Fig. 614Fig. 614.
Fig. 614.
Fig. 614is the tool post used at the back of the rest, the piecebpassing through the tool post slot. The tool rests upon the top of screweand upon the top ofbatf, and is secured by set-screws; its height is therefore adjusted by means of screwe, which is threaded inb. The set-screwsis not in this case objectionable, because it is at the back of the rest, and therefore does not obstruct the view of the work, while it is at the same time convenient to get at.
When the screw for traversing a lathe carriage is used for plain feeding, it is termed the feed screw, but when it is used to cut threads it is termed the lead screw.
A lead screw should be used for screw cutting only, so that it may be preserved as much as possible from wear. As the greater portion of threads cut in a lathe of a given size are short in comparisonwith the length of the lathe, it follows that the part of the lead screw that is in operation when the carriage or saddle is traversing over short work is most worn, while the other end is least worn, hence it is not unusual to so construct the screw and its bearings that it may be changed end for end in the lathe, to equalize the wear. By turning a lead screw end for end, therefore, to equalize the wear, the middle of the length of the screw will become the least worn, and, therefore, the most true. Hence it is better to use one end of the lead screw for general work, and to reverse it and use the other end only for screws requiring to be of very correct pitch.
To obviate the wear as much as possible the feed nut should embrace as great a length of the screw as convenient, and should be of a material that will suffer more from wear than the lead screw, or in other words shall relieve the feed screw from wear as much as possible. The wear on the nut being equal from end to end, the wearing away of one side of its thread does not vary its pitch; hence the only consideration as to its wearing qualification are the expense of its renewal and the length of time that may occur between its being engaged with the lead screw and giving motion to the lathe carriage, this time increasing in proportion as the nut thread is worn. Under quick speeds or when the lathe is in single gear, the rotation of the feed screw is so quick that not much time is lost before the carriage feeds, but when the back gear is in operation at the slowest speeds, the loss of time due to a nut much worn is an item of importance.
In some lathes the feed screw is employed for screw cutting and for operating an independent feed also. This is accomplished by cutting a feather way or spline along it, so that a worm having journal bearing in the apron of the rest carriage may envelop the lead screw and be driven by it, through the medium of a feather fast into the worm gear. The motion obtained from the worm gear is transferred through suitable gearing to the rack pinion.
The spline is cut deeper than the thread, so as to prevent the latter as far as possible from wear, by reason of the friction of the spline.
The lead screw if long should be supported, to prevent its sagging of its own weight. In some cases the lead screw is supportedin a trough along its whole length, as is done in the Sellers lathe. In other cases, bearings hanging from theV-slides, and movable along the bed, are employed.
It is desirable that the feed screw and nut be as near the middle of the carriage as possible, so that it shall pull the carriage at as short a leverage as possible, thus avoiding the liability to tilt or twist the carriage; but it is not practicable to place it midway between the lathe shears, because in that case the cuttings, &c., from the work would fall upon it, and cause excessive and rapid wear of the screw and nut.
In general the lead screw is located either in front, or at the back of the lathe, and in considering the more desirable of the two locations, we have as follows:
The feed nut should obviously remain axially true with the lead screw, as by reason of the extra weight of the front of the carriage, both it and the lathe shears wear most at the front, and the carriage, therefore, falls to the amount of its own wear and the wear of the shears. If the lead screw is used to feed with (as it should not be), the nut wears coincidently with the carriage and the shears, and the screw alignment is not impaired; but with an independent feed, only a small portion of the carriage traversing is done with the lead screw, hence the carriage lowers from the wear due to the independent feeding, and when the lead screw comes to be used its nut is not in true alignment with it. It is obviously preferable, then, to place the lead screw at the back, where the carriage and shears wear the least. Furthermore, this relieves the carriage front from the weight of the nut, &c., tending to equalize the back and front wear, while removing the nut-operating device from the front to the back of the shears, and thus reducing the number of handles in front, and thus avoid complication in small lathes.
Lathe Lead Screws.—Lead screws have their pitches in terms of the inch throughout all parts of the world; or, in other words, the lead screws of all lathes contain so many full threads per inch of length.
