IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 1 Issue 3, May 2014. www.ijiset.com

ISSN 2348 - 7968

Numerical Investigation of Ceiling Fan Noise by Using Response Surface Method

Sanjay R.Shinde1, Mangesh R.Phate2 and Rupesh V.Bhortake3

1 ME Design Student, Department of Mechanical Engineering , University of Pune, TSSM’S, PVPIT, Bavdhan, Pune, Maharashtra,411051, India

2 Faculty, Department of Mechanical Engineering , University of Pune, TSSM’S, PVPIT, Bavdhan,

Pune, Maharashtra,411051, India

3 Faculty, Department of Mechanical Engineering , University of Pune, TSSM’S, PVPIT, Bavdhan, Pune, Maharashtra,411051, India

Abstract: Sealing fans are one of main noise producing sources. Tonal noise produced at a multiple of the rotational frequency of the fan, the so-called blade passing frequency and its higher harmonics generally dominate fan noise. Noise reduction is perhaps one of the most important parameter Every noise reduction process starts with identification of noise sources & ranking the noise sources from machinery. Ceiling fans are extensively used to create an indoor breeze, improve the space air distribution and hence enhance the feeling of comfort. The fan speed, diameter, number of blades ,blade angle and location all play an important role in deciding the noise induced flow pattern features in space. Few previous studies have investigated fan induced flow and its characteristics under different geometric and operating conditions .In this study ,response surface methodology is used to predict noise characteristics. The experiments were conducted based on three different room size, three different ceiling fan rod lengths three regulator knob positions and mathematical model was developed .Sensitivity analysis was carried out to identify critical parameters.

Keywords: Response Surface Method, Ceiling Fan, Sensitivity Analysis, Optimization, MINTAB 16.

1.Introduction People feel discomfort when they get sweat in a space with a stagnant air. Therefore people try to create air breeze around their bodies either naturally or mechanically to enhance body convective heat transfer .Air motion helps sweat evaporation and accordingly brings body comfort feeling. Ceiling fans are used in offices, residences as an alternative extend the summer comfort envelope. The flow pattern features induced by ceiling fans are very help-ful for people of people of interest working in the field . So knowing flow characteristics, as a result of ceiling fan rotation would help improving the fan design in addition to selecting its

optimum placement to save energy. Therefore it is very important to select and control the input parameters for obtaining noise level .Various prediction methods can be applied to define the desired output variables through developing mathematical models to specify the relationship between the input parameters and output variables. The response surface methodology (RSM) is helpful in developing a suitable approximation for the true function relationship between the independent variables and the response variable that may characterize the nature of the noise. It has been proved by several researchers that efficient use of statistical design of experimental techniques, allow development of an empirical methodology, to incorporate a scientific approach in analysis of ceiling fan noise .Even though sufficient literature is available on analysis of ceiling fan noise, no systematic study has been reported so far to correlate the process parameters and noise. Hence, in this investigation ,the design was used to conduct experiments for exploring the interdependence of the process parameters and second order quadratic model for noise was developed from the data obtained by conducting the experiments.

2. Experimental Identifying important parameters From the literature and previous work done among

many independently controllable parameters affecting noise ,the parameters viz Room size (A),Rod length(B),Regulator knob position (C) were selected as primary parameters for the study. The room size (A) ,rod length (B) , regulator knob position (C) are the primary parameters contributing to the noise .Different combinations of parameters were used to carry out the trial runs. This was carried out by varying one of the

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ISSN 2348 - 7968 factors while keeping the rest of them at constant values.

Table1. Parameters Level selected for the Experimentation

Parameters Levels Low (1) Medium (2) High (3) (A) Room Size ( m3)

66.56 m3 167.19 m3

355.84 m3

(B) Fan Rod Length (Inch)

6.5 10.25 12

(C) Speed Knob Position

2 3 4

2.2 Conducting experiments

For conducting experiments three different room size ,three different rod length, and three different regulator knob speed position ie 2,3,4 were selected. Using FFT (Fast Fourier Transformer) analyzer noise level in (dB) were recorded. Rod length for fan were measured. Noise reading in different room ,using different rod at different regulator knob position were recorded as follows.

