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1、精選優(yōu)質(zhì)文檔-傾情為你奉上stress and strain 應(yīng)力與應(yīng)變 In any engineering structure工程結(jié)構(gòu) the individual components獨(dú)立構(gòu)件 or members will (be subjected to)受到,被附加 external forces外力 arising from由。引起 the service conditions工作環(huán)境 or environment in which the component works. 在任何的工程結(jié)構(gòu)中,每個零件,構(gòu)件將會受到來自工作環(huán)境的外力的作用。 If the component o
2、r member is in equilibrium平衡, the resultant合力 of the external forces外力 will be zero but, nevertheless不然的話, they together place a load on the member which tends to deform使變形 that member and which must be reacted作用 by internal forces內(nèi)力 set up within the material由材料提供.如果這構(gòu)件是處于平衡狀態(tài)的話,外力的合力是為零。但是他們必須由材料提
3、供的內(nèi)力來平衡。+ There are a number of different ways in which load負(fù)載 can be applied作用to a member. Loads may be classified分類 with respect to time:負(fù)載作用于構(gòu)件有許多的形式。相對于時間可以將負(fù)載分類為: (a) A static靜態(tài) load負(fù)載 is a gradually逐漸 applied作用 load for which equilibrium is reached in a relatively相對 short time.靜態(tài)負(fù)載是逐漸作用的可以在相對較
4、短的時間內(nèi)達(dá)到平衡的負(fù)載。 (b)A sustained load持續(xù)載荷 is a load that is constant維持不變 over a long period of很 time, such as the weight of a structure構(gòu)件重力. This type of load is treated處理,對待 in the same manner as a static load靜態(tài)載荷; However for some materials對一些材料, and conditions of temperature and stress, the resistanc
5、e抵抗力 to failure may be different under short time loading and under long time loading.持續(xù)載荷是可以維持很長時間不變的載荷。比如構(gòu)件的重力。這種類型的載荷和靜態(tài)載荷是同樣的處理方法。但是對于某種材料,在某些特定的溫度和外部壓力的作用下,構(gòu)件抵抗失效的能力是不同的。 (c) An impact沖擊 load is a rapidly很快的迅速的 applied load (an energy load). Vibration震動 normally results from an impact load, and
6、 equilibrium平衡 is not established確定 until the vibration振動 is eliminated消除, usually by natural damping forces阻尼力. 沖擊載荷是一種快速作用的載荷。振動常常是有沖擊載荷引起。在振動被消除之前,平衡是很難穩(wěn)定的。而消除振動的一半都是靠阻力。 (d) A repeated load重復(fù)載荷 is a load that is applied作用 and removed移動 many thousands of times.持續(xù)作用很多次,移動很多次的載荷稱為持續(xù)載荷。 (e) A fatigu
7、e or alternating load交變載荷 is a load whose magnitude and sign are changed with time.狡辯載荷是大小和符號都在不斷變化的載荷。 It has been noted above that external force applied to a body in equilibrium is reacted by internal forces set up within the material.上述的外力作用于物體時將會被材料提供的內(nèi)力抵消而達(dá)到平衡。 If, therefore因此, a bar棒子,零件 is s
8、ubjected to作用 a uniform統(tǒng)一的,制服 tension拉伸 or compression壓縮, i.e. 也就是說a force, which is uniformly applied across the cross-section截面, then the internal forces set up are also distributed分布 uniformly and the bar is said to be subjected to a uniform normal stress正應(yīng)力, the stress being defined定義 as:因此,如果零件
9、受到統(tǒng)一的拉伸或者壓縮,也就是說,力均勻的分布在截面上,此時內(nèi)力也同樣是均勻分布,此時我們就說哦這個構(gòu)件受到了正應(yīng)力的作用。這種應(yīng)力定義為: stress=press/area=P/A Stress may thus be compressive or tensile depending on the nature of the load and will be measured衡量 in units單位 of newtons牛頓 per square meter每平方米 (N/m2)or multiples倍數(shù) of this.這個力是壓力還是拉力由構(gòu)件所受的載荷確定。同時,此力可以用牛頓每
