Full Length Research Paper Analyzing the woodturning process using Taguchi methodology for dynamic systems

This paper presents a study of the woodturning performance and efficiency using the Taguchi methodology for dynamic systems. According to this methodology, the woodturning process was characterized by two generic functions: for the first one, the specific cutting energy is related linearly to the cutting power, in the second with the amount of cut. These parameters were measured depending on two control factors namely the depth of cut and the rotational speed which were varied following a design of experiment. The variability, involved during woodturning, was considered by a single variable with two levels for which signal to noise ratios and sensitivities were calculated for each combination of the design. To improve productivity of woodturning, the work efficiency analysis was based on a larger signal to noise ratio with a maximized sensitivity; to improve machining quality, the performance analysis was based on a larger signal to noise ratio but a smaller sensitivity. The optimal conditions of woodturning were obtained corresponding to cutting performance and work efficiency with reduced variability. 
 
 Key words: Woodturning, Taguchi methodology, signal to noise, sensitivity, generic function, work efficiency, performance analysis.


INTRODUCTION
Wood machining is a cutting technique converting wooden parts in size and shapes.To optimize the wood machining, not only the cutting parameters defining the workability of the material are considered, but also and, necessarily, the technical parameters concerning data acquisition and processing.One of the wood machining modes that consume the most power is turning and particularly the roughing (rough turning).Rough woodturning is an operation consisting to produce functional surfaces which need subsequent finish machining (finishing).Therefore, the smoothness will not be required, but the shaping of the part involves a consequent material removal which requires a significant processing time and as a result further energy consumption.
The energy consumption during machining is an important factor for production costs and environmental aspect.Unsuitable cutting parameters are not only sources of energy spending, but cause excessive material consumption as well as premature wear of functional components of the machine.Otherwise, optimal cutting parameters can ensure low energy consumption, secure longer machine and tool life and provide good machinability.Since cutting performance and efficiency are essential requirements in the wood industry, the optimization of cutting parameters is necessary and appropriate for cost-effective and accurate machining.
Although the kinematics of the turning operation and *Corresponding author.E-mail: bbenotmane@yahoo.fr the tools are fairly simple, this process has been a major optimization because of the importance of its applications (Passeron, 1998).This optimization has focused on lathes, tools or on the workpiece with an objective to assess the cutting forces, the power requirements and the surface roughness of wood depending on the cutting depth, the feed rate and the cutting speed.
A number of scientists have used different techniques of cutting measurement to monitor machining conditions.During the last years, notable efforts have been made to develop reliable and robust monitoring systems based on different types of sensors such as cutting force and torque, motor current and effective power, vibrations, acoustic emission or audible sound energy (Bagci, 2011).Earlier, Aguillera and Martin (2001) have emphasized the importance of measuring the cutting forces for determining the working condition.They have measured the cutting forces by an instrumental shaper with quartz piezoelectric sensors emitting electric charges to be amplified to a signal.Using the cutting forces' values, they calculated the cutting power and compared the results with the ones measured by a wattmeter.They concluded that measuring the power consumption for given cut conditions is sufficient as this permits to obtain a very good estimation of the cutting forces.
The knowledge of the cutting forces is necessary for various purposes as tool design and process optimization.Especially for the cutting of wood there are not too many useful results available.The theoretical approaches are poor and the direct measurement is difficult due to vibrations in the system.To remove disturbing vibration components from the signals especially at critical frequency ranges transfer functions and band filter algorithms were used (Scholz and Hoffmann, 1999).Recently, pragmatic process improvements for woodworking machines were attained based on data acquisition using the measurements of the energy consumption.Brownhill (2011) reported that part programming optimization and other process-related improvements can be evaluated more effectively, by displaying the electricity consumption dynamically and historically.With Ethernet connectivity, the data can also be collected into a central database for more detailed analysis and comparisons between machines and processes.This system's approach was recommended to reducing energy consumption.Some energy reduction solutions are best achieved when purchasing new equipment, however, some can be implemented by retrofitting or by upgrading software and processes.
Otherwise, Davim (2001) studied the influence of cutting conditions on the surface finish obtained by turning.The cutting speed and at less degree the feed were found to be the most influent on the surface roughness of the wood.The relationship between the response and the cited factors was represented by linear regression models with correlation coefficients (R=0.74;0.78).Non linear (exponential) regression models were Benotmane and Zirouk 2047 used by Porankiewisz et al. (2008) for a study of the dependence of the main cutting force upon the sharpness and clearance angles and the feed per revolution by straight rough turning of dry wood.
To establish the relationship between the cutting performance and the cutting parameters, several mathematical models based on conventional techniques (optimal solutions) and non-conventional techniques (near-optimal solutions) have been constructed (Mukherjee and Pradip, 2006).In conventional techniques, the design of experiment method-based including the response surface methodology and the Taguchi methodology were largely and successfully used.For non-conventional techniques the genetic algorithm method-based can be cited.Yang and Tarng (1998) have used the Taguchi method, a powerful tool to design optimization for quality, to find the optimal cutting parameters for turning bars using tungsten carbide cutting tools.The experimental results were transformed into a static signal-to-noise (S/N) ratio.However, the use of the dynamic S/N ratio to achieve the performance and efficiency analysis is recommended (Taguchi et al., 2005).Takahashi et al. (2000) evaluated the turning parameters of a stainless steel part by measuring the total power consumption of the main motor.The authors have used an L 18 (2 17 ) orthogonal array (designed by Taguchi) with the concept of the generic function and dynamic S/N ratios.They reported good reproducibility of gain in signal to noise ratios calculated for electrical power consumed during machining.
Conveniently, the aim of this work is firstly the development of an input/output interface for measuring continuously the cutting power and secondly the optimization of the rough woodturning parameters using the Taguchi robust design methodology for dynamic systems.