Lead screws are usually provided with square threads of the usual form, or with threads whose sides have about fifteen degrees of angle, so that the two halves of the feed nut may be let together to take up the wear. It is obvious that in aV-thread or in a thread whose sides are at an angle, the feeding strain tends to force the two halves of the feed nut apart, and therefore places a strain on the feed-nut operating mechanism that does not exist in the case of a square thread. Furthermore it can be shown that with aV-thread the opportunities to lock the carriage on a wrong place, after traversing it back by hand in screw cutting, are increased, thus augmenting the liability to cut intermediate and improper threads.
Fig. 615Fig. 615.
Fig. 615.
InFig. 615, for example, we have a pitch of lead screw of three threads per inch, and the gears arranged to cut six threads per inch on the work. As the bottom wheel has twice as many teeth as the top one, it is clear that, while the top one makes one, the bottom one will make half revolution, and the lead screw will make half a turn for every turn the work makes. Now, suppose the tool point to stand opposite to spacea, and the nut (supposing it to have but one thread only, which is all that is required for our purpose), stand opposite to spaced. Suppose, further, that the lathe makes one revolution, and spacebon the work will have moved to occupy the position occupied by spacea, or, rather, there will still be a place atafully in front of the tool, as should be the case, but the lead screw will have made half revolution, the topeof the thread coming opposite to the feed nut, as in the position of tool and nut shown in the figure attandn; hence the nut would not engage, without moving the lathe carriage sideways, and thus throwing the tool to one side of the thread in the work. When, however, the work had made another revolution, both the feed screw and the work would again come into position for the tool and nut to engage properly, and it follows that in this case the tool will always fall into proper position for the nut to be locked.
It is obvious, however, that had the lead screw thread been a square one, and the nut thread to accurately fit to the lead screw thread, so as to completely fill it, then the nut could not engagewith the lead screw until the lathe had made a complete revolution, at which time the work will have made two full or complete revolutions, and the tool would, therefore, fall into proper position to follow in the groove or part of a thread cut at the first tool traverse.
Fig. 616Fig. 616.
Fig. 616.
InFig. 616, we have the same lead screw geared to cut five or an odd number of threads per inch. The tool and the nut are shown in position to properly engage, but suppose, the nut being disengaged, that the work makes one revolution, and during this period the lead screw will have made3⁄5ths of a revolution, hence the nut will not be in position to engage properly, because, although spacebwill have travelled forward so as to occupy the position of spaceain the figure (that is, there will be a space fairly in front of the tool point), yet the nut will not engage properly, because the nut point will not be opposite to the bottom of the lead screw thread. When the work has made its second revolution, and spacecmoves to the position occupied bya, the lead screw will have made6⁄5or 11⁄5revolutions, and the nut cannot engage properly; when the lathe has made its third revolution, the lead screw will have made 14⁄5revolutions and the nut will still fall to one side of the thread space, and will not lock properly. The work having made its fourth turn, the lead screw will have made 22⁄5turns, and the nut will not be in position to lock fairly. The work having made its fifth turn, however, the lead screw will have made three turns, and the threads will fall into the same position that they occupy in the figure, and both tool and feed nut will fall into their proper positions in their respective threads. It does not follow, however, that, the lead screw having aV-shaped thread, the nut cannot be forced to engage but once in every five turns of the lead screw, because, were this the case, it would be impossible to lock the nut in an improper position.
Fig. 617Fig. 617.
Fig. 617.
