Volume 4, issue 8, 2025
183
METHODS FOR ENSURING THE RELIABILITY AND ECONOMIC EFFICIENCY OF
AUTOMOTIVE ENGINES OPERATING IN HOT CLIMATIC CONDITIONS
Karimkhodzhaev Nazirzhon
Associate professor of the department
Automotive engineering and transport of
Andijan State Technical Institute,
knazirjon@mail.ru
Abstract:
This study explores methods for ensuring the reliable operation of automotive engines
under hot climatic conditions. It emphasizes the importance of balancing reliability with
economic factors, particularly through analyzing the relationship between component/system
reliability and associated costs. The paper highlights the collaborative role of designers and
reliability engineers, noting that traditional design methods alone are insufficient for modern
engine development. Key topics include the use of safety factors, the limitations of empirical
design approaches, and the need for optimized solutions incorporating new materials and
technologies. The research also discusses statistical approaches to stress-strength analysis and the
practical challenges posed by cost, time, and rapid technological change.
Keywords (one line):
engine reliability, hot climate, safety factor, mechanical components,
design optimization, operational analysis, reliability theory, cost analysis,
To ensure a given probability of failure-free operation, one of the main factors is to take into
account the condition of minimum costs, for which it is necessary to determine the relationship
between reliability and costs for each element and engine system. In practice, it is not always
possible to use this condition due to the lack of data on the costs required to ensure a given level
of reliability [1].
The creation of reliable elements, systems and engines themselves is possible only if the efforts
of designers and operational reliability specialists are combined. At the same time, the main role
is assigned to the designer, and the reliability specialist supplements his knowledge by analyzing
the reliability of the engine design and statistical analysis of operational data. At the present
stage, the principle of ensuring the reliability of engines, based on the simple application of
rational design methods, is insufficient to give a given reliability to an engine as a complex
system. In this regard, it becomes necessary to single out an independent section in the theory of
reliability, which would study the issues of reliability of elements and systems of engines. The
following factors may serve as the basis for this [2-5]:
1) insufficient design experience. The pace of technology change is so fast that it is almost
impossible for engine designers to complete the design;
2) cost and time constraints. Cost and time are important, so the designer is not able to learn from
past mistakes, i.e. trial and error is not acceptable here;
3) the need to optimize resources. The creation of a working engine design must be optimized
under constraints on such parameters as cost, reliability, weight, efficiency, performance and
dimensions.
Result and discussion.
The nature of the change in the distribution of stresses and strength is
shown in Fig.3. For convenience, it is assumed that the stress distribution is constant, while the
strength distribution changes with time. If the distributions of stresses and strength are known,
then according to the results of the relationship between them, it is possible to determine the
reliability of the work [6].
Volume 4, issue 8, 2025
184
When designing the mechanical elements of the engine, a certain margin of safety is chosen, set
by arbitrary strength factors. Such an approach to the choice of coefficients in a number of cases
makes it possible to obtain a satisfactory design of engine parts, especially if their values are
chosen on the basis of experience. But in modern conditions, when creating new engine designs,
new approaches, new materials and more consistent methods are required.
In this case, it is important to consider the following indicators[8]:
1. Safety factor. In practice, there are several ways to calculate the safety factor S
f
. This factor
can be defined as the ratio of the average strength μ
s
to the average stress μ
s
'. In this case, μ
s
is
a parameter that determines the appearance of a failure, and μ
s
' - causing failure.
S
f
=
μ
s
μ
'
s
≥1.
If the stress and strength are distributed according to the normal law, the use of the coefficient S
f
is very convenient. The method of choosing the safety factor is shown in fig. 4 It should be noted
that if the stress and strength have a large range of variability, the coefficient S
f
loses its
meaning.
Figure 1. Distribution of stresses (b) and strength ( v ) depending on the time ( t ) of work:
a - at time t
1
; b - at time t
2
; 1 - stress distribution; 2 - strength; 3 - constant distribution of
stresses; 4— strength distribution over time interval ( t
2
—t
1
)
2. Margin of safety. It is determined by the formula Sm \ u003d S
f
-1.
Coefficient Sm as S
f
is a random variable, it reflects the idea of the need to separate the average
values of stress and strength.
In cases where reliability is assessed according to the established distributions of stress and
strength parameters, traditional methods such as the Lagrange multiplier method, integer, linear
Volume 4, issue 8, 2025
185
and dynamic programming methods can be used to optimize the reliability of the mechanical
elements of the engine.
