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GEARSpur and helical gears. A gear having tooth elements that are straight and parallel to its axis is known as a spur gear. A spur pair can be used to connect parallel shafts only. Parallel shafts, however, can also be connected by gears of another type, and a spur gear can be mated with a gear of a different type. (Fig.1.1).To prevent jamming as a result of thermal expansion, to aid lubrication, and to compensate for avoidable inaccuracies in manufacture, all power-transmitting, gears must have backlash. This means that on the gear, and vice versa. On instrument gears, backlash can eliminated by using a gear split down its middle, one half being rotatable relative to the other. A spring forces the split gear teeth to occupy the full width of the pinion space.Helical gears have certain advantages; for example, when connecting parallel shafts they have a higher loadcarrying than spur gears with the same tooth numbers and cut with the same cutter. Because of the overlapping action of the teeth, they are smoother in action and can operate at higher pitch-line to the axis of rotation, helical gears create an axial thrust. If used singly, this thrust must be absorbed in the same blank. Depending on the method of manufacture, the gear may be of the continuous-tooth herringbone variety or a double-helical gear with a space between the two halves to permit the cutting tool to run out. Double-helical gears are well suited for the efficient transmission of power at highspeeds.Helical gears can also be used to connect nonparallel, non-intersecting shafts at any angle to one another. Ninety degrees is the commonest angle at which such gears are used.Worm and bevel gears. In order to achieve line contact and improve the loadcarrying capacity of the crossed-axis helical gears, the gear can be made to curve partially around the pinion, in somewhat the same way that a nut envelops a screw. The result would be a cylindrical worm and gear.Worm gears provide the simplest means of obtaining large rations in a single pair. They are usually less efficient than parallel-shaft gears, however, because of an additional sliding movement along the teeth. Because of their similarity, the efficiency of a worm and gear depends on the same factors as the efficiency of a screw. Single-thread worms of large diameter have small lead angles and low efficiencies. Multiple-thread worms have larger lead angles and higher efficiencies(Fig.1.2)For transmitting rotary motion and torque around corners, bevel gears are commonly used. The connected shafts, whose axes would intersect if extended, are usually but not necessarily at right angles to one another.When adapted for shafts that do not intersect, spiral bevel gears are called hypoid gears. The pitch surfaces of these gears are not rolling cones, and the ratio of their mean diameters is not equal to the speed Consequently, the pinion may have few teeth and be made as large as necessary to carry the load. The profiles of the teeth on bevel gears are not involutes; they are of such a shape that the tools for the teeth are easier to make and maintain than involute cutting tools. Since bevel gears come in, as long as they are conjugate to one another they need not be conjugate to other gears with different both numbers.1 Early History of Gearing The earliest written descriptions of gears are said to have been made by Aristotle in the fourth century B.C. It has been pointed out that the passage attributed to Aristotle by some was actually from the writings of his school, in “Mechanical Problems of Aristotle”(Ca.280 B.C). In the passage in question, there was no mention of gear teeth on the parallel wheels, and they may just as well have been smooth wheels in frictional