CHAPTER 6 A STUDY ON DISC BRAKE SQUEAL USING DESIGN OF EXPERIMENTS

134 CHAPTER 6 A STUDY ON DISC BRAKE SQUEAL USING DESIGN OF EXPERIMENTS 6.1 INTRODUCTION In spite of the large amount of research work that has been carried out to solve the squeal problem during the last decades, occurrence of disc brake squeal in practice indicates that there are still many challenges ahead and brake squeal is still a complex phenomenon. This may be due to the fact that brake squeal is influenced by a large number of variables including materials of brake components, geometry of components, component interaction, many operating and environmental condition. If a parametric study is used by changing one-factor-at-a-time to investigate the number of variables, one needs to run large number of FE simulations, as done in the previous chapter. It will be a complicated task involving immense computational effort. Therefore, in order to reduce the computational cost in optimization, in addition to find the interactions of variables, a new combined approach is required by integrating the FE simulation with design of experiments (DOE). Design of experiments is a series of tests in which allowable changes are made to the input variables of a system and the effects on response variables are measured (Montgomery 005). DOE is applicable to both physical processes and computer simulation models. Generally speaking, there are problems with the traditional experimental method of changing one

135 factor at a time, i.e., its inefficiency and its inability to determine effects that are caused by several factors acting in combination. The objectives of DOE used in this work are: 1. To conduct and analyse controlled tests to evaluate the factors that are affecting a response variable.. To specify the particular setting levels of the combinations of factors at which the individual runs in the experiment are to be conducted. 3. To produce a predicted model to detect interactions among the factors, and optimise the brake pads. Products or processes can be treated like a system, if it produces a set of responses for a given set of inputs. Disc brake system can also be treated like a system as shown in Figure 6.1. Systems like disc brake system produce unwanted outputs namely squeal noise for a set of inputs parameters. The present study is aimed at establishing the input-output relationships for prediction of brake squeal. Figure 6.1 Disc brake squeal system

136 There are many types of DOE techniques available as reported by Haftka et al (1998). In the present study, two DOE methods are used as follow: (i) Taguchi method and (ii) response surface method (RSM). In the first section, FE simulations and an experimental design based on the orthogonal array of the Taguchi method are conducted to investigate the influence of material characteristics on the occurrence of squeal. In the subsequent phases, design of experiments with response surface methodology (RSM) is used to develop the input-output relationships of the disc brake system to optimization the brake pad considering various parameters like Young s modulus of the pad back plate, back plate thickness, chamfer of the friction material and different types of slot configurations. 6. TAGUCHI METHOD In the present work, Taguchi method is integrated to find out the significant contributions of the different types of materials and its interaction with other design parameters in reducing the squeal propensity. The disc brake corner consists of a number of components that are made by different types of materials. Influence of assembly components on squeal are being studied and explored by researchers through various methodologies. Of all components disc, pad, caliper and anchor bracket are being widely considered for studies. From the literature and previous works, it is found that different types of materials are employed for manufacturing these components. Hence in the present study, an attempt is made to find out the influences of material selection for the brake components through Taguchi method. 6..1 Description of Taguchi Method Taguchi method is based on design of any system as a three phase program: 1. System design,. Parameter design and 3.Tolerance design.

137 In the system design, a basic functional prototype design is produced depending on engineering knowledge. Since the system design is an initial functional design, it may be far from optimum in terms of quality and cost. Then, the role of parameter design is coming to optimise the settings of the parameter values in order to improve quality characteristics and to identify the product parameter values under the optimal condition. In addition, it is intended that the optimal parameter values obtained from the parameter design are insensitive to the variation of environmental conditions and other noise factors. Finally, the tolerance design is used to determine and analyse tolerances around the optimal settings recommended by the parameter design. The tolerance design is required if the reduced variation obtained by the parameter design does not meet the required product performance (Tarng and Yang 1998). According to Taguchi, all machines or set-up are classified as engineering systems (if it produces a set of responses for a given set of inputs). Those systems can be classified in to two categories. They are: i) Static and ii) Dynamic. The dynamic system has signal factors (input from the end user) in addition to control and noise factors, whereas in static system signal factors are not present. Optimization of materials of disc brake components is a static system shown in Figure 6.1. In this section, parameter design is used to arrive at the optimum levels for types of materials in order to minimize of the squeal occurrence during braking. According to Taguchi, two major tools are employed to achieve any quality goal or any robust design (Phadke 1989). They are: 1. Orthogonal arrays, which are used to study many parameters simultaneously.. Signal -to- Noise ratio (S/N ratio), which measures quality.

