Multi-objective optimisation with finite element analysis of profile shifted altered tooth sum spur gear

ABSTRACTTraditional gear design approaches provide design parameters that meet only one design requirement at a time. However, a major problem with this kind of approach is the deficit for high consistency and reliability. The objective of the article is to present a multi-objective design optimisation procedure for addendum modified spur gear with altered tooth sum. The design procedure involves implementation of Particle Swarm Optimisation (PSO) and a hybrid PSO- Teaching-learning based optimisation (PSO-TLBO) algorithm for simultaneous optimisation of the weight and contact or hertzian stress along line of action of the spur gear drive. The design optimisation was validated through stress analysis of the optimised spur gear set, using Finite element analysis (FEA) with various mesh types and grain size. Afterwards, manufacturing of the optimised non-standard gear set with metallic (EN24) and a composite (Hylum) gear material using standard tooling. This indicates that with the proposed design optimisation approach there is a possibility of meeting the requirement for efficient, compact, and reliable gear set with reduced computational cost. This study suggests that it is possible to determine a set of optimised design variables that can meet more than one design criteria at a time.KEYWORDS: Spur gearoptimum weightcontact stressprofile modificationaltered tooth sumFEM Nomenclature a=Center distanceCr=Surface reliability factord0=Outside diameter of boss (mm)Fs=Induced bending load (Lewis formula)I=Geometry factorKr=Bending reliability factorL=Length of boss (mm)Sfe=Surface fatigue strength (MPa)x=Design variable vector gearbw=Thickness of web (mm)Cs=Surface factordp=Drilled hole diameter (mm)Fn=Normal loadJ=Lewis Geometry factorKms=Mean stress factorlw=Thickness of rim (mm)τ=Shaft shear strength (MPa)y=Lewis tooth form factorCl=Surface fatigue life factorD1&D2=Pitch circle diameter of pinion and gearDr=Dedendum circle diameter (mm)Fp=Wear load (N)Ko=Over load factorKv=Velocity factorn=Number of drilled holesσ=Gear material strength (MPa)σcomposite=Gear material strength (MPa) for composite materialCp=Elastic coefficient (MPa)Di=Inside diameter of rim (mm)F(x)=Objective functiongi(x)=ConstraintsKm=Mounting factorKw=Load factorSn=Standard moore endurance limitv=Pitch line velocity (m/s)Disclosure statementNo potential conflict of interest was reported by the authors.Data access statementThe data that support the findings of this study are available from the corresponding author [sumanta.panda@gmail.com] upon reasonable request.