机器人履带行走系统机械结构设计
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毕业设计(论文)任务书 机械工程 系 机械设计制造及其自动化 专业学生姓名 学 号 起讫日期 设计地点 指导教师签字 专业负责人审查签字 课题名称机器人履带行走系统设计一、毕业设计(论文)工作内容和要求1、选题背景机器人技术、营救行动技术、灾难学等多学科知识有机融合,研制与开发用于搜寻和营救的灾难救援机器人,是机器人学研究中一个富有挑战性的新领域。面临及其危险和恶劣的灾难环境,灾难救援机器人可以代替和协助救助人员执行相关作业。灾难救援机器人不仅能够用于城市救援、消防、公安、采矿和环保等领域,同时在国防、军事和星球探测等方面也有着良好的应用背景。机器人技术是国家发展迫切需要的战略必争的核心技术之一,将在国民经济和安全中起着重要的作用和有着重大的战略意义。能够穿越复杂环境实施救援作业的机器人具有广阔的应用价值。相对于轮式移动机构而言,履带式行走机构(tracked mobile mechanism)具有支承面积大,接地比压小,越野机动性能高,爬坡、越障、跨沟能力强等优点。2、工作内容与需要提供的基础资料(1)工作内容(a)履带式行走系统机构与机械结构设计;(b)履带式行走系统控制方案设计;(c)履带式行走救援机器人越野与机动性能分析;(d)履带式行走救援机器人静态稳定性分析与负载能力分析。(2)基本传动方案以能穿越复杂环境(如台阶、楼梯、斜坡、壕沟、障碍等)到达指定场所实施多种救援任务为目标,构建救援机器人履带式行走系统实现方案。(3)原始条件及数据(a)最大进退速度:20m/min; (b)最大行进坡度角:25;(c)最大越障高度:100mm; (d)最大跨越宽度:150mm;(e)最小转弯半径:600mm; (f)最大负载能力:15kg;(g)最大外形尺寸:700mm(长)300mm(宽)300mm(高)。3、要求完成的成果和相应的技术指标(1)文档3000汉字的英文翻译并附原文;开题报告一份,总字数不少于3000汉字;毕业设计报告(论文)一份,字数不少于10000汉字,符合规范化格式要求。毕业设计业务总结一份(进入学生档案);(2)实物成果(如:图纸、软硬件、产品等)的规格与数量或性能指标要求;完成设计图纸(装配图A1一张,零件图一套)二、工作进度要求(按周次填写)第1周 完成英文翻译,提交英文翻译给指导老师批阅。第2周 英文翻译经指导老师批阅合格并确认后,上传至“毕业设计管理系统”,译文封面用标准模板。围绕课题查阅文献资料。第3周 查阅文献资料,撰写开题报告。第4周 完成开题报告,经指导老师批阅合格并确认后,上传至“毕业设计管理系统”。开题报告封面用标准模板。第5周 完成方案设计、电机选型、运动设计及承载能力设计。第6周 进行初步结构设计。第7周 中期检查,在“毕业设计管理系统”上完成“中期检查报告”的填写。第8周 绘制装配图。第9周 完成装配图。第10周 完成零件图。第11周 完成“毕业设计报告(论文)”的撰写,并提交给指导老师批阅和确认。第12周 上传“毕业设计报告(论文)”和附件至“毕业设计管理系统”。封面用标准模板。第13周 评阅、成果验收,规范化检查。第14周 答辩评分 三、主要参考文献(35篇)1 莫海军,朱文坚履带式移动机器人越障稳定性分析J机械科学与技术,2007,26(1):65-672 陈淑艳,陈文家履带式移动机器人研究综述J机电工程,2007,24(12):109-1123 肖俊君,尚建忠,罗自荣一种多姿态便携式履带机器人传动和结构设计J机械设计,2007,24(3):10-124 刘志彬履带式移动机器人建模与动态仿真研究D. 呼和浩特:内蒙古工业大学硕士学位论文,2009外文资料翻译翻译资料名称(外文) GEARS 翻译资料名称(中文) 齿轮 院 (系): 机械工程系 专 业: 机械设计制造及其自动化 姓 名: 学 号: 指导教师: 完成日期: 齿轮齿轮是成对运转的直接接触体,它们通过连续啮合的称作齿的突出物把运动和力从一根转轴传递带另一根转轴上,或从一根转轴传递到齿条上。图7所示是四种主要的齿轮(正齿轮、斜齿轮、蜗轮和锥齿轮)以及齿条小齿轮. 齿廓 齿轮齿的接触面必须排列得使传动是流畅的,即所传递的负载决不能依赖摩擦接触。正如在分析直接接触体时所指出的,这要求接触面上的公法线一定既不能通过主动轮的枢轴,也不能通过从动轮的枢轴。 大多数齿轮的齿廓还要求具有能使齿轮的速比保持不变的那样一种外形(本文只讨论这种齿轮,除非另作说明)。这就要求公法线必须与两齿轮枢轴的连线在一定点相交。 正如在讨论直接接触体的那一节所指出的,摆线好渐开线齿廓不但能保证流畅传动而且能获得等速比,即共轭作用。 我们已经列举了渐开线用作齿轮齿廓的一些优点。评价齿轮齿廓时所要考虑的因素包括制造的难易程度、对调整不良的敏感性以及承受负载的能力。在所有这几方面,渐开线都优于或比得上摆线。然而,渐开线不适用于只有六、七个齿每齿能转六十度角的从动齿轮齿。这是钟表齿轮的要求。由于摆线齿或近似于尖拱形(圆弧形)的齿能满足这一点,所以它们用于钟表和小型仪表中。另一类用于钟表装置的小齿轮是钝齿小齿轮,或者称为针齿轮。这种齿是由固定在两块端板之间的许多段很短的经过抛光的硬质钢丝制作,和它配合的齿轮上的齿呈现共轭外摆线形。利用滚柱来代替固定的针齿,可以减少摩擦力。 最近在某些国家,建议对齿轮采用圆形齿廓。因为互相接触的一对渐开线都是凸形 的,其接触应力比圆形齿廓所能获得的一对凹凸形齿廓的应力要大。尽管圆形齿廓的接触面承载能力比较高,然而这种齿轮使用的比较少。因为它们没有渐开线齿轮所具有的那种齿廓互换性,并且难于制造,对中心距的变化也非常敏感。 尽管也存在某些缺点,渐开线仍然是最常用的齿轮齿廓。就传递运动而论,一对齿轮的齿无论具有什么形状都无关重要,只要这些齿是互相啮合就行,也就是说,只要能以等速比传递运动就行。需要着重考虑 的问题是制造的方便程度和互换性。 蜗杠及其啮合齿轮是不可分的,切削该齿轮所用的刀具(滚齿刀)基本上同蜗杆是完全一样的东西。英国某些制造厂比较喜欢采用渐开线齿廓的蜗杆;在美国,这种类型的齿轮很少采用渐开线。 基本关系 一对齿轮中比较小的一个叫小齿轮,较大的一个叫大齿轮。如果小齿轮在主动轴上,这对齿轮起减速装置的作用;如果大齿轮装在主动轴上,这对齿轮起加速装置的作用。齿轮装置较常用语减速而不是用于加速。 如果一个齿数为N的齿轮的转速为n转/分,则乘积Nn的量纲是“每分钟齿数”。这一乘积对于互配的两个齿轮来说必须是相等的,如果在通过啮合区时想让每一个齿都能从互陪齿轮获得一个互陪齿的话。对于各种类型的啮合齿轮来说,齿轮传动比和转速比都是根据大齿轮的齿数同小齿轮的齿数的比值得出来的。如果大齿轮的齿数为100,互配小齿轮的齿数为20则比值5.