**4.5 Tool paths described by polynomial spline**

The polynomial Spline curve can also be used to describe complex tool paths (SOUZA et al, 2010). Therefore the NC program generated will not contain the traditional commands (G01, G02 or G03), but there is a new syntax which illustrates the tool path and the polygon control which defines the curve. The Cartesian points are used to define the polygon. There are different syntaxes for the entrance of the spline data. This variation agrees with the numerical commands used. Below can be found an example of syntax for Spline movement which is generated in accordance with nomenclature of CNC FANUC.

For the generation of CNC programs using polynomials Spline, the CAM systems permit this resource which do not generate directly. The CNC programs contain Spline functions that are generated leaving a CNC linear program in straight segments. With this initial tolerance is used to calculate the linear program adding the tolerance calculation of the Spline program. For the process to be adequate the user should scientifically plan the most efficient way to work with these tolerances. Bibliographical research done during the development of this work has found very practical analysis.

YAU e KUO (2001) developed an application that converted traditional CNC generated programs for interpolation linear in CNC programs with Spline format. This method of work has implemented sophisticated numerical commands. In this case the data entered into a CNC program containing commands G01 and internally the CNC converts the straight paths into Spline equations, proportioning better performance than the traditional method of straight segments, however this conversion must be attributed to another value of tolerance. A deeper understanding can be found in SOUZA (2004) and SOUZA & COELHO (2007)ª,b.

Where:

564 Mechanical Engineering

a. **Block Processing Time**. To run the machine in linear path, the points of the NC program have to be interpolated to obtain the movement in one or more machine axis. This task is done by the CNC interpolator. The interpolator has to calculate the speed of each servomotor of the machine tool in every block. The real-time interpolator converts the CL path to the motion trajectories of the orthogonal machine axes so as to coordinate their motion in three-axis surface machining. This task is known as CNC

b. **Control loop.** In addition to the interpolation, the current CNC controller also has to check feedback devices in order to maintain the machine's high precision. The machine closes a control loop using devices such as encoders and linear scales. In the CNC machine system, the practical tool location is measured by the feedback devices at a specific time, i.e., sampling interval. The sampling interval is about 0.001 seconds, depending on the CNC milling machine; this represents another task to be calculated by

c. **Motion algorithms**. Other algorithms developed to aid machine motion and positioning, such as look-ahead, feed forward control, and jerk limitation are also implemented in present CNC machine. Therefore, all the tasks mentioned above have

When machining complex geometries, the machine often encounters curved surfaces, where short segments are required to closely follow the profile. When that occurs with the NC program set with high feed rates the machine slows down and sometimes oscillates

Feed rate oscillation happens even in the most updated CNC machines and depends on servo response, feedback devices, CNC characteristics and its implementation on the

The polynomial Spline curve can also be used to describe complex tool paths (SOUZA et al, 2010). Therefore the NC program generated will not contain the traditional commands (G01, G02 or G03), but there is a new syntax which illustrates the tool path and the polygon control which defines the curve. The Cartesian points are used to define the polygon. There are different syntaxes for the entrance of the spline data. This variation agrees with the numerical commands used. Below can be found an example of syntax for Spline movement

For the generation of CNC programs using polynomials Spline, the CAM systems permit this resource which do not generate directly. The CNC programs contain Spline functions that are generated leaving a CNC linear program in straight segments. With this initial tolerance is used to calculate the linear program adding the tolerance calculation of the Spline program. For the process to be adequate the user should scientifically plan the most efficient way to work with these tolerances. Bibliographical research done during the

YAU e KUO (2001) developed an application that converted traditional CNC generated programs for interpolation linear in CNC programs with Spline format. This method of

which is generated in accordance with nomenclature of CNC FANUC.

development of this work has found very practical analysis.

block processing time. The main CNC tasks are presented as follows:

to be done by the CNC in a very short time.

**4.5 Tool paths described by polynomial spline** 

the CNC.

machine tool.

imitating a vibration behaviour.

G6.2 – syntax of NURBS [P] – degree of the polynomial equation [K] - vector on the control point (knot) [X,Y,Z] – coordinate of the control points [R] – weight on the control points (weight)

Fig. 9. Spline program line for the FANUC command
