Int. J. Mach. Tools Manafact, Vo]. 31, No. 3, pp,305-314, 1991, 0890--6955/9153.00 + .00
Printed in Great Britain Pergamon Press plc
D Y N A M I C P E R F O R M A N C E I M P R O V E M E N T O F A N E L E C T R I C A L D I S C H A R G E M A C H I N E U S I N G A N E X P E R I M E N T A L D E S I G N M E T H O D A N D E X P E R I M E N T A L
M O D A L A N A L Y S I S
~VAN-TECK R I M , * H A N - K E E JANG* a n d KWANG-JOON KIM*
Almtract--An orthogonal array method is used in.the design of experimental variables for the identification of their effects on the dynamics of the tool-head system of an electrical discharge machine. The purpose of the identification was to develop formulae for the prediction of resonant frequencies under a given configuration of the machine, so that the servo motor driving frequency at which the tool-head system was excited in the vertical direction could be maximized. Modal tests were carried out on the tool-head system to determine the weakest point of the most problematic dynamic mode and it was found to be the tool clamping device, which was therefore modified. The improvements are shown in terms of the resonant frequencies, the vibration magnitudes and the mode shapes.
1. INTRODUCTION
As THE applications of the electrical discharge machining (EDM) to the newly developed hard materials were increased owing to its inherent characteristics, i.e. no physical cutting forces between tool and workpiece, various problems were tackled for the improvement of machining performance [1-5]. Forced oscillation of the tool in the vertical direction can be a solution for such a purpose, which provides a hydraulic pumping action that helps to keep the chips in suspension and facilitates the chip removal from the machining gap, thus minimizing arcing and damage to the work or electrodes [6]. Since the amount of the tool movement must be less than that of the machining overcut gap, it is desirable in order to increase the pumping effect to maximize the oscillating frequency with the magnitude held at a given level.
One point to note with the above requirement is that the excitation of the tool in the vertical direction causes also the tool system to vibrate in the horizontal directions, and subsequently deteriorates the machining accuracy. Another point, which can be accepted in general, is that the first horizontal resonant frequency of the tool-head system would be lower than the vertical one from the viewpoint of structural stiffness.
For a given machine, hence, it is assumed that the first horizontal resonance will be a constraint on t]~e motor exciting frequency and recommended to have formulae for predicting the lowest horizontal resonant frequency and the vibration amplitude at that frequency under a given configuration of the machine such as tool weight, ram position, etc., which will enable the right choice of the tool exciting frequency under each machining condition.
In this paper are shown the results of a case study on an EDM which has a vertically excited tool head, where an experimental design method was applied to predict the lowest horizontal resonant frequency and the vibration amplitude, and an experimental modal analysis was performed to find the weak point at that dynamic mode. Improve- ments of the dynamic performance obtained by modifying the weak part are shown.
2. PRELIMINARY TEST ON THE WHOLE STRUCTURE
Figure 1 shows the EDM under study with the coordinates used, where the head, column, body and linear guide denoted, respectively, by H, C, B and LG are fixed
*Department of Mechanical Engineering, KAIST, Cheongryang, Seoul, Korea.
H'rH 3 1 - 3 - E
3O5
z
Y
Fie. 1. The electrical discharge machine under study and locations of variables.
parts, and the DC servomotor, ball screw, ram, slider, tool holder, tool and table denoted respectively by M, BS, R, S, TH, T and TL are movable parts. A detailed diagram of the tooling system is shown in Fig. 2, where the tool shank is stuck onto the tool holder and the tool holder is then clamped into the ram. $1, $2 and $3 indicate the sensor locations.
The preload acting in the horizontal
(x-y)
plane between the linear guide and the slider can be adjusted by the torque given on the screws TB and TC as shown in Fig.1. In Fig. 2, H A is a knob for preventing an unwanted rotational motion and TA a screw for adjusting the clamping force of the tool holder in the vertical direction.
