PLANE EULER

Application

Use the PLANE EULER function to define the working plane by three Euler angles.

Description of function

Euler angles define a working plane as three rotations layered on top of one another, starting from the non-tilted workpiece coordinate system W-CS.

Use the third Euler angle to optionally align the tilted X axis.

Euler angle EULPR

Euler angle EULNU

Euler angle EULROT

All three angles must be defined even if one or several angles equals 0.

At first, the rotations layered on top of one another happen around the non-tilted Z axis, then around the tilted X axis and finally around the tilted Z axis.

 
Tip

This view equals three PLANE RELATIV functions programmed one-by-one, first with SPC, then with SPA and finally with SPC again.

PLANE RELATIV

The same result can be achieved by a PLANE SPATIAL function with the spatial angles SPC and SPA, followed by a rotation (e.g., with the TRANS ROTATION function).

PLANE SPATIAL

Rotations with TRANS ROTATION

Application example

NC programs contained in this User's Manual are suggestions for solutions. The NC programs or individual NC blocks must be adapted before being used on a machine.

Change the following contents as needed:

  • Tools
  • Cutting parameters
  • Feed rates
  • Clearance height or safe position
  • Machine-specific positions (e.g., with M91)
  • Paths of program calls

Some NC programs depend on the machine kinematics. Adapt these NC programs to your machine kinematics before the first test run.

In addition, test the NC programs using the simulation before the actual program run.

 
Tip

With a program test you determine whether the NC program can be used with the available software options, the active machine kinematics and the current machine configuration.

Example

11 PLANE EULER EULPR+0 EULNU45 EULROT0 TURN MB MAX FMAX SYM- TABLE ROT

Initial state

The initial state shows the position and orientation of the working plane coordinate system WPL-CS while still non-tilted. The workpiece datum which in the example was shifted to the top chamfer edge defines the position. The active workpiece datum also defines the position around which the control orients or rotates the WPL-CS.

Orientation of the tool axis

Using the defined Euler angle EULNU, the control orients the Z axis of the WPL-CS to be perpendicular with the chamfer surface. The rotation by the EULNU angle is around the non-tilted X axis.

The orientation of the tilted X axis equals the orientation of the non-tilted X axis.

The orientation of the tilted Y axis results automatically because all axes are perpendicular to one another.

 
Tip

When programming the machining of the chamfer within a subprogram, an all-round chamfer can be produced by using four working plane definitions.

If the example defines the working plane of the first chamfer, the remaining chamfers can be programmed using the following Euler angles:

  • EULPR+90, EULNU45 and EULROT0 for the second chamfer
  • EULPR+180, EULNU45 and EULROT0 for the third chamfer
  • EULPR+270, EULNU45 and EULROT0 for the fourth chamfer

The values are referenced to the non-tilted workpiece coordinate system W-CS.

Remember that the workpiece datum must be shifted before each working plane definition.

Input

NC programs contained in this User's Manual are suggestions for solutions. The NC programs or individual NC blocks must be adapted before being used on a machine.

Change the following contents as needed:

  • Tools
  • Cutting parameters
  • Feed rates
  • Clearance height or safe position
  • Machine-specific positions (e.g., with M91)
  • Paths of program calls

Some NC programs depend on the machine kinematics. Adapt these NC programs to your machine kinematics before the first test run.

In addition, test the NC programs using the simulation before the actual program run.

 
Tip

With a program test you determine whether the NC program can be used with the available software options, the active machine kinematics and the current machine configuration.

Example

11 PLANE EULER EULPR+0 EULNU45 EULROT0 TURN MB MAX FMAX SYM- TABLE ROT

The NC function includes the following syntax elements:

Syntax element

Meaning

PLANE EULER

Syntax initiator for the working plane definition by means of three Euler angles

EULPR

Rotation around the Z axis of the workpiece coordinate system W-CS

Input: -180.000000...+180.000000

EULNU

Rotation around the X axis of the tilted working plane coordinate system WPL-CS

Input: 0...180.000000

EULROT

Rotation around the Z axis of the tilted WPL-CS

Input: 0...360.000000

MOVE, TURN or STAY

Type of rotary axis positioning

 
Tip

Depending on the selection, the optional syntax elements MB, DIST and F, F AUTO or FMAX can be defined.

Rotary axis positioning

SYM or SEQ

Select an unambiguous tilting solution

Tilting solution

Optional syntax element

COORD ROT or TABLE ROT

Transformation type

Transformation types

Optional syntax element

Definition

Abbreviation

Definition

EULPR

Precession angle

EULNU

Nutation angle

EULROT

Angle of rotation