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stress and strain 应力与应变 In any engineering structure工程结构 the individual components独立构件 or members will (be subjected to)受到,被附加 external forces外力 arising from由。引起 the service conditions工作环境 or environment in which the component works. 在任何的工程结构中,每个零件,构件将会受到来自工作环境的外力的作用。 If the component or member is in equilibrium平衡, the resultant合力 of the external forces外力 will be zero but, nevertheless不然的话, they together place a load on the member which tends to deform使变形 that member and which must be reacted作用 by internal forces内力 set up within the material由材料提供.如果这构件是处于平衡状态的话,外力的合力是为零。但是他们必须由材料提供的内力来平衡。+ There are a number of different ways in which load负载 can be applied作用to a member. Loads may be classified分类 with respect to time:负载作用于构件有许多的形式。相对于时间可以将负载分类为: (a) A static静态 load负载 is a gradually逐渐 applied作用 load for which equilibrium is reached in a relatively相对 short time.静态负载是逐渐作用的可以在相对较短的时间内达到平衡的负载。 (b)A sustained load持续载荷 is a load that is constant维持不变 over a long period of很 time, such as the weight of a structure构件重力. This type of load is treated处理,对待 in the same manner as a static load静态载荷; However for some materials对一些材料, and conditions of temperature and stress, the resistance抵抗力 to failure may be different under short time loading and under long time loading.持续载荷是可以维持很长时间不变的载荷。比如构件的重力。这种类型的载荷和静态载荷是同样的处理方法。但是对于某种材料,在某些特定的温度和外部压力的作用下,构件抵抗失效的能力是不同的。 (c) An impact冲击 load is a rapidly很快的迅速的 applied load (an energy load). Vibration震动 normally results from an impact load, and equilibrium平衡 is not established确定 until the vibration振动 is eliminated消除, usually by natural damping forces阻尼力. 冲击载荷是一种快速作用的载荷。振动常常是有冲击载荷引起。在振动被消除之前,平衡是很难稳定的。而消除振动的一半都是靠阻力。 (d) A repeated load重复载荷 is a load that is applied作用 and removed移动 many thousands of times.持续作用很多次,移动很多次的载荷称为持续载荷。 (e) A fatigue or alternating load交变载荷 is a load whose magnitude and sign are changed with time.狡辩载荷是大小和符号都在不断变化的载荷。 It has been noted above that external force applied to a body in equilibrium is reacted by internal forces set up within the material.上述的外力作用于物体时将会被材料提供的内力抵消而达到平衡。 If, therefore因此, a bar棒子,零件 is subjected to作用 a uniform统一的,制服 tension拉伸 or compression压缩, i.e. 也就是说a force, which is uniformly applied across the cross-section截面, then the internal forces set up are also distributed分布 uniformly and the bar is said to be subjected to a uniform normal stress正应力, the stress being defined定义 as:因此,如果零件受到统一的拉伸或者压缩,也就是说,力均匀的分布在截面上,此时内力也同样是均匀分布,此时我们就说哦这个构件受到了正应力的作用。这种应力定义为: stress=press/area=P/A Stress may thus be compressive or tensile depending on the nature of the load and will be measured衡量 in units单位 of newtons牛顿 per square meter每平方米 (N/m2)or multiples倍数 of this.这个力是压力还是拉力由构件所受的载荷确定。同时,此力可以用牛顿每平方米或者它的倍数来衡量。 If a bar is subjected to an axial load轴向载荷, and hence因此 a stress, the bar will change in length. If the bar has an original length L and changes in length by an amount L, the strain应变 produced产生的 is defined as follows:如果构件受到轴向的载荷,此时构件的长度会发生变化。如果构件的本身长度是L,改变了&L则,产生的应变定义为: strain=chang in lengyh/original length=&l/l Strain is thus a measure度量 of the deformation变形 of the material and is non-dimensional无量纲的, i.e. it has no unit没有单位; it is simply a ratio比例,比率,比值 of two quantities数量,数值 with the same unit.因此,应变是材料形变的度量,而且它是无量纲的。也就是说它没有单位。它只是两个有相同的单位的数值之间的比值。Tensile stress张应力 and strain拉应力 are considered被认为是 positive正的 in sense在某种程度. Compressive压应力 stress and strain are considered negative负的 in sense. Thus a negative strain produces a decrease in length.