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基于ProE渐开线齿轮的建模和传动仿真【带CAD图纸设计说明书】
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附录二故障的分析、尺寸的决定以及凸轮的分析和应用 前言介绍：作为一名设计工程师有必要知道零件如何发生和为什么会发生故障，以便通过进行最低限度的维修以保证机器的可靠性。有时一次零件的故障或者失效可能是很严重的一件事情，比如，当一辆汽车正在高速行驶的时候，突然汽车的轮胎发生爆炸等。另一方面，一个零件发生故障也可能只是一件微不足道的小事，只是给你造成了一点小麻烦。一个例子是在一个汽车冷却系统里的暖气装置软管的松动。后者发生的这次故障造成的结果通常只不过是一些暖气装置里冷却剂的损失，是一种很容易被发现并且被改正的情况。能够被零件进行吸收的载荷是相当重要的。一般说来，与静载重相比较，有两个相反方向的动载荷将会引起更大的问题，因此，疲劳强度必须被考虑。另一个关键是材料是可延展性的还是脆性的。例如，脆的材料被认为在存在疲劳的地方是不能够被使用的。很多人错误的把一个零件发生故障或者失效理解成这样就意味着一个零件遭到了实际的物理破损。无论如何，一名设计工程师必须从一个更广泛的范围来考虑和理解变形是究竟如何发生的。一种具有延展性的材料，在破裂之前必将发生很大程度的变形。发生了过度的变形，但并没有产生裂缝，也可能会引起一台机器出毛病，因为发生畸变的零件会干扰下一个零件的移动。因此，每当它不能够再履行它要求达到的性能的时候，一个零件就都算是被毁坏了（即使它的表面没有被损毁）。有时故障可能是由于两个两个相互搭配的零件之间的不正常的磨擦或者异常的振动引起的。故障也可能是由一种叫蠕变的现象引起的，这种现象是指金属在高温下时一种材料的塑性流动。此外，一个零件的实际形状可能会引起故障的发生。例如，应力的集中可能就是由于轮廓的突然变化引起的，这一点也需要被考虑到。当有用两个相反方向的动载荷，材料不具有很好的可延展性时，对应力考虑的评估就特别重要。一般说来，设计工程师必须考虑故障可能发生的全部方式，包括如下一些方面：压力变形磨损腐蚀振动环境破坏固定设备松动在选择零件的大小与形状的时候，也必须考虑到一些可能会产生外部负载影响的空间因素，例如几何学间断性，为了达到要求的外形轮廓及使用相关的连接件，也会产生相应的残余应力。凸轮是被应用的最广泛的机械结构之一。凸轮是一种仅仅有两个组件构成的设备。主动件本身就是凸轮，而输出件被称为从动件。通过使用凸轮，一个简单的输入动作可以被修改成几乎可以想像得到的任何输出运动。常见的一些关于凸轮应用的例子有：凸轮轴和汽车发动机工程的装配专用机床自动电唱机印刷机自动的洗衣机自动的洗碗机高速凸轮(凸轮超过1000 rpm的速度)的轮廓必须从数学意义上来定义。无论如何，大多数凸轮以低速(少于500 rpm)运行而中速的凸轮可以通过一个大比例的图形表示出来。一般说来，凸轮的速度和输出负载越大，凸轮的轮廓在被床上被加工时就一定要更加精密。材料的设计属性当他们与抗拉的试验有关时，材料的下列设计特性被定义如下。静强度：一个零件的强度是指零件在不会失去它被要求的能力的前提下能够承受的最大应力。因此静强度可以被认为是大约等于比例极限，从理论上来说，我们可以认为在这种情况下，材料没有发生塑性变形和物理破坏。刚度：刚度是指材料抵抗变形的一种属性。这条斜的模数线以及弹性模数是一种衡量材料的刚度的一种方法。弹性：弹性是指零件能够吸收能量但并没有发生永久变形的一种材料的属性。吸收的能量的多少可以通过下面弹性区域内的应力图表来描述出来。韧性：韧性和弹性是两种相似的特性。无论如何，韧性是一种可以吸收能量并且不会发生破裂的能力。因此可以通过应力图里面的总面积来描述韧性。显而易见，脆性材料的韧性和弹性非常低，并且大约相等。脆性：一种脆性的材料就是指在任何可以被看出来的塑性变形之前就发生破裂的材料。脆性的材料一般被认为不适合用来做机床的零部件，因为当遇到由轴肩，孔，槽，或者键槽等几何应力集中源引起的高的应力时，脆性材料是无法来产生局部屈服的现象以适应高的应力环境的。延展性：一种延展性材料会在破裂之前表现出很大程度上的塑性变形现象。延展性是通过可延展的零件在发生破裂前后的面积和长度的百分比来测量的。一个在发生破裂的零件，其伸长量如果为5%，则认为该伸长量就是可延展性和脆性材料分界线。可锻性：可锻性从根本上来说是指材料的一种在承受挤压或压缩是可以发生塑性变形的能力，同时，它也是一种在金属被滚压成钢板时所需金属的重要性能。硬度：一种材料的硬度是指它抵抗挤压或者拉伸它的能力。一般说来，材料越硬，它的脆性也越大，因此，弹性越小。同样，一种材料的极限强度粗略与它的硬度成正比。机械加工性能（或切削性）：机械加工性能是指材料的一种容易被加工的性能。通常，材料越硬，越难以加工。压应力和剪应力除抗拉的试验之外，还有其它一些可以提供有用信息的静载荷的实验类型。压缩测试：大多数可延展材料大约有相同特性，当它们处于受压状态的紧张状态时。极限强度，无论如何，不能够被用于评价压力状态。当一件具有可延展性的样品受压发生塑性变形时，材料的其它部分会凸出来，但是在这种紧张的状态下，材料通常不会发生物理上的破裂。因此，一种可延展的材料通常是由于变形受压而损坏的，并不是压力的原因。剪应力测试：轴，螺钉，铆钉和焊接件被用这样一种方式定位以致于生产了剪应力。一张抗拉试验的试验图纸就可以说明问题。当压力大到可以使材料发生永久变形或发生破坏时，这时的压力就被定义为极限剪切强度。极限剪切强度，无论如何，不等于处于紧张状态的极限强度。例如，以钢的材料为例，最后的剪切强度是处于紧张状态大约极限强度的75%。当在机器零部件里遇到剪应力时，这个差别就一定要考虑到了。动力载荷不会在各种不同的形式的力之间不停发生变化的作用力被叫作静载荷或者稳定载荷。此外，我们通常也把很少发生变化的作用力叫作静载荷。在拉伸实验中，被分次、逐渐的加载的作用力也被叫作静载荷。另一方面，在大小和方向上经常发生变化的力则被称为动载荷。动载荷可以被再细分为以下的3种类型。变载荷：所谓变载荷，就是说载荷的大小在变，但是方向不变的载荷。比如说，变载荷会产生忽大忽小的张应力，但不会产生压应力。周期性载荷：像这样的话，如果大小和方向同时改变，则就是说这种载荷会反复周期性的产生变化的拉应力和压应力，这种现象往往就伴随着应力在方向和大小上的周期性变化。冲击载荷：这类载荷是由于冲击作用产生的。一个例子就是一台升降机坠落到位于通道底部的一套弹簧装置上，这套装置产生的力会比升降机本身的重量大上好几倍。当汽车的一个轮胎碰撞到道路上的一个突起或者路上的一个洞时，相同的冲击荷载的类型也会在汽车的减震器弹簧上发生。如果材料的某处经常会产生大量的周期性作用力，那么在材料的表面就很可能会出现裂缝。裂缝最初是在应力超过它极限压力的地方开始出现的，而通常这往往是有微小的表面缺陷的地方，例如有一处材料出现瑕疵或者一道极小的划痕。当循环的次数增加时，最初的裂缝开始在轴的周围的逐渐产生许多类似的裂缝。所以说，第一道裂缝的意义就是指应力集中的地方，它会加速其它裂缝的产生。一旦整个的外围斗出现了裂缝，裂缝就会开始向轴的中心转移。最后，当剩下的固体的内部地区变得足够小，且当压力超过极限强度时，轴就会突然发生断裂。对断面的检查可以发现一种非常有趣的图案。外部的一个环形部分相对光滑一些，因为原来表面上相互交错的裂缝之间不断地发生磨擦导致了这种现象的产生。无论如何，中心部分是粗糙的，表明中心是突然发生了断裂，类似于脆性材料断裂时的现象。这就表明了一个有趣的事实。当正在使用的机器零件由于静载荷的原因出现问题时，由于材料具有的延展性，他们通常会发生一定程度的变形。尽管许多地由于静压力导致的零件故障可以通过频繁的做实际的观察并且替换全部发生变形的零件来避免。不管怎样，疲劳失效有助于起到警告的作用。汽车中发生故障的零件中的90%的原因都是因为疲劳的作用。一种材料的疲劳强度是指在压力的反复作用下的抵抗产生裂缝的能力。持久极限是用来评价一种材料的疲劳强度的一个重要参数。进一步说明就是，持久极限就是指在无限循环的作用力下不引起失效的压力值。让我们回头来看疲劳试验机器的。试验是这样被进行的：一件小的重物被插入，电动机被启动。在试样的失效过程中，由计算寄存器记录下循环的次数N，并且弯曲压力的相应最大量由第2.5 方程式计算。然后用一个新的样品替换掉被毁坏的样品，并且将另一个重物插入以增加负荷量。压力的新的数值再次被计算，并且相同的程序再次被重复进行，直到零件的失效只需要一个完整周期时为止。然后根据压力值和所需的循环的次数来绘制一个图。该图被称为持久极限曲线或者S-N 曲线。由于这需要的前提是要进行无限次的循环，所以我们可以以100万个循环用来作循环参考单位。因此，持久极限可以那里看到，该材料是在承受了100万个循环后而没有发生失效的。