Suppose, for example, that we have inFig. 617, the same piece of work and lead screw as inFig. 616, and that a first groove,a, has been cut with the tool in the position shown, and the nut engaged in the position marked 1. Now, suppose the nut be disengaged and the work allowed to make one revolution, then the lead screw will, during this revolution, revolve3⁄5of a revolution, and the position of the nut point with relation to the lead screw will be as at position 2. If, then, the nut was forced into the lead screw thread, it would, acting on the wedge principle, move the carriage to the right sufficiently to permit the nut to engage fully in threadg, and the tool would then cut a second groove on threadb. If the nut then be withdrawn from threadg, and the work allowed to make another revolution, the nut will stand in a precisely similar position with relation to the lead screw thread as it did in position 2, and by forcing it down into threadhthe carriage would be again forced to the right, causing a third thread,c, to be cut. By repeating the operation of withdrawing the nut, letting the work make another revolution and then engaging the nut again, it will seat in threadk, and a fourth threaddwill be cut. On again repeating the operation, however, the nut will come into position 5, and, on being drawn home into thread, or, rather, into spacel, the tool will fall into grooveaagain. Thus there will be four threads, each having a pitch equal to that of the lead screw. The second (b) of these four will fall to the left of threadato an amount or distance equal to2⁄5of the pitch of the lead screw, because, in forcing the nut from position 2 down into the lead screw, the slide rest, and therefore the tool, will be moved to the right2⁄5of the pitch of the lead screw. The third threadcwill fall to the left of threadbalso to an amount equal to2⁄5of the pitch of the lead screw, because, in forcing the thread to seat itself into threadhfrom position 3, the slide rest was again moved (to that amount) to the right. The fourth threaddwill fall to the left of threadcto the same amount and for the same reason.
But in this case, as before, if the lead screw had a square thread and the nut threads completely filled the spaces between the lead screw threads, then the nut could not engage at the 2nd, 3rd, or 4th work revolution, hence the false threadsb,c, andd, could not have been cut, even though the feed nut was disengaged and the lathe carriage was traversed back by hand.
Fig. 618Fig. 618.
Fig. 618.
Now, suppose that two threads on the work measure less than the amount the lead screw advances during the time that the work makes a revolution, and if the lead screw has aV-shaped thread, the case is altered. We have, for example, inFig. 618, a pitch of lead screw of 3 to cut 12 and 13 threads respectively. In the case of the 13 threads it will be seen that, supposing there to have been a first cut taken on the work, and the feed nut to be disengaged while the work makes a revolution, then the lead screw will revolve3⁄13revolution and the pointaon the lead screw will have moved up to pointb, and the nut point remaining atn, seating it in the thread, would cause it to engage with the same thread that it did before, and no second thread would be cut. If the nut be then released, the work allowed to make another revolution and the nut again closed, the operation would be the same asbefore, and no error would be induced, and so on. Suppose, further, that after the nut was disengaged the lathe was permitted to make two revolutions, and the lead screw would make6⁄13, or less than half a turn, and closing it would still cause it to pass back into the same thread on the lead screw and produce correct work. But if after the nut was released the work made three turns, the lead screw would make9⁄13of a turn, and the nut would fall on the right-hand side of the lead screw thread, and in closing would move the lathe carriage to the right, causing the tool to cut a second thread. Now, the same operation that occurred with the first thread would during the next three trials occur with the second thread, and at the next or seventh trial a third thread would be cut, which would be again operated upon during the next succeeding three trials. At the eleventh trial a fourth thread would be cut, but on the next three trials the tool would again fall into the groove first cut and the work proceed correctly. In the case of the 12 threads, the thread cut at the first and second trials would be correct. At the third trial the nut would seat itself in the groovecof the lead screw, causing the carriage to move to the right to a distance equal to twice the pitch of thread being cut, but the tool would still fall into the same groove in the work, as it also would on the fourth. At the fifth trial the process would be repeated, and so on, so that no second thread would be cut.
Fig. 619Fig. 619.
Fig. 619.
It may now be noted that if we draw the lead screw and the thread to be cut as in the figure, and draw the dotted lines shown, then those that meet the bottom of the thread on the lead screw, and also meet the groove cut on the work, at the first trial, represent the cases in which the nut will fall naturally into its proper position for the tool to fall into the correct groove, while whenever the nut is being forced home it seats in a groove in the lead screw, the bottom of which groove meets a line drawn from the first thread cut; the results obtained will be made correct by reason of the movement given to the slide nut when artificially seating the nut. This is shown to be the case inFig. 619, which represents a lead screw having an even number of threads per inch, and from which it appears that in cutting 12 threads (an even number also) the nut cannot be engaged wrong, whereas in the case of 13 threads it can be engaged right three times in 13 trials, and 10 times wrong, the latter causing the tool to cut three wrong threads.
