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Experimental optimization of process parameters in laser cutting of polycarbonate gears/Eksperimentinis polikarbonatiniu krumpliaraciu lazerinio pjovimo proceso parametru optimizavimas.

1. Introduction

Polycarbonate is widely used due to its mechanical, optical, thermal and chemical properties. Tensile strength (55-75 MPa), Young's modulus (2-2.4 GPa) and hardness (~70HRC) recommend the material also for manufacturing of gears, which work with low power or special conditions transmissions. Moulding and extrusion, commonly used to machine polycarbonate pieces, are not appropriate to obtain complex shape and preciseness as gears require. Also, the usual cutting technology of gears is long-lasting and inefficient if some faster machining process can be found. Generally speaking, specially designed technologies must be designed and implemented for machining particular materials or parts [1-2]. In the present case a nonconventional technology, for instance laser cutting suites much better.

Still, laser cutting is not very simple to apply. Targets regarding piece's characteristics (precision in shape and dimension, roughness, thermal side-effects etc.), time of machining and energetic supply needed, are hard to attain without a process optimization. The large number of parameters involved, exclude the choice by random of their values. There are optical, electrical and mechanical factors, which influence the laser cutting process. Different combinations of their possible values might satisfy requirements to attain different target criteria (diverse in nature and value). From optical standpoint, laser cutting is a nonimaging application. The quality of the optical system included in the structure of a laser cutting machine, influences directly the general traits of the process. Flexibility and preciseness are required in order to ensure easy transforming of radiant beam's properties (spot size, defocus facilities, and variable energetic density).

Control of electrical parameters, such as power supply, ensures appropriate energetic properties of the cutting beam (for pulse lasers, also pulse duration and pause duration are very important).

Mechanical design of the nozzle, precision and speed of cutting head's displacement are involved in accuracy and efficiency of machining. Establishing the most suited combination of values for all these parameters needs a mathematical approach. There are several optimization process methods, among which, the Taguchi method proved to be one of the best.

The subject of machining is a set of four gears making part of a two-step transmission. Geometrical complexity, precision of tooth pitch, roughness of flanks, variety of modulus and number of teeth recommend a flexible technology such as laser cutting.

2. Experimental equipment

Effective machining of sample pieces was achieved using an existing laser cutting machine, whose optical system was improved [3-6]. The computer aided equipment uses a C[O.sub.2] pulse laser source, 2 kW power. The machine belongs to C.A.L.F.A. laboratories at I.U.T. Bethune, Universite d'Artois, France. A general image and the scheme of the machine are presented in Fig. 1.


The general features of the laser cutting machine are wavelength, [micro]m; beam divergence, deg; emitted power, W; cutting speed, mm/s; vertical position of the spot, duration of pulse and pause, ms; chemical nature, pressure and flow of the gas, distance between nozzle and piece, mm; nozzle's internal geometry and exit diameter. Some of these parameters are fixed so their values can not be changed. Others are variable within certain ranges and can be used to optimize the machining process.


3. General design of the experimental optimization program

The plan on which the optimization program developed is briefly presented in Fig. 2.

4. Choice of influence parameters and working combinations in order to apply Taguchi method in process optimization

Traditional quality optimization methods search for dispersion or unsteadiness of a product's feature and aim to reduce or eliminate causes. Taguchi strategy introduces the concept of noise for the sources which spoil quality and states that minimization of noise-factors' impact brings in better efficiency in processes optimization [7-9].


Accordingly to Genichi Taguchi's concept (Fig. 3), loss of quality occurs not only if the product is outside the tolerance limits, but even if it is inside these limits. The quadric function of quality loss, defined by Taguchi for target criteria is mathematically expressed as:

L(y) = k[(y - [y.sub.N]).sup.2] (1)

where: L(y) is the value of loss expressed in currency/product; y is the value of the quality feature involved; [y.sub.N] is the nominal value (target); k is a constant to quantify global financial loss.