描绘的关系对于钢的材料来说更为典型，因为当N 接近非常大的数字时，曲线就会变得水平。因此持久极限等于曲线接近一条水平的切线时的压力水平。由于包含了大量的循环，在绘图时，N通常会被按照对数标度来画，如图2.14 b中所示。当采用这样的方法做时，水平的直线就可以更容易发现材料的持久极限值。对于钢的材料来说，持久极限值大约等于极限强度的50%。无论如何，已经加工完成的表面如果不是一样的光滑，持久极限的值就会被降低。例如，对于钢材料的零件来说，63 微英寸（ in ）的机械加工的表面，零件的持久极限占理论的持久极限的百分比降低到了大约40%。而对于粗糙的表面来说 （300in，甚至更多），百分比可能降低到25%左右的水平。最常见的疲劳损坏的类型通常是由于弯曲应力所引起的。其次就是扭应力导致的失效，而由于轴向负载引起的疲劳失效却极少发生。弹性材料通常使用从零到最大值之间变化的剪应力值来做实验，以此来模拟材料实际的受力方式。就一些有色金属而论，当循环的次数变得非常大时，疲劳曲线不会随着循环次数的增大而变得水平。，而疲劳曲线的继续变小，表明不管作用力有多么的小，多次的应力反复作用都会引起零件的失效。这样的一种材料据说没有持久极限。对于大多数有色金属来说，它们都有一个持久极限，数值大小大约是极限强度的25%。温度对屈服强度和弹性模数的影响一般说来，当在说明一种拥有特殊的属性的材料时，如弹性模数和屈服强度，表示这些性能在室温环境下就可以存在。在低的或者较高的温度下，材料的特性可能会有很大的不同。例如，很多金属在低温时会变得更脆。此外，当温度升高时，材料的弹性模数和屈服强度都会变差。图2.23 显示了低碳钢的屈服强度在从室温升高到1000oC过程中被降低了大约70%。当温度升高时，显示了低碳钢在弹性模数E方面的削减。正如从图上可以看见的那样，弹性模数在从室温升高到1000oC过程中大约降低了30%。从这张图表中，我们也能看到在室温下承受了一定载荷而不会发生变形的零件却可能在高温时承受相同载荷时发生永久变形。蠕变： 一种塑性变形的现象由于温度效应的影响，金属中产生了一种被称为蠕变的现象，一个承受了一定的载荷的零件的塑性变形是按照一个时间函数来逐渐增加的。蠕变现象在室温的条件下也是存在的，但它发生的过程是如此之慢，以致于很少变得像在预期寿命中温度被升高到300oC或更多时那样显著，逐渐增加的塑性变形可能在一段短的时期内变得很明显。材料的抗蠕变强度是指材料抵抗蠕变的属性，并且抗蠕变强度的数据可以通过处理长期的蠕变试验(模拟实际零件的操作条件)来获得。在试验的过程中，给定的材料在规定的温度下的塑性应变被被进行了实时监控。由于蠕变是一种塑性变形现象，发生了蠕变的零件的尺寸可能就会被永久的改变。因此，如果一个零件是在很强的强度下运转的话，那么设计工程师必须精确地预言将在机器的使用寿命期间可能发生的蠕变的次数。否则，与此伴随的或者相关的问题就可能发生。在高温下，当螺栓被用来紧固零件时，蠕变就可能变成一个必须解决的问题。处在压力状态下的螺钉，蠕变是按照一个时间函数来发生的。因为变形是塑性的，夹紧力的损失将可能导致螺纹连接件的意外松动。像这种特殊的现象，通常被称为松弛，我们可以通过进行适当的蠕变强度时测试来确定是不是发生了蠕变。显示了三种承受了恒定的张紧力的低碳钢零件的典型的蠕变曲线。从中，我们可以注意到在高温条件下，蠕变发生的速度逐渐加速，直到零件失效。从图表里的时间轴上(x轴)，我们可以描述在10年的时间里，这种产品的预期寿命。总结机器设计者必须理解进行抗拉的静止强度的测试目的。这种试验可以确定被在设计方程式过程中使用的许多金属的机械特性。像弹性模数，比例极限，屈服强度，弹性，以及延展性等等可以根据抗拉试验来决定它们的特性。动载荷是指那些，在大小和方向上发生变化并且可能需要对机器零件在抵抗失效能力上的研究。由于应力的反复作用，允许使用的安全应力是基于材料的持久极限而不是基于屈服强度或者是极限强度。压力集中在机器零件改变尺寸的位置发生，例如在一块平的金属板上的一个孔或者一块平板、一个沟槽、一个圆轴上的皮带在宽度方向上的突然变化。尤其是在一块平板上或一块条板上有一个孔的情况下，当孔的大小减少时，最大应力的值相对于平均应力变得大得多。减少的压力集中影响的方法通常就是使在形状上的变化更有规律性。被设计出来的机械零件被用于在低于屈服强度或者极限强度的一些允许的环境下使用。这种方法可以用来照顾到在加工期间像材料属性的变化和残余应力的产生这样的未知因素， 以及用来做近似而不是精确计算的方程式。根据屈服强度或者极限强度来确定安全系数以决定安全应力的大小。温度能影响金属的机械特性。温度的增加可能会引起金属的热胀和蠕变，并且还可能降低它的屈服强度和它的弹性模数。如果大多数金属不被允许在温度发生变化时发生膨胀或者收缩，那么压力就会被当做载荷来看待。这现象在依靠干涉配合来进行零件装配时是有益的。一个毂或者孔的内径比与它相配的轴或者圆柱的直径小一点。先将毂加热后，由于热胀冷缩，此时可以轻松的将轴插入其中。当它冷却以后，同样由于热胀冷缩，它的内孔直径会变小，从而对插入其中的轴产生了很大的摩擦力，有效的防止了轴的松动。计算机辅助制造构造的类型盘形凸轮. 这类凸轮是最受欢迎的类型之一，因为这种凸轮的设计和制造是比较简单和容易的。可以注意到从动件移动到了与凸轮的旋转轴垂直的位置。所有的凸轮都按照两个不同的实体在运转时不会互相碰撞的基本原理来运行。因此，随着凸轮的旋转（在这种情况下，一般是逆时针转），从动件要么向上移动要么就接受适当的约束。我们应该把注意力集中于防止从动件发生粘接和使从动件的运动满足生产的要求。当从动件向下移动时，弹簧需要使从动件的棍子和凸轮的轮廓保持。棍子是被用来减少齿轮接触表面的磨擦力的。对于凸轮的每次旋转来说，从动件通过对凸轮底部死点的冲击使其移动到顶端。 一个带有一个尖顶从动件的盘形凸轮。复杂的动作可以通过这类从动件产生，因为一个点能够精确地跟随着凸轮轮廓的任何突然变化。无论如何，这种设计局限于负荷是非常小的应用里；否则两个实体的接触点将会被磨损掉，从而导致一系列的问题出现。盘形凸轮的两个另外的变量分别是旋转的从动件和从动件的偏移量。当需要的是旋转的运动时，一个旋转的从动件就会被使用。关于从动件的偏移量，我们需要注意从动件的偏移量的大小是取决于像压力角和凸轮外轮廓等参数的，这两个参数稍后将会被介绍。没有偏移量的从动件被称作同轴心的从动件。传递动力的凸轮：如图所描绘的被用来传递动力的凸轮。当凸轮朝着水平的方向传递运动时，从动件会产生上下滑动。从这里我们可以看出，一个旋转的从动件和一个滑动的从动件都可以被使用。这种类型的动作通常会被用在一些生产用于凸轮上的产品的专用机床上。这种设计上的变化在旋转和传输动力的三维的凸轮上体现了出来。例如，一块手工制造的步枪原料被放在一台专用车床上。这块原料的形状是要求能够实现以各凸轮所要达到的功能。当它旋转并传输动力时，从动件就可以控制用来把一块木材加工成生产步枪原料的机床。主动凸轮：在上述的凸轮设计中，凸轮和从动件之间在往返运动中保持接触是通过弹簧力的作用来保证的。无论如何，处于高速运转中的凸轮，用来保持凸轮和从动件之间的接触的弹簧力可能会变得很大，这是由于凸轮在高速运动中的加速度会产生额外的动作用力，接触的位置可能会发生变形。在这种情况下，接触面可能产生过大的压力，这样将会导致零件过早的被磨损。主动凸轮是不需要弹簧的，因为从动件被迫在两个方向上与凸轮接触。这样的主动凸轮可以分为4类：圆柱形的凸轮，开槽的盘形凸轮(也叫表面凸轮)，分型板凸轮，以及共轭凸轮。圆柱形凸轮圆柱形凸轮可以使从动件实现不断的往复运动，一个旋转的从动件的应用实例。通过凸轮上槽沟的设计，我们可以实现使用几个凸轮轴来完成从动件的圆周分布。开槽的盘形凸轮：我们可以看到一个带有旋转的从动件的分型板凸轮，但是这样的设计也可以被用于传递动力的从动件上面。凸轮E和F一起绕着凸轮轴B旋转。凸轮E始终保持与滚筒C接触，而凸轮F则一直和滚筒D保持着接触。滚筒C和滚筒D都被安装在一根直角杠杆上，而这个直角杠杆是绕着点A 摆动的从动件。当凸轮F提供个滚筒D的需要的动作时，凸轮E则被用于给滚筒C提供需要的动作。共轭凸轮这种类型的凸轮，由一个被安装在凸轮轴偏心处的圆凸轮组成。从动件每次的摆度等于两倍的凸轮的偏心矩e。这样的凸轮会生产简谐振运动而没有保留时间。计算机辅助制造的专有名词在我们涉及凸轮的设计之前，我们很有必要知道各种各样被用于鉴别凸轮的重要的设计参数。如果你把凸轮想像成是不动的，而从动件是绕着凸轮转动的，那么，你将更容易理解对凸轮的描述。轨迹点：是指尖顶从动件的终点或者辊子中心或者辊子之类的从动件的终点。凸轮轮廓：凸轮的实际形状。基圆：是指能够画出来的且与凸轮的轮廓线相切的最小的圆。它的中心也就是凸轮轴的中心。凸轮轴里的最小的半径就是基圆的半径。啮合曲线：假定凸轮是固定不动的，从动件绕着凸轮旋转的，那么，轨迹点的路径就是啮合曲线。