To prevent end motion of a lead screw it should have collars on both sides of one bearing, and not one at each bearing. By this means the screw will be permitted to expand and contract under variations of atmospheric temperature, without binding against the bearing faces.
When a lead screw is long it requires to be supported, otherwise, either its weight will be supported or lifted by the feed nut in gear, or if that nut does not lift the screw, the thread cut will be finer than that due to the pitch of the lead screw, by reason of its deflection or sag.
A lead screw should preferably be as near as possible to the middle of the lathe shears, and as close to the surface as possible, so as to bring it as nearly in line with the strain on the tool as possible, but on account of the cuttings, which falling upon the screw would cause it to wear rapidly, it is usual to locate it on one side, so as to protect it from the cuttings. It is better to locate it on the front side of the lathe rather than on the back, because the strain of the cut falls mainly on the front side (especially in work of large diameter when this strain is usually greatest) and it is desirable to pull the carriage as near in a line with the resistance of the cut as possible, because the farther off the feed nut from the cutting tool point, the greater the tendency to twist the carriage on the shears.
To preserve the nut from wear, it should be made as long as convenient, as, say, five or six times the diameter of the lead screw; it is usually made, however, three or four diameters.
It is obvious that the pitch of the thread should be as accurate as possible, but it has not as yet been found practicable to produce a screw so accurate that it would not show an error, if sufficient of its length be tested, as, say, several feet.
Fig. 620Fig. 620.
Fig. 620.
If the error in a screw be equal, and in the same direction at all parts of its length, various devices may be employed to correct it. ThusFig. 620represents a device employed by the Pratt and Whitney Co.
It was first ascertained by testing the lathe that its lead screw was too short by7⁄100ths of a revolution in a length of 2 feet, the pitch of its thread being 6 to an inch. Now in 2 feet of the screw there would be 144 threads, and since7⁄100ths (the part of a revolution the thread was too short) ×1⁄6(the pitch of the thread) =7⁄600ths (which was called1⁄85th), the error amounted to1⁄85th inch in 144 turns of the screw. The construction of the device employed to correct this error is as follows: InFig. 620,arepresents the bearing of the feed screw of the lathe, andbba sleeve, a sliding fit upona, prevented from revolving by the pinh, while still having liberty to move endways.crepresents a casing affording journal bearing tobb, having a fixed gear-wheel at its endc′, and an external thread upon a hub at that end.dis the flange ofcto fasten the device to the shears of the latter, being held by screws.erepresents an arm fast upon the collar of the feed screw, and carrying the pinionf, the latter being in gear with the pinionc′, and also withg, which is a pinion containing twointernal threads, one fitting tobatb, and the other fitting tocatc, the former having a pitch of 27 threads to an inch, the latter a pitch of 25 to an inch.
The operation is as follows:—The ordinary change wheels are connected to the feed screw, or lead screw, as it is sometimes termed, atjin the usual manner. The armebeing fast to the feed screw will revolve with it, and cause the pinionfto revolve around the stationary gear-wheelc′.falso gears withg. Now,fis of 12 diametrical pitch and contains 26 teeth,c′is of 12 diametrical pitch and contains 37 teeth, andgis of 12 diametrical pitch and contains 36 teeth. It follows that the pinionf, while moving around the fixed gearc′, will revolve the piniong(which acts as a nut), to an amount depending upon the difference in the number of its teeth and those of fixed gearc′(in this case as 36 is to 37), and upon the difference in the pitches of the two threads, so that at each revolutiongwill move the feed screw ahead of the speed imparted by the change gears, the end of the sleevebabutting against the collar of the feed screw to move it forward.
In this case there are 36 turns of the feed screwafor one turn of the nut piniong, the thread on sleevebbeing 27, and that on the hub ofcbeing 25 to the inch; hence, 36 turns of the feed screw gives an end motion to the sleevebof1⁄25minus1⁄27=2⁄675, and1⁄36of that =1⁄12150of an inch = the amount of sliding motion of the sleeveb, for each revolution of the lathe feed screw. By varying the proportions between the number of teeth inc′andgand the pitches of the two threads in a proper and suitable ratio, the device enables the cutting of a true thread from any untrue one in which the variation is regular.
