To address the insufficient calibration accuracy caused by sensor noise, robot absolute positioning errors, and error accumulation in traditional linear solving methods for hand-eye calibration of welding industrial robots, this paper proposes a high-precision hand-eye calibration method based on contact constraints and iterative optimization. Firstly, a circular calibration board with crosshair features is designed, and the true coordinates of corner points in the base coordinate system are obtained by controlling the precise contact between the robot end-effector and the calibration board corners. Secondly, binocular structured light 3D reconstruction technology is employed to extract corresponding corner point cloud data in the camera coordinate system. Then, the hand-eye calibration problem is transformed into solving the rigid transformation matrix AX = XB. An innovative error model based on real-world spatial coordinate constraints is constructed, with initial hand-eye parameters derived using the matrix Kronecker product method. Finally, to mitigate noise interference and outlier effects, a Cauchy robust kernel function is introduced to construct an adaptive weighting mechanism, combined with Iteratively Reweighted Least Squares (IRLS) and Levenberg-Marquardt (LM) algorithms for nonlinear optimization. The experimental results demonstrate that the proposed method exhibits higher stability and precision, with an average positioning error of less than 0.5 mm, meeting the requirements for multi-scenario industrial applications.