On the Investigation of Variations in the Axial Force of a Drill and Its Torque as Functions of Diameter, Depth of Penetration, and Rotational Speed When Drilling Cast Iron and Iron
Abstract Generated abstract
This paper examines the poorly established relationships between twist drill performance and drill diameter, penetration depth, feed, and rotational speed when drilling cast iron and iron. After reviewing earlier experimental and theoretical work, it describes low-cost dynamometric apparatus built for a lathe at the Tomsk Technological Institute to measure axial thrust and torque during controlled drilling tests with Morse twist drills of varying diameters. The reported tables and comparisons indicate that both axial force and torque generally increase with drill diameter and depth of penetration, while the dependence is not simply proportional and is affected by material, drill geometry, and operating conditions. The study contributes additional experimental data and methodological detail intended to supplement prior investigations of drilling resistance and energy expenditure.
Full Text
Prof. T. I. Tikhonov
On the Question of Investigating Changes in the Axial Force of a Drill and Its Torque as a Function of Changes in Diameter, Depth of Penetration, and Rotational Speed of the Drill When Working in Cast Iron and Iron
The American twist drill appeared in the 1860s in America and, as a result of considerable design improvements to the drill itself made by the Morse factory, it became very widespread in factory practice. Despite the considerable time that has passed since the appearance of the twist drill, in practice its operation has been studied comparatively little. When working with a twist drill, the main work is performed by the lower cutting edges of the drill. Assuming that the lower cutting edges of the drill work in a horizontal plane, the following mathematical dependence may be written for the work of the lower cutting edges of the drill. If we call the cutting coefficient \(A\), and the drill diameter \(D\), then the elementary work of one blade when the drill rotates through an angle \(d\theta\) will be
\[ A \cdot dr \frac{b}{2} r d\theta, \]
where \(b\) is the feed of the drill for one complete revolution of the drill, equal to twice the thickness of the chip removed, and \(r\) is the radius of the hole being drilled.
Further, the total work of one drill blade for an entire revolution will be
\[ \frac{1}{2}\int_{0}^{\pi}\int_{0}^{\frac{D}{2}} \frac{1}{2} A \cdot b \cdot dr \cdot r d\theta = \frac{1}{2}\pi \cdot A b \frac{1}{2}\left(\frac{D}{2}\right)^2 = \frac{1}{16}\pi A b D^2; \]
therefore, the work of the two blades of the drill will be expressed as
\[ \frac{1}{8}\pi A b D^2. \]
Thus, from the last equation it is evident that the work of the drill depends on the cutting coefficient of the metal, is proportional to the feed of the drill, and is directly proportional to the square of the drill diameter.
Comparatively few experiments have been carried out to determine the work of a drill. Thus, in the 1850s the French engineer Coquilhat conducted an experiment on the work of a simple drill and came to the conclusion that the work of the drill for one revolution is proportional to the square of the diameter and to the feed of the drill. The experiment was carried out on a lathe, with the workpiece rotating and the drill receiving only longitudinal feed. The drill was fixed in a special lever with a weight, by means of which it was held against rotation; by shifting the weight on the lever, equilibrium was obtained, and from this it was already easy to determine the torque and the work of the drill for one revolution. This method made it possible to eliminate the harmful resistances of the machine. To measure the force with which the drill was pressed against the bottom of the hole being drilled, the drill was mounted on a carriage moving along the machine; the carriage itself was set in motion by a weight through a pulley; when the weight was changed, evidently, the feed of the drill also changed.
In the fifties of the last century an experiment was carried out by Clarenval, in which the force of the drill was determined by a driving dynamometer, and the work of the idle running of the machine was not deducted. From his experiments Clarenval observed that the work of the drill is proportional to the square of the diameter of the drill plus a certain constant term, i.e. \(Q = A + B D^{2}\). Then Clarenval observed that the work of the drill increases with the depth of the hole, which is quite understandable, for the work of friction of the drill against the wall of the hole and against the chips increases with the deepening of the drill. The experiment of the German engineer Heim1 confirmed the proportionality of the work of the drill to the feed of the drill per one revolution. Heim’s method of investigation was the same as Coquil’s, but the force was determined by a driving dynamometer. The final conclusion of all the preceding investigators is very inconsistent, and to say definitely, on the basis of them, how the dependence of the work of the drill on the feed of the drill and its diameter is expressed is impossible; thus, according to Coquil’s calculation, the pressure required in feeding the drill varied from 12 to 20 klg. per 1 mm of length of the cutting edge of the drill (for holes in iron), while according to Ritschel’s calculations, under the same conditions, this pressure varies from 5 to 10 klg.; of course, this pressure depends strongly on the angle of sharpening of the drill, and it is quite possible that such a large difference arose from an unequal degree of sharpening of the drills. Finally, in 1907–1908, at the Municipal School of Technology in Manchester, Dempster Smith and P. Polyakov carried out experiments on the forces acting on twist drills when working in cast iron and steel2. The experiments were carried out on a specially adapted horizontal milling machine; the axial pressure was determined by a manometer inserted into a special reservoir, on the wall of which (a membrane) the end of the working drill acted. The torque of the drill was determined by a special lever connected with the workpiece and acting on the platform of a scale. The material for the investigations was mild steel, steel of medium hardness, and hard steel; then soft cast iron, cast iron of medium hardness, and hard cast iron. From the latter experimental investigations the author obtained:
1) The expenditure—net—of energy is expressed by
\[ \left(\frac{2\pi \cdot nT}{1000 \cdot 75 \cdot 6}\ \text{horsepower}\right), \]
i.e. the expenditure actually on drilling, after subtracting the resistances in the machine, for a given drill diameter and a given feed, is proportional to the number of revolutions or to the cutting speed.
2) The net expenditure of energy is proportional to the torque and, when working in soft cast iron or steel of medium hardness, varies as \(t^{0.7}\), for a given drill diameter and a given cutting speed (where \(t\) is the feed of the drill in mm per 1 revolution).
3) For a given feed and a given cutting speed, the energy expenditure for drilling increases not as rapidly as the drill diameter, but only as \(d^{0.8}\), where \(d\) is the drill diameter in mm.
4) The torque and the energy expenditure for drilling when working in steel of medium hardness are approximately 2.1 times greater than when working in soft cast iron, if the cutting speed and the feed are the same in both cases.
5) The net expenditure of energy per \(1\ \mathrm{mm}^3\) per minute (i.e., the specific expenditure of energy) does not depend on the number of revolutions of the drill and is inversely proportional to \(d^{0.2} t^{0.3}\), or approximately to \(\sqrt[5]{d}\,\sqrt[3]{t}\), for its value is equal to
\[ \frac{2\pi nT}{1000\cdot 75\cdot 60}\cdot \frac{n d^2 t n}{4} = \frac{4\cdot 2\pi n c d^{0.8} t^{0.7}}{1000\cdot 75\cdot 60\cdot \pi d^2 t n} = \frac{K}{d^{0.2} t^{0.3}}, \]
where \(C\) and \(K\) are constant quantities. If the diameter \(d\) of the drill remains constant and if we give the feed the values \(0.0635\ \mathrm{mm}\), \(0.254\ \mathrm{mm}\), \(1.016\ \mathrm{mm}\), then the specific expenditure of energy will vary in the ratio \(1 : 0.66 : 0.435\); but if \(t\) remains constant, and \(d\) is given the values \(12.7\ \mathrm{mm}\), \(50.8\ \mathrm{mm}\), and \(101.6\ \mathrm{mm}\), then the specific expenditure of energy will vary in the ratio \(1 : 0.76 : 0.66\).
6) With a drill having two cutting edges, the actual depth of the chip removed by each edge will be \(t/2\); with a drill having 3 edges, \(t/3\), etc. If, therefore, the number of cutting edges is increased while leaving \(t\) unchanged, the cutting pressure will be that which corresponds to a proportionally smaller feed. If the cutting edges of the drill are not sharpened alike, so that all the drilling work is performed by one cutting edge, then the cutting pressure will be that which corresponds to double feed. The smaller the feed, the greater the cutting pressure and, consequently, the specific expenditure of energy.
7) The feed force when working in cast iron or steel increases not proportionally to the feed for a given drill diameter, and not proportionally to the diameter for a given feed.
8) The lower end of the drill increases the torque only very slightly, but the feed force by approximately 20%.
9) When working in steel with the supply of lubricant, the torque (specific expenditure of energy) decreases by 28% at a feed of \(0.0635\ \mathrm{mm}\) and by 8% at a feed of \(0.726\ \mathrm{mm}\). The reduction of the feed force with lubrication may be estimated, for all feeds, at approximately 25%.
10) The most commonly used point angle of twist drills is \(120^\circ\). A larger angle reduces the torque and increases the feed force; a smaller angle increases the torque and reduces the feed force. But since the energy expenditure required for feeding the drill amounts to a maximum of 1% of its total expenditure, in order to reduce the latter it is necessary to reduce the torque; from this point of view, a drill with a large point angle is more economical.
11) By reducing the pitch of the drill spiral, one can obtain a sharper cutting angle, with a smaller feed force and a smaller torque, without this change being accompanied by a change in the point angle of the drill usual in practice (equal to \(120^\circ\)); but such a reduction would shorten the service life of the drill.
12) With a smaller value of the point angle of the drill, the length of the cutting edges becomes greater; correspondingly, the danger of blunting the drill also becomes greater.
13) When calculating the time required to drill a hole of a definite depth, it is necessary to take into account the height of the drill point; the latter is:
| At a point angle equal to | Height |
|---|---|
| \(90^\circ\) | \(0.5d\) |
| \(120^\circ\) | \(0.29d\) |
| \(150^\circ\) | \(0.134d\) |
Although the latest studies in the field of drill operation, carried out by R. Polyakov and Dempster Smith, were made on a fairly broad scale and on a well-adapted machine, the results obtained by them cannot be regarded as exhaustive. In order somewhat to supplement the existing investigations in the field of the operation of the twist drill, in the mechanical workshops of the Tomsk Technological Institute I carried out, with the assistance of students of the institute, small experiments for the indicated purpose; for this a small lathe was used (distance between centers 950 mm and height of centers 165 mm), to which a special dynamometric apparatus was constructed.^1) The lathe was driven by a special electric motor through a countershaft.
The drill was fixed in a special spindle mounted on a board, which in turn was rigidly connected with the lower carriage plate of the lathe and therefore could have only, together with it, a translational motion along the axis of the machine. The cylindrical workpiece was secured in the chuck of the machine and could rotate only together with it; the workpiece was fastened so that its end face, to be drilled, was vertical. The feed of the drill was constant and was produced automatically. The magnitude of the feed, depending, other conditions being equal, on the number of teeth on the change gears of the large back gear of the machine, was equal to 0.206 mm per one revolution of the main spindle of the machine. In view of the existence of this feed, when the main spindle of the lathe rotated, the drill pressed upon the workpiece, and the magnitude of this pressure was measured by means of a dynamometer fastened to the same board of the machine on which the spindle was fastened; the arrangement of the dynamometer itself for measuring the axial force consisted of the following: on the above-mentioned board two bearings were fixed immovably, serving to support a spindle that could have one motion—rotation about its axis—and another along it; at the rear part of this spindle, where a ball thrust bearing was arranged (see Fig. 1), by means of a hardened steel part grooved to fit the ball, there adjoined another spindle, passing inside a spring and with its rear end, turned to a cone, resting against the lower end of a pointer; the latter, rotating about a horizontal axis, slid with its other end along a graduated scale and indicated the force existing along the axis of the drill. To effect central tension of the spring, the latter was rigidly connected at its front end with a nut of special construction, which in turn was screwed into a fixed bearing; the rear end of this spring, likewise rigidly connected with a nut of the same construction, passed freely into the rear bearing. The indicated dynamometer, after each of its runs, was checked, and careful attention was paid to ensuring that the pointer, in the absence of axial pressure, indicated zero on the scale. The scales were graduated by the resources of the mechanical workshops themselves. Since, under loading of the spring up to 600 kg, the readings observed at the free end of the pointer were identical with the readings given upon successive unloading of the spring, it could be concluded that the graduation gave quite satisfactory results. In view of the undesirability of heating the spring, which would have been necessary for graduation in a mechanical laboratory—
^1) It should be noted that, owing to the lack of funds in the institute workshops, in setting up the experiments it was necessary to pay particular attention to making the experimental arrangement inexpensive.
the torques of the Institute and the subsequent fitting of the stand for placing the spring on the machine, it was necessary to abandon the graduation on the instruments of Mechanical Laboratory I-a and to replace it by graduation at the place of work. The appearance of this operation is shown in the diagram of Fig. 2. For measuring the torque required to prevent the drill from rotating together with the blank, there existed the following device: on the same board “B” (see Fig. 2) a mold of strip iron was placed, provided with three visible blocks; these blocks, in order to eliminate friction, were provided with balls on axles. A lever was placed on the spindle, by means of a key and a groove; at the end corresponding to the front part of the machine this lever, by means of a soldered ring, was connected with a graduated dynamometer; the other end of the latter, by means of a thin steel wire passed over the blocks, was connected with the opposite end of the lever—not directly, but through a ball block located below; this block was arranged in such a way that it could move progressively in a vertical direction. This made it possible to tighten or loosen the wire, and in such a way that the pointer of the vertically positioned dynamometer showed zero and the lever itself, with its upper planed face, coincided with the horizontal plane; the latter was checked with a level. The scheme of the connections of the lever for measuring the torque and the arrangement of the tension block are shown in Fig. 3.