It is usual to fasten to the side of the lathe head stock a brass plate, giving a table of threads, and the wheels that will cut them, and obviously such tables vary according to the pitch of the lead screw, but a universal table may be constructed, such as the following table (prepared by the author) that will serve for any lathe.
At the top of the table is the number of teeth in wheels, advancing by four from 12 to 80 teeth, but it may be carried as much beyond 80 as desired. On the left hand of the table is a column of the same wheels. At the bottom of the scale are pitches of lead screw from 3 up to 20 threads per inch. Over each lead screw pitch are thread pitches, thus on lead screw pitch 4 we have 20, 19, 18, and so on.
The use of the table is asfollows:—
Find the pitch of the lead screw, and at the head of that column is the number of teeth for the lathe stud or mandril. Then find in that column the number of threads to be cut, and on the same line, but at the left hand, will be found the number of teeth for the lead screw.
Example.—The lead screw has a pitch of 4, and I require to cut 13 threads per inch. At the head of the column is 16, and on a line with the 13 of the column, but on the left is 52, each number being marked by a * hence the 16 and 52 are the wheels; if we have not those wheels, multiply both by 2 and 32, and 104 will answer.
If the pitch of the lead screw is 2 threads per inch, the wheels must advance by 6 teeth, as indicatedbelow:—
This table may be used for compound lathes by simply dividing the pitch of the lead screw by the ratio of the compounded pair of wheels. For example, for the wheels to cut 8 threads per inch, the pitch of lead screw being 4 and the compounded gears 2 to 1, as the ratio of the compounded pair is 2 to 1, we divide the pitch of lead screw by 2, which gives us 2, and we thus find the wheels in the column of pitch of lead screw 2, getting 12 and 48 as the required wheels, the 12 going on top of the lathe because it is at the top of the table, and the 48 on the lead screw because it is at the left-hand end of the table, and the lead screw gear is at the left-hand end of the lathe.
The table may be made for half threads as well as whole ones bysimply advancing the left-hand column by two teeth, instead of by four,thus:—
For quarter threads we advance the left-hand column by one tooth, or for thirds of threads by three teeth, and so on.
If we require to find what wheels to provide for a lathe, we take the pitch of the lead screw for the numerator, and the pitch required for the denominator, and multiply them first by 2, then by 3, then by 4, and so on, continuing until the numerator or denominator is as large as it can be to give the required proportion of teeth, and not exceed the greatest number that the largest wheel can contain.
For example: A lathe has single gear, and its lead screw pitch is 8 per inch, what wheels will cut 18, 17, 16, 15, 14, or 13 threads per inch?
If we suppose that the greatest number of teeth permissible in one wheel is not to exceed 100, then in this table we have all the combinations of wheels that can be used to cut the given pitches; and having made out such a table, comprising all the pitches to be cut, we may select therefrom the least number of wheels that will cut those pitches. The whole table being made out it will be found, of course, that the numerators of the fractions are the same in each case; that is, in this case, 16, 18, 24, 32, and so on as far as we choose to carry the multiplication of the numerator. We shall also find that the denominators diminish in a regular order: thus taking the fractions whose numerators are in each case 16, we find their denominators are, as we pass down the column, 36, 34, 32, 30, 28, and 26, respectively, thus decreasing by 2, which is the number we multiplied the left-hand column by to obtain them. Similarly in the fractions whose numerators are 24, the denominators diminish by 3, being respectively 54, 51, 48, 45, 42, and 39; hence the construction of such a table is a very simple matter so far as whole numbered threads are concerned, as no multiplication is necessary save for the first line representing the finest pitch to be cut.
For fractional threads, however, instead of using the pitch of the lead screw for the numerator, we must reduce it to terms of the fraction it is required to cut. For example, for 51⁄2threads we proceed as follows. The pitch of the lead screw is 8, and in 8 there are 16 halves, hence we use 16 instead of 8, and as in the 51⁄2there are 11 halves we use the fraction16⁄11and multiply it first by 2, then by 3, and then by 4, and so on, obtaining as follows:16⁄11,32⁄22,48⁄33,64⁄44, obtaining as before three sets of wheels either of which will cut the required pitch. In selecting from such a table the wheels to cut any required number of pitches, the set must, in order to cut a thread of the same pitch as the lead screw, contain two wheels having the same number of teeth.
