Estimation of weld bead depth for in-process control

The key geometric attribute of a major class of welds is the depth of penetration. However, no robust method exists for direct measurement of this quantity, although both ultrasonic and X-ray approaches have been attempted. In this paper, a method for real-time estimation of the depth is presented. The estimator is based on an inverse heat transfer solution whereby accessible surface temperatures on the top and back side of the weldment are used to solve for the isotherms internal to the weldment. The depth is then found by seeking the isotherm corresponding to the melting temperature of the material. The solution employs a three-dimensional analytical heat conduction relationship with a multiple heat source description that is shown to adequately describe many types of weld cross sections. Using a combined Gauss-Newton and steepest descent method, the measured surface temperatures are used to drive an iterative solution for the necessary heat source description (intensity and distribution). Open-loop experiments under a variety of welding conditions using four- and six-point surface radiation measurements and involving destructive measurement of the weld profile indicate that the method can provide depth estimates of acceptable accuracy for in-process control.