SECTION III. MILLWORK: SHAFTING, GEARING, PULLEYS, ETC. TOOTHED WHEEL GEARING. Wheel Gearing.-Where motion has to be transmitted with precision, toothed wheel gearing must be used. The teeth should be so formed that the wheels will work together with the smallest amount of friction, and work smoothly and uniformly with a constantly equal power and with comparatively little noise, in the same manner as if two plain cylinders were rolling upon each other by the friction of their own pitch circles. As a wheel acts as a lever of a length represented by its radius, the leverage is governed by the diameter; but in making calculations, the number of teeth is used instead of the diameter. As fine-pitch wheels have a smoother and more uniform action than coarse ones, the pitch should always be made as fine as possible, consistent with the power transmitted. In calculating gearing, the diameter of the pitch-circle is taken as the diameter of the wheel, and when the wheels are properly in gear their pitch-circles meet and roll upon each other, Bevel and Mitre Wheels must be regarded as two cones rolling upon each other, and the teeth are drawn upon the same principle as those of spur wheels, the maximum pitch diameter being always taken as the diameter of bevel and mitre wheels. Form of Teeth of Wheels.-The following simple method of forming the teeth of wheels gives good results. Teeth thus formed and wheels made to the following proportions work accurately and smoothly together, wear uniformly, maintain their shape, and make very little noise in working. The utmost strength being given to the roots of the teeth, the liability to breakage and wear and tear is reduced to a minimum, and all wheels of the same pitch work properly together. When the flank-or side of the tooth below the pitch line-is curved, the radius of the flank equals the pitch of the tooth, and the point from which this radius is struck is part of the pitch in depth below the pitch line, as shown at Fig. 23. 5 15 The radius of the point or face of the tooth, or that portion of the tooth above the pitch circle,-equals the pitch for wheels with less than 21 teeth, and the pitch for wheels with upwards of 20 teeth. The point from which each radius is struck, is part of the pitch in depth, below the pitch line; the radius of the curve at the root of the tooth is the pitch. The flank of the tooth may also be made flat or parallel, and joined to the rim with a curve at the root of the tooth having a radius of the pitch, for wheels with more than 20 teeth; but for wheels with flat flanks with less than 21 teeth, the flanks should radiate towards the wheel centre, and the roots of the teeth should join the rim with a small curve. PROPORTIONS OF IRON TOOTHED WHEEL GEARING. See Fig. 23. Divide the pitch into 15 equal parts, then take the following proportions, viz. : From the pitch line of the wheel to the top of the tooth = 5 parts. Space between the teeth at the pitch line = 8 parts. Depth of feather or rib under the rim = 8 parts. Thickness of feather or rib under the rim = 7 parts. Thickness of the arm = 7 parts. Thickness of the feather or rib on the arm = 4 parts. Depth of the feather or Thickness of the feather or rib round the boss = 7 parts. Radius of curve at the root of the tooth = 2 parts. See Fig. 23. Radius of the point or face of the tooth of wheels with upwards of 20 teeth 11 parts. Radius of the point or face of the tooth of wheels with less than 21 teeth = 9 parts. Point below the pitch line of the wheel, from which the radius of the point or face of the tooth is struck = 1 part. = Breadth of the arm at the rim = 1 the pitch of the teeth, when the wheel face does not exceed 24 times the pitch in width; and 2 times the pitch for widths of face from 2 to 3 times the pitch; and 3 times the pitch for widths of face equal to 4 times the pitch. Breadth of the arm at the boss, should be increased by tapering the arm down from the rim to the boss, at the rate of inch per foot, on each side of the arm. The tendency of the strain being to twist the arm, the power acts with the greatest effect near the boss. Fig. 24 shows a form of tooth used for crab wheels, called knuckle gear. Fig. 25 shows the way to project a pair of bevel wheels, with their shafts at right angles, Fig. 25. Fig. 26 shows the way to project a pair of angle wheels, or bevel wheels, with their shafts at an angle of 65°. Fig. 26. Number of Arms.-Wheels under 2 feet diameter should have 4 arms; wheels from 2 to 7 feet 6 inches diameter, 6 arms; wheels from 8 to 12 feet, 8 arms; and wheels from 13 to 16 feet diameter, 10 arms. Width of Face.-The least width of face necessary to resist the full transverse strain on the tooth is 1 times the pitch, but for the sake of durability the width should not be less than 2 times the pitch; 24 times the pitch is the usual width. The following are good proportions : Pitch of wheel, in inches Width of face of wheel, in inches 2 2 2 3 3 3 4 4 5 5 6 7 8 9 10 11 12 15 Mortice Wheels.--The wood teeth of a mortice wheel are made thicker than the teeth of its iron fellow, to compensate for the difference in strength of the material; consequently the thickness of the iron tooth has to be reduced, and the length of tooth is also reduced so as to be in proportion to the thickness. Thickness of wood cog = 9 parts. Thickness of tooth of iron wheel or fellow 6 parts. From the pitch line to the top of tooth = 4 parts. From the pitch line to the bottom of the tooth = 5 parts. Thickness of the rim the pitch of the teeth multiplied by 1.2. Width of face of wheel same as for spur and bevel wheels given above. Width of mortice or shank of wood cog = inch narrower than the face of the tooth. Thickness of metal at each end of mortice = 6 parts. No clearance is required; the wood cogs should be trimmed to fit accurately between the iron teeth. When a pair of wheels of large diameter and quick speed work together, the larger one should have wood teeth, and the smaller one iron teeth. Wood teeth wear out sooner, but are not more liable to break than iron teeth. Hornbeam and crab-tree are the best woods for making the cogs, and when working they should be smeared with a mixture of soft soap and plumbago. Worm-Wheels.-When the shafts are at right angles, the action of a worm and worm wheel is similar to that of a rack and pinion, and the formation of the teeth at the section at the centre of a worm wheel, should be the same as those of a spur wheel of the same diameter, and the section of the thread of the worm should be the same as the teeth of a rack of the same pitch of tooth. Each revolution of the worm, turns the worm-wheel, to the extent of one tooth with a single thread worm, and 2 teeth with a double thread worm. The teeth of worm-wheels are made shorter than spur wheels. The amount the teeth are angled or skewed is equal to the pitch of the teeth. Thickness of tooth = 7 parts. Space between the teeth = 8 parts. From the pitch line to the top of the tooth = 4 parts. From the pitch line to the bottom of the tooth = Radius of the point or face of the tooth = 9 parts. Width of face of tooth = 1 times the pitch. 5 parts. Pitch of Small Wheels.-The pitch of change wheels and other small wheels, is reckoned on the diameter of the pitch circle, of the wheel instead of the circumference, and it is called the pitch per inch-thus 8 per inch, 10 per inch, and so on. To find the number of teeth, in a wheel of a given diameter and pitch per inch : Multiply the diameter of the pitch circle in inches, by the given pitch per inch. To find the diameter of the pitch circle, to contain a given number of teeth of a given pitch per inch : Divide the number of teeth by the required pitch per inch. TABLE 18.-PITCH PER INCH IN DIAMETER AND CIRCULAR PITCH |