优圆：优圆是指与啮合曲线相切，且它的中心也在分配轴的中心的圆。压力角：压力角是指从动件的运动方向与节圆上辊子的中心所在的点之间的角度。凸轮外形：与凸轮轮廓相同。BDC：是Bottom Dead Center的缩写，是指从动件离凸轮中心最近的位置。行程：是指从动件在BDC 和TDC之间走过的路程的长度。高度上的行程：是指从动件从BDC转到TDC的时高度的变化值。返程：是指从动件从TDC转到BDC时所需时间。轮廓平行线：是指当凸轮在转动时，从动件可以和凸轮的中心保持恒定的距离不变的轨迹。我们可以获得对压力角的意义有一个更清楚、更深刻的理解。在这里，FT是影响辊子的一个合力。在任何一个接触点的地方，它一定是与表面垂直的。FT的方向显而易见不与从动件运动的方向平行。相反，它时通过压力角来表明从动件的运动的方向的。因此，力FT可以被分解为水平方向的力FH和垂直方向的力FV两部分。垂直分量是向上驱动从动件的那个力，因此，忽略了摩擦力，就等于从动件所受的力。水平方向的力没有座有用功，但是它仍然是不可或缺的。事实上，它试图使从动件能够沿着它的方向走。这样就可能会损坏从动件或者使从动件被卡死。很明显，我们希望压力角能够尽可能的减小测向力的大小。一个实际的经验法则是设计凸轮轮廓时，应使压力角的度数不超过30。压力角的大小，一般说来，取决于从动件的以下四个参数：基圆的大小。从动件相对主动件的圆心的偏移量的大小。滚筒直径的大小。凸轮轮廓平面(取决于使用的从动件运动的从动件行程和类型)。如果凸轮的要求没有改变，那么前面提到的一些参数就不能被改变。例如空间的限制。在我们已经学习过了如何设计凸轮之后，我们将学到减小压力角的各种各样的方法。附录三 Journal of Materials Processing Technology 143144 (2003) 237241 Failure Analysis，Dimensional Determination And Analysis，Applications Of Camsa University College of Drobeta Turnu Severin, University of Craiova, Strada A1.I Cuza, nr. 13, Craiova, Romaniab University of Minas Gerais, Belo Horizonte, Brazil INTRODUCTIONIt is absolutely essential that a design engineer know how and why parts fail so that reliable machines that require minimum maintenance can be designedSometimes a failure can be serious，such as when a tire blows out on an automobile traveling at high speedOn the other hand，a failure may be no more than a nuisanceAn example is the loosening of the radiator hose in an automobile cooling systemThe consequence of this latter failure is usually the loss of some radiator coolant，a condition that is readily detected and correctedThe type of load a part absorbs is just as significant as the magnitudeGenerally speaking，dynamic loads with direction reversals cause greater difficulty than static loads，and therefore，fatigue strength must be consideredAnother concern is whether the material is ductile or brittleFor example，brittle materials are considered to be unacceptable where fatigue is involvedMany people mistakingly interpret the word failure to mean the actual breakage of a partHowever，a design engineer must consider a broader understanding of what appreciable deformation occursA ductile material，however will deform a large amount prior to ruptureExcessive deformation，without fracture，may cause a machine to fail because the deformed part interferes with a moving second partTherefore，a part fails(even if it has not physically broken)whenever it no longer fulfills its required functionSometimes failure may be due to abnormal friction or vibration between two mating partsFailure also may be due to a phenomenon called creep，which is the plastic flow of a material under load at elevated temperaturesIn addition，the actual shape of a part may be responsible for failureFor example，stress concentrations due to sudden changes in contour must be taken into accountEvaluation of stress considerations is especially important when there are dynamic loads with direction reversals and the material is not very ductileIn general，the design engineer must consider all possible modes of failure，which include the followingStressDeformationWearCorrosionVibrationEnvironmental damageLoosening of fastening devicesThe part sizes and shapes selected also must take into account many dimensional factors that produce external load effects，such as geometric discontinuities，residual stresses due to forming of desired contours，and the application of interference fit jointsCams are among the most versatile mechanisms availableA cam is a simple two-member deviceThe input member is the cam itself，while the output member is called the followerThrough the use of cams，a simple input motion can be modified into almost any conceivable output motion that is desiredSome of the common applications of cams areCamshaft and distributor