Systems of Hydraulic Drives  Dynamics of a hydraulic drive of the turn mechanism of the auto concrete pump BR14
Dynamics of a hydraulic drive of the turn mechanism of the auto concrete pump BR14
To define stresses in the boom metal structure, arising from inertial loads at dispersal and braking of a rotary platform,
it is necessary to know values of maximal angular accelerations. When turn of a platform is carried out by a volumetric
hydraulic drive, values of angular accelerations depend as on parameters actually the turn mechanism (an instant of inertia
of a rotary part, transfer number of the turn mechanism), and from parameters of the hydraulic system putting it in the action.
Therefore the problem of definition of maximal angular accelerations of a rotary part reduces to a problem of dynamics of a
hydraulic drive of the turn mechanism. An example of such research is the dynamic analysis of a hydraulic drive of the turn
mechanism of the auto concrete pump BR14, executed on conceptual designing stage of the machine [6].
Fig. 1.
On Fig. 1 the basic circuit diagram of a hydraulic drive of the turn mechanism of the auto concrete pump BR14 is presented.
Supply of a working liquid to the hydraulic motor 7 is carried out by the pump 1 at simultaneous inclusion of spools 2, 3 and 4,
moved by means of electromagnets. At inclusion of the spool 4 piston of the hydraulic breaker 5 moves and there is a disconnection
of the block brake 6. At inclusion of electromagnets spools (including 4) and the piston of the hydraulic breaker come back by
action of springs in original position, the brake locking occurs.
For protection of hydraulic system from excessive high pressures in the circuit diagram the pilot operated pressure relief valves 8
are stipulated. The throttle established in a drain hydro line on an output of the spool 4, provides a delay in the brake operation,
as it is of lay type. The last circumstance, as well as existing initial opencircuit at shorting of the brake allows to consider,
that braking of the turn mechanism is carried out by purely hydraulic way, that is at switching spool 3 to a neutral position a
cutoff of a working liquid from the pump occurs; the hydraulic motor, rotating by inertia, passes in socalled «a pump mode»,
forcing a liquid in a cut off volume of the drain hydro line. Pressure in this cavity raises and there is the hydraulic motor
braking. At dispersal of the turn mechanism the brake in an initial stage will be closed, therefore it is necessary to consider
influence of the brake moment on the hydraulic motor shaft at dispersal.
For decision of the posed problem the universal program of dynamic analysis of hydraulic systems of any structure HYDRA was
used.
Fig. 2.
The simplified circuit diagram (Fig. 2) contains of 13 elements connected in 16 nodes. The resulted simplified hydraulic diagram
differs from the basic diagram by number of simplifications: some hydraulic elements are replaced by their appropriating functional
characteristics. Flow Q_{1} (t), operating in node 1, simulates the pump supply in hydraulic system by
means of an operating spool (poses. 1 and 2, Fig. 1); by means of throttles of variable through passage section
f_{thr1} (t) and f_{thr2} (t) modeling process of inclusion of the basic
directional spool valve of the hydraulic drive of the turn mechanism (pose 3, Fig. 1), and the throttle
f_{thr3} (t) simulates work of pressure relief valve (pose 8, Fig. 1) by its static characteristic
Q (p_{14} – p_{15}), that is dependence of flow in node 14 from the pressure differential
in nodes 14 and 15. The moment on the hydraulic motor shaft of M_{brake} (t) in node 7 models the brake
action.
Let's consider the characteristics of external perturbations presented on Fig. 3.
Fig. 3.
According to passport data of the directional control valve VE10.44 (pose 3, Fig. 18) the value of overlapping is 1.3 mm at a course
from a neutral position to the working one of 3.2 mm. Thus, the insensibility zone for this directional control valve makes ~40%
from the general course of a spool in one side. Proceeding from geometry of the directional control valve, the maximal area of
through passage section of the channel is reached at moving a spool on 1 mm from the beginning of opening of the channel. In view
of that time of inclusion of a spool makes ~0.06 s, and shutdowns ~0.04 s (the passport data), as well as considering geometrical
symmetry of the directional control valve, we shall receive (Fig. 3, a, c) dependences of functions of through
passage sections of throttles f_{thr1} and f_{thr2}, simulating channels of the directional
control valve (pose 3, Fig. 1).
According to the resulted data at inclusion of the spool its insensibility zone on time makes ~0.024 s, and regulation zone ~0.019 s.
At shutdown of the spool the same temporary intervals are less in 1.5 times. Similar dependence (Fig. 3, a) is accepted
for a flow Q_{1} (t), simulating the pump supply through the directional control valve (pose 2, Fig. 1).
The static characteristic of pressure relief valve Q (p_{14} – p_{15}) is resulted
in the graph form on Fig. 3, b. This dependence is included into the equation for definition f_{thr3}
– functions of through passage section of the throttle connecting nodes 14 and 15, and considers a possibility of change of a
sign on flow (the pressure differential). That one dependence describes both of the pressure relief valves of hydraulic system.
