Machines for Drilling Raise Boreholes
Abstract Generated abstract
This paper surveys raise-boring machines used for drilling large-diameter vertical and inclined holes in underground mining, with emphasis on Soviet equipment and selected foreign designs. It compares serial machines such as the SBM-3u and LBS-2 with experimental developments including the MBS, BRM, and PPG types, discussing their kinematic schemes, feed systems, drilling tools, operating ranges, productivity, and shortcomings observed in industrial tests. The review identifies two main development directions: improving drilling regimes through adjustable feed and force, and changing machine layouts to reduce auxiliary time and increase installation efficiency. It concludes with a classification of machines by drilling technology, feed and transmission method, and availability of directional alignment devices, while noting that practical effectiveness depends on specific mining and engineering conditions.
Full Text
Machines for Drilling Raise Holes
O. D. Alimov, I. V. Rodionov, D. N. Malikov, V. N. Karminskii
In the last decade, underground drilling operations have become widely used in the mining industry.
Fig. 1. Kinematic diagram of the SBM-3u:
1 — drilling tool; 2 — centering lantern; 3 — spindle (screw); 4 — friction clutch; 5 — electric motor; 6 — reducer; 7 — setting device; 8 — feed nut.
The drilling of raise and inclined holes of large diameter, both in the USSR and abroad, is carried out by special raise-boring machines. Each of these ma-
shafts has its own design features and the associated technology for driving holes. This paper gives a brief review of the designs of raise-boring machines and makes an attempt to classify them according to design and technological characteristics.
At present, for drilling raise holes in the USSR, the SBM-3u raise-boring machine and the LBS-2 light raise-boring rig are produced in series. These machines [1–4] have one and the same basic kinematic scheme and the same
Fig. 2. Light raise-boring rig LBS-2.
technology for driving holes, and are used in the mining industry both in the USSR and abroad.
The reducers of the SBM-3u and LBS-2 (Figs. 1, 2), with screw differential mechanisms, transform the rotary motion of the motor into rotary and reciprocating motion of the spindle. The translational motion is produced by the difference in the number of revolutions of the spindle (screw) and the feed nut. The reducer parts are protected against overload by a friction clutch adjusted for a definite axial feed force.
The hole is drilled with a drilling tool consisting of a pilot bit and a reamer of either direct or reverse action. Rotation and feed of the drilling tool are effected by the spindle of the machine reducer, to which it is connected by means of a string of rods. The useful length of each rod is 600 mm. The use of rods of the indicated length has an adverse effect
on drilling productivity, since the time spent on extending the drill string amounts to 40–60% of the time required to drill the hole.
The SBM-3u rotary-percussion drilling machine (see table) is intended for drilling coal-discharge holes in steeply dipping seams, as well as water-discharge, ventilation, and other holes both in steeply dipping and in gently dipping seams, in the plane of their occurrence. The holes are drilled from the bottom upward with a diameter of 390 mm and, if necessary, are reamed on the return stroke to a diameter of 850 mm. The feed rate of the drilling tool is not adjustable, which does not permit the effective use of the machine’s power when drilling holes in coals of different strength.
The large weight and dimensions of the SBM-3u machine entail considerable labor expenditure for installing and transporting it to a new workplace. Transportation is carried out along rail tracks and by dragging. At the workplace, if necessary, the machine is braced with props. Drilling of holes with the SBM-3u machine can be carried out only from workings having a cross-section sufficient for its installation (from haulage drifts or crosscuts). Despite the presence of the indicated shortcomings, the SBM-3u is the only machine used for drilling raise holes up to 150 m long and up to 850 mm in diameter.
The light LBS-2 drilling-and-rotary-percussion rig (see table) is intended for direct drilling (without reverse reaming) of vertical, inclined, horizontal, and flat holes 300 mm in diameter through coal in the plane of seam occurrence. The rig has two feed speeds, which is its advantage in comparison with the SBM-3u machine. Its small dimensions and comparatively low weight, as well as the possibility of dismantling it into separate units, make it possible to use the rig when drilling holes from small-section workings (intermediate drifts). This circumstance increases the maneuverability of the installation and raises work productivity. The principal drawback of the rig is the impossibility of drilling a large-section hole. As a result of certain design changes proposed by a Kuzbass innovator—the drilling foreman M. V. Vasiliev—it became possible to use the LBS-2 for drilling and enlarging holes on the return stroke to a diameter of up to 500 mm. In this case, however, the rig has only one feed speed.