contact. Therefore, the attribution of gearing to Aristotle is, most likely, incorrect.The real beginning of gearing was probably with Archimedes who about 250 B.C. invented the endless screw turning a toothed wheel, which was used in engines of war. Archimedes also used gears to simu-early forms of wagon mileage indicators (odometer) and surveying instruments. These devices were probably “thought” experiments of Heron of Alexandria (ca. A.D.60), who wrote on the subjects of theoretical mechanics and the basic elements of mechanism. The oldest surviving relic containing gears is the Antikythera mechanism, so named because of the Greek island of that name near which the mechanism was discovered in a sunken ship in 1900. Professor Price of Yale University has written an authoritative account of this mechanism. The mechanism is not only the earliest relic of gearing, but it also is an extremely complex arrangement of epicyclic differential gearing. The mechanism is identified as a calendrical computing mechanism for the sun and moon, and has been dated to about 87 B.C.The art of gearing was carried through the European dark ages after the fall of Rome, appearing in Islamic instruments such as the geared astrolabes which were used to calculate the positions of the celestial bodies. Perhaps the art was relearned by the clock-and instrument-making artisans of fourteenth-century Europe, or perhaps some crystallizing ideas and mechanisms were imported from the East after the crusades of the eleventh through the thirteenth centuries.It appears that the English abbot of St.Albans monastery, born Richard of Wallingford, in A.D. 1330, reinvented the epicyclic gearing concept. He applied it to an astronomical clock, which he began to build at that time and which was completed after his death.A mechanical clock of a slightly later period was conceived by Giovanni de Dondi(1348-1364). Diagrams of this clock, which did not use differential gearing, appear in the sketchbooks of Leonardo da Vinci, who designed geared mechanisms himself. In 1967 two of da Vincis manuscripts, lost in the National Library in Madrid since 1830, were rediscovered. One of the manuscripts, written between 1493 and 1497 and known as “Codex Madrid I” , contains 382 pages with some 1600 sketches. Included among this display of Lenardos artistic skill and engineering ability are his studies of gearing. Among these are tooth profile designs and gearing arrangements that were centuries ahead of their “invention”.2 Beginning of Modern Gear Technology In the period 1450 to 1750, the mathematics of gear-tooth profiles and theories of geared mechanisms became established. Albrecht Durer is credited with discovering the epicycloidal shape(ca. 1525). Philip de la Hire is said to have worked out the analysis of epicycloids and recommended the involute curve for gear teeth (ca. 1694). Leonard Euler worked out the law of conjugate action(ca.1754). Gears deigned according to this law have a steady speed ratio.Since the industrial revolution in mid-nineteenth century, the art of gearing blossomed, and gear designs steadily became based on more scientific principles. In 1893 Wilfred Lewis published a formula for computing stress in gear teeth. This formula is in wide use today in gear design. In 1899 George B.Grant, the founder of five gear manufacturing companies, published “A Treatise on Gear Wheels” . New inventions led to new applications for gearing. For example, in the early part of this century (1910), parallel shaft gears were introduced to reduce the speed of the newly developed reaction steam turbine enough to turn the driving screws of ocean-going vessels. This application achieved an overall increase in efficiency of 25 percent in sea travel.The need for more accurate and quiet-running