3. Development of mathematical model 3.1Response surface methodology Response surface methodology(RSM) is a collection of mathematical and statistical technique useful for analyzing problems in which several independent variables or response and the goal is to optimize the response. In many experimental conditions, it is possible to represent independent factors in quantitative form as given in Eq.(1).Then these factors can be thought of as having a functional relationship or response as follows:

Y=Φ(x1,x2,…,xk)±er Eq.(1). Between the response Y and x1, x2, …, xk of k quantitative factors , the function Φ is called response surface or response function. The residual er measures the experimental errors. For a given set of independent variables, a characteristic surface is responded .When the mathematical form of Φ is not known, it can be approximate satisfactorily within the experimental region by polynomial. In the present investigation, RSM has been applied for developing the mathematical model in

the form of multiple regression equations for quality characteristics of noise. In applying the response surface methodology, the independent variable was viewed as surface to which a mathematical model is fitted.

Table-2. Observation Table

RUN

Parameters Noise

Room size Fan rod

length

Speed

knob

position

X2

1 66.56 6.5 2 48.1

2 66.56 6.5 2 49.3

3 66.56 6.5 2 50.7

4 66.56 10.25 3 52.3

5 66.56 10.25 3 53.6

6 66.56 10.25 3 54.3

7 66.56 12 4 57.6

8 66.56 12 4 58.7

9 66.56 12 4 60.4

10 167.19 6.5 3 51.5

11 167.19 6.5 3 52.6

12 167.19 6.5 3 53.2

13 167.19 10.25 4 60.3

14 167.19 10.25 4 60.7

15 167.19 10.25 4 62

16 167.19 12 2 53.2

17 167.19 12 2 54.3

18 167.19 12 2 53.4

19 355.84 6.5 4 57.3

20 355.84 6.5 4 58.9

21 355.84 6.5 4 60.8

22 355.84 10.25 2 48.3

23 355.84 10.25 2 49.2

24 355.84 10.25 2 50.3

25 355.84 12 3 48.5

26 355.84 12 3 51.6

27 355.84 12 3 53.2

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The second order polynomial (regression) equation used to represent the response surface Y is given by Y = b0 +Σbi xi +Σbii xi +Σbij xi x j + e Eq.(2). And for the three factors, the selected polynomial could be expressed as Noise(X2)=b0+b1(A)+b2(B)+b3(C)+b11(A2)+b22(B2)+b33(C2)+ b12(AS)+b13(AB)+b23(BC)

Eq.(3). 3.2 Response Surface Regression: X2 versus A, B, C The analysis was done using coded units. Table.3 Estimated Regression Coefficients for X2 Term Coef SE Coef T P Constant

41.21 4.28 9.60 0.000

A 7.77 2.56 3.03 0.007 B 9.97 3.33 2.99 0.008 C -8.43 2.50 -3.36 0.003 A*A -2.18 0.55 -3.96 0.001 B*B -1.38 0.63 -2.18 0.042 C*C 2.12 0.63 3.33 0.004 A*B -1.52 0.63 -2.39 0.028 A*C 1.81 0.63 2.84 0.011 In order to estimate the regression coefficients , a number of experimental design techniques are available .In this work ,table (4) was used which fits the second order response surfaces very accurately. Central composite face cantered design matrix .The final modal was developed using only these coefficient and the final mathematical model to estimate noise is given by

Second order Response Surface Model for the fan noise response is as given below :

Noise ( X2) = 0.08778 -0.29333 *A +2.67556* B +0.30278 * C +0.10889* A2 -0.37333 * B2 - 0.18500*C2 -0.52444*A*B - 0.41444 * A* C ( Eqn. 4)

3.3 Checking adequacy of model The adequacy of the developed model was tested using the analysis of variance (ANOVA) are given in the table 4.The determination coefficient (R2) indicates the goodness of fit for the model. In this case the value of the determination coefficient (R2=0.9333) indicates that only 7% of the total variations are not explained by the model. The value of adjusted determination coefficient (R2=0.8499) is also high ,which indicates a high significance of model. Predicted R2 is also in a good agreement with the adjusted R2 . Adequate precision compares the predicted values at the design points to the average prediction error. At the same time a value of the press (73.68 ) indicates improved precision and reliability of the conducted experiments. The value of probability＞F in Table 3 for model is less than 0.05, which indicates that the model is significant. In the same way, room size (A), rod length(B),regulator knob position (C) , interaction effect of room size with rod length (AB), interaction effect of room size with regulator knob position(AC), and second order term of room size, rod length, knob position, have significant effect. Lack of fit is non-significant as it is desired. The normal probability plot of the noise response X2 as shown in fig 2d revels that the residuals are falling on straight line, which mean the error are distributed normally. All the above consideration indicates an excellent adequacy of the regression model. Each observed value is compared with predicated value calculated from model in fig.2c

