**5.6 An introduction to tool path calculation for free form geometries**

The calculation of the tool path is the main function of the software CAM. The result of the final part is straightly related with the quality of the tool path, implying in the quality of the surface machined, dimensional errors and times of path calculation and real machining. The algorithms and the methodologies for tool path calculation are developed by each software house, and represent industrial secrets.

In the current procedure used for most commercial CAM codes to generate free form tool paths, the system first calculates the cutter-contact points (CC) over the 3D CAD geometry. Then the tool offset is included resulting in the cutter-location (CL) points, which are used to generate the NC program blocks; using the traditional method to create a free-form tool path, i.e., the linear interpolation of straight-line segments, with continuity C0. These CL points are easily transformed into the ordinary G01 CNC code, according to DIN 66025.

Fig. 15. Points that describe a complex tool path for milling

The length of these segments is related with the tolerances of calculation in the CAM and the degree of curvature of the surface. The CAM software adjusts the tool path segment lengths to fit inside a tolerance band defined by the user, known as "chord error". The smaller the tolerance band, the closer the tool path will be it to you the original CAD 3D model. The smaller the tolerance band, the closer the tool path will be to the original CAD 3D model. Thus linear segments are generated by such a procedure and, for highly curved paths, the number of segments increases dramatically, along with the CNC program size. The Figure 16 shows the influence of the curvature of the surface in the length of the segments of straight lines of a program CNC, calculated inside a same band of tolerance.

Some CAM systems allow to establish through a band of variation, limits of tolerances with the possibility of deviation from the path inward and/or for outward of the geometry. The

Advanced Free Form Manufacturing by Computer Aided Systems – Cax 573

interpolation to describe a tool path. That combination can maintain the continuity of the curve C1 and showed many advantages about the isolated utilization of segments of straight line (SOUZA, 2004). This approach, however, can only be applied to planar motion by interpolating two axes of the CNC machine, since the great majority of CAD / CAM / CNC are unable to carry out circular interpolation in three dimensions. Thus, it has aimed utilize

After the CAM calculates and simulates the tool paths, there is the phase of post-processing,

CC

Tool path

Surface curvature and normal

CL

The initial calculation in the system CAM generates a generic file, without specifications.

The post-processing has the function of encode the paths calculated by any software CAM

Post-processor – computational program that reads the file CLF and converts it into a

For each equipment, machine/CNC should be developed a specific post-processor. The procedure for the creation of post-processors and development of programs CNC is

The information of the machine is related to its physical characteristics, as maxim movement of the axes, number of axes, speeds etc. Regarding the numerical control, there is a wide range of CNCs on the market today, ISO 66025 standardizes the main functions codes CNC. There are several distinctions among suppliers. The simplest cases involve, as example, the utilization of point or comma for separate decimal places; number of decimal places demanded; block end

which is responsible for transforming these paths into CNC programs.

in specific commands for a given configuration machine/CNC.

Therefore, two elements are necessary for create the program CNC: Tool path calculated by the CAM in computational format (CLF).

program to be performed in a given combination of machine/CNC.

character need; command for beginning and end of program, among others.

polynomials Spline to describe complex tool paths.

Surface

Fig. 17. Determination of CL by CC

This file is known like Cutter Location File (CLF).

**5.8 Post-process task** 

presented in the Figure 18.

lower the tolerance band, the closer will be the tool paths from the surface to be machined, however, smaller will be the followings segments of lines, CNC programs will possess greater volume of data, since more lines comprise the program and this characteristic will be able to limit the feed rate during machining, particularly in complex forms. The machine reduces the programmed feed rate, as studied by SOUZA & COELHO (2007).

Fig. 16. Tolerance to calculate the CNC programs

The path of the tool calculated by a system CAM represents the central extremity of the tool, and by that, the path is not a simple offset of the surface it be machined. To develop the calculation, the software should identify two positions: a) Point of contact of the tool with the surface, known as CC - Cutter Contact and b) the point that represents the path of the tool (its central extremity), named of CL - Cutter Location.

The lines of the programs CNC, referring the paths of the tool, contain the Cartesian information of each points CL. It must be noticed that the Cutter Contact is the point which should be inside this band of tolerance and not the path of the tool or the Cutter Location.

Deferential ways exist to calculate both, the CC and CL. These algorithms are virtues of a CAM, therefore can have repercussions in the time of calculation, time of machining and quality of the surface machined. Initially, in a certain moment, and then it should calculate the final point the tool centre (CL) points that are linearly interpolated to generate the tool paths.

An approach for calculate the CC in polynomial surfaces is the division of the own polygon of control of that describes the curve or surface. This subdivision can identify points about the curve or surfaces, which can be the CC. Others approaches are developed for such end.

After it identified the CC, the CL must be calculated. The Figure 17 exemplifies a possibility to calculate the CL for two points of a path, considering that a previous algorithm already have found the CC. In this example, knowing to normal of the surface in the point desired (CC) and angle that this normal is found regarding the axis of the coordinates, is able to the CL be found through the ray of the tool.