所以不管大齿轮的转速如何,小齿轮的转速都是大齿轮的5倍。 如果两根轴是平行的,该大齿轮和小齿轮可以用一对速度比与这对齿轮相同的通过纯滚动接触传递运动的圆柱体来代替。在这两个齿轮上,称这两个假想的圆柱体的圆称作节圆;这两个节圆可供分析齿轮的参数之用。这两个圆的切点称作节点,因为节点位于中心线上,所以节点是两个齿轮纯滚动接触的唯一的一点。两根轴上不平行,不相交的一对齿轮也有节圆,但滚动节圆的概念对它是不适用的。 齿轮的型式主要取决于轴的布置;此外,某几种类型的齿轮比其它几种更适用于速度变化很大的场合。这意味着如果对轴的布置有某种特殊的要求,齿轮的型式或多或少也就确定了。反之,若果所需要的某种速度变化要求某种型式的齿轮,那么轴的位置也就确定了。 直齿轮和斜齿轮 齿轮其轮齿与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型式的齿轮来连接,并且一个直齿轮可以同一个不同形式的齿轮互配。 在图6中,如果互配的渐开线直齿轮的一对齿的齿廓都是渐开线,那么,因为接触在r点开始并在s点结束,为了获得连续传动,一对齿在s点脱离接触之前,另一对齿必须在r点开始接触。这种情况是否出现取决于吃的间距和直线rs的长度,而rs的长度取决于齿伸出节圆上下的量。这些尺寸的使用值已经标准化了。 因为节圆是纯滚动的,互配齿轮两个节圆上齿的距离必须相等。这个距离记做p,他是齿的尺寸的计量参数,是相邻的两个齿在节圆上相应的两点之间的距离。 为了避免由于热膨胀而出现的卡顿现象,为了润滑,为了补偿在制造是不可避免的误差,所有传递动力的齿轮必须具有侧向间隙。这意味着在互配齿轮的节圆上,小齿轮的间隙宽度必须稍大于大齿轮的宽度,反之亦然。在仪表齿轮上,可以利用中部分开的配合齿轮来消除侧向间隙,它的一半可相对于另一半转动。弹簧迫使配合齿轮的齿占满小齿轮的间隙的整个空间。 如果一个渐开线直齿小齿轮是用橡皮做的,并且被均匀扭转使其两端面绕轴线相对转动,则原来是直的、其方向同轴线平行的轮齿素线就会变成螺旋线。那么这个小齿轮实际上就会变成一个斜齿轮。 斜齿轮具备某些有点,例如,当连接两根平行轴时,斜齿轮比齿数相同并用相同刀具切削出来的直齿轮具有较高的承载能力。由于齿轮的重叠作用工作比较平稳,并且与直齿轮相比能以比较高的节线速度运转。节线速度是节圆的速度。因为齿轮倾斜于旋转轴的方向,所以斜齿轮会产生轴向推力。如果单个使用,这一推力必须有轴承来承受。推力问题可以通过在同一培件上切削两列方向相反的斜齿的方法来克服。根据制造方法的不同,齿轮可以做成连续人字形的,或者做成双斜齿形的,在两列斜齿之间留一间隙以便让切削刀具通过。双斜齿轮非常适用于高速高效的传递动力。这种齿轮的一个重要用途是用在船舶上的齿轮蜗轮传动。在一条排水量八万吨的客轮上,有四个单级减速人字齿轮箱,从每分钟1500转和1050转的几台涡轮机把总功率160000马力传递到每分钟180转的螺旋桨轴上。每个大型从动齿轮的直径接近于13.5英尺。斜齿轮也能用来连接不平行也不相交的相互成任何角度的轴。90度是这种齿轮最常用的角度。当两根轴平行时,互配齿轮的轮齿之间的接触是“线接触”,不管齿轮是直齿轮还是斜齿轮。当轴倾斜时,接触就变成了“点接触”。因此,交叉轴(不平行也不相交)斜齿轮的承载能力就不及平行轴斜齿轮。然而,交叉轴斜齿轮不易调整,所以常用于只有摩擦力是唯一阻碍运动的力的仪表和定位机构上。如上所述,适用于平行轴齿轮的滚动节圆的概念,不适用于不平行也不相交的轴。这意味着一对齿轮当它们的轴相互交叉时,比相互平行时更容易获得大的速比,比如100。在平行轴的情况下,小齿轮的节径应是大齿轮节径的1/100,这个比较不现实。在交叉轴的情况下,小齿轮只要有一个斜齿就行其大小要适应足够的强度的需要。这个小齿轮看上去就像一个螺旋。而大齿轮则有一百个牙。蜗轮蜗杆和锥齿轮 为了使交叉轴斜齿轮获得线接触并且改进他的承载能力,可以把大齿轮做成弯曲的,部分包在小齿轮上,有点像螺母套在螺丝上一样。结果就形成一个柱形蜗杆和蜗轮。蜗杆也可以做成沙漏形(即两端粗中间细,象计量时间用的沙漏的形状)而不是圆柱形的,以便部分包在小轮上。这就导致承载能力的进一步提高。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,蜗轮蜗杆的效率通常低于平行轴齿轮,因为沿轮齿方向会产生额外的滑动。由于它们的类似性蜗轮蜗杆的效率也同样取决于影响螺纹效率的那些因素。大直径的单线蜗杆的导角很小并且效率很低。多线蜗杆的导角较大并且效率也比较高。如果导角约为15度,摩擦系数小于0.15,则其效率约为55%至95%不等,涡轮就能驱动蜗杆。这样的组合可以组成结构紧凑的增速装置;它们已经用来驱动飞机发动机的增压器。在自锁式蜗轮蜗杆中,蜗轮不能驱动蜗杆,并且效率而已低于50%。为了使传递的转动和扭转能转一个角度,常常使用伞齿轮。所连接的两根轴如果延长后其轴线就会相交,它们彼此通常(但不是必须)相交成90度。伞齿轮的节面是滚动的截锥,而在厚度和高度上都必须逐渐减小的轮齿即可以是直的,也可以是弧形的。虽然弧齿伞齿轮称作螺旋伞齿轮,但轮齿的曲线通常是一个圆弧。轮齿的曲率可以导致轮齿重叠工作从而使动力的传递比直齿平稳。对于高转速和高扭矩来说,螺旋伞齿轮由于直齿伞齿轮,很象在两轴平行的情况下,斜齿轮优于正齿轮一样。适用于两轴不相交的螺旋伞齿轮称作偏轴锥齿轮。这种齿轮的节面不是滚动的,并且它们的平均直径比不等于速比。因此,小齿轮的齿数可以比较小,并使其大小能适应承载的需要。这就使之比两轴相交有更高的速比,正向交叉轴斜齿轮和蜗轮蜗杆能比平行轴斜齿轮提供更高的速比一样。不需要成比例的滚动节面是一个有利之处。螺旋锥齿轮在汽车上用来连接驱动轴和后轴。驱动轴上的小齿轮的轴线低于大齿轮的轴线,这就使发动机和车子的重心得以降低。因为轴不相交,所以从安装在一根小齿轮轴上的几个小齿轮可以驱动几根轮轴,像卡车的传动轴那样。锥齿轮的齿廓不是渐开线形,它们的形状使切齿轮刀具比渐开线刀具更易于制造和维修。因为锥齿轮都是成对供应的,只要它们的相互啮合的,它们就不需要同齿数的其他齿轮啮合。齿轮系和减速器 一对齿轮能获得的最大传动比因齿轮的类型和用途而异。各种类型的齿轮在平均负载条件下最大传动比的近似值如下:直齿轮:8;平行轴斜齿轮:10;直齿锥齿轮:6;螺旋锥齿轮:8;直角交错齿轮:12;蜗轮蜗杆:80。对轻载齿轮、仪表齿轮和定位齿轮来说,这一比值还可以更大点。用类似于和偏轴伞齿轮啮合的锥形蜗杆的齿轮装置可以获得高达400或400以上的传动比。对于重载齿轮,上述比值可能太高,这会造成这样一种情况,即传动比过高找不到合适的小齿轮。因为一对齿轮的传动比是齿数的商,并且因为一对适用的齿轮的齿数的最大值和最小值通常都有一个极限,因此一对齿轮所能获得的传动比值也有一定限度。为了扩大其比值范围,必须采用几对齿轮或齿轮轮系。