Under normal operational conditions, the ram is dynamically excited with the servo motor in the vertical direction in order to optimize the machining condition as mentioned above. In such cases, the machining accuracy is principaly dependent upon the relative vibration in the horizontal plane between the tool and the workpiece. Although it is therefore preferred to investigate the relative vibrations, as preliminary investigations, however, absolute vibrations were obtained for the ease of measurements from various points of the whole structure.
In Fig. 3, the power spectra of the input voltage into the motor and the output accelerations at the tool in the three orthogonal directions are shown, which were measured while the motor was driven with a band-limited white noise. The motor was subsequently driven with a sinusoidal input having a frequency corresponding to the first horizontal resonant frequencies as shown in Fig. 3 and the deformation shape of the whole structure was measured. Although the shape is not shown here, vibrations of the table were negligible compared with those of the tool-head system consisting of the head, sliding mechanism, ram, tool holder, and tool. Hence it was decided to measure absolute vibrations, and the scope of interest was narrowed down to the tool-head system.
Dynamic Performance Improvement 307
T
A HAzt__
x
FIG. 2. Detailed diagram of tool holder and locations of each variable.
IE 0 IE-I
~ 1E-2
~. IE-3 IE-4 IE-5
0 2O
(Hz)
(a) I n p u t into t h e m o t o r
180
1E-2 IE-3
~
IE-4 g tZ-S1E-B IE-?
0 20 180
(az)
(c) Acceleration in the x-direction
IE-2 IE-3
~ l E - 4 tz-s
IE-6 IE-?
(b)
20 180
(Hz)
Acceleration in the z-direction IE-2
1E-3
~ 1 E - 4 iE-s
IE-6 IE-?
0 20 180
(Hz)
(d) Acceleration in the y-direction
FIG. 3. Power spectra of the input into the motor and vibrations of the tool. (a) Input into the motor. (b) Acceleration in the z-direction. (c) Acceleration into the x-direction. (d) Acceleration in the y-direction.
(1) Tool mass.
(2) Vertical position of ram.
(3) Torque on the bolt TA.
(4) Torque on the bolt TB for preloading of linear guide in the y-direction.
(5) Torque on the bolt TC for preloading of linear guide in the x-direction.
(6) Location of the acceleration pick-up.
Therefore six variables in total were used to design the experimental conditions.
3. MEASUREMENT AND ANALYSIS OF THE TOOL HEAD VIBRATIONS USING ORTHOGONAL ARRAYS
A lot of experiments would be required in general for an accurate prediction of the dynamic characteristics of the tool-head system under the varying conditions of the six variables. If each of the six variables can have three choices, for example, the total number of combinations of the six variables would be 3 6 = 729, which it would not be possible to achieve in practice. As a solution to overcome this difficulty, a method of using orthogonal arrays was used in this study.
Under the assumption that the six variables chosen as above influence the dynamics of the tool-head system independently, three levels were assigned to each variable as shown in the Tables 1 and 2 sets of orthogonal arrays as shown in the Table 2 were used for the experimentations. The three levels of each variable were determined by
TABLE 1. VARIABLES FOR THE EXPERIMENTAL DESIGN
Level 1 2 3 Currently
Variable (Small) (Medium) (Large) used
Torque A (kgf-cm) 20.0 30.0 40.0 20.0
Torque B (kgf-cm) 100.0 150.0 200.0 120.0
Torque C (kgf-cm) 20.0 50.0 80.0 20.0-50.0
Tool mass (kg) 1.4 5.5 9.4
Ram position Low Middle High
Sensor position Tool (S1) Tool Holder Ram ($3)
($2)
TABLE 2. EIGHTEEN CONDITIONS OF THE SIX EXPERIMENTAL VARIABLES
Variables A B C Tool Ram Sensor
Experiment no. mass position position
1 2 1 1 1 1 1
2 2 2 2 2 2 2
3 2 3 3 3 3 3
4 1 1 1 2 2 3
5 1 2 2 3 3 1
6 1 3 3 1 1 2
7 3 1 2 1 3 2
8 3 2 3 2 1 3
9 3 3 1 3 2 1
10 2 1 3 3 2 2
11 2 2 1 1 3 3
12 2 3 2 2 1 1
13 1 1 2 3 1 3
14 1 2 3 1 2 1
15 1 3 1 2 3 2
16 3 1 3 2 3 1
17 3 2 1 3 1 2
18 3 3 2 1 2 3
Dynamic Performance Improvement 309 considering typical conditions in the actual assembling process of the machine and the machining process by the machine. T h e levels of variables in each experimental design shown in Table 2 are arranged so that each column might be orthogonal to the others within the same, set and can be easily obtained from references [7]. For an illustration, the condition of the experimental design No. 5 are given as follows:
T o r q u e A on the part T A : 20 kgf--cm T o r q u e B on the Part TB : 150 kgf-cm T o r q u e C on the part TC : 50 kgf--cm
T o o l mass : 9.4 kg
R a m position : Low Sensor position : Tool.
