The cutting angle is illustrated in Fig. 1. For hard and brittle metals it is best to have this angle large; for soft tenacious metals it is best to have the cutting angle small. For example, the cutting angle usually varies from 75 for I brass and cast iron to 40 for steel and even less for copper and aluminum. Thin, keen tools with a small cutting angle will not stand up under severe cutting conditions as well as the blunt ones, because the blunt tools conduct heat away from the tip more effectively.

The rake angle is illustrated in Figs. 1 and 2. The dimension of the rake angle determines the amount of deformation or cold working of the metal chip removed. This cold working is diminished, and the heat generation is also diminished when the rake angle is increased. With large rake angles the forces acting between the chip, or turning, and the tool are more tangential than normal. It is desirable to diminish normal forces when cutting soft tenacious metals which tend to stick to the tool. For brass, the rake angle should be nearly zero-it may be even a little less than zero. (See Fig. 2.)

In the lathe the clearance angle is the angle included between the inner surface of the tool and the direction of relative motion at the tip of the tool. (See Fig. 1.) It is important, especially for boring, to have this angle great enough to prevent the heel of the tool from riding on the work. Clearance angles vary from 35 for soft tenacious metals to 10 for cast iron and brass.

The higher speeds of the lathe should be used for cutting brass except when turning castings or using the cutting-off tool. Unless the proper speed is used with the cutting-off tool, it will chatter. The proper speed and feed for this tool depends upon the size of the work, but in general these factors are to be determined by trial. A wooden plug inserted in a tube lessens chattering when the cutting-off tool is used. Fig. 3 shows a method of shaping a cutting-off tool which minimizes chattering. In this tool, side rake is balanced against asymmetry of the end so that the tool cuts squarely into the material. The point of the tool is ground on the side of the tool adjacent to the piece on which a finished edge is desired. The other piece may exhibit a slight burr.

For cutting steel, the speed should be as fast as the tool will stand without burning. For final cuts, however, a moderate speed gives a better finish.

Tools with a round nose give smooth finish cuts. Fig. 4 shows such a tool having about 10 clearance for cutting either brass or cast iron. The tool shown here has a slight double side rake, and it will cut in the direction of either the headstock or the tailstock. The function of a lubricant in cutting metals is in most cases primarily to cool the chip and tool to prevent sticking. Brass, bronze, and cast iron may be machined dry, (except in the operations of tapping, knurling, and polishing, for which machine oil is used). Soluble oil or lard oil is used for tenacious metals such as steel. Kerosene or turpentine is often used for aluminum. Milk may be used for copper. Lead and babbitt are turned dry, but they are oiled for filing, drilling, and threading.

In the four-jawed chuck the jaws are capable of independent adjustment. Therefore the accuracy of the centering of the work in a four-jawed chuck will depend upon the skill of the mechanic. With a dial indicator, and a little practice, work can be centered within 0.0002 of an inch in 5 or 10 minutes. The four-jawed chuck can also be used for holding eccentric or irregular work.

A dial indicator is a measuring device which can be mounted on the tool post in such a way that a projecting 1 inch lever or plunger will bear against the work as it turns. The dial then indicates the eccentricity of the work directly in thousandths of an inch. It can be supplied with attachments for reaching into holes. It is sometimes desirable, however, to center a piece of work on a prick-punch mark. In this case a pencil with a rubber eraser in its end may be used. The tip is inserted in the prick-punch mark, and the eraser is placed in the tailstock. The indicator is then placed to bear against the pencil, and as the work is rotated, it shows the eccentricity of the punch mark.

The primary operation which a lathe can perform is to execute a truly circular cut on a piece of material. This operation is accomplished by mounting the work directly on the spindle, or by mounting it between the spindle and the fixed bearing in the tailstock, so that it can be rotated against the tool. The perfection of roundness of the work depends in either case upon the perfection of the spindle bearings. If the spindle wobbles, the tool cut is, of course, not true.

The tool is mounted so that it can be moved in a horizontal plane passing nearly through the rotation axis. As the work rotates, the moving tool makes a continuum of circular cuts. These generate, in general, a conical surface. Of the possible cones two are of special interest in machine work: one, that of zero taper, is the cylinder, and the other, that of infinite taper, is the flat surface produced by a facing cut. All others come under the head of taper cutting.

