Multi Response Optimization of Machining Parameters in Spur Gear Hobbing process by using Taguchi based GRA

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Multi Response Optimization of Machining

Parameters in Spur Gear Hobbing process by using Taguchi based GRA

Omesh Manuja Department of Mechanical

Engineering, D. J. Sanghvi College of

Engineering, Mumbai - 400 056, Maharashtra, India.

Frank Crasta Professor, Department of Mechanical

Engineering, D. J. Sanghvi College of

Engineering, Mumbai - 400 056.

Dr. Vijaykumar. K N Head of Department, Department of Mechanical

Engineering, D. J. Sanghvi College of

Engineering, Mumbai - 400 056.

Abstract: Gear hobbing is one of the major manufacturing processes in the industry. Hobbing is a continuous gear generation process widely used in the industry for high or low volume production of external cylindrical gears.

Optimization is one of the techniques used in manufacturing sectors to arrive at the best manufacturing conditions. This is an essential need for industries for manufacturing of quality products at lower cost.

This project focuses on improving the productivity & quality of gear hobbing Experiments are performed as per L₂₇ orthogonal array on EN8 work piece & M35 hob.

Modern engineering practices are demanding higher & higher accuracies along with productivity.

Taguchi method is used for selecting the design of experiments and Grey Relational Analysis is used to optimize the performance characteristics like Material Removal Rate & Surface Roughness.

Keywords – Optimization, Taguchi method, Grey Relational Analysis, hobbing process.

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1. INTRODUCTION

Improvement of productivity maintaining quality is the general goal of every organization. Improvement in productivity of the process ultimately leads to the growth or development of the organization.

In the existing global scenario, it is utmost important to achieve & maintain the productivity levels &

quality levels in manufacturing to get the desired quality standards at competitive costs.

This has emphasized the need to utilize all the manufacturing facilities in the optimum manner to result in best possible outputs.

In the present study we have focused on increasing the productivity & quality levels of spur gear hobbing process on vertical gear hobbing machine- PFAUTER, Italy make.

The present productivity levels are intended to be improved by conducting the experiments & selecting the optimum levels of parameters.

Parameters upon which focus is made are Speed of Tool, Feed of Tool and Depth of Cut.

Research made on this topic is briefly described.

Hobbing cycle time decreases with the increase in number of hob starts and ultimately it results in increase in productivity.

Taguchi method is a powerful tool for design of experiments (DOE) which serves as a basis for optimization of various engineering processes. It is an important tool to identify the critical parameters and also predict optimal settings for each process parameter.

Taguchi method uses the S/N ratio of the response instead of the response itself to decide the level of the input parameter to optimize the output response. Such procedure is beneficial when it is used to optimize single response, but not suitable to optimize multiple responses.

Optimisation of the process parameters has assumed significant research interest in machining operations, since it has the capability to recommend optimal parametric combination under a given set of constraint(s), thus providing useful information to the machining industries.

Grey relational analysis (GRA) utilises a specific concept of information. It defines situations with no information as black, and those with perfect information as white. In other words, GRA converts a multi-objective

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optimization problem in to a single objective optimization process.

Grey-relational analysis has been utilized for simultaneous optimization of cutting parameters in order to obtain favourable performance characteristics in machining.

2. EXPERIMENTAL DETAILS AND METHODOLOGY

During the experiments, EN8

work-piece was machined with M35 hob on PFAUTER, Italy make hobbing machine. Experiments were conducted as per L₂₇ Orthogonal Array design. Machining parameters considered were Speed of Tool, Feed of Tool and Depth of Cut.

Three levels of each parameter were chosen.

Parameter Level-1 Level-2 Level-3

A. Speed (RPM)

71 140 220

B. Feed (mm/min)

4 5 5.8

C. Depth of Cut (mm)

2.38 2.88 3.38

Table-1: Process Parameters & their levels

Here the performance characteristics selected are Material Removal Rate & Surface Roughness.

Material Removal Rate relates to the productivity of the machining process & Surface Roughness relates to the quality of the machining process.

In this study our attempt is to maximize the Material Removal Rate & minimize the Surface Roughness.

Determination of MRR was carried out during the experiment while surface roughness was measured after the machining operation.

MRR was calculated by the expression: W_b – Wa / T_m

Here, W_b – Weight of work-piece before machining, W_a - Weight of work-piece after machining, Tm – Machining time.

Surface Roughness is measured by TalySurf-4 of Taylor Hobson.

2.1 Design of Experiments

The three process parameters in gear hobbing each taken in three levels is shown in Table-1 are represented in an orthogonal array. The experiment was designed using Taguchi method. L₂₇ Orthogonal Array design was selected

In this paper the process parameters considered are speed, feed rate and depth of cut. And we are optimizing the values of MRR & Surface Roughness. As we need the MRR to be high and Surface Roughness to be low, so this problem is a multiple-objective optimization case.

