It is often necessary, in connection with lathe work, to turn parts tapering instead of straight or cylindrical. If the work is mounted between the centers, one method of turning a taper is to set the tailstock center out of alignment with the headstock center. When both of these centers are in line, the movement of the tool is parallel to the axis of the work and, consequently, a cylindrical surface is produced; but if the tailstock _h_{1}_ is set out of alignment, as shown in Fig. 1, the work will then be turned tapering as the tool is traversed from _a_ to _b_, because the axis _x--x_ is at an angle with the movement of the tool. Furthermore the amount of taper or the difference between the diameters at the ends for a given length, will depend on how much center _h_{1}_ is set over from the central position.

[Ill.u.s.tration: Fig. 1. Taper Turning by the Offset-center Method]

[Ill.u.s.tration: Fig. 2. Examples of Taper Work]

The amount of taper is usually given on drawings in inches per foot, or the difference in the diameter at points twelve inches apart. For example, the taper of the piece shown at _A_, Fig. 2, is 1 inch per foot, as the length of the tapering surface is just twelve inches and the difference between the diameters at the ends is 1 inch. The conical roller shown at _B_ has a total length of 9 inches and a tapering surface 6 inches long, and in this case the taper per foot is also 1 inch, there being a difference of 1/2 inch in a length of 6 inches or 1 inch in twice that length. When the taper per foot is known, the amount that the tailstock center should be set over for turning that taper can easily be estimated, but it should be remembered that the setting obtained in this way is not absolutely correct, and is only intended to locate the center approximately. When a taper needs to be at all accurate, it is tested with a gage, or by other means, after taking a trial cut, as will be explained later, and the tailstock center is readjusted accordingly. There are also more accurate methods of setting the center, than by figuring the amount of offset, but as the latter is often convenient this will be referred to first.

=Setting Tailstock Center for Taper Turning.=--Suppose the tailstock center is to be set for turning part _C_, Fig. 2, to a taper of approximately 1 inch per foot. In this case the center would simply be moved toward the front of the machine 1/2 inch, or one-half the required taper per foot, because the total length of the work happens to be just 12 inches. This setting, however, would not be correct for all work requiring a taper of 1 inch per foot, as the adjustment depends not only on the _amount_ of the taper but on the _total length_ of the piece.

[Ill.u.s.tration: Fig. 3. Detail View of Lathe Tailstock]

For example, the taper roller _B_ has a taper of 1 inch per foot, but the center, in this case, would be offset less than one-half the taper per foot, because the total length is only 9 inches. For lengths longer or shorter than twelve inches, the taper per inch should be found first; this is then multiplied by the _total_ length of the work (not the length of the taper) which gives the taper for that length, and one-half this taper is the amount to set over the center. For example, the taper per inch of part _B_ equals 1 inch divided by 12 = 1/12 inch. The total length of 9 inches multiplied by 1/12 inch = 3/4 inch, and 1/2 of 3/4 = 3/8, which is the distance that the tailstock center should be offset.

In this example if the taper per foot were not known, and only the diameters of the large and small ends of the tapered part were given, the difference between these diameters should first be found (2-1/2-2 = 1/2); this difference should then be divided by the length of the taper (1/2 6 = 1/12 inch) to obtain the taper per inch. The taper per inch times the _total_ length represents what the taper would be if it extended throughout the entire length, and one-half of this equals the offset, which is 3/8 inch.

=Example of Taper Turning.=--As a practical example of taper turning let us a.s.sume that the piece A, Fig. 4, which has been centered and rough-turned as shown, is to be made into a taper plug, as indicated at _B_, to fit a ring gage as at _C_. If the required taper is 1-1/2 inch per foot and the total length is 8 inches, the tailstock center would be offset 1/2 inch.

[Ill.u.s.tration: Fig. 4. Taper Plug and Gage]

To adjust the tailstock, the nuts _N_ (Fig. 3) are first loosened and then the upper part _A_ is shifted sidewise by turning screw _S_. Scales are provided on some tailstocks for measuring the amount of this adjustment; if there is no scale, draw a line across the movable and stationary parts _A_ and _B_, when the tailstock is set for straight turning. The movement of the upper line in relation to the lower will then show the offset, which can be measured with a scale.

