Skillful Feed Rate Control for Machine Tools Usinga Fuzzy

							Skillful Feed Rate Control for Machine Tools Using a Fuzzy Reasoning
( (( ) (( )ASA ( ) ) )
Fukuoka Industrial Technology Center Fukuoka Industrial Technology Center MEIHO Co. Ltd. ASA Systems Inc. Fukumoto Kogyo Co. Ltd. Graduate School of Science and Engineering, Saga University

) (( )

( ) (( ) )

) (( )ASA (( ) ) )

Fusaomi Nagata Yukihiro Kusumoto Masaaki Omoto, Tetsuo Hase Kiminori Yasuda, Osamu Tsukamoto Masuo Fukumoto, Kaori Saito Keigo Watanabe

Abstract: Cycle time reduction is one of the most important elements in manufacturing industries where NC machine tools and industrial robots are used. For example, the feed-rate of a polishing robot is moderately given small values in order to keep a stable contact situation, when a workpiece has a large curvature. In this paper, we propose an advanced feed-rate control for machine tools so that the feed-rate along free-formed surface can be regulated suitably. It is known that the smaller the curvatures of the workpiece modeled by a 3D CAD are, the larger the distance between two adjacent steps of cutter location (CL) data generated by the main-processor of the CAM is. Accordingly, considering the curvature results in acquiring the distance between two adjacent steps of the CL data. The proposed method can change the feed-rate by using a simple fuzzy reasoning. Promising results are shown through experiments using a mold polishing robot and an NC machine tool with a rotary unit.

1.
NC

3 CAD/CAM CAM CL CAM .

90

CL CL 1, 2, 3, . . . , l : l Fig. 1

p(i) = [px (i) py (i) pz (i)]T (i = CL ) CL

d(i) = p(i + 1) − p(i) ∆d(i) = d(i + 1) − d(i) d(i) NC ∆d(i)

NC

2.

Fig. 1

Image of curvature and point density in CL data.

k x(k) ∈ ∆vnorm (i) ˜ Rule 1 IF d(i) is A1 , THEN vnorm (i) = cA 1 ˜ Rule 2 IF d(i) is A2 , THEN vnorm (i) = cA 2 . . . ˜ Rule L IF d(i) is AL , THEN vnorm (i) = cA L and ˜ Rule 1 IF ∆d(i) is B1 , THEN ∆vnorm (i) = cB 1 ˜ Rule 2 IF ∆d(i) is B2 , THEN ∆vnorm (i) = cB 2 . . . ˜L , THEN ∆vnorm (i) = cB Rule L IF ∆d(i) is B L ˜ Aj (j = 1, ..., L) d(i) ∆d(i) cA j j
A ωj = µAj {d(i)} B ωj = µBj {∆d(i)} 3

x(k) ∈ [p(i), p(i + 1)] vnorm (i)

Fig. 2

Mold polishing robot based on an industrial robot JS-10 with 6-DOF.

Desired Position and Direction Desired Position and Direction Generator Based on CL Data Generator Based on CL Data

fd od (k)
Force Feedback Force Feedback Control Law Control Law

vn (k)

f (k)

˜ Bj j cB j L j

xd (k)

Position Feedforward Position Feedforward Control Law Control Law

vt (k)
+

+

F/T Sensor F/T Sensor Cartesian-Based Cartesian-Based Servo Controller Servo Controller

Σ
+

Polishing Polishing Robot Robot

Position Feedback Position Feedback Control Law Control Law

vp (k) x (k)

(1) (2)

Fig. 3

Block diagram of the hybrid position/force controller for a mold polishing robot.

µX (•)

X

3.
L A cA ω j j j=1 L A ωk k=1 L B cB ω j j j=1 L B ωk k=1

CL (3)

vnorm (i) =

3.1 Fig. 2 (4) [1, 2] 6 PC

∆vnorm (i) =

vnorm ˆ

vnorm (i) = vnorm (i) + ∆vnorm (i) ˆ

(5) z Fig. 3 (6) β q(k) ∈
6

6

µX (x) = exp{log(0.5)(x − α)2 β 2 } α

f (k) ∈

3 3

x(k) ∈

fd xd (k) ∈
3

od (k) ∈ CL

3

CAM

Z-axis

v(k) ∈

3

v(k) = v t (k) + v n (k) + v p (k) v t (k) CL

(7)

( )

(1) CL data
p(i -1)

( )

( ) ( )

p(i)

t(i) v t (k) = vnorm (i) ˆ t(i) t(i) = p(i + 1) − p(i) v n (k) od (k) v p (k) 0.2 mm

(8) v t (k)

p(i+1)

Workpiece B A

X-axis

Fig. 4

Relation between the tool’s center and CL data.

