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    As a general rule of thumb , the difference betweem the operating speed and the critical speed should be at least 20 percent. Many shafts are supported by three or more bearings, which means that the problem is statically indeterminate .text on strenth of materials give methods of soving such problems. The design effort should be in keeping with the economics of a given situation , for example , if one line shaft supported by three or more bearings id needed , it probably would be cheaper to make conservative assumptions as to moments and design it as though it were determinate . the extra cost of an oversize shaft may be less than the extra cost of an elaborate design analysis. Another important aspect of shaft design is the method of directly connecting one shaft to another , this is accomplished by devices such as rigid and flexiable couplings.
    A coupling is a device for connecting the ends of adjacent shafts. In machine construction , couplings are used to effect a semipermanent connection between adjacent rotating shafts , the connection is permanent in the sense that it is not meant to be broken during the useful life of the machinem , but it can be broken and restored in an emergency or when worn parts are replaced. There are several types of shaft couplings, their characteristics depend on the purpose for which they are used , if an exceptionally long shaft is required in a manufacturing plant or a propeller shaft on a ship , it is made in sections that are coupled together with rigid couplings.
     A common type of rigid coupling consists of two mating radial flanges that are attached by key driven hubs to the ends of adjacent shaft sections and bolted together through the flanges to forma rigid connection. Alignment of the connected shafts in usually effected by means of a rabbet joint on the face of the flanges. In connecting shafts belonging to separate device ( such as an electric motor and a gearbox),precise aligning of the shafts is difficult and a fkexible coupling is used . this coupling connects the shafts in such a way as to minimize the harmful effects of shafts misalignment of loads and to move freely(float) in the axial diection without interfering with one another . flexiable couplings can also serve to reduce the intensity of shock loads and vibrations transmitted from one shaft to another
    运动学的基本目的是去计一个机械零件的理想运动,然后再用数学的方法去描绘该零件的位置,速度和加速度,再运用这些参数来设计零件。因为,对于大部分固着在地球上的机械系统来说,与之联系最密切的是时间,将加速度和动态力定义成时间作用的结果。相应地,应力是作用在物体上的外力和惯性力的作用结果。所以机械设计的内容是要建立一种在该机器的使用寿命内保证其安全的系统,目的是要在一定的工况要求下,对材料进行选择,使材料的应力在许用极限应力之内。这一点很明显要求所有的系统要在理想的限制内工作。在机械设计中,零件受到的最大力是取决于材料本身的动态性能。这些动态力引起了零件的加速度,加速度又要回到运动学中去计算,这是机械设计的基础。运动分析是最基本的也是最早出现在设计的过程中的,它对与任何一个零件的成功设计够起着至关重要的作用。在设计过程中很差的运动学分析会带来麻烦和错误。论文网
    根据机构所具有的自由度,任何机械系统都可以被分类。系统的自由度是在任何时候限制它的位置独立的参数数目。
    在通常情况下,刚体在相关的平面内能实现复杂的自由运动,这个运动同时包括转动和平移。在三纬空间内,在可以饶任何轴转动的同时可以沿着三个坐标平移。在一个平面或是一个二文的空间内,复杂运动变成了饶一个(垂直与这个平面的)轴线的转动和同时发生的可以被分解为沿在这个平面内的两个坐标轴的平移分量。为了简化,我们将当前的讨论限制在二文的运动系统中。接下来将要介绍相关的术语:
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