STUDY OF THE GEAR-SCREW MECHANISM OF THE AUTOMATIC FEEDER OF AN ELECTROPNEUMATIC DRILLING HAMMER

P. M. Alabuzhev, O. D. Alimov, I. V. Rodionov,
D. N. Malikov

Introduction

Up to the present time, mining practice has not had at its disposal drilling hammers with an electric drive. At the same time, the need for such machines for drilling blast-holes and boreholes is keenly felt in the mining, coal, and construction industries, as well as in geological exploration. Numerous attempts to create high-productivity electric drilling hammers have so far been unsuccessful.

Experimental and theoretical investigations [1, 2] have established that at present it is possible to create high-productivity electric column-type drilling hammers equivalent in impact power to drilling hammers of the KTsM-4 type.

As a result of joint work by researchers of the Tomsk Polytechnic Institute and engineers of the Tomsk Electromechanical Plant, a design was developed for an electropneumatic drilling hammer with automatic feed. This hammer (Fig. 1) consists of four main units: an impact unit operating on the electrovacuum principle, a mechanism for rotating the drill, a mechanism for automatic feeding of the drilling hammer, and an electric motor. The mechanisms for drill rotation and for automatic feeding of the drilling hammer constitute a single connected system—the feeder mechanism.

The question of the design of the feeder, which feeds the drilling hammer to the working face, is of great practical importance: first, with an unsatisfactory feeder, a column-type drilling hammer cannot provide the results required in practice; second, the productivity of drilling operations can be increased with multi-hammer servicing, which can be accomplished only if there are automatic feeding devices that eliminate continuous intervention by the driller in controlling the machine’s operating process.

Proceeding from an analysis of percussive-rotary drilling [2], it fol-

... that the automatic feeder of a column-mounted drilling hammer must provide not only the advance of the drilling hammer toward the face with a constant pressing force and vary the feed rate depending on the hardness of the rock, but also reduce this force, and also withdraw the drilling hammer a certain distance backward in the event that the drill bit jams in cracks of the rock being broken.

The most advanced feeders, which have found wide application in pneumatic drilling hammers (the screw type with a pneumatic motor in the KTsM-4, piston feeders in telescopic drilling hammers), do not satisfy all the requirements indicated above. At best, they provide a definite feed force during drilling and make it possible to vary the feed rate depending on the hardness of the rock. In addition, these feeders cannot be used in electric drilling hammers, since it would be inexpedient to use, alongside the main electric drive, a pneumatic drive.

Fig. 1. Kinematic diagram of an electropneumatic drilling hammer with automatic feed.

At the same time, we should point out that we are not aware of designs of feeders for drilling hammers with an electric drive. The principal difficulty in creating such feeders lies in the considerable complexity of their constructive execution, especially when the entire machine is made explosion-proof. Everything stated above raised the question of the need for a more thorough theoretical and experimental investigation of the automatic-feeder mechanism of the above-described electropneumatic drilling hammer.

In the investigation the aim was set: to verify the correctness of the theoretical premises adopted in designing

automatic feeder, and to determine its serviceability, to develop working formulas and nomograms for calculating analogous feeding devices for certain preassigned parameters of drilling machines.

For the purpose of experimentally investigating the serviceability of the automatic feeder, the latter was manufactured by the Tomsk Electromechanical Plant as an independent unit. The experimental investigation was carried out in the Mining Machines Laboratory of the Tomsk Polytechnic Institute. According to preliminary data, the feeder mechanism operates quite satisfactorily*.

In the present work some results of a theoretical investigation of the automatic feeder are presented.

Description of the design of the automatic-feeder mechanism

The gear-screw mechanism of the automatic feeder (Figs. 1 and 2), which performs the feed of the drilling hammer and the rotation of the drill, consists of a series of gear wheels (4, 11, 10, 7, 8, 9, 5, 6), including an asymmetric cylindrical differential, a lead screw 12, a nut 17, and bushings 15 and 18.

Fig. 2. Diagram of the forces and moments acting on the links of the automatic-feeder mechanism.

* The results of this investigation are set forth in an article included in the present collection.

The differential mechanism is formed by wheel 4, which is the carrier of the pins of three planet gears 11, and by two central wheels 7—8 and 10. The large central wheel 7—8 has two toothed rims 7 and 8. The inner rim 8 is in mesh with the planet gears 11 of the differential, and the outer one is in mesh with gear wheel 9, which is connected by a key to the feed nut 17. In addition, gear wheel 7—8, through the hub, key, and bushing 15 with a hexagonal hole for the shank of drill 16, transmits rotation to the latter. Thus, from central wheel 7—8, the feed nut 17 and drill 16 are set in rotation.

