(a) A spindle E turning in conical bearings. (b) A hollow drum or wheel F, with vernier, rigidly attached to the spindle. (c) A recording dial or counting disc G, geared to the spindle by a worm and worm wheel so as to rotate once for every ten revolutions of the drum. The periphery of the drum is graduated into equal divisions, numbered from 1 to 0, and each numbered division is further graduated into ten equal parts. The counting disc or dial has ten numbered graduations as shown in the cut. E FIG. 24. In tracing a diagram the instrument rests on the point P and the roller drum, the area being traced in a clockwise direction by the point T. When T has passed completely around the diagram, the reading is taken as follows. 1. Dial Reading. Each graduation mark on the dial denotes 10 units of area. Therefore there are ten times as many units of area as the number of units in the graduation mark just beyond the index 0 on the limb of the sliding piece. Thus the reading is 40 when the graduation mark 4 is just beyond the limb index 0. 2. Drum Reading. Each numbered graduation on the drum denotes 1 unit of area; each unnumbered graduation denotes .1 of a unit of area. Therefore the drum reading is the unnumbered graduation just beyond or coincident with the vernier zero. Thus 5.8 units of area is the drum reading when the 8th unnumbered graduation following 5 is beyond the vernier zero. 3. Vernier Reading. .01 of a unit of area. Each line on the vernier denotes Therefore if line 7 of the vernier coincides with a line of the drum, the vernier reading is .07 unit of area. 116. Problems. In solving the problems below whenever a measurement is required, arrange the work as follows: (1) Problem number and title. (2) Number and name of measured piece. (3) Name of instrument and the manufacturer. (4) A carefully drawn sketch showing the instrument reading. (5) Explanation of the reading by a statement of the bar vernier or other graduations, computation of vernier unit, and addition of scale readings. Any suitable instrument on the table may be used. If a piece is measured by more than one instrument, show sketch of reading on each. Handle the instruments carefully, do not hit one against another or against the pieces to be measured, adjust them lightly to the piece, and hold them steady while measurement is taken. 1. Examine and sketch a planimeter. Write the names of its various parts as indicated by letters on the sketch. 2. Describe the drum graduation. Each numbered graduation denotes how many units of area? Therefore each unnumbered graduation denotes what part of a unit of area? 3. The 5th unnumbered graduation following 4 is just beyond the zero of the vernier. What is the drum reading if the instrument is set so that I on the carrier bar, is aligned with L on the end of the sliding piece? 4. Set M on the carrier bar in alignment with L on the sliding piece. Turn the drum to record 6.3 units of area. What is the unit? 5. In a sketch show a vernier reading of .03 of a unit of area. 6. Sketch a disc or dial reading of 50 square inches. 7. What is the area when the scales are set as follows: Vernier, 2d line coincident, Drum, 8 and 3d unnumbered beyond zero vernier, Disc, 6 beyond limb index. 8. Determine the area of the diagram here shown, in square inches. FIG. 25. Reset the instrument and trace the area in metric units. Check both readings by reducing the square inches to square centimeters, and by reducing the square centimeters as read, to square inches. 9. On the work-book paper trace the outlines of not less than five of the irregularly shaped models at the desk and determine and tabulate the areas both in U. S. and metric units. 10. With the micrometer and the vernier caliper measure and tabulate the dimensions of such machine tools or models on the desk as may be assigned. CHAPTER VI TAPER 117. Definition. Taper has been variously defined, but as used in this chapter it is the difference in diameters in turned work and the difference in widths or thicknesses in unturned work, for any given length measured along the axis of the work. In the shop the problem of taper is always a question of how much the tail-stock of a lathe must be set over in order to turn a required taper. Two things and two only, determine the set-over or poppet movement as it is sometimes called: (1) The taper for any given unit of length, (2) The length of the work over all. Therefore in order to compute set-over, both these things must be known. 118. Formulas for Taper. Enter the following notation in the work-book: S-set-over in inches, t; taper per inch, tf-taper per foot, T = total taper, D=diameter at large end of taper, d = diameter at small end of taper, L= length of tapered part measured along the axis, (1) Formulate taper per inch in terms of taper per foot. (2) Formulate taper per foot in terms of taper per inch. (3) Formulate the total taper in terms of the diameters at the beginning and at the end of the taper. (4) Formulate the taper per inch in terms of the total taper and the length of the tapered part in inches. (5) Formulate the taper per inch in terms of the total taper and the length of the tapered part in feet. 119. Laws and Formulas for Set-over. There are two laws for the throw or set-over of the poppet head: (1) The set-over in inches equals the taper per inch multiplied by one-half the total length of the work in inches. (2) The set-over in inches equals one-half the difference. of the diameters at the ends of the taper, multiplied by the total length of the piece in inches and divided by the total length of the taper in inches. 118. Formulate each of these laws, using the notation in paragraph 120. Problems. Solve the following problems in the work-book, with a carefully drawn figure for each: 1. Standard Tapers. The following are the standard tapers: American, Brown & Sharpe, Jarno, 9/1 16 1// 2 to 1 foot, to 1 foot, except No. 10, which is .5161 to 1 ft. .6" to 1 foot. g" to 1 foot. Tabulate the data, and formulate, compute, and tabulate the taper per inch of each standard. 2. Determine what standard is used in the piece here shown in section, and compute the diameter at the small end. |