RKB Optimal Design of Rolling-Contact Bearings Via Evolutionary Algorithms0 pages

OPTIMAL DESIGN OF ROLLING-CONTACT BEARINGS VIA EVOLUTIONARY
ALGORITHMS
RKB TECHNICAL REVIEW - APRIL 2011
Optimal Design of Rolling-Contact Bearings
Via Evolutionary Algorithms
Lucian Tudose, Cristina Stanescu
RKB Bearing Industries - Advanced Calculations and Optimization Department
Abstract: RKB Bearing Industries Group has been using Evolutionary Algorithms for long, well
aware that optimized products can make a difference in performance compared to the
other producers. This paper is a brief review of the main aspects of the optimal design and a
report on the achievements of the RKB Advanced Calculations and Optimization
Department in the field. The differences between optimal design and conventional design
are pointed out by way of a very simple example of mechanical design. Multi-objective
optimal design via Evolutionary Algorithms of a specific cylindrical roller bearing is also
presented.
Key words: Optimization, Bearing, Evolutionary algorithms, Optimal design
1. Optimal design in modern engineering
Optimization is an important concept in engineering. Finding any solution to a problem is not nearly as good as
finding the one optimal solution to the problem. In the last decades the complexity of conceived products have met
an extraordinary growth and it is estimated that, in the near future, designing a product will have to take into
consideration a multitude of factors including actual design, manufacturing and logistics (supplying and distribution).
The ever growing complexity of design problems obviously requires appropriate instruments. The present tendency in
technical design of products is optimal design, which means conceiving and solving a mathematical programming
problem based on the mathematical model of a real engineering problem.
2. Structure of mathematical programming problems
In mathematics, optimization, or mathematical programming, refers to choosing the best element from some set of
available alternatives. Often, this number of possible alternatives is infinite or, at least, very high in computational
time terms. It is worth noting here that the term mathematical programming is not directly related to computer
programming.
A mathematical programming problem has to fit to a certain format. Let the decision (design) variable vector be:
x x1, x 2 , ... , x p
and suppose that its components are laying in the ranges:
l
l
u
l
u
x1 x1, x1 , x 2 x 2 , x 2 , ... , x p x p , x u
p
Consider also the objective function (mono-objective optimization) or objective functions (multi-objective
optimization) and a set of constraints (all of these are functions of the decision vector x ). Note that mono-objective
optimization and multi-objective optimization respectively are two totally different approaches as will be seen in the
following pages. To solve this mathematical programming problem means that one has to find x so that:
f1 x min or max
f x min or max
objective function(s): 2
fm x min or max
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