Wood turning parameters
Wood turning is a manufacturing mechanical process involving single edge tools which cut (removes material) from the surface of a workpiece animated by a rotational movement (cutting action), which is the principal movement of the process.The tool is moved in an additional translation (linear or not) called feed movement, allowing to define the profile of the workpiece.The combination of these two movements, as well as the shape of the active part of the tool is used to obtain the machining shape of revolution: cylinders, planes, cones or complex shapes of revolution (Passeron, 1998).
Straight turning provides the work-piece a cylindrical shape.
In woodturning, parts have initially sharp edges and need to be round and roughly shaped.Rough woodturning is the most dominating and consuming electric energy among other turning operations (finishing, copy turning, facing, etc.).Cutting power is an important parameter, especially in the case of rough operations, as it makes it possible to select and invest in a machine with a power output suited to the operation being carried out on one hand, and on the other, to obtain the cutting conditions that allow the machine's power to be used in the most effective way possible (Lyubchenko and Drujkov, 1990).Next to the cutting power, the rate of material removal is also a performance parameter.Both of them depend on the following cutting parameters whose equations are easily deduced using the schema for a turning operation (Figure 1).
The cutting parameters for straight turning are: i) the depth of cut a p (mm) which is ) usually used instead of the cutting speed is given by: ), which is defined . (3) The required cutting power W (Watt) can be estimated using the following formula: where F c is the cutting force (N).
The material removal rate (MRR) (cm 3 min −1 ) represents the ratio of the amount (volume) of material cut (removed) to the cutting time and is defined as: (5) Combining these two equations yields (6) This equation describes the power needed to perform a cut per the material removal, thus the specific energy.The required cutting powers W must be compared to the available power on the machine, taking into account the machine's efficiency and characteristics.

Materials and equipment
Wood species of a softwood (Pinus sylvestris) without knots, with a moisture content fixed at 15%, assumed to have the same and homogeneous characteristics were cut into the following dimensions: (60 x 60 x 400) mm and have served for the turning.The cutting tests were performed on a semiautomatic woodworking lathe.A roughing gouge made from HSS was used for turning.
The effective power consumed for cutting (electric consumption) was measured using a data acquisition system connected to the lathe.The system is an interface between the machine and a PC and acting as a wattmeter so to be connected in the same way, that is, the two inputs of the interface with one phase of the three phase distribution board located at the power source for the lathe and the output of the interface with the parallel port (printer port) of the PC.

