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Power Loss Optimization in Journal Bearing based on Genetic Algorithm
Approach
1
Leeladhar Rajput1 , Ganesh Prasad Shukla1, Anulal Mahto2, Sharad Chandra Srivastava 3
Department of Industrial & Production Engineering, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh,
India.
2
Department of Mechanical Engineering, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh, India.
3
Department of Production Engineering, BIT Mesra, Ranchi, Jharkhand
Abstract: The process of optimizing the design factors of a hydrodynamic bearing is a
challenging and time-consuming endeavor to complete. Due to the usual and time-consuming
nature of conventional design processes, This study aims to use a genetic algorithm to
determine the optimum bearing configurations for reducing power loss and to create an ideal
plain journal bearing. After the power loss equation has been derived, a genetic algorithm is
developed using suitable parameters, the number of design variables, including the population
size, and the rates of crossover and mutation. A selection procedure that is focused on physical
fitness is used. In this investigation, the oil viscosity, the radial clearance of the bearings, and
the journal speed are potential design input variables. The suggested algorithm demonstrates
rapid convergence while producing results that are superior to those already available in the
literature. It is a direct result of the genetic algorithm being a more effective heuristic than other
random search methods.
Keywords: Genetic algorithm, optimization, journal bearing, design variables
1. Introduction
The field of research known as tribology examines physics and chemistry. Wear friction
analysis and lubrication behavior are all part of the mechanics of rubbing surfaces. Efforts
have been made to minimize friction and wear since ancient times so that people and goods
can be moved more cheaply from one location to another. According to Tower [1], the
enormous pressure created by the oil film forming between the shaft and bearing was
enough to force the plug out of the hole. Simultaneously, journal-bearing friction was of
interest to Petroff [2]. His research found a correlation between frictional force and bearing
operation parameters. Although he established the concept of fluid film lubrication for
hydrodynamic bearing, it is his fault that he should have recognized that the oil film also
delivers the pressure produced by the tower. Reynolds [3] was able to develop his theory
of fluid film lubrication in hydrodynamic journal bearings and create a formulation for
hydrodynamic lubrication as a result of these developments. Hydrodynamic pressure
between shaft and bearing is explained by the Reynolds equation resulting from a wedge-
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shaped converging film, the oil's viscosity, and the surface motion. By integrating the
Reynolds equation, frictional force, load-carrying capacity, pressure distribution, etc., have
all been reduced to an analytical formula thanks to the work of Sommerfeld [4]. Bearings
are utilized in various machines, and these equations provide a foundation for designing
such bearings.
Figure 1: Schematic representation of hydrodynamic journal bearing [19]
Rouch, K.E. [5] researched the damping of bearings, which is determined by the actions of
the bearings that support the shaft. Shaft-bearing system’s stability is affected by the
stiffness properties of the rotating system design, as determined by the research of J.W.
Lund, and K.K.Thomsen [6]. The power loss performance goal is an essential consideration
while designing, creating, and enhancing hydrodynamic bearings. In this investigation, the
fundamental objective of designing plain journal bearings is the minimization of power
loss. An essential issue in journal-bearing lubrication is the value of the optimized oil film
thickness, the angle between the lines of the center and the vertical, which is referred to as
the attitude angle (Basu, S.K. et al. [7]). The sole condition for this bearing is that the
lubricant be supplied adequately and continuously. Feeding the lubricant/oil under pressure
with this bearing type is unnecessary.
Kalyanmoy Debet al. [8], who used six carefully chosen test functions to draw their
conclusions, offered a comprehensive comparison of several evolutionary methods for
multi-objective optimization. Each test function has its own unique quirk (such as
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multimodality or lying) designed to slow down the evolutionary optimization process and
prevent it from reaching the Pareto-optimal front. To evaluate the characteristics of four
different Evolutionary Algorithms, Eckart Zitzler and Lothar Thiele [9] used a multiobjective problem along with nine different configurations. In addition, they introduced the
Strength Pareto Evolutionary Algorithm (SPEA), an evolutionary approach to multi-criteria
optimization that represents a novel mix of four separate multi-objective EAs. The optimal
design methodology for enhancing the functional properties of fluid-film steadily loaded
journal bearings has been provided by H. Hirani et al. [11]. finite difference technique is
implemented to calculate the flow rate and power loss with reasonable precision. The
axiomatic design provides the inner workings of the objective functions. At the same time,
the Pareto optimal concept, a genetic algorithm to account for the bearing's multimodality,
and the generation of a Pareto optimal front all play essential roles in achieving this goal.