张应力和拉应力在被定义为正的,而压应力被认为是负的。因此负的压应力造成长度的减少。 A material is said to be elastic有弹性的 if it returns to its original, unloaded dimensions大小 when load is removed.如果材料在外力卸去的时候长度回复到了受力前的正常情况,我们就说这种材料有弹性。 A particular特别的 form形式 of elasticity弹性 which applies to a large range of engineering material工程材料, at least over part of their load range负载范围, produces deformations变形 which are proportional to成比例的 the loads producing them.很多材料都有这种特性,至少在一定范围内,变形与负荷是成正比的。 Since loads are proportional to成比例 the stress they produce and deformations are proportional to the strains, this also implies意味着 that, whilst material are elastic, stress is proportional to strain. Hookes law胡克定律 therefore states that负载可以产生成比例的应力,而应力又可以产生成比例的形变。也就意味着材料有弹性。用胡克定律表示 This law is obeyed服从 within certain limits by most ferrous alloys铁基合金 and it can even be assumed理论上 to apply to other engineering materials such as concrete混凝土, timber木材 and non-ferrous alloys有色金属 with reasonable合理的,可接受的 accuracy准确性,精度.此定律适用于大部分的铁基合金,理论上还可以用于其它工程材料,例如混凝土,木材,有色金属。并且精度还可接受。 Whilst同时 a material is elastic the deformation produced by any load will be completely recovered when the load is removed; there is no permanent deformation残留变形,永久变形.如果材料是弹性的,那如果负载去掉之后,由负载造成的变形将会完全消失不会留下残留变形。 Within the elastic limits of materials, i.e. within the limits in which Hookes law applies, it has been shown that在材料的弹性极限内,也就是说,在胡克定律允许的范围内,表现为: stress/strain=E This constant常数 is given the symbol符号 E and termed被称为 the modulus of elasticity弹性模量 or Youngs modulus杨氏模量. Thus这个常数由符号E表示,并被称为弹性模量或者杨氏模量。 Youngs modulus E is generally assumed假定 to be the same in tension or compression and for most engineering materials has a high numerical value数值. Typically代表性的, E=200*109N/m2 for steel钢 , so that it will be observed观察 from Eq.(2.5) that strains are normally very small.一半假设杨氏模量E在拉压时是相同的。对大多数的材料来说,它的数值都比较大,代表性的,钢的是200*109,从仪器中观察到的是2.5,应变是很小的。 In most common engineering applications应用 strains rarely exceed很少超过 0.1%. The actual真实的 value of Youngs modulus for any material is normally determined by carrying out a standard test on a specimen of the material. As we look around us we see a world full of “things”: machines, devices设备, tools; things that we have designed, built, and used; things made of wood, metals, ceramics陶瓷, and plastics. We know from experience that some things are better than others; they last longer, cost less, are quieter, look better, or are easier to use.当我们环顾四周,我们可以看到世界充满了“东西”。机器,设备,工具;我们设计,建造,使用的东西;用木头,金属,陶瓷,塑料制造的东西。我们凭借经验可以知道,一些东西比另一些东西更好,更便宜,更持久,更漂亮和更易于使用。 Ideally理想的, however, every such item项目 has been designed according to some set of “functional requirements”功能要求 as perceived感知 by the designers that is, it has been designed so as to answer the question, “Exactly what function should it perform执行?” In the world of engineering, the major function frequently频繁的 is to support some type of loading due to weight, inertia惯性, pressure, etc. 然而,理想的化的,每个项目都是根据设计者的感知到的功能要求来设计的。也就是说,它是设计来解决一些问题,那么它们需要执行什么功能呢?在工程界中,最频繁的功能就是用来支持各种形式的由重力,惯性,压力引起的载荷。 From the beams衡梁 in our homes to the wings of an airplane, there must be an appropriate melding结合 of materials, dimensions规模,大小, and fastenings连接件 to produce structures that will perform their functions功能 reliably可靠的 for a reasonable cost over a reasonable lifetime. 从家里的衡梁到飞机的翅膀,都必须由合适的材料,规模,连接件的配合,从而生产出有可靠功能和合理寿命的结构设备。 