138 steps: The parameter design of the Taguchi method includes the following 1. Identify the quality characteristics and parameters to be evaluated.. Determine the number of levels for the parameters and possible interactions between the parameters. 3. Select the appropriate orthogonal array and assign the parameters to the orthogonal array. 4. Conduct the experiments based on the arrangement of the orthogonal array. 5. Analyse the experimental results using the signal-to-noise ratio and statistical analysis of variance. 6. Select the optimal levels of parameters. 7. Verify the optimal parameters through the confirmation experiment. 6.. Selection of Variables and their Levels Based on the detailed literature survey, the disc brake corner consists of a number of components that are made by different types of materials. Of all components the disc, pad, caliper and anchor bracket are important and their design have effects on the squeal generation. To select the optimum materials for the disc brake components for effective reduction of brake squeal, the following parameters are considered for the experiments, as listed in Table 6.1.

139 Table 6.1 Materials parameters and their levels for Taguchi method Factors Friction material (A) Rotor (B) Caliper (C) Anchor bracket (D) Level 1 3 Soft Medium Stiff C/C-Sic Al-MMC Cast iron Aluminum Cast iron Steel Aluminum Cast iron Steel 6..3 Taguchi Design Array The present set of simulations is conducted as per the Taguchi L 9 orthogonal design array to identify the most significant variables by ranking with respect to their relative impact on the squeal occurrence. The L 9 orthogonal array consists of four control parameters at three levels, as shown in Table 6.. Table 6. Design layout using Taguchi L 9 array TEST Friction material (A) Rotor (B) Caliper (C) Anchor bracket (D) 1 1 1 1 1 1 3 1 3 3 3 4 1 3 5 3 1 6 3 1 7 3 1 3 8 3 1 3 9 3 3 1

140 6..4 Signal-to-Noise Ratio In the Taguchi method, the S/N ratio is computed to analyse the deviation between the simulated value and the desired value. Usually, there are three types of quality characteristic in the analysis of the signal-to-noise ratio, (i.e. the lower-the-better, the higher-the-better, and nominal-the-better). Since, the requirement is to minimize the squeal occurrence through selection a proper materials; smaller-the-better quality characteristic is employed. The S/N ratio is given by: 10log( MSD) (6.1) where MSD is the mean-square deviation for the output characteristic. MSD for the smaller-the-better quality characteristic is calculated by the following equation, MSD 1 N n i1 Y i (6.) where Y i is the squeal response for the i th test, n denotes the number of tests and N is the total number of data points. The function -log is a monotonically decreasing one, it means that we should maximize the S/N value. The S/N values are calculated using Equs.6.1 and 6.. Table 6.3, shows the response table for S/N ratios using smaller-the-better approach. Table 6.3 Response table for S/N ratios using smaller-the-better Level A B C D 1 -.6-17.93-17.68-16.31-15.67-15.45-17.7-18.11 3-13.33-17.87-15.87-16.84 Delta 8.93.48 1.85 1.79 Rank 1 3 4

141 6..5 Results of Taguchi Method From the Figure 6. of main effects plot and from Table 6.3 of S/N ratio, it is observed that A3-B-C3-D and A3-B-C3-D3 are the optimum combination for minimum squeal. Similarly, A1-B1-C1-D is the combination for maximum squeal. These combinations are not included in the simulation runs. Hence, additional three confirmation tests are run at these combinations. The results are shown in Table 6.4. Main Effects Plot for Means pad rotor 1 10 8 Mean of Means 6 4 1 1 caliper 3 1 bracket 3 10 8 6 4 1 3 1 3 Figure 6. Main effects plot of the variables on the squeal generation Table 6.4 Verification simulation results Run A B C D S/N ratio Predicted Simulated Difference 1 0.5 C/C-SiC Al CI -4.714 15 16 1 4 Al-MMC Steel Steel -11.498 3.33 3 0.66 3 4 Al-MMC Steel Al -10.34.33 3 0.66 As is seen from the Table 6.4, the predicted results of squeal occurrence using Taguchi method and simulated results from FE model found to be in good agreement. It shows the adequacy of the approach in prediction