Boedo and Eshkabilov et al. [12] developed a genetic algorithm strategy for determining
the best form for the fluid film under continual journal rotation. One of their primary
objectives was improving carrying capacity. However, because of the severe constraints
imposed on the journal-bearing design, this is called a multi-objective problem. Minimizing
temperature increase, power loss, and oil feed flow are all examples of objective functions
with a single, best solution. Since finding a single ideal solution that satisfies everyone's
needs is impossible, there must be several optimal solutions. H. Saruhan et al. [13] set out
to apply a Genetic Algorithm to develop the best possible pre-loaded fluid film bearing
three lobes. The study presents comparisons between its findings and those acquired via
numerical optimization. The length-to-diameter ratio is one design variable the Author will
explore—bearing radial clearance and lobe arc length. Clearance arrangements of journal
bearings fluid-film were proposed by Koichi Matsuda et al. [15] to increase the overall
circular bearing's stability at high rotational speeds. To illustrate an arbitrary clearance
arrangement of journal bearings, we choose a Fourier series, and An efficiency index is
calculated by summing the whirl-frequency ratios over an extensive range of eccentricity
ratios and then square-rooting the result. K. Matsumoto et al. [16] detail an optimization
process called the optimal design methodology, which is a cross between sequential
quadratic programming and the direct search method. The maximum rate of increase in oil
film temperature, the rate of leaking, and the inverted speed at which the journal begins to
rotate anticlockwise constitute the objective function.
Hiromu Hashimoto [17] has refined a method for building short journal bearings with high
speed for turbulent and laminar flow conditions using a mix of SQP, GA, and DS. By
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adjusting for factors like radial clearance, slenderness ratio, and average lubricant viscosity,
the modified turbulent Reynolds equation can be used to derive simplified closed-form
design equations for quantities like eccentricity ratio, friction force, film temperature rise,
supply lubricant quantity, and whirl initiation velocity. A. Seirig et al. [18] offer an
automated method for selecting the settings of hydrodynamic journal bearings to provide
optimal performance under a range of load and speed situations. Journal-bearing
applications in equipment such as diesel engines working in laminar flow are examined,
and the optimization approach proposed by B. Kirankumar et al. [19] to minimize power
loss, temperature rise, and side leakage is referred to in this paper. In their recent article, S.
Gupta et al. When appropriately designed, rolling bearings can offer high-performance
levels over many years with minimal maintenance. This calls for an optimal design process,
namely multi-objective optimization, to simultaneously realize all these goals.
Several factors, including diameter, length, radial clearance, groove shape, viscosity,
position, etc., determine the functionality of the journal bearing. Designing a bearing can
be done by hand using one of several methods. The choice of bearing design factors is
typically made through trial and error method, utilizing several design charts. However,
there is currently no way to ensure the final composition has the best possible qualities.
Engineers have begun using optimization strategies in bearing design due to the rising
expectation of lower prices. Many academics have only considered unrealistic onedimensional instances to optimize bearing dimensions with less computational effort.
2. Theoretical & formulations
John Holland and his colleagues created genetic algorithms in the '60s and '70s as an
abstraction or model of biological evolution using Darwin's theory of natural selection.
Holland initially used crossover, recombination, mutation, and choice to study adaptive and
artificial systems. These genetic operators form the backbone of genetic algorithms used to
solve problems. Since then, many genetic algorithm variants have been developed and
applied to a wide variety of optimization problems, including those involving graph
coloring, pattern recognition, financial markets, efficient design of airfoils in aerospace
engineering, and multi-objective engineering optimization, to name a few. Genetic material
is exchanged between mating organisms. The offspring may inherit one parent's
chromosomes yet carry those of the other. Recombination is the term for this phenomenon.
Occasionally, a mutation can occur in a gene. Rarely will a mutant gene cause the
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phenotypic to change, but when it does, it will be expressed as a novel phenotype. Natural
selection, genetic recombination, and random variation are the driving forces behind the
diversity of life on Earth. Survival of the fittest, natural selection, and gene mutation play
crucial roles in the development of an organism through time.
A simplified flowchart illustrating this is provided below as well:
Figure 2: Genetic Algorithm Workflow Diagram [11]
The fitness function is an integral part of every genetic algorithm. The fitness function
evaluates the coded variable vectors and chooses the most optimal strings for the solution
based on these ratings. The three vectors of design variables are represented by the binary
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digits 0 and 1. The vector of design parameters has a binary string representation that, when
placed head-to-tail, forms a single long string called a chromosome. An answer to the
design dilemma can be found on this chromosome. Genetic algorithms are a method of
problem-solving that takes inspiration from the strategies employed by nature. They arrive
at their solutions through the same selection, recombination, and mutation process. The
work presented is an application of the evolutionary algorithm to the problem of designing
the best possible fluid film journal bearing, with the goal of achieving the lowest possible
power loss.
