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Shaft Solid shafts. As a machine component a shaft is commonly a cylindrical bar that supports and rotates with devices for receiving and delivering rotary motion and torque .The crankshaft of a reciprocating engine receive its rotary motion from each of the cranks, via the pistons and connecting roads (the slider-crank mechanisms), and delivers it by means of couplings, gears, chains or belts to the transmission, camshaft, pumps, and other devices. The camshafts, driven by a gear or chain from the crankshaft, has only one receiver or input, but each cam on the shaft delivers rotary motion to the valve-actuating mechanisms. An axle is usually defined as a stationary cylindrical member on which wheels and pulleys can rotate, but the rotating shafts that drive the rear wheels of an automobile are also called axles, no doubt a carryover from horse-and-buggy days. It is common practice to speak short shafts on machines as spindles, especially tool-carrying or work-carrying shafts on machine tools. In the days when all machines in a shop were driven by one large electric motor or prime mover, it was necessary to have long line shafts running length of the shop and supplying power, by belt, to shorter couter shafts, jack shafts, or head shafts. These line shafts were assembled form separate lengths of shafting clampled together by rigid couplings. Although it is usually more convenient to drive each machine with a separate electric motor, and the present-day trend is in this direction, there are still some oil engine receives its rotary motion from each of the cranks, via the pistons and connecting roads (the slider-crank mechanisms) , and delivers it by means of couplings, gears, chains or belts to the transmission, camshaft, pumps, and other devices. The camshafts, driven by a gear or chain from the crankshaft, has only one receiver or input, but each cam on the shaft delivers rotary motion to the valve-actuating mechanisms. An axle is usually defined as a stationary cylindrical member on which wheels and pulleys can rotate, but the rotating shafts that drive the rear wheels of an automobile are also called axles, no doubt a carryover from horse-and-buggy days. It is common practice to speak short shafts on machines as spindles, especially tool-carrying or work-carrying shafts on machine tools. In the days when all machines in a shop were driven by one large electric motor or prime mover, it was necessary to have long line shafts running length of the shop and supplying power, by belt, to shorter coutershafts, jackshafts, or headshafts. These line shafts were assembled form separate lengths of shafting clampled together by rigid couplings. Although it is usually more convenient to drive each machine with a separate electric motor, and the present-day trend is in this direction, there are still some situation in which a group drive is more economical. A single-throw crankshaft that could be used in a single-cylinder reciprocating engine or pump is shown in Figure 21. The journals A and B rotate in the main bearings, C is the crankpin that fits in a bearing on the end of the connecting rod and moves on a circle of radius R about the main bearings, while D and E are the cheeks or webs. The throw R is one half the stroks of the piston, which is connected, by the wrist pin, to the other end of the connecting rod and guided so as to move on a straight path passing throw the axis XX. On a multiple-cylinder engine the crankshaft has multiple throws-eight for a straight eight and for a V-8-arranged in a suitable angular relationship. Stress and strains. In operation, shafts are subjected to a shearing