12 kgf/mm 3.2 CL fd 3) (1) (5) (8) i 3 1) 2) 1) 3) 1) x(k) ∈ [p(i), p(i+1)] p(i + 1) Fig. 4 (1) p(i + 1) Fig. 4(4) A 2) 1) |fx (k)| > fd x(k) ∈ [p(i), p(i + 1)] x vmax − vmin d(i) ∆d(i) vbase (5) B 0.1 vmax vmin (5) x(k) , d(i) ∆d(i) β 0.2 Table 1 Fig. 5(a),(b) x(k) CL
k

Fig. 4

v t (n) ≥ t(i)
n=ki

(9)

ki ( ) t(i) (= d(i)) (9) Fig. 4(1) (5) CL 3.3

Table 1

Consequent constants in fuzzy reasoning part tuned for a mold polishing robot. The upper and lower tables are designed for d(i) and ∆d(i), respectively. Note that vbase = vmax − vmin .

cA 1 vmin + 0.1vbase cB 1 −vmin

cA 2 vmin + 0.3vbase cB 2 −0.7vmin

cA 3 vmin + 0.9vbase cB 3 −0.3vmin

cA 4 vmin + 1.5vbase cB 4 0.3vmin

cA 5 vmin + 2.1vbase cB 5 0.7vmin

cA 6 vmin + 2.7vbase cB 6 vmin

1

~ A1

~ A2

~ A3

~ A4

~ A5

~ A6
[mm]

30

µ Aj
0.5

20

10

0

(a)Distance between two adjacent steps of CL data

0

30

0

10

20

1

~ B1

~ B2

~ B3

~ B4

~ B5

[mm] 0 -30 70 [mm/min] 60 50 40 30 20 10 0 0 1000 2000 3000 4000 5000

(a)

30

40

d 
i =OO? ~ B6

50

µB j
0.5

(b)The increment of the distance

0 -50

-30

-10

(b)

10

30

∆d 
i =OO?

50

Fig. 5

Antecedent membership functions designed for d(i) and ∆d(i).

Time index k (c) Norm of variable feed rate

Fig. 7

Norm of variable feed rate generated from the fuzzy reasoning for a polishing robot.

30% Fig. 6 Polishing scene with variable feed rates.

4.

NC
NC

vmax

vmin Fig. 2 JS-10 Fig. 6 Fig. 7 Fig. 8 50mm/s CL 4.1 3

vmax 10mm/s

vmin

NC [3]

( CL (F2000.0 ) . NC 2

) NC

Fig. 9 60mm 0.3mm 0.57 1000mm/min

Fig. 8 NC machine tool with a rotary unit.

Pick feed

4.2

Fig. 5 Table 2 Fig. 10 3 Fig. 9 Example of zigzag path on a flat model.

CL

Fig. 11(a),(b),(c) d(i) ∆d(i) ˜ F (i) d(i) 2250 mm/min

450 mm/min Fmin 2000 mm/min Fmax Fmin d(i) Fig. 10 Fmax Fig. 11(c) Fmin d(i) 600 mm/min Fig. 11(c) 20% Fig. 12
Machining scene by using the proposed system.

600 mm/min

600 mm/min

Table 2

Consequent constants in fuzzy reasoning part tuned for an NC machine tool. The upper and lower tables are designed for d(i) and ∆d(i), respectively. Note that Fbase = Fmax − Fmin .

cA 1 Fmin + 0.1Fbase cB 1 −0.5Fmin

cA 2 Fmin + 0.2Fbase cB 2 −0.2Fmin

cA 3 Fmin + 0.4Fbase cB 3 −0.1Fmin

cA 4 Fmin + 0.6Fbase cB 4 0.1Fmin

cA 5 Fmin + 0.8Fbase cB 5 0.2Fmin

cA 6 Fmin + Fbase cB 6 0.5Fmin

100 [mm] 50 0 100 [mm]

(a)Distance between two adjacent steps of CL data

0

-100 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400

(b)The increment of the distance

Fig. 12

Examples of paint roller machined by the proposed system.

[mm/min]

, , Vol. 70, No. 1, pp. 59–64, 2004 [2]
0 100 200 300 400

Step i (c) Variable feed rate

C

, , Vol. 71, No. 701, pp. 178–184, 2005

Fig. 11

An example of the variable feed rate, in which the total number of step is 400, Fmax = 2000 mm/min and Fmin = 600 mm/min.

[3]

F. Nagata, Y. Kusumoto, K. Hasebe, et al.: PostProcessor Using a Fuzzy Feed Rate Generator for MultiAxis NC Machine Tools with a Rotary Unit, Procs. of 2005 International Conference on Control, Automation and Systems (ICCAS 2005), pp. 438–443, 2005.

5.
CAD 807-0831 Tel:093-691-0260 Fax:093-691-0252 E-mail: nagata@fitc.pref.fukuoka.jp http://fmv5.fitc.pref.fukuoka.jp/ 3 3-6-1

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