INVESTIGATION OF THE COMPLIANCE OF FLEXIBLE HOSES IN HYDRAULIC SYSTEMS OF MACHINE TOOLS AND MACHINES

I. A. NEMIROVSKII, O. I. VASENKOV, Yu. Ya. KOMISARENKO

(Presented by the scientific seminar of the Department of Machine-Building Technology)

In the hydraulic systems of drives and controls of machines and machine tools, flexible pipelines—hoses of cord-metal construction—are widely used.

It is known that, under the action of pressure varying with time, flexible hoses deform, as a result of which the volume of the hose cavity changes [1, 2, 3, 4, 5]. These changes in the volume of the hose cavity, as it were, modulate the flow rate of the liquid through the hose, being reflected in the quality of the dynamic processes taking place in the hydraulic system.

Usually, in calculations of the dynamics of hydraulic systems, the compliance of hoses and the compressibility of the liquid are taken into account by a constant coefficient. It is assumed here that the modulus of elasticity of pipelines with a working fluid, made of steel and copper tubes, is
$E_{\text{tr}} = 14000 \div 16000 \ \text{kg}/\text{cm}^2$, while for an RVD flexible hose of size $16 \times 29.5 \ \text{mm}$ in the pressure range $3 \div 7 \ \text{kg}/\text{cm}^2$,
$E_{\text{sh}} = 230 \ \text{kg}/\text{cm}^2$; in the pressure zone above $20 \ \text{kg}/\text{cm}^2$,
$E_{\text{sh}} = 1250 \ \text{kg}/\text{cm}^2$ [4].

It should be noted that the use of the term “modulus of elasticity of a pipeline” seems to us somewhat unfortunate, since this quantity depends not only on the moduli of elasticity of the working fluid and of the pipeline material, but also on the geometric dimensions of the latter. The term “conditional dynamic modulus of elasticity” [6], previously used by the authors of the present article, should likewise be regarded as unfortunate.

In our opinion, one should use the concept of the “coefficient of compliance of a pipeline with a working fluid”:

\[ k=\frac{dW}{dp}\cdot \frac{1}{W_0}, \tag{1} \]

where $W_0$ is the initial volume of the hose cavity;
$W$ is the value of the volume of the hose cavity at pressure $p$. Then the increment of the flow rate of the liquid through the flexible hose, caused by pressure pulsation, will be equal to:

\[ \Delta Q_{\text{sh}} = - \frac{dp}{dt}\cdot k \cdot W_0. \tag{2} \]

It is of interest to compare the compliance of hoses of various designs and sizes, and also to establish the exact dependence of the magnitude of compliance on pressure. For this purpose the authors have carried out

investigation of the compliance of flexible hoses on the apparatus, the diagram of which is shown in Fig. 1.

A fitting 5 of the flexible hose 4 is screwed into the body 6. The second fitting of the hose is plugged with stopper 3, which has an opening that was closed by screw 1 with gasket 2. A diaphragm transducer, consisting of body 7, diaphragm 10, and cover 9, was used as the pressure gauge. The pressure value was recorded from the magnitude of the deformation of the diaphragm, which was measured by indicator 8. Plunger 15, with diameter \(d_{\text{п}}\), was lapped to the opening in body 6 so that the clearance between the plunger and the opening was \(0.004\ \text{mm}\).

To increase tightness, the plunger was additionally sealed with a round rubber ring 16. At a pressure in the hose and body equal to \(100\ \text{kg}/\text{cm}^2\), and with plunger 15 immobile for 30 minutes, no pressure drop was observed.

Fig. 1. Diagram of the apparatus for investigating the compliance of flexible hoses

The plunger was moved by means of screw 14, while angular fixation of the plunger was carried out by pin 11. Indicator 12, mounted on stand 13, recorded the displacement of the plunger, i.e., the magnitude of the increase in the hose volume \(\Delta W_0\). The pressure increment in the system was recorded by indicator 8. The value \(k(p)\) was calculated for pressure intervals equal to \(2\ \text{kg}/\text{cm}^2\) by the formula

\[ k(p)=\frac{\Delta W}{\Delta p}\cdot\frac{1}{W_0} =\frac{\Delta W}{2W_0}. \tag{3} \]

In this, the value \(\Delta W\) was taken with allowance for the volume increments caused by the compressibility of the liquid filling the cavity of body 6 and diaphragm transducer 7, and by deformation of diaphragm 10.

