Gears and gear drive
Gears are the most durable and rugged of all mechanical drives. They can transmit high power at efficiencies up to 98% and with long service lives. For this reason, gears rather than belts or chains are found in automotive transmissions and most heavy-duty machine drives. On the other hand, gears are more expensive than other drives, especially if they are machined and not made from power metal or plastic.
Gear cost increases sharply with demands for high precision and accuracy. So it is important to establish tolerance requirements appropriate for the application. Gears that transmit heavy loads or than operate at high speeds are not particularly expensive, but gears that must do both are costly.
Silent gears also are expensive. Instrument and computer gears tend to be costly because speed or displacement ratios must be exact. At the other extreme, gears operating at low speed in exposed locations are normally termed no critical and are made to minimum quality standards.
For tooth forms, size, and quality, industrial practice is to follow standards set up by the American Gear Manufactures Association (AGMA).
Tooth form
Standards published by AGMA establish gear proportions and tooth profiles. Tooth geometry is determined primarily by pitch, depth, and pressure angle.
Pitch：Standards pitches are usually whole numbers when measured as diametral pitch P. Coarse-pitch gearing has teeth larger than 20 diametral pitch –usually 0.5 to 19.99. Fine-pitch gearing usually has teeth of diametral pitch 20 to 200.
Depth: Standardized in terms of pitch. Standard full-depth have working depth of 2/p. If the teeth have equal addenda(as in standard interchangeable gears) the addendum is 1/p. Stub teeth have a working depth usually 20% less than full-depth teeth. Full-depth teeth have a larger contract ratio than stub teeth. Gears with small numbers of teeth may have undercut so than they do not interfere with one another during engagement. Undercutting reduce active pro weakens the tooth.
Mating gears with long and short addendum have larger load-carrying capacity than standard gears. The addendum of the smaller gear (pinion) is increased while that of larger
gear is decreased, leaving the whole depth the same. This form is know as recess-action gearing.
Pressure Angle: Standard angles are 0
25. Earlier standards include a
20and 0
14-02/1pressure angle that is still used. Pressure angle affects the force that tends to separate mating gears. High pressure angle decreases the contact ratio (ratio of the number of teeth in contact) but provides a tooth of higher capacity and allows gears to have fewer teeth without undercutting.
Backlash: Shortest distances between the non-contacting surfaces of adjacent teeth .
Gears are commonly specified according to AGMA Class Number, which is a code denoting important quality characteristics. Quality number denote tooth-element tolerances. The higher the number, the closer the tolerance. Number 8 to 16 apply to fine-pitch gearing.
Gears are heat-treated by case-hardening, through-hardening, nitriding, or precipitation hardening. In general, harder gears are stronger and last longer than soft ones. Thus, hardening is a device that cuts the weight and size of gears. Some processes, such as flame-hardening, improve service life but do not necessarily improve strength.
Design checklist
The larger in a pair is called the gear, the smaller is called the pinion.
Gear Ratio: The number of teeth in the gear divide by the number of teeth in the pinion. Also, ratio of the speed of the pinion to the speed of the gear. In reduction gears, the ratio of input to output speeds.
Gear Efficiency:Ratio of output power to input power. (includes consideration of power losses in the gears, in bearings, and from windage and churning of lubricant.) Speed: In a given gear normally limited to some specific pitchline velocity. Speed capabilities can be increased by improving accuracy of the gear teeth and by improving balance of the rotating parts.
Power: Load and speed capacity is determined by gear dimensions and by type of gear. Helical and helical-type gears have the greatest capacity (to approximately 30,000 hp). Spiral bevel gear are normally limited to 5,000 hp, and worm gears are usually limited to about 750 hp.
Special requirements
Matched-Set Gearing:In applications requiring extremely high accuracy, it may be
necessary to match pinion and gear profiles and leads so that mismatch does not exceed the tolerance on pro lead for the intended application.
Tooth Spacing:Some gears require high accuracy in the circular of teeth. Thus, specification of pitch may be required in addition to an accuracy class specification.
Backlash:The AMGA standards recommend backlash ranges to provide proper running clearances for mating gears. An overly tight mesh may produce overload. However, zero backlash is required in some applications.