The small central wheel 10 is connected through a bushing by a keyed joint to gear wheel 5, which works in pair with wheel 6. Wheel 6 is mounted on bushing 18, which on the inner surface embracing the screw has two keyed projections that enter the longitudinal grooves of the feed screw 12 with a right-hand thread. The feed screw can rotate in supports 19, fastened to the bed of the trough-shaped fixed frame of the feeder, but cannot move in the axial direction. The key grooves are cut along the entire length of screw 12; therefore wheel 6 can not only rotate the screw but also move freely along its axis. To brake the feed screw, a friction multi-disk brake clutch 14 is installed at the cantilever end of its shaft.

Since the bearings of gear wheels 9 and 6, nut 17, and bushing 18 are secured on the body of the drilling hammer and can move relative to the screw only together with it, when the nut is screwed on or off, the drilling hammer is fed toward the face or away from the face relative to the fixed guides of the feeder. The feed is effected by the difference in angular velocities of screw 12 and nut 17. Bushing 18 enters at one end into feed nut 17, forming with it a sliding-friction pair, and at the other end rests on bearing 20a, secured in the body of the drilling hammer.

The gear wheels of the automatic feeder have the following parameters: module of engagement \(m=2\) mm; number of teeth \(z_4=64,\ z_5=61,\ z_6=36;\ z_7=62;\ z_8=54;\ z_9=35;\ z_{10}=30;\ z_{11}=12\).

Feed screw: trapezoidal thread, right-hand, thread angle \(2\beta=30^\circ\), mean thread diameter \(d_{\mathrm{cp}}=27\) mm, number of thread starts \(i=4\), screw lead \(a=it=24\) mm, screw pitch \(t=\dfrac{a}{i}=6\) mm.

Structure of the kinematic chain

The differential gear mechanism, which is part of the mechanism for feeding and rotating the drill, has: number of moving links \(n=4\), number of rotating pairs of class V \(p_5=4\), number of pairs of class IV \(p_4=2\). The fixed link of the mechanism is the body of the drilling hammer. Since all links perform motions in parallel—

...parallel planes, it is a plane mechanism to which P. L. Chebyshev’s structural formula [3, p. 102] may be applied in order to determine the degree of mobility of the kinematic chain,

\[ W = 3n - 2p_5 - p_4 = 2. \]

Thus, in kinematic terms, the mechanism in question is a mechanical system with two degrees of freedom.

The central wheels of the mechanism, \(7—8\) and \(10\), are connected with one another by an additional transmission with one degree of freedom, consisting of gears \(5\) and \(6\), the sleeve, the lead screw, the nut, and wheel \(9\). This connection determines a definite dependence between the angular velocities of the indicated central wheels. It follows from this that the automatic-feeder mechanism is a closed differential mechanism, for setting which in motion it is sufficient to have one driving member; this role is performed by the carrier—gear \(4\). The drill \(16\) and the central wheel \(7—8\) are connected with one another and have the same rotational speed, which depends on the change in resistance to rotation of the drill in the borehole. Therefore the law of motion of central wheel \(10\), and consequently also of the lead screw, likewise depends on the change of this resistance during the drilling process.

Kinematic study of the automatic-feeder mechanism

The angular velocities of the gears of the differential mechanism were determined by the tabular method, according to the Swamp rule [4, 5].

In the subsequent discussion it is assumed that the carrier—wheel \(4\)—rotates counterclockwise, when viewed along the screw from the side of the brake clutch \(14\) toward the face.

We investigated the following possible operating cases of the drilling hammer:

1. The lead screw does not rotate (it is braked by the friction clutch), therefore \(n_{\mathrm{в}} = n_6 = n_5 = n_{10} = 0\), and the differential mechanism is transformed into a planetary one, in which the fixed member is central wheel \(10\), the driving member is carrier \(4\), and the driven member is wheel \(7—8\).

The number of revolutions of the double-crown wheel \(7—8\) (the drill) is

\[ n_{7-8} = n_{\mathrm{б}} = -n_4\left(1+\frac{z_{10}}{z_8}\right)\ \text{rev/min}. \]

The number of revolutions of wheel \(9\) (the lead nut) is

\[ n_9 = n_{\mathrm{г}} = n_4\left(1+\frac{z_{10}}{z_8}\right)\frac{z_7}{z_9}\ \text{rev/min}. \]

Since the lead screw is stationary, the nut, as it rotates, will screw itself onto it and move the drilling hammer toward the face at a speed

\[ V = a n_{\mathrm{g}} = a n . \]

1. The drill has become jammed in a crack in the rock being broken. The central gear \(7\text{–}8\) is stationary; gear \(9\) and the nut of the lead screw do not rotate. As a result, we have a planetary mechanism with a fixed member—the gear \(7\text{–}8\), the driving member—the carrier \(4\), and the driven member—the central gear \(10\).

\[ (n_{7-8}=n_9=n_{\mathrm{g}}=0). \]

