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附录1：轴的设计一、 结构设计轴通常采用实心或空心的圆形横截面。在强度相当的情况下，空心轴的重量比实心轴要轻许多，但其加工成本比实心轴的要高。轴大多承受扭转应力和弯曲应力，或是二者的组合，有时，也可能受其他应力。由于零部件在轴上的安装位置对轴的受力有影响，因此，仔细地布局好轴承位置对控制轴爹尺寸大小将很有帮助。轴的尺寸算好以后，经常要修正其直径（只能增大）以适应标准轴承，算出的只是最小尺寸。1.轴的常用尺寸表1-1列出了钢（圆形，实心）轴的常用尺寸，这些只是名义尺寸，设计者必须计算出精确的尺寸以便很好地与轴承配合。因为加工费时费力，故应从原料上去除最少的金属，在不同的轴向位置，去除金属会改变轴的直径。为保证应力集中最小，应设计出合适的圆角半径。如没有足够的圆角，直径的突然变化会引起所谓的“应力集中”现象。因此，才从应力角度来看，需要较大的圆角半径。然而，因为半径干涉，大圆角也会使滑轮、凸轮、齿轮等零件难于安装，这类零件的孔通常须加工成锥面以跳过轴径变化处的过渡半径。最后分析时，必须在轴的理想半径和其他零件的倒角之间找出一个折衷的方案。米制轴的尺寸与 机械零件（如滚动轴承）的密植尺寸的孔相配合的轴，其直径用毫米来规定。尽管轴应车削到合适尺寸以得到极其精确的配合，表3-2还是给出了通用的名义尺寸。扭转纯受扭的轴的受力方程如下，这些方程只对圆形实心和空心轴适用。（实心轴）Table 1-1 Some of common shaft sizes ( solid circular, in )0.50.6250.750.87511.1251.251.3751.5 1.6251.751.87522.1252.252.3752.52.6252.752.87533.1253.253.3753.53.6253.753.875555.255.56 Table1-2 Typical metric shaft diameters (mm)4567891012(0.472)15172025(0.984)3035404550(1.969)5560657075(2.953)80859095100(3.937)105110120130140150(5.901)160170180190200(7.874)220240260280(11.02)（空心轴）式中 扭矩（英寸磅） 设计剪应力（磅/平方英寸）D实心轴直径（英寸）空心轴直径（英寸）空心轴内径（英寸）N每分钟的转数（转/分）极惯性矩（英寸，in）, C中性轴与最外层纤维的距离（英寸）例1 计算转速为100转/分，传递功率的1.2马力的实心轴的直径，设计剪应力为6000磅/平方英寸，轴只受扭转。 解 （英寸磅）=英寸 (最小值).直径选为英寸。2.扭转变形（实心轴）轴的扭转量很重要。一种经验方法是，在每二十倍于直径的轴的长度上扭转变形不超过1度。比如，如果轴工作部分（长度）是40英寸，轴的直径是2英寸，可允许1度的扭转变形。在一些应用场合中，扭转角必须比这要小，下面的方面的方程适用于扭转变形。 D=式中 轴的受扭长度（英寸）；剪切弹性模量（磅/平方英寸）；扭转角（弧度）。图1-1表示的是受扭轴上的扭转角。贴图例2 2英寸传动轴，传递功率20马力，转速200转/分，相距30英寸的两个滑轮分别引起扭转变形，如果剪切弹性模量是12000000磅/平方英寸，计算扭转角度（度）。 解 （英寸磅） （弧度）（度）3.弯扭组合（实心轴）轴常受弯扭组合力。在这种情况下，有多种方法来计算轴径。最简单的方法是计算出等效的弯矩和扭矩然后代入弯扭标准方程。计算等效力矩的方程如下： ,式中 等效扭矩（英寸磅） 等效弯矩（英寸磅） 扭转方程则为：弯曲方程为：两个方程都需要计算，取两个直径中较大值作为计算尺寸。重要的是要记住，在扭转公式中用许用键应力，在弯曲公式中用许用拉应力。下例表明如何使用这种方法。贴图例3 在图1-2中，轴传递功率10马力，转速500转/分，假设设计剪应力是6000磅/平方英寸，扭转应力是8000磅/平方英寸，试计算直径（轴的重量不计）解 首先计算两个支反力。此时，左轴承是600磅，右轴承是200磅，最大的弯矩值是（600）（5）=3000英寸磅。则：（英寸磅）（英寸磅）（英寸磅）（英寸）（英寸）在给定条件下的轴的安全尺寸是两者之中的较大值，即1.59英寸。二、结构设计1.普通碳素钢任何炼钢方法都能炼出只含有0.05（甚至更少）碳的钢。由于只有少量的碳，钢的性能接近于纯铁，具有很高塑性和很低的强度。从便于成形和使用角度看，高塑性和低强度是变形所需要的，然而，从产品设计角度来说，需要比这种低碳钢更高的强度。增加强度最适用的方法是在钢中增加或保留一些碳。然而，必须明白，强度的增加只有在损失塑性的情况下才能实现，因此，最终总是在塑性和强度之间形成某种折衷。因为成分控制和增碳过程有一定难度，高碳高强度钢的成本比低碳钢高。最常用的普通碳素钢 因成本低，实际使用的大多数钢是普通碳素钢，它们由铁和碳组成，普通碳素钢的碳含量可分为低碳、中碳、高碳三类。除了用来控制硫的锰元素以外，其他元素只有很少量而被认为是杂质，有时它们对材料的性能可能有较小的影响。低碳钢 含碳大约0.060.25的钢称为低碳钢，它们很难通过热处理淬硬，因为碳的含量太低，很难形成硬的马氏体结构，从而使热处理相对不起作用。大量的低碳钢被做成薄板材、带材、棒材、板材、管材和线材等结构。很多这类材料最后通过冷加工来提高硬度、强度和表面质量。含碳小于等于20的钢可以经受较大的塑性流动，经常用作深拉成形零件或可用作表面硬化材料的塑性心部。低碳钢容易铜焊、熔焊和锻造。中碳钢 中碳钢（0.250.5）含有足够的碳，可通过热处理得到所需强度、硬度、切削加工性或其他特性。此类普碳钢的硬度不能显著提高到满意地作为切削刀具，但承载能力可提高很多，同时保留足够的塑性和良好的韧性。大多数钢在热轧状态提供，经常需进行切削加工。它能焊接，但比低碳钢难得多，因为焊接热量在局部区域引起了组织结构的变化。高碳钢 高碳钢含有0.51.6的碳，这类钢称为工具和模具钢，硬度是这类钢所需的主要性能。因为组织转变快，淬透性低，这种钢几乎都是用水淬火。即使用这种激烈的处理方式，并有变形和开裂的危险，这种钢很少能完全淬透，淬硬层厚度不超过1英寸。实际上，在同样强度下，热处理淬硬的普通碳素钢的塑性比合金钢的低，但即使如此，因其成本低，仍常使用碳素钢。2.合金钢 普通碳素钢可用于许多场合，也是最便宜的钢种，因此使用的最多，但它们对某些工作要求不能完全满足。这时可通过加入一些元素形成合金的方式来提高钢的某一项或几项性能。即使是普通碳素钢，也是铁、碳和锰的合金，但合金钢中除了这些元素外，其他元素含量大于普通碳素钢的杂质含量，如锰含量要大于1.5。合金元素影响淬透性 人们对淬透性的兴趣是间接的。淬透性通常与完全淬火时硬化深度的能力有关系。然而，随着等温曲线右移，即使在未完全硬化时，材料的性能也能显著改变。在热轧或锻打后，材料通常采用空冷。所有合金通常使等温曲线右移，空冷时得到比普通碳钢细的珠光体。这种细珠光体有较高的硬度和强度，可能会降低塑性，对切削加工性也有影响。可焊性 总的说来，合金元素对可焊性产生坏影响，这也是影响淬透性的一种反应，焊接区块冷时，合金会使焊接区形成硬的、韧性差的结构，经常导致开裂和变形。晶粒尺寸和韧性 在奥氏体阶段，镍对防止晶粒长大有特别有益的作用。对淬透性而言，对性能影响大的晶粒细化过程就只是次要影响。细晶粒结构会使淬透性变差，但对韧性影响很大。对硬度和强度相等的两种钢，细晶粒的钢塑性较好，反映在图表中就是韧性高，但这种高韧性，对切削加工性是有害的。 耐腐蚀能力 总的来说，大多数纯金属耐腐蚀能力相对较好，含有杂质或少量合金元素时会降低其耐腐蚀能力。对钢而言，碳会显著降低其耐腐蚀能力。铜和磷含量少时对减轻腐蚀有利，镍在含量大约5时对减轻腐蚀也是有利的，铬在含量大于10时特别有益，会产生一种称为不锈钢的合金钢。许多工具钢，因其铬含量高而实际上也是不锈钢，虽然设计中没作这种要求。3.低合金结构钢 市场上已有多种多样的低合金结构钢，它们是屈服强度比普通碳钢高的低成本结构材料。外加少量的一些合金元素不需经过热处理就可提高热轧钢的屈服强度，比普碳钢高3040。在高应力条件下，可减少横截面尺寸2530，同时增加成本1550，这就取决于合金元素的量和种类。4.低合金AISI钢高性能高成本 低合金AISI（美国钢铁协会）钢中的合金元素主要用于提高淬透性，它们比普碳钢贵得多，通常只在必需时使用，用于热处理硬化和回火条件下。