In Sect. 1, a coordinate system for tooth surface formation with cutter errors is established to derive the tooth surface equation. In Sect. 2, the tooth contact analysis model and load tooth contact analysis model are established, and the formulas of the tooth surface contact ellipse and main curvature direction angles are derived. In Sect. 3, the influences of the cutter errors on the contact ellipses, the tooth surface contact trace, and the loaded contact characteristics are analyzed.

The relationship between installation error and contact performance was studied. The tooth surface equation and contact ellipse were deduced, and the imprinting experiment was realized. The tooth contact analysis (TCA) model was developed to investigate the influence of the installation error on the contact area. The formulas of the gap and flexibility matrix were given to develop the loaded TCA (LTCA) model. The influence of the installation error on load distribution was investigated.

Firstly, the tooth surface modification method based on the parabolic forming blade and cutter inclination was proposed. Next, the modified tooth surface equation was deduced and the 3D reconstruction of the modified tooth surface is realized. Then, the influence of modification parameters on tooth surface curvature characteristics was analysed. Finally, the tooth contact analysis model was established to discuss the influence of modification parameters on the elliptical contact area.