It can be seen in Table 2 that the columnwise sum of the levels of each variable in the first set, consisting of Ex. No. 1 to 9, is the same as the one in the second set consisting of E,x. No. 10 to 18, which means that the mean dynamic characteristics obtained from the first set should be theoretically the same as those obtained from the second set. H o w e v e r , some variations in the level of each variable cannot be completely avoided in the real world.
For every condition of the experimental variables shown in Table 2, a band-limited white noise signal was input to the servo m o t o r in the same way as in the preliminary test, and the accelerations were measured in the x- and y-directions. From the estimated autospectra of these signals, the first resonant frequencies and the vibration levels in each direction were obtained, respectively, by picking the frequencies of the first peaks and by calculating the square root of the peak magnitude times the frequency resolution, and are shown in Table 3.
T h e variations of the resonant frequencies and the vibration magnitudes with the change of each of the 6 variables are shown in Fig. 4, which were obtained from Table 3 by taking averages of the results in such a way that the effects of the other variables might be averaged to zero. Resonant frequencies in the x- and y-directions, denoted by to,x and to,:~, respectively, are scaled on the right axis, and the vibration levels in
TABLE 3. THE FIRST RESONANT FREQUENCIES AND THE VIBRATION AMPLITUDES IN EACH EXPERIMENT
E ~periment x-direction y-direction
no. Resonant A m p l i t u d e R e s o n a n t Amplitude
frequency (v.m) frequency (0.m)
(Hz) (Hz)
1 83.8 0.87 79.4 1.18
2 49.4 0.65 46.9 1.80
3 40.6 3.63 36.3 1.76
4 47.5 2.48 47.5 1.19
5 35.0 1.63 32.5 6.74
6 79.4 0.91 75.6 1.23
7 80.0 0.92 68.8 1.50
8 50.0 0.65 50.6 0.25
9 40.6 2.79 37.5 5.12
10 40.0 0.88 36.9 1.18
11 80.0 0.73 69.4 0.96
12 48.1 2.26 48.1 2.29
13 35.0 0.43 34.4 2.26
14 76.9 2.34 71.3 1.30
15 48.1 1.22 41.9 1.13
16 51.9 0.76 46.3 6.74
17 41.9 0.89 38.8 0.81
18 85.0 0.75 77.5 1.01
i 2 30 ,,.. 2 30 2 3
. ~ o l , I o ~ o
i
, , o o~. 20 30 40 100 150 200 20 50 80
(a) Torque A(kgf-cm) (b) Torque B(kgf-cm) (c)Torque C(kgf-cm)
4 SO 4 ~ 360
i
2 O & 2 30 2 3--
o l , I o ~ o, , , o o
57 1.4 5.5 9.4 up middle down tool holder ram (d) Tool mass(kg) (e) Ram position (f) Sensor position
o : x - d i r e c t i o n a l r e s o n a n c e f r e q u e n c y Wnx
• : y - d i r e c t i o n a l r e s o n a n c e f r e q u e n c y COny o : x - d i r e c t i o n a l a m p l i t u d e X
Lx : y - d i r e c t i o n a l a m p l i t u d e Y
FIG. 4. Variation of the resonant frequencies and vibration amplitudes with respect to each of the 6 variables.
each direction, denoted by X and Y, are scaled on the left axis. What could be derived in the qualitative aspects by looking into Fig. 4 (a)-(f) are as follows.
