Computers in Industry 23 (1993) 199-204 199 Elsevier

Applications

Automatic feed-rate control command generation A step towards intelligent CNC

Song Qian Department of Precision Instruments and Mechanics, Tsinghua University, Beijing, China

Received September 15, 1992; accepted April 28, 1993

The automatic control of feed rate, acceleration and jerk of cutting tools has become prominent recently as these factors influence the performance of CNC machine tools signifi- cantly. A number of factors which limit the real-time move- ment of cutting tools in the space interpolation are thus analyzed, and a practical method called the "J-method" is proposed to perform the on-line, automatic control of feed rate, acceleration and jerk.

Keywords: Feed rate Variation; Judgement; CNC; Real time; Interpolation

1. Introduction

Conventional CNC machine tools have two kinds of on-line feed-rate adjustment: adjust manually and adjust for emergency (for example, Siemens 850, Funuc 6 and Cincinnati 950). The first is performed when inappropriate machining parameters are applied and an improvement is required; the second works when some emer- gency event occurs, such as mistakes in a part program. Today's high-performance CNC systems can perform much bet ter than most of the servo systems because of the development of VLSI, which, together with the impending automation, introduces on-line monitoring and adaptive con- trol at the lowest hierarchy of C I M - - C N C and the manufacturing ce l l - - to make them more in- telligent. So machining parameters are expected

to be controlled automatically. Although both feed rate and depth of cut decide the metal moving rate, feed rate is preferred in adaptive control because: (1) It is somewhat easier to adjust the feed rate

on-line than to change the depth of cut as the former does not require a variation of the cutting contour [1].

(2) Feed-rate adjustment plays a major role in surface roughness control.

(3) Feed rate has a greater influence on tool life than the depth of cut, which can be easily seen through Taylor algorithms. In this sense, to adjust the feed rate is more efficient in tool-life control.

(4) The feed rate and depth of cut are equally important for the metal-moving rate, the ma- jor factor of efficiency.

However, the on-line control of feed rate is con- fronted with a number of limiting factors.

2. Limitations of contouring feed rate

2.1. Calculation precision

In most CNC systems, iteration is used to perform a rough interpolation; a finer interpola- tion is performed automatically by the closed-loop position control system. The approximation by a

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200 Applications ~, omputer~ m lndu.~lt3'

Y

/

i ,.\ Fig. 1. Limitations of precision and maximum acceleration.

straight line segment causes a geometrical error. Referring to Fig. 1, when a circle is approximated by linear segments, the longest chord AB gener- ated to approximate the circle as a rough interpo- lation result is decided by the precision e al- lowed. It is, generally, the longest distance that the command system generates during the sam- piing time. Consequently, a limitation on the highest tracking speed of the cutting tool arises.

2.2. Maximum acceleration and speed of the servo system

For each axial movement, there is a maximum acceleration decided by the servo system. This results in another limitation of the speed. For example, if the cutting tool goes along CDE, the X-direction speed of the cutting tool at point D should be zero, which means that the feed rate of the cutting tool at point C should be limited so that it can decelerate properly (see Fig. 1).

Song Qian is a Higher lecturer of the Department of Preci- sion Instruments and Mechanics, Tsinghua University, Bei- jing, China. He received his MS and BS at the same depart- ment in 1987 and 1984. His research interests now cover CAM, CNC, real-time control, on-line monitoring and adap- tive control, fuzzy theory.

2.3. 7he continuation of the part s'egtnents

If the maximum acceleration of each axis is Amax, then, at each corner of the contour, there must be a maximum feedrate a{ each corner as (see Fig. 2):

~'~ = A ,~,~f/min{i cos a~ -- cos ~ ~ .

cos/3 - c o s },

cos r ~ -- cos > ~ i}, ( I )

where T is the sampling time and cos a. co s /L cos T are cartesian cosines.

2.4. Dynamic errors O[ the drit:m.v sys'wm

II is preferred that some kinds of acceleration and deceleration be performed l o minimize the tracking error:

.d .... .4( t ) (2~)

3, Requirements of the tracking velocity control on intelligent CNC

(1) Generate commands according to the coded feed-rate number (FRN) given.