In addition to the machines mentioned, in recent years a number of models of new rotary-percussion drilling machines have been developed in the USSR and are undergoing industrial testing. The development of new machines has proceeded along two principal lines. Let us consider each of them.
The first line is characterized by the desire to increase machine productivity by ensuring their ra-
Table 1
| Technical characteristic | LBS-2 | SBM-3U | PTG-3 | MBS-1 | MBS-2 | BRM-1 |
|---|---|---|---|---|---|---|
| Borehole diameter, mm: when drilling | 300 | 390 | 700 | 390 | 390 | 390 |
| Borehole diameter, mm: when reaming | — | 850 | — | 850 | 850 | — |
| Borehole inclination angle, deg | 0–90 | 0–90 | 40–90 | 0–90 | 0–90 | 40–90 |
| Borehole length, m: at an angle of 45–90° | 60 | 150 | 40 | 80 | 100 | 150 |
| Borehole length, m: at an angle of 0–45° | 30 | 70–80 | — | 40 | 40 | — |
| Machine productivity, m/shift: when drilling | 28 | 40 | 30 | 38 | — | 35 |
| Machine productivity, m/shift: when reaming | — | 23 | — | 17.8 | — | — |
| Machine productivity, m/shift: when lowering the tool | 60 | 60 | — | 60 | — | — |
| Useful length of one rod, mm | 600 | 600 | — | 900 | 600 | 800 |
| Engine power for actuating the tool, kW | 4.2 | 16.0 | 6.5* | 11.0 | 8.0 | 9.0* |
| Total power, kW | 4.2 | 16.0 | 7.3* | 11.0 | — | 12.0* |
| Overall dimensions of the machine in the vertical position, mm: height | 1772 | 2300 | 670 | 2198 | 1823 | 2100 |
| Overall dimensions of the machine in the vertical position, mm: length | 920 | 2220 | 2220 | 1800 | 1240 | — |
| Overall dimensions of the machine in the vertical position, mm: width | 632 | 1160 | 670 | 910 | 870 | — |
| Weight of the machine without drilling tool, kg | 570 | 2884 | 552 | 1655 | 1030 | 1580 |
| Weight of drilling tool at maximum borehole length, kg | 1344 | 6346 | — | 4340 | 4340 | 2835 |
| Weight of drilling tool at maximum borehole length, kg | 1456 | 9230 | 1922 | 6000 | 5460 | 4415 |
* Engine power, hp.
operation at increased drilling regimes. For this purpose the machines are equipped with devices for smooth regulation of the speed and feed force of the drilling tool at the face. The Kuznetsk Branch of Giprouglemash is working in this direction; its team has developed the MBS-1 drilling-and-reaming machine (Fig. 3, table). The MBS-1 machine, like the SBM-3u machine, is intended for drilling holes 390 mm in diameter and reaming them on the return stroke to a diameter of 850 mm. The distinctive feature of the MBS-1 machine, as compared with the SBM-3u, is the presence of hydraulic feed of the drilling tool to the face, which makes it possible to vary the feed speed and force over wide limits and thereby to make the fullest use of the machine power under various mining and geological conditions. In terms of weight and overall dimensions, the MBS-1 machine occupies an intermediate position between the SBM-3u and the LBS-2.
Fig. 3. Kinematic diagram of the MBS-1:
1—drilling tool; 2—centering lantern; 3—feed hydraulic jacks; 4—spindle; 5—reducer; 6—hydraulic pump; 7—motor.
Prototype models of the MBS-1 machine underwent industrial tests. As a result of the tests, certain shortcomings in the machine design were revealed. The main one was that the hydraulic system of the machine proved insufficiently reliable. On the basis of the results of industrial tests, Giprouglemash eliminated a number of shortcomings in the design of the MBS-1, and in 1957 the Anzherka plant “Svet Shakhtyora” produced an experimental batch of MBS-2 machines, which are currently undergoing industrial tests.
The second direction is characterized by a change in the structural schemes of raise-drilling machines in order to reduce the time spent on auxiliary operations during drilling and to increase the efficiency of the entire installation. In this direction, prototype models of the BRM-1 [5] and PPG-3 [7] machines were created.
The BRM-1 machine (Fig. 4) is intended for drilling raise holes under the conditions of the Donbass. A distinctive feature of this machine is that the tool drive is provided by a motor that enters the hole after the tool. Feed of the rod string is carried out by hydraulic jacks.
