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外文翻譯 Kinematics and dynamics of machinery One princple aim of kinemarics is to creat the designed motions of the subject mechanical parts and then mathematically compute the positions, velocities ,and accelerations ,which those motions will creat on the parts. Since ,for most earthbound mechanical systems ,the mass remains essentially constant with time defining the accelerations as a function of time then also defines the dynamic forces as a function of time. Stressin turn, will be a function of both applied and inerials forces . since engineering design is charged with creating systems which will not fail during their expected service life the goal is to keep stresses within acceptable limits for the materials chosen and the environmental conditions encountered. This obvisely requies that all system forces be defined and kept within desired limits. In mechinery , the largest forces encountered are often those due to the dynamics of the machine itself. These dynamic forces are proportional to acceletation, which brings us back to kinematics ,the foundation of mechanical design. Very basic and early decisions in the design process invovling kinematics wii prove troublesome and perform badly. Any mechanical system can be classified according to the number of degree of freedom which it possesses.the systems DOF is equal to the number of independent parameters which are needed to uniquely define its posion in space at any instant of time. A rigid body free to move within a reference frame will ,in the general case, have complex motoin, which is simultaneous combination of rotation and translation. In three-dimensional space , there may be rotation about any axis and also simultaneous translation which can be resoled into componention along three axes, in a plane ,or two-dimentional space ,complex motion becomes a combination of simultaneous along two axes in the plane. For simplicity ,we will limit our present discusstions to the case of planar motion: Pure rotation the body pessesses one point (center of rotation)which has no motion with respect to the stationary frame of reference. All other points on the body describe arcs about that center. A reference line drawn on the body through the center changes only its angulai orientation. Pure translation all points on the body describe parallel paths. A reference line drawn on the body changes its linear posion but does not change its angular oriention. Complex motion a simulaneous combination of rotion and translationm . any reference line drawn on the body will change both its linear pisition and its angular orientation. Points on the body will travel non-parallel paths ,and there will be , at every instant , a center of rotation , which will continuously change location. Linkages are the bacis building blocks of all mechanisms. All common forms of mechanisms cams , gears ,belts , chains are in fact variations of linkages. Linkages are made up of links and kinematic pairs. A link is an (assumed)rigid body which possesses at least two or more links (at their nodes), which connection allows some motion, or potential motionbetween he connected links. The term lower pair is used ti describe jionts with surface contact , as with a pin surrounded by a hole. The term higher pair is used to describe jionts with point or line contact ,but if there is any clerance between pin and hole (as there must be for motion ),so-called surface contact in the pin jiont actually becomes line contact , as the pin contacts actually has contact only at discrete points , which are the tops of the surfaces’ asperities. The main practical advantage of lower pairs over higher pairs is their better ability to trap lubricant between their envloping surface. This is especially true for the rotating pin joint. The lubricant is more easily squeezed out of a higher pair .as result , the pin joint is preferred for low wear and long life . When designing machinery, we must first do a complete kinematic analysis of our design , in order to obtain information about the acceleration of the moving parts .we next want te use newton’s second law to caculate the dynamic forces, but to do so we need to know the masses of all the moving parts which have these known acceletations. These parts do not exit yet ! as with any design in order to make a first pass at the caculation . we will then have to itnerate to better an better solutions as we generate more information. A first estimate of your parts’ masses can be obtained by assuming some reasonable shapes and size for all the parts and choosing approriate materials. Then caculate the volume of each part and multipy its volume by material’s mass density (not weight density ) to obtain a first approximation of its mass . these mass values can then be used in Newton’s equation. How will we know whether our chosen sizes and shapes of links are even acceptable, let alone optimal unfortunately , we will not know untill we have carried the computations all the way through a complete stress and deflection analysis of the parts. It it often the case ,especially with long , thin elements such as shafts or slender links,that the deflections of the parts, redesign them ,and repeat the force ,stress ,and deflection analysis . design is , unavoidably ,an iterative process . It is also worth nothing that ,unlike a static force situation in which a failed design might be fixed by adding more mass to the part to strenthen it ,to do so in a dynamic force situation can have a deleterious effect . more mass with the same acceleration will generate even higher forces and thus higher stresses ! the machine desiger often need to remove mass (in the right places) form parts in order to reduce the stesses and deflections due to F=ma, thus the designer needs to have a good understanding of both material properties and stess and deflection analysis to properlyshape and size parts for minimum mass while maximzing the strength and stiffness needed to withstand the dynamic forces. One of the primary considerations in designing any machine or strucre is that the trength must be sufficiently greater than the stress to assure both safety and reliability. To assure that mechanical parts do not fail in service ,it is necessary to learn why they sometimes do fail. Then we shall be able to relate the stresses with the strenths to achieve safety . Ideally, in designing any machine elementthe engineer should have at his disposal should have been made on speciments having the same heat treatment ,surface roughness ,and size as the element he prosses to design ;and the tests should be made under exactly the same loading conditions as the part will experience in service . this means that ,if the part is to experience a bending and torsionit should be tested under combined bending and torsion. Such tests will provide very useful and