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REAL TIME 5-AXIS NURBS CURVE INTERPOLATOR Sungchul Jee and Taehoon Koo Processing Sequence CAD Comparing with Linear interpolation Example A CL file necessarily includes coordinates and tool orientation vector in local coordinates. ▪ The proposed 5-axis NURBS interpolation format can be applied to various configuration of 5-axis machining centers without modifying the NC code. ▪ The results of simulation and experiment validate the superiority of the proposed NURBS interpolator over the conventional linear interpolator. 6 control points and duplicated knots at start and end points Geometry information NURBS-IGES format CAM 5-axis NURBS G-code CNC CL file format Interpreter (ISO-6983) 5-axis NURBS interpolator Parser CATIA format: x_, y_, z_, i_, j_, k_ Ex) GOTO / -35.014, -65.185, 102.102, -0.416, -0.110, 0.902 HyperMill format: x[/_] y[/_] z[/_] u[/_] v[/_] w[/ _] Ex) 31:oL[10](x[/10.0] y[/31.2] z[/21.3] u[/0] v[/-0.557] w[/0.830] Vector converter TCP control Added a new parser rule and a vector conversion rule Coordinate data and tool orientation vectors The vector converter decomposes the tool orientation into two angles for rotational axes depending on machine configuration. Interpolated data is transformed to joint axial movement by TCP(Tool Center Point) control Objective: ▪ To propose a new 5-axis NURBS interpolator that can be easily cope with post-processing of CL files from a CAM system To evaluate and compare with the conventional linear interpolator Rational B-spline curve entity (Type 126) Ex) 126,5,3,1,0,1,0,0.,0.,0.,0.,0.333333,0.666667,1.,1.,1. ,1.,1.,1., 7P 4 1.,1.,1.,1.,-178.,109.,0.,-166.,128.,0.,- 144.,109.,0.,-109., 7P 5 Machine configuration parameters Sample code G106 F0.9 X-43 Y-43 Z0 X-30.787 Y-34.290 Z9 X-18.574 Y-25.581 Z9 X-6.361 Y-16.872 Z-9 X5.850 Y-8.163 Z-9 X18.063 Y0.545 Z0 I-0.569 J-0.406 K0.7 I-0.429 J-0.429 K0.7 I-0.347 J-0.370 K0.7 I-0.381 J-0.149 K0.7 I-0.299 J-0.090 K0.7 I-0.158 J-0.113 K0.7 R0 R0 R0 R0.25 R0.5 R0.75 R1 R1 R1 TTTR A C New G-code Format The proposed G-code Independent of machine tool’s rotational axes Format Description G106 P_ ; X_ Y_ Z_ I_ J_ K_ R_ W_; G106: Start NURBS interpolation P: Degree of a NURBS curve X, Y, Z: Control point I, J, K: Tool axis vector R: Knot W: Weight (default value = 1) Experiment M echatrolink II protocol <Servo System > Yaskaw a S-II <C ontrol PC > Sim ultaneous 5-Axis C ontrol system N T110 digital comm nunication board D igital m otion netw ork system PC Islottype S-II Max. allowable chord error for linear interpolation : 1μm Feedrate : 0.9m/m Feedrate Contour error Tool orientation error 0 20 40 60 80 0 5 10 15 20 25 F ee d rate [m m /s] 5-A xis N U R B S Interpola tion Lin ear In terpo latio n Length of C urve [m m] 0 20 40 60 80 0 1 2 3 4 5 L en g th o f C urve [m m] C o n to u r e rro r [m m x 10 -3 ] 5-A xis N U R B S inte rpo latio n Lin ea r in terp po la tio n 0 20 40 60 80 0.000 0.004 0.008 0.012 0.016 T oolO rie n tation E rro r [d e g .] 5 -A xis N U R B S Inte rpo la tion L inea r In te rp o lation Length of C u rve [m m]

5 Axis NURBS curve interpolator using tool axis vector command

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Page 1: 5 Axis NURBS curve interpolator using tool axis vector command

REAL TIME 5-AXIS NURBS CURVE INTERPOLA-TOR

Sungchul Jee and Taehoon Koo

Processing Sequence CAD

Comparing with Linear interpolation Example

A CL file necessarily includes coordinates and tool orientation vec-tor in local coordinates.

