Article
citation information:
Zhilevich, M., Ermilov, S., Kapski,
D., Vovk, Y., Lyashuk, O., Vovk, I. Method of calculating the design parameters of a
modulator anti-lock braking system with a high flow of working fluid. Scientific Journal of Silesian University of
Technology. Series Transport. 2021, 110,
199-210. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2021.110.16.
Mikhail ZHILEVICH[1], Sergey ERMILOV[2], Denis KAPSKI[3], Yuriy VOVK[4], Oleg LYASHUK[5], Iryna VOVK[6]
METHOD
OF CALCULATING THE DESIGN PARAMETERS OF A MODULATOR ANTI-LOCK BRAKING
SYSTEM WITH A HIGH FLOW OF WORKING FLUID
Summary. The design dimensions
of the executive hydraulic cylinders of the brake system of heavy-duty
mining dump trucks cause high fluid flow during the braking process. Therefore,
dimensions of the anti-blocking system modulator spool pair require unique
electromagnets or hydraulic amplifiers to control. These solutions do not allow
the required modulator performance. Thus, a modulator scheme with a division of
the flow of fluid from the source to the brake cylinders was developed. This
scheme allows during emergency braking passing, an additional amount of
fluid to cylinders through the valve, installed parallel to the main valve
upon pressure increase phase and controlled by the pressure difference. The
task is to develop a method for calculating the main structural dimensions of a
modulator. The calculation of the valve of the second cascade, installed in
parallel to the main stage, is carried out for the emergency braking mode with
the maximum flow rate to ensure the required performance of the braking system.
The balance of fluid flows equations is compiled at the key points. The flow
rate of the fluid through each of the valves is determined by the Torricelli
formula, and the pressure difference across the valves is assuned equal. The
obtained relations allows building a family of Q-p curves, which can be used to
select the diameter and stroke of the additional valve depending on the
flow rate in the brake system.
Keywords: anti-lock braking system, hydraulic brake
system, modulator, method of calculating, dump truck
1.
INTRODUCTION
A mandatory
requirement for modern cars is to ensure a minimum braking distance while
maintaining a stable and controlled movement during braking. To fulfil this
condition, anti-lock braking systems (ABS) are used. The first known ABS
patents date back to the late 1920s. However, until the end of the 1940s, such
systems were used only on experimental and sports cars. Active research began
after the introduction of electronic ABS on Ford cars in 1969.
Currently, ABS
is an obligatory structural part of almost the entire range of cars. Pneumatic
antilock braking systems were widely used. Hydraulic ones are usually used in
light-duty cars and trucks. As a rule, improvement of systems is currently
carried out by developing optimal control algorithms for the anti-lock system
with an established structure and design of actuators [1].
Following
UNECE Regulation No. 13, the use of ABS in heavy-duty vehicles is not regulated
[2]. However, international manufacturers are working on the installation of
ABS prototypes in mining trucks (BelAZ, Liebherr, Caterpillar) [3-5]. One of
the main problems in the implementation of anti-lock systems on mining trucks
is the large size of the actuators, and as a result, the high flow rate of the
working fluid in the brake drive.
2. LITERATURE REVIEW
ABS is a closed system of automatic control, the main task of which is
to change the speed of rotation of the wheels of a vehicle by adjusting the
pressure in the brake lines during braking. The ABS actuator that controls the
pressure in the brake cylinders is a pressure modulator.
As a rule, the design of the modulator includes actuating elements of
the spool or valve type with electromagnetic control. In [6], a comparative
analysis of such executive elements is carried out. The calculations showed
that for the operation of the spool-type actuators, a 20% lower electromagnet
force is required, while valve elements have a higher sensitivity. It further
found that the stability of the flow characteristics at equal pressures for
spool valves provided in the frequency range 25-40% greater than for valve
valves [6]. In this regard, it recommended using valve elements only in
multiphase modulators for draining the liquid and relieving pressure. The
apparatus with spool type actuators has no application restrictions and can be
installed in both the pressure and the drain lines of a hydraulic brake drive.
By the type of duty cycle, modulators are built based on discrete
elements and can be two-phase and three-phase ones. The advantage of a
two-phase cycle is the simplicity of the design of the ABS modulator. However,
a three-phase cycle allows reducing the flow rate of the working fluid and
increasing the average braking torque. The presence of a holding phase helps to
prevent water hammer and wave processes in pipelines with a sharp change in the
direction of fluid flow.
The two-phase algorithm of the open-drive modulator implemented using a
three-line on-off valve. For three-phase and multiphase algorithms,
combinations of such valves are used.
The use of proportional equipment allows creating a multi-phase
non-cyclic algorithm to maintain the braking torque in a given optimal range
during braking of the vehicle.
The classification scheme of ABS modulators is shown in Figure 1.
Design features of hydraulic modulators and their work are considered in
[6-8].