When the adjustment has been made, nuts _N_ are tightened and the part to be turned, with a dog attached, is placed between the centers the same as for straight turning. The taper end is then reduced by turning, but before it is near the finished size, the work is removed and the taper tested by inserting it in the gage. If it is much out, this can be felt, as the end that is too small can be shaken in the hole. Suppose the plug did not taper enough and only the small end came into contact with the gage, as shown somewhat exaggerated at _D_; in that case the center would be shifted a little more towards the front, whereas if the taper were too steep, the adjustment would, of course, be in the opposite direction. A light cut would then be taken, to be followed by another test. If the plug should fit the gage so well that there was no perceptible shake, it could be tested more closely as follows: Draw three or four chalk lines along the tapering surface, place the work in the gage and turn it a few times. The chalk marks will then show whether the taper of the plug corresponds to that of the gage; for example, if the taper is too great, the marks will be rubbed out on the large end, but if the taper is correct, the lines throughout their length will be partially erased.

[Ill.u.s.tration: Fig. 5. Setting Work for Taper Turning by use of Caliper Gage]

Another and more accurate method of testing tapers is to apply a thin coat of Prussian-blue to one-half of the tapering surface, in a lengthwise direction. The work is then inserted in the hole or gage and turned to mark the bearing. If the taper is correct, the bearing marks will be evenly distributed, whereas if the taper is incorrect, they will appear at one end. Tapering pieces that have to be driven tightly into a hole, such as a piston-rod, can be tested by the location of the bearing marks produced by actual contact.

After the taper is found to be correct, the plug is reduced in size until it just enters the gage as at _C_. The final cut should leave it slightly above the required size, so that a smooth surface can be obtained by filing. It should be mentioned that on work of this kind, especially if great accuracy is required, the final finish is often obtained by grinding in a regular grinding machine, instead of by filing. When this method is employed, a lathe is used merely to rough-turn the part close to size.

[Ill.u.s.tration: Fig. 6. Side View showing Relative Positions of Gage and Work]

When the amount that the tailstock center should be offset is determined by calculating, as in the foregoing example, it is usually necessary to make slight changes afterward, and the work should be tested before it is too near the finished size so that in case one or more trial cuts are necessary, there will be material enough to permit this. When there are a number of tapered pieces to be turned to the same taper, the adjustment of the tailstock center will have to be changed unless the total length of each piece and the depth of the center holes are the same in each case.

=Setting the Tailstock Center with a Caliper Tool.=--Another method of setting the tailstock center for taper turning is ill.u.s.trated in Fig. 5.

The end of an engine piston-rod is to be made tapering as at A and to dimensions _a_, _b_, _c_ and _d_. It is first turned with the centers in line as at _B_. The end _d_ is reduced to diameter _b_ up to the beginning of the taper and it is then turned to diameter _a_ as far as the taper part _c_ extends. The tailstock center is next set over by guess and a caliper tool is clamped in the toolpost. This tool, a side view of which is shown in Fig. 6, has a pointer _p_ that is free to swing about pivot _r_, which should be set to about the same height as the center of the work. The tailstock center is adjusted until this pointer just touches the work when in the positions shown by the full and dotted lines at _C_, Fig. 5; that is, until the pointer makes contact at the beginning and end of the taper part. The travel of the carriage will then be parallel to a line _x--x_, representing the taper; consequently, if a tool is started at the small end, as shown by the dotted lines at _D_, with the nose just grazing the work, it will also just graze it when fed to the extreme left as shown. Of course, if the taper were at all steep, more than one cut would be taken.

[Ill.u.s.tration: Fig. 7. Obtaining Tailstock Center Adjustment by use of Square]

If these various operations are carefully performed, a fairly accurate taper can be produced. The straight end _d_ is reduced to size after the tail-center is set back to the central position. Some mechanics turn notches or grooves at the beginning and end of the tapering part, having diameters equal to the largest and smallest part of the taper; the work is then set by these grooves with a caliper tool. The advantage of the first method is that most of the metal is removed while the centers are in alignment.

[Ill.u.s.tration: Fig. 8. Second Step in Adjusting Tailstock Center by use of Square]

=Setting the Tailstock Center with a Square.=--Still another method of adjusting the tailstock for taper turning, which is very simple and eliminates all figuring, is as follows: The part to be made tapering is first turned cylindrical or straight for 3 or 4 inches of its length, after the ends have been properly centered and faced square. The work is then removed and the tailstock is shifted along the bed until the distance _a--b_ between the extreme points of the centers is exactly 1 foot. The center is next offset a distance _b--c_ equal to one-half the required taper per foot, after which a parallel strip _D_, having true sides, is clamped in the toolpost. Part _D_ is then set at right angles to a line pa.s.sing from one center point to the other. This can be done conveniently by holding a 1-foot square (preferably with a sliding head) against one side of _D_ and adjusting the latter in the toolpost until edge _E_ of the square blade is exactly in line with both center points.

