Analytical–FEM modeling and stiffness–mass optimization of BCC lattice-core polymer spur gears for additive manufacturing

• Lattice body compliance is incorporated into analytical gear mesh stiffness • FEM results agree with analytical predictions within 5% deviation • Unit-cell size accounts for approximately 74–75% of stiffness variation • Pareto optimization enables about 52% mass reduction • Tooth-tip deflection is limited to 0.349 mm at the optimal design This study proposes an analytical–numerical framework for evaluating mesh stiffness in polymer lattice-core gears manufactured by additive manufacturing, in which lattice body compliance is explicitly integrated into analytical gear mesh-stiffness modeling. A three-dimensional mesh-stiffness model augments classical tooth compliance components, with a gear-body compliance term K body derived from the Gibson–Ashby scaling law for bending-dominated lattices. A response surface methodology based on a face-centered central composite design (FCCCD) is employed to quantify the influence of unit-cell size and strut diameter on translational mesh stiffness, tooth-tip deflection, and mass reduction. Unit-cell size is the dominant factor, explaining approximately 74–75% of the variance, while strut diameter provides secondary stiffening. A balanced design (a ≈ 10 mm, t ≈ 1 mm) achieves approximately 52% mass reduction while maintaining deformation within acceptable limits, offering practical guidance for early stage design. The proposed framework establishes a direct analytical link between lattice topology and gear mesh stiffness, providing a reliable, design-oriented tool for lightweight polymer gears in mechatronic and automotive applications. Experimental validation and extension to TPMS and graded lattices are identified as directions for future work.