As noted earlier, in ABS modulators of hydraulic brake drives, disc-type
spool valves with electromagnetic control are usually used. The low flow rates
of the hydraulic fluid in the hydraulic brake drive allow the use of valves
with small spool sizes. In this case, the controls are commercially available
electromagnets, since it does not require much effort to move the spools.
However, on particularly heavy-duty vehicles, the dimensions of the executive
hydraulic cylinders, and as a consequence, the flow rate of the working fluid
increase significantly. Accordingly, the structural dimensions of the spool
pairs of the modulator and their inertia grow. To control such spools, it is
necessary to use either hydraulic boosters, which reduces the speed of the brake
drive as a whole and does not allow providing the required frequency of
operation of the modulator, or special forced electromagnets that provide the
specified frequency and force on the plunger.
Fig. 1. Classification of ABS modulators
The circuit solution [9], justified in [10], presented in Figure 2,
allows to reduce the inertia of the elements of the hydraulic modulator and to
ensure the given speed of the anti-lock system at high flow rates of the
working fluid. The required actuator response speed is achieved by dividing the
flow of the working fluid into the main and auxiliary using an additional
normally closed valve installed parallel to the main.
3. METHODOLOGY
The proposed modulator applied when the anti-lock braking system operated
using a two- or three-phase algorithm.
During the braking phase, the electromagnets 9 and 11 are disconnected.
The fluid flow passes from the pressure source through inlet valve 1 to the
brake cylinder. As the conditional passage of the inlet is small, it causes a
pressure drop to occur in lines 2 and 3, transmitted via control lines 7 and 8
to the shut-off element of the auxiliary valve 6, which held through a spring
13 in the upper position according to the scheme. When the pressure
differential reaches a certain value, the auxiliary valve’s spool 6 moves
down according to the scheme, passing an additional flow of working fluid to
the brake cylinder through line 3.
1 – inlet valve; 2 – supply line of the working fluid; 3
– line for supplying a working fluid to the brake cylinder; 4 –
exhaust valve; 5 – line pressure relief; 6 – auxiliary valve; 7, 8
– control lines of the auxiliary valve; 9, – control valve of the
intake valve; 10 – intake valve return spring, 11 – exhaust
solenoid control valve; 12 – exhaust valve return spring; 13 –
additional auxiliary return spring
Fig. 2. Hydraulic modulator
The braking phase carried out when the control signals supplied to the
electromagnets 9 and 11. In this case, the pressure drop in lines 7 and 8 becomes
equal to zero and the auxiliary valve 6 closes. The fluid from the brake
cylinder through valve 4 and line 5 is discharged.
The holding phase (when using the three-phase cyclic algorithm) provided
by removing the signal from the electromagnet 11 of the valve 4 with the
control signal turned on the electromagnet 9 of the inlet valve 1. The spoon of
the exhaust valve 4 shifted to the right according to the scheme and cuts off
the hydraulic cylinder from the drain line. The valve 1 is in the left position
in the scheme because the pressure in the lines 7 and 8 are equal and the spoon
of the valve 6 is in the upper position according to the scheme by the spring
13.
4. RESULTS
4.1. Determination of the modulator main parameters for a hydraulic
actuator with a large flow of working fluid
When performing the static calculation, the following assumptions were
observed:
- no friction losses;
- all elements of the modulator are absolutely rigid;
- the modulator is absolutely tight.
The design scheme of the modulator for the braking phase is shown in
Figure 3.
Fig. 3. The design scheme of the modulator
(braking phase)
In the calculations, it assumed that the dimensions of the hydraulic valve
V1 of the first cascade (the main hydraulic valve of the braking phase) is
known in advance or can be set based on the sizes of the spool pairs of
serially produced hydraulic valves with electromagnetic control. The
calculation of the valve V3 of the second cascade installed parallel to the
main one, carried out for emergency braking with the maximum flow rate of the
working fluid, which provides the specified quick-action brake system.
The balance of the flow rate of the working fluid in the node N1
represented as the equality of the sums of the flow rates of the fluid at the
input Qin and output Qout.
The inlet flow rate Qin is the fluid flow Q coming from the
pressure source.
The output flow rate Qout represented by the sum of expenses:
,
(1)
where Qv1, Qv3 are flow rates in valves V1 and V3,
respectively.
The flow rate of the working fluid through the hydraulic valve is
determined by the formula:
,
(2)
where:
μi is the flow coefficient of the i-th valve;
Δpi is pressure drop of the i-th valve;
ρ is the density of the working fluid;
Si is the area of the bore of the working window of the
i-th valve.
The pressure drops on both valves are taken equal to:
.
(3)
For a cylindrical spool, the flow area determined by the Eq.:
,
(4)
where:
dspi is the diameter of the spool pair of the i-th valve;
xi is movement of the spool of the i-th valve.
Substituting expressions (3) and (4) in (2), we obtain:
.