Quiet Gears: To make gears as quit as possible, specify the finest pitch allowable for load conditions. (In some instances, however, pitch is coarsened to change mesh frequency to produce a more pleasant, lower-pitch sound.) Use a low pressure angle. Use a modified pro include root and tip relief. Allow enough backlash. Use high quality numbers. Specify a surface finish of 20 in. or better. Balance the gear set. Use a nonintegral ratio so that the same teeth do not repeatedly engage if both gear and pinion are hardened steel. (If the gear is made of a soft material, an integral ratio allows the gear to cold-work and conform to the pinion, thereby promoting quiet operation.) Make sure critical are at least 20% apart from operating speeding or speed multiples and from frequency of tooth mesh.
Multiple mesh gear
Multiple mesh refers to move than one pair of gear operating in a train. Can be on parallel or nonparallel axes and on intersection or nonintersecting shafts. They permit higer speed ratios than are feasible with a single pair of gears .
Series trains:Overall ratio is input shaft speed divided by output speed ,also the product of individual ratios at each mesh ,except in planetary gears .Ratio is most easily found by dividing the product of numbers of teeth of driven gears by the product of numbers of teeth of driving gears.
Speed increasers (with step-up rather than step-down ratios) may require special care in manufacturing and design. They often involve high speeds and may creste problems in gear dynamics. Also, frictional and drag forces are magnified which, in extreme cases , may lead to operational problems.
Epicyclic Gearing:Normally, a gear axis remains fixed and only the gears rotates. But in an epicyclic gear train, various gears axes rotate about one anther to provide specialized output motions. With suitable clutchse and brakes, an epicyclic train serves as the planetary
gear commonly found in automatic transmissions.
Epicyclic trains may use spur or helical gears, external or internal, or bevel gears. In transmissions, the epicyclic (or planetary) gears usually have multiple planets to increase load capacity.
In most cases, improved kinematic accuracy in a gearset decreases gear mesh excitation and results in lower drive noise. Gearset accuracy can be increased by modifying the tooth involute profile, by substituting higher quality gearing with tighter manufacturing tolerances, and by improving tooth surface finish. However, if gear mesh excitation generaters resonance somewhere in the drive system, nothing short of a “perfect” gearset will substantially reduce vibration and noise.
Tooth profiles are modified to avoid interferences which can result from deflections in the gears, shafts, and housing as teeth engage and disendgage. If these tooth interferences are not compensated for by pro, gears load capacity can be seriously reduced. In addition, the drive will be noisier because tooth interferences generate high dynamic loads. Interferences typically are eliminated by reliving the tooth tip, the tooth flank, or both. Such pro are especially important for high-load , high-speed drives. The graph of sound pressure levelvs tip relief illustrates how tooth pro can affect overall drive noise. If the tip relief is less than this optimum value, drive noise increases because of greater tooth interference; a greater amount of tip relief also increase noise because the contact ratio is decreased.
Tighter manufacturing tolerances also produce quietier gears. Tolerances for such parameters as pro, pitch AGMA quality level. For instance, the graph depicting SPL vs both speed and gear quality shows how noise decreases example, noise is reduced significantly by an increase in accuracy from an AGMA Qn 11 quality to an AGNA Qn 15 quality. However, for most commercial drive applications, it is doubtful that the resulting substantial cost increase for such an accuracy improvement can be justified simply on the basis of reduced drive noise.
Previously, it was mentioned that gears must have adequate clearance when loaded to prevent tooth interference during the course of meshing. Tip and flank relief are common pro that control such interference. Gears also require adequate backlash and root clearance. Noise considerations make backlash an important parameter to evaluate during drive design. Sufficient backlash must be provided under all load and temperature conditions to avoid a
tight mesh, which creates excessively high noise level. A tight mesh due to insufficient backlash occurs when the drive and coast side of a tooth are in contact simultaneously. On the other hand, gears with excessive backlash also are noisy because of impacting teeth during periods of no load or reversing load. Adequate backlash should be provided by tooth thinning rather than by increase in center distance. Tooth thinning dose not decrease the contact ratio, whereas an increase in center distance does. However, tooth thinning does reduce the bending fatigue, a reduction which is small for most gearing systems.