Having installed the instrument in the above-described manner and putting the drill into operation, the latter was prevented from rotating together with the blank by moving up or releasing the little handwheel and thereby raising or lowering the lower movable block until the lever became horizontal; for this, an elongation of the wire at the expense of the dynamometer spring was required, and consequently its pointer showed one or another division on the scale. Since at that time a couple of forces was acting on the lever, knowing the reading on the dynamometer scale and the length of the lever, it was possible, at any given moment of the drill’s work, to determine the torque that had to be expended in order to prevent rotation of the drill.
The first experiments were made with cylindrical cast-iron blanks, cast in sand, which after cooling were cut into three parts, each about 5″ long. The chemical composition of the cast iron taken was as follows: total carbon 2.82%, graphite 2.54%, silicon 2.16%, manganese 0.61, phosphorus 0.21, and sulfur 0.07. The material was distinguished by density and uniform structure. Before each drilling, the future hole was marked with a center punch. The work was carried out without lubrication. All the drills with which the experiment was performed were from a new, unused set of American Morse twist drills, by Shukhardt and Schütte. The drills had diameters: \(^{1}/_{16}\)", \(^{1}/_{8}\)", \(^{1}/_{4}\)", \(^{3}/_{8}\)", \(^{1}/_{2}\)", \(^{5}/_{8}\)", \(^{3}/_{4}\)", \(^{7}/_{8}\)" and \(1\)"—with an angle at the apex of the cutting cone of about 120°. With each drill, at the same peripheral speed at the drill and a feed constant for all drills, two holes were drilled; the corresponding dynamometer readings were noted, from which an average value was taken and entered in the tables below.
Readings for each drill were taken at the moment of its sinking to its cone of sharpening and then through each diameter up to three diameters of penetration; the data thereby obtained are entered in the same tables.
The average of all readings for one and the same drill and one and the same speed is placed there as well. In these same tables are indicated the number of revolutions of the main spindle of the machine corresponding to the circumferential
speed at the cutting edge of the drill and the deviation from the normal, most advantageous speed in one direction or another, in %.
The change in the number of revolutions of the main spindle of the machine was carried out collectively by means of stepped pulleys on the transmission shaft of the machine and on the machine itself, through an intermediate shaft and by means of an ordinary rheostat, with which the number of revolutions of the electric motor driving the lathe was varied. In order not to put the drill under difficult working conditions, since during operation a frictional force arises between the cutting edges of the drill and the workpiece being machined, as a result of which heating occurs and, consequently, damage to the drill, and since this frictional force is directly dependent on the speed, then for each drill, depending on the material being machined and on the diameter of the drill, standards for the number of revolutions were developed. These standards were adopted with the calculation that the circumferential speed at the cutting edges of the drill for all diameters should remain approximately constant and equal to the most advantageous one. There is an indication (see Cold Working of Metals, by T. I. Tikhonov, publ. 1904) that the most advantageous speed in drilling should be somewhat less than the speed of turning on a lathe, and this speed for cast iron is equal to 75 mm/sec. Prof. Time advises taking the speed in drilling equal to the speed in turning.—Prof. Gattsuk gives data of the “Morse” factory for modern twist drills in the form of 100 mm/sec for cast iron and iron. On this basis, as the initial, normal speed for the experiments, the speed according to the table of the factory Schuchardt and Schütte was adopted, which also recommends that the drilling speeds indicated in the table be used when machining materials with its drills.
Extracts from this table are given below:
| Drill No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Drill diameter in mm | 1¹⁵⁄₃₂ | 3⁹⁄₃₂ | 5⁹⁄₃₂ | 8⁹⁄₃₂ | 11¹⁄₄ | 13 | 14¹⁄₂ | 16 | 17¹⁄₂ | 19¹⁄₂ | 21 | 22¹⁄₂ | 24 | 25¹⁄₂ | ||
| Drill diameter in inches | ¹⁄₁₆ | ⅛ | ³⁄₁₆ | ¼ | ⁵⁄₁₆ | ⅜ | ⁷⁄₁₆ | ½ | ⁹⁄₁₆ | ⅝ | ¹¹⁄₁₆ | ¾ | ¹³⁄₁₆ | ⅞ | ¹⁵⁄₁₆ | 1 |
| When drilling steel | 940 | 460 | 310 | 230 | 190 | 150 | 130 | 115 | 100 | 95 | 85 | 75 | 70 | 65 | 62 | 58 |
| When drilling iron | 1280 | 660 | 420 | 320 | 260 | 220 | 185 | 160 | 140 | 130 | 115 | 105 | 100 | 90 | 85 | 80 |
In this table, for each drill, depending on its diameter, with one and the same material of the workpiece, the number of revolutions of the drill (in our experiments, of the main spindle of the machine) is given, which promotes the most favorable circumferential speed at the cutting edges of the drill, which, in turn, promotes the service life of the drill under ordinary factory conditions. The most advantageous number of revolutions for drills when working with cast iron was taken as equal, according to the table, to the most advantageous number of revolutions when working with iron.—In this case the circumferential speed on the drill fluctuates within the limits of 100–150 mm/sec; from this speed the deviations in the numbers of revolutions were taken, and in all, for each drill, seven such variations were made. The results of these experiments, as well as the mean figures from them, are placed in the appended Tables I–VII.
How speed affects resistance to chip cutting is shown by experiments carried out by Prof. Sellergren (Mechanical Technology by T. I. Tikhonov), who found that increasing the speed for brass and cast iron entails a slight lowering of the resistance, and this decrease amounts to only 3–4%, in the pre-
within the limits of speeds that are encountered in practice. Denister-Smith and R. Polyakov carried out experiments in order to determine the change in torque and feed force when the cutting speed was varied in soft cast iron without lubrication; the speed in these experiments varied from 7.5 to 126 revolutions per minute. The result of these experiments was as follows: the cutting speed has no appreciable effect either on the torque or on the feed force. From this, as a consequence, it follows that it is more advantageous to increase the diameter of the drill or the feed, but not the cutting speed, because the expenditure of net energy, i.e., its expenditure actually on drilling after deducting the resistances in the machine, is expressed by the formula:
\[ P=\frac{2\pi nT}{1000 \cdot 75 \cdot 60}\ \mathrm{H.P.}, \]
where \(T\) is the torque in \( \mathrm{klg./metr.}\); “\(n\)” is the number of revolutions of the drill, in our experiments the number of revolutions of the main spindle of the machine; in other words, the expenditure of net energy is directly proportional to the number of revolutions or to the cutting speed.—The resistance in the machine also increases with an increase in speed, and with a change in feed remains almost unchanged.
Our experiments on the change in the axial force of the drill and its torque are expressed partly in the form of figures placed in the preceding tables, and partly in the form of curves constructed with the aim of forming a clear idea of the manner in which the drilling speed affects the change in the feed force, torque, and depth of penetration of the drill.
All the data for the curves are taken from the above tables. For each drill, depending on its penetration at the end of sharpening, at one diameter, at two, and at three, readings were obtained of the axial force and the magnitude of the torque, and from the latter readings an average figure was taken. Along the axis of abscissas is laid off the number of revolutions, and along the axis of ordinates this average axial force; thus, for each drill, curves were obtained expressing changes in the magnitude of the axial force depending on the change in speed, while for each curve the amount of penetration is relatively constant.
Dotted lines are used for curves corresponding to the change of the average of the last three horizontal forces at a given speed, depending on the change of this speed. For each drill, on these same diagrams, changes in the magnitude of the torque are plotted depending on the change in the number of revolutions; each curve has a relatively constant value of drill penetration. From these four curves a resultant curve is obtained, again denoted by a dotted line, showing the general dependence of the change in torque on the change in drill speed.
The scales are indicated for each of the curves. From all these curves the following is seen: (Fig. 4, drill \(1/4''\).) The axial force increases together with an increase in the penetration of the drill into the workpiece; moreover, during the period of penetration of the drill from its cone to the first full diameter, the axial forces increase rather strongly; with further penetration of the drill from the 1st diameter to the 2nd and further to the 3rd, the axial forces increase considerably less. This phenomenon runs like a red thread through all the diagrams. The same can be said with regard to the magnitude of the torque. When the drill penetrates (see Fig. 4) to its sharpening cone, the axial force of the drill varies within small limits, sometimes increasing, sometimes decreasing around a certain average pressure equal to 100 klg.; the limits of variation of this force,
Drill \(1/2''\).—When the drill is sunk to one diameter, two and three diameters, the axial force varies within small limits, but noticeably in all three cases, decreasing as the speed increases.—The curve of mean axial forces remains almost constant, i.e. a horizontal line, and shows a force equal to approximately 160 klg.—The torque varies very slightly, and the curve of the mean torque is almost a horizontal line.
Drill \(3/8''\). When the drill is sunk to its point cone, the axial force also varies about a certain mean force, and this force \(=\sim 125\) klg.; the range of variation is approximately the same as in the preceding case; as the drill speed approaches 245 revolutions, the axial force remains constant and equal to 125 klg., then begins to increase, approximately from 290 revolutions per minute. The most advantageous speed will be 220 revolutions (see the “Morse” table for twist drills). The most advantageous speed according to the curve, when the drill is sunk to the cone, in the sense of the minimum value of the axial force, is also obtained at 220 revolutions.—When the drill is sunk to one, two, and three diameters, the change in the curves is insignificant; the curve of mean pressures on the drill is also almost a horizontal line.—The magnitude of the change in torque, both as a function of the change in the sinking of the drill and of the drilling speed, also varies within very small limits.
Drill \(1/2''\), Fig. 5. The normal speed according to the table is \(n = 160\) rev. per min. The axial forces vary very slightly; however, they decrease as this normal speed is approached and then increase somewhat more sharply, which is clearly visible from the curves corresponding to whole diameters.—The smallest force is observed at 165 revolutions.—The curve of mean pressures is identical with its curves.—The same character of the curves is observed when the magnitude of the torque changes. Taking into account the nonuniformity of cast iron and the small variation in speeds, as, for example, for the drill \(1/4''\), where drilling had to be continued, it may be assumed that the magnitude of the change in axial force and torque depends little on the change in the rotational speed of the drill.
