A method for assessing geometrical errors in layered manufacturing. Part 2: mathematical modelling and numerical evaluation

摘要

Layered manufacturing based rapid prototyping processes are subjected to not only a staircase effect owing to the approximating process used, but also an accumulated error transfer between layers. Certain types of error such as surface tilting and layer thickness variations that occur in one layer can transfer to other layers above it. This paper describes a mathematical model based on the physical and geometrical models discussed in Part 1 of the paper. The model uses the matrix transformationmethod to analyse the effect of transformation of local errors to the multiple layer global errors. A data preparation error transformation matrix is used to describe the error interactions between layers during the data preparation stage. A disturbanceerror transformation matrix is used to describe the error interaction within each layer and error propagation between layers during the part building process. This model describes geometrical error analysis involving profiling error, layer inclination and layer thickness variations. Numerical evaluation of the model is carried out for a typical benchmark component.