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附录1 The Introduction of the gears In the force analysis of spur gears,the forces are assumed to act in a single plance.We shall study gears in which the forces have three dimensions.The reason for this ,in the case of helical gears,is that the teeth are not arallel to the axis of rotation.And in the case of bevel gears. the rotational axes are not parallel to each other.There are also other reasons,as we shall learn. Helical gears are used to transmit motion between parallel shafts.The helix angle is the same on each gear, but one gear must have a right-hand helix and the other a left-hand helix.The shape of the tooth is an involute helicoid.If a piece of paper cut in the shape of a parallelogram is wrapped around a cylinder,the angular edge of the paper becomes a helic.If we unwind this paper ,each point on the angular edge generates an onvolute curve.The surface obtained when everu point on the edge generates an involute is called an involute helicoid. The initial contact of spur-gear teeth is a line extending all the way across the face of the tooth. The initial contact of helical gear teeth is a point ,which changes into a line as the teeth come into more engagement.In spur gears the line of contact is parallel to jthe axis of the rotation;in helied gears the ability to transmit heavy loads at high loads at high speeds.Helical gears subject the shaft bearings to both radial and thrust loads.When the thrust loads brcome high or are objectionable for other reasons,it may be desirable to use double helical grars.A double helical gear(herringbone)is equitcalent to two helical gears of opposite hand, mounted side by side on the same shaft.They develop opposite thrust reactions and thus cancel out the thrust load.When two or more single helical gears are mounted on the same shaft, the hand of the gears should be selected so as to produce the minimum thrust load. Crossed-helical,or spiral,gears are those in which the shaft centerlines are neither parallel nor intersecting. The teeth of crossed-helical fears have point cntact with each other, which changes to line contact as the gears wear in.For this reason they will carry out very small loads and are mainly for instrumental applications,and are definitely not crossed helical gear and a helical gear until they are mounted in mesh with each other. They are manufactured in the same way. A pair of meshed crossed helical gears usually of crossed-helical gears,the minimum sliding velocity is obtained when the helix angle are equal.However,when the helix angle are not equal,the gear with the larger helix angle should be used as the driver if both gears have the same hand. Worm gears are similar to crossed helical gears.The pinion or worm has a small number of teeth,ususlly one to four,and since they completely wrap around the pitch cylinder they are called thteads.Tts mating gear is called a worm gear, which is not a true helical gear.A worm and gear are uesd to provide a high angular-velocity reduction between nouintersecting shafts which are usually at right angle.The worm gear is not a helical gear because its face is point contact. However,a disadvantage of worm gearing is the high sliding velocities across the teech, the same as with crossed helical gears. Worm gearing are either single or double enveloping. A single-enveloping gearing is one in which the gear wraps around or partially encoloses the norm.A gearing in which each element partially encoloses the other is,of course,a double-enveloping worm gearing.The important difference between the two is that area contact exists between the teeth of double-enveloping gears