For a sample containing n pieces, measuring allows computation of mean value [bar.y] and standard deviation s. The function of quality loss becomes

L(y) = [ks'.sup.2] = k[[s([[y.sub.N]/[bar.y]])].sup.2] = k[y.sub.N.sup.2] [[s.sup.2]/[[bar.y].sup.2]] (2)

In relation (2) k and [y.sub.N] are constant, so that loss minimization requires maximization of the ratio [[[bar.y].sup.2]/[s.sup.2]], which mathematically corresponds to tendency n [right arrow] [infinity]. The expression of the signal/noise ratio for target criteria is given in relationship (3)

[S/N] = 10log [[[[bar.y].sup.2]/[s.sup.2]] - [1/n]] [dB] (3)

The complete factorial experiments plan studies all possible combinations of selected factors' levels. Theoretically, they are complete. However, the time needed for experiments is very long and costs are very high (for instance, an experiment involving 15 factors at 2 levels requires [2.sup.15] = 32768 pieces).

The fractional factorial experiments plan is based on the idea that certain possible combinations of factors provide enough efficient information, so that the number of effective experiments may be considerably reduced. Table 1 presents a complete factorial experiment in a classic version for 3 factors at 2 levels. Table 2 shows a complete factorial Taguchi plan.

Tables 3 and 4 illustrate two alternatives of fractional factorial Taguchi plan. In order to compute the effects of an independent factor, the experimental plan must be orthogonal.

Triangle shaped tables and linear graphs are associated to the most of standard Taguchi matrices and are used to define columns which study interactions. Taguchi method, generally, uses a standard L8 matrix (Table 5).

Practical procedure to fulfil a Taguchi experimental plan assumes the creation of a table, containing influence parameters, measured values and responses (Table 6).

It is necessary to compute the mean effect S/N of each level's factor and the value of interactions related to the mean value of response S/N. Responses related to factors and interactions are written in matrices.

For the given application, a set of parameters, considered to be the most influent on the process of machining, were selected. They are speed, power supply, duration of pulse, duration of pause, defocus and gas flow.

For each of the six parameters above, two levels and one interaction was set. That means [2.sup.7] experiments are needed. The optimization criterion was established to be the value of flank roughness parameter [R.sub.a]. The target is "nominal value" type ([R.sub.a] = 0.8 [micro]m). Further mathematical approach is based on fractional factorial experiments plans provided by Taguchi method. These plans considerably reduce the number of required experiments (to only 8). Table 7 indicates the values of the process factors for 8 combinations (A...H).

5. CAD of gears and generation of NC code

The laser cutting equipment used to machine the gear samples is supplied together with the software Laser DX3, which is an extension of AutoCAD so it is able to import to *.dxf files. Dimensioning and geometrical calculus of the transmission with total transmission ratio i = 4 was accomplished and for each type of gear an AutoCAD drawing was saved in *.dxf format. Flank shape is normal convolute. First step of the transmission needed a modulus [m.sub.1,2] = 1.5. The second one was dimensioned at [m.sub.3,4] = 2. The four types of gears machined for the experiment are shown in Fig. 4.


The numerical command file, adapted to the management file format, specific to the machine's software allows the transfer of the numerical code from Laser DX3 to equipment's computer. The numerical code translates the drawing of the piece into complete commands regarding entrance and exit points of the nozzle, displacement of the cutting head along a path, which reproduces the contour of the piece, displacement segments without cutting and so on.

6. Experimental results

Five gears were machined for each of parameters combinations (A ... H). Each gear sample was measured with a Mahr electronic measuring device. Table 8 presents the results of measurement. Odd columns of the table indicate the combination (A.... H) and denote the sample (A1 ... A5 .... H1 ... H5). Even columns contain the measured values of [R.sub.a]. The last line indicates the mean value of the parameter [R.sub.a], for a given combination.

7. Optimization of process parameters by means of Taguchi method

The complex array statistical calculus required by Taguchi method implementation needs automated computation. The appropriate software Qualitek was run in order to process the numerical data.

The program builds the inner array accordingly to fractional factorial experiments plan and uses for the terms in array the measured values of roughness ([R.sub.a] parameter) from Table 8.

The window in Fig. 5 displays data type, which is "signal/noise ratio", optimization criterion type, which is "nominal is the best". Nearby the criterion type is written the target value of the criterion, [R.sub.a] = 0.8 [micro]m.


Bellow these settings, all 40 values are put into a matrix, where each line corresponds to a certain combination of parameters. The last column shows the S/N ratio of each line.

Finally, an optimal combination of factors resulted. It is presented in Fig. 6.

The program predicts an S/N ratio of ~18 (initially it was ~10), which means that using the optimum parameters the roughness of pieces will get values much more gathered around the target. Next window summarizes the current status and expected status properties of the process (Fig. 7).