As mentioned above, we have used grey relational analysis to convert this multi objective optimization problem to a single objective optimization.

3. Grey Relational Analysis

In Grey Relational Analysis, the first step is data pre-processing. This avoids the problem of different scales, units and targets.

The following steps are followed in GRA:

 Experimental data are normalised in the range between zero and one.

 Next, the grey relational coefficient is calculated from the normalised experimental data to express the relationship between the ideal (best) and the actual experimental data.

 Grey relational grade is then computed by averaging the weighted grey relational coefficients corresponding to each performance characteristic.

 The parameters significantly affecting the process are found out.

 Optimal levels of process parameters are then chosen.

3.1 Data Pre-processing

In Grey Relational Analysis, data pre-processing is the first step performed to normalize the random grey data with different measurement units to transfer them to dimensionless parameters.

Thus data pre-processing converts the original sequences to a set of comparable sequences.

The original reference sequence & pre-processed are represented by x₀⁽⁰⁾(k) & x_i⁽⁰⁾ (k),

Here,

i = 1, 2, 3 ...m ( m is number of experiments)

k = 1, 2, 3...n

( n is the total number of observations of data)

Depending on the quality characteristics, there are different categories for normalizing the original sequence of data.

1. If the original sequence data has quality characteristics as „Larger the Better‟, then the original data is processed as „Larger the Best‟

x_i^*(k) = x_i^o(k) – min x_i^o(k) max x^o(k) – min x^o(k)

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as „Smaller the Better‟, then the original data is processed as „Smaller the Best‟

x_i^*(k) = max x_i^o(k) – x_i^o(k) max x_i^o(k) – min x_i^o(k) here,

max x_i^o(k) & min x_i^o(k) are the maximum &

minimum values respectively of the original sequence x_i^o(k).

Comparable sequence x_i^o(k) is the normalised sequence of original data.

3.2 Grey Relational Co-efficient:

To calculate the Grey Relational Co-efficient, first we need to calculate the deviation sequence.

Deviation sequence ∆oi (k) is calculated from the reference sequence x_i^o(k) & comparability sequence x_i^*(k) as-

∆oi (k) = | x_i^o(k) - x_i^*(k) | ∆_min = min_i min_k ∆oi (k)

∆max = max_i max_k ∆oi (k)

The Grey Relational Co-efficient is calculated from the deviation sequence by using the following relation:

Γ(x0*(k)_, x_i^*(k)) = ∆min + δ. ∆max

∆oi (k) + δ. ∆max

0 ˂ Γ(x0*(k)_, x_i^*(k)) ≤ 1

ζ is the distinguishing co-efficient. Its value is chosen to be 0.5.

The purpose of defining this co-efficient is to show the relational degree between the reference sequence x_i^o(k) &

comparability sequence x_i^*(k), Where,

i = 1, 2, 3...m, k = 1, 2, 3... ....n

3.3 Grey Relational Grade:

The Grey Relational Grade is a weighted sum of the Grey Relational Co-efficient.

It is defined as follows:

Γ(x₀^*_, x_i^*) = ^𝒏_𝒌=𝟏.βk .γ (x0

*(k)_, x_i^*(k))

The Grey Relational Grade represents the level of correlation between the reference sequence & the comparability sequence.

The Grey Relational Grade also indicates the degree of influence that comparability sequence could exert over reference sequence.

Exp.

No.

A B C MRR SR MRR

x_i^* (k)

SR x_i^* (k)

MRR ( Γ )

SR ( Γ )

GRG (γ)

1 71 4 2.38 0.6024 1.0353 0 0.328 0.333333 0.426512 0.379923

2 71 4 2.88 0.878 0.764 0.041 0.66 0.342607 0.595026 0.468817

3 71 4 3.38 1.6295 0.646 0.151 0.804 0.370727 0.718597 0.544662

4 71 5 2.38 0.8407 0.8193 0.035 0.592 0.34132 0.550661 0.445991

5 71 5 2.88 1.2085 0.9617 0.089 0.418 0.354434 0.461979 0.408207

6 71 5 3.38 2.1714 0.957 0.231 0.424 0.394042 0.464468 0.429255

7 71 5.8 2.38 0.9501 0.7757 0.051 0.645 0.345113 0.585069 0.465091

8 71 5.8 2.88 1.3793 1.0327 0.114 0.331 0.360855 0.427643 0.394249

9 71 5.8 3.38 2.5907 1.303 0.293 0 0.414182 0.333333 0.373758

10 140 4 2.38 1.5556 0.616 0.14 0.841 0.367755 0.75861 0.563183

11 140 4 2.88 2.0902 0.7207 0.219 0.713 0.390351 0.635082 0.512717

12 140 4 3.38 3.9916 0.5867 0.499 0.877 0.49955 0.802182 0.650866

13 140 5 2.38 1.8793 0.542 0.188 0.932 0.381098 0.879507 0.630303

14 140 5 2.88 2.9007 0.6927 0.339 0.747 0.430478 0.664011 0.547245

15 140 5 3.38 5.5402 0.833 0.727 0.575 0.646998 0.540716 0.593857

16 140 5.8 2.38 2.1763 0.7417 0.232 0.687 0.39426 0.615006 0.504633

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17 140 5.8 2.88 3.1405 0.8233 0.374 0.587 0.443971 0.547705 0.495838

