Analysis of mechanical error in a fused deposition process using a stochastic approach

A stochastic model has been developed for studying the mechanical error in different rapid prototyping (RP) processes. Tolerances and clearances, which cause mechanical error, have been assumed to be random variables. The coordinates of a point on the work surface traced by the laser beam or the tip of the extruder head is expressed as a function of the random variables involved in the process. Using a unified approach for the RP processes, the mechanical error in the fused deposition process is analysed. In a numerical example, the mechanical error has been found for a grid of points traced by the nozzle tip. The three-sigma bands of the error in tracing example curves are plotted. This is the band in which the nozzle tips of 99.73% of machines, produced on a mass scale, lie for the given tolerances and clearances. Stringent values of tolerances and clearances reduce the error at the nozzle tip, but the cost of manufacturing and assembling the machines may become prohibitive.