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Table 4. ANOVA results for the Noise of Fan

. Source DOF Square SS Adjusted SS Mean Square F Value p-value

probability＞F Regression 8 458.253 458.253 57.2817 31.49 0.000 Linear 3 361.326 60.811 020.2703 11.14 0.000 A 1 2.645 16.728 16.7282 9.20 0.007 B 1 4.014 16.291 16.2910 8.95 0.008 C 1 354.663 20.648 20.6481 11.35 0.003 Square 3 79.885 61.378 20.4592 11.25 0.000 A * A 1 28.602 28.602 28.6017 15.72 0.001 B * B 1 1.402 8.681 8.6806 4.77 0.042 C * C 1 49.882 20.267 20.2672 11.14 0.004 Interaction

2 17.042 17.042 8.5211 4.68 0.023

A * B 1 2.282 10.427 10.4272 5.73 0.028 A * C 1 14.762 14.761 14.7606 8.11 0.011 Residual Error

18 32.747 32.747 1.8193

Pure Error 18 32.747 32.747 1.8193 Total 26 491.000 Std deviation

1.34880

R2 0.9333

Press 73.68 Adjusted R2 0.8499 Predicted R2 0.9037

2624222018161412108642

2

1

0

-1

-2

-3

Observation Order

Re

sid

ua

l

Versus Order(response is X2)

( 2a )

210-1-2

7

6

5

4

3

2

1

0

Residual

Fre

qu

en

cy

Histogram(response is X2)

( 2b )

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ISSN 2348 - 7968

62605856545250

2

1

0

-1

-2

-3

Fitted Value

Re

sid

ua

l

Versus Fits(response is X2)

(2c)

3210-1-2-3

99

95

90

80706050403020

10

5

1

Residual

Pe

rce

nt

Normal Probability Plot(response is X2)

( 2d )

Fig 2 : Residual plot for the Noise of ceiling fan

3.4 Optimizing parameters Contour plots show distinctive circular shape indicative of possible independence of factors with response. Contour plots play a very important role in the study of the response surface. By generating contour plots using software for response surface analysis, the optimum is located with reasonable accuracy by characterizing the shape of the surface. If a contour patterning of circular shaped contours occurs, it tends to suggest independence of factor effects while elliptical contours as may indicate factor interactions Response surfaces have been developed for both the models, taking two parameters in the middle level and two parameters in the X and Y axis and response in Z axis. The response surfaces clearly reveal the optimal response point. RSM is used to find the optimal set of process parameters that produce a maximum or minimum value of the response. In the present investigation the process parameters corresponding to the noise are considered as optimum (analysing the contour graphs and by solving Eq.(4)). Hence, when these optimized process parameters are used, then it will be possible to attain the minimum noise Fig.3 presents three dimensional response surface plots for the response noise obtained from the regression model. Fig.4(a) exhibits almost a circular contour, which suggests independence of factor effect namely room size. It is relatively easy by examining the contour plots (Figs.4(b) and 4(c)), that changes in the noise are more sensitive to changes in room size than changes in rod length and knob position.

350

2

52

54

1

56

2 13

X2

B

A

C 2Hold Values

Surface Plot of X2 vs B, A

( 3a )

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3

50 2

55

1

60

2 13

X2

C

B

A 2Hold Values

Surface Plot of X2 vs C, B

( 3b )

3

502

55

1

60

2 13

X2

C

A

B 2Hold Values

Surface Plot of X2 vs C, A

(3c) Fig 3 : Surface plot for the Noise of ceiling fan

A

B

3.02.52.01.51.0

3.0

2.5

2.0

1.5

1.0

C 2Hold Values

> – – – – – < 50

50 5151 5252 5353 5454 55

55

X2

Contour Plot of X2 vs B, A

( 4a )

B

C

3.02.52.01.51.0

3.0

2.5

2.0

1.5

1.0

A 2Hold Values

> – – – – < 52

52 5454 5656 5858 60

60

X2

Contour Plot of X2 vs C, B

( 4 b )