14 of the squeal. Figure 6.3, shows the statistics deviation of the number of squeal occurrence in the disc brake system. 0 Simulated Predicted 16 Deviation % 1 8 4 0 1 3 No. of test Figure 6.3 Comparison between predicted and simulated squeal using Taguchi and FE Based on the Taguchi method and S/N ratio, contributions of material components are computed and plotted, as shown in Figure 6.4. It is found that the pad friction material contributes 56% of the total system instability (generation of squeal). It is followed by the rotor material, which contributes % of the system instability. Caliper and bracket materials contribute 11% each. Figure 6.4 Contribution of materials of the brake components

143 6.3 RESPONSE SURFACE METHOD Response surface method (RSM) is considered as one of the most common optimisation methods used in recent years. Many successful attempts are made for improvement of quality and optimisation of products by using these techniques in various spectrums of industries (Thangvavel et al 006, Khuri and Cornell 1996, Myers and Montgomery 003, Myers et al 004, Montgomery 005). In this work, the application of statistical design is conducted to understand the influencing factors of the brake pad on the disc brake squeal noise by integrating finite element simulations with statistical regression techniques. The input-output relationships between the brake squeal and the brake pad geometry is constructed for possible prediction of the squeal using various geometrical configurations of the disc brake. A non-liner mathematical model is developed based on the most influencing factors and the simulation experiment is used to prove its adequacy. In order to reduce CPU time and allowing for more configurations to be computed, the full FE model of the disc brake corner is reduced to a simplified model that consists of disc, pads, piston and paw finger. In this section, a study and the possibility to prevent certain in-plane mode at unstable frequency.77 khz which causes the occurrence of squeal for the three models, as shown in Table 6.5. It is described that the rotor and brake pads are the main components contribution to produce squeal at unstable frequency.77 khz. Therefore, a more detailed description of the influence of pad structural modifications on reducing squeal using DOE is given in the following sections.

144 Table 6.5 Unstable frequency at.77 khz for three FE models Model no. FE models In-plane mode shape 1 Disc brake assembly and steering knuckle assembly (Brake corner model) Disc brake assembly without steering knuckle assembly (brake assembly model) 3 Disc, pads, piston and paw finger (simplified brake model) 6.3.1 RSM Methodology Disc brake squeal is dependent upon number of control factors. These factors can be broadly classified into two categories. They are: i) Fixed factors and ii) Variable factors.

145 The fixed factors are factors in the disc brake system, which requires to be kept unchanged. These factors are very hard to change or rather not possible to change once the simulation is made for a particular structural modification. The variable factors can be varied to improve and achieve the desired results in the squeal performance. In order to arrive at the most influential variables and its effects, a two phase strategies is adopted. In the first phase, initial screening with various variables is taken up. Fractional factorial design (FFD) of experiments is conducted to identify the most influential variables. Subsequently, in the second phase, central composite design (CCD) based Response surface methodology (RSM) is deployed to develop a non-linear model for the prediction of disc brake squeal. Furthermore, a statistical analysis of variance (ANOVA) is performed to find out which parameters are statistically significant. The optimal combination of the parameters can then be predicted, based on the above analysis. Finally, a confirmation experiment is conducted to verify the optimal parameters obtained from the parameter design. 6.3.1.1 Setting up of fixed factors Squeal in brake system is relatively complex. Inputs (both fixed and variable factors) affect the output. The disc brake system in abstract form is shown in Figure 6.1. For the present work, factors like the hydraulic pressure, rotational velocity of the disc, friction coefficient at the contact interactions between the brake components and the materials and geometry of the disc brake components are kept constant and the brake pads under these conditions will be optimized.

146 6.3.1. Selection of controllable factors Based on the literature survey and discussions with service engineers, six controllable factors are taken up for initial screening. They are listed in the Table 6.6 and discussed in the following sections. i) Variation of Young s modulus of back plate. The Young s modulus of the back plate is a critical variable and various researchers have attempted (Liu et al 007) variation in the Young s modulus value. In this study, Young s modulus is varied between 190 GPa and 0 GPa. ii) Variation of back plates thickness. Commonly used back plate thickness is about 5 mm for the type of the brake system under study. In order to understand the effects of back plate thickness, it is varied between 3.5 mm and 6.5 mm. iii) Variation of the chamfer size The original pads for the commercial brake did not contain any chamfer. During the literature survey, this parameter is found to contribute to a certain extent to the squeal (Dai and Lim 008, Dunlap et al 1999). Hence, an angle of 45º is provided on both sides of the friction material and the size of chamfer is varied between 4 mm and 8 mm. iv) Slots configurations on the pad In this study, a double slot configuration is considered, as shown in Figure 6.5. This configuration has three variables. They are the slot width, slot angle or orientation and the distance between the two slots. The slot width is