gears became obvious with the advent of the automobile. Although the hypoid gear was within our manufacturing capabilities by 1916, it was not used practically until 1926, when it was used in the Packard automobile. The hypoid gear made it possible to lower the drive shaft and gain more usable floor space. By 1937 almost all cars used hypoid-geared rear axles. Special lubricant antiwear additives were formulated in the 1920s which made it practical to use hypoid gearing. In 1931 Earle Buchingham, chairman of an American Society of Mechanical Engineers (ASME) research committee on gearing, published a milestone report on gear-tooth dynamic loading. This led to a better understanding of why faster-running gears sometimes could not carry as much load as slower-running gears.High-strength alloy steels for gearing were developed during the 1920s and 1930s . Nitriding and case-hardening was introduced in 1950. Extremely clean steels produced by vacuum melting processes introduced in1960 have proved effective in prolonging gear life.Since the early 1960s there has been increased use of industrial gas turbines for electric power generation. In the range of 1000 to 14000 hp, epicyclic gear systems have been used successfully. Pitch-line velocities are form 50 to 100m/s(10000 to 20000 ft/min). These gear sets must work reliably for 10000 to 30000 hp between overhaule.In 1976 bevel gears produced to drive a compressor test stand ran stand ran successfully for 235h at 2984kw and 200m/s. form all indications these gears could be used in an industrial application if needed. A reasonable maximum pitch-line velocity for commercial spiral-bevel gears with curved teeth is 60m/s.Gear system development methods have been advanced in which lightweight, highly loaded gears are used in aircraft applications. The problems of strength and dynamic loads, as well as resonant frequencies for such gearing, are now treatable with techniques such as finite-element analysis, siren and impulse testing for mode shapes, and application of damping treatments where required.齿 轮 直齿轮和斜齿轮 轮齿是直的、而方向又与其轴平行的齿轮称作直齿轮。一对直齿轮只能用来连接平行轴。然而，平行轴也可以用其他形式的齿轮来连接，一个直齿轮可以同一个不同形式的齿轮互相啮合，如图1-1。为了避免由于热膨胀而出现的卡住现象；为了便于润滑和补偿制造中不可避免的误差，所有传递动力的齿轮必须具有侧向间隙。这就是说在互相啮合齿轮的节圆上，小齿轮的间隙宽度必须稍大于大齿轮的齿厚，反之亦然。在仪表齿轮上，可以利用从中间分开的拼合齿轮来消除侧向间隙，它的一半可相对于另一半转动。弹簧迫使拼和齿轮的齿占满小齿轮间隙的整个宽度。斜齿轮具有某些优点。例如：连接两平行轴时，斜齿轮比齿数相同、用相同刀具切削的直齿轮有较高的承载能力。由于轮齿的重迭作用，斜齿轮工作比较平稳、允许比直齿轮有更高的节线速度。节线速度是节圆的速度。由于轮齿与旋转轴倾斜，所以斜齿轮会产生轴向推力。如果单个使用，这一推力必须由轴承来承受。推力问题可以通过在同一坯见切削两组斜齿来克服。根据制造方法的不同，齿轮可以是连续人字形的，或者在两列斜齿之间留一间隙的双斜齿形的，以便切削刀具通过。双斜齿齿轮非常使用于高速高效的传递动力。斜齿轮也能用来连接既不平行也不相交的相互成任何角度的轴。最常用的角度为。蜗轮蜗杆和伞齿轮为了使交叉轴斜齿轮获得线接触和提高承载能力，可以把大齿轮做成部分绕小齿轮弯曲，就象螺母套在螺杆上一样，结果就形成一个柱形蜗杆和蜗轮。蜗轮蜗杆提供了获得一对大速比齿轮的最简单的方法。然而，由于沿齿的附加滑动使蜗轮蜗杆的效率通常低于平行轴齿轮。同样，其效率还取决于影响螺纹效率的那些因素。大直径的单头蜗杆的导角很小，效率很低，而多头蜗杆的导角较大，效率也比较高，见图1-2。为了使传递的转动和扭矩能转一个角度，常常是用伞齿轮。所连的两跟轴，如果延长其轴线就会相交，它们通常互成。两轴不相交的螺旋伞齿轮称作偏轴伞齿轮。这种齿轮的节面不是滚锥，它们的平均直径比不等于速比。因此，小齿轮的齿数较小，其大小能适应承载的需要。伞齿轮的齿廓不是渐开线形的。它们的形状使切齿刀具比渐开线刀具更易于制造和维修。由于伞齿轮是成对使用的，因此，只要它们能互相共轭，就不需要与齿数不同的其他齿轮共轭。图1直齿轮 图2螺蜗轮蜗杆船齿轮的早期发展史有关齿轮的最早的论著认为，齿轮是在公元前四世纪由Aristotle发明的。书中指出：齿轮是由Aristotle发明的这段文字实际上出自其母校的论著：“关于Aristotle的机械问题”（约公元前280年）。问题是在有关章节中，并没有体积在平行的轮子上有齿轮，而只是光华的轮子，靠摩擦接触。因此，认为齿轮是由发明的说法不见得是正确的。实际上，齿轮机构可能是在公元前约250年由Archimedes发明的，他发明了螺杆用以驱动一个带齿的轮子，这种轮子用于军用发动机。Archimedes也用齿轮来仿造天体比例仪。Archimedian螺旋机构一直用语测程计及高度和角度测量装置，这是早期使用的四轮马车里程计（里程表）和测量仪。这些装置被认为是埃及及亚力大实验装置，他写了关于理论力学及基本机械零件的论著。所查到的最早的齿轮的遗物是Antikythera机构，这是根据希腊岛屿的名字而命名的，因为这中机构是1900年在靠近Antikythera岛发现的沉船中出现的。yale大学的Price教授写了论述这一机构的权威专著。这一机构不仅是齿轮传动机构的最早遗物，也是极为复杂的行星齿轮传动机构，它也被认为是用于表示太阳和月亮运行的日历计算机构，并可追溯到公元前87年。在罗马衰败之后的萧条时期，齿轮传动技术传遍了整个欧洲并在穆斯林仪表中得到应用，如计算天体位置的齿轮观测仪。也许是这一技术又被14世纪欧洲的钟表仪器制造专家再次采用，也许是一些奇特的构思，在十一世纪至十三世纪的改举运行之后，这些机构又从东方引入。似乎是英国St.Alba的住持于1930年又发明了行星齿轮的构思，他将其用于天文钟表，并实施建造，但当他死后才竣工。稍后机械钟表是由Giovanni de Dondi设计的。根据Lenonardo da Vinci手稿，钟表设计图中并没有差动齿轮