precise information . they tell the engineer what factor of safety to use and what the reliability is for a given service life .whenever such data are available for design purposes the engineer can be assure that he is doing the best justified if failure of the part may endanger human life ,or if the part is manufactured in sufficiently large quantities. Automobiles and refrigrerators, for example, have very good reliabilities because the parts are made in such large quantities that they can be thoroughly tested in advance of manufacture , the cost of making these is very low when it is divided by the total number of parts manufactrued. You can now appreciate the following four design categories : (1)failure of the part would endanger human life ,or the part ismade in extremely large quantities ;consequently, an elaborate testingprogram is justified during design . (2)the part is made in large enough quantities so that a moderate serues of tests is feasible. (3)The part is made in such small quantities that testing is not justified at all ; or the design must be completed so rapidlly that there is not enough time for testing. (4) The part has already been designed, manufactured, and tested and found to be unsatisfactory. Analysis is required to understand why the part is unsatisfactory and what to do to improve it. It is with the last three categories that we shall be mostly concerned.this means that the designer will usually have only published values of yield strenth , ultimate strength,and percentage elongation . with this meager information the engieer is expected to design against static and dynamic loads, biaxial and triaxial stress states , high and low temperatures and large and small parts! The data usually available for design have been obtained from the simple tension test ,where the load was applied gradually and the strain given time to develop. Yet these same data must be used in designing parts with complicated dynamic loads applied thousands of times per minute. No wonder machine parts sometimes fail. To sum up, the fundamental problem of the designer is to use the simple tension test data and relate them to the strength of the part regardless of the stress or the loading situation. It is possible for two metal to have exactly the same strength and hardness, yet one of these metals may have a supeior ability to aborb overloads, because of the property called ductility. Dutility is measured by the percentage elongation which occurs in the material at frature. The usual divding line between ductility and brittleness is 5 percent elongation. Amaterial having less than 5percent elongation at fracture is said to bebrittle while one having more is said to be ductile. The elongation of a material is usuallu measured over 50mm gauge lengthsiece this id not a measure of the actual strain, another method of determining ductility is sometimes used . after the speciman has been fractured, measurements are made of the area of the cross section at the fracture. Ductility can then be expressed as the percentage reduction in cross sectional area. The characteristic of a ductile material which permits it to aborb largeoverloads is an additional safety factot in design. Ductility is also important because it is a measure of that property of a material which permits it to be cold-worked .such operations as bending and drawing are metal-processing operations which require ductile materials. When a materals