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ScienceDirect Procedía
Engineering
Procedía Engineering 144 (2016) 1102 - 1109
www.elsevier.com/locate/procedia
12th International Conference on Vibration Problems, ICOVP 2015
Design of Experiments For Optimization Of Automotive Suspension System Using Quarter Car Test Rig
Anirban C. Mitraa , Kiranchand G. R.b, Tanushri Sonic, Nilotpal Banerjeed
a Asst. Professor in Mechanical Engg. Dept. M.E.S College of Engineering, Pune-411001, INDIA . bc Undergraduate Scholar, M.E.S College of Engineering, Pune-411001, INDIA.
Professor in Mechanical Engg. Dept .National Institute of Technology, Durgapur-713213, INDIA.
Abstract
The recent years have witnessed an accelerated invention and innovation in suspension design. This project aims at finding the ideal combination of suspension and steering geometry parameters viz. tire pressure (typ), damping coefficient (cs), spring stiffness (ks), sprung mass (m), camber (cma), toe (toe) and wheel speed (N), so that the Ride Comfort (RC) is increased while maintaining an optimal degree of Road Holding (RH) using Design of Experiments. The high R-sq value of 97.70%, R-sq (pred) value of 91.85% and the R-sq (adj) value of 95.81% for RC and the corresponding values of 97.99%, 92.98% and 96.33% respectively for RH show the high reliability and predictability of the experimental models. The experimental models were then validated by executing the optimized set on the test rig with an average accuracy of 80%.
© 2016 The Authors.Publishedby Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).
Peer-reviewunderresponsibilityofthe organizingcommitteeof ICOVP2015
Keywords: Ride Comfort; Road Holding; Design of Experiments; Fractional Factorial
1. Introduction
It is desired that passengers have a comfortable ride as well as a good control over the vehicle. The suspension systems carries the total load of the vehicle and provide comfort to passengers and also delivers a good road holding when the vehicle travels on a rough terrain.
In the work done by P.S. Els et al. it has been found that the spring and damper characteristics required for ride comfort and handling lie on opposite extremes of the design space [1].
* Corresponding author. Tel.: +91-9420320632. E-mail address: amitra@mescoepune.org
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of ICOVP 2015
doi:10.1016/j.proeng.2016.05.071
Ride comfort is dependent on human perception. The ISO 2631-1:1997 standards [2] is used in Europe, the BS 6841 (1987) in UK [3], VDI 2057 [4] is used in Germany and the AAP [5] in USA.
The vibration transferred to the human occupant at the vehicle seat-person interface is measured and a comfort rating is determined based on the above standards. In this paper, ISO 2631-1:1997 standards are followed, which suggest R.M.S. acceleration of sprung mass to be used as a parameter to measure ride comfort.
Road holding is measured by the relative displacement between road and un-sprung mass [6]. For the proper road holding, there should always be a contact between the tire and the road. P.S. Els et al. [1] have stated that ride comfort has been extensively researched but handling has been eluded despite studies pertaining to the topic.
Various researchers have optimized the primary suspension parameters of the passive suspension system by using Genetic Algorithm [7]. A variety of MATLAB simulation and analysis tools and ancillaries have been implemented for the same purpose. Finite Element Methods and Multibody System Dynamics Software have fulfilled specific optimization goals as far as the ride comfort is concerned. Marzbanrad Et al [8] utilized a quarter car model developed in MATLAB and optimized the fundamental variables for ride comfort.
All these researches lack real world credibility as these are based on theoretical models which are prone to human errors and assumptions. Moreover, a variety of other parameters such as the steering geometry inclinations have been proved to have a direct impact on the dynamic behavior and performance of the vehicle [9].
This work aims to optimize ride comfort and road holding by taking all the major variables viz. sprung mass, stiffness, damping rate, tire pressure, camber and toe. Real time data was assimilated from a quarter car test rig and the results were optimized using the statistical Design of Experimentation Methodology.
Nomenclature
RC Ride comfort
RH Road holding
typ Tire Pressure
cma Camber
ks Spring stiffness
cs Damping Coefficient
m Sprung mass
2. Quarter Car Test Rig
To analyze the impact of various parameters on RC and RH, a quarter car test rig was designed and fabricated as shown in Figure 1 and raw data was assimilated with the help of NI Lab VIEW® data acquisition software. Provision has been made for varying camber, toe and different spring-damper combinations.
3. Design Of Experiments
The main motive is to create the objective functions for optimization of two primary responses, namely Ride Comfort (RC in m/s2) and Road Holding (RH in cm) with the six influential parameters viz. sprung mass (m in Kg), camber (cma in degrees), toe (in mm), spring stiffness (ks in N/m), damping coefficient (cs in N-s/m) and tire pressure (typ in psi).
As compared to other methods such as Full Factorial Method, Fractional Factorial Method, Placket-Burman Screens etc., the fractional factorial method can tackle more than four factors, requires very few experimental runs and identifies all the significant terms involved, hence this method has been used for optimization [10]. Resolution IV was chosen for the design as this would estimate the main effects and the two-way interactions, without confounding them with the higher order interactions [11].