stress, whose magnitude depends on the torque and the dimensions of the cross section. This stress is a measure of resistance that the shaft material offers to the applied torque. All shafts that transmit a torque are subjected to torsional shearing stresses. In addition to the shearing stresses, twisted shafts are also subjected to shearing distortions. The distorted state is usually defined by the angle of twist per unit length; i.e., the retation of one cross section of a shaft relative to another cross section at a unit distance from it. Shafts that carry gears and pulleys are bent as well as twisted, and the magniude of the bending stresses, which are tensile on the convex side of the bend and compressive on the concave side, will depend on the load, the distance between the bearings of the shaft cross section. The combination of bending and twisting produces a state of stress in the shaft that is more complex than the state of pure shears produced by torsion alone or the state of tension-compression produced by bending alone. To the designer of shaft it is important to know if the shaft is likely to fail because of an excessive normal stress. If a piece of chalk is twisted, it will invariably rupture on a plane at about 45 degrees to the axis. This is because the maximum tensile stresses act on this plane, and chalk is weak in tension. Steel shafting is usually designed so that the maximum shearing stress produced by bending and torsion is less than a specified maximum. Shafts with circular cross sections are easier to produce in the steel mill, easier to machine, and easier to support in bearings than shafts with other cross section; there is seldom any need for using noncircular shapes. In addition, the strength and stiffness, both in bending and torsion, are more easily calculated for circular shafts. Lastly, for a given amount of materials the circular shafts has the smallest maximum shearing stress for a given torque, and the highest torsional rigidity. The shearing in a circular shaft is highest at the surface and drops off to zero at the axis. This means that most of the torque is carried by the material on and near the surface. Critical speeds. In the same way that a violin string vibrates when stroked with a bow, a cylindrical shaft suspended between two bearings has a natural frequency of lateral vibration. If the speed of revolution of the shaft coincides with the natural frequency, the shaft experience a whirling critical speed and become noisy. These speeds are more likely to occur with long, flexible shafts than with short, stiff ones. The natural frequency of a shaft can be raised by increasing its stiffness. If a slender rod is fixed to the ceiling ta one end and supports a heavy disk at the other end, the disk will oscillate back and forth around the rod axis like a torsion pendulum if given an initial twist and let go. The frequency of the oscillations will depend on the torsional stiffness of the rod and the weight of the disk; the stiffer the rod and the lighter the disk the higher the frequency. Similar torsional oscillations can occur in the crankshafts of reciprocating engines, particularly those with many crank throws and a heavy flywheel. Each crank throw and part of the associated connecting rod acts like a small flywheel, and for the crankshaft as a whole, there are a number of ways or modes in which there small flywheels can oscillate back and forth around the shaft axis in opposition to one another and to the main flywheel. For each of these modes there corresponds a natural frequency of oscillation. When the engine is operating the torques delivered to the crankshaft by the connecting rods fluctuate, and