齿轮和齿轮传动
在所有的机械传动形式中，齿轮传动是一种最结实耐用的传动方式。它们可以传递很大的功率，效率可以达到98%，并且服务年限长。由于具有以上优点，齿轮传动比皮带装置等其它传动方式更常见于自动式传动机构和重载机构中。在另一方面，齿轮比其它传动方案贵得多，特别是精加工齿轮和合金钢材料的。齿轮的制造成本会随便着精度和公差的要求急剧增加。因此，在合适的范围内选一个合理的公差带就显得尤其重要。用于大功率传递和高速传递的齿轮传动系统不是特别的贵，但是用合金钢材料和精加工的齿轮成本比较高。
低噪声齿轮机构也很昂贵。精密仪器和电脑里用的齿轮机构住住是相当昂贵的，因为它们对速度和传动比的要求很高。低速的开式传动的被定义为非临界状态，并且以此作为齿轮的最小标准。齿轮的形状、尺寸、性质和工业用途都遵循美国齿轮制造协会所制定的标准。
美国齿轮制造协会发布的标准说明齿轮系的传动比分配比例和齿的轮廓。齿的几何形状主要是由节距、齿高和压力角来确定的。
节距：标准节距通常都是整数。大节距齿轮的节距直径比它的节距的二十倍还大，一般在0.5～19.99之间。小节距齿轮的节距直径一在20～200之间。
齿高：以节距为标准，齿轮的工作齿面高度是全齿高的一半。如果齿轮有相同的齿高那么齿高是节距的倒数。变位齿轮它的工作时的啮合深度通常比它的全齿高少20%，以防止产生根切身。不变位齿轮比变位齿轮的传动比更大。齿数较少的齿轮可能会产生根切，所以大切削深度的齿轮比起它们来在啮合时候齿轮互不影响。减少齿轮的有效齿廓会使齿轮的强度削弱。让变位齿轮和不变位齿轮相啮和能传递比标准齿轮更大的功率。两个个啮合的齿轮当变位齿轮齿高减小时，不变位齿轮向变位后的齿轮深入一些，保证啮合高度不变。这就是众所周知的间歇性齿轮。
压力角：压力角通常取020和025。早期的压力角还包括14-1/20，现在仍然在使用。
压力角的大小会影响相啮合齿轮的强度。大的压力角可以减少齿轮在啮合时的齿数，而且利用不变位齿轮还能够传递更大的功率。
齿侧间隙：在两个啮合的齿之间非接触最小的那个间隙。齿轮传动系统都严格按照美国齿轮制造协会所制定的等级制造，每个指标都表示齿轮的一项重要性能。特性指数表示齿轮元素的公差，等级数目越高，它越接近于公差。等级3～5应用于大节距齿轮，8～16应用于小节距齿轮。
齿轮通过热处理提高强度，比如表面硬化、淬火、氮化、回火。一般而言，硬齿面的齿轮系统比软齿面的齿轮系统使用寿命更长更坚固。因而，淬火可以减小齿轮的尺寸
和重量。有些处理方式，例如表面淬火可以提高齿轮的使用寿命但是没有必要提高它的强度。
齿轮传动系统的校核项目：
在一对相啮合的齿轮中，大的那个是从动轮，小的是主动轮。
齿数比：大齿轮的齿数除以小齿轮的齿数。同样也是小齿轮的线速度除以大齿轮的线速度。在齿轮减速机构中，是输入速度与输出速度的比值。
齿轮传动的效率：齿轮输出功率与输入功率的比值。（包括考虑传动时的功率损失，轴承、联轴器、和润滑的功率损失）
在一些给定的齿轮中，节圆线速度是限定的。齿轮传动速率可以通过提高齿轮制造精度、增加回转件的平衡性来提高。负荷速度和传递功率大小受齿轮尺寸和齿轮类型的限制。斜齿轮和斜齿轮系所能传递的功率最大，可以近似达到30000马力、弧齿锥齿轮一般限制在5000马力、蜗轮蜗杆传动限制在大约750马力。
工艺要求：
齿轮配合：在工艺上要求比较高精度的齿轮系统中，对于防止错齿、齿廓与齿廓接触和从动齿轮的啮合，不会超过规定的范围是很有必要的。
齿间隙：有些齿轮对齿廓的精度要求相当高，因此，齿轮的规格等级必须符合所规定的精度等级。
无声传动装置：将齿轮传动系统制造得尽可能的静音。为了达到此目的可以有以下多种方法供选择，选择小螺距齿轮来满足负荷状态的要求；在某些特定情况下，可以改变齿轮的啮合次数来使传动声音减小，或者使声音更加低沉以达到静音的目的；用压力角较小和对齿轮根尖都进行过修正的齿轮；允许足够大的齿间隙；采用高的特性指数；
或者更小；合理分配齿轮系的传动比；采用一个非整数的传动保证表面粗糙度在20in
比，那么一样的齿轮就不会重复的啮合如果它们都是硬化钢材料。如果齿轮由软钢制成且传动比为整数，则齿轮必须冷作处理以满足工作的要求，从而实现无声传动。保证速度临界点大于全速运行的20%或者通过增加齿轮啮合次数来成倍增加的转速。
齿轮系传动装置是指在一个传动装置中有不只一对齿轮在啮合工作。可以是相互平行或不平行的轴，相交或不相交的轴。在实际应用中，他们可以达到很高的速度比相对于只有一对齿轮啮合的传动装置。串联齿轮系，所有啮合齿轮的传动比都是将输入轴的转速降到输出轴的转速。总的传动比是所有传动比的乘积，行星轮系不适用这种计算方法。这种传动装置的传动比很好计算，就是将每一对啮合齿轮的传动比相乘。增速器在设计和制造方面有特殊的工艺要求。他们通常包括很高的速度还可能有一些齿轮动力学
里一些很极端的问题，同样，摩擦力和拉力也包含在里面，在这种情况下还可能进一步导致操作的问题。
行星轮系传动：通常在一个传动装置中，齿轮轴线是固定不变的的仅仅是轴上的齿轮在转动。但是在一个行星轮系中，不同的齿轮轴围着太阳轮地轴线转动给特定的输出装置提供动力。行星轮传动再配合离合器和刹车装置，就可以组成一个无级变速的自动驾驶系统。行星轮传动可以用直齿或者斜齿，内齿轮或者外齿轮，或者锥齿轮。在传递过程中，可以通过增加行星轮的个数来达到传递更大功率的要求。
在许多情况下, 提高齿轮系中相啮合齿轮的运动精确度可以降低机构运行的噪音。修改齿轮渐开线齿形可以提高齿轮的精确度，用高精度的制造公差来保证高质量的齿轮啮合质量；提高齿面的粗糙度。但是，如果在一个传动系统的某个地方发生振动那么一个“完美”的齿轮机构将会减少振动和噪声。修正齿轮的齿廓可以避免在传动过程中由于偏差、轴的偏移、机壳的不标准而产生干涉。如果齿轮干涉不能通过修正齿廓来消除那么齿轮上的载荷应该减少。当齿轮载荷很大时，机构噪声会更大因为内部传递的齿轮发生了干涉。消除干涉可以通过改变齿高、齿侧间隙或者两者都做。齿轮变位对于重载机构和高速传动机构尤其重要。声音压力水平曲线图可以很形象地说明齿轮变位可以影响齿轮机构的噪声。如果减少的量比最适宜量小的话，那么机构会产生更大的噪声，因为齿轮干涉。减少过多的齿高度噪声也会增强因为接触比例减小了。
高制造公差等级的齿轮也可以实现无声传动，那样的公差等级作为齿廓的形位误差可以达到美国齿轮制造协会的质量水平。这个图表描述了速度和齿轮质量对声音压力水平的影响，还有如何减小噪声的方法。当齿轮的精度等级由美国齿轮制造协会规定的11级增加到15级时，噪声明显的减小了。但是对于商业用的传动机构来说，花费这么大的代价在降低噪声上是不划算的，因为还有别的更廉价的方式来降低噪声。
以前有个说法，为了防止齿轮干涉两个相啮合的齿轮必须经过修正。齿顶高和齿侧间隙都是很常用的齿廓修正以保证齿轮不发生干涉。齿轮传动系统也需要有适当的齿侧间隙和齿根修正。在设计齿轮机构中，齿侧间隙是评定噪声的一个重要参数。必须有足够的齿侧间隙和合理的载荷、温度状况来防止齿轮的干涉，否则会产生很大的噪声。干涉是由于齿侧间隙不足造成，工作的齿面和不工作齿面同时接触上了。另一方面，过大的齿侧间隙也会产生噪声，因为在齿轮无载荷啮合周期内或回动载荷会对齿轮产生冲击。要获得合理的齿侧间隙，减少齿的个数比增加轴的中心距效果更好。减少齿数不会减少齿轮接触比例，反之增大中心距也不会。但是减少齿数会减小齿轮的挠曲疲劳，这个减小量对一个齿轮系统来说是很小的。