In this case:

\[ n_{10}=n_5=-n_4\left(1+\frac{z_8}{z_{10}}\right)\ \text{rev/min}, \]

\[ n_6=n_{\mathrm{v}}=+n_4\left(1+\frac{z_8}{z_{10}}\right)\frac{z_5}{z_6}\ \text{rev/min}. \]

Through gears \(10, 5, 6\) and bushing \(18\), rotation is transmitted to the lead screw, which moves the nut and, together with it, the body of the drilling hammer, relative to the stationary feeder body to the left, away from the face, at a speed

\[ V=a n_{\mathrm{v}}=a n_6 . \]

1. General case of operation of the feed mechanism and drill rotation. In the general case all the members, with the exception of the feeder body, are movable, and the mechanism becomes differential. It is evident that, with a constant rotational speed of the driving member \(4\), all the driven members will at a given instant have different angular velocities. Moreover, when the resistance on the drill changes, i.e., when the number of revolutions of the central gear \(7\text{–}8\) changes, the speeds of all the remaining members will vary within the range of the two cases considered above, the modes of which are limiting modes of operation of the drilling hammer. On the basis of what has been said, the following expressions may be written:

\[ -\,n_4=\mathrm{const}, \]

\[ 0<n_{7-8}=n_9<-n_4\left(1+\frac{z_{10}}{z_8}\right), \]

\[ 0<n_{10}=n_5<-n_4\left(1+\frac{z_8}{z_{10}}\right), \]

\[ 0\le n_9=n_{\mathrm{g}}<+n_4\left(1+\frac{z_{10}}{z_8}\right)\frac{z_7}{z_9}, \]

\[ 0\le n_6=n_{\mathrm{v}}<+n_4\left(1+\frac{z_8}{z_{10}}\right)\frac{z_5}{z_6}. \]

where the plus sign denotes the direction of rotation clockwise, when looking along the screw from the side of the brake coupling toward the face, and the minus sign denotes the opposite direction.

Let us find the interrelation between the angular velocities of the links of the differential mechanism. Suppose that, at a constant angular velocity of driver 4, the drill and the central wheel 7—8 connected with it make \(K n_4\) revolutions per minute, where \(K\) is a coefficient characterizing the operating mode of the feeder. We shall apply the tabular method (see the table). From row 5 of the table we have:

\[ -n_4=\mathrm{const}, \tag{1} \]

\[ n_{7-8}=n_6=-K n_4, \tag{2} \]

\[ n_{10}=K n_4 \frac{z_8}{z_{10}}-n_4\left(1+\frac{z_8}{z_{10}}\right), \tag{3} \]

\[ n_9=n_{\mathrm{g}}=+K n_4 \frac{z_7}{z_9}, \tag{4} \]

\[ n_6=n_{\mathrm{v}}=n_4\left(1+\frac{z_8}{z_{10}}\right)\frac{z_5}{z_6} -K n_4 \frac{z_9}{z_{10}}\cdot\frac{z_5}{z_6}. \tag{5} \]

Solving equations (4) and (5) simultaneously, we find the dependence \(n_{\mathrm{g}}=f(n_{\mathrm{v}})\) in the form

\[ \frac{n_{\mathrm{v}}} {n_4\left(1+\frac{z_8}{z_{10}}\right)\frac{z_5}{z_6}} + \frac{n_{\mathrm{g}}} {n_4\left(1+\frac{z_{10}}{z_8}\right)\frac{z_7}{z_9}} =1. \tag{6} \]

From equations (2) and (5) we obtain \(n_{\mathrm{v}}=\varphi(n_{\mathrm{b}})\)

\[ \frac{n_{\mathrm{v}}} {n_4\left(1+\frac{z_8}{z_{10}}\right)\frac{z_5}{z_6}} - \frac{n_{\mathrm{b}}} {n_4\left(1+\frac{z_{10}}{z_8}\right)} =1. \tag{7} \]

The feed rate of the drilling hammer is determined by the difference between the angular velocities of the lead nut \((n_{\mathrm{g}}=n_9)\) and the lead screw \((n_{\mathrm{v}}=n_6)\), and is equal to

\[ V=(n_{\mathrm{g}}-n_{\mathrm{v}})a. \tag{8} \]

Substituting into equation (8) the value of \(n_{\mathrm{g}}\) from equation (6), we determine \(V=\psi(n_{\mathrm{v}})\),

\[ \frac{V} {n_4 a\,\frac{z_7}{z_9}\left(1+\frac{z_{10}}{z_8}\right)} + \frac{n_{\mathrm{v}}} {n_4\, \frac{\frac{z_7}{z_9}\left(1+\frac{z_{10}}{z_8}\right)} {1+\frac{z_7}{z_9}\frac{z_{10}}{z_8}\frac{z_6}{z_5}}} =1. \tag{9} \]

Table 6

The dependence \(V = F(n_b)\) can be established if, in equation (9), \(n_v\) is replaced by the expression obtained from equation (7),

\[ \frac{V}{n_4 a\left(1+\frac{z_8}{z_{10}}\right)\frac{z_5}{z_6}} + \frac{n_b}{ \left(1+\frac{z_{10}}{z_8}\right) \frac{n_4}{ \left(1+\frac{z_7}{z_9}\cdot\frac{z_{10}}{z_8}\cdot\frac{z_6}{z_5}\right)} } = -1 . \tag{10} \]

The functional dependencies established in general form,

\[ n_g=f(n_v), \quad n_v=\varphi(n_b), \quad V=\psi(n_v) \quad \text{and} \quad V=F(n_b), \]

are equations of straight lines in the intercepts cut off on the coordinate axes.