if the crankshaft speed is such that these fluctuating impulses are delivered at a speed corresponding to one of the natural torsional frequencies of the shaft, torsional oscillations will be superimposed on the rotary motion of the shafts. Such speed are known as torsional critical speeds, and they can cause shaft failures. A number of devices to control the oscillations of crankshafts have been invented. Flexible shafts. A flexible shaft consists of a number of superimposed tightly wound right-and left-hand layers of helically wound wires wrapped about a single center wire or mandrel. The shaft is connected to source of power and the driven member by special fittings attached to the end of the shaft. Flexible easings of metallic or nonmetallic materials, which guide and protect the shaft and retain the lubricant, are also available. Compared with solid shafts, flexible shafts can be bent to much smaller radii without being overstressed. For transmitting power around corners and for considerable distances flexible shafts are usually cheaper and more convenient than belts, chains, or gears. Most speedometers on automobiles are driven by flexible shafts running from the transmission to the dashboard. When a valve, a switch, or other control devices is in a hard-to-reach location, it can be operated by a flexible shaft from a more convenient position. For portable tools such as sanders, grinders, and drilling machines, flexible shafts are practically indispensable. KEY, SPLINES AND PINS Keys, splines, and pins. When power is being transmitted from a machine member such as a coupling, a gear, a flywheel, or a pulley to the shaft on which it is mounted, means must be provided for preventing relative motion between the shaft and the member. On helical and bevel gears, relative movement along the shaft caused by the thrust(axial) loads is prevented by a step in the shaft or by having the gear contact the bearing directly or through a tubular spacer. When axial loads are incidental and of small magnitude, the members are kept from sliding along the shaft by means of a set screw. The primary purpose of keys, splines, and pins is to prevent relative rotary movement. A commonly used type of key has a square cross section and is sunk half in the shaft and half in the hub of the other member. If the key is made of steel(which is commonly the case)of the same strength as the shaft and has a width and depth equal to one fourth of the shaft diameter(this proportion is closely approximated in practice) then it will have the same torque capacity as the solid shaft if its length is 1.57 times that of the shaft diameter. Another common type of key has a rectangular cross section with a depth to width ratio of 0.75. Both of these keys may either be straight or tapered in depth. The straight keys fit snugly on the sides of the key ways only, the tapered keys on all sides. Gib-head keys are tapered keys with a projection on one end to facilitate removal. Woodruff keys are widely used on machine tools and motor vehicles. The key is a segment of a disk and fits in a keyway in the shaft that is with a special milling cutter. Though the extra depth of these keys weakens the shaft considerably, it prevents any tendency of the key to rotate or move axially. Woodruff keys are particularly suitable for tapering shaft ends. Because they weaken the shafts less, keys with straight or tapered circular cross sections are sometimes used in place of square and rectangular keys, but the keyways, half in the shaft and half in the shaft and half in the hub, must be cut with a drill after assembly,and interchangeability of parts is practically impossible. When a large gear blank