Generation of a cylindrical surface is possible if the tool moves truly parallel to the axis of rotation of the work. In practice this is never the case, although in good lathes the error is usually negligible. When the work is mounted on the spindle, this parallel motion of the tool in respect to the axis is possible only if the ways of the carriage are parallel to the spindle, and if the ways themselves are straight. They are usually quite straight in the horizontal sense, but in the vertical sense the wearing of the ways tends to make them concave, with the result that the carriage moves up and down as it travels. For this reason it is always desirable to have the tip of the tool at the same height from the ways as the axis of rotation, for the error introduced by its up and down motion is then minimized.

If the work is mounted on dead centers, that is, if it is supported on conical points between the spindle and the tailstock and is turned by a dog bearing on the face plate, then truth of the work depends upon parallelism of the ways to a line between the two points, or centers. The tailstock is usually in error. It may be out of line laterally, a fault that one can usually correct by taking a trial cut, measuring the two ends, and setting the tailstock over again, using the adjusting screws which are usually provided. If the tailstock center is too high or too low, there is little to be done except to keep the tool at the average height of the two centers, thus minimizing the errors. Sometimes the ram, or plunger, in the tailstock which carries the center does not move parallel to the axis of the spindle. Thus, it may be well centered when the ram is retracted but not when the ram is extended. Sometimes the tip of the dead center, that is, the center in the tailstock, is bent or worn, in which case the remedy is obvious. If the live center, the one in the spindle, is untrue, it makes no difference unless the work is to be reversed and further machined. The live center is usually of soft steel, and for nice work it is common practice to true it by turning down its tip before mounting the work.

One way to turn a cylinder of uniform diameter is to lash the work to the face plate with thongs and to support it with a follower rest mounted on the carriage directly opposite the tool. This practice will insure uniformity of diameter but will not insure the straightness of the work. Sometimes in machining slender objects, one end of the work is held in a chuck while the other end is supported by the tailstock. This is bad practice, for the removal of the material from the work may relieve internal stresses, especially in cold-rolled steel and in rolled or drawn brass. As a result, when the work is removed from the lathe, it is found to be bent, the tailstock having supported the work in a flexed condition. The better practice is to support the work between centers, using a follower rest to prevent flexure. Occasionally, a second tool is mounted on the opposite side of the work and in an inverted position. This serves to preserve the uniform diameter of the work. In thread cutting it can also serve to reduce the drunkenness of a long screw thread, but it obviously requires very accurate setting of the two tools.

In boring cylindrical holes, if the work is mounted on the spindle, the truth of the work is solely dependent upon the truth of the ways. If the work is mounted on the carriage, however, a boring bar can be threaded through the rough bored hole and mounted between dead centers. A tool mounted on this bar describes a very nearly perfect circle, and as the work is fed over it, a hole of uniform diameter is automatically generated. The straightness of the ways determines the straightness of the hole, but parallelism (or the lack of it) of the ways to the axis of the spindle or to the axis of the boring is of no moment. For short holes a fly cutter may be mounted on the spindle, and the result will be the same as with a boring bar. In most work which can be mounted on the spindle the hole is bored to almost the required size, and then a reamer is passed through it to bring it to size and uniform diameter.

In turning long tapers, a taper attachment should be used, if one is available. If not, the work is mounted on dead centers, and the tailstock is set over the proper amount. The angle of taper is a function of both the amount of the setover and the length of the work. Since the length of the work, that is, the distance between the points where the axis of the work intersects the axes of the headstock and the tailstock, cannot be accurately measured, it is impossible to predetermine the exact angle of the taper which will be cut. Consequently, the amount of setover of the tailstock must be determined by trial.