The coefficient \(K=\dfrac{n_{7-8}}{n_4}=\dfrac{n_b}{n_4}\) varies within the following limits: the lead screw does not rotate, and the drilling hammer moves toward the face,

\[ K=1+\frac{z_{10}}{z_8}. \]

The drill has jammed,

\[ n_{7-8}=n_b=0,\quad K=0. \]

For \(K=1\):

\[ n_{7-8}=n_b=-n_4, \]

\[ n_{10}=-n_4, \]

\[ n_g=n_9=+n_4\frac{z_7}{z_9}, \]

\[ n_v=n_6=+n_4\frac{z_5}{z_6}, \]

\[ V=(n_g-n_v)a=n_4\left(\frac{z_7}{z_9}-\frac{z_5}{z_6}\right)a. \]

As a result of substituting into equations (6), (7), (9), and (10) the numerical values of the known quantities entering them for the designed automatic feeder, we obtain the following dependencies:

\[ \frac{n_v}{4{,}746n_4}+\frac{n_g}{2{,}752n_4}=1, \tag{11} \]

\[ \frac{n_v}{4{,}746n_4}-\frac{n_b}{1{,}555n_4}=1, \tag{12} \]

\[ \frac{V}{6{,}631n_4}+\frac{n_v}{1{,}746n_4}=1, \tag{13} \]

\[ \frac{V}{11{,}38n_4}+\frac{n_b}{0{,}983n_4}=-1. \tag{14} \]

For \(n_4 = 175\) rpm the formulas take the form:

\[ n_{\mathrm{v}} = 830 - 1.722 n_{\mathrm{g}}, \tag{15} \]

\[ n_{\mathrm{v}} = 830 + 3.052 n_{\mathrm{c}}, \tag{16} \]

\[ V = 1160 - 3.803 n_{\mathrm{v}}, \tag{17} \]

\[ V = -(1992 + 1.158 n_{\mathrm{b}}), \tag{18} \]

where \(n_{\mathrm{v}}, n_{\mathrm{g}}, n_{\mathrm{b}}\) are given in rpm; \(V\) is in cm/min. When using equations (11–18), the directions of rotation of the gear wheels must be taken into account; therefore the values \(+n_{\mathrm{g}}, +n_{\mathrm{v}}\), and \(-n_{\mathrm{b}}\) must be substituted.

Fig. 3. Nomogram characterizing the kinematics of the automatic feeder.

The graphs constructed from equations (15), (16), (17), and (18) are combined into the nomogram shown in Fig. 3. The nomogram makes it possible, from a specified value of the speed of any one link, to determine the speeds of all the remaining links. Thus, by using the nomogram, one can kinematically characterize the entire variety of operating modes of the drilling hammer that is provided by this gear-screw automatic feeder. For example, suppose the feed speed of the machine toward the face is specified as \(V = +200\) cm/min. It is necessary to determine the angular velocities of the screw, the nut, and the drill steel. On the measuring line \(V\), the specified speed corresponds to point \(A\). Through point \(A\) we draw a vertical straight line...

the straight line \(MN\), which intersects the lines representing the laws of distribution of the quantities sought at points \(Б\), \(В\), and \(Г\). The projections of points \(Б\), \(В\), and \(Г\) onto the corresponding coordinate axes determine the unknown quantities: \(n_{\mathrm{в}}=+255\) rpm, \(n_{\mathrm{г}}=+330\) rpm, \(n_{\mathrm{б}}=-190\) rpm.

In conclusion, we note that, using the dependences represented by equations (6), (7), (9), and (10), it is possible not only to analyze the given feeder, but also to synthesize a new mechanism.

Statics of the automatic feeder mechanism

Let us assume that, at a constant speed of the driver 4, the central gears 7—8 and 10 of the differential mechanism rotate at the given moment with angular velocities \(n_{\mathrm{в}}\) and \(n_{10}\).