For power loss, the criterion function is = 2π3 µD3Ns2L/ C
Fobjective = power loss objective
Fitness Function = Fobjective
(1)
(2)
(a) Two variables optimization problem
Objective: To reduce the power loss of journal bearings resulting from the developed
function
F=
Subjected to: 1≤ μ ≤16, 35≤ C ≥ 70
μ = Oil viscosity of lubricant (mPa)
C= Radial clearance (μm)
Optimization Technique: Genetic Algorithm
Selection: Fitness value-based selection method
Initial Population: 20
Probability of crossover: 0.70
Probability of mutation: 0.010
(b) Three variables optimization problem
Objective: To reduce the power loss of journal bearings resulting from the developed function
F=
Subjected to: 1.0 ≤ μ ≤ 16.0, 35.0 ≤ C ≥ 70.0, 40≤ Ns ≥50
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μ = lubricant oil viscosity in mPa-s
C= The radial clearance in μm
Ns = speed in rad/s
Optimization approach: Genetic Algorithm
Selection: Selection technique based on fitness value
The population at the start: 20.0
Probability of crossover: 0.70
Probability of mutation: 0.010
3. Result and Discussions
A genetic algorithm was employed by Hirani et al. [11] in the axiomatic design of a journal
bearing. The proposed objective function is verified by plugging in the variables values (used
by Hirani, H. et al. [11]). It provides power loss estimates roughly in the ballpark of what that
other team found. The minimum power loss is achieved in journal bearings within the
recommended limitations stated in Table 1, and it is necessary to minimize this objective
function.
Table 1: Comparison of power loss values obtained in present work with reference
S.I. No
Design Variable
Power loss as per
Power loss as per
Percentage
[μ/C]
[11]
present work
Error
[mPa-s / μm]
(in Watts)
(in Watts)
1
[6.47/30.0000]
671.5048
641.9540
4.4%
2
[6.34/30.0000]
663.8143
629.0553
5.23%
[μ is lubricating oil viscosity measured in mPa-s and C is the radial clearance in μm]
The results produced in the present work deviate slightly from the reference values. Therefore,
further studies in the suggested activity can use the stated objective function. According to the
proposed procedure, the genetic algorithm was run using a MATLAB-created computer
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program, and a selection approach based on fitness values was used. The first variety utilizes
journal-bearing characteristics chosen following the research paper's methodology. Here,
MATLAB's genetic algorithm is used for the three-variable issues to get the best possible
power loss value. Taking into account 25 generations, we selected depending on fitness values.
The same genetic method has been used for the optimization issue provided, with the oil
viscosity, radial clearance, and journal speed of the bearing all taken into account. Thus, in
the 25th generation, a minimum power loss of 406.6342 W is generated. At the 25th
generation, the algorithm reached convergence. After the second generation, a strategy using
random crossover and mutation probability was used.
Figure 3: Optimization using three variables (minimization of power loss) convergence
diagram.
The convergence diagram for the three variable issues is represented in Figure 3, which
shows the best genes' fitness values over multiple generations. If the genes' fitness in the
most recent generations is very close to being the same, then the algorithm has converged.
Figure 4: Oil viscosity and power loss dependence for three variable optimisation
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Power loss due to the first design variable, oil viscosity, varies between generations, as seen in
Figure 4.
Figure 5: Oil viscosity and power loss dependence for three variable optimisation
Figure 5 displays the generational differences in power loss for a journal bearing with a variable
radial clearance from the second design generation.
Figure 6: Dependence of power loss on journal speed for three variables optimization
Power loss on the third design variable (journal speed) varies from generation to generation, as
shown in Figure 6. This is a three-variable optimization issue with the goal of minimizing
power loss.
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Figure 7: Genealogy for three variable optimizations (Minimization of power loss)
Family trees for optimization issues with two variables are shown in Figure 7. Genealogy is
the study of family trees. The following table summarises the color coding of generational
lines. Red lines represent mutant offspring. Blue lines represent children who cross over and
Black lines denote people of eminence.
The pattern of genes and designs represented that the power loss in a journal bearing is reduced
by increasing the distance between their values. A genetic method tailored to the optimization
of journal-bearing designs was also proposed. The proposed genetic algorithm worked well for
designing the journal-bearing design variable. The accuracy and adaptability were satisfactory.
Regarding time spent searching for a solution, the genetic algorithm performed admirably. This
technique can handle issues with as few as two variables and as many as three variables. The
proposed evolutionary algorithm includes a novel component that allows for creating new
solutions via one, two, or multi-point crossover (with the nature of the crossover being
generated randomly). This unique quality improves the stochastic features of the genetic
algorithm by ensuring a more even mixing of genes throughout the development of newer
iterations. Results from the first problem can be used to infer a given pattern of design variables,
which, in most cases, leads to a more optimal value for the objective function.
4. Conclusion
The current work demonstrates both the development of the genetic algorithm method and the
potential use of the technology while addressing a hydrodynamic journal bearing. The
fundamental goal of this endeavor is to create bearing arrangements that maximize the goal of
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suffering the least amount of power loss feasible. The findings obtained from this investigation
are superior to those obtained by conducting the research using a gradient-based optimization
technique. Iterative optimization is used in place of a starting point to find the values of the
design variables that maximize the objective function. MATLAB is used to run the computer
program that implements the genetic technique, and it is also used to construct the mathematical
derivation for the fitness function.
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