The compound-slide rest is used to cut short tapers. It is usually the least accurate feature of the lathe, so that high precision with it is not to be expected. The graduations l which are used to determine the angle of motion are generally very inaccurate and should be regarded only as something on which to base an estimate. The slide, because of its shortness, is usually not straight. It can nevertheless be used successfully for turning and boring short tapers to match, such as for lug valves and stopcocks, since the errors of curvature can be made to match. The female part is first mounted on the spindle, and the tapered hole is bored with the boring tool cutting on the far side of the hole, the lathe running backwards. When this is done, the face plate or chuck holding the piece should be removed bodily from the lathe, leaving the work undisturbed. This will permit the replacing of it for further operations, if necessary, without having to recenter the work. The male taper is then mounted, preferably between dead centers, and turned, the compound rest being used as it was set for boring, thereby insuring that the tapers will match. If the slide is not straight, the tool should be set so that its tip overhangs the slide as much as did the boring tool for the female part. If the same part of the slide is used, the errors in one taper will match those of the other. The male part, being on dead centers, may be removed from the lathe and tried in the female part and replaced for further machining, until the desired fit is obtained. For the final fit they should be lapped together with Bon Aim or some other suitable abrasive. (See Fig. 5.)

We cannot go into the arts of filing and scraping. They are treated in many of the standard works on machine practice and tool making. Filing and scraping afford the machinist opportunity for the fullest display of his manual skill. Both are, like the figuring of an optical surface, a process of delicate testing alternated with the careful manual removal of metal in order to obtain the desired surface. In filing, the testing is usually executed with the ordinary measuring instruments-the straightedge, the square, and the calipers. In scraping, the testing is done with Prussian blue, and always the two parts are scraped until an intimate and complete contact between them is obtained. Testing flats are made three at a time. The three plates are each scraped until any one of them will make satisfactory contact with either of the other two.

From the above discussion it will be noted that the limits of accuracy characteristic of the different operations can be roughly classified. There are, on the one hand, operations such as the generation of a circular cut, or the fitting of a taper to a cone by lapping, which are automatically accurate to a high degree. There are other operations which depend upon the truth built into the machine, for example, the cutting of a straight cylinder in a lathe or the milling of ways. Finally, there are those operations which depend upon the skill of the machinist. Examples are the mounting of work in the machine in order to have new cuts consistent with former ones, and the execution of filing operations to a line. There are many opportunities for the machinist to use his ingenuity to advantage in the attainment of precision. We have already mentioned examples in which the cuts on work in the three-jawed chuck are all done at one mounting, and in which the same part of the compound-slide ways are used for cutting male and female tapers, and so forth.

Soft soldering. Good soldered joints require thorough cleaning and, in addition, the use of a so-called "flux." The function of the flux is to etch the surface free of contamination and protect it, as well as the solder, from oxidation.

The most useful flux for soft soldering is made from a mixture of 2 parts zinc chloride to 1 part ammonium chloride dissolved in a minimum amount of water. This flux is often spattered about when the soldering copper is applied, and unless it is thoroughly removed, it promotes corrosion, especially on iron. If the work is washed with soda solution, the corrosive action of zinc chloride and acid flux is, in large measure, neutralized. In addition to corrosion, the spattered flux may also give rise to electrically conducting surface layers on parts of the apparatus where high insulation is required. For such work, a solution of rosin in alcohol is an excellent nonconducting flux (for soldering copper wires). Also, so-called- noncorrosive pastes are available at most hardware stores. These are made from vaseline (90 per cent) and ammonium chloride (10 per cent).

Three things are needed for successful soldering. In addition to cleanliness and flux, sufficient heat is required. Some soldering is done entirely with a flame, while some is done entirely with a soldering iron. However, the nicest jobs are done with a combination of these, especially when the work is on complicated apparatus and when several relatively large parts are to be joined together. A soft flame played over the surface of the whole work supplies basic heat, keeping the work at a temperature of 125 to 150C. The higher temperature that is required for soldering is then obtained locally by the application of the hot soldering copper. This soldering procedure minimizes the danger of melting off parts previously joined, a possibility to contend with when a flame alone is used. Also, the amount of solder added and the extent to which the solder flows is more easily controlled with the soldering copper than with a flame alone. On the other hand, the use of a flame to supply basic heat facilitates heating with the soldering iron and increases the effectiveness with which the molten solder can be made to wet the work and flow as desired.