On the side of gear 4, the total driving force \(P_4\) is applied to the pins of the three planet gears. To simplify the problem, we consider this force as reduced to the axis of one planet gear (Fig. 2). Since the load \(P_4\) is concentrated at the center of planet gear 11, the pressures \(P_8\) and \(P_{10}\), which are circumferential forces applied to gears 8 and 10, are equal to each other. Then the moments acting on the main coaxial shafts with gears 4, 8, and 10 will be equal to:

\[ M_4=P_4 l, \]

\[ M_8=P_8 r_8=\frac{P_4}{2}\cdot \frac{m z_8}{2}, \]

\[ M_{10}=P_{10} r_{10}=\frac{P_4}{2}\cdot \frac{m z_{10}}{2}, \]

where \(l\) is the radius of rotation of the pin of planet gear 11,
\(r_8\) and \(r_{10}\) are the pitch-circle radii of gears 8 and 10.
Since

\[ l=\frac{r_8+r_{10}}{2}, \]

then

\[ M_4=M_8+M_{10}. \tag{19} \]

The equations expressing the dependences between the moments on the coaxial shafts in the differential mechanism, taking friction losses into account, have the form:

\[ M_4=\frac{M_8}{\eta}\left(1+\frac{z_{10}}{z_8}\right), \tag{20} \]

\[ M_4=\frac{M_{10}}{\eta}\left(1+\frac{z_8}{z_{10}}\right), \tag{21} \]

where \(\eta\) is the efficiency of the differential mechanism, in which all three principal links are movable. The determination of \(\eta\) will be given below.

The central double-crown gear \(7\)—\(8\) simultaneously transmits rotation to the drill \(16\) and to the traveling nut \(17\); therefore one may write

\[ M_8 = M_b + M_{\mathrm{r}}^{8}, \tag{22} \]

where \(M_b\) is the component of \(M_8\) going to overcome the moment of resistance to rotation of the drill;

\(M_{\mathrm{r}}^{8}\) is the component of \(M_8\) equal to the moment of resistance, reduced to the shaft of gear \(8\), associated with the rotation of the traveling nut \(17\) relative to the traveling screw \(12\).

During operation of the feeder the quantity \(M_b\) varies within the limits from \(M_b=0\) (the drill rotates freely) to \(M_b=M_{b\max}\) (the drill is jammed)

\[ M_{\mathrm{r}}^{8}=\frac{M_{\mathrm{r}}}{i_{7-9}\eta_1}, \tag{23} \]

where \(M_{\mathrm{r}}=M_{\mathrm{fr.r}}=F \dfrac{d_{\mathrm{cp}}}{2}\tg(\alpha+\varphi)\) is the torque on the nut, numerically equal to the moment of resistance in the thread of the screw–nut pair; \(F=F_b+F_{b.m}\) is the axial force acting between the nut and the screw; it represents the total force of resistance to feeding the drilling hammer onto the face, reduced to the screw axis;

\(F_b\) is the force pressing the drill against the face;

\(F_{b.m}\) is the force of resistance to displacement of the drilling hammer along the guides of the feeder body;

\(d_{\mathrm{cp}}\) is the mean diameter of the thread;

\(\alpha\) is the lead angle of the screw line;

\(\varphi\) is the friction angle of the screw–nut pair;

\(i_{7-9}=\dfrac{z_9}{z_7}\) is the gear ratio;

\(\eta_1\) is the efficiency of the transmission from gear \(8\) to the nut.

After substituting the quantities entering into equation (22), we obtain

\[ M_8 = M_b + F\frac{d_{\mathrm{cp}}}{2\eta_1}\tg(\alpha+\varphi)\frac{z_7}{z_9}. \tag{24} \]

To ensure rotation of the drill and feeding of the drilling hammer onto the face, it is necessary to overcome the moment \(M_8\); for this purpose a corresponding moment must be created on the central gear \(10\).

Let us denote by \(M_{\mathrm{v}}\) the torque on the screw axis, which is transmitted through gearing \(5\)--\(6\) from the shaft of the central wheel \(10\). Then the torque on wheel \(10\) will be equal to

\[ M_{10}=M_{\mathrm{v}}\frac{z_5}{z_6}\cdot \frac{1}{\eta_2}, \tag{25} \]

where \(\eta_2\) is the efficiency of the transmission from the shaft of wheel \(5\) to the screw shaft.

From an analysis of the pattern of forces and moments acting on the links of the mechanism (Fig. 2), it follows that the torques \(M_{\mathrm{g}}\) and \(M_{\mathrm{v}}\) always have the same direction. The resistance corresponding to these moments is produced artificially by means of a multiple-disk brake clutch \(14\), which consists of two groups of steel disks. One group of disks is connected with the fixed housing of the feeder, and the other with the lead screw. The total reactive moment \(M_{\mathrm{t}}\) of the resistance to rotation produced by the brake clutch must therefore be equal to

\[ M_{\mathrm{t}}=M_{\mathrm{g}}+M_{\mathrm{v}}. \tag{26} \]

Let us consider how the automatic feeder responds to a change in the resistance to rotation of the drill.