In practice实际上, engineering mechanics工程力学,机械工程 methods are used in two quite different ways:事实上,工程力学方法被用于两个截然不同的方面: (1) The development of any new device装置,设备 requires an interactive交互式的, iterative反复的 consideration of考虑 form, size, materials, loads, durability耐久性, safety, and cost.装置的发展要求有对形状,尺寸,材料,负载,耐久性,安全和消费的交互式的反复的考虑。 (2) When a device fails (unexpectedly失效) it is often necessary to carry out a study to pinpoint查明 the cause of failure and to identify鉴定 potential潜在的 corrective measures补救措施. Our best designs often evolve进化,发展 through a successive elimination逐次消元 of weak points.当一个产品失效的时候,应该去找出失效的原因,并且看看是否有潜在的补救措施。我们的最好的设计常常是通过不断减少弱点来得到的。 To many engineers, both of the above processes过程 can prove to be absolutely 绝对的fascinating迷人的 and enjoyable, not to mention更不必说 lucrative有利可图.对于设计师来说,上面的两个过程都是非常的迷人,有趣的。更不必说它还是有利可图可以赚钱的。 In any “real” problem there is never sufficient足够 good, useful information; we seldom know the actual loads and operating conditions工作条件 with any precision精度, and the analyses are seldom exact. 在任何现实的情况中,都没有足够的信息,我们很少知道真实的载荷,工作条件。精度和分析几乎没有什么保证。 While our mathematics数学运算 may be precise精确, the overall analysis全分析 is generally only approximate近似的, and different skilled people can obtain获得 different solutions. In the study of engineering mechanics, most of the problems will be sufficiently “idealized理想化的” to permit允许 unique solutions唯一解, but it should be clear that the “real world” is far less idealized, and that you usually will have to perform some idealization in order to obtain a solution. 就算我们的数学运算是完全精确的,全非西也就只能是近似。用不同的方法可以获得不同的结果。在工程机械的研究中,我们经常需要用到理想化的思想,来允许唯一解。但是我们要知道,现实世界远非理想,我们经常要用这个思想来解决问题。 The technical工艺的 areas we will consider are frequently频繁的 called “statics” and “strength of materials,” “statics” referring to the study of forces acting on stationary devices, and “strength of materials” referring to the effects of those forces on the structure (deformations, load limits, etc.). While a great many devices are not, in fact, static, the methods developed here are perfectly applicable to适用于 dynamic situations动态情况 if the extra loadings associated with与。有关 the dynamics are taken into account 被考虑(we shall briefly短暂的 mention how this is done). Whenever the dynamic forces动力 are small relative to the static loadings, the system is usually considered to be static.大部分设备并不是静态的,这里提出的方法适用于动态,如果与动态有关的额外载荷被考虑进去。任何时候只要动力与静态载荷有任何的关系,那么系统就被认为是静态的。 In engineering mechanics, we will appreciate欣赏到 the various各种各样 types of approximations近似法 that are inherent in固有的 any real problem: 在工程机械中,我们可以欣赏到各种各样形式的近似法来解决固有的问题。 Primarily首先, we will be discussing things which are in “equilibrium,” i.e., not accelerating加速的. However, if we look closely enough, everything is accelerating. We will consider many structural members结构部件 to be “weightless” but they never are. We will deal with forces that act at a “point” but all forces act over an area. We will consider some parts to be “rigid坚硬的” but all bodies will deform under load.首先,我们讨论处于平衡中的物体,也就是说没有加速的。然而,如果我们仔细观察,可以看到所有物体都是运动的,我们会认为构件是没有重量的,但是他们总有重量。我们会认为力作用在点上,但是力总是作用在面上的,我们认为一些部分是坚硬的,但是任何物体在力的作用下都会变形。 We will make many assumptions假定 that clearly are false. But these assumptions should always render the problem easier, more tractable易处理的. You will discover that the goal is to make as many simplifying assumptions as possible without seriously degrading退化 the result.我们会假定一些显然是错误的东西。但是这些假设会使问题变得简单,更易处理。你会发现我们的目的是找到尽量简单的假设,只要不使结果严重变形。 