is to be selected to resist wear erosion ,or plastic deformaton, hardness is generally the most important property. Several methods of hardness testing are available, depending upon which particular property is most desired. The four hardness numbers in greatest use are the Brinell Rockwell Vickers, and Knoop. Most hardness-testing systems employ a standard load which is applied to a ball or pyramid in contact with the material to be tested. The hardness is an easy property to measure , because the test is nondestructive and test specimens are not required . usually the test can be conducted directly on actual machine element . Virtually all machines contain shafts. The most common shape for shafts is circular and the cross section can be either solid or hollow hollow shafts can result in weight savings. Rectangular shafts are sometimes used, as in screw driver bladers ,socket wrenches and control knob stem. A shaft must have adequate torsional strength to transmit torque and not be over stressed. If must also be torsionally stiff enough so that one mounted component does not deviate excessively from its original angular position relative to a second component mounted on the same shaft. Generally speakingthe angle of twist should not exceed one degree in a shaft length equal to 20 diameters. Shafts are mounted in bearing and transmit power through such device as gears, pulleys,cams and clutches. These devices introduce forces which attempt to bend the shaft;hence, tha shaft must be rigid enough to prevent overloading of the supporting bearings ,in general, the bending deflection of a shaft should not exceed 0.01 in per ft of length between bearing supports. In addition .the shaft must be able to sustain a combination of bending and torsional loads. Thus an equivalent load must be considered which takes into account both torsion and bending . also ,the allowable stress must contain a factor of safety which includes fatigue, since torsional and bending stress reversals occur. For fiameters less than 3 in ,the usual shaft material is cold-rolled steel containing about 0.4 percent carbon. Shafts ate either cold-rolled or forged in sizes from 3in. to 5 in. for sizes above 5 in. shafts are forged and machined to size plastic shafts are widely used for light load applications . one advantage of using plastic is safty in electrical applications, since plastic is a poor confuctor of electricity. Components such as gears and pulleys are mounted on shafts by means of key. The design of the key and the corresponding keyway in the shaft must be properly evaluated. For example, stress concentrations occur in shafts due to keyways ,and the material removed to form the keyway further weakens the shaft. If shafts are run at critical speeds , severe vibrations can occur which can seriously damage a machine .it is important to know the magnitude of these critical speeds so that they can be avoided. As a general rule of thumb ,the difference between the operating speed and the critical speed should be at least 20 percent. Many shafts are supported by three or more bearings, which means that the problem is statically indeterminate .text on strenth of materials give methods of soving such problems. The design effort should be in keeping with the economics of a given situation , for example , if one line shaft supported by three or more bearings id needed , it probably would be cheaper to make conservative assumptions as to