147 varied between 1 mm and 3 mm. The slot angle/orientation is altered between 5º and 15º. The distance between the slots is varied between 30 mm and 50 mm. Figure 6.5 Various factors of the brake pad geometry 6.3.1.3 First Phase: Screening FFD of experiments If any experiment involves the study of the effects of two or more factors, then factorial designs are more efficient than one-factor-at-a-time experiments. Furthermore, a factorial design is necessary when interactions may be present and to avoid misleading conclusions (Montgomery, 005). In a full factorial experiment, responses are measured at all combinations of the factor levels, which may result in a large number of runs. In this case, a twolevel full factorial design with eight factors requires 64 runs. Hence, for initial screening, fractional factorial design is used. The minimum fractional factorial design for a two-level of six factors is 1/8 th of the full factorial designs i.e. 8 runs. Therefore, in the first phase, an L8 FFD array is used for

148 screening. Parameters used for the initial screening and its levels are indicated in Table 6.6. Table 6.6 Initial screening parameters and their levels Factor Level Coded Uncoded Units Low High A Back plate Young s modulus GPa 190 0 B Back plate thickness mm 3.5 6.5 C Friction material chamfer mm 4 8 D Slot width mm 1 3 E Distance between slots mm 30 50 F Slot angle Deg. 5 15 A total number of eight trials are conducted and the positive real part is predicted for each case. The recorded positive real parts of the complex eigenvalues along with FFD array is tabulated in Table 6.7. FFD results are analysed and the Pareto chart of the effects is plotted to determine the magnitude and the importance of the effects Figure 6.6. It displays the absolute values of the effects of each factor. Main effects plot shown in Figure 6.7 also confirms the contributions of the factors considered. The y- axis and the x-axis in the Figure 6.7 represent the positive real value and the levels of the variables respectively. From the main effects plot, it can be inferred that, the back plate Young s modulus, chamfering, slot distance and slot angle are found to be the most significant parameters on squeal. On the other hand, slot width and back plate thickness are less significant. Hence, in the second investigation, the four most influential variables are short-listed for subsequent studies.

149 Table 6.7 L8 Initial FFD array and measured real parts Run A B C D E F Real Part 1 190 3.5 4 3 50 15 1.0 0 3.5 4 1 30 15 14.90 3 190 6.5 4 1 50 5 3.00 4 0 6.5 4 3 30 5 18.15 5 190 3.5 8 3 30 5 16.89 6 0 3.5 8 1 50 5 5.1 7 190 6.5 8 1 30 15 14.85 8 0 6.5 8 3 50 15 4.0 Figure 6.6 Pareto chart of effects of initial screening

150 Figure 6.7 Main effects of factors 6.3.1.4 Second Phase: RSM -CCD of Experiments CCD is one of the most important experimental designs used for optimizing parameters. CCD is nothing but k factorial design augmented with centre points and axial points. CCD is far more efficient than running 3 k factorial design with quantitative factors (Montgomery 005). Hence CCD approach is selected for the present study. In light of the screening experiments, a decision is taken to study the effects of the top four factors, namely; Young s modulus of the pad back plate, chamfer, and slot angle and distance between two slots. The variables and their levels are listed in Table 6.8. The CCD of experiments for four factors consists of the following: 1. Full factorial design for the four factors ( 4 ). one centre point runs

151 3. Eight axial points with value. The value is the distance between centre point and some additional axial points to fit a non-linear curve. A second order polynomial equation is developed to study the effects of the variables on the positive real part as the following. ' Let f (y) be the true physical response function and f ( y) be its approximated function using the second order polynomials. The general form of the second order polynomial equation is as follows: m m m1 m ' 0 i i ii i ij i j i 1 i 1 i 1 j i1 f Y A Ax Ax Axx (6.3) where m is the total number of variables, x i is the i th design variable and the A o, A i are the unknown coefficients. For n sampling of design variables x ki (k = 1,, n ; i = 1,, m) and the corresponding function values f k (k = 1,, n), Equation 6.3 leads to n equations as given below; m m m1 m 1 0 i 1i ii 1i ij 1i 1j i 1 i 1 i 1 j i1 f A Ax Ax Axx m m m1 m 0 i i ii i ij i j i 1 i 1 i 1 j i1 f A Ax Ax Ax x m m m1 m n 0 i ni ii ni ij ni nj i 1 i 1 i 1 j i1 f A Ax Ax Axx,., (6.4) The above equation contains linear terms, squared terms and interaction terms. Equation 6.4 can be rewritten in matrix form as T T f A X b X CX (6.5) 0