Suppose that, as a result of an increase in the resistance to rotation of the drill in the borehole, the moment \(M_{\mathrm{b}}\) has increased by the amount \(\Delta M_{\mathrm{b}}\). With the increase of \(M_{\mathrm{b}}\), the circumferential force \(P_{11}\), representing the pressure of the tooth of wheel \(8\) on the tooth of satellite \(11\), receives an increment

\[ \Delta P_{11}=\frac{\Delta M_{\mathrm{b}}}{r_8}, \]

as a result of which the equilibrium of the whole system is disturbed. The force \(\Delta P_{11}\), with respect to the axis of rotation of the satellite, creates a moment \(\Delta M_{11}=\Delta P_{11}r_{11}\), which, in turn, causes an additional pressure

\[ \Delta P_{10}=\Delta P_{11}=\frac{\Delta M_{11}}{r_{11}} \]

of the satellite tooth on the tooth of wheel \(10\). As a result, the torque on the central wheel \(10\) increases by the amount \(\Delta M_{10}=\Delta P_{10}r_{10}\), which ultimately leads to an increase in the moment \(M_{\mathrm{v}}\) rotating the screw by

\[ \Delta M_{\mathrm{v}}=\Delta M_{10}\frac{r_6}{r_5}. \]

At the same time, with the increase of \(M_{\mathrm{b}}\), the torque on the nut decreases by the amount

\[ \Delta M_{\mathrm{g}}=\Delta M_{\mathrm{b}}\frac{r_9}{r_7}. \]

As a result of the redistribution of moments, the angular velocity of the screw \(n_{\mathrm{v}}\) increases while the speed of the nut \(n_{\mathrm{g}}\) decreases. Therefore, as the resistance to rotation of the drill increases, the feed rate \(V\) decreases; when \(n_{\mathrm{v}}=n_{\mathrm{g}}\), \(V=0\). With a further increase in \(M_{\mathrm{b}}\), the inequality \(n_{\mathrm{v}}>n_{\mathrm{g}}\) will be observed, owing to which the feed rate becomes negative and the hammer will move away from the bottom of the hole. In the limiting case--jamming of the drill bit in the borehole, when \(n_{\mathrm{b}}=0\), the differential mechanism is transformed into a planetary mechanism with fixed central wheels.

wheels 7–8 and the nut of the lead screw \((n_{\mathrm{g}}=0)\). In this case the screw will acquire the maximum angular velocity of rotation

\[ n_{\mathrm{v}\,\max} = n_4\left(1+\frac{z_8}{z_{10}}\right)\frac{z_5}{z_6} \]

and there will occur a rapid withdrawal of the body of the drilling hammer from the face with the velocity

\[ V_{\max} = -\,n_4\left(1+\frac{z_8}{z_{10}}\right)\frac{z_5}{z_6}\,a . \]

Let us point out that the kinematic ratios of the automatic-feeder mechanism can be selected by calculation in such a way that the required withdrawal of the drilling hammer when the drill jams is accomplished in the time between two impacts of the drill on the rock.

When the resistance to rotation of the drill in the blasthole decreases, a process opposite to that described will occur.

The maximum feed rate of the drilling hammer at the face corresponds to the case in which the drill encounters no resistance from the blasthole. In this case the resistances associated with rotation of the drill will be insignificant. Therefore the sum of the moments rotating the screw and the nut will be less than the moment produced by the brake clutch. It follows from this that screw 12 will become stationary, and the differential mechanism will turn into a planetary mechanism with fixed central gear 10, driving carrier 4, and driven central gear 8. In this case the nut will rotate with the maximum number of revolutions

\[ n_{\mathrm{g}\,\max} = +\,n_4\frac{z_7}{z_9}\left(1+\frac{z_{10}}{z_8}\right), \]

and the greatest feed rate will be equal to

\[ V_{\max} = +\,n_4\frac{z_7}{z_9}\left(1+\frac{z_{10}}{z_8}\right)a . \]

A change in the resistance to the drill in the blasthole also causes a change in the number of revolutions of the drill. Thus, for example, when the resistance increases because of the hardness of the rock or other factors, the rotational speed of the drill decreases simultaneously with a decrease in the feed rate. The indicated change in the number of revolutions of the drill, at a constant number of impacts, leads to a decrease in the angle of rotation of the drill bit between two impacts relative to the bottom of the blasthole. Conversely, when the resistance to rotation decreases (when drilling weaker rocks), the feed rate and the angle of rotation of the drill between impacts increase. Such a dependence of the change in the angle of rotation of the drill between two impacts fully satisfies the requirements imposed on rotary devices of the drill from the point of view of reducing the energy consumption of the process of breaking rock and increasing drilling productivity.

The above analysis of the operation of the mechanism of the gear-screw automatic feeder makes it possible to conclude that it not only automates the feed, but also protects the entire system from possible overloads. This is achieved by introducing into the design of the automatic feeder a differential mechanism and a multidisc brake clutch.