After part _D_ is set, it should be clamped carefully to prevent changing the position. The angle between the side of _D_ and an imaginary line which is perpendicular to axis _a--b_ is now equal to one-half the angle of the required taper.

The axis of the part to be turned should be set parallel with line _E_, which can be done by setting the cylindrical surface which was previously finished, at right angles to the side of _D_. In order to do this the work is first placed between centers, the tailstock being shifted along the bed if necessary; the tail-center is then adjusted laterally until the finished cylindrical surface is square with the side of _D_. A small try-square can be used for testing the position of the work, as indicated in Fig. 8. If the length of the work is less than 1 foot, it will be necessary to move the center toward the rear of the machine, and if the length is greater than 1 foot, the adjustment is, of course, in the opposite direction.

[Ill.u.s.tration: Fig. 9. A Lathe Taper Attachment]

=The Taper Attachment.=--Turning tapers by setting over the tailstock center has some objectionable features. When the lathe centers are not in alignment, as when set for taper turning, they bear unevenly in the work centers because the axis of the work is at an angle with them; this causes the work centers to wear unevenly and results in inaccuracy.

Furthermore, the adjustment of the tailstock center must be changed when turning duplicate tapers, unless the length of each piece and the depth of the center holes are the same. To overcome these objections, many modern lathes are equipped with a special device for turning tapers, known as a taper attachment, which permits the lathe centers to be kept in alignment, as for cylindrical turning, and enables more accurate work to be done.

[Ill.u.s.tration: Fig. 10. Sectional View of Taper Attachment]

Taper attachments, like lathes, vary some in their construction, but all operate on the same principle. An improved form of taper attachment is ill.u.s.trated in Figs. 9 and 10. Fig. 9 shows a plan view of a lathe carriage with an attachment fitted to it, and Fig. 10 a sectional view.

This attachment has an arm _A_ on which is mounted a slide _S_ that can be turned about a central pivot by adjusting screw _D_. The arm _A_ is supported by, and is free to slide on, a bracket _B_ (see also sectional view) that is fastened to the carriage, and on one end of the arm there is a clamp _C_ that is attached to the lathe bed when turning tapers. On the slide _S_ there is a shoe _F_ that is connected to bar _E_ which pa.s.ses beneath the toolslide. The rear end of the cross-feed screw is connected to this bar, and the latter is clamped to the toolslide when the attachment is in use.

When a taper is to be turned, the carriage is moved opposite the taper part and clamp _C_ is fastened to the bed; this holds arm _A_ and slide _S_ stationary so that the carriage, with bracket _B_ and shoe _F_, can be moved with relation to the slide. If this slide _S_ is set at an angle, as shown, the shoe as it moves along causes the toolslide and tool to move in or out, but if the slide is set parallel to the carriage travel, the toolslide remains stationary. Now if the tool, as it feeds lengthwise of the work, is also gradually moved crosswise, it will turn a taper, and as this crosswise movement is caused by the angularity of slide _S_, different tapers are obtained by setting the slide to different positions.

By means of a graduated scale _G_ at the end of slide _S_, the taper that will be obtained for any angular position of the slide is shown. On some attachments there are two sets of graduations, one giving the taper in inches per foot and the other in degrees. While tapers are ordinarily given in inches per foot on drawings, sometimes the taper is given in degrees instead. The attachment is set for turning tapers by adjusting slide _S_ until pointer _p_ is opposite the division or fractional part of a division representing the taper. The whole divisions on the scale represent taper in inches per foot, and by means of the sub-divisions, the slide can be set for turning fractional parts of an inch per foot.

When slide _S_ is properly set, it is clamped to arm _A_ by the nuts _N_. Bar _E_ is also clamped to the toolslide by bolt _H_, as previously stated. The attachment is disconnected for straight turning by simply loosening clamp _C_ and the bolt _H_.

=Application of Taper Attachment.=--Practical examples of lathe work, which ill.u.s.trate the use of the taper attachment, are shown in Figs, 11 and 12. Fig. 11 shows how a taper hole is bored in an engine piston-head, preparatory to reaming. The casting must be held either in a chuck _C_ or on a faceplate if too large for the chuck. The side of the casting (after it has been "chucked") should run true, and also the circ.u.mference, unless the cored hole for the rod is considerably out of center, in which case the work should be shifted to divide the error.