(1) Torque A, B and C affect the resonant frequencies of the tool-head system to a negligible extent, and the vibration level in an inconsistent manner.
(2) Resonant frequencies are dependent upon the tool mass more than the other variables, and increase with the decrease of the tool mass as could be expected.
(3) The lower the ram is positioned, the lower the resonant frequencies are, which could also be expected because the contacting length between the slide and the guide is decreased.
(4) Resonant frequencies in the x-direction is higher than the ones in the y-direction and the vibration level in the x-direction is lower than the one in the y-direction, which is ascribed to the open structure of the sliding mechanism in the x-direction as shown in Fig. 1.
(5) The tool is far more sensitive to the vertical excitation than the ram, which could be also expected, and the tool is preferred f o r the sensor location.
For practical purposes, it would be essential to have formulae which can predict the dynamics of the system in the quantitative aspects so that the motor driving frequency can be increased as high as the horizontal vibration level of the tool-head is tolerable.
The following quadratic equations were fitted to the numerical data shown in Table 3 using a least squares method
6
Yi(xl, x2 ... x6) = ~ (aisx2+bitxj) + ci, i = 1, 2, 3, and 4
j = J
where: xj = Torque A (kgf-cm); Xa = Torque B (kgf-cm); x3 = Torque C (kgf--cm);
x4 = Tool mass (kg); x5 = Ram position; x6 = Sensor position; Y~ = x-directional resonant frequency (Hz); Ya = y-directional resonant frequency (Hz); Y3 = x-directional vibration magnitude (p.m); and I"4 = y-directional vibration magnitude (l~m).
The results for the coefficients au, b u and ci are shown in Table 4, where it can be seen that the quadratic formula might be reduced to a linear formula except for j = 5
Dynamic Performance Improvement 311
TABLE 4. COEFFICIENTS FOR TSE PREDICTION OF THE RESONANCE FREQUENCIES AND THE VIBRATION AMPLITUDES
i 1 2 3 4
j a u bu aq bu au b e a o b u
1 - 0 . 0 1 0 0.854 - 0 . 0 0 9 0.696 -0.026 1.358 0.076 - 4 . 1 7 9 2 13.0005 -0.131 0.0004 - 0 . 1 0 6 0.0014 -0.340 -0.0004 0.025
3 13.0014 -0.153 0.0014 -0.132 0.0050 -0.503 -0.003 0.388
4 13.6352 -12.11 0.4701 -9.773 0.0551 0.084 0.2359 4.306
5 -C.417 1.458 1.0950 1.725 - 4 . 7 2 2 21.90 1.4667 4.712
6 -C.259 0.879 1.0950 - 4 . 4 3 2 6.3343 - 2 3 . 0 6 11.327 -30.44
ci 91.256 89.127 15.229 38.356
(ram position) and j = 6 (sensor position) because the value of aij is negligibly small compared with b u for j = 1-4. The formulae were checked by comparing the predictions with the actual measurements under a condition which had not been taken for the experimental design. One set of the comparison results for the resonant frequencies are shown in Table 5, from which it can be found that the predictions of the resonant frequencies are quite acceptable.
4. D Y N A M I C P E R F O R M A N C E I M P R O V E M E N T B A S E D U P O N T H E E X P E R I M E N T A L M O D A L A N A L Y S I S
Since the fir,;t resonant frequencies were the major constraints in increasing the servo motor exciting frequency, a modal test was carried out on the tool-head system to figure out wha! component was most responsible for those modes. Under the experimen- tal condition taken above as shown in Table 5, where the vibrations would be expected to be rather large, the accelerations were measured from 30 points on the system (8 points on the tool; 12 points on the tool holder; 10 points on the ram) in the x- and y-directions while the structure was given impulses on the tool. By picking the peak points of the imaginary parts of the frequency response functions, mode shapes were obtained as shown in Fig. 5, where a kink can be observed at the connection between the tool and the tool holder. Therefore, the clamping mechanism of the tool holder was suspected to be the weakest part in the first mode.