Generally there is no clear method to determine确定 how completely, or how precisely, to treat a problem: If our analysis is too simple, we may not get a pertinent相关的 answer; if our analysis is too detailed详细, we may not be able to obtain得到 any answer. It is usually preferable to start with a relatively simple analysis and then add more detail as required to obtain a practical solution. During the past two decades, there has been a tremendous growth in the availability of computerized methods for solving problems that previously were beyond solution because the time required to solve them would have been prohibitive. At the same time the cost of computer capability and use has decreased by orders of magnitude. We are experiencing an influx of “personal computers” on campus, in the home, and in business.Lesson 6 Shaft轴 DesignA shaft is a rotating旋转 or stationary固定的 member零件,构件, usually of circular圆形的 cross section横截面, having mounted安装 upon it such elements as gears齿轮, pulleys滑轮, flywheels飞轮, and other power-transmission传动装置 elements.轴类零件一般都是固定的或者是旋转体。截面一般都是圆形,并且有齿轮,滑轮,飞轮或者其他的传动装置安装在上面。If a shaft carries安装 several gears or pulleys齿轮或者滑轮, different sections截面 of the shaft will be subjected to承受 different torques力矩, because the total power delivered to传递 the shaft is taken off piecemeal分散成片 at various points. Hence one must note记录 the amount of torque力矩 on each part of the shaft. Then study the distribution分布 of the bending moment弯矩, preferably较好的 sketching草图( freehand is all right) the shear force切应力 and bending moment diagrams弯矩图.如果轴上安装了几个齿轮和滑轮,不同的截面将会承受不同的力矩。因为传递到轴上的总力被分散到了不同的点。因此我们必须分别记录不同部分的力矩,然后研究弯矩的分布,较好的画出切应力和弯矩的图。From this preliminary examination预备考试,预先检查, which is a problem in mechanics, we note the section截面 where the bending moment弯矩 is a maximum and the section where the torque扭矩 is a maximum. If these maximums occur at the same section, the diameter直径 needed for that section is determined- and used for the entire整个的 shaft when the diameter is to be constant恒定. If the maximums do not occur at the same section, determine the diameter for the section of maximum torque and also for the section of maximum bending moment, and use the larger value.从之前的检查我们可以知道,我们在工程中注意弯矩和扭矩达到最大的截面。如果这些截面重合,那么我们就说当此直径恒定的时候,截面的的直径也就定了,当然此轴的尺寸也就定下来了。如果两个面没有重合,那么我们就取其中大的那个。 The diameter of shaft is often varied from point to point , sometimes for structure reasons. In this case, check the stress or determine the size needed for each section. The designer makes certain that all sections of the shaft are subjected to safe stresses, taking due note of holes, keyways, and other stress raisers应力集中装置.轴各部分的直径常常是不同的。一些是结构的原因。这种时候,我们要检查上面的应力并且决定所需面的尺寸。设计师要特别注意孔,键槽和其他的应力集中装置,确保所有的截面所受的力都在允许范围内。 Hollow洞 round shafts园轴 sometimes serve a useful purpose, usually in large sizes, though they are more expensive than solid ones. They have the advantage of being stronger and stiffer更硬的, weight for weight, because the outer fibers外部纤维 are more effective in resisting the applied moments, and they respond better to heat treatment because quenching淬火 can proceed outward as well as inward.孔轴常常可以发挥重要的作用,它们的尺寸一般都比较大,而且比一般的实心轴更贵。它们的优点是等质量的情况下更加的硬,因为外部的纤维更有利于承受应力,而且由于它们可以内外同时进行热处理所以效果可以更好。 Deflection偏差 is a significant重大的 consideration in the design of shafts. Criteria标准条件 for the limiting torsional deflection扭转变形 vary from 0.25 degree per meter of length for machinery shafts to 1 degree per meter or 1 degree in a length of 20 diameters for transmission shafting传动轴. Even short shafts become special problems in rigidity硬度 when the load is applied in impulses脉冲, as on an automobile crankshaft汽车机轴. The impulses脉冲 produce a torsional vibration扭转变形, usually compensated by torsional-vibration dampers扭转减震器 in an automotive engine汽车发动机.