中英文对照外文翻译 汽车变速器设计 我们知道，汽车发动机在一定的转速下能够达到最好的状态，此时发出的功率比较大，燃油经济性也比较好。因此，我们希望发动机总是在最好的状态下工作。但是，汽车在使用的时候需要有不同的速度，这样就产生了矛盾。这个矛盾要通过变速器来解决。 汽车变速器的作用用一句话概括，就叫做变速变扭，即增速减扭或减速增扭。为什么减速可以增扭，而增速又要减扭呢？设发动机输出的功率不变，功率可以表示为 N = w T，其中w是转动的角速度，T 是扭距。当N固定的时候，w与T是成反比的。所以增速必减扭，减速必增扭。汽车变速器齿轮传动就根据变速变扭的原理，分成各个档位对应不同的传动比，以适应不同的运行状况。 一般的手动变速器内设置输入轴、中间轴和输出轴，又称三轴式，另外还有倒档轴。三轴式是变速器的主体结构，输入轴的转速也就是发动机的转速，输出轴转速则是中间轴与输出轴之间不同齿轮啮合所产生的转速。不同的齿轮啮合就有不同的传动比，也就有了不同的转速。例如郑州日产ZN6481W2G型SUV车手动变速器，它的传动比分别是：1档3.704:１；2档2.202:1；3档1.414:1；4档1:1；5档（超速档）0.802:1。 当汽车启动司机选择1档时，拨叉将1/2档同步器向后接合1档
齿轮并将它锁定输出轴上，动力经输入轴、中间轴和输出轴上的1档齿轮，1档齿轮带动输出轴，输出轴将动力传递到传动轴上（红色箭头）。典型1档变速齿轮传动比是3:1,也就是说输入轴转3圈，输出轴转1圈。 当汽车增速司机选择2档时，拨叉将1/2档同步器与1档分离后接合2档齿轮并锁定输出轴上，动力传递路线相似，所不同的是输出轴上的1档齿轮换成2档齿轮带动输出轴。典型2档变速齿轮传动比是2.2:1，输入轴转2.2圈，输出轴转1圈，比1档转速增加，扭矩降低。 当汽车加油增速司机选择3档时，拨叉使1/2档同步器回到空档位置，又使3/4档同步器移动直至将3档齿轮锁定在输出轴上，使动力可以从轴入轴—中间轴—输出轴上的3档变速齿轮，通过3档变速齿轮带动输出轴。典型3档传动比是1.7:1，输入轴转1.7圈，输出轴转1圈，是进一步的增速。 当汽车加油增速司机选择4档时，拨叉将3/4档同步器脱离3档齿轮直接与输入轴主动齿轮接合，动力直接从输入轴传递到输出轴，此时传动比1:1，即输出轴与输入轴转速一样。由于动力不经中间轴，又称直接档，该档传动比的传动效率最高。汽车多数运行时间都用直接档以达到最好的燃油经济性。 换档时要先进入空档，变速器处于空档时变速齿轮没有锁定在输出轴上，它们不能带动输出轴转动，没有动力输出。 一般汽车手动变速器传动比主要分上述1－4档，通常设计者首先确定最低（1档）与最高（4档）传动比后，中间各档传动比一
翻译部分 英文原文 Gear mechanisms Gear mechanisms are used for transmitting motion and power from one shaft to another by means of the positive contact of successively engaging teeth. In about 2,600B.C., Chinese are known to have used a chariot incorporating a complex series of gears like those illustrated in Fig.2.7. Aristotle, in the fourth century B .C .wrote of gears as if they were commonplace. In the fifteenth century A.D., Leonardo da Vinci designed a multitude of devices incorporating many kinds of gears. In comparison with belt and chain drives ,gear drives are more compact ,can operate at high speeds, and can be used where precise timing is desired. The transmission efficiency of gears is as high as 98 percent. On the other hand, gears are usually more costly and require more attention to lubrication, cleanliness, shaft alignment, etc., and usually operate in a closed case with provision for proper lubrication. Gear mechanisms can be divided into planar gear mechanisms and spatial gear mechanisms. Planar gear mechanisms are used to transmit motion and spatial gear mechanisms. Planar gear mechanisms are used to transmit motion and power between parallel shafts ,and spatial gear mechanisms between nonparallel shafts. Types of gears (1)Spur gears. The spur gear has a cylindrical pitch surface and has straight teeth parallel to its axis as shown in Fig. 2.8. They are used to transmit motion and power between parallel shafts. The tooth surfaces of spur gears contact on a straight line parallel to the axes of gears. This implies that tooth profiles go into and out of contact along the whole facewidth at the same time. This will therefore result in the sudden loading and sudden unloading on teeth as profiles go into and out of contact. As aresult, vibration and noise are produced. (2)Helical gears. These gears have their