A seam to be soldered is first "tinned" at a high heat, and then at a lower temperature a fillet is made with the help of the soldering copper. The purpose of the fillet is to insure that the solder does not draw away and allow an opening to form in the seam as it cools. Fig. 6 shows how a recess cut in an inconspicuous place will serve the same purpose as a fillet.

Many of the alloy steels, as well as cast iron, magnesium, aluminum, tungsten, and molybdenum, cannot be easily soft-soldered.

Hard soldering. Although there are some intermediate solders which melt at temperatures between the melting temperatures of soft solder and silver solder, they have never had wide use. These solders may be useful in special cases, but for general work they do not have the reputation of silver solder, which, for strength, ductility, wetting power, penetration, and resistance to corrosion, is unsurpassed.

The heat for silver soldering is obtained with the oxyacetylene torch for large work and with an air-gas or oxygen-gas torch for small work. The metal to be soldered is preheated, with the application of the flame favoring those parts which are most massive and which have the highest heat conduction. A general preheating of the whole work prevents warping and also facilitates the intense final heating of the joints that are to be brazed.

The regions to be wet and joined by the silver alloy are painted with a thin paste mixture of 5 to 10 parts of powdered borax, 1 part powdered boracic acid, and water. Dry borax can also be used. The use of paste has the advantage of neatly defining the areas which will be wet with the alloy. The alloy will spread over the surface only to the extent that it has been brushed with the paste. The flux for stainless steel is made from 1 part borax and 1 part boracic acid, and these powders are wet with a saturated zinc chloride solution.

For large work the silver solder is applied in the form of wire or rod after the work is well fluxed and has attained the proper temperature. The solder wire should also be coated with flux. For small work small pieces of silver solder, either short lengths of wire or bits of sheet solder, may be applied, together with flux, before the work is heated. When the parts to be joined fit together neatly, only a film of the silver solder is needed to give a good joint. The use of more solder is wasteful. Charcoal (medicated so that it does not burn) and asbestos blocks can be used for holding the work and for proper positioning of the parts to be joined. (See Fig. 7.)

After the joint is made, the flux is best removed by quenching the work in cold water. This procedure is not recommended for large parts or for those requiring high accuracy, since some warping is always produced by quenching. Borax flux will dissolve slowly in hot dilute sulphuric acid in cases in which such treatment can be applied.

Spot welding. Another much-used method of joining metals in the laboratory is spot welding with an electric current. Ordinarily, the spot-welding apparatus obtains its electric energy from a transformer with a capacity of 1 or 2 kilowatts. The primary winding is connected to the alternating-current supply and it is equipped with taps or is connected in series with a rheostat to control the welding current. The secondary winding is usually a few turns of heavy copper wire on rod (about 5/32 inch in diameter), with the winding ratio such that the secondary delivers about 6 volts. The heavy copper winding terminates at two copper electrodes, which serve to apply the potential to the joint to be welded. The welding is effected by the Joule heat generated between the metal surfaces to be welded when the current is passed in the primary of the transformer for a fraction of a second. The heating produced is regulated by the rheostat and by the length of the time that the switch is closed. The electrodes are brought in contact with the work, and a definite pressure is applied, usually by means of a foot pedal. The pressure and duration of the current are important. Inadequate pressure results in burning and "spitting" at the joint, while too much pressure decreases the joint resistance and consequently the heating action.

Metals which weld together best are those of similar melting temperature . and heat conduction K. Table I shows the relative spot-welding characteristics of the different laboratory metals as determined by Espe and Knoll. Wires with different melting temperatures and heat conductivities weld together best when their diameters d are related as follows:

. (1)

Instrument design. Defections. The subject of instrument design is one to which a great many authors have given their attention. We will treat of the general aspects of the subject, such as the application of the principle of kinematical design and the calculation of deflections and flexures as they pertain to instruments.

When an element of an instrument is subjected to varying forces that are due to uneven friction between the moving parts, the designer must be able to determine the effect of these variations.

Such problems are often difficult to solve precisely, owing to the complex geometry involved. However, it is often sufficient for the designer to know the answer to within 50 or 100 per cent. Estimations to this accuracy are often possible if one makes an ingenious choice of a simple geometric shape whose deflection may be taken as a first approximation to the deflection of the part in question. The formulas for determining the deflections of the simple geometrical shapes, variously loaded and supported, are given in Fig. 8. The moments of inertia of the cross section of beams about the axis passing through their center of gravity are required for these calculations. The moments of inertia for rectangular bars, rods, tubes, and I-beams are given in Fig. 9.