18 140 5.8 3.38 5.9937 0.7777 0.794 0.643 0.708115 0.583431 0.645773

19 220 4 2.38 1.784 0.7103 0.174 0.726 0.377074 0.645578 0.511326

20 220 4 2.88 2.7663 0.62 0.319 0.836 0.423263 0.753012 0.588138

21 220 4 3.38 5.3333 0.6877 0.697 0.753 0.622432 0.669434 0.645933

22 220 5 2.38 2.1004 0.486 0.221 1 0.390808 1 0.695404

23 220 5 2.88 3.2143 0.633 0.385 0.82 0.44827 0.735402 0.591836

24 220 5 3.38 6.5693 0.6727 0.879 0.772 0.804764 0.686342 0.745553

25 220 5.8 2.38 2.6389 0.7593 0.3 0.666 0.416632 0.599161 0.507897

26 220 5.8 2.88 3.9916 0.7347 0.499 0.696 0.49955 0.621581 0.560566

27 220 5.8 3.38 7.393 0.634 1 0.819 1 0.733999 0.867

Table-2: Experimental results and GRG γMean = 0.546964

4. RESULTS AND DISCUSSIONS

Here using Grey Relational Analysis, multiple performances are unified to a single response, i.e., GRG, for ease in optimisation. Three process parameters are considered for optimising MRR and Surface Roughness simultaneously.

The steps for calculation of GRG are mentioned. The experimental findings in Table-2 are used to calculate the normalised MRR and Surface Roughness, which are presented in same table. These normalised values are used to calculate GRC‟s for both the responses.

Subsequently, GRG is evaluated from GRC‟s for each experimental run. According to GRG rules, all the experimental runs are related to „higher is better policy‟

(Tosun and Pihtili (2010)).

The mean of the GRG for each level of the machining parameters, and the total mean of GRG is summarised in Table- 3 for each factor levels.

The higher value of GRG means comparability sequence has a stronger correlation to the reference sequence.

Speed (A)

Feed (B)

Depth of Cut (C) (C) Level-1 0.434439 0.540618 0.5226387 Level-2 0.571601 0.565294 0.5075122

Level-3 0.63485 0.534978 0.6107396

∆

Max - Min

0.200411 0.030316 0.1032273

Rank 1 3 2

Table-3: Response table for GRG

Table-3 indicates the effect of machining parameters on the multi-performance characteristics for maximum MRR and minimum surface roughness.

4.1. Confirmatory Experiment

The estimated or predicted GRG (γ) at the optimum level of the machining parameter can be calculated by:

γ Predicted = γ_Mean + ∑ (γOptimal - γ_Mean )(for all parameters)

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Machining Parameters

Optimal Machining Parameters %

Improvement Predicted Experimental

Combination Level

A3-B3-C2 A3-B2-C3 A3-B2-C3

MRR 3.9916 6.5693 64.58

SR 0.7347 0.6727 8.44

GRG 0.560566 0.716956 0.745553

Table -4: Confirmatory Experiment Result

Where γ_Mean is the mean of GRGs of all experimental runs, γ_Optimal is the mean of GRG at the optimum level of parameter.

To demonstrate the method of quantifying the quality improvement, the initial machining parameters are assumed to be Speed of Cutter = 220 RPM, Feed of Cutter = 5.8 mm/rev, Depth of Cut = 2.88 mm. With this setting, the experimental values of Surface Roughness and MRR were 0.7347 μm and 3.9916 mm³/min respectively.

Table - 4 shows the optimum parameters and the predicted SR, MRR and GRG.

From the above table we can see that surface roughness decreased by 8.44% and MRR increased by 64.58%.

Thus, it can be concluded that the quality characteristics can be greatly improved through application of Taguchi based GRA.

5. CONCLUSIONS

In this study, L₂₇ Orthogonal Array Taguchi design was used to study the influence of machining parameters on Material Removal Rate and Surface Roughness during hobbing of EN8 gear.

The Grey Relation Analysis was adopted to optimise the machining parameters in hobbing operation.

The optimal setting of machining parameters was found to be: Speed of Cutter = 220 RPM, Feed of Cutter = 5 mm/rev, Depth of Cut = 3.38 mm.

A confirmatory test was done to validate the findings and an improvement of 33.00 % in GRG was observed.

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