shaft of automotive engineProduction machine toolsAutomatic record playersAutomatic washing machinesAutomatic dishwashersThe contour of high-speed cams (cam speed in excess of 1000 rpm) must be determined mathematicallyHowever，the vast majority of cams operate at low speeds(less than 500 rpm) or medium-speed cams can be determined graphically using a large-scale layoutIn general，the greater the cam speed and output load，the greater must be the precision with which the cam contour is machinedDESIGN PROPERTIES OF MATERIALSThe following design properties of materials are defined as they relate to the tensile testFigure 1Static Strength The strength of a part is the maximum stress that the part can sustain without losing its ability to perform its required functionThus the static strength may be considered to be approximately equal to the proportional limit，since no plastic deformation takes place and no damage theoretically is done to the materialStiffness Stiffness is the deformation-resisting property of a materialThe slope of the modulus line and，hence，the modulus of elasticity are measures of the stiffness of a materialResilience Resilience is the property of a material that permits it to absorb energy without permanent deformationThe amount of energy absorbed is represented by the area underneath the stress-strain diagram within the elastic regionToughness Resilience and toughness are similar propertiesHowever，toughness is the ability to absorb energy without ruptureThus toughness is represented by the total area underneath the stress-strain diagram， as depicted in FigureObviously，the toughness and resilience of brittle materials are very low and are approximately equalBrittleness A brittle material is one that ruptures before any appreciable plastic deformation takes placeBrittle materials are generally considered undesirable for machine components because they are unable to yield locally at locations of high stress because of geometric stress raisers such as shoulders，holes，notches，or keywaysDuctility A ductility material exhibits a large amount of plastic deformation prior to ruptureDuctility is measured by the percent of area and percent elongation of a part loaded to ruptureA 5%elongation at rupture is considered to be the dividing line between ductile and brittle materialsMalleability Malleability is essentially a measure of the compressive ductility of a material and，as such，is an important characteristic of metals that are to be rolled into sheetsHardness The hardness of a material is its ability to resist indentation or scratchingGenerally speaking，the harder a material，the more brittle it is and，hence，the less resilientAlso，the ultimate strength of a material is roughly proportional to its hardnessMachinability Machinability is a measure of the relative ease with which a material can be machinedIn general，the harder the material，the more difficult it is to machineCOMPRESSION AND SHEAR STATIC STRENGTHIn addition to the tensile tests，there are other types of static load testing that provide valuable informationCompression Testing Most ductile materials have approximately the same properties in compression as in tensionThe ultimate strength，however，can not be evaluated for compressionAs a ductile specimen flows plastically in compression，the material bulges out，but there is no physical rupture as is the case in tensionTherefore，a ductile material fails in compression as a result of deformation，not stressShear Testing Shafts，bolts，rivets，and welds are located in such a way that shear stresses are producedA plot of the tensile testThe ultimate shearing strength is defined as the stress at which failure occursThe ultimate strength in shear，however，does not equal the ultimate strength