Drill \(3/8''\). The normal speed according to the table is \(n = 130\) revolutions per minute.—The magnitude of the feed force noticeably decreases when the drill reaches a speed close to normal, but greater than it and equal to [[unclear: number]] revolutions per minute; thereafter it increases slightly and, beginning with 155 revolutions, remains constant.—The curve of torque, namely the mean, from a certain limit begins to fall sharply with an increase in the number of revolutions. The curves corresponding to the individual diameters remain almost constant.
Drill \(3/4''\). Normal speed: \(n = 105\) revolutions per minute. Here, more markedly than in the preceding curves, there is a noticeable fall in axial pressure and torque as 105 revolutions are approached, and then the torque increases slightly and, beginning with 115 revolutions, remains constant to the end of the investigation. The axial force, however, continues to decrease further, and this is clearly visible both from the curves of the individual diameters and from the curve of mean axial pressures.—The increase in axial force when the drill is sunk to its point cone at 140 revolutions is explained simply by a lag in the count, since before the drill is sunk to a diameter the force increases very rapidly. The following drills present a somewhat different picture.
Drill \(7/8''\). Normal speed: \(n = 90\) rev. per minute.—The axial force and torque decrease as \(n = 70\) rev. is approached.
per min., then increase, remaining for some time constant within the limits of a change in speed of about 90 rev. per min. (the peripheral speed of the cutting edges of the drill = 106.2 mm/sec), and then begin to increase with an increase in the number of revolutions.
The same phenomenon is also observed for the next drill. It may be assumed that, in general, drills of large diameters give a poorer, less clear and distinct curve of the variation of axial forces and torque. It is possible that here the nonuniformity of the cast iron had an effect. Unfortunately, it was not possible to repeat the experiments.
Drill 1″, Fig. 6. The normal speed at \(n = 80\) rev. per min. The axial force and torque change at first in jumps, now increasing, now decreasing; they have their smallest value at approximately 90 revolutions per minute, and then both begin to rise rapidly.—The low values of the axial force and torque observed for some drills, for example \(1/4''\), \(3/8''\), \(1/2''\), \(5/8''\), and \(1''\), when the first four points of the curves are obtained, at the lowest speed, are explained by the existence in a new drill of sharp cutting edges, which become blunted in subsequent operations.
Figs. 7 and 8 present a summary of all the mean curves of those drills with which the investigations were carried out. Fig. 7 shows the variation of the axial force, and Fig. 8 the variation of the torque, as a function of the variation in drilling speed.
From all these curves it is evident what a strong influence the diameter of the drill has on the increase of the axial force and torque; namely, as the diameter of the drill itself increases, it greatly increases these quantities.
A noticeable influence of the change in cutting speed on the change in the axial force and torque is not seen in the majority of drills. In the \(3/4''\) drill a strong drop in pressure is observed with an increase in speed, while at the same time the magnitude of the torque remains unchanged. Strong variations in the changes of axial force and torque in the 1″ drill also disturb the general picture. But since these two drills give a dependence of the change of the two factors on speed that differs from one another, and exceptionally so, then—taking into account the nonuniformity of the cast iron, according to the curves of axial forces and torques of all the other drills—it may be assumed that if both these factors do not remain completely indifferent to the change in drilling speed, then in any case they change very little with its change. In other words, the proposition expressed by the author of the present note (in the book Cold Working of Metals, published in 1904), that the force required for removing chips by a drill depends very little, or not at all, on speed, is confirmed.
Regarding the influence of the drilling depth on the axial force and torque, this was discussed earlier.
The second half of the experiments with the drill when working in iron was carried out on the same lathe on which the experiments with cast iron were made. The drill was likewise fixed in the spindle of the lathe, and the workpiece in its chuck. The axial force of the drill was measured by means of the same spring dynamometer with the same graduation.—The magnitude of the torque was determined as in the preceding investigations.—The number of revolutions of the main spindle of the lathe remained unchanged, and only the magnitude of the feed was changed, by means of interchangeable gears of the large back gear of the lathe. The magnitude of the feed in mm per one revolution of the main spindle of the lathe, in increasing order, was as follows:
0.143 mm, 0.1718 mm, 0.19 mm, 0.206 mm. In the investigations a new set of American Morse spiral drills was used, of Shukhardt and Schütte make. The iron used for the tests was welded from a single bar. The chemical composition of the iron was as follows: C—0.14%, Si—0.025 and Mn—0.065; sulfur and phosphorus—traces.
As in the tests with cast iron, dynamometer readings were taken when the drill had penetrated to its point cone, to one diameter, two, and three. Further, for a given feed and drill diameter, from the figures corresponding to each of the noted drill penetrations, the mean figure was taken and entered in the table given below. From the four figures characterizing the axial force and the magnitude of the torque when the drill had penetrated to three of its diameters, the mean figure was taken, which was also entered in the appended Tables VIII–XI. Using the data of these tables, curves were constructed for a visual representation of how changes in feed, drill diameter, and depth of penetration affect the change in axial pressure and torque. The curves for each given feed are constructed as follows: along the abscissa axis are laid off the drill diameters, and along the ordinate axis the magnitudes of the axial forces acting at the moment of penetration to the point cone, one diameter, two and three diameters; at these same moments the magnitudes of the torques are noted and likewise laid off along the ordinate axis. From these curves the following is seen (Figs. 9–11). The axial force gradually increases with an increase in the drill diameter, just as does the magnitude of the torque; the axial force and torque gradually increase with increasing depth of drilling penetration at one and the same feed; the axial force and torque gradually increase with increasing feed for one and the same drill.
The deviation of some points of the diagrams from the general law is explained by the influence of greater or lesser dullness of the drill cutting edges, since the latter, when working in iron, become noticeably very blunt, as is seen from the following: during operation the feeds went in this order: 0.1718 mm; 0.19 mm; 0.206 mm and 0.143 mm. The \(3/4''\) drill broke at a feed of 0.1718 mm and was replaced by a new one, and this circumstance caused a sharp drop in the axial force for the drill of this diameter. The influence of this drill on the curve is visible in all subsequent diagrams. The \(9/16''\) drill broke at a feed \(= 0.206\) mm; the same picture was repeated. The feed curves 0.1718 and 0.19, as obtained by working with drills from the same set, avoided the influence of a drill from the new set. The \(13/16''\) drill was not present at all in our first set and was replaced from another set; therefore its influence is visible on the diagrams of all feeds.
In Fig. 12 are constructed curves of the change in axial force and torque as a function of the change in the magnitude of the feed. In this direction experiments were carried out by Dempster Smith and Polyakov, who state that, for a given drill diameter, the increases in feed force with increasing feeds themselves, of the kind encountered in factory practice, vary approximately according to the law of a straight line. The torque also changes, namely increases, although not as rapidly as the feed forces. The curves obtained in our diagrams do not fully confirm these propositions. Thus, for example, the increase in axial force as a function of increasing feed occurs along a straight line for a \(7/8''\) drill; the torque for this drill also changes according to a law closely approaching the law of variation found by Polyakov. The \(1/2''\) drill has curves of the same character.
The \(^{11}/_{16}\)" drill also approximately obeys the same law. From the very arrangement of these curves it is evident that, as the diameter increases, the curves are situated higher and higher; whence it follows that, at the same feeds, with an increase in the drill diameter, the axial force and the magnitude of the torque increase. The deviation of some points, as, for example, the last point in the curve for the \(^{9}/_{16}\)" drill, is a consequence of the breakage of the drill at this feed of 0.206 mm per revolution. The displacement of points at the feed \(=0.143\) mm per revolution (which mainly affected the deviation of the constructed curves from straight lines) can be explained by the circumstance that it had not been intended to work at all with a feed \(=0.143\) mm; it had been planned to work with feed rates from 0.1718 mm, gradually increasing them to 0.272 mm per one revolution of the main spindle of the machine. But in view of the fact that, at one and the same feed, the axial force increased together with the increase in drill diameter, and that with an increase in feed this force increased still more, and at a feed \(=0.206\) mm and a drill diameter \(=^{7}/_{8}\)" this force became equal to 670 kg, a danger arose for the integrity of the machine; to prevent this, the largest feed was replaced by a feed \(=0.143\) mm. It was necessary to work with this feed after the drills had already worked with other, higher feeds; the cutting edges of the drills had managed to become rather dulled, and as a result the axial forces obtained were greater than at the feed \(=0.1718\) mm. This circumstance, in connection with the fact that the \(^{13}/_{16}\)" drill was not available at all in our set and had to be replaced by another, and that the \(^{3}/_{4}\)" and \(^{9}/_{16}\)" drills broke and in further investigations it was also necessary to use other drills, introduced discrepancies into the curves and prevented tracing, with greater or lesser probability, the law of variation of the magnitude of the feed force and torque with variation in the magnitude of the feed itself.
In order to investigate the rate of dulling of the cutting edges of the drill when working in iron, a test was undertaken of the changes in the axial force of the drill and its torque as functions of the gradual penetration of the drill into the workpiece and of the number of holes drilled; the feed remained constant and equal to \(=0.206\) mm. Two drills were taken, with diameters \(^{1}/_{2}\)" and \(^{5}/_{16}\)", and several rows of holes were drilled, 10 in all with each drill. Readings were taken after every 3 mm of drill penetration; for this purpose, a graduated ruler was attached to the spindle into which the drill was inserted, and a vernier was fixed immovably on the ways of the machine, its pointer indicating the amount of drill penetration. On the basis of the data obtained from the last observations, curves were constructed for the variations of axial force and torque as functions of the variation in drilling duration and the amount of drill penetration (see Fig. 13). Along the abscissa axis are plotted the 1st drilling, 2nd, 3rd, and so on; along the ordinate axis, the axial forces. From these curves it is evident how strongly the axial force increases as a function of drill penetration: during the period of drill penetration over the first 3 mm, the axial force grows rapidly, then more slowly as further deepening proceeds. At the same time it is evident how strongly the drill becomes dull during operation: the \(^{1}/_{2}\)" drill became dull considerably faster than the \(^{5}/_{16}\)" drill.
In conclusion it must be noted that the result of the last small experiments agrees in many respects with the data from the experiments of Mr. Polyakov. Some details of the drill operation, owing to the local conditions that arose, have remained without detailed elucidation, but the continuation of the indicated experiments will be undertaken in the near future when more favorable conditions for the work arise.
To the article by Prof. P. I. Tikhonov.
On the question of studying changes in the axial thrust of a drill and its torque.
Fig. 1.
Visible labels in the figure: $A'$, $H'$, $48$.
Fig. 3.
Visible labels in the figure: $A$, $1000$, $C$.
Fig. 2.
Visible labels in the figure: $B$, $A$.
Fig. 4
Torques
- Drill diameter
- Number of revolutions
Fig. 4. [[unclear: material and drilling-depth note]]
Fig. [[unclear]]
Axial forces
- Drill diameter
- Number of revolutions
Drill diam.
[[unclear: remaining handwritten/printed note]]
Fig. 4
Drill diameter
Fig. 4.
[[unclear: caption beginning “Fig. 5…”; “drill diameter”; “50 mm” appears visible]]
Fig. 5
Axial forces
- Drill diameter
Drill diam.
[[unclear: caption beginning “Fig. 5…”; “drilling depth 50 mm” appears visible]]
Fig. [[unclear]]
Torques
- Drill diameter
- Number of revolutions
[[unclear: caption; “Fig. 5…”, “drill diameter”, and “20 mm” appear visible]]
Fig. [[unclear]]
Axial forces
- Drill diameter
Drill diam.
[[unclear: caption; “Fig. 5…”, “drill diameter”, and “20 mm” appear visible]]
Feed: 0.143 mm per revolution.
Scale of forces: 1 mm = 5 kg.
Axial force, kg
Drill diameters: 1/4", 5/16", 3/8", 7/16", 1/2", 9/16", 5/8", 11/16", 3/4", 13/16", 7/8"
Fig. 9. Scale of torques: 20 mm = 1 kg·m.