齿轮系的总速比是每对齿轮的速比的乘积。在某些情况下,用齿轮不能获得精确的速比,但采用两对或几对齿轮,就能使所要求的速比接近任何精确度。为了使机械制造者和使用者方便起见,根据工业通用的式样,制造了各种不同类型,结构,速比和能力的成套减速器;这些减速器有一个外壳,外壳里面装有轴承,轴,齿轮,润滑剂和油封。增速器通常是定做的。在连续运转的情况下,由于轮齿,润滑剂,轴承和油封中的摩擦作用,所有减速器都会发热。如果发热的速度比散发到大气中速度快,润滑剂就会变质,齿轮或轴承就会损坏。GEARS Gears are direct-contact bodies , operating in pairs, that transmit motion and force from one rotating shaft to another , or from a shaft to a slide (rack), by means of successively engaging projections called teeth . The four main types of gears ( spur , helical, worm ,and bevel) and a rack and pinon are shown in Figure 7.Tooth profiles. The contacting surfaces of gear teeth must be aligned in such a way that the drive is positive ; the load transmitted must not depend on frictional contact . As shown in the treatment of direct-contact bodies , this requires that the common normal to the surfaces must not passs through the follower .Most gears are also required to hae tooth proflies of such a shape that the velocity ratio of the gears remains constant (unless otherwise noted ,this article will deal with such gears only ).thid requires that the common nomarl must cut the line between the pivots at a fixed point.As shown in the section on direct-contact bodies,cycloidal and involute profiles provide both a positive drive and a uniform velocity ration; i.e. , conjugate action .Some of the adantage of the involute as a geartooth profile have already been enumerated. The factors to be consided in evaluating a gear-tooth profile include ease of manufacture, sensitivity to maladjustment , and load-carrying capicity . On all of these counts the involute is superior or equal to the cycloid . Involutes , however ,are unsuitable for the teeth of driven gears having as few as six or seven teeth and capable of action through 60 degrees of rotation.This is a requirement for watch and clock gears , and since they can supply it , cycloidal teeth or ogival (circular are )approximations thereto are used on watches ,clocks, and small instrucments. Another type of pionn used in clockwork is the lantern pinon , or pin gear .The teeth are short lengths of hard ,polished ,steel wire held between two end plates, and the teeth on the mating gear are conjugate epicycloids.By using rollers in place of fixed pins , the friction is reduced. Circular profile have proposed for gears , most recently in some countires . Since contacting involutes are both convex , the contact stresses are higher than in a convex-concave pair such as can be obtained with circular-profile gears are seldom used,because they lack the profile interchangeability of involute gears , are difficult to manufacture ,and are sensitive to centre-distance variations.In spite of some deficiencies , the involute is still the most commonly used gear-tooth profile . As far as the transmition of motion is concerned , it does not matter what shape the teeth on a gear