10、平方米或者它的倍數(shù)來衡量。 If a bar is subjected to an axial load軸向載荷, and hence因此 a stress, the bar will change in length. If the bar has an original length L and changes in length by an amount L, the strain應(yīng)變 produced產(chǎn)生的 is defined as follows:如果構(gòu)件受到軸向的載荷,此時構(gòu)件的長度會發(fā)生變化。如果構(gòu)件的本身長度是L,改變了&L則,產(chǎn)生的應(yīng)變定義為: strain=chang i
11、n lengyh/original length=&l/l Strain is thus a measure度量 of the deformation變形 of the material and is non-dimensional無量綱的, i.e. it has no unit沒有單位; it is simply a ratio比例,比率,比值 of two quantities數(shù)量,數(shù)值 with the same unit.因此,應(yīng)變是材料形變的度量,而且它是無量綱的。也就是說它沒有單位。它只是兩個有相同的單位的數(shù)值之間的比值。Tensile stress張應(yīng)力 and strain拉
12、應(yīng)力 are considered被認(rèn)為是 positive正的 in sense在某種程度. Compressive壓應(yīng)力 stress and strain are considered negative負(fù)的 in sense. Thus a negative strain produces a decrease in length.張應(yīng)力和拉應(yīng)力在被定義為正的,而壓應(yīng)力被認(rèn)為是負(fù)的。因此負(fù)的壓應(yīng)力造成長度的減少。 A material is said to be elastic有彈性的 if it returns to its original, unloaded dimensions大
13、小 when load is removed.如果材料在外力卸去的時候長度回復(fù)到了受力前的正常情況,我們就說這種材料有彈性。 A particular特別的 form形式 of elasticity彈性 which applies to a large range of engineering material工程材料, at least over part of their load range負(fù)載范圍, produces deformations變形 which are proportional to成比例的 the loads producing them.很多材料都有這種特性,至少在一
14、定范圍內(nèi),變形與負(fù)荷是成正比的。 Since loads are proportional to成比例 the stress they produce and deformations are proportional to the strains, this also implies意味著 that, whilst material are elastic, stress is proportional to strain. Hookes law胡克定律 therefore states that負(fù)載可以產(chǎn)生成比例的應(yīng)力,而應(yīng)力又可以產(chǎn)生成比例的形變。也就意味著材料有彈性。用胡克定律表示 T
15、his law is obeyed服從 within certain limits by most ferrous alloys鐵基合金 and it can even be assumed理論上 to apply to other engineering materials such as concrete混凝土, timber木材 and non-ferrous alloys有色金屬 with reasonable合理的,可接受的 accuracy準(zhǔn)確性,精度.此定律適用于大部分的鐵基合金,理論上還可以用于其它工程材料,例如混凝土,木材,有色金屬。并且精度還可接受。 Whilst同時 a
16、material is elastic the deformation produced by any load will be completely recovered when the load is removed; there is no permanent deformation殘留變形,永久變形.如果材料是彈性的,那如果負(fù)載去掉之后,由負(fù)載造成的變形將會完全消失不會留下殘留變形。 Within the elastic limits of materials, i.e. within the limits in which Hookes law applies, it has bee
17、n shown that在材料的彈性極限內(nèi),也就是說,在胡克定律允許的范圍內(nèi),表現(xiàn)為: stress/strain=E This constant常數(shù) is given the symbol符號 E and termed被稱為 the modulus of elasticity彈性模量 or Youngs modulus楊氏模量. Thus這個常數(shù)由符號E表示,并被稱為彈性模量或者楊氏模量。 Youngs modulus E is generally assumed假定 to be the same in tension or compression and for most engineer
18、ing materials has a high numerical value數(shù)值. Typically代表性的, E=200*109N/m2 for steel鋼 , so that it will be observed觀察 from Eq.(2.5) that strains are normally very small.一半假設(shè)楊氏模量E在拉壓時是相同的。對大多數(shù)的材料來說,它的數(shù)值都比較大,代表性的,鋼的是200*109,從儀器中觀察到的是2.5,應(yīng)變是很小的。 In most common engineering applications應(yīng)用 strains rarely ex
19、ceed很少超過 0.1%. The actual真實的 value of Youngs modulus for any material is normally determined by carrying out a standard test on a specimen of the material. As we look around us we see a world full of “things”: machines, devices設(shè)備, tools; things that we have designed, built, and used; things made of