Torque, kg·meters
Drill diameters: 1/4", 5/16", 3/8", 7/16", 1/2", 9/16", 5/8", 11/16", 3/4", 13/16", 7/8"
P
Axial force, kg
Fig. 10.
At 810 revolutions.
Scale of forces: \(1\ \mathrm{mm} = 5\ \mathrm{kg}\).
Scale of moments: \(1\ \mathrm{mm} = [[unclear]]\ \mathrm{kg\text{-}m}\).
Axes and labels visible in the graphs:
- Drill diameters: \(1/4''\), \(5/16''\), \(3/8''\), \(7/16''\), \(1/2''\), \(9/16''\), \(5/8''\), \(11/16''\), \(3/4''\), \(13/16''\), \(7/8''\).
- Axial forces.
- Torques.
- Scale of drill diameters.
- Scale of forces.
- Scale of moments: \(1\ \mathrm{mm} = [[unclear]]\ \mathrm{kg\text{-}m}\).
Fig. 11. Feed \(0.006''\) per revolution.
Scale of forces: \(1\ \mathrm{mm} = 5\ \mathrm{kg}\).
Axial forces
Drill diameters: \(1/4''\), \(5/16''\), \(3/8''\), \(7/16''\), \(1/2''\), \(9/16''\), \(5/8''\), \(11/16''\), \(3/4''\), \(13/16''\), \(7/8''\).
Torques
Drill diameters: \(1/4''\), \(5/16''\), \(3/8''\), \(7/16''\), \(1/2''\), \(9/16''\), \(5/8''\), \(11/16''\), \(3/4''\), \(13/16''\), \(7/8''\).
Scale of torques: \(20\ \mathrm{mm} = 1\ \mathrm{kg\cdot m}\).
Torque moments.
Axial forces.
Boring.
Feed \(a = 1/2\).
Feed \(a = 1/4\).
Feed, \(a\).
Maximum forces, 1 mm/min, 5 kg.
Maximum forces, 1 mm/min = 2 kg.
Table I.
Drill diameter \(d = 1/4''\).
Feed—0,206 mm;
Axial force—\(P\) kg.
Torque—\(Q\) kg./meter
Normal drill speed:
\(n = 320\) rev. per min.; \(v = 106,34\) mm/sec
| Number of revolutions per minute; speed mm/sec | Penetration in \(d/o\) | Hole No. | \(P\) | \(Q\) | No. | \(P\) | \(Q\) | Average \(P\) | Average \(Q\) | Average of 3 \(P\) | Average of 3 \(Q\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(n=148\) \(v=49,136\) |
— | 1 | 85 | 0,15 | 1 | 95 | 0,15 | 90 | 0,15 | — | — |
| \(n=148\) \(v=49,136\) |
— | — | 140 | 0,25 | — | 140 | 0,25 | 140 | 0,25 | 163,3 | 0,25 |
| \(n=148\) \(v=49,136\) |
— | — | 170 | 0,25 | — | 170 | 0,25 | 170 | 0,25 | — | — |
| \(n=148\) \(v=49,136\) |
— | — | 180 | 0,25 | — | 180 | 0,25 | 180 | 0,25 | — | — |
| \(n=175\) \(v=58,1\) |
— | 1 | 105 | 0,20 | 1 | 105 | 0,2 | 105 | 0,2 | — | — |
| \(n=175\) \(v=58,1\) |
— | — | 145 | 0,25 | — | 145 | 0,25 | 145 | 0,25 | 166,6 | 0,283 |
| \(n=175\) \(v=58,1\) |
— | — | 170 | 0,30 | — | 170 | 0,3 | 170 | 0,30 | — | — |
| \(n=175\) \(v=58,1\) |
— | — | 185 | 0,30 | — | 185 | 0,3 | 185 | 0,30 | — | — |
| \(n=202\) \(v=67,064\) |
— | 1 | 90 | 0,15 | 1 | 105 | 0,15 | 97,5 | 0,15 | — | — |
| \(n=202\) \(v=67,064\) |
— | — | 140 | 0,25 | — | 145 | 0,25 | 142,5 | 0,25 | 165 | 0,283 |
| \(n=202\) \(v=67,064\) |
— | — | 170 | 0,30 | — | 170 | 0,30 | 170 | 0,30 | — | — |
| \(n=202\) \(v=67,064\) |
— | — | 180 | 0,30 | — | 185 | 0,30 | 182,5 | 0,30 | — | — |
| \(n=230\) \(v=76,36\) |
— | 1 | 110 | 0,15 | 1 | 105 | 0,15 | 107,5 | 0,15 | — | — |
| \(n=230\) \(v=76,36\) |
— | — | 145 | 0,25 | — | 145 | 0,25 | 145 | 0,25 | 165 | 0,283 |
| \(n=230\) \(v=76,36\) |
— | — | 170 | 0,30 | — | 170 | 0,30 | 170 | 0,30 | — | — |
| \(n=230\) \(v=76,36\) |
— | — | 180 | 0,30 | — | 180 | 0,30 | 180 | 0,30 | — | — |
| \(n=257\) \(v=85,324\) |
— | 1 | 90 | 0,15 | 1 | 100 | 0,15 | 95 | 0,15 | — | — |
| \(n=257\) \(v=85,324\) |
— | — | 140 | 0,25 | — | 145 | 0,25 | 142,5 | 0,25 | 164,2 | 0,283 |
| \(n=257\) \(v=85,324\) |
— | — | 170 | 0,30 | — | 170 | 0,30 | 170 | 0,30 | — | — |
| \(n=257\) \(v=85,324\) |
— | — | 180 | 0,30 | — | 180 | 0,30 | 180 | 0,30 | — | — |
| \(n=284\) \(v=94,288\) |
— | 1 | 105 | 0,15 | 1 | 100 | 0,15 | 102,5 | 0,15 | — | — |
| \(n=284\) \(v=94,288\) |
— | — | 145 | 0,25 | — | 140 | 0,25 | 142,5 | 0,25 | 163,3 | 0,25 |
| \(n=284\) \(v=94,288\) |
— | — | 170 | 0,25 | — | 165 | 0,25 | 167,5 | 0,25 | — | — |
| \(n=284\) \(v=94,288\) |
— | — | 180 | 0,25 | — | 180 | 0,25 | 180 | 0,25 | — | — |
| \(n=300\) \(v=99,6\) |
— | 1 | 100 | 0,15 | 1 | 100 | 0,15 | 100 | 0,15 | — | — |
| \(n=300\) \(v=99,6\) |
— | — | 140 | 0,25 | — | 145 | 0,25 | 142,5 | 0,25 | 162,5 | 0,283 |
| \(n=300\) \(v=99,6\) |
— | — | 165 | 0,30 | — | 165 | 0,30 | 165 | 0,30 | — | — |
| \(n=300\) \(v=99,6\) |
— | — | 180 | 0,30 | — | 180 | 0,30 | 180 | 0,30 | — | — |
Table II.
Drill diameter: \(d = 1/8''\).
Feed = 0.206 mm.
Normal drilling speed: \(n = 220\) rev./min.; \(v = 109.8\) mm/sec.
| \(n,\ v\) | Deviation, % | Drill No. | \(P\) | \(Q\) | No. | \(P\) | \(Q\) | Average \(P\) | Average \(Q\) | Average from 3 tests \(P\) | Average from 3 tests \(Q\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(n = 136\) \(v = 67.7\) |
— | 1 | 115 | 0.30 | 1 | 120 | 0.30 | 117.5 | 0.30 | — | — |
| \(n = 136\) \(v = 67.7\) |
— | — | 170 | 0.45 | — | 170 | 0.45 | 170 | 0.45 | 179.16 | 0.458 |
| \(n = 136\) \(v = 67.7\) |
— | — | 180 | 0.50 | — | 185 | 0.45 | 182.5 | 0.45 | — | — |
| \(n = 136\) \(v = 67.7\) |
— | — | 185 | 0.45 | — | 185 | 0.45 | 185 | 0.475 | — | — |
| \(n = 176\) \(v = 87.55\) |
— | 1 | 125 | 0.30 | 1 | 130 | 0.30 | 127.5 | 0.30 | — | — |
| \(n = 176\) \(v = 87.55\) |
— | — | 170 | 0.40 | — | 175 | 0.40 | 172.5 | 0.40 | 180 | 0.441 |
| \(n = 176\) \(v = 87.55\) |
— | — | 180 | 0.45 | — | 185 | 0.45 | 182.5 | 0.45 | — | — |
| \(n = 176\) \(v = 87.55\) |
— | — | 180 | 0.45 | — | 190 | 0.50 | 185 | 0.475 | — | — |
| \(n = 200\) \(v = 99.5\) |
— | 1 | 125 | 0.30 | 1 | 130 | 0.30 | 127.5 | 0.30 | — | — |
| \(n = 200\) \(v = 99.5\) |
— | — | 175 | 0.40 | — | 170 | 0.40 | 172.5 | 0.40 | 181.6 | 0.433 |
| \(n = 200\) \(v = 99.5\) |
— | — | 185 | 0.45 | — | 185 | 0.45 | 185 | 0.45 | — | — |
| \(n = 200\) \(v = 99.5\) |
— | — | 185 | 0.45 | — | 190 | 0.45 | 187.5 | 0.45 | — | — |
| \(n = 220\) \(v = 109.24\) |
— | 1 | 110 | 0.30 | 1 | 130 | 0.30 | 120 | 0.30 | — | — |
| \(n = 220\) \(v = 109.24\) |
— | — | 175 | 0.45 | — | 175 | 0.45 | 175 | 0.45 | 180.8 | 0.45 |
| \(n = 220\) \(v = 109.24\) |
— | — | 180 | 0.45 | — | 185 | 0.45 | 182.5 | 0.45 | — | — |
| \(n = 220\) \(v = 109.24\) |
— | — | 185 | 0.45 | — | 185 | 0.45 | 185 | 0.45 | — | — |
| \(n = 244\) \(v = 121.3\) |
— | 1 | 120 | 0.30 | 2 | 130 | 0.30 | 125 | 0.30 | — | — |
| \(n = 244\) \(v = 121.3\) |
— | — | 165 | 0.45 | — | 170 | 0.45 | 170 | 0.45 | 179.1 | 0.458 |
| \(n = 244\) \(v = 121.3\) |
— | — | 180 | 0.45 | — | 185 | 0.45 | 182.5 | 0.45 | — | — |
| \(n = 244\) \(v = 121.3\) |
— | — | 180 | 0.45 | — | 190 | 0.50 | 185 | 0.45 | — | — |
| \(n = 272\) \(v = 136\) |
— | 2 | 120 | 0.35 | 2 | 130 | 0.35 | 125 | 0.35 | — | — |
| \(n = 272\) \(v = 136\) |
— | — | 170 | 0.45 | — | 180 | 0.45 | 175 | 0.45 | 181.6 | 0.458 |
| \(n = 272\) \(v = 136\) |
— | — | 180 | 0.45 | — | 180 | 0.45 | 182.5 | 0.45 | — | — |
| \(n = 272\) \(v = 136\) |
— | — | 185 | 0.45 | — | 190 | 0.50 | 187.5 | 0.475 | — | — |
| \(n = 296\) \(v = 147\) |
— | 2 | 125 | 0.35 | 2 | 130 | 0.35 | 127.5 | 0.35 | — | — |
| \(n = 296\) \(v = 147\) |
— | — | 175 | 0.40 | — | 180 | 0.45 | 177.5 | 0.425 | 184.1 | 0.441 |
| \(n = 296\) \(v = 147\) |
— | — | 185 | 0.45 | — | 185 | 0.45 | 185 | 0.45 | — | — |
| \(n = 296\) \(v = 147\) |
— | — | 190 | 0.45 | — | 190 | 0.45 | 190 | 0.45 | — | — |
Table III.
Drill diameter: \(d = 1/2''\)
Feed—0,206 mm.