in tensionFor example，in the case of steel，the ultimate shear strength is approximately 75% of the ultimate strength in tensionThis difference must be taken into account when shear stresses are encountered in machine componentsDYNAMIC LOADSAn applied force that does not vary in any manner is called a static or steady loadIt is also common practice to consider applied forces that seldom vary to be static loadsThe force that is gradually applied during a tensile test is therefore a static loadOn the other hand，forces that vary frequently in magnitude and direction are called dynamic loadsDynamic loads can be subdivided to the following three categoriesVarying Load With varying loads，the magnitude changes，but the direction does notFor example，the load may produce high and low tensile stresses but no compressive stressesReversing Load In this case，both the magnitude and direction changeThese load reversals produce alternately varying tensile and compressive stresses that are commonly referred to as stress reversalsShock Load This type of load is due to impactOne example is an elevator dropping on a nest of springs at the bottom of a chuteThe resulting maximum spring force can be many times greater than the weight of the elevator，The same type of shock load occurs in automobile springs when a tire hits a bump or hole in the roadFATIGUE FAILURE-THE ENDURANCE LIMIT DIAGRAMThe test specimen in Figure 2.10a，after a given number of stress reversals will experience a crack at the outer surface where the stress is greatestThe initial crack starts where the stress exceeds the strength of the grain on which it actsThis is usually where there is a small surface defect，such as a material flaw or a tiny scratchAs the number of cycles increases，the initial crack begins to propagate into a continuous series of cracks all around the periphery of the shaftThe conception of the initial crack is itself a stress concentration that accelerates the crack propagation phenomenonOnce the entire periphery becomes cracked，the cracks start to move toward the center of the shaftFinally，when the remaining solid inner area becomes small enough，the stress exceeds the ultimate strength and the shaft suddenly breaksInspection of the break reveals a very interesting pattern，as shown in Figure 2The outer annular area is relatively smooth because mating cracked surfaces had rubbed against each otherHowever，the center portion is rough，indicating a sudden rupture similar to that experienced with the fracture of brittle materialsThis brings out an interesting factWhen actual machine parts fail as a result of static loads，they normally deform appreciably because of the ductility of the materialFigure 2Thus many static failures can be avoided by making frequent visual observations and replacing all deformed partsHowever，fatigue failures give to warningFatigue fail mated that over 90% of broken automobile parts have failed through fatigueThe fatigue strength of a material is its ability to resist the propagation of cracks under stress reversalsEndurance limit is a parameter used to measure the fatigue strength of a materialBy definition，the endurance limit is the stress value below which an infinite number of cycles will not cause failureLet us return our attention to the fatigue testing machineThe test is run as follows：A small weight is inserted and the motor is turned onAt failure of the test specimen，the counter registers the number of cycles N，and the corresponding maximum bending stress is calculated from Equation 2.5The broken specimen is then replaced by an identical one，and an additional weight is inserted to increase the loadA new value of stress is calculated，and the procedure is repeated until failure requires only one complete