15 where X T = (x 1, x,... x n ), b = (6.6) ( 1 A n A, A,... ) T and C is the symmetric matrix C 1 1 A11 A1.. A1 n 1 1 A1 A.. A n.......... 1 1 A 1 A n A n nn (6.6) Equation (6.4) will be differentiated with respect to X and equated to zero in order to obtain different unknown coefficients of the second-order polynomial equation. Table 6.8 Coded levels of variable and actual values for CCD Factor Level Coded Uncoded Units Low High A Back plate Young s modulus GPa 190 0 C Friction material chamfer mm 4 8 E Distance between slots mm 30 50 F Angle of slots Deg. 5 15 A total number of twenty five trials are conducted and a set of data is collected as per the structure of CCD of experiments. Table 6.9 lists the experimental results. A significance test is conducted to examine the effects of different parameters and their interaction terms on the positive real parts. Table 6.10 shows the estimated coefficients for the positive real parts.

153 Table 6.9 Simulated experimental results of CCD Run A C E F Real Part 1 190 4 30 5 31.1 0 4 30 5 19.33 3 190 9 30 5 18.53 4 0 9 30 5 8.00 5 190 4 50 5.37 6 0 4 50 5 17.00 7 190 9 50 5 1.10 8 0 9 50 5 4.87 9 190 4 30 15 7.3 10 0 4 30 15 13.80 11 190 9 30 15 13.76 1 0 9 30 15 7.00 13 190 4 50 15 0.90 14 0 4 50 15 11.78 15 190 9 50 15 8.54 16 0 9 50 15 4.1 17 170 7 40 10 9.00 18 50 7 40 10 11.00 19 10 3 40 10 13.90 0 10 11 40 10.00 1 10 7 0 10 14.50 10 7 60 10 11.33 3 10 7 40 0 17.00 4 10 7 40 0 9.00 5 10 7 40 10 8.00

154 Table 6.10 Estimated regression coefficient for the real parts Term Coeff SE Coeff T P Constant 554.413 66.6846 8.314 0.000 A -3.958 0.5164-7.665 0.000 C -7.778.758 -.80 0.018 E -3.08 0.709-4.70 0.00 F -1.980 1.831-1.543 0.154 A*A 0.008 0.001 6.498 0.000 C*C 0.081 0.116 0.71 0.488 E*E 0.014 0.0049.950 0.015 F*F 0.058 0.0194.994 0.013 A*C 0.00 0.011 1.781 0.105 A*E 0.008 0.008.76 0.00 A*F 0.000 0.0056 0.061 0.953 C*E 0.008 0.0170 0.46 0.654 C*F 0.08 0.0339 0.819 0.43 E*F 0.005 0.0085 0.614 0.553 The terms used in the Table 6.10 are as follows. The term coeff stands for coefficients used in the regression equation for representing relationships between the positive real parts of the complex eigenvalues and the various factors. The term SE coeff stands for the standard error for the estimated coefficients, which measures the precision of the estimates. The term T values are calculated as the ratio of corresponding value under coefficient and standard error. The T value of the independent variable can be used to test whether the predictor significantly predicts the response. The P value determines the appropriateness of rejecting the null hypothesis in a hypothesis test. The P-values range from 0 to 1. The P-values less than 0.05 indicate that the corresponding model terms are significant.

