Abstract
This article concentrates on optimization of fatigue life, i.e., dynamic capacity of rolling element bearings by using a novel optimization approach known as Teaching–Learning-Based optimization. The optimization technique is applied to two cases of bearing, i.e., deep groove ball bearing and cylindrical roller bearing, by considering a large number of bearings and their associated constraints. The chosen problems involve around 9 design variables and the optimized result obtained shows considerable improvement over the previous results, standard catalogues and handbooks. Efforts are also made to validate the obtained results using finite element analysis approach and the simulated results of contact stress and deformation at the contact between inner race and roller are found in close agreement with the obtained optimum results. Thus, this article proves good applicability of proposed optimization approach in bearing design which will be useful to the on field designers to improve the performance of bearings.
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Abbreviations
- D :
-
Outer diameter of bearing
- d :
-
Bore diameter of bearing
- B :
-
Width of bearing
- \({D}_{\mathrm{m}}\) :
-
Pitch diameter
- \({D}_{\mathrm{b}}\) :
-
Ball diameter
- \({f}_{\mathrm{i}}\) :
-
The inner and outer raceway curvature radius coefficient
- \({f}_{\mathrm{o}}\) :
-
The inner and outer raceway curvature radius coefficient
- Z :
-
Number of rolling elements
- \({C}_{\mathrm{d}}\) :
-
Dynamic load rating
- \(\propto \) :
-
Contact angle
- L :
-
Life of the bearing
- a :
-
Constant defined by Lundberg–Palmgren [2]
- \(K_{{D\min }} ,K_{{D\max }} ,\varepsilon , {e},{\beta }\) :
-
Constraints to basic design variables [9]
- \(\phi _{{ 0}}\) :
-
Maximum tolerable assembly angle
- \({r}_{1}\) :
-
Outer ring chamfering height
- \({r}_{2}\) :
-
Outer ring chamfer width
- \({r}_{3}\) :
-
Inner ring chamfer height
- \({r}_{4}\) :
-
Inner ring chamfer width
- \({l}_{\mathrm{e}}\) :
-
Effective length of roller
- \({D}_{\mathrm{r}}\) :
-
Mean diameter of the roller
- \({\lambda }\) :
-
Reduction factor,
- \({\nu }\) :
-
Factor to account for edge loading
- \({b}_{\mathrm{m}}\) :
-
Factor to put up improvements in geometrical accuracies
- \(\gamma \) :
-
Ratio of diameter of rolling element and pitch diameter
- d :
-
Number of design variables
- \({N}_{\mathrm{n}}\) :
-
Population size
- \({m}_{1}, {m}_{2}, \ldots ,{m}_{\mathrm{n}}\) :
-
Mean of population column wise
- \({T}_{\mathrm{F}}\) :
-
Teacher factor
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Dandagwhal, R.D., Kalyankar, V.D. Design Optimization of Rolling Element Bearings Using Advanced Optimization Technique. Arab J Sci Eng 44, 7407–7422 (2019). https://doi.org/10.1007/s13369-019-03767-0
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DOI: https://doi.org/10.1007/s13369-019-03767-0