与普碳钢相比，屈服强度高3040，其抗拉强度高1020。同样的拉伸强度和硬度时面积可减少3040，冲击强度大约提高两倍。5.不锈钢大量使用且最重要的合金钢是一组抗化学腐蚀能力极高的高铬钢。这类钢的大多数在高温下有好的力学性能，这类钢最早称为不锈钢，随着在高温下使用的增加，它们经常也称为耐热耐腐蚀钢。 马氏体不锈钢 在钢中加入少量铬，或在一些高铬钢中加入硅或铝，这种钢对热处理的响应象低合金钢一样强。这种钢具有正常的 相向相的转变，可采用与普碳钢或低碳钢的热处理方法硬化。这种钢称为马氏体钢，其中含铬46的钢最常用。铁素体不锈钢 含铬量达30或更多时，铁碳平衡相图的奥氏体区缩小，钢失去了用通常热处理方法硬化的能力。这种钢称为铁素体钢，特别适用于有高耐腐蚀性要求的冷加工产品。奥氏体不锈钢 高铬钢再加上8以上的镍或镍与锰，相图的铁素体区就会缩小。最典型的钢含18和8镍，称为奥氏体不锈钢。它们不能用通常钢的热处理方法硬化，但可附加少量的其他元素通过固溶强化使它们硬化。6.工具模具钢大量的工具（与切削刀具不同）和模具用朴碳钢或低合金钢制造，这只是因为它们的价格便宜，但这些材料有很多缺点。它们的淬透性差，硬度高而塑性低，温度升高时不能很好地保持硬度。锰钢 锰工具模具钢是油淬硬化钢，在热处理时很少变形或开裂。为提高淬透性，钢中含有0.851.00的碳和1.51.75的锰，并有少量铬、钒、钼来提高硬度和韧性。铬钢 高铬工具模具钢通常在油中淬硬，但有一些铬钢淬透性好，在空冷时就能淬硬。有一组高铬钢加有许多钨、钒（有时还有钴）来提高其高温硬度，它们称为高速钢。附录2：SHAFT DESIGNConfiguration designShafts are usually of circular cross section ;either solid or hollow sections can be used .A hollow shaft weighs considerably less than a solid shaft of comparable strength, but is somewhat more expensive .Shafts are subjected to torsion ,bending, or a combination of bearing can do much to control the size of shafts, as the loading is affected ( upward only ) to fit a standard bearing .Calculations merely indicate the minimum size.Common Shaft SizesTable 3-1 lists some of the common available sizes for steel ( round, solid) shafting. These are nominal sizes only .A designer must accurately compute the exact size so that it will fit properly into bearings .Since any machining is costly ,a minimal amount of metal should be removed from stock sizes. Any metal removed in certain locations changes the shaft diameter in various axial positions. Therefore, proper radii must be provided to minimize stress concentrations. Abrupt changes in diameter without sufficient radii produce so called “stress raisers.” Thus it is desirablefrom the standpoint of stressto provide large radii. However, large radii also make it difficult to mount such other components as pulleys, cams, gears, and so on because of radius interference .Often, the bore of such other components has to be chamfered to clear radii at the point where a shaft changes diameter. In the final analysis, a compromise has to be made between ideal shaft radii and the undercutting of other components.Table 3-1 Some of common shaft sizes ( solid circular, in )0.50.6250.750.87511.1251.251.3751.5 1.6251.751.87522.1252.252.3752.52.6252.752.87533.1253.253.3753.53.6253.753.875555.255.56 Table 3-2 Typical metric shaft diameters (mm)4567891012(0.472)15172025(0.984)3035404550(1.969)5560657075(2.953)80859095100(3.937)105110120130140150(5.901)160170180190200(7.874)220240260280(11.02)Metric Shaft SizesThe diameters of shafts made compatible with metric-sized bores of mechanical components ( such as antifriction bearings ) are specified in millimeters. Although any shaft size can be turned to provide extremely accurate fits, Table 3-2 shows popular nominal sizes.TorsionEquations for a shaft in pure torsion are listed below; these equations are for round solid and round hollow sections only: For solid shafts; For hollow shafts;Where design stress in shear (psi),D=diameter of solid shaft (in.),outside diameter of hollow shaft (in.),=inside diameter of hollow shaft (in.),horsepower, N=revolutions per minute (rpm),porlar moment of inertia (in),c=distance from neutral axis to outermost fiber (in.).Example 1Compute the diameter of a solid shaft that rotates 100 rpm transmits1.2hp . The design stress for shear is to be 6000 psi and shaft is subjected to torsion only.Solutionin-lb= (minimum).The amount of twist in a shaft is important .One rule of thumb is to restrict the torsional deflection to one degree in a length equal to 20 diameters. For example, if the active part of a shaft is 40in. and the shaft diameter is 2 in.,1 deg of torsional deflection would be permitted. In some applications, the angle of twist must be smaller than this. The following equation applies to torsional deflection:D=Where L=length of shaft subjected to twist (in.),G=shear modulus of elasticity ( psi ),=angle of twist ( rad ).Fig.3-1 shows the angle of twist ( greatly exaggerated ) that appears when torque is applied to a shaft.