外文文献原文Helical，Worm and Bevel GearsIn the force analysis of spur gars, the forces are assumed to act in a single plain. In this lesson we shall study gears in which the forces have three dimensions. The reason for this, in the case of helical gears, is that the teeth are not parallel to the axis of rotation. And in the case of bevel gears, the rotational axes are not parallel to each other. There are other reasons, as we shall learn.Helical gears are used to transmit motion between parallel shafts. The helix angle is the same on each gear, but one gear must have a righthand helix and the other a lefthand helix. The shape of the tooth is an involute helicoids. If a piece of paper cut in the shape of a parallclogram is wrapped around a cylinder, the angular edge of the paper becomes a helix. If we unwind this paper, each point on the angular edge generates an involute curve. The surface obtained when every point on the edge generates an involute is called an involute helicoids.The initial contact of spurgear teeth is a line extending all the way across the face of the tooth. The initial contact of helical gear teeth is a point,which changes into a line as the teeth come into more engagement. In spur gears the line of contact is parallel to the axis of the rotation; in helical gears, the line is diagonal across the face of the tooth.It is this gradual engagement of the teeth and the smooth transfer of load from one tooth to another ,which give helical gears the ability to transmit heavy loads at high speeds. Helical gears subject the shaft bearings to both radial and thrust loads. When the thrust loads become high or are objectionable for other reasons, it may be desirable to use double helical gears. A double helical gear（herringbone）is equivalent to two helical gears of opposite hand, mounted side by side on the same shaft. They develop opposite thrust reaction and thus cancel out the thrust load. When two or more single helical gears are mounted on the same shaft, the hand of the gears should be selected so as to produce the minimum thrust load.Crossedhelical, or spiral, gears are those in which the shaft centerlines are neither parallel nor intersecting. The teeth of crossed-helical gears have point contact with each other, which changes to line contact as the gears wear in. For this reason they will carry out very small loads and are mainly for instrumental applications, and are definitely not recommended for use in the transmission of power. There is no difference between a crossed helical gear and a helical gear until they are mounted in mesh with each other. They are manufactured in the same way. A pair of meshed crossed helical gears usually have the same hand; that is, a right-hand driver goes with a right hand driven. In the design of crossed-helical gears, the minimum sliding velocity is obtained when the helix angle are equal. However, when the helix angle are not equal, the gear with the larger helix angle should he used as the driver if both gears have the same hand.Worm gears are similar to crossed helical gears. The pinion or worm has a small number of teeth, usually one to four, and since they completely wrap around the pitch cylinder they are called threads. Its mating gear is called a worm gear, which is not a true helical gear. A worm and worm gear are used to provide a high angular-velocity reduction between nonintersecting shafts which are usually at right angle. The worm gear is not a helical gear because its face is made concave to fit the curvature, nature of the worm in order to provide line contact instead of point contact. However, a disadvantage of worm gearing is the high sliding velocities across the teeth, the same as with crossed helical gears. Worn gearing are either single or double enveloping. A single enveloping gearing is one in which the gear wraps around or partially encloses the worm, A gearing in which each element partially encloses the other is, of course, a double enveloping worm gearing. The important difference between the two is that area contact exists between the teeth of double enveloping gears while only line contact between those of single-enveloping gears. The worm and worm gear of a set have the same hand of helix as for crossed helical gears, but the helix angles are usually quite different. The helix angle on the worm is generally quite large, and that on the gear very small. Because of this, it is usual to specify the lead angle on the worm, which is the complement of the worm helix angle, and the helix angle on the gear; the two angles are equal for a 9O deg. shaft angle.When gears are to be used to transmit motion between intersecting shafts, some form of bevel gear is required. Although bevel gears are usually made for a shaft angle of 9O deg., they may be produced for almost any shaft angle. The teeth may be east, milled, or generated. Only the generated teeth may be classed as accurate. In a typical bevel gear mounting, one of