ANALYSIS OF THE DYNAMICS OF PUMPING STATIONS IN HYDRAULIC SYSTEMS OF METAL-CUTTING MACHINE TOOLS

I. A. Nemirovskii, Yu. Ya. Komisarenko

(Presented by the Department of Mechanical-Engineering Technology)

The hydraulic systems of the drives and controls of metal-cutting machine tools, as a rule, have individual pumping stations consisting of an oil tank, a pump and an electric motor, a safety-overflow valve, a filter, a pressure gauge, and pipelines.

A pumping station may operate in the constant-pressure (CP) mode, when the hydraulic system consumes part of the pump delivery and the excess oil is discharged through the overflow valve, or in the constant-flow (CF) mode, when the entire pump delivery is consumed by the hydraulic system and the pressure at the system inlet is lower than the setting pressure of the overflow valve and varies depending on the forces overcome by the hydraulic motor.

In real pumping stations, in the CP mode the pressure is not strictly constant, and in the CF mode the flow consumed by the hydraulic system decreases as the pressure increases because of leakage in the pump.

Transient processes in the hydraulic system are affected by the dynamic characteristics of the pumping station. In the CP mode, rapid changes in the flow consumed by the hydraulic system cause corresponding changes in the flow through the overflow valve and, owing to the inertia of the valve, pressure oscillations. In this case the operating mode of the pumping station may be called a CP mode only conditionally.

In the CF mode, owing to rapid changes in the inertial and other loads of the hydraulic motor, pressure pulsations occur, which lead to changes in the capacity of the pipeline, flexible hoses, and other cavities present in the pumping station and subject to pressure oscillations. In addition, pressure pulsations cause changes in leakage in the pump.

The present paper sets forth a method and some results of experimental investigations of the dynamic characteristics of pumping stations.

The layout of the experimental installation is shown in Fig. 1. The working fluid was delivered by a vane pump 3. The pressure in the system was measured by pressure gauge 5, and in dynamic investigations the pressure oscillations were sensed by transducers 6 and 9. The pressure transducer used as the sensing element had a membrane to which wire strain gauges were bonded. The natural frequency of oscillation of the pressure transducers was about 1500 cps. To study the effect of filter 4 on

dynamic characteristics of the station, provision was made for the possibility of switching it in according to variants indicated in Fig. 1 by positions 4 and 4a. Throttles 1 and 11 were used in investigations of the dynamic stiffness of flexible hoses 7. The pumping-station system included overflow valve 2.

Fig. 1. Diagram of the experimental setup for determining the dynamic characteristics of pumping stations.

All the hydraulic equipment from which the experimental setup was assembled was standard: a vane pump of type G12-12; filter G41-12; valves G54-12 and G52-12; throttles G77-14. The investigations consisted in analyzing the influence of individual elements of the pumping station on the nature of the transient process under a step input action.

To apply a step input action, an input device (ID) was designed and manufactured, the principal parts of which are spool box 10 (Fig. 1) and flat spool 8.

Structurally, the ID was made in the form of a flat spool displaced by an impact spring mechanism (Fig. 2).

When flywheel 3 is rotated, rod 1 rises upward, carrying with it striker 16, which is gripped by a ball lock consisting of plunger 8 and balls 9.

The upper end of striker 16 thereby compresses spring 10. Under the action of spring 19, flat spool 18 assumes the upper extreme position, in which the working slot of spool 18 coincides with the corresponding slots in body 17. Upon further rotation of flywheel 3, the upper end of bushing 6 bears against the end of cover 4 and the bushing stops. Plunger 8, connected with bushing 4 by pin 7, also stops. Rod 1, continuing to screw into the nut of flywheel 3, allows balls 9 to enter the recess of plunger 8. Under the action of spring 10, striker 16 releases from the recessed balls 9 and strikes the end of spool 18, moving it to the lower position and closing the path of oil through the slots in the body.

To cock the impact mechanism, it is necessary, by rotating flywheel 3, to move rod 1 downward to the stop. In this case plunger 8 will move in the hole of rod 1 and will spread balls 9, which will grip striker 16.

During investigations of the dynamic stiffness of flexible hoses with the ID closed (position 10 in Fig. 1) and valve 2 disconnected,

the required pressure \(p\) was set in the system by throttle 1; then the operating slot of the control valve was opened, and by throttle 11 the pressure \(p' < p\) was set. The spring mechanism of the control valve was switched on, which closed the flat spool within a very short interval of time. The pressure changes occurring during the transient process were sensed by pressure transducers, amplified, and recorded by an MPO-2 oscillograph.

Fig. 2. Device for applying a step input action.

To record the instant of actuation of the control valve and the duration of motion of the flat spool, an electrical-contact device was used—

device (Fig. 2). At the moment the striker 16 touches the end face of spool 18, pin 11 opens contacts 12 and 14, breaking the circuit that shunts the loop marking the beginning of the motion of spool 18. At the end of the opening of the working slot by spool 18, pin 11 opens the next pair of contacts, 13 and 15, which break the supply circuit of the loop. Prolonged operation of the impact device showed high stability of the time \(t_3\) for closing the spool. In practice this time did not depend on the pressure in the system and was \(t_3 = 0.0013\) sec.