The side of the casting for a short s.p.a.ce around the hole is faced true with a round nose turning tool, after which the rough-cored hole is bored with an ordinary boring tool _t_, and then it is finished with a reamer to exactly the right size and taper.

This particular taper attachment is set to whatever taper is given on the drawing, by loosening nuts _N_ and turning slide _S_ until pointer _P_ is opposite that division on the scale which represents the taper.

The attachment is then ready, after bolt _H_ and nuts _N_ are tightened, and clamp _C_ is fastened to the lathe bed. The hole is bored just as though it were straight, and as the carriage advances, the tool is gradually moved inward by the attachment. If the lathe did not have a taper attachment, the taper hole could be bored by using the compound rest.

[Ill.u.s.tration: Fig. 11. Lathe with Taper Attachment arranged for Boring Taper Hole in Engine Piston]

The hole should be bored slightly less than the finish size to allow for reaming. When a reamer is used in the lathe, the outer end is supported by the tailstock center and should have a deep center-hole. The lathe is run very slowly for reaming and the reamer is fed into the work by feeding out the tailstock spindle. The reamer can be kept from revolving, either by attaching a heavy dog to the end or, if the end is squared, by the use of a wrench long enough to rest against the lathe carriage. A common method is to clamp a dog to the reamer shank, and then place the tool-rest beneath it to prevent rotation. If the shank of a tool is clamped to the toolpost so that the dog rests against it, the reamer will be prevented from slipping off the center as it tends to do; with this arrangement, the carriage is gradually moved along as the tailstock spindle is fed outward. Some reamers are provided with stop-collars which come against the finished side of the casting when the hole has been reamed to size.

After the reaming operation, the casting is removed from the chuck and a taper mandrel is driven into the hole for turning the outside of the piston. This mandrel should run true on its centers, as otherwise the outside surface of the piston will not be true with the bored hole. The driving dog, especially for large work of this kind, should be heavy and stiff, because light flexible clamps or dogs vibrate and frequently cause chattering. For such heavy work it is also preferable to drive at two points on opposite sides of the faceplate, but the driving pins should be carefully adjusted to secure a uniform bearing on both sides.

The foregoing method of machining a piston is one that would ordinarily be followed when using a standard engine lathe, and it would, perhaps, be as economical as any if only one piston were being made; but where such work is done in large quant.i.ties, time could be saved by proceeding in a different way. For example, the boring and reaming operation could be performed much faster in a turret lathe, which is a type designed for just such work, but a turret lathe cannot be used for as great a variety of turning operations as a lathe of the regular type. There are also many other cla.s.ses of work that can be turned more quickly in special types of machines, but as more or less time is required for arranging these special machines and often special tools have to be made, the ordinary lathe is frequently indispensable when only a few parts are needed; in addition, it is better adapted to some turning operations than any other machine.

Fig. 12 ill.u.s.trates how a taper attachment would be used for turning the taper fitting for the crosshead end of an engine piston-rod. Even though this taper corresponds to the taper of the hole in the piston, slide _S_ would have to be reset to the corresponding division on the opposite side of the central zero mark, because the taper of the hole decreased in size during the boring operation, whereas the rod is smallest at the beginning of the cut, so that the tool must move outward rather than inward as it advances. The taper part is turned practically the same as a cylindrical part; that is, the power feed is used and, as the carriage moves along the bed, the tool is gradually moved outward by the taper attachment.

[Ill.u.s.tration: Fig. 12. Taper Attachment Set for Turning Taper End of Piston-rod]

If the rod is being fitted directly to the crosshead (as is usually the case), the approximate size of the small end of the taper could be determined by calipering, the calipers being set to the size of the hole at a distance from the shoulder or face side of the crosshead, equal to the length of the taper fitting on the rod. If the crosshead were bored originally to fit a standard plug gage, the taper on the rod could be turned with reference to this gage, but, whatever the method, the taper should be tested before turning too close to the finished size. The test is made by removing the rod from the lathe and driving it tightly into the crosshead. This shows how near the taper is to size, and when the rod is driven out, the bearing marks show whether the taper is exactly right or not. If the rod could be driven in until the shoulder is, say, 1/8 inch from the crosshead face, it would then be near enough to finish to size by filing. When filing, the lathe is run much faster than for turning, and most of the filing should be done where the bearing marks are the heaviest, to distribute the bearing throughout the length of the taper. Care should be taken when driving the rod in or out, to protect the center-holes in the ends by using a "soft" hammer or holding a piece of soft metal against the driving end.