Fig. 10 gives the formulas for calculating the collapsing pressures for spherical and cylindrical shells and plane circular plates loaded with an external pressure. These formulas are useful for designing vacuum tanks.

In making apparatus, the physicist seldom needs, for reasons of economy, to limit the mass of the instrument. Accordingly, for the construction of spectrometers and other instruments, which require very accurate relative positioning of the various elements, the physicist often uses an I-beam of generous proportions and excessive strength. If the instrument is a spectrometer, one or more of the faces of the I-beam are planed to afford a base for the mounting of lenses, slits, and a prism or grating table.

Kinematical design. The different ways in which the principle of kinematical design may be used for positioning the various elements of an instrument are illustrated by Figs. 11 to 23.

According to the principle of kinematical design, a body must have at least (6-n) points in contact with a second reference body if it is to have only n degrees of freedom, relative to the reference body. Fig. 11 shows a spherical ball held in a trihedral cavity in a plate by the force of gravity. Relative to the plate, the center of the ball is uniquely defined by the three contacts with the plate. There remain three degrees of freedom of rotation for the ball about three mutually perpendicular axes.

The principle of kinematical design is further illustrated by Fig. 12, which shows a tripod with a ball at the extremity of each of its legs. The plate on which the tripod rests has a V-groove and a trihedral cavity in its surface. One ball rests in the cavity, the second in the groove, and the third on the plane surface of the plate. When one of the balls is in the trihedral cavity, then, as far as translations are concerned, the tripod may be regarded as fixed by the three points of bearing between the ball and the sides of the trihedral cavity. If, however, a second foot rests in the V-groove, there are two more point contacts between the ball and the sides of the groove. The tripod is now restrained by five point contacts and has, accordingly, one degree of freedom, which is a rotation about an axis passing through the centers of the constrained balls. The tripod's position is finally completely determined when the third leg comes to rest on the plane, giving the sixth point of contact.

Fig. 13 shows another way in which the tripod may have its position uniquely defined relative to a base plate. Here the terminal balls of the tripod legs rest in radial grooves machined in the plate. Each ball makes two contacts with the base plate, making a total of six contacts.

These applications of kinematical design are often useful, as, for example, when the base plate is attached to an instrument and the tripod carries some element which must be repeatedly removed and replaced in exactly the same position. The application shown in Fig. 13 has the advantage over the one shown in Fig. 12 that the centers of the table and the base plate have the same relation to each other laterally, independent of difference in their temperature expansion.

Fig. 14 shows a case in which one degree of freedom, that is, of translation, is achieved by placing two balls in V-grooves, with the third on a flat surface. Five contacts between the plate and the tripod are involved.

Other examples of the achievement of one degree of freedom by five appropriate contacts are shown in Figs. 15 to 19. The method shown in Fig. 15, and especially Fig. 16, is often used for typewriter carriages.

Figs. 17 and 18 are more or less self-explanatory. In Fig. 17 gravity acts as the so-called locator. The locator, as its name implies, insures that the bearing points remain in contact. The arrangement shown in Fig. 18 is used by the Leitz Company for the vertical motion of their microscope tube.

Fig. 19 shows a simple and easily constructed device used to move a Foucault testing knife edge. Its design is kinematical.

In most of the examples given here the contacting areas are small. Accordingly, the wear on them may be great. Often, in practice, point contacts are extended to line contacts as shown in Figs. 20, 21, and 22. Or, point contacts may be extended to surface contacts, as shown in Fig. 24. Even so, one still retains substantially all of the virtues of the more rigorous type of design, where contact areas are small. And, in addition, wear is materially reduced.

Fig. 20 shows how one degree of freedom is achieved for focusing the reading microscope of the Cambridge Instrument Company's comparator. Fig. 21 shows a type of support which might be used for an optical bench. For example, with it a lens holder may be moved back and forth along two horizontal rods and clamped at any desired position.