tooth elements at an angle or helix to the axis of the gear(Fig.2.9). The tooth surfaces of two engaging helical gears inn planar gear mechanisms contact on a straight line inclined to the axes of the gears. The length of the contact line changes gradually from zero to maximum and then from maximum to zero. The loading and unloading of the teeth become gradual and smooth. Helical gears may be used to transmit motion and power between parallel shafts[Fig. 2.9(a)]or shafts at an angle to each other[Fig. 2.9(d)]. A herringbone gear [Fig. 2.9(c)] is equivalent to a right-hand and a left-hand helical gear placed side by side. Because
英文原文： SHAFT AND GEAR DESIGN Abstract: The important position of the wheel gear and shaft can' t falter in traditional machine and modern machines. The wheel gear and shafts mainly install the direction that delivers the dint at the principal axis box. The passing to process to make them can is divided into many model numbers, useding for many situations respectively. So we must be the multilayers to the understanding of the wheel gear and shaft in many ways Key words : Wheel gear ; Shaft In the force analysis of spur gears, the forces are assumed to act in a single plane .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 parallel 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 helix. If we unwind this paper, each point on the angular edge generates an involute curve. The surface obtained when every 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 the axis of the rotation; in helical gears, the line is diagonal across the face of the tooth. It is this gradual of the teeth and the smooth transfer of load from one tooth to another, which give helical gears the ability to transmit heavy loads at high speeds. Helical gears subject the shaft bearings to both radial and thrust loads. When the thrust loads become high or are objectionable for other reasons, it may be desirable to use double helical gears. A double helical gear (herringbone) is equivalent to two helical gears of opposite hand, mounted side byside 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 contact 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 recommended for use in the transmission of power There is on difference between a crossed heli cal 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 have the same hand; that is , a right-hand driver goes with a right-hand driven. In the design 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, usually one to four, and since they completely wrap around the pitch cylinder they are called threads. Its mating gear is called a worm gear, which is not a true helical gear. A worm and worm