cycleA plot is then made of stress versus number of cycles to failureFigure shows the plot，which is called the endurance limit or S-N curveSince it would take forever to achieve an infinite number of cycles，1 million cycles is used as a referenceHence the endurance limit can be found by noting that it is the stress level below which the material can sustain 1 million cycles without failureThe relationship depicted is typical for steel，because the curve becomes horizontal as N approaches a very large numberThus the endurance limit equals the stress level where the curve approaches a horizontal tangentOwing to the large number of cycles involved，N is usually plotted on a logarithmic scaleWhen this is done，the endurance limit value can be readily detected by the horizontal straight lineFor steel，the endurance limit equals approximately 50% of the ultimate strengthHowever，if the surface finish is not of polished equality，the value of the endurance limit will be lowerFor example，for steel par ts with a machined surface finish of 63 microinches ( in)，the percentage drops to about 40%For rough surfaces (300inor greater)，the percentage may be as low as 25%The most common type of fatigue is that due to bendingThe next most frequent is torsion failure，whereas fatigue due to axial loads occurs very seldomSpring materials are usually tested by applying variable shear stresses that alternate from zero to a maximum value，simulating the actual stress patternsIn the case of some nonferrous metals，the fatigue curve does not level off as the number of cycles becomes very largeThis continuing toward zero stress means that a large number of stress reversals will cause failure regardless of how small the value of stress isSuch a material is said to have no endurance limitFor most nonferrous metals having an endurance limit，the value is about 25% of the ultimate strengthEFFECTS OF TEMPERATURE ON YIELD STRENGTH AND MODULUS OF ELASTICITYGenerally speaking，when stating that a material possesses specified values of properties such as modulus of elasticity and yield strength，it is implied that these values exist at room temperatureAt low or elevated temperatures，the properties of materials may be drastically differentFor example，many metals are more brittle at low temperaturesIn addition，the modulus of elasticity and yield strength deteriorate as the temperature increasesshows that the yield strength for mild steel is reduced by about 70% in going from room temperature to 1000oFFigure 3 shows the reduction in the modulus of elasticity E for mild steel as the temperature increasesAs can be seen from the graph，a 30% reduction in modulus of elasticity occurs in going from room temperature to 1000oFIn this figure，we also can see that a part loaded below the proportional limit at room temperature can be permanently deformed under the same load at elevated temperaturesFigure3CREEP: A PLASTIC PHENOMENONTemperature effects bring us to a phenomenon called creep，which is the increasing plastic deformation of a part under constant load as a function of timeCreep also occurs at room temperature，but the process is so slow that it rarely becomes significant during the expected life of the temperature is raised to 300oC or more，the increasing plastic deformation can become significant within a relatively short period of timeThe creep strength of a material is its ability to resist creep，and creep strength data can be obtained by conducting long-time creep tests simulating actual part operating conditionsDuring the test，the plastic strain is monitored for given material at specified temperaturesSince creep is a plastic deformation phenomenon，the dimensions of a part experiencing creep are permanently alteredThus，if a part operates with