20、wood, metals, ceramics陶瓷, and plastics. We know from experience that some things are better than others; they last longer, cost less, are quieter, look better, or are easier to use.當(dāng)我們環(huán)顧四周,我們可以看到世界充滿了“東西”。機(jī)器,設(shè)備,工具;我們設(shè)計,建造,使用的東西;用木頭,金屬,陶瓷,塑料制造的東西。我們憑借經(jīng)驗可以知道,一些東西比另一些東西更好,更便宜,更持久,更漂亮和更易于使用。 Ideally理想的,
21、 however, every such item項目 has been designed according to some set of “functional requirements”功能要求 as perceived感知 by the designers that is, it has been designed so as to answer the question, “Exactly what function should it perform執(zhí)行?” In the world of engineering, the major function frequently頻繁的
22、is to support some type of loading due to weight, inertia慣性, pressure, etc. 然而,理想的化的,每個項目都是根據(jù)設(shè)計者的感知到的功能要求來設(shè)計的。也就是說,它是設(shè)計來解決一些問題,那么它們需要執(zhí)行什么功能呢?在工程界中,最頻繁的功能就是用來支持各種形式的由重力,慣性,壓力引起的載荷。 From the beams衡梁 in our homes to the wings of an airplane, there must be an appropriate melding結(jié)合 of materials, dimensio
23、ns規(guī)模,大小, and fastenings連接件 to produce structures that will perform their functions功能 reliably可靠的 for a reasonable cost over a reasonable lifetime. 從家里的衡梁到飛機(jī)的翅膀,都必須由合適的材料,規(guī)模,連接件的配合,從而生產(chǎn)出有可靠功能和合理壽命的結(jié)構(gòu)設(shè)備。 In practice實際上, engineering mechanics工程力學(xué),機(jī)械工程 methods are used in two quite different ways:事實上,工程
24、力學(xué)方法被用于兩個截然不同的方面: (1) The development of any new device裝置,設(shè)備 requires an interactive交互式的, iterative反復(fù)的 consideration of考慮 form, size, materials, loads, durability耐久性, safety, and cost.裝置的發(fā)展要求有對形狀,尺寸,材料,負(fù)載,耐久性,安全和消費(fèi)的交互式的反復(fù)的考慮。 (2) When a device fails (unexpectedly失效) it is often necessary to carry ou
25、t a study to pinpoint查明 the cause of failure and to identify鑒定 potential潛在的 corrective measures補(bǔ)救措施. Our best designs often evolve進(jìn)化,發(fā)展 through a successive elimination逐次消元 of weak points.當(dāng)一個產(chǎn)品失效的時候,應(yīng)該去找出失效的原因,并且看看是否有潛在的補(bǔ)救措施。我們的最好的設(shè)計常常是通過不斷減少弱點來得到的。 To many engineers, both of the above processes過程 c
26、an prove to be absolutely 絕對的fascinating迷人的 and enjoyable, not to mention更不必說 lucrative有利可圖.對于設(shè)計師來說,上面的兩個過程都是非常的迷人,有趣的。更不必說它還是有利可圖可以賺錢的。 In any “real” problem there is never sufficient足夠 good, useful information; we seldom know the actual loads and operating conditions工作條件 with any precision精度, and
27、the analyses are seldom exact. 在任何現(xiàn)實的情況中,都沒有足夠的信息,我們很少知道真實的載荷,工作條件。精度和分析幾乎沒有什么保證。 While our mathematics數(shù)學(xué)運(yùn)算 may be precise精確, the overall analysis全分析 is generally only approximate近似的, and different skilled people can obtain獲得 different solutions. In the study of engineering mechanics, most of the pr
28、oblems will be sufficiently “idealized理想化的” to permit允許 unique solutions唯一解, but it should be clear that the “real world” is far less idealized, and that you usually will have to perform some idealization in order to obtain a solution. 就算我們的數(shù)學(xué)運(yùn)算是完全精確的,全非西也就只能是近似。用不同的方法可以獲得不同的結(jié)果。在工程機(jī)械的研究中,我們經(jīng)常需要用到理想化
29、的思想,來允許唯一解。但是我們要知道,現(xiàn)實世界遠(yuǎn)非理想,我們經(jīng)常要用這個思想來解決問題。 The technical工藝的 areas we will consider are frequently頻繁的 called “statics” and “strength of materials,” “statics” referring to the study of forces acting on stationary devices, and “strength of materials” referring to the effects of those forces on the st