The tool holder which clamped the tool by point contact was replaced with a new one which clamped the tool by surface contact as shown in Fig. 6. The new tool holder, which is commercially available, clamps the tool by using hydraulic pressure. The mode shapes of the modified tool-head system are shown in Fig. 7. By comparing it with those in the Fig. 5, it can be found that the kink disappeared in the modified system and the lowe~,;t natural frequency was increased by 4.2. Hz. In Fig. 8, the dynamic characteristics of the tool-head system with the original and the new tool holder are shown with respect to the tool mass and the ram position which are the most influential experimental variables. It can be seen that the vibration levels were decreased and the resonant frequencies were increased in the modified system.
TABLE 5. COMPARISON OF THE RESONANCE FRE- QUENCIES BETWEEN PREDICTIONS AND ACTUAL MEASUREMENTS. Experimental condition: T A = 40 kgf-cm; TB = 200 kgf-cm; TC = 50 kgf-cm;
Tool mass = 9.4 kg; Ram position = Low;
Sensor position = $3
Predictions Measurements
oJ.x (Hz) 40.0 40.0
tn. v (Hz) 34.1 37.0
y
I]ll bP
I C -
X
(a) First mode shape (36.8Hz) (b) Second mode shape (41.THz) FIG. 5. Mode shapes of the original system.
1
~ / o i l
J
FiG.
6. Diagram of a new tool holder design.
312
y x
(a) First m o d e shape(41Hz) (b) Second m o d e shape(43Hz)
FIG. 7. M o d e shapes of thc modificd system.
i00 50 i! i0050
OT ~ l O ~ 0
:> 1.4 5.5 9.4 up m i d d l e down
Tool m a s s ( k g ) Ram p o s i t i o n (a) D y n a m i c characteristics of the original tooling s y s t e m
0~"-- , l 0#. ol , i 0
1.4 5.5 9.4 up m i d d l e down
Tool mass(kg) R a m position
(b) D y n a m i c characteristics of the n e w tooling s y s t e m o : x-directional resonance frequency COnx
, :y-directional resonance frequency COny
o : x - d i r e c t i o n a l amplitude X :y-directional amplitude Y
FIG. 8. Comparison of dynamic characteristics of the original and new tooling system. (a) Dynamic character- istics of the original tooling system. (b) Dynamic characteristics of the new tooling system.
313
effects of six variables on the dynamics of the tool-head system of an EDM were identified with a minimum number of experimentations. The results were presented in the quantitative aspects as well as in the qualitative aspects. The tool mass and the ram position were most influential on the resonant frequencies and the vibration magnitudes.
The formulae for predicting the dynamic characteristics of the tool-head system were derived in order that they might be used to limit the servo motor driving frequency and their accuracy was confirmed.
Based on the experimental modal analysis of the tool-head system, the weak point of the lowest dynamic mode was found to be the tool clamping. Therefore, the old tool clamping device which had point contact was replaced with a new one which had surface contact so that more joint stiffness could be provided. The improvements were shown in terms of the mode shapes and the resonant frequencies and the vibration magnitudes.
REFERENCES
[1] J. R. CROOKALL and B. C. KOHR, Int. J. Mach. Tool Des. Res. 15, 1 (1974).
[2] J. L. GUERRERO-ALUAREZ, J. E. GREEN and B. F. VON TURKOVICH, Tram. ASME J. Engng Ind. 95 (1973).
[3] Y. WINOGgAD and M. ALMAGOR, Tram. ASME J. Engng Mater. TechnoL 99 (1973).
[4] H. CORNEUSSEN, R. SNOEY and J. P. KROTI-I, Ann. CIRP 27 (1978).
[5] DE BRUYN, A. J. PEKELHARING and T. H. DELFT, Ann. CIRP 29 (1980).
[6] T. J. DROZDA and C. WICK, Tool and Manufacturing Engineers Handbook Volume I: Machining, 4th edn. SME (1983).
[7] GENICHI TAGUCHI, System of Experimental Design. UNIPUS/Kraus International Publications (1987).