The impact device provided for synchronization of the switching-on of the impact mechanism and of the oscillograph tape-drive mechanism. Synchronization was carried out by contact device 5, switched on by the adjustable stop 2.

Investigations of flexible hoses of size \(10 \times 22 \times 2150\) mm showed that the time required for the pressure shock wave, formed when the impact device operated, to pass along the hose was considerably less than that obtained by calculation from the classical formula, confirmed in many works [1, 2] and used in calculations of hydraulic systems of metal-cutting machine tools [3].

This may be explained by the fact that, during transient processes, the pressure in the hoses changes so rapidly that, owing to the inertia of the hose walls, their deformation under pressure pulsations will be less than under a gradual, static load.

There occurs, as it were, an increase in the stiffness of the hose with oil. This increased stiffness may be characterized by the conditional reduced modulus of elasticity of the hose with oil, \(E'_{\mathrm{pr}}\). The value of \(E'_{\mathrm{pr}}\), naturally, depends on the rate of pressure change in the hose, \(\frac{dp}{dt}\). The maximum value of \(E'_{\mathrm{pr}}\) will occur at the greatest rate of pressure change, which takes place in the case of propagation along the hose of a pressure shock wave from hydraulic impact.

The velocity of the pressure shock wave is equal to [1]

\[ a = \frac{\sqrt{\dfrac{E_{\mathrm{m}} g}{\gamma}}} {\sqrt{1 + \dfrac{E_{\mathrm{m}} d}{E_{\mathrm{sh}} \delta}}}, \tag{1} \]

where \(a\) is the velocity of propagation of the pressure shock wave in hydraulic impact;
\(g\) is the acceleration due to gravity;
\(\gamma\) is the specific weight of the oil;
\(d\) is the internal diameter of the hose;
\(\delta\) is the wall thickness of the hose;
\(E_{\mathrm{sh}}\) is the modulus of elasticity of the material of the hose walls.
\(E_{\mathrm{m}}\) is the bulk modulus of elasticity of the oil filling the flexible hose.

If the value of \(a\) is determined experimentally, then from formula (1) one can find the value \(E'_{\mathrm{sh}}\), which may be taken as the conditional modulus of elasticity of the hose walls; i.e., the value \(E'_{\mathrm{sh}}\) determined in this way takes into account the inertia of the hose walls during their deformation while the pressure pulse passes with velocity \(a\)

\[ E'_{\mathrm{sh}} = \frac{\dfrac{d}{\delta}} {\dfrac{g}{\gamma} \cdot \dfrac{1}{a^2} - \dfrac{1}{E_{\mathrm{m}}}} . \tag{2} \]

Assuming, conventionally, that the mechanical characteristics of the material of the hose walls are identical throughout the entire wall thickness, and considering the hose as a thin-walled tube, the reduced modulus of elasticity of an oil-filled hose can be calculated from the formula

\[ E_{\mathrm{red}}=\frac{1}{\dfrac{d}{\delta}\cdot\dfrac{1}{E_{\mathrm{h}}}+\dfrac{1}{E_{\mathrm{o}}}} . \tag{3} \]

If in formula (3), instead of \(E_{\mathrm{h}}\), the value \(E'_{\mathrm{h}}\) from expression (2) is substituted, then the resulting value \(E'_{\mathrm{red}}\) may be taken as the conditional reduced modulus of elasticity of oil-filled hoses

\[ E'_{\mathrm{red}}=\frac{\gamma}{g}\cdot a^{2}. \tag{4} \]

The quantity \(a\) was determined from the formula

\[ a=\frac{2L}{t_y}, \tag{5} \]

where \(L\) is the length of the hose under investigation;
\(t\) is the time for the pressure wave to travel to the end of the hose and back.

The time \(t_y\) was determined from the oscillogram. A specimen oscillogram is shown in Fig. 3.

Fig. 3. Oscillogram of hydraulic shock in a hose.

The results of investigations of the stiffness of flexible hoses are presented in Fig. 4. Curve 3 gives the dependence of the reduced dynamic modu-

Fig. 4. Dependence of the static and conditional reduced moduli of elasticity of the hose walls and of the hose with oil on pressure.

Fig. 5. Experimental dependence of the bulk modulus of elasticity of oil \(E_m\) on pressure.

the elasticity \(E'_{\mathrm{pr}}\) of the hose with oil as a function of pressure, constructed from formula (5) with allowance for the values of \(a\) obtained experimentally.

For comparison, Fig. 4 shows the dependence of the reduced static modulus of elasticity \(E_{\mathrm{pr}}\) of the hose with oil on pressure (curve 1), obtained by the authors experimentally by static loading according to the method described by V. A. Leshchenko [4].

As can be seen from Fig. 4, the character of the dependences \(E_{\mathrm{pr}} = f(p)\) and \(E'_{\mathrm{pr}} = f'(p)\) is the same, but the values of \(E'_{\mathrm{pr}}\) are 60–80% greater than \(E_{\mathrm{pr}}\). The difference reaches its greatest value at low pressures.