According to the designer’s concept, bringing the motor up to the tool should eliminate the power losses that occur during rotation of the drill string and, consequently, increase the speed and productivity.
the drilling capacity, and also reduce borehole curvature.
The BRM-1 machine consists of five main assemblies: a special rotary pneumatic motor, the drilling tool from the SBM-3U machine, a drill-rod string, a hydraulic feed device, and a supporting frame. The operating principle of the machine is as follows. A rotary pneumatic motor with a reduction gear is fastened at the end of the drill-rod string; the latter consists of a two-stage planetary transmission. The drive shaft of the reduction gear rotates the conical reamer with the pilot bit.
Fig. 4. BRM-1 raise-boring machine:
1—drilling tool; 2—pneumatic motor; 3—drill rod; 4—hydraulic jacks.
The motor is mounted on special skids, which bear against the walls of the borehole. Between the supporting skids of the lantern and the motor housing there are gaps for the passage of cuttings. The pneumatic motor and the conical reamer are fed into the borehole by two double-acting jacks.
The drill-rod string consists of separate tubular rods 800 mm long. The rods are connected by means of couplings with conical threads. To prevent bending of the drill-rod string, supporting lanterns are used, installed at every 4 m of borehole length. A special device is provided for setting the string at the required angle to the horizontal.
Compressed air is supplied to the pneumatic motor through the tubular drill-rod string, while the exhaust air is directed to the cutting tool, which promotes better removal of cuttings, cooling of the tool, and ventilation of the borehole.
Production tests of experimental models of the BRM-1 were carried out in 1952–54 at the mines of the StalinuGol combine. The average drilling speed, in machine time, reached 14.6 linear m/hour in seams of below-average hardness with a dip angle of 70–72°. Machine time amounted to 35.7%, preparatory and finishing operations to 42.1%, and other losses to 22.2% of the total time for drilling the borehole. The machine time for drilling the length of one rod, depending on the physicomechanical properties of the coal, ranged from 1.3 to 6 min.
After 30 m of the borehole had been driven, a decrease in drilling speed was observed, which is explained by the drop in pressure of the compressed air supplied to the pneumatic motor. Despite the fact that, when the BRM-1 machine operates, the rods do not rotate, the drilling process is accompanied by the drill bit drifting away from the center of the borehole, as also occurs during operation of the SBM-3u and LBS-2 machines.
Industrial tests of the BRM-1 have not been completed. In 1958 the Anzhero plant “Miner’s Light” is to manufacture several experimental models of this machine. After these models have been tested, the question of using BRM-1-type raise-boring machines will be decided.
In 1952, the inventor Ya. Ya. Gumennik created the PPG-1 drilling machine, and in 1954, on this basis, experimental models of the PPG-3 pneumatic heading machine were manufactured by the Novosibirsk Experimental Plant of Giprouglemash.
The PPG-3 pneumatic heading machine (Fig. 5, table) is intended for driving directed raise boreholes 700 mm in diameter along thick, steeply dipping seams in mines hazardous for gas and dust, and also for drilling boreholes along seams with a variable dip angle.
The working member of the PPG-3 consists of a drill bit, which breaks the coal at the center of the face, and two rods on which working disks with teeth are mounted. The toothed disks perform a complex motion: together with the rods they move around the axis of the borehole and, in addition, rotate around the axes of the rods. As a result, the teeth describe spherical elongated hypocycloids, forming narrow concentric grooves on the surface of the face. Special teeth fastened to the rods serve to break down the remaining pillars.
The working member is fed to the face by means of three guiding caterpillar tracks arranged at an angle of 120° to one another. The caterpillars are braced against the walls of the borehole by means of jacks and, pushing off from them, move the entire system.
The PPG-3 is equipped with two pneumatic motors: one, with a power of 6.5 hp, actuates the working member; the other, with a power of 0.8 hp, drives the caterpillar travel.
Before collaring, the heading machine is located in a metal cylinder mounted on a carriage. The cylinder is set in the specified direction and wedged in place. During the collaring process
the drifter, by means of its tracks, exits the cylinder into the borehole, after which the guiding device is removed.
The cutting head of the pneumatic drifter is hinged to the machine frame and is spring-loaded on two sides in a plane perpendicular to the axis of the hinges. This allows it to deflect by a certain angle, the maximum value of which depends
Fig. 5. Pneumatic drifter PPG-3.
on the position of the locking pins in the sockets of the body. This circumstance makes it possible to use the PPG-3 for drilling holes in seams with a variable dip angle.
