Defining Scanning Trajectory for on-Machine Inspection Using a Laser-Plane Scanner

Abstract

Scan path planning for on-machine inspection in a 5-axis machine tool is still a challenge to measure part geometry in a minimum amount of time with a given scanning quality. Indeed, as the laser-plane scanner takes the place of the cutting tool, the time allocated to measurement must be reduced, but not at detrimental of the quality. In this direction, this paper proposes a method for scan path planning in a 5-axis machine tool with the control of scanning overlap. This method is an adaptation of a method dedicated to a robot that has proved its efficiency for part inspection.

Appendix: Modeling of the 5 Axis Milling Machine Structure

The Mikron UCP 710 is a 5-axis milling center with an industrial numerical controller Siemens 840D. The architecture of this machine is CAXYZ for which two rotations are applied to the part, and the tool orientation is fixed in the machine frame (Fig. 6).

Fig. 6.

Definition of different frames [16]

The different frames are defined from the architecture of the machine [16]:

• The spindle frame (O_br, x_br, y_br, z_br) is linked to the spindle, the scanner frame (O_C, x_c, y_c, z_c) is linked to the scanner,

• The machine frame (O_m, x_m, y_m, z_m) is linked to the machine structure; its axes are parallel to the XYZ axes; z_m is parallel to the tool axis,

• The tilt frame (S, x_b, y_b, z_b) is linked to the tilt table; x_b is parallel to x_m, S is located on the A axis,

• The table frame (R, x_p, y_p, z_p) is linked to the rotary table; z_p is parallel to z_b, R is defined as the intersection between the C axis and the upper face of the table;

• The programming frame (O_pr, x_pr, y_pr, z_pr) is linked to the part, which represents the frame used for scan path planning.

To transform between different frames, we define the matrix that converts a vector expressed in the one frame into another frame:

$$\begin{aligned} P_{cbr} & = \left[ {\begin{array}{*{20}c} {\cos (W)} & {\sin (W)} & 0 & {x_{{\varvec{O}_{\varvec{c}} \varvec{O}_{{\varvec{br}}} }} } \\ { - \sin (W)} & {\cos (W)} & 0 & {y_{{\varvec{O}_{\varvec{c}} \varvec{O}_{{\varvec{br}}} }} } \\ 0 & 0 & 1 & {z_{{\varvec{O}_{\varvec{c}} \varvec{O}_{{\varvec{br}}} }} } \\ 0 & 0 & 0 & 1 \\ \end{array} } \right];P_{brm} = \left[ {\begin{array}{*{20}c} 1 & 0 & 0 & {x_{{\varvec{O}_{{\varvec{br}}} \varvec{O}_{\varvec{m}} }} } \\ 0 & 1 & 0 & {y_{{\varvec{O}_{{\varvec{br}}} \varvec{O}_{\varvec{m}} }} } \\ 0 & 0 & 1 & {z_{{\varvec{O}_{{\varvec{br}}} \varvec{O}_{\varvec{m}} }} } \\ 0 & 0 & 0 & 1 \\ \end{array} } \right]; \\ P_{mb} & = \left[ {\begin{array}{*{20}c} 1 & 0 & 0 & {x_{{\varvec{O}_{\varvec{m}} \varvec{S}}} } \\ 0 & {\cos (A)} & {\sin (A)} & {y_{{\varvec{O}_{\varvec{m}} \varvec{S}}} } \\ 0 & { - \sin (A)} & {\cos (A)} & {z_{{\varvec{O}_{\varvec{m}} \varvec{S}}} } \\ 0 & 0 & 0 & 1 \\ \end{array} } \right] \\ \end{aligned}$$

where $P_{cbr}$ is the transformation matrix between the scanner frame and the spindle; $P_{brm}$, the transformation matrix between the spindle frame and the machine frame and $P_{mb}$, the transformation matrix between the machine frame and the tilt frame.

$$P_{bp} = \left[ {\begin{array}{*{20}c} {\cos (C)} & {\sin (C)} & 0 & {x_{{\varvec{SR}}} } \\ { - \sin (C)} & {\cos (C)} & 0 & {y_{{\varvec{SR}}} } \\ 0 & 0 & 1 & {z_{{\varvec{SR}}} } \\ 0 & 0 & 0 & 1 \\ \end{array} } \right];P_{ppr} = \left[ {\begin{array}{*{20}c} 1 & 0 & 0 & {x_{{\varvec{RO}_{{\varvec{pr}}} }} } \\ 0 & 1 & 0 & {y_{{\varvec{RO}_{{\varvec{pr}}} }} } \\ 0 & 0 & 1 & {z_{{\varvec{RO}_{{\varvec{pr}}} }} } \\ 0 & 0 & 0 & 1 \\ \end{array} } \right]$$

where $P_{bp}$ is the transformation matrix between the tilt frame and the rotary table frame and $P_{ppr}$ is the transformation matrix between the rotary table frame and the part frame.

The kinematic transformation matrix M from the sensor to the part is then defined as following: M = $P_{ppr}^{ - 1} \cdot P_{bp}^{ - 1} \cdot P_{mb}^{ - 1} \cdot P_{brm}^{ - 1} \cdot P_{cbr}^{ - 1} .$