From expression (3) we obtain

\[ E_{\mathrm{shl}} = \frac{\dfrac{d}{\delta}} {\dfrac{1}{E_{\mathrm{pr}}} - \dfrac{1}{E_{\mathrm{m}}}} . \tag{6} \]

Using formula (6), the values of the static \(E_{\mathrm{shl}}\) and conditional \(E'_{\mathrm{shl}}\) moduli of elasticity were calculated for different pressures (respectively, curves 2 and 4 in Fig. 4). Since the value of the volumetric modulus of elasticity of the oil \(E_{\mathrm{m}}\) depends to a considerable degree on pressure, in calculations by formula (6) the value of \(E_{\mathrm{m}}\) corresponding to the pressure for which \(E_{\mathrm{shl}}\) or \(E'_{\mathrm{shl}}\) was determined was taken into account. The dependence \(E_{\mathrm{m}} = f(p)\) was obtained by the authors according to the approved method [4] and is shown in Fig. 5.

Figure 6 presents oscillograms of transient processes in the presence of flexible hoses (Fig. 6a) and without them (Fig. 6b). From a comparison of these oscillograms it may be concluded that, when a hose is present, the “ascending” portion of the transient-process curve is considerably lengthened. Since the form and duration of the “descending” portion do not depend on the presence of hoses, the duration of the transient process in a system with hoses increases, i.e., the inertia of the entire pumping station increases.

To determine the influence of the filter on the dynamics of the pumping station, two series of experiments were carried out: with the filter connected according to the usual scheme (position 4 in Fig. 1), and with the filter connected according to the scheme shown at position \(4a\) in Fig. 1. In the first case the filter was located between the relief valve 2 and the hydraulic distributor. In the second case the filter was on a blind branch, and its inclusion provided for keeping unchanged the total volume of the cavities filled with oil under pressure.

Figure 6 presents oscillograms of the transient processes of the system with the filter in the main line (Fig. 6v) and with the filter on a branch (Fig. 6g). Comparing the oscillograms, it may be concluded that installing the filter in the main line leads to a shortening of the “ascending” branch of the curve, which considerably reduces the duration of the transient process.

Of decisive importance for the character of the transient process in the pumping-station system is the dynamic characteristic of the safety-relief valve.

Figures 6a, 6b, 6v, and 6g show oscillograms of the transient process in the pumping-station system including the relief valve G52-12.

Figures 6d and 6e show analogous oscillograms, but with the pressure spool valve G54-12 included in the system instead of the valve G52-12.

The oscillograms show that, for the system including the spool valve G54-12, the duration and character of the transient process differ considerably from the parameters of the transient process of the system with the spool valve G52-12.

Fig. 6. Oscillograms of transient processes in the pumping-station system:
a) without a flexible hose, with a G52-12 valve and a filter;
b) with a flexible hose \(10 \times 22 \times 2150\), with a G52-12 valve and a filter;
c) with a filter in the main line, a flexible hose, and a G52-12 valve;
d) without a filter in the main line, with a flexible hose and a G52-12 valve;
e) with a G54-12 pressure spool valve, with a hose and a filter;
f) with a G54-12 pressure spool valve, without a hose, with a filter.

The experiments were carried out at various pressures in the system and at various absolute values of the step input action.

On the basis of the investigations carried out, the following conclusions may be drawn:

1. The transient process is substantially affected by the rigidity of the pipelines connecting the pumping station with the hydraulic system. Flexible hoses have low rigidity, but in rapidly occurring dynamic processes the rigidity of flexible hoses increases by 60–80%. In analyzing the dynamics of hydraulic systems, it is necessary to take into account the conditional rigidity of hoses with oil as a function of the rate of change of pressure in the system, \(\frac{dp}{dt}\).

2. The presence of a filter in the main line between the overflow valve and the machine-tool hydraulic system reduces the time of the transient process in the pumping-station system.

3. The overflow valve has a decisive influence on the character of the transient process. Valves of type Г54 possess greater speed of response. At the same time, the system with valve Г52 is more stable.

4. The minimum transient-process time was obtained in the system without flexible hoses, with a filter and valve Г54.

The greatest transient-process time is in the system with flexible hoses, valve Г52, and without a filter in the main line.

Thus, the characteristics and combinations of the elements of the pumping station substantially affect the dynamics both of the station itself and of the hydraulic system fed by the pumping station.

In dynamic calculations of various hydraulic systems, it is necessary to take into account the real dynamic characteristics of the pumping stations feeding these systems.

REFERENCES

1. Zhukovskii N. E. On hydraulic shock in water-supply pipes. Moscow–Leningrad, GITL, 1949.

2. Bergeron L. From hydraulic shock in pipes to discharge in an electrical network. Gostekhizdat, Moscow, 1962.

3. Khailovich E. M. Hydraulic drives and hydraulic automation of machine tools. Moscow, Mashgiz, 1959.

4. Leshchenko V. A. Hydraulic tracking drives for the automation of machine tools. Moscow, Mashgiz, 1962.