30、ructure (deformations, load limits, etc.). While a great many devices are not, in fact, static, the methods developed here are perfectly applicable to適用于 dynamic situations動態(tài)情況 if the extra loadings associated with與。有關(guān) the dynamics are taken into account 被考慮(we shall briefly短暫的 mention how this is d
31、one). Whenever the dynamic forces動力 are small relative to the static loadings, the system is usually considered to be static.大部分設(shè)備并不是靜態(tài)的,這里提出的方法適用于動態(tài),如果與動態(tài)有關(guān)的額外載荷被考慮進(jìn)去。任何時候只要動力與靜態(tài)載荷有任何的關(guān)系,那么系統(tǒng)就被認(rèn)為是靜態(tài)的。 In engineering mechanics, we will appreciate欣賞到 the various各種各樣 types of approximations近似法 that ar
32、e inherent in固有的 any real problem: 在工程機(jī)械中,我們可以欣賞到各種各樣形式的近似法來解決固有的問題。 Primarily首先, we will be discussing things which are in “equilibrium,” i.e., not accelerating加速的. However, if we look closely enough, everything is accelerating. We will consider many structural members結(jié)構(gòu)部件 to be “weightless” but th
33、ey never are. We will deal with forces that act at a “point” but all forces act over an area. We will consider some parts to be “rigid堅硬的” but all bodies will deform under load.首先,我們討論處于平衡中的物體,也就是說沒有加速的。然而,如果我們仔細(xì)觀察,可以看到所有物體都是運(yùn)動的,我們會認(rèn)為構(gòu)件是沒有重量的,但是他們總有重量。我們會認(rèn)為力作用在點上,但是力總是作用在面上的,我們認(rèn)為一些部分是堅硬的,但是任何物體在力的作用
34、下都會變形。 We will make many assumptions假定 that clearly are false. But these assumptions should always render the problem easier, more tractable易處理的. You will discover that the goal is to make as many simplifying assumptions as possible without seriously degrading退化 the result.我們會假定一些顯然是錯誤的東西。但是這些假設(shè)會使問題
35、變得簡單,更易處理。你會發(fā)現(xiàn)我們的目的是找到盡量簡單的假設(shè),只要不使結(jié)果嚴(yán)重變形。 Generally there is no clear method to determine確定 how completely, or how precisely, to treat a problem: If our analysis is too simple, we may not get a pertinent相關(guān)的 answer; if our analysis is too detailed詳細(xì), we may not be able to obtain得到 any answer. It is u
36、sually preferable to start with a relatively simple analysis and then add more detail as required to obtain a practical solution. During the past two decades, there has been a tremendous growth in the availability of computerized methods for solving problems that previously were beyond solution beca
37、use the time required to solve them would have been prohibitive. At the same time the cost of computer capability and use has decreased by orders of magnitude. We are experiencing an influx of “personal computers” on campus, in the home, and in business.Lesson 6 Shaft軸 DesignA shaft is a rotating旋轉(zhuǎn)
38、or stationary固定的 member零件,構(gòu)件, usually of circular圓形的 cross section橫截面, having mounted安裝 upon it such elements as gears齒輪, pulleys滑輪, flywheels飛輪, and other power-transmission傳動裝置 elements.軸類零件一般都是固定的或者是旋轉(zhuǎn)體。截面一般都是圓形,并且有齒輪,滑輪,飛輪或者其他的傳動裝置安裝在上面。If a shaft carries安裝 several gears or pulleys齒輪或者滑輪, differ
39、ent sections截面 of the shaft will be subjected to承受 different torques力矩, because the total power delivered to傳遞 the shaft is taken off piecemeal分散成片 at various points. Hence one must note記錄 the amount of torque力矩 on each part of the shaft. Then study the distribution分布 of the bending moment彎矩, prefer
