  Pitch Surfaces of Spur Wheels.—Let two smooth rollers be placed in contact with their axes parallel, and let one of them rotate about its axis; then if there is no slipping the other roller will rotate in the opposite direction with the same surface velocity; and if D1, D2 be the diameters of the rollers, and N1, N2 their speeds in revolutions per minute, it follows as in belt gearing that—
If there be considerable resistance to the motion of the follower slipping may take place, and it may stop. To prevent this the rollers may be provided with teeth; then they become spur wheels; and if the teeth be so shaped that the ratio of the speeds of the toothed rollers at any instant is the same as Pitch Circle.—A section of the pitch surface of a toothed wheel by a plane perpendicular to its axis is a circle, and is called a pitch circle. We may also say that the pitch circle is the edge of the pitch surface. The pitch circle is generally traced on the side of a toothed wheel, and is rather nearer the points of the teeth than the roots. Pitch of Teeth.—The distance from the centre of one tooth to the centre of the next, or from the front of one to the front of the next, measured at the pitch circle, is called the pitch of the teeth. If D be the diameter of the pitch circle of a wheel, n the number of teeth, and p the pitch of the teeth, then D × 3·1416 = n × p. Fig. 34. Fig. 34. By the diameter of a wheel is meant the diameter of its pitch circle. Form and Proportions of Teeth.—The ordinary form of wheel teeth is shown in fig. 34. The curves of the teeth should be cycloidal curves, although they are generally drawn in as arcs of circles. It does not fall within the scope of this work to discuss the correct forms of wheel teeth. The student will find the theory of the teeth of wheels clearly and fully explained in Goodeve's 'Elements of Mechanism,' and in Unwin's 'Machine Design.' The following proportions for the teeth of ordinary toothed wheels may be taken as representing average practice:—
Exercise 34: Spur Wheel.—Fig. 35 shows the elevation and sectional plan of a portion of a cast-iron spur wheel. The diameter of the pitch circle is 237/8 inches, and the pitch of the teeth is 1½ inches, so that there will be 50 teeth in the wheel. The wheel has six arms. Draw a complete elevation of the wheel and a half sectional plan, also a half-plan without any section. Draw also a cross section of one arm. Scale 4 inches to a foot. Fig. 35. Fig. 35. Mortise Wheels.—When two wheels gearing together run at a high speed the teeth of one are made of wood. These teeth, or cogs, as they are generally called, have tenons formed on them, which fit into mortises in the rim of the wheel. This wheel with the wooden teeth is called a mortise wheel. An example of a mortise wheel is shown in fig. 36. Fig. 36. Fig. 36. Bevil Wheels.—In bevil wheels the pitch surfaces are parts of cones. Bevil wheels are used to connect shafts which are inclined to one another, whereas spur wheels are used to connect parallel shafts. In fig. 36 is shown a pair of bevil wheels in gear, one of them being a mortise wheel. At (a) is a separate drawing, to a smaller scale, of the pitch cones. The pitch cones are shown on the drawing of the complete wheels by dotted lines. The diameters of bevil wheels are the diameters of the bases of their pitch cones. Exercise 35: Pair of Bevil Wheels.—Draw the sectional elevation of the bevil wheels shown in gear in fig. 36. Commence by drawing the centre lines of the shafts, which in this example are at right angles to one another; then draw the pitch cones shown by dotted lines. Next put in the teeth which come into the plane of the section, then complete the sections of the wheels. The pinion or smaller wheel has 25 teeth, and the wheel has 50 teeth, which makes the pitch a little over 3 inches. Each tooth of the mortise wheel is secured as shown by an iron pin 5/16 inch diameter. Scale 3 inches to a foot. |
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