Fig. 8 shows graphically the scattering of results corresponding to current state and predicted one. One can notice that for the current state the distribution curve is displaced with respect to the target. In optimal conditions, the dispersion is much less than [+ or -]3[sigma] (limited by vertical lines). The frequency curve presents a peak ~2.5 higher and a narrow aperture centred about the target vertical line.

In order to validate the theoretical optimization, a confirmation experiment was achieved. A set of five sample gears were machined using the optimal combination of factors indicated by Qualitek (Fig. 6). The pieces were measured and the results are presented in Table 9.



The analysis of data got with the confirmation experiment indicates a better value of S/N ratio (24.459) than the predicted one (18.321).

Quality statistical data of the pieces machined at experimentally chosen parameters improved substantially after optimal values were used in a confirmation experiment (Table 10).

8. Conclusions

Fractional factorial experiments plans stated by Taguchi method and a specialized software-Qualitek-proved to be quick, economic (only 40 samples needed effective machining for optimizing six parameters in two levels and one interaction organized in 8 combinations) and very efficient. For the pieces machined in optimal conditions S/N ratio is even better than the predicted one. The mean value is very close to the nominal target, which significantly improves the quality of the lot of pieces. The machining becomes very precise, considering the optimization criterion. As well, the process itself becomes desirable instead of traditional technology. Auxiliary devices such as moulds were totally eliminated and the machining duration decreased considerably (3-4 minutes/piece in function of number of teeth).

Received March 07, 2011

Accepted March 29, 2012


[1.] Aouici, H.; Yallese, M.A.; Fnides, B.; Mabrouki, T. 2010. Machinability investigation in hard turning of AISI H11 hot work steel with CBN tool, Mechanika 6(86): 71-77.

[2.] Modler, K.-H.; Lovasz, E.-C.; Bar, G.F.; Neumann, R.; Perju, D.; Perner, M.; Margineanu, D. 2009. Geeral method for the synthesis of general linkages with non-circular gears. Elsevier Ltd. Mechanism and Machine Theory 44: 726-738.


[4.] Gruescu, C.; Ionescu, C.; Nicoara, I.; Breaban, F. 2008. Increase of precision and efficiency of laser cutting by means of optical system optimization. Proceedings of the 6th International Conference of DAAAM Baltic. Talinn: 245-250.

[5.] Smith, W.J. 1995. Modern Optical Engineering. New York: McGraw Hill.

[6.] Naumann, A.; Schroder, G. 1992. Bauelemente der Optik. Taschenbuch der technischen Optik. Munchen; Wien: Carl Hanser Verlag.

[7.] Taguchi, G., and all. 2000. Robust Engineering. New York : McGraw-Hill.

[8.] Taguchi, G., and all. 1989. Quality Engineering in Production Systems. New York: McGraw-Hill.

[9.] Pugna, A.; and all. 2006. Optimizing the hydrothermal growth process parameters of the [alpha]-quartz monocrystals using taguchi's robust design, New Trends in Collaborative Design. Poznan: 327-336.

C.M. Gruescu, University Politehnica Timisoara, 2 Pta.Victoriei, 300222 Timisoara, Romania,

C.L. Ionescu, University Politehnica Timisoara, 2 Pta.Victoriei, 300222 Timisoara, Romania, E-mail:

I. Nicoara, University Politehnica Timisoara, 2 Pta.Victoriei, 300222 Timisoara, Romania, E-mail:

A. Lovasz, University Politehnica Timisoara, 2 Pta.Victoriei, 300222 Timisoara, Romania,

E-mail: 10.5755/j01.mech.18.2.1561
Table 1

Complete classic experimental plan

          C1   C2

A1   B1   R1   R2
     B2   R3   R4

B1   B1   R5   R6
     B2   R7   R8

Table 2

Complete Taguchi experimental plan

Nr.    Factors under   Result of
exp.       study       experiment
           A B C

1      1     1     1       R1
2      1     1     2       R2
3      1     2     1       R3
4      1     2     2       R4
5      2     1     1       R5
6      2     1     2       R6
7      2     2     1       R7
8      2     2     2       R8

Table 3

Fractional experimental Taguchi plan
(alternative I)

Nr.    Factors under   Result of
exp.       study       experiment
           A B C

1      1     1    1        R1
4      1     2    2        R4
6      2     1    2        R6
7      2     2    1        R7

Table 4

Fractional experimental Taguchi plan
(alternative II)

Nr.    Factors under   Result of
exp.       study       experiment
          A B C