Before the start of each test, the working liquid was pumped through the system, delivered by a pumping station that was connected to body 6 through opening 17 and a sealed high-pressure valve (the valve is not shown in Fig. 1). The liquid was bled from the hose through the opening in stopper 3. After the working liquid had been warmed to a temperature of \(40^\circ\text{C}\), the opening in stopper 3 was closed by screw 1 with the pumping station operating (the overflow valve of which was set to a pressure somewhat lower than the lower pressure value of the range being investigated).

Then, by adjusting the valve of the pumping station, the pressure was raised to the required value, and the pumping station was isolated from the cavity of housing 6 by a valve.

By moving plunger 15, the pressure in the hose was increased by 2 kg/cm²; the displacement of the plunger, \(\Delta l\), was recorded by indicator 12, and the value of \(\Delta W\) was calculated:

\[ \Delta W = \frac{\pi d_{\mathrm{p}}^{2}}{4}\,\Delta l . \tag{4} \]

The compliance of the following hoses was investigated:

SRTI P \(\varnothing\) 20—150 ati, GOST 6286-60, \(L=1750\);

DSNS P \(\varnothing\) 16—165 ati, GOST 6286-60, \(L=540\); and \(L=1280\)

Fig. 2. Dependence of the coefficient \(\kappa(p)\) on the pressure in the hose. The symbols denote the values of \(\kappa(p)\) for the hoses:

SRTI P \(\varnothing\) 20—150 ati, \(L=1750\) — \(\triangle\),
DSNS P \(\varnothing\) 16—165 ati, \(L=540\) — \(\times\),
DSNS P \(\varnothing\) 16—165 ati, \(L=1280\) — \(\cdot\),
LRTI \(\varnothing\) 12—210 ati, \(L=590\) — \(\vee\),
LRTI \(\varnothing\) 20—150 ati, \(L=510\) — \(\odot\),
22G10—150S, \(L=1800\) —,
24G12—150S, \(L=1800\) — \(\square\).

LRTI \(\varnothing\) 12—210 ATI, GOST 6286-60, \(L=590\);

LRTI \(\varnothing\) 20—150 ATI, GOST 6286-60, \(L=510\);

24G12—150S, \(\varnothing\) 12, \(L=1800\), and 22G10—150S, \(\varnothing\) 10, \(L=1800\).

The results of the investigation are presented in Fig. 2 and make it possible to draw the following conclusions:

1. The values of the compliance coefficient \(\kappa(p)\) for hoses of the tested types and sizes lie within a fairly narrow range of values, which makes it possible to recommend the data of Fig. 2 for calculating the compliance of hoses of any sizes of these types; in this case curve \(A\) in Fig. 2 may be used.

2. In the region of low pressures \((1 \div 5\ \text{kg}/\text{cm}^2)\), the value of \(\kappa(p)\) is several times greater than the value of \(\kappa(p)\) for the range \(10 \div 15\ \text{kg}/\text{cm}^2\) and above.

3. If, during operation of the hydraulic system, the pressure in the hoses varies over a wide range that includes the region of low pressures, the analysis of dynamic processes should be carried out with allowance for the nonlinear dependence of the coefficient \(\kappa(p)\) on the pressure \(p\), as shown in Fig. 2.

REFERENCES

1. T. M. Bashta. Machine-Building Hydraulics. Mashgiz, 1963.

2. I. Z. Zaichenko. Self-Oscillations in Hydraulic Drives of Metal-Cutting Machine Tools. Mashgiz, 1958.

3. B. L. Korobochkin. Selection of optimal parameters of hydraulic tracking systems of copying machine tools. Machine Tools and Tools, No. 6, 1956.

4. V. A. Leshchenko. Tracking Hydraulic Drives for Automation of Machine Tools. Mashgiz, 1962.

5. E. M. Khaimovich. Hydraulic Drives and Hydraulic Automation of Metal-Cutting Machine Tools. Mashgiz, 1959.

6. I. A. Nemirovskii, Yu. Ya. Komisarenko. Analysis of the dynamics of pumping stations of hydraulic systems of machine tools. Proceedings of TPI, Tomsk, 1964.