tight clearances，the design engineer must accurately predict the amount of creep that will occur during t he life of the machineOtherwise，problems such binding or interference can occurCreep also can be a problem in the case where bolts are used to clamp tow parts together at elevated temperaturesThe bolts，under tension，will creep as a function of timeSince the deformation is plastic，loss of clamping force will result in an undesirable loosening of the bolted jointThe extent of this particular phenomenon，called relaxation，can be determined by running appropriate creep strength testsFigure shows typical creep curves for three samples of a mild steel part under a constant tensile loadNotice that for the high-temperature case the creep tends to accelerate until the part failsThe time line in the graph (the x-axis) may represent a period of 10 years，the anticipated life of the productSUMMARYThe machine designer must understand the purpose of the static tensile strength testThis test determines a number of mechanical properties of metals that are used in design equationsSuch terms as modulus of elasticity，proportional limit，yield strength，ultimate strength，resilience，and ductility define properties that can be determined from the tensile testDynamic loads are those which vary in magnitude and direction and may require an investigation of the machine parts resistance to failureStress reversals may require that the allowable design stress be based on the endurance limit of the material rather than on the yield strength or ultimate strengthStress concentration occurs at locations where a machine part changes size，such as a hole in a flat plate or a sudden change in width of a flat plate or a groove or fillet on a circular shaftNote that for the case of a hole in a flat or bar，the value of the maximum stress becomes much larger in relation to the average stress as the size of the hole decreasesMethods of reducing the effect of stress concentration usually involve making the shape change more gradualMachine parts are designed to operate at some allowable stress below the yield strength or ultimate strengthThis approach is used to take care of such unknown factors as material property variations and residual stresses produced during manufacture and the fact that the equations used may be approximate rather that exactThe factor of safety is applied to the yield strength or the ultimate strength to determine the allowable stressTemperature can affect the mechanical properties of metalsIncreases in temperature may cause a metal to expand and creep and may reduce its yield strength and its modulus of elasticityIf most metals are not allowed to expand or contract with a change in temperature，then stresses are set up that may be added to the stresses from the loadThis phenomenon is useful in assembling parts by means of interference fitsA hub or ring has an inside diameter slightly smaller than the mating shaft or postThe hub is then heated so that it expands enough to slip over the shaftWhen it cools，it exerts a pressure on the shaft resulting in a strong frictional force that prevents looseningTYPES OF CAM CONFIGURATIONSPlate CamsThis type of cam is the most popular type because it is easy to design and manufactureFigure shows a plate camNotice that the follower moves perpendicular to the axis of rotation of the camshaftAll cams operate on the principle that no two objects can occupy the same space at the same timeThus，as the cam rotates ( in this case，counterclockwise )，the follower must either move upward or bind inside the guideWe will focus our attention on the prevention of binding and attainment of the desired output follower motionThe spring is required to maintain contact between the roller of the