(5)
The flow-differential characteristic of the valve of the second cascade
obtained from formula (5) is the dependence of the pressure loss Δp on
several variables: the passing flow Q and the ratio of the spool diameter dsp3
of the valve of the second cascade and its stroke x3:
,
(6)
In addition, from equation (5), the dependence of the product of the
parameters of the working window of the auxiliary valve Р3
dз3xз3 can be obtained as a function of several variables: pressure
loss Δp and flow rate Q:
,
(7)
The obtained dependences (6) and (7) allow us to build a family of
flow-differential characteristics. According to these characteristics, it is
possible to select the diameter and stroke of the valve spool of the second
cascade depending on the flow rate in the brake system and allowable pressure
losses on the modulator, thus, ultimately design a standard range of modulators
for brake systems with different flow rates.
5. RESULTS
The initial data for calculating the flow-differential characteristic is
presented in Table 1, while the initial data for calculating the parameters of
the working window dsp3x3 of the auxiliary valve P3 is shown in Table 2.
The calculation results are presented in Figures 4 and 5.
The obtained characteristics (Fig. 4 and Fig. 5) show that increasing
the area of the working window of the auxiliary valve V3 will significantly
reduce the pressure drop across the modulator.
Tab. 1
The initial data for the calculation of
flow-differential characteristics
|
Fluid density |
ρ |
880 kg/m3 |
|
Fluid flow |
Q |
40–120 l/min |
|
The coefficient of flow of the
main valve V1 |
μ1 |
0.65 |
|
Spool diameter of the main
valve V1 |
dsp1 |
8 mm; 10 mm |
|
Spool stroke of the main valve
V1 |
hsp1 |
0.5 mm; 1.0 mm |
|
The coefficient of flow of the
auxiliary valve V3 |
μ3 |
0.65 |
|
Spool diameter of the auxiliary
valve V3 |
dsp3 |
10 mm; 16 mm; 20 mm; 25 mm; 32
mm |
|
Spool stroke of the auxiliary
valve V3 |
hsp3 |
1.0 mm; 1.5 mm; 2.0 mm; 2.5 mm;
3.0 mm |
Tab. 2
The source data for calculating the parameters of
the worker windows dsp3×x3 of the auxiliary
valve V3
|
Fluid density |
ρ |
880 kg/m3 |
|
Fluid flow |
Q |
40–120 l/min |
|
The coefficient of flow of the
main valve V1 |
μ1 |
0.65 |
|
Spool diameter of the main valve
V1 |
dзол1 |
8 mm; 10 mm |
|
Spool stroke of the main valve
V1 |
hзол1 |
0.5 mm; 1.0 mm |
|
The coefficient of flow of the
auxiliary valve V3 |
μ3 |
0.65 |
|
Differential pressure on the
auxiliary valve P3 |
Δp |
0.5 MPa; 1.0 MPa; 1.5 MPa; 2,0 MPa; 3.5 MPa |
6. CONCLUSIONS
The designed scheme allows the use of hydraulic
valves with ordinary electromagnetic control elements as intake and exhaust
valves of an ABS modulator of brake systems with a high flow rate of
working fluid.
The calculated static characteristics of the modulator
according to the quality criteria correspond to the expected ones, which
confirms the adequacy of the proposed model.
The selection of the structural dimensions of a
normally closed valve installed parallel to the inlet valve makes it
possible to create a standard range of modulators for systems with different
flow rates of the working fluid based on the use of standard, widely used
hydraulic control valves and electromagnetic control devices as inlet and
outlet valves.
a
Fig. 4a. Flow-rate characteristic
of the proposed modulator with parameters of the working window of the main
valve V1; a) dsp1×x1=8mm×0.5mm; b) dsp1×x1=8mm×1.0mm;
с) dsp1×x1=10mm×0.5mm; d) dsp1×x1=10mm×1.0mm
b
Fig. 4b. Flow-rate
characteristic of the proposed modulator with parameters of the working window
of the main valve V1; a) dsp1×x1=8mm×0.5mm;
b) dsp1×x1=8mm×1.0mm; с) dsp1×x1=10mm×0.5mm; d) dsp1×x1=10mm×1.0mm
c
Fig. 4c. Flow-rate
characteristic of the proposed modulator with parameters of the working window
of the main valve V1; a) dsp1×x1=8mm×0.5mm;
b) dsp1×x1=8mm×1.0mm; с) dsp1×x1=10mm×0.5mm; d) dsp1×x1=10mm×1.0mm
d
Fig. 4d. Flow-rate
characteristic of the proposed modulator with parameters of the working window
of the main valve V1; a) dsp1×x1=8mm×0.5mm;
b) dsp1×x1=8mm×1.0mm; с) dsp1×x1=10mm×0.5mm; d) dsp1×x1=10mm×1.0mm
a
Fig. 5a. The design scheme of the modulator
(braking phase)
b
Fig. 5b. The design scheme of the modulator
(braking phase)
c d
Fig. 5c. The design scheme of the modulator
(braking phase)
Fig. 5d. The design scheme of the modulator (braking
phase)
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