[Ill.u.s.tration: Fig. 13. Tool Point should be in same Horizontal Plane as Axis of Work for Taper Turning]

After the crosshead end is finished, the rod is reversed in the lathe for turning the piston end. The dog is clamped to the finished end, preferably over a piece of sheet copper to prevent the surface from being marred. When turning this end, either the piston reamer or the finished hole in the piston can be calipered. The size and angle of the taper are tested by driving the rod into the piston, and the end should be fitted so that by driving tightly, the shoulder will just come up against the finished face of the piston. When the taper is finished, the attachment is disengaged and a finishing cut is taken over the body of the rod, unless it is to be finished by grinding, which is the modern and most economical method.

=Height of Tool when Turning Tapers.=--The cutting edge of the tool, when turning tapers, should be at the same height as the center or axis of the work, whether an attachment is used or not. The importance of this will be apparent by referring to Fig. 13. To turn the taper shown, the tool _T_ would be moved back a distance _x_ (a.s.suming that an attachment is used) while traversing the length _l_. As an ill.u.s.tration, if the tool could be placed as high as point _a_, the setting of the attachment remaining as before, the tool would again move back a distance _x_, while traversing a distance _l_, but the large end would be under-sized (as shown by the dotted line) if the diameters of the small ends were the same in each case. Of course, if the tool point were only slightly above or below the center, the resulting error would also be small. The tool can easily be set central by comparing the height of the cutting edge at the point of the tool with one of the lathe centers before placing the work in the lathe.

[Ill.u.s.tration: Fig. 14. Plan View showing Method of Turning a Taper with the Compound Rest]

=Taper Turning with the Compound Rest.=--The amount of taper that can be turned by setting over the tailstock center and by the taper attachment is limited, as the centers can only be offset a certain distance, and the slide _S_ (Fig. 9) of the attachment cannot be swiveled beyond a certain position. For steep tapers, the compound rest _E_ is swiveled to the required angle and used as indicated in Fig. 14, which shows a plan view of a rest set for turning the valve _V_. This compound rest is an upper slide mounted on the lower or main cross-slide _D_, and it can be turned to any angular position so that the tool, which ordinarily is moved either lengthwise or crosswise of the bed, can be fed at an angle.

The base of the compound rest is graduated in degrees and the position of these graduations shows to what angle the upper slide is set. Suppose the seat of valve _V_ is to be turned to an angle of 45 degrees with the axis or center, as shown on the drawing at _A_, Fig. 15. To set the compound rest, nuts _n_ on either side, which hold it rigidly to the lower slide, are first loosened and the slide is then turned until the 45-degree graduation is exactly opposite the zero line; the slide is then tightened in this position. A cut is next taken across the valve by operating handle _w_ and feeding the tool in the direction of the arrow.

[Ill.u.s.tration: Fig. 15. Example of Taper Work Turned by using Compound Rest]

In this particular instance the compound rest is set to the same angle given on the drawing, but this is not always the case. If the draftsman had given the included angle of 90 degrees, as shown at _B_, which would be another way of expressing it, the setting of the compound rest would, of course, be the same as before, or to 45 degrees, but the number of degrees marked on the drawing does not correspond with the angle to which the rest must be set. As another ill.u.s.tration, suppose the valve were to be turned to an angle of 30 degrees with the axis as shown at _C_. In this case the compound rest would not be set to 30 degrees but to 60 degrees, because in order to turn the work to an angle of 30 degrees, the rest must be 60 degrees from its zero position, as shown.

From this it will be seen that the number of degrees marked on the drawing does not necessarily correspond to the angle to which the rest must be set, as the graduations on the rest show the number of degrees that it is moved from its zero position, which corresponds to the line _a--b_. The angle to which the compound rest should be set can be found, when the drawing is marked as at _A_ or _C_, by subtracting the angle given from 90 degrees. When the included angle is given, as at _B_, subtract one-half the included angle from 90 degrees to obtain the required setting. Of course, when using a compound rest, the lathe centers are set in line as for straight turning, as otherwise the angle will be incorrect.

Rules for Figuring Tapers