(2) If the segments traveled arc continuous and the surface roughness is required, the system could control the tool with the least change of feed rate.

!z \ i z'

xZ", ,,,,

Fig. 2. Continuity of the part segments (b'~x ~ maximum possible feed rate of each axial movement: V~ = maximum feed rate at the end of each span; t/~-~ maximum possible

feed rate at the beginning of each span).

Computem in Industry 20 [

Pre -p roces s d

Calculate limitations

Calculate the

acceleration span

+ l I terat ions .'

Fig. 3. Feed-rate command generation.

(3) If adaptive control is applied, the feed rate adjustment command can be processed in re- sponse to the requirement of adaptive control as soon as possible.

(4) If a monitoring system is applied on the ma- chine tool and an emergency is detected (for example, there is a tool breakage), there should be an immediate response.

4. On-line command generation of feed-rate vari- ation

Because of the limitations mentioned above, it must be judged whether the feed-rate will violate these limitations whenever there is a feed-rate change. This judgement should be simple enough to be used in real-time control. Several blocks should be looked ahead (see Fig. 3 and Table 1): (1) Calculate the maximum feed rate according

to eqn. (1); for the example shown in Fig. 2:

V 1 = 2 A L + V 2. V2, (3)

Vm~ × = Fm,×/min(cos a , cos/3, cos y ) , (4)

Song Qian / Automatic feed-rate control command generation

Table 1 Cartesian cosines

Line Circle (spiral)

cos a X,I / L Yic/R cos/3 ~1/L Xic /R cos 3' Z i l / L AZ c/O n

L is the length and Xil, YH, Zil are cartesian values of the line segment• R is the radius, 0 the angle and X,., Y~, Z~. are the cartesian values of the circukar segment.

where Vma x is the maximum possible feed rate decided by Fma x.

(2) Calculate the maximum speed, Vp, decided by the precision at each point shown in Fig. 1:

Vp = V'(8Re) , (5)

if circular interpolation is being applied.

V~< min{Vl, Vmax, Vp}. (6)

(3) Calculate the acceleration and deceleration span through eqn. (2). It includes nonlinear acceleration and jerk control in feed-rate variation.

(4) While all the limitations have been set, the iterations can be performed accordingly [1,2].

5. Real-time control procedure management

In the design of CNC systems, it is very diffi- cult to prescribe the accurate sampling time when the system is still in a very early stage of design. So a method called the " J -method" is used to get a flexible software structure, and the best dy- namic response to a feed-rate adjustment re- quest. Obviously the ideal response to a variation

- - - , - T - - - - - ~

~-T1 "~T2-

~,-- T - - - - - - ~ - . - - T ~ . . - T ~

~ T 1 ~ J - T 2

0 TIME Fig. 4. Quickest response to feed-rate variation (T = sampling time; T I = judgement time; T 2 = interpolation time).

202 Applications (omputers m Industry'

command should be as shown in Fig. 4. The interpolation and the judgment before changing the tracking speed variation should be performed during one sampling time. The real-time proce- dure can be derived as follows:

Because of the calculation needed in TI, and the highly simplified calculation of T 2 [1,2], the following always holds:

T, > T2, (7)

T~ + T:>> T:. (8)

However, as the feed rate does not always vary, if T t and T z were always set in a sampling time, the machining procedure would be inefficient, for T would be too long, and

F = ABmax/(Tl + T2) = ABmax/T (9)

would be small (Fig. 1). In other cases, not every CNC system requires

such a response to feed-rate adjustment. Hence, there is a demand for a flexible configuration so the relation between T1, T 2 and T can be ad- justed. It is suggested to define a variable J. When J iterations have been done, there will be a judgement as in Fig. 1. This is the basic idea of the J-method. The letter " J " in the J-method has two meanings: (1)judgement; and (2) J sampling times, which represents the delay of the CNC system in response to the feed-rate variation command. So, J sets a simple condition of leaving the interpolation procedure and entering the judgement procedure before further interpola-

tions. When the ./-method is applied, the proce- dure of the CNC system is as shown in Fig. 5.