Development of the interface
An Input/output interface was required to transfer instantaneously data (measured powers) from the power source of the motor (input) to the computer (output).It needed a power supply which consists of a three windings linear transformer (220-6 Vx2) whose terminals were separated to obtain a dual voltage polarity (+5 V and -5 V) required for the amplifiers.The excess of voltage (6 V) will be spent by rectification using two diode bridges (Graetz circuit) to which was added two capacitors for voltage smoothing.The hardware of the interface has been developed according to the common instructions in the specified literature (Hirst, 1994).The following diagram shows the steps of its operation (Figure 2).
A specific program at this interface was developed in C ++ language using the steps: -acquisition data -conversion calculation -filtration -screen display -file saving filtered and unfiltered data.
The calibration was performed and preliminary test were carried out to validate the use of this device for suitable applications.

Taguchi robust design methodology
Taguchi applied the concept of S/N ratio originated in the electrical engineering field, to establish the optimum conditions from the experiments (Ranjit, 1990).He developed this concept in the quality engineering, which is a generic technology and therefore, a common problem occurs also for the mechanical field.Taguchi robust design methodology consists of reducing the variability by optimizing the process parameters such that the response (output) becomes insensitive to the cause of variation (noise).This approach is named the robustness strategy and uses the following tools (Phadke, 2010): i) The parameter diagram (P-Diagram) is used to classify the variables associated with the process into noise, control, signal (input), and response (output) factors; ii) The Ideal Function (generic function) is used to mathematically specify the ideal form of the signal-response relationship for a perfect system work; iii) Orthogonal arrays are used for gathering dependable information about control factors (design parameters) with a small number of experiments; iv) The Signal-to-Noise Ratio is used for predicting the performance through laboratory experiments; v) Quadratic Loss Function (also known as Quality Loss Function) is used to quantify the loss due to deviation from target performance.This principle is related to tolerance design and online quality engineering.

P-diagram
The P-diagram showing the approach of the Taguchi robust design on the woodturning process is presented (Figure 3).According to the Taguchi methodology the rough woodturning was considered a dynamic system characterized by the specific cutting energy yi (output), which is obtained by the product between power Wi and time Ti of cutting.The signal factors, as an input, decide the output and can be achieved by the cutting power measured for different durations or also the amount of cut Mj removed during different durations Tj.The input is depending on two control factors (the depth of cut x1 and the rotational speed x2) involving noise factors (the variability).It is needed to indicate that a signal factor has a linear (but not always) impact on the mean response, however has no (or trivial) impact on the variability of the response.A control factor is one that impacts process variability and may or may not Table 1.The control factors used and their levels.

Factors Levels
Rotational speed, x2 (rpm) -1 0 +1 2000 3500 5000 impact the process mean response (Montgomery, 2001).The noise factors can be different: unbalance, tool sharpness, wood anisotropy, inaccurate measurements.In practice, they are difficult to control.Two different analyses can be performed for evaluating the process functionality: work efficiency and cutting performance in order to improve together productivity and quality of the process.These analyses are based on generic functions.

Generic function
For dynamic systems, the concept of the generic function is to establish a desirable linear relationship between the objective output and the means to generate it.Since the signal input decides the output, the process optimization involves determining the best control factor levels so that the input/output ratio is closest to the desired (ideal) relationship.
For the work efficiency, the generic function is where is the specific cutting energy calculated as area measured in that is, the product of power and time of cutting, is the cumulative sum of cutting time in , is the sensitivity of the system, and represents the error term; For the cutting performance, the generic function is (8 where y is also the specific cutting energy, M is the amount of cut measured in (cm 3 ), β is the sensitivity of the system, and є represents the error term.
The square roots are used: -to make both sides equivalent to energy when they are squared, -to rationally calculate the S/N ratios based on these generic functions.

