A frequency-domain approach to determining the path separation for spray coating

Many modern spray deposition processes, such as spray painting or coating, are automated by using a robot to move an applicator in a series of passes over the surface being sprayed. Determining the robot path that creates the required coat thickness over the surface can be considered as an optimization problem, which traditionally has been solved in the spatial domain. In this paper, results from sampling theory are used to transfer the problem into the spatial frequency domain, which determines the optimal separation between passes. The paper also shows how angled raster patterns can be combined to provide a continuous path over the surface that generates the required distribution of deposited material. Note to Practitioners-This paper is motivated by the problem of producing a given distribution of coat thickness during an automated spraying or deposition process. The coating is applied by an applicator that is moved by a robot whose path consists of a series of passes over a surface, and the aim is to determine the separation between the passes and the changes to the deposition rate or robot velocity that will produce the required thickness distribution. In many applications, a uniform thickness is required over the surface, but this paper also considers the problem of producing a shaped thickness profile. The analysis uses ideas from Shannon´s sampling theorem to move the problem into the frequency domain, which provides a direct link between the Fourier transform of spray footprint on the surface and the separation of passes of the applicator as it moves over the surface. The paper also introduces a scanning strategy that consists of a combination of two sets of angled raster scans. Compared to paths consisting of conventional scans, this has the advantage that it reduces the time that the robot spends off the edge of the surface.