An interrupt is arranged to transmit the com- mand generated to the servo system at each sam- pling time; this takes little time because of the simple work in the interrupt procedure. Hence:

T~ + J T 2 + J T 3 = J T , (10)

where T 3 is the interruption time,

T > T2. (11)

If J = I, then T = T z + T, leading to the quick- est response as in Fig. 4. If J is unlimited, then T = T 2 i.e. no variations of feed rate are per- formed.

The J-method gives a simple way of deciding the relation among the judgment time, interpola- tion time, sampling time, and hardware speed. The speed of the hardware should give the result:

T~< Thove, (12)

where Thope is the data sampling time of the servo system;

2 J T <~ Hoping delay time in response to

feed-rate variation. (13)

6. Emergency response in the J method

When an emergency event is detected in the manufacturing procedure, it is preferred to stop

int int int int int int int int int int

. . . . . .

1 T2 T2 T2 ~-T 1--~'JT21"1"2 T2 "1" 1-="~T2 "r'2 T2

Fig. 5. The J-method in command generation.

Computers in Industry 203

Table 2 Example CNC system

Kinds of geometric components Space line, circle, spiral Number of axes 3-5 Geometrical span 15,000 mm Hardware 8086/8087 (5.0 MHz) Acceleration A = A(t)= constant Basic length unit (BLU) 0.001 mm Highest feed rate of each axis 15,000 m m / m i n T 1 9 ms T 2 2 ms T 3 0.06 ms T 6 ms

Song Qian /Automatic feed-rate control command generation

Table 3 Possible delays when applying the J-method

Number of J Possible response Response delay to channels delay (s) emergency (s)

1 3 0.018-0.036 0.006 2 9 0.054-0.108 0.006

cost of only some additional memory for holding the inner results of iterations in case of an emer- gency.

the tracking along the contour given by the part program or to retract the cutting tool as soon as possible, and not to stop immediately, which would result in a huge jerk that causes a signifi- cant vibration and may ruin the machine tool. As for the method proposed here, because the judg- ment is always made in the real-time procedure of the interpolation, the speed of each axis will never rise to an uncontrollable level. Whenever an emergency happens, the CNC system can pro- pose the quickest response by giving deceleration interpolation results to each axis, as there is no judgment required as to whether the speed will exceed the limitations. The practical procedure management can be as shown in Fig. 6.

Thus, the J-method allows a response to an emergency in the shortest possible time, at the

7. Example and results

An example of a CNC system is given in Table 2. Table 3 shows the results obtained for this system.

8. Conclusion

A practical method, the J-method, to perform on-line feed-rate control is proposed which is simple enough to be used in real-time intelligent CNC systems. The advantages are: (1) The CNC system will have a flexible response

time which allows the best incorporation of the dynamic quality of the machine tool and the control system hardware. No matter how

int int int int

'iT2/' f T1 T2 "1"2

int

int int

! 1

int int int int

1 I.- .....

Fig. 6. Management of the response to an emergency.

204 Applications (omputers in Industry

many channels are being controlled, the quickest response system can be obtained.

(2) Feed-rate adjustment can be handled intelli- gently under the command of an expert sys- tem, adaptive control and monitoring systems.

(3) CNC systems with sampling-timed structure can be improved through the J-method for the preparation of intelligent control.

Acknowledgment

Thanks are due to Mr. Jantao Hu and Dali Fu for their programming work.

References

[1] Yan-wo Pen, CNC System, Northwestern Industrial Uni- versity Publication, 1988, pp. 1- t50

[2] Yoram Koren, Computer Control o! Manufacturing Sv,~- terns, McGraw-Hill, 1983, pp. 115--J4i.

[3] Jui-Jen Chou and D.C.H. Yang, "On the generation of coordinated motion of five-axis CNC/CMM machines", ASMEJ. Eng. Ind., Vol. 114, February' 1992, pp. t5-22.

[4] Tiao Tong and Dai-je Cheng, Multi-Processor and Intelli- gent Multi-Computer Systems. Chongqing University, 1988, pp. 10--163.