The orthogonal array (design of experiment)
For this experiment a complete factorial design providing a good accuracy for results analysis was chosen (Schimmerling et al., 1998).Table 1 shows the used factors and their levels.
For the specified design, the tests were carried out and the cutting power was measured for each run and the corresponding specific energies were found.Since the number r of taken measures is depending on the developed device, it was convenient to choose r = 500 for the purpose of observing its synchronization with the current frequency and to avoid interferences.The current frequency was equal to 50 Hz in one hand, and the duration of one pass of machining 10 s on the other hand.Moreover, it was considered that in rough turning the feed rate can be maintained constant related to a rough surface.Then, the selected feed rate was 2.5 m/min.The noise factors are not only difficult to be implemented, but also require large number of trials.Thus, they were pooled into a single variable N with two levels: N1 and N2, that are defined: N1: abnormal conditions where the cutting power is lesser, that is, corresponding to low energy consumption, N2: abnormal conditions where the cutting power is greater, that is, corresponding to high energy consumption.

The S/N ratio and sensitivity determination
Next, for each run of the design, the S/N ratios and the sensitivities  were determined following the procedure described below.

Work efficiency:
For each run of the design, k=10 intervals of 1 s for each, were chosen.The data of the cutting time Ti versus the corresponding cutting power Wi were reported as well for N1 as for N2 into a diagram as shown in Table 2.
Then, using the reported data the total variation of the cutting power ST, which is a sum of squares of the square root of each cumulative cutting power was computed ; . (9) The product of time and power used for cutting was computed so as to effectively reflect its variability: The data of these terms for each run were reported in ANOVA tables which structure is represented (Table 3).
The S/N ratio nq of the qth run is given by ( 17) The estimate of the slope for the qth run is given by (18) The system's sensitivity Sq for the qth run is defined by the equation: ( Cutting performance: For each run of the design, l = 3 cuts were realized and the corresponding cutting power and amounts of cut were measured.The data were presented in a diagram as shown in Table 4.
Then, using the reported data the required terms for S/N ratios and sensitivities were calculated that are: The total variation of the cutting power, ST , (20) The variation caused by the linear effect   The error variation S (24) The error variance V (25) The data of these terms for each run were reported into ANOVA tables which structure is similar to Table 3.The S/N ratios, the estimate of the slope and the system's sensitivity were calculated following the same equations cited above (17, 18 and 19).

Reproducibility of gain
Finally, the S/N ratios and sensitivities were analyzed.Two-step optimization was achieved: -For work efficiency, the features of these two indexes had been "the larger S/N ratio is the best" and the maximum system's sensitivity for minimizing the system's variability; -For cutting performance, the features had been "the larger S/N ratio is the best" and the smaller system's sensitivity for maximizing the amount of cut with minimum consumption of energy.
The gain in S/N ratio and sensitivities was calculated by the difference between the average responses at optimal conditions and initial conditions.The initial conditions were chosen at the settings x1 = 0 and x2 =0.The reproducibility of gain was performed by confirmatory experiments; a positive gain indicating the significance of the optimal conditions.

RESULTS ANALYSIS USING THE DYNAMIC SN RATIOS Presentation
According to the explained above procedure, for all the runs, the S/N ratios and the sensitivities were computed on the basis of the experimental and converted data that are presented in Table 5 for work efficiency analysis and in Table 6 for performance analysis.SN ratios and sensitivity for each experiment are summarized in Table 7.

Data analysis and two-step optimization
The data were analyzed based on three indexes: linearity, dynamic S/N ratio and sensitivity.Linearity has been checked by fitting the data for each trial.The main effects of the control factors on the responses (S/N ratio or sensitivity) were determined based on modeling by experimental design.The S/N ratio and sensitivity were optimized for each type of analysis.

Work efficiency analysis
Figure 4 illustrate the relationship between the cumulative values of the cutting power y i and the cumulative cutting time for all the trials of the design.The linearity as a desirable item is improved.
The effects of control factors x 1 and x 2 on S/N ratios and sensitivities are represented in Figure 5.The larger S/N ratio and the larger sensitivity are observable for the level (+1) for both factors, that is, for run N°5.This means that cutting is performed with a large electric consumption which causes variability in dimensions, unbalance, premature wear of sharp edges and moving parts warm of the lathe.

Cutting performance analysis
In this case, the linearity between the specific energy and the amount of cut has been improved.The effects of control factors x 1 and x 2 on S/N ratios and sensitivities are represented in Figure 6.The larger S/N ratio and the smaller sensitivity are observable for the combination x 1 = 1; x 2 = -1, that is, for run N°4.This means, in difference to previous analysis, that cutting is achieved with quite a small amount of power: that is, cutting smoothly and power effectively.