Preliminary adjustment of the automatic feeder in order to select the most appropriate operating modes of the drilling hammer is carried out by changing the force \(Q\) compressing the friction disks of clutch 14 (Fig. 1), and consequently by changing the resistance to rotation of the lead screw.

Equations (19)—(26) make it possible to establish the following relationships between the quantities characterizing the operation of the automatic-feeder mechanism:

\[ A M_6 + B F - M_4 = 0, \tag{27} \]

where

\[ A = \frac{z_6}{z_5}\cdot \frac{z_{10}}{z_8}\eta_2; \qquad B = \frac{d_{\mathrm{cp}}}{2}\tan(\alpha+\varphi) \left(1+\frac{z_6}{z_5}\cdot \frac{z_7}{z_9}\cdot \frac{z_{10}}{z_8}\cdot \frac{\eta_2}{\eta_1}\right); \]

\[ M_4 = M_6\frac{1}{\eta} \left[ 1- \frac{ \frac{z_7}{z_9}\cdot \frac{1}{\eta_1} - \frac{z_5}{z_6}\cdot \frac{1}{\eta_2} }{ \frac{z_5}{z_6}\cdot \frac{z_8}{z_{10}}\cdot \frac{1}{\eta_2}\cdot \left( 1+\frac{z_6}{z_5}\cdot \frac{z_7}{z_9}\cdot \frac{z_{10}}{z_8}\cdot \frac{\eta_2}{\eta_1} \right) } \right] + \]

\[ + M_T\frac{1}{\eta} \left[ \frac{z_5}{z_6}\cdot \frac{1}{\eta_2} + \frac{ \frac{z_7}{z_9}\cdot \frac{1}{\eta_1} - \frac{z_5}{z_6}\cdot \frac{1}{\eta_2} }{ \left( 1+\frac{z_6}{z_5}\cdot \frac{z_7}{z_9}\cdot \frac{z_{10}}{z_8}\cdot \frac{\eta_2}{\eta_1} \right) } \right]. \tag{28} \]

As was shown, the feeder mechanism is a closed differential mechanism that includes a screw kinematic pair. Methods for determining the efficiency of such mechanisms are not known to us. Therefore, for an approximate assessment of friction losses we proceed as follows. We determine the efficiency of the differential mechanism, and then, through partial efficiencies, take into account the losses in the transmissions from the central wheels 8 and 10 to the nut and the lead screw. A more exact solution of this question should be the subject of a special investigation of a theoretical and experimental nature.

At present there exist a number of methods for determining friction losses and the efficiency of planetary mechanisms [4; 6; 7]. “Of all the techniques for determining the efficiency of planetary transmissions, the most rational is that in which the required value is expressed through the efficiency \(\eta^{\mathrm{H}}\) (or the loss coefficient \(\psi^{\mathrm{H}}=1-\eta^{\mathrm{H}}\)) of the simple transmission obtained from the planetary one by stopping the carrier, i.e., by imparting to all links the angular velocity of the carrier with the opposite sign” [6, p. 196].

To estimate friction losses in the differential mechanism of the feeder, we shall use the method set forth in [9]. For the general case of operation of the mechanism, when all three main links are movable (carrier 4, central wheels 8 and 10), on average we shall have \(\eta=0.96\).

The efficiency of transmission from central wheel 8 to nut 17, taking into account losses in meshing, in rolling bearings, and friction losses of bushing 18 against nut 17, is taken as \(\eta_1=0.90\).

The efficiency of transmission from the shaft of wheel 5 to the screw shaft (losses in meshing, in the supports of the lead screw, and friction losses in the grooves during displacement of bushing 18 along the axis of the lead screw) is \(\eta_2=0.85\).

Fig. 4. Graph of the variation of the feed force \(F\) as a function of the variation of the torque on the drill \(M_b\) at \(M_t=\mathrm{const}\).

Let us determine the constant coefficients \(A\) and \(B\) entering equation (27) from the data for the feeder being designed:

\[ A=\frac{z_6}{z_5}\cdot\frac{z_{10}}{z_8}\eta_2=0.28; \]

\[ B=\frac{d_{\mathrm{av}}}{2}\operatorname{tg}(\alpha+\varphi)\left(1+\frac{z_6}{z_5}\cdot\frac{z_7}{z_9}\cdot\frac{z_{10}}{z_8}\cdot\frac{\eta_2}{\eta_1}\right)=1.21; \]

\[ \operatorname{tg}\alpha=\frac{a}{\pi d_{\mathrm{av}}}=0.28308;\quad \alpha=15^\circ48'. \]

The lead screw is provided with a trapezoidal thread with an included angle at the crest \(2\beta=30^\circ\); therefore the reduced coefficient of friction in the thread is equal to

\[ f'=\operatorname{tg}\varphi=\frac{f}{\cos\beta}=0.2588. \]

Under operating conditions, considerable contamination of the thread is possible; therefore we take \(f=0.25\) [5, p. 332].