Rice. 2. Choice of safety factor ( S
f
) depending on the ratio between stress distributions (b) and
strength ( ν ):
1 - stress distribution; 2 - strength
At the same time, reliability characteristics can be optimized under restrictions on costs, weight
and dimensions (volume).
Below is a method for optimizing the reliability of the mechanical elements of the engine with a
normal distribution of stress and strength parameters. In this case, the probability of failure-free
operation is defined as:
R=
−n
∞ 1
2π
e
−y
2
/2
dy
,
where
n= S
п
−S
н
(σ
2
S
п
tℎ
+σ
2
S
н
t)
−1/2
;
S
н
— average voltage;
Sn is the average strength;
σ
S
п
tℎ
'
σ
Sнt
are the standard deviation of strength and stress,
respectively. In this case, stress and strength are statistically independent quantities.
To increase the probability of failure-free operation, the lower limit of integration should be as
small as possible. Then the minimization of total costs for a given value of R can be represented
as
R=R
1
S
п
+k
2
σ
S
п
tℎ
+R
3
S
н
+R
4
σ
S
п
t
,
under the restriction
(S
п
−S
н
)(σ
S
п
t
)̄1/2 ≥ y , k - total costs;
k(Sп)
is the function of the cost of
providing medium strength (monotonically increasing function);
R
3
(S
н
)
is the stability cost
function against the average stress value (monotonically decreasing function;
k
2
(σ
S
п
tℎ
)
is the
cost function of maintaining a given strength standard deviation,
k
4
σ
S
н
t
−
the stability cost
function is within the stress standard deviation; y is the value determined by the coupling
equation for the required level of probability of no- failure operation. Lagrange equation in this
case takes the form
F S
п
S
н
σ
S
п
tℎ,
σ
s
н
t,
λ =k+λ S
п
−S
н
−y(σ
2
S
п
tℎ
+σ
2
S
н
t
)
1/2
To determine the optimal solution of this_equation, we differentiate it with respect to each
variable λ,
S
п
, S
н
, σ
S
п
tℎ,
σ
s
н
t,
and equating each derivative to zero, we get:
Volume 4, issue 8, 2025
186
S
п
−S
н
−y σ
2
S
п
tℎ
+σ
2
S
н
1
2
=0;
k
4
σ
S
н
t
=
λyσs
н
t
σs
п
tℎ+σ
2S
нt
;
k
2
σ
S
п
tℎ
=
λyσ
S
п
tℎ
σ
S
п
tℎ
+σ
S
н
t
; k
3
S
н
=λ, k"
1
S
п
=−λ.
Here, the dot denotes the partial derivative with respect to
σ
S
н
t'
, the dash with respect to
S
н
, two
dots with respect to
σ
S
п
tℎ
, and two dashes with respect to
S
п
. By solving a system of equations,
one can find the values of
S
п
, S
н
, σ
S
п
tℎ
, λ
, K for locally optimal conditions. To determine the
general extremum of the objective function, it is necessary to find the values of the objective
function for all locally optimal solutions.
Literatures:
1.
Каюмов Б. А. Обеспечение надежности системы питания современных бензиновых
двигателей в условиях жаркого климата. Андижан: ООО « Андижоннашриёт-
манбаа».2019.-104 с.
2.
Кузнецов С.П. Испытания и обеспечение надежности газотурбинных двигателей:
Рыбинск: РГАТА, 2005 – 180 с.
3.
Охотников Б. Л. Эксплуатация двигателей внутреннего сгорания : учебное пособие /
Б. Л. Охотников. – Екатеринбург : Изд-во Урал. ун-та, 2014. – 140 с.
4.
GMN3600 – Generic Supplier Analysis/Development/Validation Process Tasks and
Deliverables for All Programs and Commodities. 2014. – 24 р.
5.
GMW 15443 – Passenger Vehicle Established Road Regions General Durability Test. –
GMNA. QRD test procedure, july 2008 – 18 p.
6.
Надежность технических систем. Справочник Беляев Ю. К., Богатырев В. А.,
Болотин В. В. и др. Под ред. Ушакова И. А. М.: Радио и связь. 1985. 608 с.
7.
Николаенко А. В. Теория, конструкция и расчет автотракторных двигателей. М.:
Колос. 1984. 335 с.
8.
Шеховцев А.Ф. и др. Конструктивные отличия и особенности эксплуатация
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