Reproducibility of gain
The conducted analysis resulted to different findings.The     process efficiency is accompanied with a larger sensitivity to noise.The cutting specific energy is maximum (maximum power) and the variability is important.However, the process performance involves lower sensitivity, what minimizes electric power per unit removal amount as well as minimizes energy loss.The improvement in the SN ratio is then due to the opportunity of cutting more using a slight quantity of electricity.Obviously, the optimal settings can be comparatively found between those corresponding to the indexes features.The configuration related by the factors' levels x 1 = 1 and x 2 = -1, that is, run N°4 is the optimal.Table 8 shows the gain obtained due to the process optimization.
The large gain in S/N ratio represents a significant variability reduction.The reproducibility is confirmed through confirmatory experiments for the optimal and initial settings.Relatively good reproducibility of SN ratio and sensitivity is obtained.
Subsequently, as β 2 decreases (β 1 increases for work efficiency); this suggests that cutting produces a great deal of work with a small amount of electric power.

DISCUSSION
This paper discussed the optimized rough woodturning conditions using the robust design methodology.The cutting force exceeds 75 N for the woodturning process; the average dispersions (variances) were also high (Porankiewisz et al., 2008).This variability is confirmed by other studies (Davim, 2001).
In the present paper, the approach of optimizing the cutting conditions differs from that using regression models or response surface methodology (RSM).It should be noted that the use of regression models is related to application conditions which are difficult to achieve in machining processes.First, the model is supposed consisting of two additive parts: one deterministic and the other random.Second, the deterministic part is also assumed to be composed of additive elements.The random part is supposed to be distributed normally with constant variance (homoscedasticity).These conditions are prior to regression analysis.In the above cited studies, (but also in others cited therein) different regression models were used: linear without interaction effects between factors, and some with strong or weak interaction effects.The additivity and constancy of variances do not seem to be appropriately respected.Moreover, some models were fitted with low coefficients of determination.The presence in the model of interaction effects may adjust the model (R 2 close to 1), but its occurrence must be interpreted physically.In most cases the interaction between control factors is synonymous with poor reproducibility.The reproducibility as a criterion of variability can be expected with the use of the generic function selected appropriately to avoid interactions.

Conclusion
In this paper, the rough woodturning efficiency and performance were analyzed based on the principle of generic function, which provides a linear dependence between the specific cutting energy and each of time of cutting and material removed.The specific cutting energy was determined based on the cutting power which was measured using a data acquisition system input/output type (analog/digital) developed for that purpose.The Taguchi robust design methodology for dynamic systems was successfully used to optimize the woodturning process.Thus, three indexes were improved: the linearity, the signal to noise ratio and the sensitivity.Although power measurements were subjects to fluctuations due to variability sources, the linearity between the cumulative power and the cumulative time of cutting was observed.This inherent variability involved stretched power values and needed to be reduced.Therefore, The rough woodturning optimization based on dynamic signal to noise ratios and sensitivities, allowed obtaining better cutting performance and working efficiency.Hence, the reproducibility of gains in signal to noise ratios which signifies a variability reduction was obtained.

Figure 1 .
Figure 1.Schema of the turning operation.
) is the diameter of the piece and the indexes 1 and 2 indicate before and after working respectively).ii) the feed per rotation f (mm) iii) the cutting speed v c

Figure 3 .
Figure 3. P-diagram for the woodturning process as a dynamic characteristic.

Figure 4 .
Figure 4. Change in cumulative cutting power during wood turning: Under N1 and N2 conditions (data for run N°1 to N°9) as (a to i), respectively.

Table 2 .
Diagram for data time versus cutting power for a run.

Table 3 .
Structure of ANOVA table.

Table 4 .
Diagram for amount removed and cutting power for a run.

Table 5 .
Data time versus cutting power for Runs N°1 to 9.

Table 6 .
Data of amount removed versus cutting power for Runs N°1 to 9.

Table 7 .
Values of computed S/N ratios, sensitivities and slopes.