Experience on the use of vibrating hammers with a longitudinal action revealed their high efficiency in the sinking of the various elements. In addition, during the operation of these hammers it turned out that they are short-lived and relatively energy-consuming. These two shortcomings are due primarily to the high impact velocities of the vibrating hammers of this type, at which a sinking in various soil conditions is assured.

According to experimental studies, for sinking tubular elements it is possible to reduce the impact velocities of the vibrating hammer while preserving its driving ability due to l:he use of longitudinal impacts in conjunction with rotational vibrations. Subsequent theoretical studies (B. B. Rubin, 1976) defined the data of the experiments more precisely and manifested the ranges of the parameters of vibrating hammers of longitudinal-rotational action, in which their advantages over vibrating hammers of longitudinal action are most essentially manifested.

The influence of two specific characteristics of vibrating hammers of the longitudinal-rotational type was revealed in the following: the friction in the slides and the Coriolis force of inertia, on the driving ability of hammers of this type.

The presence of a frictional force in the guides of a vibrating hammer of longitudinal-rotational action is a typical characteristic of arrangements of this type because the torque from the vibroexciter is transferred precisely through the slides to the driving element.

In addition, it is necessary to investigate the dynamic property of vibrating hammers of the longitudinal-rotational type — the presence of the Coriolis force of inertia, the development of which is induced by the fact that the vibrohammer-driving element system effects a complex movement, consisting of a relative movement-rotation of the eccentrics of the vibroexciter and the migratory movement-rotation of the system around the vertical axis. In other words, the eccentrics of the vibroexciter move in the rotating system of reference.

The calculation scheme of the system investigated is presented in Fig. 28. The problem is solved with the additional assumption to Sections 5, Section 6 and Section 7: the driving element is stationary during the flight of the vibrating hammer, which corresponds to an exceeding of the torque of the frictional forces over the active torque from the compelling force.

Taking into account the assumptions of the equation of motion of the system and the boundary conditions for them, they can be written in the form of the equations (G. G. Azbel, B. B. Rubin, and Yu. A. Druzhinin, 1978) given below.

For the stage of the flight of the impact part

(45)

It follows from the system (45) that the phase angle a is determined from the following equation for the vibrating hammer of longitudinal-rotational action

(46)

For the stage of driving a tubular element

(47)

where *r _{D}* is the eccentricity of the eccentrics.

The problem was solved on a computer, using the dimensionless variables and the parameters of (9), (41) and (44) and also the additional ones:

(48)

The calculations revealed that the driving ability of the vibrating hammer is substantially dependent on the fractional force in its slides. The dependence of the displacement of the driving element on the coefficient of friction in the slides is plotted in Fig. 29. The ratio of the dimensionless values of the displacement of the tubular element *y _{0}/y* per cycle, expressed in percentages, is plotted here on the ordinate, when

*f*= 0 and

_{1}*f*≠ 0 respectively.

_{1}It is evident from Fig. 29 that with an increase in the coefficient of friction and consequently the mean frictional force also in the slides, the displacement of the driven element per cycle decreases according to a law close to the linear. With an increase in the negative backlash of sin *α* (41), the depth of sinking of the element with a constant frictional coefficient decreases, i.e., the angle of slope of the curves to the abscissa tan *γ = y _{0}/yf*

_{1}– the intensity in the variation in sinking depth per cycle – increases.

An increase in the stiffness of the vibrating hammer springs also leads to some increase in tan γ, but not as substantial as with an increase in the negative backlash.

The tan *γ* value is practically independent of the lateral and frontal resistances and also of *v _{2}δ*. Thus, with a variation in the dimensionless resistance of the soil (

*f + γ*) = 2 – 10 and when

*v*= δ 0 – 0.75, tan γ varies by 0.5 – 1.0%.

_{2}The influence of the Coriolis force of inertia on the driving capacity of a vibrating hammer of longitudinal-rotational action is insignificant. The calculations revealed that the maximum variation in the sinking of the tubular element per cycle under the influence of the Coriolis force of inertia is 2%.

Thus, special measures that assure a coefficient of friction in the slides of the hammer less than 0.01 are required in designing vibrating hammers of longitudinal-rotational action. With regard to the influence of the Coriolis force of inertia, it cannot be taken into account in the vibrating hammer calculations.

In analyzing the results obtained, the dimensionless displacements of the tube under the action of longitudinal impacts and rotational vibrations *y _{P,V}* were compared with its displacements under the action of only longitudinal impacts

*y*. The corresponding dependences of the ratio

_{P}*y*/y on the sin

_{P,V}*α*value are plotted in Fig. 30 at various dimensionless resistances of the soil to the driving.

An analysis of these graphs indicates that the advantages of the impact mode with rotational vibrations of the tube over the mode with only longitudinal impacts increase with increasing sin *α*, where these advantages are greater with decreasing soil resistance. It follows from the data obtained that the ratio *y _{P,V}/y* increases with an increase in the rotational component of the vibrations φ and correspondingly with a decrease in the

*y*/φ ratio.

_{P,V}Driving a tube with longitudinal impacts and rotational vibrations when sin *α* > 0.4 is most effective in comparison with the longitudinal mode when the impact velocity y1 decreases with increasing sin *α*.

An analysis reveals that with an increase in the frontal resistance of the soil the advantages of driving a tube with longitudinal impacts and rotational vibrations decrease. The ratio *y _{P,V}*/

*y*decreases most sharply at small

_{P}*f + γ*values.

Figure 31 shows the graphs of the dimensionless displacements of the tube under the action of longitudinal impacts and rotational vibrations at different dimensionless soil resistances *f + γ* and *ξ _{1}*. It follows from an analysis of the graphs on Fig. 30 that with the optimal parameters of the vibrating hammer with a longitudinal-rotational action the value

*ξ*should be in the 0.1 – 0.3 interval because the maximum settlings from each impact are assured with these

_{1}*ξ*values.

_{1}

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