moments and design it as though it were determinate . the extra cost of an oversize shaft may be less than the extra cost of an elaborate design analysis. Another important aspect of shaft design is the method of directly connecting one shaft to another , this is accomplished by devices such as rigid and flexiable couplings. A coupling is a device for connecting the ends of adjacent shafts. In machine construction , couplings are used to effect a semipermanent connection between adjacent rotating shafts , the connection is permanent in the sense that it is not meant to be broken during the useful life of the machine , but it can be broken and restored in an emergency or when worn parts are replaced. There are several types of shaft couplings, their characteristics depend on the purpose for which they are used , if an exceptionally long shaft is required in a manufacturing plant or a propeller shaft on a ship , it is made in sections that are coupled together with rigid couplings. A common type of rigid coupling consists of two mating radial flanges that are attached by key driven hubs to the ends of adjacent haft sections and bolted together through the flanges to form a rigid connection. Alignment of the connected shafts in usually effected by means of a rabbet joint on the face of the flanges. In connecting shafts belonging to separate device such as an electric motor and a gearbox),precise aligning of the shafts is difficult and a fkexible coupling is used . this coupling connects the shafts in such a way as to minimize the harmful effects of shafts misalignment of loads and to move freely float in the axial diection without interfering with one another . flexiable couplings can also serve to reduce the intensity of shock loads and vibrations transmitted from one shaft to another . 機械運動和動力學(xué) 運動學(xué)的基本目的是去設(shè)計一個機械零件的理想運動，然后再用數(shù)學(xué)的方法 去描繪該零件的位置，速度和加速度，再運用這些參數(shù)來設(shè)計零件。因為，對于大部分固著在地球上的機械系統(tǒng)來說，與之聯(lián)系最密切的是時間，將加速度和動態(tài)力定義成時間作用的結(jié)果。相應(yīng)地，應(yīng)力是作用在物體上的外力和慣性力的作用結(jié)果。所以機械設(shè)計的內(nèi)容是要建立一種在該機器的使用壽命內(nèi)保證其安全的系統(tǒng)，目的是要在一定的工況要求下，對材料進行選擇，使材料的應(yīng)力在許用極限應(yīng)力之內(nèi)。這一點很明顯要求所有的系統(tǒng)要在理想的限制內(nèi)工作。在機械設(shè)計中，零件受到的最大力是取決于材料本身的動態(tài)性能。這些動態(tài)力引起了零件的加速度，加速度又要回到運動學(xué)中去計算，這是機械設(shè)計的基礎(chǔ)。運動分析是最基本的也是最早出現(xiàn)在設(shè)計的過程中的，它對與任何一個零件的成功設(shè)計夠起著至關(guān)重要的作用。在設(shè)計過程中很差的運動學(xué)分析會帶來麻煩和錯誤。 根據(jù)機構(gòu)所具有的自由度，任何機械系統(tǒng)都可以被分類。系統(tǒng)的自由度是在 任何時候限制它的位置獨立的參數(shù)數(shù)目。 在通常情況下，剛體在相關(guān)的平面內(nèi)能實現(xiàn)復(fù)雜的自由運動，這個運動同時 包括轉(zhuǎn)動和平移。在三緯空間內(nèi)，在可以饒任何軸轉(zhuǎn)動的同時可以沿著三個坐標 平移。在一個平面或是一個二維的空間內(nèi)，復(fù)雜運動變成了饒一個(垂直與這個平面的)軸線的轉(zhuǎn)動和同時發(fā)生的可以被分解為沿在這個平面內(nèi)的兩個坐標軸的平移分量。為了簡化，我們將當(dāng)前的討論限制在二維的運動系統(tǒng)中。接下來將要介紹相關(guān)的術(shù)語: 純轉(zhuǎn)動 物體圍繞著在相對于一個靜止的坐標系靜止的一點(回轉(zhuǎn)中心)轉(zhuǎn)動。 其他所有物體上的點都可以用相對中心的弧來描述。在物體上的參考線通過中心，只有在角度方向上有變化。。 純平動 所有在物體上的點在平行的路徑上平移。物體上的參考線在線性位 置上有變化，而在角度方向上沒有發(fā)生變化。 復(fù)雜運動 同時包含轉(zhuǎn)動和平動的運動。在物體上的參考線在沿線性點平動 的同時又在角度方向上有變化。物體上的點不會在沿著平行的路徑移動，他們在 饒中心轉(zhuǎn)動的同時也不停著改變著位置。 鉸鏈是聯(lián)接所有機構(gòu)的基本的構(gòu)件。所有一般形式的機械，(齒輪，帶，鏈)實際上都是不同類型的鉸鏈，鉸鏈組成了聯(lián)接和運動部件。 聯(lián)接是一個剛體和另外的連接件至少有兩個結(jié)點。 運動部件(也稱接頭)是在兩個連接件的結(jié)合部分，這個結(jié)合允許相對的運動，允許連接件之間潛在的運動。 術(shù)語低副是用來描繪接頭間的面接觸。，如針和孔的結(jié)合面。高副是用來描繪 接頭間的點和線接觸。但是如果在針和孔之間有間隙存在(當(dāng)它們之間用于有相對運動時)當(dāng)針和孔只有一面接觸時，在針間的面聯(lián)接實際上已經(jīng)變成了線接觸。 類似的，微觀上看，在平面滑動的桿件實際上只存在一些相關(guān)點的接觸，那是表面凹凸不平的突點，低副相對于高副的優(yōu)點是有利于接觸表面之間的潤滑，這一點對于旋轉(zhuǎn)接頭來說是確實存在的。在高副中潤滑易被擠出來。