<p>Existing face gear modification research focuses on point contact for contact path control, but suffers from reduced load capacity and lacks systematic understanding of how modification parameters and assembly errors affect contact characteristics. To address these issues, a modified tooth flank is proposed for face gears to achieve high contact strength. Considering the time-varying characteristic of the angle between the contact line and gear axis along the contact path, a parabolic contact zone equation with controllable contact line length is established to construct a finite line contact region and optimize the contact path. Second-order modification is introduced along the contact line to develop a modified face tooth flank model that accounts for assembly errors. A quasi-Hertzian contact model incorporating nonlinear effects from modification parameters and assembly errors is developed to analyze their influence on contact characteristics via key parameters such as equivalent curvature, contact-line angular deviation, and contact clearance. A three-dimensional modified tooth flank model is constructed and validated via finite element simulation. Comparison across multiple configurations demonstrates that the proposed model effectively avoids edge contact, increases contact-line length and area, and reduces average contact stress by 16.0%, 44.3%, and 28.4% under various assembly errors. The model exhibits low sensitivity to assembly errors, thereby facilitating the assembly of face gear pairs. Compared to the finite element method, the quasi-Hertzian contact model offers significantly higher computational efficiency, making it well-suited for parametric studies, while maintaining good agreement with FEA results, with a maximum deviation of less than 5%.</p>