▪ The proposed 5-axis NURBS interpolation format can be applied to various configuration of 5-axis machining centers without modifying the NC code.▪ The results of simulation and experiment validate the superiority of the proposed NURBS interpolator over the conventional linear interpolator.

6 control points and duplicated knots at start and end points

Geometry information

NURBS-IGES format

CAM

5-axis NURBS G-code CNC

CL file format

Interpreter (ISO-6983)

5-axis NURBS interpolator

Parser

CATIA format: x_, y_, z_, i_, j_, k_Ex) GOTO / -35.014, -65.185, 102.102, -0.416, -0.110, 0.902

HyperMill format: x[/_] y[/_] z[/_] u[/_] v[/_] w[/_]Ex) 31:oL[10](x[/10.0] y[/31.2] z[/21.3] u[/0] v[/-0.557] w[/0.830]

Vector converter

TCP control

Added a new parser rule and a vector conversion rule

Coordinate data andtool orientation vectors

The vector converter decomposes the tool orientation into two angles for rotational axes depending on machine configuration.

Interpolated data is transformed to joint axial movement by TCP(Tool Center Point) control

Objective: ▪ To propose a new 5-axis NURBS interpolator that can be easily cope with post-processing of CL files from a CAM system

▪ To evaluate and compare with the conventional linear interpolator

Rational B-spline curve entity (Type 126)Ex) 126,5,3,1,0,1,0,0.,0.,0.,0.,0.333333,0.666667,1.,1.,1.,1.,1.,1., 7P 4 1.,1.,1.,1.,-178.,109.,0.,-166.,128.,0.,-144.,109.,0.,-109., 7P 5

Machine configuration parameters

Sample codeG106 F0.9X-43 Y-43 Z0X-30.787 Y-34.290 Z9X-18.574 Y-25.581 Z9X-6.361 Y-16.872 Z-9X5.850 Y-8.163 Z-9X18.063 Y0.545 Z0I-0.569 J-0.406 K0.7I-0.429 J-0.429 K0.7I-0.347 J-0.370 K0.7I-0.381 J-0.149 K0.7I-0.299 J-0.090 K0.7I-0.158 J-0.113 K0.7R0 R0 R0 R0.25 R0.5 R0.75R1 R1 R1

TTTR

A

C

New G-code Format The proposed G-code

Independent of machine tool’s rotational axes

Format DescriptionG106 P_ ; X_ Y_ Z_ I_ J_ K_ R_ W_;…

G106: Start NURBS interpolation P: Degree of a NURBS curve X, Y, Z: Control pointI, J, K: Tool axis vector R: KnotW: Weight (default value = 1)

Experiment

Mechatrolink IIprotocol

<Servo System>Yaskawa S-II

<Control PC>Simultaneous 5-Axis

Control system

NT110 digital commnunication

board

Digital motion network system

PCI slot type

S-II

0 20 40 60 800

5

10

15

20

25

Feed

rate

[mm

/s]

5-Axis NURBS Interpolation Linear Interpolation

Length of Curve [mm]

0 20 40 60 800

1

2

3

4

5

Length of Curve [mm]

Cont

our e

rror [

mm

x 10

-3] 5-Axis NURBS interpolation

Linear interppolation

0 20 40 60 800.000

0.004

0.008

0.012

0.016

To

ol Or

ienta

tion

Erro

r [de

g.]

5-Axis NURBS Interpolation Linear Interpolation

Length of Curve [mm]

Max. allowable chord error for linear interpolation : 1μm Feedrate : 0.9m/m

Feedrate

Contour error

Tool orientation error