is made by shrinking a high-strength rim on a cheaper cast center, circular keys, snugly fitted, are frequently used to ensure a permanent connection. Splines are permanent keys integral with the shaft, fitting in keyways cut in the hub. The dimensions of splined fittings are standardized for both permanent (press) fits and sliding fits. The teeth have either straight or involute profiles;the latter are stronger, more easily measured, and have a self-centring action when twisted. Tapered circular pins can be used to restrain shaft-mounted members from both axial and rotary movement. The pin fits snugly in a reamed tapered hole that is perpendicular to the shaft surface. A number of straight pins that grip by deforming elastically or plastically when driven into straight holes are commercially available. All the keys and pins that have been described are standard driving devices. In some cases they inadequate, and unorthodox means must be employed. For driving small gear in which there is no room between the bore and the roots of the teeth for a longitudinal keyway, a transverse radial slot on the end of the gear can be made to fit a radial protuberance on the shaft. For transmitting moderate loads, a cheaper and effective connection can be made by forming a series of longitudinal serrations on the shaft with a knurling tool and pressing the shaft into the hole in the driven member, it will cut grooves in the hole and provide, in effect, a press-fitted splined connection. Press and shrink fits are also used, and they can provide surprisingly firm connections, but the dimensions of the connected member must be closely controlled. 軸 實心軸 軸作為機(jī)械零件通常是一根圓柱形桿,用來支 撐部件并隨部件一起轉(zhuǎn)動以接受和傳遞轉(zhuǎn)動和扭矩。往復(fù)式發(fā)動機(jī)的曲軸接受每一根曲軸通過活塞和連桿(滑塊 -曲柄機(jī)構(gòu))傳來的轉(zhuǎn)動,并通過聯(lián)軸器、齒輪、鏈條或皮帶把轉(zhuǎn)動傳遞到變速箱、凸輪軸、泵和其它裝置。由曲軸通過齒輪或鏈條驅(qū)動的凸輪軸只有一根受力軸即輸入軸,但軸上的每一個凸輪都能把轉(zhuǎn)動傳遞給氣門的傳動機(jī)構(gòu)溝。 輪軸通常的定義是車輪和皮帶輪能在其上旋轉(zhuǎn)的一根固定的圓柱形構(gòu)件,但驅(qū)動汽車后輪的旋轉(zhuǎn)軸也叫輪軸,這可能是從過去馬車時代傳下來的。通常習(xí)慣上把機(jī)器上的短軸叫做主軸(或心軸),特別是指機(jī)床上安裝刀具和工件的軸。 在以前一個車間里所有的機(jī)器都由一個大電動機(jī)或原動機(jī)的,這樣就必須有一根同車間一樣長的主傳動軸(即天軸)通過皮帶把動力供給較短的副軸、中間軸或頂軸。這種主傳動軸是用一節(jié)節(jié)的軸裝配起來的,用剛性聯(lián)軸器固定在一起。盡管一般說來用單獨的電動機(jī)來驅(qū)動每一臺機(jī)器更為方便,并且現(xiàn)代的趨勢也是按照這個方向發(fā)展的,但現(xiàn)在仍有某些場合采用分組傳動更為經(jīng)濟(jì)。 應(yīng)力和變力 軸在轉(zhuǎn)動時承受剪應(yīng)力,其大小取決于扭矩和斷面的尺寸。這個剪應(yīng)力是軸的材料對作用扭矩所產(chǎn)生的抗力的一種量度。所有傳遞扭矩的軸都承受扭轉(zhuǎn)剪應(yīng)力。 除剪應(yīng)力之外,傳 遞扭矩的軸還會產(chǎn)生剪切變形。扭轉(zhuǎn)的狀態(tài)通常用每單位長度的扭轉(zhuǎn)角來表示,即用軸的某一截面所轉(zhuǎn)過的角度來表示。 安裝齒輪和皮帶輪的軸不但會產(chǎn)生扭矩,而且還會產(chǎn)生彎矩,彎曲應(yīng)力(在凸面是拉應(yīng)力,在凹面是壓應(yīng)力)的大小取決于兩軸承間的距離及軸的截面尺寸, 彎曲和扭轉(zhuǎn)綜合起來使軸內(nèi)所產(chǎn)生的受力狀態(tài)比單純扭轉(zhuǎn)所產(chǎn)生的純剪切狀態(tài)或單純彎曲所產(chǎn)生的拉伸壓縮狀態(tài)更為復(fù)雜。 對軸的設(shè)計工作者來說,重要的是要知道軸是否可能產(chǎn)生過大的發(fā)向應(yīng)力或過大的剪應(yīng)力以致?lián)p壞。如果扭轉(zhuǎn)一支粉筆,它必定在同軸線成 45角的平面上而不是在與軸線 垂直的平面上斷裂。這是因為最大的應(yīng)力就作用在這個平面上,而粉筆的抗拉強(qiáng)度是很差的。通常在設(shè)計鋼軸時要使彎曲和扭轉(zhuǎn)產(chǎn)生的最大剪應(yīng)力小于規(guī)定的最大設(shè)計應(yīng)力。 圓形截面的軸與其它截面的軸相比,在扎鋼上更易于扎制,且更易于加工,同時也易于支撐在軸承上。因此,在實際應(yīng)用中很少使用非遠(yuǎn)行截面的軸。此外,圓軸的強(qiáng)度和剛度,無論是在彎曲或是扭轉(zhuǎn)時,都較易與計算。最后,對一定量的材料來說,圓軸對一定的扭矩所產(chǎn)生的最大剪應(yīng)力最小,而抗扭剛度則最大。 圓軸內(nèi)的剪應(yīng)力在表面最大,而在軸線部分則降到零。這就是說大部分扭矩是由表面和靠 近表面的材料來承受的。 臨界轉(zhuǎn)速 用弓拉小提琴時琴弦會發(fā)生振動,同樣,支撐在兩軸承之間的圓軸也有一個自然的橫向振動頻率。如果軸的轉(zhuǎn)速與自然頻率重合,軸就處于臨界轉(zhuǎn)速并發(fā)出噪音。多半長的撓性軸比短的剛性軸更容易出現(xiàn)臨界轉(zhuǎn)速。軸的自然頻率可隨其剛度的增加而提高。 如果把一根細(xì)長桿的一端固定在天花板上,另一端支撐一個很重的圓盤,如果給圓盤一個起始的扭矩就把手松開,圓盤就會像扭擺一樣繞桿軸來回振動。振動的頻率取決于桿的抗扭剛度和圓盤的重量;桿的剛度越大且圓盤越輕則頻率越高。往復(fù)式發(fā)動機(jī)的曲軸也會產(chǎn)生類似的扭轉(zhuǎn)振動 。特別是多拐曲軸和帶有很重飛輪的曲軸更是如此。每一個曲拐和與之相聯(lián)的連桿部分的作用就像一個小飛輪,并且對作為一個整體的曲軸來說,這些小飛輪能按很多種方式彼此安相反的方向與主飛輪反反方向地繞軸線來回振動。 當(dāng)發(fā)動機(jī)
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