Normal speed:
\(n = 160\) rev./min.; \(v = 108,8\) mm/sec.
| \(n^x\), \(v^x\) | Deviation, % | No. | P. | Q. | No. | P. | Q. | Average P. | Average Q. | Average of 3 obs. P. | Average of 3 obs. Q. |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(n=104\); \(v=70,72\) | — | 2 | 140 | 0,50 | 2 | 150 | 0,55 | 145 | 0,525 | — | — |
| \(n=104\); \(v=70,72\) | — | — | 195 | 0,80 | — | 200 | 0,80 | 197,5 | 0,80 | 205,8 | 0,83 |
| \(n=104\); \(v=70,72\) | — | — | 205 | 0,85 | — | 210 | 0,85 | 207,5 | 0,85 | — | — |
| \(n=104\); \(v=70,72\) | — | — | 210 | 0,85 | — | 215 | 0,85 | 212,5 | 0,85 | — | — |
| \(n=124\); \(v=84,32\) | — | 2 | 150 | 0,60 | 2 | 160 | 0,60 | 152,5 | 0,60 | — | — |
| \(n=124\); \(v=84,32\) | — | — | 200 | 0,80 | — | 200 | 0,80 | 200 | 0,80 | 207,5 | 0,83 |
| \(n=124\); \(v=84,32\) | — | — | 210 | 0,85 | — | 210 | 0,85 | 210 | 0,85 | — | — |
| \(n=124\); \(v=84,32\) | — | — | 215 | 0,85 | — | 210 | 0,85 | 212,5 | 0,85 | — | — |
| \(n=140\); \(v=95,2\) | — | 2 | 160 | 0,65 | 2 | 160 | 0,60 | 160 | 0,625 | — | — |
| \(n=140\); \(v=95,2\) | — | — | 200 | 0,80 | — | 200 | 0,80 | 200 | 0,80 | 205,8 | 0,825 |
| \(n=140\); \(v=95,2\) | — | — | 210 | 0,80 | — | 205 | 0,85 | 207,5 | 0,825 | — | — |
| \(n=140\); \(v=95,2\) | — | — | 210 | 0,85 | — | 210 | 0,85 | 210 | 0,85 | — | — |
| \(n=156\); \(v=106,08\) | — | 2 | 160 | 0,70 | 2 | 155 | 0,65 | 157,5 | 0,675 | — | — |
| \(n=156\); \(v=106,08\) | — | — | 200 | 0,80 | — | 195 | 0,80 | 197,5 | 0,80 | 204,1 | 0,808 |
| \(n=156\); \(v=106,08\) | — | — | 205 | 0,80 | — | 205 | 0,80 | 205 | 0,80 | — | — |
| \(n=156\); \(v=106,08\) | — | — | 210 | 0,85 | — | 210 | 0,80 | 210 | 0,825 | — | — |
| \(n=180\); \(v=122,4\) | — | 3 | 160 | 0,65 | 3 | 165 | 0,65 | 162,5 | 0,65 | — | — |
| \(n=180\); \(v=122,4\) | — | — | 210 | 0,80 | — | 205 | 0,80 | 207,5 | 0,80 | 213,1 | 0,83 |
| \(n=180\); \(v=122,4\) | — | — | 215 | 0,85 | — | 215 | 0,85 | 215 | 0,85 | — | — |
| \(n=180\); \(v=122,4\) | — | — | 220 | 0,85 | — | 215 | 0,85 | 217,5 | 0,85 | — | — |
| \(n=196\); \(v=133,28\) | — | 3 | 155 | 0,60 | 3 | 160 | 0,70 | 157,5 | 0,65 | — | — |
| \(n=196\); \(v=133,28\) | — | — | 205 | 0,80 | — | 200 | 0,80 | 202,5 | 0,80 | 209,1 | 0,83 |
| \(n=196\); \(v=133,28\) | — | — | 210 | 0,85 | — | 210 | 0,85 | 210 | 0,85 | — | — |
| \(n=196\); \(v=133,28\) | — | — | 215 | 0,85 | — | 215 | 0,85 | 215 | 0,85 | — | — |
| \(n=216\); \(v=146,88\) | — | 3 | 160 | 0,65 | 3 | 165 | 0,70 | 162,5 | 0,675 | — | — |
| \(n=216\); \(v=146,88\) | — | — | 205 | 0,80 | — | 200 | 0,80 | 202,5 | 0,80 | 2 | 825 |
| \(n=216\); \(v=146,88\) | — | — | 210 | 0,85 | — | 205 | 0,80 | 207,5 | 0,825 | — | — |
| \(n=216\); \(v=146,88\) | — | — | 212 | 0,85 | — | 210 | 0,85 | 210 | 0,85 | — | — |
Table IV.
Drill diameter: \(d = 5/8''\)
Feed — 0,206 mm.
Normal drill speed:
\(n = 130\) rev. per min.; \(v = 108,85\) mm/sec.
| \(n\), \(v\) | Deviation in % | No. | P. | Q. | No. | P. | Q. | Average P. | Average Q. | Average of 3 P. | Average of 3 Q. |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(n=84\) | — | 3 | 185 | 0,84 | 3 | 195 | 0,90 | 190 | 0,87 | — | — |
| \(v=70,308\) | — | — | 245 | 1,15 | — | 245 | 1,15 | 245 | 1,15 | 254,5 | 1,18 |
| \(n=84\) | — | — | 260 | 1,2 | — | 255 | 1,20 | 267,5 | 1,20 | — | — |
| \(v=70,308\) | — | — | 262 | 1,2 | — | 260 | 1,20 | 261 | 1,20 | — | — |
| \(n=100\) | — | 3 | 190 | 0,9 | 4 | 200 | 0,95 | 195 | 0,925 | — | — |
| \(v=83,70\) | — | — | 245 | 1,15 | — | 255 | 1,20 | 250 | 1,175 | 257,5 | 1,23 |
| \(n=100\) | — | — | 255 | 1,20 | — | 260 | 1,30 | 257,5 | 1,25 | — | — |
| \(v=83,70\) | — | — | 260 | 1,25 | — | 270 | 1,30 | 265 | 1,275 | — | — |
| \(n=116\) | — | 4 | 195 | 0,85 | 4 | 200 | 0,95 | 197,5 | 0,90 | — | — |
| \(v=97,092\) | — | — | 250 | 1,15 | — | 250 | 1,15 | 250 | 1,15 | 258,3 | 1,19 |
| \(n=116\) | — | — | 260 | 1,20 | — | 260 | 1,20 | 260 | 1,20 | — | — |
| \(v=97,092\) | — | — | 265 | 1,20 | — | 265 | 1,25 | 265 | 1,225 | — | — |
| \(n=130\) | — | 4 | 200 | 1,00 | 4 | 190 | 0,85 | 195 | 0,925 | — | — |
| \(v=108,81\) | — | — | 252 | 1,20 | — | 250 | 1,15 | 251 | 1,175 | 257,6 | 1,21 |
| \(n=130\) | — | — | 260 | 1,25 | — | 260 | 1,20 | 260 | 1,225 | — | — |
| \(v=108,81\) | — | — | 262 | 1,30 | — | 263 | 1,20 | 263 | 1,25 | — | — |
| \(n=144\) | — | 4 | 200 | 0,90 | 4 | 195 | 0,90 | 197,5 | 0,90 | — | — |
| \(v=120,53\) | — | — | 145 | 1,15 | — | 245 | 1,15 | 245 | 1,15 | 251,6 | 1,18 |
| \(n=144\) | — | — | 255 | 1,20 | — | 250 | 1,20 | 252,5 | 1,20 | — | — |
| \(v=120,53\) | — | — | 260 | 1,20 | — | 255 | 1,20 | 257,5 | 1,20 | — | — |
| \(n=156\) | — | 5 | 195 | 0,90 | 5 | 195 | 0,95 | 195 | 0,925 | — | — |
| \(v=130,57\) | — | — | 250 | 1,15 | — | 250 | 1,20 | 250 | 1,175 | 255,8 | 1,225 |
| \(n=156\) | — | — | 260 | 1,25 | — | 255 | 1,25 | 257,5 | 1,25 | — | — |
| \(v=130,57\) | — | — | 260 | 1,25 | — | 260 | 1,25 | 260 | 1,25 | — | — |
| \(n=176\) | — | 5 | 200 | 0,90 | 6 | 205 | 0,95 | 202,5 | 0,925 | — | — |
| \(v=147,32\) | — | — | 250 | 1,15 | — | 250 | 1,15 | 250 | 1,15 | 255,8 | 1,18 |
| \(n=176\) | — | — | 255 | 1,20 | — | 260 | 1,20 | 257,5 | 1,20 | — | — |
| \(v=147,32\) | — | — | 255 | 1,20 | — | 260 | 1,20 | 260 | 1,20 | — | — |
Table V.
Drill diameter: \(d = 3/4''\)
Feed = 0,206 mm.
Normal drill speed:
\[ n = 105 \text{ rev. per min.; } v = 107,15 \text{ mm/sec.} \]
| \(n''\), \(v''\) | Elongation, % | No. | \(P\) | \(Q\) | No. | \(P\) | \(Q\) | Average \(P\) | Average \(Q\) | Average of 3 \(P\) | Average of 3 \(Q\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(n=69\), \(v=70,38\) | — | 6 | 210 | 1,05 | 6 | 210 | 1,05 | 210 | 1,05 | — | — |
| \(n=69\), \(v=70,38\) | — | — | 275 | 1,65 | — | 280 | 1,70 | 277,5 | 1,675 | 290 | 1,69 |
| \(n=69\), \(v=70,38\) | — | — | 295 | 1,70 | — | 290 | 1,70 | 292,5 | 1,70 | — | — |
| \(n=69\), \(v=70,38\) | — | — | 300 | 1,70 | — | 300 | 1,70 | 300 | 1,70 | — | — |
| \(n=80\), \(v=81,6\) | — | 6 | 210 | 1,10 | 6 | 270 | 1,10 | 210 | 1,10 | — | — |
| \(n=80\), \(v=81,6\) | — | — | 275 | 1,75 | — | 275 | 1,75 | 275 | 1,75 | 285,3 | 1,78 |
| \(n=80\), \(v=81,6\) | — | — | 290 | 1,80 | — | 290 | 1,80 | 290 | 1,80 | — | — |
| \(n=80\), \(v=81,6\) | — | — | 292 | 1,80 | — | 292 | 1,80 | 291 | 1,80 | — | — |
| \(n=92\), \(v=93,84\) | — | 7 | 215 | 1,15 | 7 | 220 | 1,25 | 217,5 | 1,20 | — | — |
| \(n=92\), \(v=93,84\) | — | — | 280 | 1,70 | — | 275 | 1,65 | 277,5 | 1,675 | 284,1 | 1,72 |
| \(n=92\), \(v=93,84\) | — | — | 290 | 1,80 | — | 280 | 1,70 | 285 | 1,75 | — | — |
| \(n=92\), \(v=93,84\) | — | — | 295 | 1,80 | — | 285 | 1,70 | 290 | 1,75 | — | — |
| \(n=105\), \(v=107,1\) | — | 7 | 220 | 1,30 | 7 | 215 | 1,20 | 217,5 | 1,25 | — | — |
| \(n=105\), \(v=107,1\) | — | — | 270 | 1,60 | — | 270 | 1,60 | 270 | 1,60 | 277,8 | 1,65 |
| \(n=105\), \(v=107,1\) | — | — | 280 | 1,65 | — | 280 | 1,70 | 280 | 1,675 | — | — |
| \(n=105\), \(v=107,1\) | — | — | 285 | 1,70 | — | 282 | 1,70 | 283,5 | 1,70 | — | — |
| \(n=117\), \(v=119,34\) | — | 7 | 215 | 1,20 | 8 | 220 | 1,20 | 217,5 | 1,20 | — | — |
| \(n=117\), \(v=119,34\) | — | — | 285 | 1,60 | — | 285 | 1,70 | 275 | 1,65 | 281,1 | 1,70 |
| \(n=117\), \(v=119,34\) | — | — | 280 | 1,70 | — | 290 | 1,75 | 285 | 1,725 | — | — |
| \(n=117\), \(v=119,34\) | — | — | 282 | 1,70 | — | 295 | 1,75 | 283,5 | 1,725 | — | — |
| \(n=129\), \(v=131,58\) | — | 8 | 215 | 1,15 | 8 | 215 | 1,20 | 215 | 1,175 | — | — |
| \(n=129\), \(v=131,58\) | — | — | 275 | 1,65 | — | 270 | 1,70 | 274,5 | 1,675 | 278,3 | 1,70 |
| \(n=129\), \(v=131,58\) | — | — | 280 | 1,70 | — | 280 | 1,70 | 280 | 1,70 | — | — |
| \(n=129\), \(v=131,58\) | — | — | 280 | 1,75 | — | 280 | 1,70 | 282,5 | 1,725 | — | — |
| \(n=141\), \(v=143,82\) | — | 8 | 215 | 1,10 | 8 | 210 | 1,15 | 212,5 | 1,125 | — | — |
| \(n=141\), \(v=143,82\) | — | — | 270 | 1,65 | — | 270 | 1,70 | 270 | 1,675 | 275,8 | 1,70 |
| \(n=141\), \(v=143,82\) | — | — | 280 | 1,70 | — | 275 | 1,70 | 277,5 | 1,70 | — | — |
| \(n=141\), \(v=143,82\) | — | — | 280 | 1,75 | — | 280 | 1,70 | 280 | 1,725 | — | — |
Table VI.