Industrial tests of experimental PPG-3 prototypes were carried out in the mines of the Kuzbass under the conditions of ten seams. During the test period, two drifters drilled a total of 500 linear m of holes with a diameter of 700 mm. As a result of the tests it was established that the cutting tool of the PPG-3 provides effective destruction of coal of any hardness; at the same time the rate of advance reaches 6 linear m/hour. At the same time, the design of the pro-
the raise borer has a number of shortcomings. Its running gear proved insufficiently strong. In addition, it does not ensure the specified drilling direction, since it lacks the appropriate steering and control mechanisms. Straight-line drilling of holes is achieved only in seams having a homogeneous structure. In the presence of crumpled coal packs, the pneumatic raise borer loses thrust and its feed ceases or becomes insignificant.
On the basis of the PPG-3 design, and taking into account the results of industrial tests, design work is currently being carried out at the Kuznetsk branch of Giprouglemash to create a more advanced PPG-5 pneumatic raise borer, prototypes of which are to be manufactured in 1958.
In addition to research into the creation of new drilling equipment in the two indicated directions, work is being carried out in the USSR to improve the drilling tool when using, as the drive, drilling-and-blasting machines that have proved most satisfactory in practice. Thus, for example, NIGRI [7] has created a drilling assembly for driving raise holes 1.1 m in diameter in hard rocks with a compressive strength of up to 1400 kg/cm².
The working member of the drilling assembly consists of three conical drums on which cutting teeth are fastened. The drums are arranged at an angle of 120° to one another. The teeth move in a complex planetary motion; together with the drums they rotate about the axis of the hole and, in addition, about the axes of the drums. The resultant speed of motion of the teeth relative to the face surface ranges from 4.75 to 10.2 m/sec.
Feed of the drilling assembly along the axis of the hole is carried out by the SBM-3u machine, while rotation of the working member is provided by a 21.5 kW motor mounted in the body of the assembly.
Laboratory tests on a stand in 1954 established the serviceability of the assembly when drilling upward from below in hard rocks and concrete blocks at a driving rate of from 0.46 to 1.5 running m/hour.
At the Department of Mining Machines and Mine Transport of the Tomsk Polytechnic Institute, research is being conducted to find means of mechanization for driving raise workings. For reaming holes 390 mm in diameter, drilled at an angle by an SBM-3u machine, to a diameter of 1500 mm, the first design version of the RUP-1 reamer has been developed [6]. The drive of the reamer is an SBM-3u machine connected to it by a drill string.
Destruction of the face is carried out by two crowns, each having four cutting teeth.
As theoretical studies have shown, the RUP-1 reamer can provide reaming of holes up to a diameter
1,500 mm when the SBM-3u raise-boring machine is used as the drive. The Anzherka “Svet Shakhtera” plant has manufactured pilot models of the reamer. Their industrial tests will be carried out in 1958.
In foreign practice, for drilling large-diameter holes, both experimental rigs for exploratory drilling and machines for drilling degassing holes are used. For drilling and reaming raise holes, a number of foreign firms produce special drilling machines and drifting units. The most widespread are the raise-boring machines of the “Korfmann” firm.
Fig. 6. Drilling machine type GB-20.
The GB-20 drilling machine of the “Korfmann” firm (Fig. 6) is intended for drilling holes with a diameter of up to 500 mm in rock, coal, and rock salt [8]. As the drive of the machine
either an air motor or a 22 hp electric motor may be used. The reduction gear provides operation at three speeds: 50, 75, and 10 rpm. The feed varies within the range from 50 to 400 mm/min. The total weight of the machine is 2080 kg. The entire installation is mounted on a base plate measuring 1.5 × 1.5 m. The height of the machine is 2.35 m. The drill rods, 1.5 m long and 76 mm in diameter, are equipped with special tubes for flushing.
For exploratory drilling and for drilling large-diameter holes (for ventilation and other purposes) through rock and coal in inclined and steeply dipping seams, the PVI/12 drilling machine of the firm “Hösse und Graefer” [8] is used.
Fig. 7. PVI/12 drilling machine.
