<p>This research develops a precise mathematical representation of spiral bevel gear tooth surfaces, integrating higher-order terms in machine-tool configuration parameters. A loaded tooth contact analysis (LTCA) is conducted under rated conditions, exploring the correlations between higher-order coefficients of velocity ratio and radial distance and meshing characteristics. The findings indicate that when the variation transitions from negative to positive, the contact area corresponding to the second-order velocity ratio coefficient moves from the heel-root region toward the toe-top zone. The maximum contact stress increases, then decreases, and increases again. The transmission error peak-to-peak value (TE-PPV) rises. The position of maximum root bending stress (MRBS) moves toward the toe. The 1st-order radial distance coefficient causes the contact pattern to transition from the toe-top region toward the heel-root area. The proportion of the contact region declines. Meanwhile, the peak contact stress initially drops, subsequently rises, and then falls once more. The TE-PPV exhibits an initial increase, followed by a decrease, and subsequently rises once more. The maximum root bending stress follows the same trend, and its position shifts from the toe to the heel. When examining the influence of velocity ratio’s higher-order coefficients, the 0th-order coefficient demonstrates inferior meshing characteristics, whereas incorporating higher-order terms significantly enhances meshing performance. In the variation of higher-order coefficients of radial distance, the 4th-order coefficient yields the best overall meshing characteristics, while the 6th-order coefficient results in the poorest.</p>