Drill diameter: \(d = 7/8''\)
Feed = 0.206 mm.
Normal drill speed:
\(n = 90\) rev. per min.; \(v = 105.97\) mm/sec.
| \(n\), \(v\) | Inclination in % | No. | P. | Q. | No. | P. | Q. | Average P. | Average Q. | Average of 3×1 P. | Average of 3×1 Q. |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(n=58\) \(v=68.44\) |
— | 9 | 240 | 1.75 | 9 | 245 | 1.75 | 242.5 | 1.75 | — | — |
| \(n=58\) \(v=68.44\) |
— | — | 310 | 2.35 | — | 310 | 2.30 | 310 | 2.325 | 320.6 | 2.39 |
| \(n=58\) \(v=68.44\) |
— | — | 325 | 2.45 | — | 320 | 2.40 | 322.5 | 2.425 | — | — |
| \(n=58\) \(v=68.44\) |
— | — | 330 | 2.45 | — | 330 | 2.40 | 330 | 2.425 | — | — |
| \(n=69\) \(v=81.42\) |
— | 9 | 230 | 1.60 | 9 | 240 | 1.75 | 235 | 1.675 | — | — |
| \(n=69\) \(v=81.42\) |
— | — | 300 | 2.25 | — | 300 | 2.25 | 300 | 2.25 | 312.5 | 2.28 |
| \(n=69\) \(v=81.42\) |
— | — | 320 | 2.25 | — | 315 | 2.30 | 317.5 | 2.275 | — | — |
| \(n=69\) \(v=81.42\) |
— | — | 320 | 2.30 | — | 320 | 2.35 | 320 | 2.325 | — | — |
| \(n=80\) \(v=94.4\) |
— | 10 | 250 | 2.00 | 10 | 250 | 1.75 | 250 | 1.875 | — | — |
| \(n=80\) \(v=94.4\) |
— | — | 325 | 2.25 | — | 310 | 2.30 | 317.5 | 2.275 | 326.6 | 2.36 |
| \(n=80\) \(v=94.4\) |
— | — | 335 | 2.45 | — | 325 | 2.35 | 330 | 2.40 | — | — |
| \(n=80\) \(v=94.4\) |
— | — | 340 | 2.40 | — | 325 | 2.40 | 332.5 | 2.40 | — | — |
| \(n=90\) \(v=106.2\) |
— | 10 | 230 | 1.75 | 11 | 250 | 1.75 | 240 | 1.75 | — | — |
| \(n=90\) \(v=106.2\) |
— | — | 310 | 2.35 | — | 320 | 2.35 | 315 | 2.35 | 325.8 | 2.39 |
| \(n=90\) \(v=106.2\) |
— | — | 320 | 2.40 | — | 340 | 2.40 | 330 | 2.40 | — | — |
| \(n=90\) \(v=106.2\) |
— | — | 325 | 2.40 | — | 340 | 2.45 | 332 | 2.425 | — | — |
| \(n=100\) \(v=118\) |
— | 11 | 240 | 1.60 | 11 | 240 | 1.60 | 240 | 1.60 | — | — |
| \(n=100\) \(v=118\) |
— | — | 320 | 2.30 | — | 315 | 2.30 | 317.5 | 2.30 | 321.6 | 2.35 |
| \(n=100\) \(v=118\) |
— | — | 325 | 2.35 | — | 320 | 2.35 | 322.5 | 2.35 | — | — |
| \(n=100\) \(v=118\) |
— | — | 325 | 2.40 | — | 325 | 2.40 | 325 | 2.40 | — | — |
| \(n=112\) \(v=132.16\) |
— | 11 | 240 | 1.70 | 12 | 250 | 1.70 | 245 | 1.70 | — | — |
| \(n=112\) \(v=132.16\) |
— | — | 315 | 2.20 | — | 330 | 2.40 | 322.5 | 2.30 | 332.5 | 2.40 |
| \(n=112\) \(v=132.16\) |
— | — | 325 | 2.35 | — | 345 | 2.50 | 335 | 2.425 | — | — |
| \(n=112\) \(v=132.16\) |
— | — | 330 | 2.40 | — | 350 | 2.55 | 340 | 2.475 | — | — |
| \(n=122\) \(v=143.96\) |
— | 11 | 240 | 1.60 | 12 | 245 | 1.70 | 242.5 | 1.65 | — | — |
| \(n=122\) \(v=143.96\) |
— | — | 325 | 2.25 | — | 315 | 2.40 | 320 | 2.375 | 329.13 | 2.42 |
| \(n=122\) \(v=143.96\) |
— | — | 335 | 2.45 | — | 330 | 2.45 | 332.5 | 2.45 | — | — |
| \(n=122\) \(v=143.96\) |
— | — | 335 | 2.45 | — | 335 | 2.45 | 335 | 2.45 | — | — |
Table VII.
Drill diameter: \(d = 1''\).
Feed \(= 0.206\) mm.
Normal drill speed:
\(n = 80\) rev. per min.; \(v = 106.4\) mm/sec.
| \(n\), \(v\) | Deflection in % | Nos. | \(P\) | \(Q\) | Nos. | \(P\) | \(Q\) | Average \(P\) | Average \(Q\) | Average of 3 \(P\) | Average of 3 \(Q\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(n = 53\) \(v = 70.49\) |
— | 13 | 265 | 1,80 | 12 | 260 | 1,80 | 262,5 | 1,80 | — | — |
| \(n = 53\) \(v = 70.49\) |
— | — | 355 | 2,90 | — | 350 | 2,80 | 352,5 | 2,85 | 366,6 | 2,88 |
| \(n = 53\) \(v = 70.49\) |
— | — | 375 | 2,90 | — | 370 | 2,90 | 372,5 | 2,90 | — | — |
| \(n = 53\) \(v = 70.49\) |
— | — | 380 | 2,90 | — | 370 | 2,90 | 375 | 2,90 | — | — |
| \(n = 62\) \(v = 82.46\) |
— | 14 | 280 | 1,90 | 14 | 265 | 1,90 | 272,5 | 1,90 | — | — |
| \(n = 62\) \(v = 82.46\) |
— | — | 360 | 2,80 | — | 350 | 2,80 | 355 | 2,80 | 367,5 | 2,88 |
| \(n = 62\) \(v = 82.46\) |
— | — | 370 | 2,90 | — | 370 | 2,90 | 370 | 2,90 | — | — |
| \(n = 62\) \(v = 82.46\) |
— | — | 380 | 2,90 | — | 375 | 3,00 | 377,5 | 2,95 | — | — |
| \(n = 71\) \(v = 94.43\) |
— | 15 | 265 | 1,80 | 15 | 260 | 1,70 | 267,5 | 1,75 | — | — |
| \(n = 71\) \(v = 94.43\) |
— | — | 370 | 3,00 | — | 360 | 2,90 | 365 | 2,95 | 372,5 | 2,98 |
| \(n = 71\) \(v = 94.43\) |
— | — | 380 | 3,00 | — | 370 | 2,95 | 375 | 2,975 | — | — |
| \(n = 71\) \(v = 94.43\) |
— | — | 380 | 3,10 | — | 375 | 2,95 | 377,5 | 3,025 | — | — |
| \(n = 80\) \(v = 106.4\) |
— | 16 | 260 | 1,60 | 16 | 250 | 1,50 | 255 | 1,55 | — | — |
| \(n = 80\) \(v = 106.4\) |
— | — | 360 | 2,90 | — | 350 | 2,80 | 355 | 2,85 | 365,8 | 2,92 |
| \(n = 80\) \(v = 106.4\) |
— | — | 375 | 3,00 | — | 360 | 2,85 | 367,5 | 2,925 | — | — |
| \(n = 80\) \(v = 106.4\) |
— | — | 380 | 3,00 | — | 370 | 2,90 | 375 | 2,975 | — | — |
| \(n = 89\) \(v = 118.37\) |
— | 17 | 260 | 1,70 | 17 | 250 | 1,50 | 255 | 1,60 | — | — |
| \(n = 89\) \(v = 118.37\) |
— | — | 360 | 2,85 | — | 350 | 2,80 | 355 | 2,825 | 361,7 | 2,825 |
| \(n = 89\) \(v = 118.37\) |
— | — | 370 | 2,90 | — | 360 | 2,75 | 365 | 2,825 | — | — |
| \(n = 89\) \(v = 118.37\) |
— | — | 370 | 2,90 | — | 360 | 2,75 | 365 | 2,825 | — | — |
| \(n = 98\) \(v = 130.34\) |
— | 18 | 260 | 1,80 | 18 | 250 | 1,6 | 255 | 1,70 | — | — |
| \(n = 98\) \(v = 130.34\) |
— | — | 360 | 3,00 | — | 350 | 2,80 | 355 | 2,90 | 365,8 | 2,916 |
| \(n = 98\) \(v = 130.34\) |
— | — | 375 | 2,95 | — | 365 | 2,90 | 370 | 2,925 | — | — |
| \(n = 98\) \(v = 130.34\) |
— | — | 375 | 2,95 | — | 370 | 2,90 | 372,5 | 2,925 | — | — |
| \(n = 108\) \(v = 143.64\) |
— | 19 | 260 | 1,60 | 19 | 260 | 1,60 | 260 | 1,60 | — | — |
| \(n = 108\) \(v = 143.64\) |
— | — | 375 | 2,90 | — | 370 | 2,90 | 372,5 | 2,90 | 380 | 3,02 |
| \(n = 108\) \(v = 143.64\) |
— | — | 390 | 3,10 | — | 375 | 3,00 | 382,5 | 3,05 | — | — |
| \(n = 108\) \(v = 143.64\) |
— | — | 390 | 3,10 | — | 380 | 3,10 | 385 | 3,10 | — | — |
Table VIII.