贴图Example 2A 2-in. lineshaft transmits 20 hp and rotates at 200 rpm. Two pulleys spaced 30 in. apart cause a torsional deflection. If the shear modulus of elasticity is 12,000,000 psi, find the angle of twist in degrees. Solution ;Combined Torsion and Bending ( Solid Shafting )A shaft is often subjected to combined torsion and flexure. There are numerous ways of computing a shaft diameter under these conditions. The simplest is to compute equivalent bending and twisting moments for the shaft and then substitute these values into the regular equations for torsion and bending. Equations for equivalent moments are as follows;,Where equivalent bending moment ( in-lb), equivalent bending moment ( in-lb),And the bending ( or flexure ) equation becomes Both equations must be solved; the larger of the two diameters is then used for the calculated size. It is important to remember that the allowable shearing stress is used in the torsion formula; the allowable stress in tension is used in the flexure ( or bending ) formula. The following example shows how how this method is applied.Example 3贴图In Fig.3-2, the shaft transmits 10 hp at 500 rpm. Assume that the design stresses are 6000 psi (shear ) and 8000 psi ( torsion ). Compute the diameter. ( Neglect shaft weight. ) Solution. First compute the two reactions. Here, there are 600 lb on the left bearing and 200 lb on the right bearing. The maximum is then 6005=3000 in-lb.Thus,.The safe shaft size for the given conditions is the larger of the two, or 1.59 in.Material designPLAN CARBON STEEL Any steel-making process is capable of producing a product that has 0.05 or less carbon. With this small amount of carbon, the properties approach those of pure iron with maximum ductility and minimum strength. Maximum ductility is desirable for deformation processing. However, higher strengths than that obtainable with this low carbon are desirable form the standpoint of product design. The most practical means of increasing the strength is by the addition of some carbon. However, it should be fully understood that any increase of strength over that of pure iron can be obtained only at the expense of some loss of ductility, and the final choice is always a compromise of some degree. Because of the difficulty of composition control or the additional operation of increasing carbon. Plain Carbon Steels Most Used. Because of their low cost, the majority of steels used are plain carbon steels. These consist of iron combined with carbon concentrated in three ranges classed as low carbon, medium carbon, and high carbon. With the exception of manganese used to control sulphur, other elements are present only in small enough quantities to be considered as impurities, though in some cases they may have minor effect on properties of the material. Low Carbon. Steel with approximately 6 to 25 points of carbon ( 0.060.25 ) are rated as low carbon steels and are rarely hardened by heat treatment because the low carbon content permits so little formation of hard martensite that the processed in such