while only line contact between those of single-enveloping gears.The worn and worm gears while only line contact between those of single-enveloping gears.The worm and worm gear of a set have the same hand of helix as for crossed helical gears,but the helix angles are usually quite different.The helix angle on the worm is generally quite large, and that on the gear very small .Bwcause of the worm helic angle.and the helix angle on the gear;the two angles are equal for a 90-deg.Shaft angle. When gears are to be used to transmit motion between intersecting shaft,some of bevel gear is requited. Although bevel gear are usually made for a shaft angle of 90 deg.They may be produced for almost any shaft angle.The teeth may be east,milled,or generated.Only the generated teeth may be classed as accurate.In a typical bevel gear mouning,one of the gear is often mounted outboard of the bearing.This means that shaft detlection can be more pronounced and have a greater effect on the contact of teeth. Another difficulty,which occurs in predicting the stress in becel-gear teeth, is the fact the teeth are tapered.Straight bevel gears are easy to design and simple to manufacture and give veru good results in service if they are mounted and positively.As in the case of squr gears, however,they become noisy at higher values of the pitch-line velocity.In these cases it is oftern good design practice to go to the spiral bevel gears give a much smoother tooth action than straight bevel gears, and hence are useful where high speed are encountered. It is frequently desirable,as in the case of automotive differential appplicarions,to have gearing similar to bevel gears but with the shaft offset.Such gears are called hypoid gears because their pitch surfaces are hyperboloids of revolution.The tooth action between such gears is a combination of rolling and sliding along a straight line and has much in common with that of worm gears. 2 齿轮简介在直齿园柱齿轮的受力分析中，是假定各力作用在单一平面的。我们将研究作用力具有三维坐标的齿轮。因在，在斜齿轮的情况下，其齿向是不平行于回转轴线的。而在锥齿轮的情况中各回转轴线互相不平行。像我们要讨论的那样，尚有其他道理需要学习，掌握。斜齿轮用于传递平行轴之间的运动。倾斜角度每个齿轮都一样，但一个必须右旋斜齿，而另一个必须是左旋斜齿。齿的形状是一渐开线螺旋面，如果一张被剪成平行四边形(矩形)的纸张包围在齿轮圆柱体上，纸上印出齿的角刃边就变成斜线。如果我展开这张纸，在血角刃边上的每一个点久发生一渐开线曲线。直齿圆柱齿轮轮齿的初始接触处是跨过整个齿面而伸展开来的线。斜齿轮轮齿的初始接触是一点，当齿进入更多的啮合时，它就变成线。在直齿圆柱齿轮中，接触是平行于回转轴线的。在斜齿轮中，该先是跨过齿面的对角线。它是齿轮逐渐进行啮合并平稳的从一个齿到另一个齿传递运动，那样就使斜齿轮具有高速重载下平稳传递运动的能力。斜齿轮使轴的轴承承受径向和轴向力。当轴向推力变的大了或由于别的原因而产生某些影响时，那就可以使用人字齿轮。双斜齿轮（人字齿轮）是与反向的并排地装在同一轴上的两个斜齿轮等效。他们产生相反的轴向推力作用，这样就消除了轴向推力。当两个或更多个单向齿斜齿轮被在同一轴上时，齿轮的齿向应作选择。以便产生最小的轴向推力。交错轴斜齿轮或螺旋齿轮，他们是轴中心线既不相交也不平行，交错轴斜齿轮的齿彼此之间发生点接触，它随着齿轮的磨合而变成线接触。因此他们只能传递小的载荷和主要用于仪器设备中，而且肯定不能推荐在动力传动中使用。交错轴斜齿轮之间在被安装后互相捏合之前是没有任何区别的。它们是以同样的方法制造。一对相啮合的交错轴斜齿轮通常具有同样的齿向，即左旋主动齿轮跟右旋从动齿轮相啮合。在交错轴斜齿轮设计中，当该齿的斜角相等时所产生滑移速度最小。但当该齿轮的斜角不相等时，如果两个齿轮具有相同齿向的话，大斜角齿轮应用作主动齿轮。涡轮与交错轴斜齿轮相似。小齿轮即蜗杆具有较小的齿数，通常是一到四齿，由于它们完全缠绕在节圆柱上，因此它们被称为螺纹齿。与其相配的齿轮叫做蜗杆齿轮不是真正的斜齿轮。蜗杆和涡轮通常是用于向垂直相交轴之间的传动提供大的角速度减速比。涡轮不是斜齿轮。因为其齿顶面做成中凹形状以适配蜗杆曲率，目的是要形成线接触而不是点接触。然而蜗杆涡轮传动机构中存在齿间有较大滑移速度的缺点，正像交错轴斜齿轮那样。蜗杆涡轮机构有单包围和双包围机构，单包围机构就是涡轮包裹着蜗杆的一种机构。当然，如果每个构件各自局部地包围着对方的涡轮机构就是双包围涡轮蜗杆机构。这两者之间的重要区别是，在双包围涡轮组的齿轮间有面接触，而是单包围的涡轮组的轮齿间有有线接触。一个装置中的蜗杆和涡轮正像交错轴斜齿轮那样具有相同的齿向，但是其斜齿轮角的角度是极不相同的。蜗杆上的齿斜角度通常很大，而蜗杆上的则极小，因此习惯常规定蜗杆的导角，那就是蜗杆齿斜角的余角；也规定了涡轮上的齿斜角，该两角之和就等于90度得轴线交角。当齿轮要用来传递相交轴之间的运动时，就需要某种形式的锥齿轮。虽然锥齿轮通常制造成能构成90度轴交角。但它们也可产生任何角度的轴交角。齿轮可以铸出，铣制或滚切加工，仅就滚齿而言就可达一级精度。在典型的锥齿轮安装中，其中一个锥齿轮常常装于支承的外侧。这意味着轴的挠曲情况更加明显而使在轮齿接触上具有更大的影响。另外一个难题，发生在难于预示锥齿轮轮齿上的应力，实际上是由于齿轮被加工成锥状造成的。直齿锥齿轮易于设计且制造简单，如果他们安装的精密而确定，在运转中会产生良好效果。然而在直齿圆柱齿轮情况下，在节线速度较高时，他们将发出噪音。在这些情况下，螺旋锥齿轮比直齿轮能产生平稳的多的啮合作用，因此碰到高速运转的场合那是很有用的。当在汽车的各种不同用途中，有一个带偏心轴的类似锥齿轮的机构，那是常常所希望的。这样的齿轮机构叫做准双曲面齿轮机构，因为它们的节面是双曲面回转面。这种齿轮之间的轮齿作用是沿着一根直线上产生滚动与滑动相结合的运动并和蜗杆涡轮作用有着更多的共同之处。 第 5 页 共 5 页
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