A mathematical model for the shape of wave-soldered joints on printed circuit boards

(Received 7 January 1993, accepted 1 June 1993)

Abstract
The problem of automatic inspection of solder joints in Printed Circuit Boards by 3D machine vision, is addressed. To provide an appropriate theoretical background to its solution, a mathematical model for the geometric shape of a wide class of wave-soldered joints is elaborated. The formation of such joints is considered approximately as a static phenomenon and studied as a moving boundary constrained variational problem, leading to a general differential equation, which offers a satisfactory model of the joint's shape. The case of axisymmetric through-hole-soldered joints is studied in detail, by integrating numerically the corresponding equations in various cases. The use of the model for simulation of sensor data is illustrated and the possibilities of using the information provided by the model for the development of inspection algorithms, are discussed.