Gears and gear drive Gears are the most durable and rugged of all mechanical drives. They can transmit high power at efficiencies up to 98% and with long service lives. For this reason, gears rather than belts or chains are found in automotive transmissions and most heavy-duty machine drives. On the other hand, gears are more expensive than other drives, especially if they are machined and not made from power metal or plastic. Gear cost increases sharply with demands for high precision and accuracy. So it is important to establish tolerance requirements appropriate for the application. Gears that transmit heavy loads or than operate at high speeds are not particularly expensive, but gears that must do both are costly. Silent gears also are expensive. Instrument and computer gears tend to be costly because speed or displacement ratios must be exact. At the other extreme, gears operating at low speed in exposed locations are normally termed no critical and are made to minimum quality standards. For tooth forms, size, and quality, industrial practice is to follow standards set up by the American Gear Manufactures Association (AGMA). Tooth form Standards published by AGMA establish gear proportions and tooth profiles. Tooth geometry is determined primarily by pitch, depth, and pressure angle. Pitch：Standards pitches are usually whole numbers when measured as diametral pitch P. Coarse-pitch gearing has teeth larger than 20 diametral pitch –usually 0.5 to 19.99. Fine-pitch gearing usually has teeth of diametral pitch 20 to 200. Depth: Standardized in terms of pitch. Standard full-depth have working depth of 2/p. If the teeth have equal addenda(as in standard interchangeable gears) the addendum is 1/p. Stub teeth have a working depth usually 20% less than full-depth teeth. Full-depth teeth have a larger contract ratio than stub teeth. Gears with small numbers of teeth may have undercut so than they do not interfere with one another during engagement. Undercutting reduce active profile and weakens the tooth. Mating gears with long and short addendum have larger load-carrying capacity than standard gears. The addendum of the smaller gear (pinion) is increased while that of larger
Helical, Worm and Bevel Gears Gears are machine elements that transmit motion by means of successively engaging teeth. Gears transmit motion from one rotating shaft to another, or to a rack that translates. Numerous applications exist in which constant angular velocity ratio (or constant torque ratio) must be transmitted between shafts. Based on the variety of gear types available, there is no restriction that the input and the output shafts need be either in-line or parallel. Nonlinear angular velocity ratios are also available by using noncircular gears. In order to maintain a constant angular velocity, the individual tooth profile must obey the fundamental law of gearing: for a pair of gears to transmit a constant angular velocity ratio, the shape of their contacting profiles must be such that the common normal passes through a fixed point on the line of the centers. Any two mating tooth profiles that satisfy the fundamental law of gearing are called conjugate profiles. Although there are many tooth shapes possible in which a mating tooth could be designed to satisfy the fundamental law, only two are in general use: the cycloidal and involute profiles. The involute has important advantages: it is easy to manufacture