Kinematic Transformations 1

It sounds very theoretical, but it has a daily practical use on the machine tool: Thanks to kinematic transformations, complex, non-rectangular machine coordinate systems are programmed, as usual, in a rectangular workpiece coordinate system. In other words: No matter how the machine realizes the machining, it is always possible to work with the workpiece coordinates from the drawing.

Kinematic transformations are thus important helpers in the background. This series of articles provides background knowledge on these powerful CNC functions and shows use cases you probably have not thought of yet.

This kinematic transformation is used for machining with driven tools on turning centers that are not equipped with a real Y axis. Tool paths on the front-face of the turning workpieces are programmed in the G17 plane, i.e. in a rectangular workpiece coordinate system, as if there were a real Y axis. For SINUMERIK CNCs, the required kinematic transformation is activated with the CNC language command TRANSMIT.

The video shows how TRANSMIT converts the tool paths from the XY plane into a coordinated movement of the X axis and the C axis - i.e. the main spindle in position control.

However, a physical limitation of this transformation must be considered: If the tool path defined in the XY plane passes through the center of rotation of the component, the C axis would have to rotate infinitely fast in this pole position - and reverse at the same time. The speed of the main spindle is limited by the electrical energy required for this. However, by limiting the speed, the path feed rate also decreases, and the cutting conditions are therefore no longer optimal.

This transformation is used for machining on the peripheral surface of rotationally symmetrical workpieces. The tool paths are programmed in a rectangular workpiece coordinate system as if the cylindrical surface were flat, i.e. "unwound". If it is a turning machine, this is the G19 plane.

The CNC language command TRACYL activates the kinematic transformation. The video shows how the paths programmed in the ZY plane are now converted into a movement of the Z axis and the C axis (main spindle in position control).

In drilling operations on the peripheral surface, the geometry of the machining operation is imprinted by the contour of the tool: A cylindrical drill produces a cylindrical borehole (with "parallel walls") whose bottom is imprinted by the contour of the drill cutting edge.

Milling on peripheral surfaces is different: If no Y-axis is in use, the cutter is always radially oriented. A flat-bottomed pocket programmed in the G19 plane has a curved bottom after milling on the peripheral surface - which means that the shoulders of the pocket are not parallel in the direction of unwinding.

TRACYL is also used when highly precise grooves are milled on peripheral surfaces - exactly when the cutter radius compensation is required to achieve the tolerance.

This type of TRACYL requires a real Y axis in the machine: as soon as the slot geometry has a portion along the axis of rotation of the workpiece, this third axis is required. Only if the grooves are purely radial does the third geometry axis (Y axis) not come into play.

Rotationally symmetrical components are not just the domain of lathes. If the milling machine is equipped with a dividing head, for example with an A axis, TRACYL can be used there. The kinematics of 5-axis milling machining centers are in principle usable for the peripheral surface transformation.