pair have as long as they are conjugate to one another ;i,e, transmit the motion with a uniform velocity ration . The dominating considerations are manufacturing convenience and interchangability .A worm and its mating gear are inseparable , and the gear is cut with a tool that is basically a replical of the worm . Some British manufactures prefer the involute profile for worms ; in the United States, involutes are seldom used for this type of gear .Basic relations . The smaller of a gear pair is called the pinion and the larger is the gear. When the pinion is on the driving shaft the pair acts is a speed reducer ; when the gear drives , the pair is a speen increaser . Gears are more frequently used to reduce speed to increace it .If a gear having N teeth rotates at n revoltions per minute , the product Nn has the dimension “teeth per miute ” This product must be the same for both members of a mating pair if each tooth is to acquire a partner from the mating gear as it passes through the region of tooth engagement.For conjugate gears of all ypes the gear ration and the speed ration are both given by the ration of the number of teeth on the gear to the number of teeth on the pinion. If a gear has 100 teeth and a mating pinion 20, the ratio is 5 . Thus the pinion rotates five times as fast as the gear , regardless of the speed of the gear .If the shaft are parllel , the gear and the pinion could be replacled by a pair of cylinders that would tranmit the motion by pure rolling contact at the same speed ration as the gears . On the gears , the circles that represent these imaginary cylinders are called the pitch circles ; these are useful for reference purposes in the analysis of gears . Their point of tangency is called the pitch point , and since it lies on the line of centres , it is the only point at which the tooth profiles have pure rolling contact , Gears on nonparallel , non-intersecting shafts also have pitch circles, but the rolling pitch-circle concept is not valid .Gear types are determined largely by the disposition of the shafts ; in addition , certain types are better suited than others for large speed changes.This means that if a specifical disposition of the shafts is required,the type of gear is more or less fixed .On the other hand ,if a required speed change demands a certain type, the shaft position are fixed .Spur 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 ,hoewever , can also be connected by gears of another type , and a spur can be mated with a gear of a different type .In figure 6 , if the involutes are a single pair of teeth on mating involute spur gears ,then ,since contact begins at r and ends at s , to obtain continuous transmission of motion , a pair must come into contact at r beforce the preceding pair goes out of contact at s . Wheather this does or does not occur depends on the tooth spacing and the