structural shapes as sheet, strip, rod, plate, pipe, and wire. A large portion of the material is cold worked in its final processing to improve its hardness, strength, and surface-finish qualities. The grades containing 20 points or less of carbon are susceptible to considerable plastic flow and are frequently used as deep-drawn products or may be used as a ductile core for casehardened material. The low plain carbon steels are readily brazed, welded, and forged. Medium Carbon. The medium carbon steels ( 0.250.5 ) contain sufficient carbon that they may be heat treated for desirable strength, hardness, machinability, or other properties. The hardness of plain carbon steels in this range cannot be increased sufficiently for the material to serve satisfactorily as cutting tools, but the load-carrying capacity of the steels can be raised considerably, while still retaining sufficient ductility for good toughness. The majority of the steel is furnished in the hot-rolled condition and is often machined for final finishing. It can be welded, but is more difficult to join by this method than the low carbon steel because of structural changes caused by welding heat in localized areas. High Carbon. High carbon steel contains from 50 to 160 points of carbon ( 0.51.6 ) . This group of steels is classed as tool and die steel, in which hardenability, plan carbon steels nearly always must be waterquenched. Even with this drastic treatment and its associated danger of distortion or cracking, it is seldom possible to develop fully hardened structure in material more than about 1 inch in thickness. In practice the ductility of heat-treat-hardened plain carbon steel is low compared to that of alloy steels with the same strength, but, even so, carbon steel is frequently used because of its lower cost.ALLOY STEELS Although plain carbon steels work well for many uses and are the cheapest steels and therefore the most used, they cannot completely fulfill the requirements for some work. Individual or group of properties can be improved by addition of various elements in the from of alloys. Even plain carbon steels are alloys of at least iron, carbon, and manganese, but the term alloy steel refers to steels concentration or, in the case of manganese, greater than 1.5. Alloys Affect Hardenability. Interest in hardenability is indirect. Hardenability is usually thought of most in connection with depth-hardenability in a full hardening operation. However, with the isothermal transformation curves shifted to the right, the properties of a material can be materially changed even when not fully hardened. After hot-rolling or forging operations, the material usually air cools. Any alloy generally shifts the transformation curves to the right, which with air cooling results in finer pearlite than would be formed in a plain carbon steel. This finer pearlite has higher hardness and strength, which has an effect on machinability and may lower ductility. Weldability. The generally bad influence of alloys on weldability is a further reflection of the influence on hardenability. With alloys present during the rapid cooling taking place in the welding area, hard, nonductile structures are from in the steel and frequently lead to cracking and distortion. Grain Size and Toughness. Nickel in particular has a very beneficial effect by retarding grain growth in the austenite range. As with hardenability, it is the secondary effects of grain refinement that are noted in properties. A finer grain structure may actually have less hardenability, but it has its most pronounced effect