Along the frame of the machine (Fig. 7) slide carriages on which a 15 hp motor for rotating the drill and a feed motor are mounted. The drill has two rotational speeds: 40 and 80 rpm. Drill feed is effected by means of gears and two toothed racks, which are fastened to the frame. The machine develops a feed force of up to 12 t. Pipes 95 mm in diameter and 1.5 m long are used as drill rods. The motors are controlled from a portable control panel installed next to the machine.
For drilling raise ventilation workings (0.5–0.9 m in diameter and 20–30 m long) from one level to another in seams with a dip angle of 45–90°, the “Martin” machine [9] has been produced in Canada by the firm “West Canadian Collieries.” First, using ordinary drilling equipment, a pilot hole 5 cm in diameter is driven in the specified direction. Then a cable is lowered through the pilot hole; one end is attached to the drill bit, and the other is fastened to the drum of a small winch. With the aid of the winch and cable, the rotating drill bit is pulled from below upward through the pilot hole. This makes it possible to use
all the machine’s power exclusively for rotating the drill bit.
In foreign mines, a method has found application for driving large cross-section raises by first drilling small-diameter holes (59–200 mm) and subsequently enlarging them from the bottom upward with special reamers with cable feed. According to this scheme, several drilling rigs have been developed; some of them were demonstrated in 1954 at the mining-equipment exhibition in Essen.
The drilling unit of the “Bade” company [7, 10] is intended for drilling upward vertical holes in rock, raises, and blind shafts with a diameter from 1 to 1.5 m to a height of up to 250 m. First, a pilot hole 150 mm in diameter is drilled by the usual method; then a winch is installed on the upper level (Fig. 8), the cable of which, 32 mm in diameter, passes through the hole to the lower level and is fastened to the drilling unit.
Fig. 8. Diagram of drilling holes with a drilling unit of the “Bade” company:
1—drilling machine; 2—cable.
The unit (Fig. 9) consists of four main elements: a two-speed reduction gear transmitting motion to three rotating bits, three cutters on each bit, two guide caterpillar tracks, and two skis. The driving electric motor, with a power of 50 hp and a speed of 1000 rpm, is connected by cable to the electrical network of the lower level.
The rotational speed of the bits is selected depending on the hardness of the rock. A traction winch with a 25 hp drive develops a force on the cable of about 10 t at a travel speed of
5 m/min. The drilling speed is within the range from 0.3 to 1.2 m/min.
Another drilling unit of the same firm for driving raise workings through rock was used in underground mine workings.
Fig. 9. Drilling unit of the “Beid” firm.
The unit has a planetary working mechanism in the form of two working disks, each 0.75 m in diameter (working diameter \(0.75 \times 2 = 1.5\) m), with cutters fastened along the edges of the disks. Feeding of the working mechanism to the face is accomplished by means of a winch installed on the surface. The winch rope is passed through a previously drilled
hole. The entire unit—the operating member, motor, and reduction gear—is suspended on a cable and, when the latter is tensioned, is fed to the face. The broken rock falls downward under its own weight, where it is loaded into cars.
According to approximately the same arrangement as the unit of the firm “Beyd,” the SB-30 drilling machine of the firm “Salzgitter” has been created in the FRG for driving raises in rock. Its distinguishing feature is that the destruction of the face is carried out by a working member consisting of a ring with teeth arranged around its circumference (Fig. 10). The drill cuttings and pieces of core fall downward under their own weight. The cutting ring is supported by a stationary hollow cylinder on a guide pipe located eccentrically and passing along the pilot borehole.
According to reports in the foreign press, tests of the unit in rocks of relatively low strength gave good results. When drilling soft rocks, the operating member of the reamer often became jammed, and the experiments did not yield positive results.
As a result of the brief survey carried out, slot-drilling machines may be divided, according to a number of features, into the following groups.
I. According to the technology of making the holes:
1) machines that carry out drilling in solid rock (SBM-3u, LBS-2, BRM-1, MBS-1, PPP-3, GB-20 of the firm “Korfmann,” RVI/12 of the firm “Nüsse und Graefer,” etc.);
2) machines that carry out drilling along a previously drilled borehole (drilling units of the firms “Salzgitter,” “Beyd,” etc.).
II. According to the method of feed and the type of transmission between the machine and the drilling tool:
Fig. 10. Diagram of drilling large-diameter vertical boreholes with the SB-30 drilling machine:
1—cutting ring; 2—supporting ring; 3—guide pipe; 4—rod; 5—pilot borehole; 6—core; 7—machine.