2       1    1    2        R2
3       1    2    1        R3
5       2    1    1        R5
8       2    2    2        R8

Table 5

Standard L8 matrix

Nr.       Factors under study      Result of
exp.                              experiment

      A   B   C   D   E   F   G

1     1   1   1   1   1   1   1       R1
2     1   1   1   2   2   2   2       R2
3     1   2   2   1   1   2   2       R3
4     1   2   2   2   2   1   1       R4
5     2   1   2   1   2   1   2       R5
6     2   1   2   2   1   2   1       R6
7     2   2   1   1   2   2   1       R7
8     2   2   1   2   1   1   2       R8

Table 6

Complete table of parameters, measured values and responses

Nr.    Factors under study     Int        Measured values
exp.                           AD

       A   B   C   D   E   F         nr.1   nr.2   nr.3   nr.4

1      1   1   1   1   1   1    1    x11    x12    x13    x14
2      1   1   1   2   2   2    2    x21    x22    x23    x24
3      1   2   2   1   2   2    1    x31    x32    x33    x34
4      1   2   2   2   1   1    2    x41    x42    x43    x44
5      2   1   2   1   1   2    3    x51    x52    x53    x54
6      2   1   2   2   2   1    4    x61    x62    x63    x64
7      2   2   1   1   2   1    3    x71    x72    x73    x74
8      2   2   1   2   1   2    4    x81    x82    x83    x84

Nr.               Measured values

       nr.5        mean         s    S/N[dB]

1      x15    [[bar.x].sub.1]   s1   (S/N)1
2      x25    [[bar.x].sub.2]   s2   (S/N)2
3      x35    [[bar.x].sub.3]   s3   (S/N)3
4      x45    [[bar.x].sub.4]   s4   (S/N)4
5      x55    [[bar.x].sub.5]   s5   (S/N)5
6      x65    [[bar.x].sub.6]   s6   (S/N)6
7      x75    [[bar.x].sub.7]   s7   (S/N)7
8      x85    [[bar.x].sub.8]   s8   (S/N)8

Table 7

Values of factors considered for combinations A...H

Combination   Speed,   Power,   Interaction     Duration
              mm/min     kW        level      of pulse, ms

A              3000     170          1             5
B              3000     170          1             3
C              3000     180          2             5
D              3000     180          2             3
E              4500     170          1             5
F              4500     170          1             3
G              4500     180          2             5
H              4500     180          2             3

Combination     Duration        Nozzle      Cash flow,
              of pause, ms   distance, mm     1/min

A                  3             4/5            20
B                  5            4/2.5           10
C                  3            4/2.5           10
D                  5             4/5            20
E                  3             4/5            10
F                  5            4/2.5           20
G                  3            4/2.5           20
H                  5              5             10

Table 8

Parameter [R.sub.a]--Combinations A...H

A    [R.sub.a]   B   [R.sub.a]   C   [R.sub.a]   D   [R.sub.a]

1      1.02      1     1.49      1     0.49      1     1.41
2      0.89      2     1.32      2      0.7      2     1.18
3      0.97      3     1.24      3     0.52      3     1.14
4      0.94      4     1.52      4     0.72      4     1.33
5      0.86      5     1.59      5     0.71      5     1.37
       0.94            1.43            0.63            1.29

E    [R.sub.a]   F   [R.sub.a]   G   [R.sub.a]   H   [R.sub.a]

1      1.27      1     1.09      1     1.10      1     1.17
2      1.28      2     0.98      2     0.98      2     1.17
3      1.35      3     0.96      3     0.97      3     1.16
4      1.17      4     1.09      4     1.05      4     1.16
5      1.30      5     0.92      5     1.05      5     1.15
       1.27            1.01            1.03            1.16

Table 9

Roughness parameters (confirmation experiment)

Sample      1      2      3      4      5       Mean

[R.sub.a]  0.80   0.78   0.83   0.89   0.71    0.806

Table 10

Comparative data regarding initial, predicted and practically
achieved conditions

Feature               Initial     Estimated    Validation
                     conditions   conditions   experiment

S/N ratio              10.087       18.321       24.459
Mean value             1.098        0.800        0.805
Standard deviation     0.250        0.096        0.047
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Author:Gruescu, C.M.; Ionescu, C.L.; Nicoara, I.; Lovasz, A.
Article Type:Report
Geographic Code:4EXRO
Date:Mar 1, 2012
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