In order to keep the surface information intact during acquisition and analysis, it is necessary to move the data structure from a function z=f(x,y), where one height value is coded for every x,y position on a regular grid, to a curvilinear form, (x,y,z)=f(u,v), where points in space are connected to their neighbors as triangles.
A Freeform surface, called a "Shell" in Mountains®, is a point cloud (x,y,z) associated with connectivity information so that all points are connected in a triangle mesh in space. That way, the complete surface around an object can be coded. It also allows coding of undercut structures or internal cavities (see example image below).
3D View in Mountains® of a shell (or freeform surface) of metallic powder melted by a laser, Laser Powder Bed Fusion (LPBF) in additive manufacturing. Non-melted powder particles are visible above the surface, as well as a cavity below the surface. The triangle mesh and points have been overlapped on a colored surface.
Triangle meshes are commonly used in Dimensional Metrology to represent, for example, a mechanical workpiece measured by a Coordinate Measuring Machine (CMM). The difference here, is that its resolution has to be fine enough in order to allow surface texture analysis at a micrometer scale.
Freeform Surfaces can be produced by several instrumental techniques:
Mountains® 8 can load Freeform Surfaces from various file formats (STL, 3MF, OBJ, PLY). They are loaded as Shell studiables and can be displayed in an interactive 3D View and further analyzed with Operators and Studies.
Besides coordinates and connectivity information, a Shell studiable may also contain additional information, called attributes, created during acquisition or extraction, or generated by a specific Operator in Mountains®. These attributes may be color or intensity values, normal vectors, distance values from the reference surface, or any application-oriented attribute that needs to be linked to the shell studiable. An attribute can be associated with points or triangles, or even edges.
A bridge between the DigiXCT® software from Digisens and Mountains® is currently under development. This will enable extraction of accurate freeform surfaces from the density information contained in volume datasets and importation to Mountains® for surface texture analysis. The link to the original volume dataset will be maintained over time.
Mountains® 8.0 already included two specialized Operators for processing freeform surfaces:
Extract Projected Surface This operator allows the user to orient the freeform surface and position a rectangle to define the portion of the freeform surface to extract and convert to a standard surface. Useful, for example, when analyzing roughness on an internal surface (e.g. the internal surface of the chamber of a pump produce by additive manufacturing that cannot be accessed by regular profiler unless the workpiece is cut)
Extract Parametric Profile This operator intersects the freeform surface with an oriented plane in order to create a contour profile that can be analyzed in the Advanced Contour Study. This can be useful, for example, for checking angles and dimensions or even comparing the profile with a DXF model.
Digital Surf has been partnering with the Center of Precision Technologies at the University of Huddersfield (UK) to develop a set of surface texture parameters calculated on freeform surfaces. A team of talented researchers and PhD students at Huddersfield have developed the background mathematics and adapted the definitions of areal surface texture parameters to apply on freeform surfaces.
A symmetrical expression can be found for most parameters on freeform surfaces compared to standard surfaces:
Definition of Sa on a Standard Surface
Definition of Sa on a Freeform Surface
Definition of Sq on a Standard Surface
Definition of Sq on a Freeform Surface
Mathematical details can be found in the paper:
Pagani L, Qi Q, Jiang XQ, Scott PJ, Towards a new definition of areal surface texture parameters on freeform surface, Measurement 2017.
Parameters are calculated from the form deviation values associated with each point of the freeform surface. This means that a form surface has to be associated with the freeform surface. This is done by a dedicated plugin operator that fits a least-square form to the point cloud. The form can be a plane, polynomial, cylinder or sphere. It's a preliminary stage before parameters can be calculated.
In the case of an additive manufacturing component, it is usually necessary to fit a CAD model or the designed mesh to the freeform surface under test. Such fitting is a complex and computer-intensive operation. When no model is available, the reference surface may be approximated using a low-pass filter (S-Filter), the same way a waviness surface is used as the reference surface to calculate roughness heights. Smoothing filters, as well as some morphological or envelope filters and retouch tools can be useful. These functions will be available in future versions of Mountains®.
MountainsMap® Premium 8, MountainsSEM® Premium and MountainsLab® Premium all include the Shell Extension module that adds features on Freeform Surfaces. The module is also available as an option to other products.