and the center distance between a pair of involute gears can be varied without changing the velocity ratio. Thus close tolerances between shafts are not required when utilizing the involute profile. There are several standard gear types. For applications with parallel shafts, straight spur gear, parallel helical, or herringbone gears are usually used. In the case of interesting shafts, straight bevel or spiral bevel gears are employed. For nonintersecting and nonparallel shafts, crossed helical, worm, face, skew bevel or hypoid gears would be acceptable choices. For spur gears, the pitch circles of mating gears are tangent to each other. They roll on one another without sliding. The addendum is the height by which a tooth projects beyond the pitch circle (also the radial distance between the pitch circle and the addendum circle). The clearance is the amount by which the dedendum (tooth height below the pitch circle) in a given gear exceeds the addendum of its mating gear. The tooth thickness is the distance across the tooth along the arc of the pitch circle while the tooth space is the distance between adjacent teeth along the arc of the pitch circle. The backlash is the amount by which the width of the tooth space exceeds the thickness of the engaging tooth at the pitch
机械类外文翻译—轴和齿轮的设计及应用 摘要 在传统机械和现代机械中齿轮和轴的重要地位是不可动摇的。齿轮和轴主要安装在主轴箱来传递力的方向。通过加工制造它们可以分为许多的型号，分别用于许多的场合。所以我们对齿轮和轴的了解和认识必须是多层次多方位的。 关键词:齿轮；轴 在直齿圆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。因此，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。齿的形状是一溅开线螺旋面。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就发生一渐开线曲线。 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。交错轴斜齿轮与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进行制造。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。在交错轴斜齿设计中，当该齿的斜角相等时所产生滑移速度最小。然而当该齿的斜角不相等时，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。 蜗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轮，蜗轮不是真正的斜齿轮。蜗杆和蜗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。蜗轮不是斜齿轮，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。然而蜗杆蜗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。 蜗杆蜗轮机构有单包围和双包围机构。单包围机构就是蜗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蜗轮机构就是双包围蜗轮蜗杆机构。着两者之间的重要区别是，在双包围蜗轮组的轮齿间有面接触，而在单包围的蜗轮组的轮齿间有线接触。一个装置中的蜗杆和蜗轮正像交错轴斜齿轮那样具有相同的齿向，但是其斜齿齿角的角度是极不相同的。蜗杆上的齿斜角度通常很大，而蜗轮上的则极小，因此习惯常规定蜗杆的导角，那就是蜗杆齿斜角的余角；也规定了蜗轮上的齿斜角，该两角之和就等于90度的轴线交角。 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。轮齿可以铸出，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。
中英文对照资料外文翻译文献 汽车变速器设计 ----------外文翻译 我们知道，汽车发动机在一定的转速下能够达到最好的状态，此时发出的功率比较大，燃油经济性也比较好。因此，我们希望发动机总是在最好的状态下工作。但是，汽车在使用的时候需要有不同的速度，这样就产生了矛盾。这个矛盾要通过变速器来解决。 汽车变速器的作用用一句话概括，就叫做变速变扭，即增速减扭或减速增扭。为什么减速可以增扭，而增速又要减扭呢？设发动机输出的功率不变，功率可以表示为 N = w T，其中w是转动的角速度，T是扭距。当N固定的时候，w与T是成反比的。所以增速必减扭，减速必增扭。汽车变速器齿轮传动就根据变速变扭的原理，分成各个档位对应不同的传动比，以适应不同的运行状况。 一般的手动变速器内设置输入轴、中间轴和输出轴，又称三轴式，另外还有倒档轴。三轴式是变速器的主体结构，输入轴的转速也就是发动机的转速，输出轴转速则是中间轴与输出轴之间不同齿轮啮合所产生的转速。不同的齿轮啮合就有不同的传动比，也就有了不同的转速。例如郑州日产ZN6481W2G型SUV车手动变速器，它的传动比分别是：1档3.704:１；2档2.202:1；3档1.414:1；4档1:1；5档（超速档）0.802:1。 当汽车启动司机选择1档时，拨叉将1/2档同步器向后接合1档齿轮并将它锁定输出轴上，动力经输入轴、中间轴和输出轴上的1档齿轮，1档齿轮带动输出轴，输出轴将动力传递到传动轴上（红色箭头）。典型1档变速齿轮传动比是3:1,也就是说输入轴转3圈，输出轴转1圈。