在轴的设计中,偏差将会被着重考虑。传动轴的标准扭转变形范围是每米0.25度到1度。就算是微小的偏差如果加载上脉冲负载都会严重影响轴的硬度。就比如汽车的机轴,就需要汽车发动机中的扭转减震器来消除脉冲造成的扭转变形。 Data on permissible values允许值 of deflections变形 are rare, probable because the range范围 of values would be large and each situation has its own peculiarities独特性. An old rule of thumb检验的法则 for transmission shafting传动轴 is that the deflection should not exceed 0.0005L, where L is the shaft length between supports; although greater stiffness may be desired需要. 变形的允许值很小,也许是因为每种特定的情况都有其独特性。旧时后的检验法则表示就算需要更高的强度变形也不能超过轴长的0.0008倍。Preferably较好的, on transmission shafts, the pulleys and gears should be located close to bearings轴承 in order to minimize最小化 moments. If journal bearings径向轴承 with “thick film” lubrication润滑 are used, the deflection偏向 across the bearing width轴承宽度 should be only a small fraction部分 of the oil-film thickness油膜厚度; if the slope斜坡 is excessive过多 here, there will be “binding粘合” in the journal轴颈. A self-aligning bearing球面轴承 may eliminate消除 this trouble if the deflection is otherwise acceptable. 传动轴的较好的设计是将齿轮和滑轮放在靠近轴承的地方。如果使用的是涂有润滑油的径向轴承那么轴承宽度方向的偏向只能是油膜厚度的一小部分。如果斜坡过多那么就要在轴颈上涂上粘合剂。但是当变形在可接受范围内时球面轴承可以消除这种问题。 On machine tools, rigidity硬度 is a special concern because of its relation to accuracy准确性. If a shaft supports a gear, deflection is more of a consideration than if it carries a V-belt pulley皮带轮.在机械工具中,硬度被特别关注。因为他反应了其精度。装了齿轮的轴比装了皮带轮的轴更加强调偏差。 The center of mass质心 of symmetric匀称的, rotating旋转 body does not coincide with与一致 its center of rotation. This is because (a) it is impossible from a practical实际 viewpoint to get the mass uniformly distributed分布式 about the geometric几何学 center of the body and (b) the shaft on which the body rotates deflects under load, thus moving the center of mass away from the true axis, which passes through通过 the center line of the bearings. 均与的旋转体的质心与其旋转中心不重合。因为从实际情况看,质量是不可能按照其几何形状均匀分布的。因此将质心移动离开其轴心, Rotation循环 may begin about the geometric axis几何中心, but at some speed, the centrifugal force离心力 of the displaced取代 center of mass质心 will equal the deflecting forces偏转力 on the shaft; the shaft with its attached附加的 bodies will then vibrate震动 violently猛烈的, since the centrifugal force changes its direction方向 as the shaft turns. This speed is termed术语是 the critical speed临界转速. Above the critical speed, a smooth-running state光滑运行状态 of equilibrium平衡 is again reached when the body is then rotating旋转 virtually事实上 about its mass center质心 (centrifugal forces离心力 balance). 循环也许会绕着几何中心进行。但是在某些速度的情况下,被取代了的质心的离心力会与轴上的偏心力平衡,带着附加物件的轴将会猛烈的震动。知道离心力方向改变成与转动方向一致。这个速度被称为是临界转速。在此速度时,工件将会再次达到平衡的光滑运行状态。 High-speed turbines高速涡轮机 often operate运转 above the critical speed临界转速. Additional附加的 critical speeds, higher than the first, are successively相继的 attained得到, but the amplitudes振幅 of the corresponding相应的 vibrations震动 progressively逐渐的 decrease. 高速涡轮机经常在临界转速运转。更加高的附加的临界转速也常常被运用。但是相应的震动的振幅也就逐渐的减少。 Many shafts supported by three or more bearings, which means that the problem is statically静态的 indeterminate不确定的. Texts on strength of materials材料强度 give methods of solving such problems. The design effort设计工作 should be in keeping with与。相关联 the economics经济学 of a given situation. For example, if one line shaft supported by three or more bearings is needed, it probably would be cheaper to make conservative assumptions保守假设 as to moments and design it as though it were determinate. The extra
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