Fig. 22 illustrates how one degree of rotation may be obtained. The rod involved here may also translate along its axis unless a constraint is applied, as, for example, a fixed ball in contact with the end of the rod.

Fig. 23 shows how geometrical design may be applied to a tangent screw.

Generally, the construction of an instrument is easier if the design follows the kinematical principle than it is when constructed in accordance with the practices of conventional machine design. Conventional designs, in which one uses cones, ways, and lapped journals to achieve one degree of freedom, either lead to overconstraint in the position of the 3 parts or they are not uniquely defined. Only five contacts are required to constrain the parts as desired; any more are redundant, like the fourth leg of a stool.

Although one degree of translation is achieved easily by following the kinematical principle, as we have seen in Figs. 14 to 21, the conventional cone, when properly lapped, affords a better construction for the achievement of one degree of freedom of rotation.

One feature of the kinematical design which distinguishes it is exemplified by the figures illustrating one degree of translation, such as Fig. 17; although the motion may not be straight, owing to imperfect construction, still it is possible to predict the deviation from straightness from the measured errors of construction.

Steel balls are often used in kinematical design. They are obtainable matched in size to 0.00005 inch, and in addition they are truly spherical to this accuracy. Precision balls can be obtained which are spherical to within a tenth of the limit mentioned above.

Fig. 25 shows a good design of an adjustable mirror cell. It will be noted that this cell has four adjusting screws. Because it facilitates the making of the adjustments, this number is recommended instead of three, in spite of the fact that one of the screws is not needed, and its use leads to strain in the cell.

Vibrationless supports. Many delicate instruments, and particularly high-sensitivity galvanometers, must be protected from the vibrations produced by automobiles in the street, elevators, machinery in the basement, and vibrations from other sources which are always present in a building. In most cases, the vertical components of these vibrations are harmless and can be ignored. Although the effect of the horizontal components on an instrument such as a galvanometer may be small, especially if the moving system is dynamically balanced on its suspension fiber, it is, however, necessary for the most delicate work to eliminate these horizontal components as far as possible by mounting the instrument on a vibrationless support.

The problems involved in obtaining a suitable support are similar to some of the problems encountered in designing a seismograph, and anyone planning to develop a special vibrationless support of his own design will find the literature on seismographs helpful. Briefly, all vibrationless supports can be considered as an oscillating system loosely coupled mechanically to the walls, ceiling, or floor of the room. The shielding effect of the support is determined by the resonance between it and the wall. For example, if the natural period of oscillation of the support is long compared to that of the vibrations of the wall, it will be so far out of resonance that its response will be feeble. It is, of course, necessary that the support be damped so that its own natural oscillations will be suppressed. Also, it must be protected from air currents. Naturally, one selects the most stable place for mounting the vibrationless support. A pier which has a separate foundation from the rest of the building is ideal.

A modification of the Julius suspension has been designed by R. Müller. This suppresses only the horizontal vibrations. A simplified construction of his design, which has been used successfully by the author, is shown in Fig. 19, "Vacuum Thermopiles and the Measurement of Radiant Energy". The support is loaded so that it has a period of about 2 seconds. This support uses the internal friction of oil in pie pans to dampen it. Light oil is used, and the pans are filled to the height which is observed to produce maximum damping of the natural oscillations of the system. The advantages of this support over a Julius suspension are that it can be mounted on a shelf in the corner of the room and easily boxed in to protect it from air currents, whereas a Julius suspension must be hung from the ceiling. It is more difficult to make adjustments of the galvanometer with the Julius suspension than with this support because the Julius suspension is not easily clamped. The Muller support can easily be clamped for making adjustments of the galvanometer by dropping two tapered pins in the holes indicated in the figure.

One type of vibrationless support is made by placing a large mass, say a slab of stone, on a pile of newspapers. Here the shearing friction in the papers damps horizontal oscillations. Another method involves supporting the machine by steel springs wound with friction tape for damping.

Other methods of eliminating vibrations involve supporting apparatus on tennis balls or sponge rubber. These are particularly useful for stopping vibrations near their source, as, for example, preventing vibrations from vacuum pumps from being transmitted into the walls and floor of the building. The damping in this case is due to the internal friction of the rubber.