If to accept, that geometrical characteristics and speed of the directional control valves 3 and 4 (Fig. 1) coincide, without
taking into account delay of a signal in a hydraulic path of a hydraulic breaker of a brake it is possible to consider, that
variation of a relative brake moment
at disconnection of a brake occurs according to the diagram resulted on Fig. 3, a. Thus time of the beginning of falling
of a brake moment coincides with time of the beginning of variation of through passage sections of channels of the directional
control valves 3 and 4 and is defined by their insensibility zone. The rate of change of
at inclusion of a brake is given proceeding from average speed of operation of the hydraulic breaker, as well as an assumption,
that variation of the moment occurs on the first third of full moving of the hydraulic breaker piston. The hydraulic breaker has
the following sizes: diameter of the piston of 25 mm, a full course of the piston of 32 mm. At supply of flow of ~9 l/min an
average speed makes 0.3 m/s, and a time of moving ~0.1 s. From here, disconnection of a brake occurs for ~0.03 s. The diagram
of variation of a brake moment at inclusion of a brake (Fig. 3, d) considers the slow moving the piston because of
installation of a throttle on an output of the directional control valve 4 (Fig. 1), as well as opencircuit of the plunger 5
(Fig. 1) before contact of brake shoes with a drum (~2/3 a full course). The brake moment module is given, as the maximum
allowable moment of the hydraulic motor defined by the adjustment pressure of the pressure relief valve on 4.9 MPa, reduced
to a rotary part and increased from safety conditions in ~1.5 times:
where q = 17.03·10 ^{–6} m^{3} / rad – geometric volume of the hydraulic motor 210.25;
р* = 4.9 MPa – the adjustment pressure of the pressure relief valve; u = 513 – transfer number of the turn
mechanism; η = 0.945 – hydraulicandmechanical efficiency of the hydraulic motor. Then the actual brake moment is equal:
where ω_{7} – an angular speed of the hydraulic motor shaft.
The following rated positions of boom have been considered, for which three values of moment of inertia (tab. 1) are certain.
Other parameters of hydraulic elements are taken from their passport characteristics and the geometrical sizes. In tab. 2
values of maximal angular accelerations of the auto concrete pump BR14 rotary part are resulted at dispersal and braking for
three accepted rated positions of boom (tab. 1) and two values of nominal rotation frequency of rotary platform (two maximal
values of flow Q_{1}), received as a result of calculations of dynamics of the turn mechanism hydraulic drive
by the program HYDRA.
The example of the rated oscillogram illustrating dynamics of the turn mechanism hydraulic drive for the 1st rated position
of a boom is resulted on Fig. 3, e, f. Here it is designated: р_{6}, р_{8}
– pressures accordingly in nodes 6 and 8 (see the rated diagram Fig. 1), ω, φ – angular speed and angle of turn
of a platform.
For carrying out of engineeringdesign works formulas for the approached calculation of the maximal accelerations of a rotary part
have been received.
Let's consider two basic dynamic modes of the turn mechanism.
Dispersal
Let's enter a number of the assumptions comprehensible to a dispersal mode:
1) pressure in hydraulic system does not reach a level of the adjustment pressure of the pressure relief valve;
2) losses of pressure on length, in local resistance, losses of a moment on friction in the hydraulic motor, outflow of a working
liquid are insignificant also it is possible to neglect them;
3) pressure in a drain hydro line of hydraulic motor negligible and maybe is accepted equal to zero.
It is according to the accepted assumptions the simplified mathematical model describing dynamics of a hydraulic drive of the turn
mechanism, looks like:
where J – a moment of inertia of rotating parts of the turn mechanism reduced to the hydraulic motor shaft;
q – a geometric volume of the hydraulic motor; М_{b.hm} – a brake moment reduced to the hydraulic motor
shaft; Е – an equivalent volumetric module of elasticity of pipelines and sleeves of a high pressure with a liquid;
V – a volume of pipelines and sleeves of a high pressure in a pressure piping; ω_{7} – an angular speed
of the hydraulic motor shaft (node 7, Fig. 2), р_{6} – a pressure upon an input in the hydraulic motor (node 6,
Fig. 2); Q_{1} – the pump supply in node 1, Fig. 2. Considering dependences Q_{1} (t)
and
( t) on Fig. 3, we’ll receive in a general view:
Then on the segment
we have:
Having accepted the initial conditions:
and considering (9), we solve system of the differential equations (6) which is linear at
As a result of the solution it is found the maximal angular acceleration of a rotary part:
where u – a transfer number of the turn mechanism.
Calculations of the maximal angular accelerations of the turn mechanism, executed by the formula (11), have yielded the following
results resulted in tab. 3. In the same table for comparison the values of angular accelerations received by the program HYDRA
are given.
Calculations were spent at the following values of initial data: Q_{1max} = 17 l/min = 283 cm^{3}/s and
23 l/min = 383 cm^{3}/s; q = 17.03 cm^{3}/rad; τ_{0} = 0.024 s;
τ_{1} = 0.043 s; τ_{2} = 0.054 s; V = 335 cm^{3};
М_{b.hm} _{max} ≈ 118.5 N· m; J= 0.0216 kg· m^{2} and 0.0343 kg· m^{2};
Е ≈ 570 MPa.
Braking
Braking of the turn mechanism as it was marked above, occurs before inclusion of a block brake, that is by purely hydraulic way,
due to increasing of pressure in a drain pipe of the hydraulic motor with operation of the pressure relief valve. Therefore the
maximal accelerations at braking of the turn mechanism can be certain from the equation of dynamics of the hydraulic motor:
where р* – the adjustment pressure of the pressure relief valve, р* = 4.9 MPa.
Then
In tab. 4 results of calculation of maximal angular accelerations, received by means of program HYDRA and by means of the
formula (13) are presented.
The received formulas provide the way approximately to define maximal angular accelerations of the turn mechanism. At
performance of the conditions stipulated above in assumptions, the relative error has not exceeded 26% at dispersal and 23%
at braking. The executed analysis has allowed carrying out in the further calculation on strength metallic structure of boom
in view of dynamic loads.
