INTERNATIONAL MULTIDISCIPLINARY JOURNAL FOR
RESEARCH & DEVELOPMENT
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THEORETICAL METHOD FOR DETERMINING PARAMETERS OF THE VACUUM
BOOSTER (VB) IN AUTOMOBILE BRAKE SYSTEMS
Tojiboyev Sh.I.
Fergana State Technical University, Assistant
sherali.tojiboyev8@gmail.com
Abstract:
Nowadays, with the increase in the number of vehicles, the demand for traffic safety
is also rising. One of the ways to reduce the number and consequences of traffic accidents is to
improve the technical condition of the vehicle's braking system. As a result, the use of tuning
services (modification of components) is becoming more common, especially in vehicles. For
instance, analyzing and selecting boosters, and determining the feasibility of installing them
into other vehicles, has become a current and significant issue.
Keywords:
Vacuum booster, membrane surface, push rod
Introduction:
Today, to ease the driving process for the driver, boosters are being widely used.
To theoretically justify the parameters of the vacuum booster (VB), mathematical calculations
were conducted to determine the VB membrane surface and radius.
Figure 1. Vacuum booster diagram
1 - diaphragm; 2 - buffer of rod; 3 - push rod; 4 - atmospheric chamber; 5 - vacuum chamber; 6
- rod; 7 - return spring of the valve div.
The force at the vacuum chamber entrance (at the booster push rod) is determined as follows [1]:
Р
T
= Р
p
* U
p
(1)
Where: P
p
– force on the brake pedal, N (P
p
<500 N)
U
p
– transmission ratio of the brake pedal (U
p
= 3.2)
The force at the vacuum booster rod (output of the vacuum chamber) is calculated as:
P
r
= P
T
+ P
M
(2)
Where: P
m
– force generated by the booster membrane, N
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P
m
= (ρ
a
- ρ
b
) * S
m
(3)
Where: ρ
a
– pressure on the left side of the membrane, MPa
ρ
b
– pressure on the right side of the membrane, (0.065 + 0.003 MPa)
S
a
– membrane surface area (0,32 m²)
During braking, the force between the tire and the road is calculated as:
(4)
Where: M
a
– vehicle mass, kg
g – gravitational acceleration (9.81 m/s²)
φ – coefficient of adhesion
The rolling resistance moment of the car wheel is:
(5)
Where: r
w
– wheel radius, m
Force applied to the brake pad:
Pʹ =
(6)
Where: μ – friction coefficient
r
d
– distance from the wheel axle to the brake pad, m
P
ʹ
=
(7)
Force on the booster rod is calculated as:
= P
ʹ
/
(8)
The transmission ratio of the master brake cylinder is:
(9)
From the formula above, the surface areas of the master and working cylinders are:
(10)
Where: d
w.c
, d
m.c
– diameters of the working and master cylinders
Equating formulas (2) and (8):
(11)
Substituting formulas (1), (3), (7), (9) into (11), the membrane surface area (S
m
) of the vacuum
booster is determined as:
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(12)
From this formula, the radius of the vacuum booster membrane is calculated as:
(13)
Table: Vehicle Mass and VB Radius
№
Vehicle Mass
VB Radius
1.
1072
0.31
2.
1460
0.36
3.
1650
0.38
4.
2100
0.43
5.
2880
0.50
Figure 2. Graph of vacuum booster membrane radius as a function of vehicle mass
Using formula (13), the VB radii of different light vehicles can be calculated, and graphs
relating membrane radius to vehicle mass can be constructed. Based on theoretical calculations
with different vehicle masses, VB membrane radii were determined using formula (13), and a
graph was constructed from the table above.
Thus, using the above method, the vacuum boosters in light vehicles’ braking systems were
theoretically analyzed and mathematical parameters were derived. With this method,
parameters of vacuum boosters (membrane surface area, membrane radius, and pressure
difference) of various light vehicles can also be recalculated by altering these variables.
References:
1.
Осепчугов В.В., Фрумкин А.К. «Автомобиль. Анализ конструкций, элементы
расчета» М., Маш, 1989г. 304с.
2.
Shermuhamedov A.A., Astanov B.J., Tojiboyev Sh.I. (AFE 2023)
Scientific Conference Fundamental and Applied Scientific Research in the Development of
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RESEARCH & DEVELOPMENT
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