Shafts are mounted in bearings and transmit power through such devices as gears, pulleys, cams and clutches.  These devices introduce forces, which attempt to bend the shaft; hence, the shaft must be rigid enough to prevent overloading of the supporting bearings. In general, the bending deflection of a shaft should not exceed 0.01 in. per ft of length between bearing supports.
In addition, the shaft must be able to sustain a combination of bending and torsional loads. Thus an equivalent load must be considered which takes into account both prison and bending. Also the allowable stress must contain a factor of safety, which includes fatigue, since torsional and bending stress reversals occur.
For diameters less than 3 in., the usual shaft material is cold-rolled steel containing about 0.4 percent carbon. Shafts are either cold-rolled or forged in sizes from 3 in. to 5 ins. For sizes above 5 in., shafts are forged and machines to size plastic shafts are widely used for light load applications. One advantage of using plastic is safety in electrical applications, since plastic is a poor conductor of electricity.
Components such as gears and pulleys are mounted on shafts by means of key. The design of the key and the corresponding keyway in the shaft must be properly evaluated. For example, stress concentrations occur in shafts due to keyways, and the material removed to form the keyway further weakens the shaft.
If shafts are run at critical speeds, severe vibrations can occur which can seriously damage a machine. It is important to know the magnitude of these critical speeds so that they can avoided. As a general rule of thumb, the difference between the operating speed and the critical speed should be at least 20 percent.
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 flexible couplings.
A coupling is a device for connecting the ends of adjacent shafts. In machine construction, couplings are used to effect a semi permanent 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 machine, 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 purposes 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 (disks) that are attached by key-driven hubs to the ends of adjacent shaft sections and bolted together through the flanges to form a rigid connection. Alignment of the connected shafts is usually effected by means of a rabbet joint on the face of the flanges.
In connecting shafts belonging to separate devices (such as an electric motor and a gearbox), precise aligning of the shafts is difficult and a flexible coupling is used. This coupling connects the shafts in such a way as to minimize the harmful effects of shaft misalignment. Flexible couplings also permit the shafts to deflect under their separate systems of loads and to move freely (float) in the axial direction without interfering with one another. Flexible coupling can also serve to reduce the intensity of shock loads and vibration transmitted from on shaft to another.
直齿轮和斜齿轮
一个含有垂直和平行于其轴的轮齿的齿轮被称为正齿轮。一个正齿轮只能用来连接平行轴，但是平行轴也可以通过齿轮连接另一个类型的轴，正齿轮可以与其他类型的齿轮紧密配合。
为了防止由于热膨胀而造成的堵塞，帮助轮滑与弥补在生产中不可避免的误差，所有电力传输齿轮必须有齿间间隙，这意着在齿节圆上的接合的一对的齿轮的空间宽度必须略厚于齿轮的厚度。在仪表齿轮中，通过在它中间使用齿轮并股来消除反弹作用，齿轮并股就是让一半成为另一半的右枕横表。弹簧力强迫拼合齿轮的齿占领全宽的小齿轮空间。 机械结构英文文献和中文翻译(6):http://www.751com.cn/fanyi/lunwen_6770.html