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A shaft is a rotating or stationary member, usually of circular cross section, having mounted upon it such elements as gears, pulleys, flywheels, and other power-transmission elements.


If a shaft carries several gears or pulleys, different sections of the shaft will be subjected to different torques, because the total power delivered to the shaft is taken off piecemeal at various points. Hence one must note the amount of torque on each part of the shaft. Then study the distribution of the bending moment, preferably sketching( freehand is all right) the shear force and bending moment diagrams.


From this preliminary examination, which is a problem in mechanics, we note the section where the bending moment is a maximum and the section where the torque is a maximum. If these maximums occur at the same section, the diameter needed for that section is determined- and and also for the section of maximum bending moment, and use the larger value.


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).


Hollow round shafts 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, weight for weight, because the outer fibers(纤维)are more effective in resisting the applied moments(作用力矩), and they respond better to heat treatment because quenching (淬火)can proceed outward as well as inward.


Deflection(扰度)is a significant consideration in the design of shafts. Criteria for the limiting torsional deflection 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(轴系). Even short shafts become special problems in rigidity when the load is applied in impulses, as on an automobile crankshaft. The impulses produce a torsional vibration, usually compensated(补偿)by torsional-vibration dampers in an automotive engine.


Data on permissible values of deflections are rare, probable because the range of values would be large and each situation has its own peculiarities. An old rule of thumb(经验法则)for transmission shafting is that the deflection should not exceed 0.0005L, where L is the shaft length between supports; although greater stiffness may be desired.

对挠度的允许值的数据是罕见的,可能是因为值的范围将是大和每一种情况都有其自己的特点。拇指(经验法则),用于传输轴系的旧规则是,偏转不应超过0.0005L,其中L是支持件之间的轴的长度;尽管更大的刚性可能期望。Preferably, on transmission shafts, the pulleys and gears should be located close to bearings in order to minimize moments. If journal bearings with “thick film” lubrication are used, the deflection across the bearing width should be only a small fraction of the oil-film thickness;


if the slope is excessive here, there will be “binding” in the journal. A self-aligning bearing may eliminate this trouble if the deflection is otherwise acceptable.


On machine tools, rigidity is a special concern because of its relation to accuracy. If a shaft supports a gear, deflection is more of a consideration than if it carries a V-belt pulley.


The center of mass of a symmetric, rotating body does not coincide with its center of rotation. This is because (a) it is impossible from a practical viewpoint to get the mass uniformly distributed about the geometric 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 the center line of the bearings. Rotation may begin about the geometric axis,



but at some speed, the centrifugal force of the displaced center of mass will equal the deflecting forces on the shaft; the shaft with its attached bodies will then vibrate violently, since the centrifugal force changes its direction as the turns.


This speed is termed the critical speed(临界速度). Above the critical speed, a smooth-running(平稳转动) state of equilibrium is again reached when the body is then rotating virtually about its mass center (centrifugal forces balance).


High-speed turbines often operate above the critical speed. Additional critical speeds, higher than the first, are successively attained, but the amplitudes of the corresponding vibrations progressively decrease.


Many shafts supported by three or more bearings, which means that the problem is statically indeterminate. Texts on strength of materials give methods of solving such problems. The design effort(设计工作)should be in keeping with the economics 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 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(精心)design analysis.