Abstract
Gear size is one of the most important criteria in design optimization of gear set used in automotive, aeronautical and various other applications. Smaller gear size results in requirement of less material and hence reducing manufacturing cost. This paper aims at minimizing center distance of spur gear set to obtain its corresponding optimal design variables. Design variables included in this study are diametrical pitch and number of pinion teeth. Real Coded Genetic Algorithm and simulated annealing are employed for performing design optimization procedure. In this study, along with constraints on bending strength, contact strength, interference and contact ratio, scoring has been added as design constraint in design problem. All the design factors included in design procedure are considered as per AGMA standards. The recommended optimization techniques are implemented on a design example and optimum values of design variables are obtained. The obtained results are compared with those obtained by traditional design procedure to find the better solution as well as better optimization technique. Variations in input power and gear ratio have been done to verify their effect on the objective function and to further investigate a more useful optimization technique for gear design.
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Abbreviations
- a :
-
Addendum ratio
- AGMA:
-
American Gear Manufacturing Association
- b :
-
Face width (mm)
- B :
-
Width of band of contact (mm)
- C :
-
Centre distance (mm)
- \(C_{\mathrm{p}}\) :
-
Elastic coefficient of material
- \(c_{\mathrm{f}}\) :
-
Material constant for conductivity, density and specific heat
- \(C_{\mathrm{f}}\) :
-
Surface condition factor
- E :
-
Elastic modulus (GPa)
- f :
-
Coefficient of friction
- J :
-
Bending geometry factor
- I :
-
Surface durability factor
- \(K_{\mathrm{v}}\) :
-
Dynamic velocity factor
- \(K_{\mathrm{o}}\) :
-
Overload factor
- \(K_{\mathrm{m}}\) :
-
Load distribution factor
- \(K_{\mathrm{s}}\) :
-
Size factor
- \(m_{\mathrm{g}}\) :
-
Gear ratio
- \(m_{\mathrm{c}}\) :
-
Contact ratio
- N :
-
Number of teeth
- \(P_{\mathrm{d}}\) :
-
Diametrical pitch
- v :
-
Rolling velocity at point of contact(rpm)
- V :
-
Pitch line velocity (rpm)
- \(W_{\mathrm{t}}\) :
-
Transmitted load (N)
- \(\phi\) :
-
Pressure angle (rad)
- \(\phi _{\mathrm{t}}\) :
-
Transverse pressure angle (rad)
- \(\mu\) :
-
Poisson ratio
- 1:
-
Pinion
- 2:
-
Gear
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Rai, P., Barman, A.G. Design optimization of spur gear using SA and RCGA. J Braz. Soc. Mech. Sci. Eng. 40, 257 (2018). https://doi.org/10.1007/s40430-018-1180-y
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DOI: https://doi.org/10.1007/s40430-018-1180-y