40、ably較好的 sketching草圖( freehand is all right) the shear force切應(yīng)力 and bending moment diagrams彎矩圖.如果軸上安裝了幾個齒輪和滑輪,不同的截面將會承受不同的力矩。因為傳遞到軸上的總力被分散到了不同的點。因此我們必須分別記錄不同部分的力矩,然后研究彎矩的分布,較好的畫出切應(yīng)力和彎矩的圖。From this preliminary examination預(yù)備考試,預(yù)先檢查, which is a problem in mechanics, we note the section截面 where the bendi
41、ng moment彎矩 is a maximum and the section where the torque扭矩 is a maximum. If these maximums occur at the same section, the diameter直徑 needed for that section is determined- and used for the entire整個的 shaft when the diameter is to be constant恒定. If the maximums do not occur at the same section, deter
42、mine the diameter for the section of maximum torque and also for the section of maximum bending moment, and use the larger value.從之前的檢查我們可以知道,我們在工程中注意彎矩和扭矩達(dá)到最大的截面。如果這些截面重合,那么我們就說當(dāng)此直徑恒定的時候,截面的的直徑也就定了,當(dāng)然此軸的尺寸也就定下來了。如果兩個面沒有重合,那么我們就取其中大的那個。 The diameter of shaft is often varied from point to point , som
43、etimes for structure reasons. In this case, check the stress or determine the size needed for each section. The designer makes certain that all sections of the shaft are subjected to safe stresses, taking due note of holes, keyways, and other stress raisers應(yīng)力集中裝置.軸各部分的直徑常常是不同的。一些是結(jié)構(gòu)的原因。這種時候,我們要檢查上面的
44、應(yīng)力并且決定所需面的尺寸。設(shè)計師要特別注意孔,鍵槽和其他的應(yīng)力集中裝置,確保所有的截面所受的力都在允許范圍內(nèi)。 Hollow洞 round shafts園軸 sometimes serve a useful purpose, usually in large sizes, though they are more expensive than solid ones. They have the advantage of being stronger and stiffer更硬的, weight for weight, because the outer fibers外部纖維 are more
45、effective in resisting the applied moments, and they respond better to heat treatment because quenching淬火 can proceed outward as well as inward.孔軸常??梢园l(fā)揮重要的作用,它們的尺寸一般都比較大,而且比一般的實心軸更貴。它們的優(yōu)點是等質(zhì)量的情況下更加的硬,因為外部的纖維更有利于承受應(yīng)力,而且由于它們可以內(nèi)外同時進(jìn)行熱處理所以效果可以更好。 Deflection偏差 is a significant重大的 consideration in the des
46、ign of shafts. Criteria標(biāo)準(zhǔn)條件 for the limiting torsional deflection扭轉(zhuǎn)變形 vary from 0.25 degree per meter of length for machinery shafts to 1 degree per meter or 1 degree in a length of 20 diameters for transmission shafting傳動軸. Even short shafts become special problems in rigidity硬度 when the load is ap
47、plied in impulses脈沖, as on an automobile crankshaft汽車機(jī)軸. The impulses脈沖 produce a torsional vibration扭轉(zhuǎn)變形, usually compensated by torsional-vibration dampers扭轉(zhuǎn)減震器 in an automotive engine汽車發(fā)動機(jī).在軸的設(shè)計中,偏差將會被著重考慮。傳動軸的標(biāo)準(zhǔn)扭轉(zhuǎn)變形范圍是每米0.25度到1度。就算是微小的偏差如果加載上脈沖負(fù)載都會嚴(yán)重影響軸的硬度。就比如汽車的機(jī)軸,就需要汽車發(fā)動機(jī)中的扭轉(zhuǎn)減震器來消除脈沖造成的扭轉(zhuǎn)變形。 D
48、ata on permissible values允許值 of deflections變形 are rare, probable because the range范圍 of values would be large and each situation has its own peculiarities獨(dú)特性. An old rule of thumb檢驗的法則 for transmission shafting傳動軸 is that the deflection should not exceed 0.0005L, where L is the shaft length between