Now, suppose that the pitch of the lead screw was 6 instead of 8 threads per inch, and the table will be asfollows:—
Here, again, we find that in the first vertical column the denominators decrease by two for each thread less per inch, in the second column they decrease by three, and in the third by four; this decrease equalling the number the first fraction was multiplied by.
But suppose the lead screw pitch is an odd one, as, say, 3 threads per inch, and we construct the table as before,thus—
Now it is useless to multiply by 2 or by 3, because they give a less number of teeth than the smallest wheel should have, hence the first multiplier should be 4, giving the followingtable:—
By continuing the table for other pitches we shall find that in the first vertical column the denominators diminish by 4, the second column by 5, and the third by 6; and it is seen that by diminishing the pitch of the lead screw, we have rendered necessary one of two things, which is, that either larger wheels containing more teeth must be used, or the change gears must be compounded.
Assuming that the pitch of the lead screw was 5 per inch, the table would be asfollows:—
The wheels in the first column here decrease by 3, the second by 4, and the third by 5.
In nearly all lathes the advance or decrease is by 4 or by 6. In determining this rate of advance or decrease, there are several elements, among which are the following. Suppose the lathe to be geared without compounding, then the distance between the lathe spindle and the lead screw will determine what shall be the diameters of the largest and of the smallest wheel in the set, it being understood that the smallest wheel must not contain less than 12 teeth. Assume that in a given case the distance is 10 inches, and it is obvious that the pitch of the teeth at once commands consideration, because the finer the pitch the smaller the wheel that will contain 12 teeth, and the larger the wheel on the lead screw may be made. Of course the pitch must be coarse enough to give the required tooth strength.
Let it be supposed that the arc pitch is3⁄4-inch, then the pitch circumference of a 12-toothed wheel would be 9 inches and its radius 1.432 in.; this subtracted from the 10 leaves 8.568 in. as the radius, or 17.136 in. as the largest diameter of wheel that can be used on the lead screw, supposing there to be no intermediate gears. Now a wheel of this diameter would be capable of containing more than 75 teeth, but less than 76. But from the foregoing tables it will be seen that it should contain a number of teeth divisible either by 4 or by 6 without leaving a remainder, and what that number should be is easily determined by means of a table constructed as before explained. Thus from the tables it would be found that 72 teeth would be best for a lead screw having a pitch of either 8, 6, 5, or 3 threads per inch, and the screw-cutting capacity of the lathe would (unless compounded) be confined to such pitches as may be cut with wheels containing between 12 and 72 teeth both inclusive.
But assume that an arc pitch of3⁄8-inch be used for the wheel teeth, and we have as follows: A wheel of this pitch and containing 12 teeth will have a radius of 716⁄1000inches, leaving 9.284 in. as the radius of the largest wheel, assuming it to gear direct with the 12-tooth pinion. With this radius it would contain 155 teeth and a fraction of a tooth; we must, therefore, take some less number, and from what has been said, it will be obvious that this lesser number should be one divisible by either 4 or 6. If made divisible by 6, the number will be 150, because that is the highest number less than 155 that is divisible by 6 without leaving a remainder. But if made divisible by 4, it may contain 152 teeth, because that number is divisible by 4 without leaving a remainder. With 150 teeth the latter could cut a thread 121⁄2times as fine as the lead screw, because the largest wheel contains 121⁄2times as many teeth as the smallest one; or it would cut a thread 121⁄2times as coarse as the lead screw, if the largest wheel be placed on the mandril and the smallest on the lead screw. With 152 teeth the lathe would be able to cut a thread 1284⁄100times as fine or as coarse as the lead screw. Unless, however, the lathe be required to cut fractional pitches, it is unnecessary that the largest wheel have more teeth than divisible, without leaving a remainder, by the number of teeth in the smallest wheel, which being 12 we have 144 as the number of teeth for the largest wheel. In the United States standard pitches of thread, however, there are several pitches in fractions of an inch, hence it is desirable to have wheels that will cut these pitches.