Feed, 1st
0.143 mm per one revolution of the main spindle of the machine.
| Drill diameter | No. of blank | P. | Q. | No. | P. | Q. | Average P. | Average Q. | Average of 4 P. | Average of 4 Q. |
|---|---|---|---|---|---|---|---|---|---|---|
| 1/4″ | 13 | 60 | 0.10 | 13 | 80 | 0.20 | 70 | 0.15 | — | — |
| 1/4″ | — | 90 | 0.20 | — | 100 | 0.25 | 95 | 0.225 | 94.375 | 0.231 |
| 1/4″ | — | 100 | 0.25 | — | 105 | 0.25 | 102.5 | 0.25 | — | — |
| 1/4″ | — | 100 | 0.40 | — | 112 | 0.30 | 110 | 0.30 | — | — |
| 5/16″ | 13 | 90 | 0.30 | 13 | 95 | 0.25 | 92.5 | 0.275 | — | — |
| 5/16″ | — | 100 | 0.35 | — | 125 | 0.30 | 112.5 | 0.325 | 126.375 | 0.375 |
| 5/16″ | — | 140 | 0.40 | — | 155 | 0.45 | 147.5 | 0.425 | — | — |
| 5/16″ | — | 150 | 0.45 | — | 160 | 0.50 | 155 | 0.475 | — | — |
| 3/8″ | 12 | 110 | 0.30 | 12 | 130 | 0.35 | 120 | 0.325 | — | — |
| 3/8″ | — | 182 | 0.45 | — | 190 | 0.50 | 185 | 0.475 | 182.5 | 0.500 |
| 3/8″ | — | 205 | 0.55 | — | 215 | 0.60 | 210 | 0.575 | — | — |
| 3/8″ | — | 210 | 0.60 | — | 220 | 0.65 | 215 | 0.625 | — | — |
| 7/16″ | 1 | 160 | 0.45 | 1 | 155 | 0.45 | 157.5 | 0.45 | — | — |
| 7/16″ | — | 245 | 0.80 | — | 260 | 0.85 | 252.5 | 0.825 | 238.75 | 0.806 |
| 7/16″ | — | 265 | 0.90 | — | 275 | 0.95 | 270 | 0.925 | — | — |
| 7/16″ | — | 270 | 1.00 | — | 280 | 1.05 | 275 | 1.025 | — | — |
| 1/2″ | 13 | 140 | 0.35 | 13 | 150 | 0.40 | 145 | 0.375 | — | — |
| 1/2″ | — | 250 | 0.95 | — | 260 | 1.05 | 255 | 1.000 | 237.5 | 0.931 |
| 1/2″ | — | 260 | 1.10 | — | 280 | 1.15 | 270 | 1.125 | — | — |
| 1/2″ | — | 270 | 1.20 | — | 290 | 1.25 | 280 | 1.225 | — | — |
Continuation of Table VIII.
| Drill diameter | Test Nos. | P. | Q. | Nos. | P. | Q. | Average P. | Average Q. | Average of 4 P. | Average of 4 Q. |
|---|---|---|---|---|---|---|---|---|---|---|
| \(9/16''\) | 13 | 190 | 0,75 | 13 | 180 | 0,75 | 185 | 0,75 | — | — |
| \(9/16''\) | — | 275 | 1,10 | — | 270 | 1,25 | 272,5 | 1,175 | 267,5 | 1,356 |
| \(9/16''\) | — | 300 | 1,60 | — | 300 | 1,75 | 300 | 1,675 | — | — |
| \(9/16''\) | — | 315 | 1,85 | — | 310 | 1,80 | 312,5 | 1,825 | — | — |
| \(5/8''\) | 13 | 200 | 0,80 | 13 | 220 | 0,90 | 210 | 0,85 | — | — |
| \(5/8''\) | — | 310 | 1,45 | — | 315 | 1,50 | 312,5 | 1,475 | 303,75 | 1,456 |
| \(5/8''\) | — | 330 | 1,65 | — | 350 | 1,75 | 340 | 1,70 | — | — |
| \(5/8''\) | — | 345 | 1,75 | — | 360 | 1,85 | 352,5 | 1,80 | — | — |
| \(3/4''\) | 14 | 255 | 0,70 | 14 | 245 | 0,80 | 250 | 0,75 | — | — |
| \(3/4''\) | — | 460 | 2,25 | — | 450 | 2,25 | 455 | 2,25 | 417,5 | 2,306 |
| \(3/4''\) | — | 480 | 3,05 | — | 480 | 3,05 | 480 | 3,05 | — | — |
| \(3/4''\) | — | 480 | 3,15 | — | 490 | 3,2 | 485 | 3,175 | — | — |
| \(11/16''\) | 13 | 210 | 1,10 | 13 | 225 | 1,10 | 217,5 | 1,10 | — | — |
| \(11/16''\) | — | 320 | 1,60 | — | 350 | 1,75 | 335 | 1,675 | 326,625 | 1,694 |
| \(11/16''\) | — | 350 | 1,80 | — | 390 | 1,85 | 370 | 1,825 | — | — |
| \(11/16''\) | — | 370 | 2,00 | — | 400 | 2,15 | 385 | 2,075 | — | — |
| \(13/16''\) | 14 | 250 | 1,50 | 14 | 260 | 1,50 | 255 | 1,50 | — | — |
| \(13/16''\) | — | 400 | 2,50 | — | 430 | 2,75 | 415 | 2,625 | 400,625 | 2,644 |
| \(13/16''\) | — | 450 | 3,00 | — | 470 | 3,25 | 460 | 3,125 | — | — |
| \(13/16''\) | — | 465 | 3,15 | — | 480 | 3,50 | 472,5 | 3,325 | — | — |
| \(7/8''\) | 14 | 260 | 1,85 | 14 | 290 | 1,75 | 275 | 1,80 | — | — |
| \(7/8''\) | — | 430 | 3,00 | — | 500 | 3,0 | 465 | 3,0 | 498,025 | 2,644 |
| \(7/8''\) | — | 460 | 3,25 | — | 545 | 3,75 | 502,5 | 3,5 | — | — |
| \(7/8''\) | — | 470 | 3,50 | — | 550 | 4,0 | 510 | 2,75 | — | — |
Table IX.
Feed 2nd
0.1718 mm per one revolution of the machine’s main spindle.
| Drill diameter | No. | P. | Q. | No. | P. | Q. | Average P. | Average Q. | Average of 4 P. | Average of 4 Q. |
|---|---|---|---|---|---|---|---|---|---|---|
| 1/4″ | 2 | 40 | 0,25 | 8 | 80 | 0,25 | 60 | 0.25 | — | — |
| 1/4″ | — | 75 | 0,28 | — | 100 | 0,30 | 87,5 | 0,29 | 85,75 | 0,2925 |
| 1/4″ | — | 85 | 0,28 | — | 108 | 0,35 | 96,5 | 0.315 | — | — |
| 1/4″ | — | 88 | 0,28 | — | 110 | 0,35 | 99,0 | 0.315 | — | — |
| 5/16″ | 2 | 50 | 0,25 | 8 | 90 | 0,30 | 70 | 0.275 | — | — |
| 5/16″ | — | 140 | 0,50 | — | 162 | 0,50 | 151 | 0,50 | 141,5 | 0,4875 |
| 5/16″ | — | 155 | 0,50 | — | 180 | 0,65 | 167,5 | 0,575 | — | — |
| 5/16″ | — | 165 | 0,60 | — | 190 | 0,70 | 177,5 | 0,60 | — | — |
| 3/8″ | 2 | 68 | 0,25 | 8 | 115 | 0,30 | 91,2 | 0,275 | — | — |
| 3/8″ | — | 168 | 0,75 | — | 196 | 0,75 | 182 | 0,75 | 172,5 | 0,64375 |
| 3/8″ | — | 188 | 0,75 | — | 220 | 0,80 | 204 | 0,775 | — | — |
| 3/8″ | — | 195 | 0,75 | — | 230 | 0,80 | 212,5 | 0,775 | — | — |
| 7/16″ | 3 | 118 | 0,45 | 8 | 155 | 0,50 | 136,5 | 0,475 | — | — |
| 7/16″ | — | 190 | 0,85 | — | 240 | 0,85 | 215 | 0,85 | 210,375 | 0,800 |
| 7/16″ | — | 190 | 0,80 | — | 262 | 1,00 | 226 | 0,90 | — | — |
| 7/16″ | — | 255 | 0,90 | — | 273 | 1,05 | 264 | 0.975 | — | — |
| 1/2″ | 1 | 170 | 0,50 | 8 | 180 | 0,55 | 175 | 0,525 | — | — |
| 1/2″ | — | 308 | 1,25 | — | 320 | 1,50 | 314 | 1,375 | 289 | 1,32 |
| 1/2″ | — | 327 | 1,60 | — | 330 | 1,70 | 328,5 | 1,65 | — | — |
| 1/2″ | — | 332 | 1,80 | — | 345 | 1,75 | 338,5 | 1,775 | — | — |
Continuation of Table IX.
| Drill diameter | No. | P. | Q. | No. | P. | Q. | Mean P. | Mean Q. | Mean of 4 P. | Mean of 4 Q. |
|---|---|---|---|---|---|---|---|---|---|---|
| 9/16″ | 2 | 170 | 0.75 | 8 | 200 | 0.75 | 185 | 0.75 | — | — |
| 9/16″ | — | 300 | 1.25 | — | 340 | 1.50 | 320 | 1.375 | 303.5 | 1.381 |
| 9/16″ | — | 328 | 1.50 | — | 370 | 1.75 | 349 | 1.625 | — | — |
| 9/16″ | — | 340 | 1.75 | — | 380 | 1.80 | 360 | 1.775 | — | — |
| 5/8″ | 5 | 270 | 0.8 | 8 | 270 | 0.80 | 270 | 0.80 | — | — |
| 5/8″ | — | 400 | 1.5 | — | 420 | 2.30 | 410 | 1.65 | 396.875 | 1.750 |
| 5/8″ | — | 438 | 2 | — | 465 | 2.30 | 491.5 | 2.15 | — | — |
| 5/8″ | — | 432 | 2.3 | — | 480 | 2.50 | 456 | 2.40 | — | — |
| 11/16″ | 3 | 220 | 0.80 | 8 | 260 | 1.05 | 240.0 | 0.925 | — | — |
| 11/16″ | — | 375 | 2.00 | — | 430 | 2.50 | 402.5 | 2.25 | 376.5 | 2.106 |
| 11/16″ | — | 392 | 2.25 | — | 465 | 2.70 | 428.5 | 2.475 | — | — |
| 11/16″ | — | 400 | 2.40 | — | 470 | 3.15 | 439 | 2.775 | — | — |
| 3/4″ | 9 | 180 | 1.5 | 10 | 240 | 1.35 | 210 | 1.425 | — | — |
| 3/4″ | — | 360 | 2.25 | — | 390 | 2.35 | 375 | 2.30 | 375.5 | 2.406 |
| 3/4″ | — | 400 | 2.65 | — | 420 | 2.65 | 410 | 2.65 | — | — |
| 3/4″ | — | 430 | 3.00 | — | 440 | 3.5 | 435 | 3.25 | — | — |
| 13/16″ | 8 | 230 | 1.70 | 7 | 230 | 1.5 | 230 | 1.6 | — | — |
| 13/16″ | — | 405 | 2.85 | — | 400 | 2.75 | 402.5 | 2.80 | 383.125 | 2.725 |
| 13/16″ | — | 440 | 3.15 | — | 450 | 3.25 | 445 | 3.20 | — | — |
| 13/16″ | — | 450 | 3.25 | — | 460 | 3.35 | 455 | 3.30 | — | — |
| 7/8″ | 8 | 310 | 1.75 | 10 | 340 | 1.60 | 325 | 1.675 | — | — |
| 7/8″ | — | 550 | 4.5 | — | 560 | 4.8 | 555 | 4.65 | 501.25 | 4.15 |
| 7/8″ | — | 555 | 4.8 | — | 580 | 4.3 | 562.5 | 5.05 | — | — |
| 7/8″ | — | 555 | 4.9 | — | 580 | 4.55 | 562.5 | 5.125 | — | — |
Table X.
Task 3.