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A

C

3.02.52.01.51.0

3.0

2.5

2.0

1.5

1.0

B 2Hold Values

> – – – – – < 50

50 5252 5454 5656 5858 60

60

X2

Contour Plot of X2 vs C, A

(4c) Fig 4 : Contour plot for the Noise of ceiling fan

Table 5: Noise sensitivities of parameters

3.5 Sensitivity analysis Sensitivity analysis, a method to identify critical parameters and rank them by their order of importance, is paramount in model validation where attempts are made to compare the calculated output to the measured data. This type of analysis can study which parameter must be

most accurately measured, thus determining the input parameters exerting the most influence upon model outputs. Mathematically, sensitivity of a design objective function with respect to a design variable is the partial derivative of that function with respect to its variables. To obtain the sensitivity equation for room size, Eq.(4) is differentiated with respect to room size. The sensitivity equations (5), (6) and (7) represent the sensitivity of noise for room size, rod length and knob position, respectively. In this study, it is aimed to predict the tendency of noise due to a small change in parameters . Sensitivity information should be interpreted using mathematical definition of derivatives. Namely, positive sensitivity values imply an increment in the objective function by a small change in design parameter whereas negative values state the opposite. Sensitivities of process parameters on noise are presented in Table 5. ∂X2/∂A = - 0.29333+ 0.21778A - 0.5244B - 0.4144C ( Eqn. 5) ∂X2/∂B = 2.67556 - 0.7466 B - 0.5244B - 0.52444 C ( Eqn. 6) ∂X2/∂C = 0. 30278- 0.37 C - 0.5244B - 0.4144 A ( Eqn. 7) Optimization of Model 2Response Optimization Parameters Global Solution

A = 3 B = 3 C = 1 Predicted Responses X2=47.7333,Desirability=1.000000,CompositeDesirabiliy=1.000000

Fig 5 : Optimization plot for the Noise of ceiling fan

Parameters Sensitivity

S.N Room size

Rod lengt

h

Knob positi

on ∂X2/∂A ∂X2/∂B ∂X2/∂

C

1 66.5 6.5 2 9.91652 -37.05 -27.99

2 66.5 10.25 3 7.53752 -39.84 -28.36

3 66.5 12 4 6.20652 -41.15 -28.73

4 167.1 6.5 2 31.7532 -89.78 -69.65

5 167.1 10.25 3 29.3742 -92.57 -70.02

6 167.1 12 4 28.0432 -93.88 -70.39

7 355.8 6.5 2 72.6902 -188.6 -147.7

8 355.8 10.25 3 70.3112 -191.4 -148.1

9 355.8 12 4 68.9802 -192.7 -148.4

Goal Lower Target Upper Weigh

t Import

X2 Minimum

48.1 48.1 54.23 1 1

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4. Conclusions In this way it is aimed to predict tendency of noise due to small change in parameters. Positive sensitivity value simply an increment in objective function by small change in design parameter. Where as negative values state the opposite. Table 5 shows sensitivity of room size, fan rod length, and knob position on noise. The small variation of room size causes large changes in noise when room size changes. The results reveal that noise is more sensitive to room size than rod length and knob position. Form optimization it is observed that the ceiling fan noise is minimize by operating the fan at the room size 3level, rod length 3 level and the knob position at level 1.This combination gives the noise of 48.1 DB References [1]Daniel Crichton,Liping Xu,Cesare

A.Hall .Prelimainary Fan Design for a silent Aircraft,Transaction of the ASME 184/vol.129,January 2007.

[2]Dennis H .Shreve, Introduction To Vibration Technology,IRD Mechanalysis,Inc.Colombus,Ohio 43229 Nov1994.

[3]Haroshi KOBAYASHI ,Masaharu KOH,Shunichi OZAKI,Makoto YOKCHI and Takuo SATO -

Developed Adaptive Noise Absorption Control Technology for High Speed Fan Noise Reduction.JSME International Journal.series C,vol.49,Nov.3,2006.

[4]Manasi P.Joshi,E.Ramachandran and N.V.Karanth.Noise and vibration Measurement Techniques in Automotive NVH,Admet 2012 paper No VN 003.

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[6] Son H.Ho.Luis Rosario,Muhammad .Rahman.Thermal Comfort enhancement by using ceiling fan,S.H.Ho et al./Applied Thermal Engineering 29(2009)1648-1656

[7] W.Neise, B.Barsikow , Acoustic similarity laws for fans, Transactions of the ASME.162/Vol.104,May 1982.

[8] W.Neise,Review of Noise Reduction Methods for Centrifugal Fans,Journal of Engineering for industry,May 1982,Vol.104/151.

[9] Kudo T. Development of Noise reduction method for radiator fan of automobilen, Japan’s Socoety of Mechanical Engineeris of Annuaal meeting Lecters collected paper in 2004 ,(7),2004,Pp:75-76.

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