follower and the cam contour when the follower is moving downwardThe roller is used to reduce friction and hence wear at the contact surfaceFor each revolution of the cam，the follower moves through two strokes-bottom dead center to top dead center (BDC to TDC) and TDC to BDCIllustrates a plate cam with a pointed followerComplex motions can be produced with this type of follower because the point can follow precisely any sudden changes in cam contourHowever，this design is limited to applications in which the loads are very light；otherwise the contact point of both members will wear prematurely，with subsequent failureTwo additional variations of the plate cam are the pivoted follower and the offset sliding follower，which are illustratedA pivoted follower is used when rotary output motion is desiredReferring to the offset follower，note that the amount of offset used depends on such parameters as pressure angle and cam profile flatness，which will be covered laterA follower that has no offset is called an in-line followerTranslation CamsFigure 4 depicts a translation camThe follower slides up and down as the cam translates motion in the horizontal directionNote that a pivoted follower can be used as well as a sliding-type followerThis type of action is used in certain production machines in which the pattern of the product is used as the camA variation on this design would be a three-dimensional cam that rotates as well as translatesFor example，a hand-constructed rifle stock is placed in a special latheThis stock is the pattern，and it performs the function of a camAs it rotates and translates，the follower controls a tool bit that machines the production stock from a block of woodFigure 4Positive-Motion CamsIn the foregoing cam designs，the contact between the cam and the follower is ensured by the action of the spring forces during the return strokeHowever，in high-speed cams，the spring force required to maintain contact may become excessive when added to the dynamic forces generated as a result of accelerationsThis si tuation can result in unacceptably large stress at the contact surface，which in turn can result in premature wearPositive-motion cams require no spring because the follower is forced to contact the cam in two directionsThere are four basic types of positive-motion cams: the cylindrical cam，the grooved-plate cam ( also called a face cam ) ，the matched-plate cam，and the scotch yoke camCylindrical CamThe cylindrical cam shown in Figure 6.5 produces reciprocating follower motion，whereas the one shown in Figure 6.6 illustrates the application of a pivoted followerThe cam groove can be designed such that several camshaft revolutions are required to produce one complete follower cycleGrooved-plate CamIn Figure 6.8 we see a matched-plate cam with a pivoted follower，although the design also can be used with a translation followerCams E and F rotate together about the camshaft BCam E is always in contact with roller C，while cam F maintains contact with roller DRollers C and D are mounted on a bell-crank lever，which is the follower oscillating about point ACam E is designed to provide the desired motion of roller C，while cam F provides the desired motion of roller DScotch Yoke CamThis type of cam，which is depicted in Figure 6.9，consists of a circular cam mounted eccentrically on its camshaftThe stroke of the follower equals two times the eccentricity e of the camThis cam produces simple harmonic motion with no dwell timesRefer to Section 6.8 for further discussionCAM TERMINOLOGYBefore we become involved with the design of cams，it is desirable to know the various terms used to identify important cam design parametersThe following terms refer to Figu
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