1) rod-type (LBS-2, SBM-3u, MBS-1, BRM-1, GB-20, PV1/12, etc.);
2) with cable feed (drilling units of the firms “Bade” and “Salzgitter”);
3) rod-and-cable type (“Martin” of the firm “West Canadian Collieries”);
4) with crawler feed (PPG-3).
III. According to the presence of an aligning device for drilling in a specified direction:
1) with an aligning device (SBM-3u, PPG-3, LBS-2, MBS-1, GB-20);
2) without an aligning device (PV1/12).
The efficiency of using machines of one group or another can be determined sufficiently fully only with due regard for the specific mining-engineering conditions of their operation.
REFERENCES
-
A. M. Terpigorev, P. N. Demidov, M. M. Protodyakonov, Mining Machines for the Extraction of Bedded Minerals. Ugletekhizdat, 1950.
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S. I. Chugunikhin, Lightweight Raise-Boring Drill LBS-2. Ugletekhizdat, 1949.
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S. I. Chugunikhin, Raise-Boring Machines. Ugletekhizdat, 1950.
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Raise-Boring Machine SBM-3u. Glavuglemash, Anzhero-Sudzhensk, 1956.
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B. F. Skafa, Results of tests of the BRM-1 rotary drilling machine. Mechanization of Labor-Intensive and Heavy Work, No. 9, 1955.
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I. V. Rodionov, Yu. A. Rozenberg, V. N. Karminskii. Studies of reamers for raise workings. Article in the present collection.
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A. S. Arkhangel’skii, Heading Combines. Ugletekhizdat, 1956.
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Trösken K., Der Stand des drehenden Groslochbohrens im Ruhrbergbau unter Tage, Glückauf, Heft 37/38, 1954.
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“Martin” Drilling Machine, TsITI MUP USSR, 1956.
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Glebe E., Der technische Fortschritt auf der Deutschen Bergbauausstellung 1954 in Essen, Glückauf, Heft 37/38, 1954.
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D. P. Dukhovlinov, Mechanization of work in the potash mines of the GDR. Mechanization of Labor-Intensive and Heavy Work, No. 6, 1957.
Noted Misprints
| Page | Line | Printed | Should be | Responsibility |
|---|---|---|---|---|
| 13 | 1 from bottom | 7-10 | T-10 | Corr. |
| 14 | 13 from bottom | R-754 | RH-754 | » |
| 28 | 1 from bottom | $$A_y=\frac{mV_{\sigma}^{2}}{2}$$ | $$A_y=\frac{mV_{y}^{2}}{2}$$ | Auth. |
| 34 | 18–20 from bottom | 2 — diagram of oscillations of the hammer body; 3 — diagram of the angular displacement of the drill; 4 — diagram of the air pressure in the rear cavity of the hammer cylinder; 5 — diagram of the pressure in the front cavity; | Auth. | |
| 35 | 1 from bottom | Scerving Stiense | Serving Science | Ed. |
| 46 | 14 from bottom | changes | change | Typ. |
| 90–91 | Figs. 7 and 8 | swap places, retaining the figure captions in place | Auth. | |
| 97 | 10 from bottom | of the drilling hammer | of the automatic feeder | » |
| 107 | 2–3 from bottom | stop | stopping | » |
| 156 | 2 from top | surfaces | surface | Corr. |
| 166 | 14 from bottom | drilled out | drilled | Auth. |
| 179 | 9 from top | kinetic | kinematic | Corr. |
| 189 | 5 from top | (59–200 mm) | (50–200 mm) | » |
| 192 | 10 from bottom | will expand | expander | Typ. |
| 197 | 1 from top | kinetics | kinematics | Corr. |
| 198 | 3–6 from top | Read the fifth line after the second line | Typ. | |
| 199 | 14 from bottom | kinetics | kinematics | Auth. |
| 212 | 12 from top | L. B. Levenmon | L. B. Levenson | Auth. |
| 219 | 3 from bottom | $$A=a+h\ldots+h.$$ | $$A=a+h\ldots+h.\ (16)$$ | Corr. |
| 223 | 3 from top | $$-\left(30\frac{\omega}{\omega_{0}}\right)^{2}+5$$ | $$-30\left(\frac{\omega}{\omega_{0}}\right)^{2}+5$$ | Typ. |
| 224 | 19–20 from top | increased | was increasing | Corr. |
| 229 | 10 from top | AOF4-2 | AOF42-2 | Auth. |
| 243 | 11 from top | 1.15 | 1.5 | Corr. |
Order 39