当汽车增速司机选择2档时，拨叉将1/2档同步器与1档分离后接合2档齿轮并锁定输出轴上，动力传递路线相似，所不同的是输出轴上的1档齿轮换成2档齿轮带动输出轴。典型2档变速齿轮传动比是2.2:1，输入轴转2.2圈，输出轴转1圈，比1档转速增加，扭矩降低。 当汽车加油增速司机选择3档时，拨叉使1/2档同步器回到空档位置，又使3/4档同步器移动直至将3档齿轮锁定在输出轴上，使动力可以从轴入轴—中间轴—输出轴上的3档变速齿轮，通过3档变速齿轮带动输出轴。典型3档传动比是1.7:1，输入轴转1.7圈，输出轴转1圈，是进一步的增速。 当汽车加油增速司机选择4档时，拨叉将3/4档同步器脱离3档齿轮直接与输入轴主动齿轮接合，动力直接从输入轴传递到输出轴，此时传动比1:1，即输出轴与输入轴转速一样。由于动力不经中间轴，又称直接档，该档传动比的传动效率最高。汽车多数运行时间都用直接档以达到最好的燃油经济性。 换档时要先进入空档，变速器处于空档时变速齿轮没有锁定在输出轴上，它们不能带动输出轴转动，没有动力输出。 一般汽车手动变速器传动比主要分上述1－4档，通常设计者首先确定最低（1档）与最高（4档）传动比后，中间各档传动比一般按等比级数分配。另外，还有倒档和超速档，超速档又称为5档。 当汽车要加速超过同向汽车时司机选择5档，典型5档传动比是0.87:1，也就是用大齿轮带动小齿轮，当主动齿轮转0.87圈时，被动齿轮已经转完1圈了。 倒档时输出轴要向相反方向旋转。如果一对齿轮啮合时大家反向旋转，中间加上一个齿轮就会变成同向旋转。利用这个原理，倒档就要添加一个齿轮做“媒介”，将轴的转动方向调转，因此就有了一根倒档轴。倒档轴独立装在变速器壳内，与中间轴平行，当轴上齿轮分别与中间轴齿轮和输出轴齿轮啮合时，输出轴转向会相反。
The gear and shaft Reducer is a dynamic communication agencies, the use of gear speed converters, motor rotational speed reducer to the Rotary to be few, and have greater torque institutions. General helical gear reducer has reducer (including parallel shaft helical gear reducer, a worm reducer, bevel gear reducer, etc.), planetary gear reducer, Cycloid reducer, a worm reducer, a planetary friction CVT mechanical machines. The important position of the wheel gear and shaft can't falter in the design of he passing to process to make them can is divided into many model numbers , using for many situations respectively .So we must be the multilayer to the understanding of the wheel gear and shaft in reducer. In the force analysis of spur gears, the forces are assumed to act in a single plane. 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 parallel 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 involutes helicoids. 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 helix. If we unwind this paper, each point on the angular edge generates an involutes curve. The surface obtained when every point on the edge generates an involutes is called an involutes helicoids. 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 the axis of the rotation; in helical gears, the line is diagonal across the face of the tooth. It is this gradual of the teeth and the smooth transfer of load from one tooth to another, which give helical gears the ability to transmit heavy loads at high speeds. Helical gears subject the shaft bearings to both radial and thrust loads. When the thrust loads become high or are objectionable for other reasons, it may be desirable to use double helical gears. A double helical gear (herringbone) is equivalent to two helical gears of opposite hand, mounted side by side on the same shaft.
译文一：译文 齿轮和轴的介绍 摘要:在传统机械和现代机械中齿轮和轴的重要地位是不可动摇的。齿轮和轴主要安装在主轴箱来传递力的方向。通过加工制造它们可以分为许多的型号，分别用于许多的场合。所以我们对齿轮和轴的了解和认识必须是多层次多方位的。 关键词:齿轮；轴 在直齿圆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。因此，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。齿的形状是一溅开线螺旋面。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就发生一渐开线曲线。 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