on toughness; for two steels with equivalent hardness and strength, the one with finer grain will have better ductility, which is reflected in the chart as improved toughness. This improved toughness, however, may be detrimental to machinability. Corrosion Resistance. Most pure metals have relatively good corrosion resistance, which is generally lowered by impurities or small amounts of inteneional alloys. In steel, copper and phosphorus are beneficial in reducing corrosion. Nickel becomes effective in percentages of about 5, and chromium is extremely effective in percentages greater than 10, which leads to a separate class of alloy steels called stainless steels. Many tool steels, which not designed for the purpose, are in effect stainless steels because of the high percentage of chromium present.LOW ALLOY STRUCTURAL STEELS Certain low alloy steels sold under various trade names have been developed to provide a low cost structural material with higher yield strength than plain carbon steel. The addition of small amounts of some alloying elements can raise the yield strength of hot-rolled sections without heat treatment to 3040 greater than that of plain carbon steels. Designing to higher working stresses may reduce the required section size by 2530 at an increased cost of 1550, depending upon the amount and the kind of alloy. The low alloy structural steels are sold almost entirely in the from of hot-rolled structural shapes. These materials have good corrosion resistance, particularly to atmospheric exposure. Many building codes are based on the more conservative use of plain carbon steels, and the use of alloy structural steel often has no economic advantage in these cases.LOW ALLOY AISI STEELS Improved Properties at Higher Cost. The low alloy American Iron and Steel Institute ( AISI ) steels are alloyed primarily for improved hardenability. They are more costly than plain carbon steels, and their use can generally be justified only when needed in the heattreat-hardened and tempered condition. Compared to plain carbon steels, they can have 3040 higher yield strength and 1020 higher tensile strength. At equivalent tensile strengths and hardnesses, they can have 3040 higher reduction of area and approximately twice the impact strength. Usually Heat Treated. The low alloy AISI steels are those containing less than approximately 8 total alloying elements, although most commercially important steels contain less than 5. The carbon content may vary from very low to very high, but for most steels it is in the medium range that effective heat treatment may be employed for property improvement at minimum costs. The steels are used widely in automobile, machine tool, and aircraft construction, especially for the manufacture of moving parts that are subject to high stress and wear.STAINLESS STEELS Tonnage-wise, the most important of the higher alloy steels are a group of high chromium steels with extremely high corrosion and chemical resistance. Most of these steels have much better mechanical properties at high temperatures. This group was first called stainless steel. With the emphasis on high temperature use, they are frequently referred to as heat and corrosion-resistant steels. Martensitic Stainless Steel. With lower amounts of chromium or with silicon or aluminum added to some higher chromium steels, the material responds to heat treatment much as may be hardened by heat treatment similar to that used on plain carbon or low alloy steels. Steels of this class are called martensitic, and the most used ones have 4 to 6 chromium. Ferritic