155 In this present study, A, C, E, A, E, F and AE are significant model terms to the response real value. It can be observed that, though the term C is significant its square term is found to be insignificant. It indicates that, C s relationship could be linear in nature. Figure 6.8 (a) to 6.8 (f) show the 3D surface plots for the response real parts. (a) (b) (c) (d) (e) (f) Figure 6.8 3D Surface plots for the response (positive real value)

156 The following observations can be made from the surface plots: 1. From Figure 6.8 (a), it is observed that increasing Young s modulus in combination with increasing chamfer decreases positive real value.. It is observed from Figure 6.8 (b) that, as the distance between two slots are closer with increased Young s modulus reduces the positive real value. 3. From Figure 6.8(c), it is found that increasing Young s modulus of the back plate in combination with reducing angle of slot lead to decrease positive real value. 4. It is observed from Figure 6.8 (d) that, as the chamfer increases the positive real value reduces. On the other hand, as the angle in combination with increasing chamfer causes the positive real value tend to be nonlinear. 5. From Figure 6.8 (e), it can be observed that increased chamfer value have significant effect on reducing real part but its interaction with slot distance causes the positive real value to behave non-linearly. Also from Figure 6.8 (f), it is found that interaction between slot angle and slot distance causes the positive real value to exhibit nonlinear. 6.3.1.5 Analysis Of Variance (ANOVA) This method is used to pinpoint the sources of variation from one or more possible factors. It helps determine whether the variations are due to variability between or within methods. The within-method variations are variations due to individual variation within treatment groups, whereas the

157 between-method variations are due to differences between the methods. In other words, it helps assess the sources of variation that can be linked to the independent variables and determine how those variables interact and affect the predicted variable. The ANOVA is based on the following assumptions: The treatment data must be normally distributed. The variance must be the same for all treatments. All samples are randomly selected. All the samples are independent. ANOVA is a statistical technique, which can infer some important conclusions based on analysis of the experimental data. The method is very useful to reveal the level of significance of the effect of factor(s) or interaction of factors on a particular response. It can be used to check the fitness of the model and to identify the significance of input variables. The F statistic, multiple regression coefficients (R and Adj R ) and root mean square error (RMSE) are the other major statistical parameters usually employed to check and validate the model s ability for navigation and prediction (Wang 008). Computational equations for the above statistics are given below: SST ( fi f ) (6.7) i1 ' n E ( i i ) i1 SS f f (6.8) where SS T is the total sum of squares SS E is the sum of square errors f i is the measured function value at the i th design point

158 f is the mean value fi ' f i is the measured function value calculated from the polynomial at the i th design point F ( SS SS )/ df SS E/ dfe T E m (6.9) where df m and df e are the degrees of freedom of model and error respectively and it can be calculated as given under df Number of non-constant terms (6.10) m df n df 1 (6.11) e m R SSE 1 SS T (6.1) R n 1 1 1 adj R dfe (6.13) RMSE SS df E e (6.14) Larger the values of R and R adj and the smaller the value of RMSE, the better the fit. If the number of design variables is large, it is more appropriate to look at R adj. It is because; as the number of model terms increases R increases whereas R adj actually decreases, if unwanted terms are added to the model (Montegomery 007). In addition to these statistical tests, the accuracy of the prediction model can also be assessed by computing prediction error sum of squares (PRESS) and R for prediction (R prediction). The PRESS and R prediction are calculated by the Equations 6.15 and 6.16.

159 ' n ( i () i ) i1 PRESS f f (6.15) R prediction 1 PRESS SS T (6.16) where ' f (i) is the predicted value at the i th design point using the model created by (n -1) design points that exclude the i th point. ANOVA is performed to test the significance of the factors as per the Table 6.11. Table 6.11 ANOVA for real parts Source DF Seq SS Adj SS Adj MS F P-value (Prob > F) Regression 14 1378.5 1378.51 98.4465 33.78 0.000 Linear 4 116.66 173.047 43.617 14.85 0.000 Square 4 180.5 176.816 44.040 15.17 0.000 Interaction 6 35.34 35.343 5.8906.0 0.155 Residual Error 10 9.14 9.14.914 Total 4 1407.39 Different terms used in the Table 6.11 are as follows. The term DF means degrees of freedom, refers to the number of terms that will contribute to the error prediction. The term Seq SS represents the sum of squares for each term, which measures the variability in the data contributed by the term. The term Adj SS means adjusted sum of squares after removing insignificant terms from the model. The Model F-value of 33.78 implies the model is significant. The values of "Prob > F" less than 0.05 indicate model terms are significant. Figure 6.9 shows the normal probability plot of residuals. It shows that there is no abnormality in the methodology adopted (R = 0.9793). The