0.19 mm per one revolution of the machine’s main spindle.
| Drill diameter | Nos. | P. | Q. | Nos. | P. | Q. | Average P. | Average Q. | Average for 4 P. | Average for 4 Q. |
|---|---|---|---|---|---|---|---|---|---|---|
| 1/4″ | 5 | 60 | 0,2 | 9 | 60 | 0,20 | 60 | 0,20 | — | — |
| 1/4″ | — | 102 | 0,3 | — | 105 | 0,35 | 103,5 | 0,325 | 97,625 | 0,294 |
| 1/4″ | — | 110 | 0,3 | — | 112 | 0,35 | 111 | 0,325 | — | — |
| 1/4″ | — | 115 | 0,3 | — | 118 | 0,35 | 116,5 | 0,325 | — | — |
| 5/16″ | 5 | 72 | 0,20 | 9 | 102 | 0,30 | 87 | 0,25 | — | — |
| 5/16″ | — | 170 | 0,55 | — | 170 | 0,55 | 170 | 0,55 | 163 | 0,540 |
| 5/16″ | — | 190 | 0,65 | — | 195 | 0,70 | 192,5 | 0,675 | — | — |
| 5/16″ | — | 200 | 0,65 | — | 205 | 0,70 | 202,5 | 0,675 | — | — |
| 3/8″ | 5 | 110 | 0,30 | 9 | 140 | 0,50 | 125 | 0,40 | — | — |
| 3/8″ | — | 200 | 0,60 | — | 218 | 0,80 | 209 | 0,70 | 204,5 | 0,687 |
| 3/8″ | — | 230 | 0,80 | — | 248 | 0,85 | 239 | 0,825 | — | — |
| 3/8″ | — | 240 | 0,80 | — | 250 | 0,85 | 245 | 0,825 | — | — |
| 7/16″ | 6 | 125 | 0,35 | 9 | 148 | 0,50 | 136,5 | 0,425 | — | — |
| 7/16″ | — | 228 | 0,85 | — | 250 | 0,80 | 239 | 0,825 | 236,125 | 0,825 |
| 7/16″ | — | 270 | 0,90 | — | 280 | 1,10 | 275 | 1,0 | — | — |
| 7/16″ | — | 290 | 1,0 | — | 298 | 1,10 | 294 | 1,05 | — | — |
| 1/2″ | 6 | 198 | 0,5 | 9 | 195 | 0,6 | 196.5 | 0,55 | — | — |
| 1/2″ | — | 320 | 1,5 | — | 340 | 1,7 | 330 | 1,60 | 315,375 | 1,481 |
| 1/2″ | — | 360 | 1,8 | — | 370 | 1,8 | 365 | 1,80 | — | — |
| 1/2″ | — | 360 | 2,0 | — | 380 | 1,95 | 370 | 1,975 | — | — |
Continuation of Table X.
| Drill diameter | No. | P | Q | No. | P | Q | Average P | Average Q | Average of 4 P | Average of 4 Q |
|---|---|---|---|---|---|---|---|---|---|---|
| 9/16″ | 6 | 198 | 0,60 | 9 | 220 | 0,75 | 209 | 0,675 | — | — |
| 9/16″ | — | 350 | 1,50 | — | 365 | 1,70 | 357,5 | 1,60 | 336,625 | 1,487 |
| 9/16″ | — | 370 | 1,70 | — | 395 | 1,90 | 382,5 | 1,80 | — | — |
| 9/16″ | — | 380 | 1,70 | — | 415 | 2,05 | 397,5 | 1,875 | — | — |
| 5/8″ | 6 | 260 | 0,70 | 9 | 270 | 0,90 | 265 | 0,80 | — | — |
| 5/8″ | — | 420 | 1,75 | — | 445 | 1,90 | 432,5 | 1,875 | 416,0 | 1,925 |
| 5/8″ | — | 450 | 2,40 | — | 505 | 2,55 | 477,5 | 2,475 | — | — |
| 5/8″ | — | 458 | 2,50 | — | 520 | 2,70 | 489 | 2,60 | — | — |
| 11/16″ | 6 | 248 | 0,85 | 9 | 275 | 1,10 | 261,5 | 0,975 | — | — |
| 11/16″ | — | 420 | 2,60 | — | 470 | 2,90 | 445 | 2,75 | — | — |
| 11/16″ | — | 435 | 2,80 | — | 505 | 3,05 | 470 | 2,925 | — | — |
| 11/16″ | — | 440 | 3,00 | — | 510 | 3,20 | 475 | 3,10 | — | — |
| 3/4″ | 7 | 280 | 1,50 | 10 | 255 | 1,30 | 267,5 | 1,40 | — | — |
| 3/4″ | — | 418 | 2,60 | — | 410 | 2,85 | 414 | 2,725 | 404,125 | 2,631 |
| 3/4″ | — | 460 | 3,20 | — | 460 | 3,00 | 460 | 3,10 | — | — |
| 3/4″ | — | 470 | 3,30 | — | 480 | 3,30 | 475 | 3,30 | — | — |
| 13/16″ | 10 | 270 | 1,85 | — | — | — | 270 | 1,85 | — | — |
| 13/16″ | — | 460 | 3,10 | — | — | — | 460 | 3,10 | 430 | 3,10 |
| 13/16″ | — | 490 | 3,65 | — | — | — | 490 | 3,65 | — | — |
| 13/16″ | — | 500 | 3,80 | — | — | — | 500 | 3,80 | — | — |
| 7/8″ | 10 | 370 | 1,90 | 9 | — | 1,80 | 375 | 1,85 | — | — |
| 7/8″ | — | 565 | 4,05 | — | — | 5,3 | 565 | 4,575 | 537,5 | 4,100 |
| 7/8″ | — | 595 | 4,3 | — | — | 5,45 | 595 | 4,875 | — | — |
| 7/8″ | — | 620 | 4,55 | — | — | 5,6 | 620 | 5,1 | — | — |
Table XI.
Feed, 4th
0,206 mm. Per one revolution of the main spindle of the machine.
| Drill diameter | Nos. | P. | Q. | Nos. | P. | Q. | Average P. | Average Q. | Average of 4: P. | Average of 4: Q. |
|---|---|---|---|---|---|---|---|---|---|---|
| 1/4″ | 11 | 65 | 0,15 | 11 | 65 | 0,15 | 65 | 0,15 | 99,25 | 0,346 |
| 1/4″ | — | 102 | 0,40 | — | 110 | 0,40 | 106 | 0,40 | 99,25 | 0,346 |
| 1/4″ | — | 110 | 0,40 | — | 112 | 0,42 | 111 | 0,41 | 99,25 | 0,346 |
| 1/4″ | — | 115 | 0,40 | — | 115 | 0,45 | 115 | 0,425 | 99,25 | 0,346 |
| 5/16″ | 11 | 110 | 0,30 | 11 | 90 | 0,20 | 100 | 0,25 | 166,25 | 0,581 |
| 5/16″ | — | 185 | 0,65 | — | 160 | 0,60 | 172,5 | 0,625 | 166,25 | 0,581 |
| 5/16″ | — | 200 | 0,80 | — | 185 | 0,65 | 192,5 | 0,725 | 166,25 | 0,581 |
| 5/16″ | — | 202 | 0,75 | — | 190 | 0,70 | 196 | 0,725 | 166,25 | 0,581 |
| 3/8″ | 11 | 110 | 0,25 | 11 | 100 | 0,20 | 105 | 0,225 | 198,75 | 0,762 |
| 3/8″ | — | 215 | 0,95 | — | 205 | 0,85 | 210 | 0,90 | 198,75 | 0,762 |
| 3/8″ | — | 240 | 1,00 | — | 230 | 0,90 | 235 | 0,95 | 198,75 | 0,762 |
| 3/8″ | — | 245 | 1,00 | — | 240 | 0,95 | 242,5 | 0,975 | 198,75 | 0,762 |
| 7/16″ | 11 | 170 | 0,70 | 11 | 150 | 0,40 | 160 | 0,55 | 265,625 | 0,965 |
| 7/16″ | — | 260 | 1,00 | — | 280 | 1,10 | 270 | 1,05 | 265,625 | 0,965 |
| 7/16″ | — | 290 | 1,12 | — | 310 | 1,10 | 300 | 1,110 | 265,625 | 0,965 |
| 7/16″ | — | 300 | 1,20 | — | 365 | 1,10 | 332,5 | 1,12 | 265,625 | 0,965 |
| 1/2″ | 11 | 140 | 0,80 | 11 | 220 | 0,65 | 180 | 0,725 | 328,125 | 1,737 |
| 1/2″ | — | 350 | 2,00 | — | 350 | 2,00 | 350 | 2,00 | 328,125 | 1,737 |
| 1/2″ | — | 335 | 2,10 | — | 330 | 2,05 | 332,5 | 2,075 | 328,125 | 1,737 |
| 1/2″ | — | 405 | 2,20 | — | 395 | 2,10 | 400 | 2,15 | 328,125 | 1,737 |
Continuation of Table XI.
| Drill diameter | No. | P | Q | No. | P | Q | Average P | Average Q | Average of 4 P | Average of 4 Q |
|---|---|---|---|---|---|---|---|---|---|---|
| 9/16″ | 12 | 190 | 0,80 | 12 | 200 | 0,85 | 195 | 0,825 | — | — |
| 9/16″ | — | 300 | 1,25 | — | 300 | 1,40 | 300 | 1,325 | 298,75 | 1,437 |
| 9/16″ | — | 330 | 1,60 | — | 350 | 1,80 | 340 | 1,70 | — | — |
| 9/16″ | — | 350 | 1,80 | — | 370 | 2,00 | 360 | 1,90 | — | — |
| 5/8″ | 10 | 305 | 0,85 | 11 | 280 | 1,00 | 292,5 | 0,925 | — | — |
| 5/8″ | — | 500 | 2,45 | — | 490 | 2,25 | 495 | 2,35 | 476,605 | 2,294 |
| 5/8″ | — | 540 | 2,85 | — | 560 | 2,80 | 550 | 2,825 | — | — |
| 5/8″ | — | 550 | 2,90 | — | 580 | 3,25 | 565 | 3,075 | — | — |
| 3/4″ | 11 | 285 | 1,65 | 12 | 265 | 1,30 | 275 | 1,475 | — | — |
| 3/4″ | — | 480 | 3,25 | — | 485 | 3,10 | 482,5 | 3,175 | 466,25 | 3,00 |
| 3/4″ | — | 520 | 3,60 | — | 560 | 3,60 | 540 | 3,60 | — | — |
| 3/4″ | — | 550 | 3,75 | — | 585 | 3,75 | 567,5 | 3,75 | — | — |
| 11/16″ | 11 | 290 | 1,15 | 12 | 340 | 1,25 | 315 | 1,20 | — | — |
| 11/16″ | — | 495 | 3,00 | — | 530 | 3,20 | 512,5 | 3,10 | 482,50 | 2,812 |
| 11/16″ | — | 530 | 2,25 | — | 560 | 3,55 | 545 | 3,40 | — | — |
| 11/16″ | — | 545 | 3,40 | — | 570 | 3,70 | 557,5 | 3,55 | — | — |
| 13/16″ | 11 | 290 | 1,75 | 12 | 230 | 1,75 | 260 | 1,75 | — | — |
| 13/16″ | — | 485 | 4,4 | — | 455 | 3,75 | 470 | 4,075 | 453,005 | 3,510 |
| 13/16″ | — | 540 | 4,3 | — | 515 | 4,00 | 527,5 | 4,05 | — | — |
| 13/16″ | — | 560 | 4,30 | — | 550 | 4,1 | 555 | 4,20 | — | — |
| 7/8″ | 10 | 370 | 1,75 | 12 | 340 | 2,00 | 355 | 1,875 | — | — |
| 7/8″ | — | 590 | 4,05 | — | 610 | 5,05 | 600 | 4,55 | 568,75 | 4,061 |
| 7/8″ | — | 640 | 4,30 | — | 670 | 5,30 | 655 | 4,80 | — | — |
| 7/8″ | — | 660 | 4,55 | — | 670 | 5,5 | 665 | 5,025 | — | — |