49、supports; although greater stiffness may be desired需要. 變形的允許值很小,也許是因為每種特定的情況都有其獨(dú)特性。舊時后的檢驗法則表示就算需要更高的強(qiáng)度變形也不能超過軸長的0.0008倍。Preferably較好的, on transmission shafts, the pulleys and gears should be located close to bearings軸承 in order to minimize最小化 moments. If journal bearings徑向軸承 with “thick film” lubric
50、ation潤滑 are used, the deflection偏向 across the bearing width軸承寬度 should be only a small fraction部分 of the oil-film thickness油膜厚度; if the slope斜坡 is excessive過多 here, there will be “binding粘合” in the journal軸頸. A self-aligning bearing球面軸承 may eliminate消除 this trouble if the deflection is otherwise acc
51、eptable. 傳動軸的較好的設(shè)計是將齒輪和滑輪放在靠近軸承的地方。如果使用的是涂有潤滑油的徑向軸承那么軸承寬度方向的偏向只能是油膜厚度的一小部分。如果斜坡過多那么就要在軸頸上涂上粘合劑。但是當(dāng)變形在可接受范圍內(nèi)時球面軸承可以消除這種問題。 On machine tools, rigidity硬度 is a special concern because of its relation to accuracy準(zhǔn)確性. If a shaft supports a gear, deflection is more of a consideration than if it carries a V
52、-belt pulley皮帶輪.在機(jī)械工具中,硬度被特別關(guān)注。因為他反應(yīng)了其精度。裝了齒輪的軸比裝了皮帶輪的軸更加強(qiáng)調(diào)偏差。 The center of mass質(zhì)心 of symmetric勻稱的, rotating旋轉(zhuǎn) body does not coincide with與一致 its center of rotation. This is because (a) it is impossible from a practical實際 viewpoint to get the mass uniformly distributed分布式 about the geometric幾何學(xué) cen
53、ter of the body and (b) the shaft on which the body rotates deflects under load, thus moving the center of mass away from the true axis, which passes through通過 the center line of the bearings. 均與的旋轉(zhuǎn)體的質(zhì)心與其旋轉(zhuǎn)中心不重合。因為從實際情況看,質(zhì)量是不可能按照其幾何形狀均勻分布的。因此將質(zhì)心移動離開其軸心, Rotation循環(huán) may begin about the geometric axis幾
54、何中心, but at some speed, the centrifugal force離心力 of the displaced取代 center of mass質(zhì)心 will equal the deflecting forces偏轉(zhuǎn)力 on the shaft; the shaft with its attached附加的 bodies will then vibrate震動 violently猛烈的, since the centrifugal force changes its direction方向 as the shaft turns. This speed is termed術(shù)
55、語是 the critical speed臨界轉(zhuǎn)速. Above the critical speed, a smooth-running state光滑運(yùn)行狀態(tài) of equilibrium平衡 is again reached when the body is then rotating旋轉(zhuǎn) virtually事實上 about its mass center質(zhì)心 (centrifugal forces離心力 balance). 循環(huán)也許會繞著幾何中心進(jìn)行。但是在某些速度的情況下,被取代了的質(zhì)心的離心力會與軸上的偏心力平衡,帶著附加物件的軸將會猛烈的震動。知道離心力方向改變成與轉(zhuǎn)動方向一致
56、。這個速度被稱為是臨界轉(zhuǎn)速。在此速度時,工件將會再次達(dá)到平衡的光滑運(yùn)行狀態(tài)。 High-speed turbines高速渦輪機(jī) often operate運(yùn)轉(zhuǎn) above the critical speed臨界轉(zhuǎn)速. Additional附加的 critical speeds, higher than the first, are successively相繼的 attained得到, but the amplitudes振幅 of the corresponding相應(yīng)的 vibrations震動 progressively逐漸的 decrease. 高速渦輪機(jī)經(jīng)常在臨界轉(zhuǎn)速運(yùn)轉(zhuǎn)。更加高的
57、附加的臨界轉(zhuǎn)速也常常被運(yùn)用。但是相應(yīng)的震動的振幅也就逐漸的減少。 Many shafts supported by three or more bearings, which means that the problem is statically靜態(tài)的 indeterminate不確定的. Texts on strength of materials材料強(qiáng)度 give methods of solving such problems. The design effort設(shè)計工作 should be in keeping with與。相關(guān)聯(lián) the economics經(jīng)濟(jì)學(xué) of a given situation. For example, if one line shaft supported by three or more bearings is needed, it probably would be cheaper to make conservative assumptions保守假設(shè) as to moments and design it as though it were deter
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