160 R analysis is tabulated in Table 6.1. The "Pred R-Squared" of 0.8738 is in reasonable agreement with the "Adj R-Squared" of 0.9503. The statistical analysis shows that, the developed non-linear model based on central composite design is statistically adequate and can be used to navigate the design space. Figure 6.9 Normal probability plot for residuals Table 6.1 R analysis Std. Dev. 1.70711 PRESS 177.677 R-Squared 0.9793 Adj R-Squared 0.9503 Pred R-Squared 0.8738 form is given under: The response equation for positive real part (RP) value in coded

161 RP 554.413-3.958A 7.778C - 3.08E -1.980F 0.008A 0.081C 0.014E 0.058F 0.00AC 0.008AE 0.0003AF 0.008CE 0.08CF 0.005EF (6.9) 6.3.1.6 Testing of model The model is statistically validated as explained above. Performance of the developed model is also tested on randomly generated 17 test runs. Table 6.13 gives the factor settings, predicted responses, actual real parts from simulation and percentage deviation for each run. Table 6.13 Comparison between predicted versus actual simulation Runs A C E F Actual Predicted % Deviation 1 00 6 45 7 14.1 13.7 6.65 05 8 35 1 6.79 7.66-1.88 3 00 7 45 11 9.68 9.33 3.65 4 195 8 40 7 11.31 11.81-4.4 5 195 7 40 10 14.3 1.4 1.69 6 05 6 35 1 10.56 11.58-9.69 7 05 6 40 7 13.1 1.4 5.17 8 195 8 35 11 10.89 11.71-7.53 9 00 6 35 7 17. 15.81 8.10 10 0 6 35 10 9.11 8.67 4.88 11 00 8 45 10 8.46 7.63 9.79 1 195 6 45 8 13.1 14.58-10.39 13 10 7 45 8 8.51 7.9 6.88 14 195 6 40 13 13.65 14.08-3.16 15 15 8 40 13 5.15 4.50 1.69 16 195 7 35 9 16.31 14.56 10.73 17 195 8 45 13 7.9 9.03-14.01 Deviation % = [(actual value - predicted value)/ actual value] 100 Figure 6.10 shows the graphical presentation of predicted versus actual simulation. The best fit line plot of the 17 points is found to be close to

16 the ideal 45 slope line, as shown in Figure 6.11. Predicted responses show good agreement with actual results. Figure 6.1 shows the percentage deviation plot. The average absolute percentage deviation is found to be 8.4. Actual results varied between 1.69 % and -14.01% from predicted response. This indicates that designed model space can be navigated for prediction. 0 Predicted Simulated 16 Real value 1 8 4 0 1 3 4 5 6 7 8 9 10 11 1 13 14 15 16 17 No. of Tests Figure 6.10 Predicted versus actual simulation 18 16 14 Predicted 1 10 8 6 4 4 6 8 10 1 14 16 18 Simulated Figure 6.11 The best fit line plot

163 15 10 Deviation (%) 5 0-5 -10-15 1 3 4 5 6 7 8 9 10 11 1 13 14 15 16 17 No. of Tests Figure 6.1 Percentage deviations between predicted and simulated results 6.4 CONCLUDING REMARKS In this chapter, a new methodology for evaluation of different types of materials used in practice for manufacturing disc brake components are examined to reduce squeal generation. The stability analysis using complex eigenvalue analysis is integrated with Taguchi approach to find out the contributions of several types of materials and its interaction effects for effective reduction of brake squeal. The results show that the most significant improvements in brake squeal performance could be achieved by using combination of rotor material from Al MMC, cast iron caliper and friction material with elastic properties.6 GPa. It is also seen that the pad friction material is the most significant materials that has a significant effect on brake squeal. Non-linear mathematical model for the real value based on central composite design of experiments is successfully developed. The inputoutput relationship between the brake squeal and the brake pad geometry is constructed for possible prediction of the squeal using various geometrical

164 configurations of the brake pad. Influences of the various factors namely; Young s modulus of back plate, back plate thickness, chamfer, distance between two slots, slot width and angle of slot are investigated using DOE technique. A mathematical prediction model has been developed based on the most influencing factors and the validation using simulation experiments proved its adequacy. Deviations between predicted and actual simulation results are found to be within ±15%. It shows reasonable agreement and also the adequacy of the developed model in prediction. Though these investigations are predominantly for the disc brake squeal, it can also be extended to other issues. By applying this methodology, while designing brake system, corrective and iterative design steps can be initiated and implemented for betterment of component design. The proposed methodology will also remove unexpected problems during the system deployment.