結(jié)果鉸接接頭能夠減少摩擦，延長壽命。 當(dāng)我們設(shè)計機械時，為了取得運動部件的加速度信息必須首先對我們的設(shè)計 進行全面的運動分析。接下來再運用牛頓第二運動定律去計算動態(tài)力。但是這樣 做，我們需要知道所有運動部件的質(zhì)量，和加速度，這些零件還沒有存在，正如碰到的所有設(shè)計問題，我們在設(shè)計決定零件最佳尺寸和形狀時缺少足夠的信息。為了通過最初的計算我們必須估計零件的質(zhì)量和設(shè)計的其它部分。當(dāng)我們得到更多的信息時，再得到更好的解決方案。 在估計你設(shè)計的零件質(zhì)量的初期通過合理的假設(shè)零件的形狀和尺寸及其合 理選擇材料來獲得。然后計算每個零件的體積，再去乘以所選材料的質(zhì)量密度，去取得零件最初的合理質(zhì)量。這些質(zhì)量值在牛頓方程中可以運用。 我們?nèi)绾蝸砼袛辔覀兯x擇的尺寸和形狀是否合理呢?很不巧，我們要到分 析完所受應(yīng)力和失效分析后才能知道，特別是細長零件，如軸，細長的連桿，甚至在很小的應(yīng)力條件下，零件在動載的的失效形式將限制我們的設(shè)計。這種情況我們經(jīng)常碰到。 我們可能將會發(fā)現(xiàn)零件在動載荷的情況下會失效。然后我們將反過來檢查我 們初選時假設(shè)的形狀，尺寸和材料，重新來選擇設(shè)計。然后重復(fù)力，應(yīng)力和失效分析。 設(shè)計不可避免地成為一個迭代過程。 值得注意的是，在靜力作用下，可以通過增加零件的質(zhì)量來提高其強度，將不合格的設(shè)計變?yōu)楹细?，而在動態(tài)力作用的情況下，這樣做可能產(chǎn)生有害的后果。在相同的加速度條件下，更大的質(zhì)量將會產(chǎn)生更大的力，隨即也會有更大的應(yīng)力。為了降低應(yīng)力和失效，設(shè)計者要從零件上去除一些質(zhì)量。同時設(shè)計者需要對材料的特性和應(yīng)力實效分析都要有很好的了解才能通過用合理的形狀和尺寸來達到最小的質(zhì)量，與此同時，抵御動態(tài)力的強度和剛度最大。 在設(shè)計任何機器或者機構(gòu)時，所考慮的主要事件之一是其強度應(yīng)該比它所承受的應(yīng)力要大的多，以確保安全可靠性，要保證機械零件在使用過程中不發(fā)生失效，就必須知道它們在某些時候會發(fā)生失效的原因，然后，才能將應(yīng)力和強度聯(lián)系起來，以確保其安全。 設(shè)計任何機械零件的理想情況為，工程師可以利用大量的他所選的這種材料 的強度試驗數(shù)據(jù)。這些試驗應(yīng)該采用與所設(shè)計是零件有著相同是熱處理，表面粗 糙度和尺寸大小的試件進行，而且試驗應(yīng)該在與零件使用過程中承受的載荷完全相同的情況下進行。這表明，如果零件將要承受彎曲載荷，那么就應(yīng)該進行彎曲載荷的試驗。如果零件將要受彎曲和扭轉(zhuǎn)的復(fù)合載荷，那么就應(yīng)該進行彎曲和扭轉(zhuǎn)復(fù)合載荷的試驗，這些種類的試驗可以提供非常有效和精準的數(shù)據(jù)。它們可以告訴工程師應(yīng)該使用的安全系數(shù)和對于給定的壽命時的可靠性。在設(shè)計過程中，只要能夠獲得這種數(shù)據(jù)，工程師就可以盡可能好地進行工程設(shè)計工作 如果零件的失效可能危害人的生命安全，或者零件有足夠大的產(chǎn)量，則在設(shè) 計前收集這樣廣泛的數(shù)據(jù)所花費的費用是很值得的，例如，汽車和冰箱的零件的 產(chǎn)量非常的大，可以在生產(chǎn)之前對它們進行大量的試驗，使其具有較高的可靠性。 如果把進行這些試驗的費用分攤到所生產(chǎn)的零件上的話，則攤到所生產(chǎn)每個零件 的費用是非常低的。 你可以對下列四種類型的設(shè)計作出評價。 (1)零件的失效可能危害人的生命安全，或者零件的產(chǎn)量非常大，因此在設(shè)計時安排一個完善的試驗程序會被認為是合理的。 (2)零件的產(chǎn)量足夠大，可以進行適當(dāng)?shù)南盗性囼灐?(3)零件的產(chǎn)量非常小，以至于進行試驗根本不合算;或者要求很快地完成設(shè)計，以至于沒有足夠的時間進行試驗。 (4)零件已經(jīng)完成設(shè)計，制造和試驗，但其結(jié)果不能令人滿意。這時候需要采用分析的方法來弄清楚不能令人滿意的原因和應(yīng)該如何進行改進。 我們將主要對后三種類型進行討論。這就說，設(shè)計人員通常只能利用那些公 開發(fā)表的屈服強度，極限強度和延伸率等數(shù)據(jù)資料。人們期望工程師在利用那些 公開發(fā)表的資料的基礎(chǔ)上，對靜載荷和動載荷，二維應(yīng)力狀態(tài)與三維應(yīng)力狀態(tài)，高溫與低溫以及大零件和小零件進行設(shè)計! 而設(shè)計中所能利用的數(shù)據(jù)通常是從簡單的拉伸試驗中得到，其載荷是漸漸加上去的，有充分的時間產(chǎn)生應(yīng)變。到目前為止，還必須利用這些數(shù)據(jù)來設(shè)計每分鐘承受幾千次復(fù)雜的動載的作用的零件，因此機械零件有時會失效是不足為奇的。 概括地說，設(shè)計人員所遇到的基本問題是，不論對于哪一種應(yīng)力狀態(tài)或者載 荷情況，都能利用通過簡單拉伸試驗所獲得的數(shù)據(jù)并將其與零件的強度聯(lián)系起來。 可能會有兩種具有完全相同的強度和硬度值的金屬，其中一種由于其本身的 延搌性而具有很好的承受超載荷的能力， 延搌性是利用材料斷裂時的延伸率來衡量的。通常將5%的延伸率定義為延展性的分界線。斷裂時延伸率小于5%的材料稱為脆性材料，大于5%的稱為延性材料。 材料的伸長量通常是在50mm的計量長度上測量的。因為這并不是對實際應(yīng) 變量的測量，所以有時也采用另一種測量延展性的方法。這個方法在試件斷裂后 測量其斷裂處的很截面的面積。因此，延展性可以表示為橫截面的收縮率。延展性材料能夠承受較大的超載荷這個特性是設(shè)計中的一個附加的安全因素。延展性材料的重要性在于它是材料泠變形能的衡量尺度。諸如彎曲和拉伸這類金屬加工過程需要采用延性材料。在選用抗磨損、抗侵蝕或者抗塑性變形的材料時硬度通常是最主要的性能。有幾種可選用的硬度試驗方法采用哪一種方法取決于最希望測量的材料特性。最常用的四種硬度是布氏硬度洛氏硬度維氏硬度努氏硬度。 大多數(shù)硬度試驗系統(tǒng)是將一個標準的載荷加在與被試驗材料相接觸的小球 或者棱錐上。 因此硬度可以表示為所產(chǎn)生的壓痕尺寸的函數(shù)。這表明由于硬 度是非破壞性試驗而且不需要專門的試件，因而硬度是一個容易測量的性能。通?？梢灾苯釉趯嶋H的機械零件上進行硬度試驗。實際上幾乎所有的機器中都裝有軸。軸最常見的形狀是圓形其截面可以是實心的也可以是空心的空心軸可以減輕重量。有時也采用矩形軸，例如螺絲起子的頭部，套筒扳手和控制旋轉(zhuǎn)的桿。 為了在傳遞扭矩時不發(fā)生過載，軸應(yīng)該具有適當(dāng)?shù)目古姸取］S還應(yīng)該具有 足夠的抗扭剛度，以使在同一個軸上的兩個傳動零件之間的相對轉(zhuǎn)角不會過大。 一般來說在長度等于軸的直徑的20倍時軸的扭轉(zhuǎn)角不應(yīng)該超過1度。 軸安裝在軸承中通過齒輪、皮帶輪、凸輪和離合器等零件傳遞動力。通過 這些零件傳來的力可能會使軸產(chǎn)生彎曲變形。因此，軸應(yīng)該有足夠的剛度以防止 支撐軸承受離過大。總而言之，在兩個軸承之間軸在每英尺長度上的彎曲變形不應(yīng)該超過0。01英寸。 此外，軸還必須能夠承受彎矩和扭矩的組合作用。因此，要考慮考慮扭矩 與彎矩的當(dāng)量載荷。因此扭矩和彎矩會產(chǎn)生交變應(yīng)力在許用應(yīng)力中也應(yīng)該有一 個考慮疲勞現(xiàn)象的安全系數(shù)。 直徑小于3英寸的軸可以采用含碳量大約為0。4%的冷軋