length of the line rs ,which depends on the amounts that the teeth project above and below the pitch circles , Satisfactory values of dimendions have been standardized .Since the pitch circles roll on one another ,the spcing of the teeth on these circles on a mating pair must be equal . This spacing , which is known as the circular pitch p and is a measure of tooth size , is the distance between corresponding points on adjacent teeth , measured on the pitchcircle .To prevent jamming as a result of thermal expansion ,to aid lubrication , and to compensate for unavoidable inaccuracies ,all power-transmitting gears must have backlash.This means that on the pitch circkes of a mating pair ,the space width on the pinion must be slightly greter than the tooth thickness on the gear , and vice versa. On instrument gears , backlash can be eliminated by using a gear split down its middle , noe half being rotatable relative to the other . A spring force the split gear teeth to occupy the full width of the pinion space .If an involute spur pinion were made of rubber and twisted uniformly so that the ends rotated about the ais relative to one another ,the elements of the teeeth , initially straight and parallel to the axis ,would become helices.The pinion then in effect would become a helical gear .Helical gears have certain advantages; for examples , when connecting parallel shafts they have a higher load-carrying capacity 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 opeerate at higher pitch-line velocities than spur gears . The pitch-line velocity is the velocity of the pitch circle . Since the teeth are inclined to the axis of rotation , helical gears create an axial thrust. If used singly ,shis thrust must be obsorbed in the shaft bearings. The thrust problem can be overcome by cutting two sets of opposed helical teeth on 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 such gears is for geard-turbine shipdrives. On a passager liner of 80,000 tons displacement , there are four single-reduction , double-helical gearboxes transmitting a total of 160,000 horsepower from turbines rotating at 1,500 and 1,050 revolutions per minute to a propeller shaft rotating at 180 revolutions per minute . Each large driven gear was approximately 13.5 feet in diameter. 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 . When the shafts are parallel , the contact between the teeth on mating gears is “ line contact ” regarless of whether the teeth are straight ao helical . When the shafts are inclined , the contact becomes “point contact . ” For shis reason , crossed-axis helical gears do not have as much load-carring capacity as parallel-shaft helicals . They are relatively insensitive to misalignment , however, and are frequently employed in instrument and positioning mechanisms where friction is the only force opposing their motion.As stated above , the rolling-pitch-circle concept , which applies to gears on parallel shafts , does not apply to gears on nonparallel , non-intersecting shafts . This means that a large speed ration on one pair of geara , 100 for example , is more easily obtained when the axes are crossed than when they are parallel . With parallel shafts ,the pinion pitch dimmeter would have to be of the gear pitch diamater , an impracticalproportion . With crossed axes , the pinion could have only one helical tooth or thread and be as large as necessary for adequate strength .The pinion would look like a screw , and the gear would have 100 teeth .Worm and bevel gears . In order to achieve line contact and improve the load carrying capacitiy of the crossed axis helical gears ,the gear can be made to curve paritially around the pinion , in somewhat the same way that a nut envelops a screw . The result would be a cylindrical worm and gear. Worms are also made in the shape of an hourglass , instead of cylindrical , so that they partially envelop the gear . This results in a further increase in load-carring capicity .Worm gears provide the simplest means of obtaing large ratios in a single pair . they are usually less efficient than parallel-shaft gears ,however ,because of an additional sliding movement a;ong the teeth .Becaude of their similicity , 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 efficiency . Multipie-thread worms have larger lead angles and higher efficiencies . For lead angles of about 15 degrees and a coefficient of friction less than 0.15 ,the efficiency ranges from about 55 percent to 95 percent , and the gear can drive the worm .Such units make compact speed increases ; they have been used for driving superchargers on aircraft engines , In self-locking worms , the gear cannot drive the worm , and the efficiency is less than 50 percent .For transmitting rotary motion and torque around corners , beveal gears are commonly used . The connected shafts.whose axes would intersect if extended ,are usually but not necessarily at right angles to one another .The pitch surface of bevel gears are rolling ,truncated cones , and the teeth , which must be tapered in both thickness and height , are either straight or curved . Although curved tooth bevel gears are called spiral beel gears ,the curve of the teeth is usually a circular one .The curvature of the teeth results in overlapping tooth action and a smoother transmission of power than with straight teeth. For high speeeds and torpues ,spiral bevel gears are superior to straight beveal gears in much the same way that helical gears are superior to spur gears for connecting parallel shafts.When adapted for shafts that do not intersect , spiral beveal 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 ratio .Consequently ,the pinion may have few teeth and be made as large as necessary to carry the load . This permits higer speed ratios than with intersecting axes , just as crossed axis helicals and worm gears can provide higher eatios than parallel helicals .The abseence of the proportionsl rolling pitch surface requirement is a benefit . Hypoid gears are used on automobiles to connect the drive shaft is to the rear axles .The axis of the pinion on the drive shaft is below the gear axis ehich permits lowering of the engine and the center of gravity of the vehicle . Since the shafts do not intersect , several gear shafts may be driven from pinions mounted on a single pinion shaft ,as in tandem axles for trucks.The profiles of the teeth on bevel gears are not involutes ;they are such a shape that the tools for cutting the teeth are easier to make and maintain than involute cutting tools . Since bevel gears come in pairs , as long as they are conjugate to one another they need not be conjugate to one another they need not be conjugate to other gears with different tooth numbers.Gear trains and reducers .The maxiimum gear ratio obtainable with a single pair of gears varies with the type of gear and the application . The following are aproximate maxima for the various types for average load conditions : spur 8 ; parallel-shaft helical , 10 ; straight bevel 6 ; spiral bevel , 8 ; hypoid , 12 ; and worm , 80 .For lightly loaded ,instrument , and positioning gears , these ratios can be obtained with gears that resembe tapered worms meshing with hypoid gears . For heavily loaded gears , the given ratios may be so high that a reasonable gear size precludes a satisfactory pinion.Since the ratio in a single pair of gears is the quotient of the tooth numbers , and since there usually are limitation on both the minimum and maximum numbers of teeth on the available gears , follows that the number of ratios obtainable in a single pair is limited . To enlarge the coverage it is necessary to use multiple pairs , or trains . the overall speed ratio in a train is the product of the ratios in each pair . In certain cases an exact ratio cannot be obtained with gears , but by using two or more pairs , the desired ratio can be approximated to any degree of precision .As a convenience for machine builders and users , packaged speed reducer , following an industry accepted pattern , are manufactured in a wide variety of types , configurations ,speed ratios , and capacities ; these consist of a box or housing containing bearings , shafts , gears , lubricant , and shaft oil seals. Speed increasers are usually custom built.All speed reducer when operating continuously become hot because of friction in the teeth , in the lubricant , in the bearings , and in the oil seals . If the heat is generated at a faster rate than it can be dissipated to the atmosphere , the lubricant may determined and the gears or bearings fail
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