts, equality intensity shafts are good, but difficult to machining and install. Hence, there are all stepped shafts. The word “shaft” covers numerous variations and according to the loads exerted on the shafts, the shafts can be classified into three groups: (a) Shafts with only bending moments, usually called axle; (b) Shafts with only torsional moments, usually called spindle. (c) Shafts with bending and torsional moments; rotating axle fixed axle Spindle Rotary shaft (a) shaft (b) axle (c) spindle The material of shafts ① Carbon steel In common use:30、40、45steel ② Alloy steel 40Cr、40CrNi、20Cr、20Cr2Ni4A、38SiMnMo ③ Cast steel QT600—3、QT800—2 Selecting the material and heat treatment of the shafts mainly accord to the strength and wearing resistance, but not the bending and tension rigidity. 15.2 CONFIGURATION DESIGN OF SHAFTS 1. The factors relative to the configuration of shafts The location and modality of the shafts installing on machine ; The types, size, amount of elements on the shaft ; The character, magnitude orientation and distributing of load on the shaft; The types, size, collocation of bearing; The roughcast and machining technics of shafts； The assembly project of elements on shaft. 2、The conditions the configure of shafts should to satisfy The elements on the should have exact working location, convenient for to dismantle and install and rectify, Have good machining technics. 3、The names of segments of shaft 4、The ways of shaft design When select the project, it is possible to reduce the quantity of elements on shaft and deadweight of shaft, have good machining technics and proper forces on it. 955 10 4 P n T [ T ] 0.2d 3 955 104 P 955 104 3 P P d 3 3 A0 3 0.2[ T ]n 0.2[ T ] n n Where n—rotate speed of shaft（r／min） P—the power transmitted by the sh（kW） [τT]—the permissible shear stress for the shaft（MPa） A0—coefficient，Table 15—3 P d A0 3 n(1 4 ) To hollow shaft： When d＞100mm： single key groove aggrandize3%， double key groove aggrandize7%； When d≤100mm： single key groove aggrandize5～7%， double key groove aggrandize10～15% The location of elements on shaft Orientation by sleeve Used for orientation between two elements, inconvenient to locate the elements with big distance, not feasible for the occasion where rotational speed is high. Orientation by retaining rings Orientation by nuts Orientation by bearing cover Orientation by flexible retaining rings Orientation by fixed screw Orientation by fixed retaining rings Orientation by cone Peripheral orientation of elements on shaft, key、spline、interference-fit joint、fixed screw. 15.3 CONSIDERATION FOR SHAFT GEOMETRY The location of elements on shaft In order to ensure the fixed position of elements on the shaft, it is needed to fix each element on the shaft radially and axially Radial location of shafts Key joints Spline joints Pin joints interference-fit joints Axial location Locknut Shoulder fillet Locknut Snap ring End plate Screw configuration technics of shaft As long as possible to aggrandize the transition fillet radius, as soon as possible to unify the fillet radius of shaft. For install elements conveniently, we should wipe off the burr, the ends of the shaft should be 45, there must be grinding wheel outre groove to grind and cut rounding chamfer. To machining screw thread by lathe, there should be a groove for the reamer exit. The groove for keys should be in a horizontal line 15.4 CALCULATION OF SHAFT ①Calculate accord to bending-torsion strength. To ensure horizontal forces and vertical forces Calculate bending moment MH and MV Draw torque moment diagram（T） Calculate bending moment Mca M2 ( T)2 Checking the strength Mca M2 ( T)2 ca [ 1 ] W W ② Checking exactly according to fatigue strength S S Sca S S S2 2 Only normal stress 1 S S K a m Only torsional shear stress 1 S S K a m Safety factor When even material, precise calculated load and stress ,S＝1.3～1.5 When uneven material, low precise calculated load and stress, S＝1.5～1.8 When even material, lowest precise load and stress, or the diameter of shaft d＞ 200mm, S＝1.8～2.5 The measure when calculating dissatisfy Lower concentrative stress effect when configuration design; Aggrandize fillet radius； Machining with crew thread on unload region； Loosen combination of shaft and elements. Intensify mechanical property Minish the roughness of the surface Surface preening Roller compaction, rotoblast the surface Using the material with high strength, or increase the diameter of shaft ② Checking according to static strength Condition of strength SS SS SSca SS SS SS 2 2 SSca— static strength calculated safety factor of the jeopardy section SS—Calculate design safety factor according to yield strength SS S M F ( max max ) W A SSσ—the safety factor when only consider bending and axial force SSτ—the safety factor when only consider torque S SS Tmax WT 2、Checking calculate rigidity of shaft ①check by bending rigidity of shaft L y [y] [ ] dv z l di4 4 i 1 i li—the length of the i segment of stepped shaft di—the radius of the i segment of stepped shaft L—the calculated length of stepped shaft z—the number of segments of shaft in calculated length [y]—allowable flexivity of shaft，Table 15—5 [θ]—allowable deflection angle of shaft,Table 15—5 ② Check the torsional rigidity of shaft plain shaft ： T 5.73 104 [ ] Stepped shaft： GI P 1 z Ti li T—the torque on shaft 5.73 104 [ ] LG i 1 I Pi G—shear elasticity modulus of material of shaft Steel G＝8.1×104 IP—polar moment of inertia of shaft section I P d 4 32 L—the length of the shaft supporting torque Ti、li、IPi—the torque, length, polar moment of inertia of i segment of shaft z—the number of segments of stepped shaft [φ]—allowable torsion angle per mile of shaft MAIN CONTENT OF THIS CHAPTER Configuration design of shaft Three calculation methods of shaft strength Rigidity calculation of shaft, stability of vibration, etc. KEY POINTS Stepped shaft design , strength and rigidity checking Example 15.1 A transmission shaft ,given: transmitted power p=10kw,rotational speed n=120r/min,estimate the diameter of shaft. Example 15.2 There is a shaft system shown in Fig.15.6, and there are some errors and unsuitable points, mark them by order, and make a brief illustration.
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