After substituting the values of \(A\) and \(B\), equation (27) takes the form

\[ 0.28M_b+1.21F-M_t=0. \tag{29} \]

Substituting the known quantities into equation (28), we obtain

\[ M_4=1.04M_b+2.05M_t. \tag{30} \]

The dependences (29) and (30) are presented graphically in Figs. 4 and 5.

Multiplying the right- and left-hand sides of equality (30) by the quantity

\[ \frac{n_4}{71620}\,0.736, \]

we obtain:

\[ \frac{M_4 n_4}{71620}\,0.736 = \frac{1.04 M_b n_4}{71620}\,0.736 + \frac{2.05 M_t n_4}{71620}\,0.736, \tag{31} \]

where

\[ \frac{M_4 n_4}{71620}\,0.736 = P_4 \ \text{kW} \]

is the power at the driver—wheel 4;

Fig. 5. Graph of the variation of the torque at the driver-wheel 4 as a function of the variation of the torque on the drill bit.

Fig. 6. Graph of the variation of the power at driver-wheel 4 as a function of the variation of the torque on the drill bit:
\(P_t\)—power consumption for braking the screw;
\(P_b\)—power consumption for rotating the drill bit.

\[ \frac{1.04 M_b n_4}{71620}\,0.736 = P_b \ \text{kW} \]

is the power expended on rotating the drill bit;

\[ \frac{2.05 M_t n_4}{71620}\,0.736 = P_t \ \text{kW} \]

is the power consumed by the braking clutch.

Figure 6 gives the pattern of variation of the power at driver-wheel 4 (at \(n_4 = 175\ \text{rpm}\)) as a function of the torque on the drill bit at various braking torques. At \(M_t = 100\ \text{kg·cm}\), the dashed line in Fig. 6 determines the power consumption for

rotation of the drill bit and the power consumed by the brake clutch in braking the screw. It does not appear possible to estimate theoretically the total expenditure of power on friction in the mechanism. Obviously, its magnitude is small in comparison with \(P_{\mathrm{t}}\).

The efficiency of the feeder may be represented as the ratio of the power expended on rotating the drill bit, \(P_{\mathrm{b}}\), to the power on the driving wheel 4, \(P_4\),

\[ \eta_{\mathrm{feed}}=\frac{P_{\mathrm{b}}}{P_4}. \]

The useful power \(P_{\mathrm{b}}\) increases in proportion to \(M_{\mathrm{b}}\). In the drilling process, at a constant braking moment, the value of \(\eta_{\mathrm{feed}}\) is limited by the value corresponding to the maximum moment on the bit and the zero value of the feed force (Fig. 4), since any further increase in the moment on the bit causes the feeder to move away from the face and, consequently, unloads the bit. Therefore

\[ \eta_{\mathrm{feed,max}}\approx 0.65. \]

At average values of \(M_{\mathrm{b}}\) and \(F\), the efficiency is of the order of

\[ \eta_{\mathrm{feed,avg}}=0.35—0.45. \]

CONCLUSIONS

The gear-screw automatic feeder of the electropneumatic drilling hammer is an original feeding device. It not only automates the feed without the presence of special regulating apparatus, but also protects the entire system during drilling from possible overloads. This circumstance is explained by the fact that a differential mechanism and a multi-disc brake clutch have been introduced into the design of the automatic feeder. The capacity for self-regulation over wide limits of the interrelated quantities of the moment on the bit \(M_{\mathrm{b}}\) and the feed force \(F\) improves the operating conditions of drilling machines and the drilling tool, and also creates a more stable load on the motor. It should be assumed that such a mechanism will find application in mining machine building.

REFERENCES

1. P. M. Alabuzhev, O. D. Alimov. On the design of electric impact machines. Izvestiya TPI, vol. 78, Tomsk, 1954.

2. O. D. Alimov. Study of the mechanism of rock destruction in percussive-rotary drilling and of the initial parameters of drilling hammers. Candidate dissertation. Library of TPI, Tomsk, 1953.

3. I. I. Artobolevsky. Theory of Mechanisms and Machines. Gostekhizdat, 1953.

1. N. F. Rudenko. Planetary Transmissions. Mashgiz, 1947.

2. L. B. Levenson. Theory of Mechanisms and Machines. Mashgiz, 1954.

3. V. N. Kudryavtsev. Gear Transmissions. LKVVIA, 1951.

4. F. M. Kurovskii. Assessment of friction losses in mechanisms with several degrees of freedom. Transactions of the Moscow Order of Lenin Power Engineering Institute named after V. M. Molotov, vol. XVII, Gosenergoizdat, 1955.

5. V. N. Kudryavtsev. Design notes for the constructor. Planetary transmissions. Bulletin of Mechanical Engineering, No. 4, 1953.

6. V. N. Kudryavtsev. Design notes for the constructor. Planetary transmissions. Bulletin of Mechanical Engineering, No. 5, 1953.

Noted Misprints

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