Fig. 1. Quarter Car Test Rig
3.1. Data Assimilation
For the purpose of experimentation, a randomized dual-replicate orthogonal matrix, as shown in Table 1 was created in MINITAB® 16 considering the rotational speed of the wheel within blocks and the runs were conducted. Table 1. Observation Table
Replicate 1 Replicate 2
Run N (rpm) typ cma Ks cs toe m -
RC RH RC RH
1 155 35 3 18000 418 10 41 0.48 -1.8 0.45 -1.5
2 155 35 3 26000 673 20 81 0.67 1 0.65 1.2
3 155 35 1 26000 673 10 41 0.8 -1.7 0.72 -1.5
4 155 35 1 18000 418 20 81 1.24 -0.8 1.3 -1.1
5 250 35 3 18000 673 10 81 0.54 -1 0.62 -0.7
6 250 35 3 26000 418 20 41 1.2 -2.5 1.06 -1.8
7 250 35 1 26000 418 10 81 1.7 -2.6 1.5 -2.1
8 250 35 1 18000 673 20 41 1.15 0.6 1.15 0.6
9 155 40 3 26000 418 10 81 1.12 -0.7 1.17 -0.8
10 155 40 1 18000 673 10 81 0.55 -1.3 0.57 -1.2
11 155 40 1 26000 418 20 41 0.9 -0.4 0.82 -0.3
12 155 40 3 18000 673 20 41 0.54 -0.1 0.44 -0.2
13 250 40 1 18000 418 10 41 0.97 1.4 0.91 2
14 250 40 1 26000 673 20 81 1.6 0.2 1.6 0.6
15 250 40 3 26000 673 10 41 0.61 1 0.69 0.7
16 250 40 3 18000 418 20 81 1.75 -2.2 1.75 -2
3.2. Regression analysis
The regression analysis aims to fulfill the following fundamental assumptions for errors [11]:
• Normal distribution.
• Constant variance i.e. homoscedasticity
• The error term has zero mean.
• Uncorrelated errors.
• Approximate linear relationship between the response and the regressors.
The model is analyzed to determine the conformity of these assumptions to avoid any model inadequacies [11]. The first two assumptions of normality and homoscedasticity are conformed by generating the estimated effects on Table 2 and Table 3 of RC and RH.
Table 2. Estimated Effects and Coefficients for RC (coded units)
Term Effect Coef SE coef T P
Const 0.9663 0.01647 58.67 0.000
Blocks -0.1900 0.01647 -11.54 0.000
typ(psi) 0.0225 0.0113 0.01647 0.68 0.502
cma(deg) -0.2150 -0.1075 0.01647 -6.53 0.029
ks (N/m) 0.1250 0.0625 0.01647 3.79 0.000
cs (N-s/m) -0.3575 -0.1787 0.01647 -10.85 0.000
toe (mm) 0.2575 0.1288 0.01647 7.82 0.000
m 0.3150 0.1575 0.01647 9.56 0.000
typ (psi)*cma(deg) 0.2775 0.1388 0.01647 8.42 0.000
typ(psi)*m 0.1700 0.0850 0.01647 5.16 0.000
Table 3. Estimated Effects and Coefficients for RH (coded units)
Term Effect Coef SE coef T P
Const -0.5906 0.04212 -14.02 0.000
Blocks -0.1094 0.04212 -2.60 0.019
typ(psi) 0.7687 0.3844 0.04212 9.12 0.000
cma(deg) -0.2437 -0.1219 0.04212 -2.89 0.010
ks(N/m) -0.0312 -0.0156 0.04212 -0.37 0.715
cs (N-s/m) 0.9687 0.4844 0.04212 11.50 0.000
toe (mm) 0.2937 0.1469 0.04212 3.49 0.003
m -0.5062 -0.2531 0.04212 -6.01 0.000
typ (psi)*cma(deg) -0.4188 -0.2094 0.04212 -4.97 0.000
typ(psi)*m -0.9313 -0.4656 0.04212 -11.05 0.000
typ(psi)*ks(N/m) 0.5187 0.2594 0.04212 6.16 0.000
typ(psi)* cs (N-s/m) -0.6312 -0.3156 0.04212 -7.49 0.000
typ(psi)* Toe mm) -0.9812 -0.4906 0.04212 -11.65 0.000
ks(N/m)* c (N-s/m) 0.6188 0.3094 0.04212 7.34 0.000
ks(N/m)*m 0.9187 0.4594 0.04212 10.91 0.000
Implementing orthogonal design has ensured a significantly low SE Coefficient which is same throughout the separate samples; 0.01647 for RC and 0.04212 for RH. Lower the SE coefficient, higher is the precision with which the model can be predicted; which, for RC is significantly higher than that observed in case of RH.
For a qualitative appraisal, Pareto charts shown in Figure 2 and Figure 3 were generated for RC and RH respectively. It shows insensitive parameters and determines the magnitude and importance of an effect based on the critical-t value of 2.11. Table 2 and Table 3 shows that, tire pressure exhibits a P-value of 0.502 for RC and spring stiffness has a value of 0.715 for RH and thus are insignificant, but can't be removed because of significant interactions. Also the blocks are significant which denotes that speed has a significant influence on both the responses.
Pareto Chart of the Standardized Effects
(response is RC_ms (m/s2), Alpha = 0.05)
Pareto Chart of the Standardized Effects
(response is RH(cm), Alpha = 0.05)
ks(N/m )
ks(N/m) cs(N -s/m)
Standardized Effect
Standardized Effect
Fig. 2. Pareto Chart for RC
Fig. 3. Pareto Chart for RH
After removal of insignificant factors from the model, 'Goodness of Fit' of the regression model is verified by employing quantitative and qualitative methods. The R-Sq value of RC 96.21% and RH 97.99% indicate that the models are properly explained by input variables with 3.79% and 2.11% variation respectively, due to error or by some noise factors; as shown in Table 4.
Table 4. Regression Statistics for RC & RH
Variables
Values for RC
Values for RH
S Standard Deviation 0.238292 0.0931641
PRESS Prediction Sum of Squares 0.34203 0.40399
R-Sq Coeff. of Multiple Determination 97.99% 96.21%
R-Sq (pred) Predicted Coeff. of Determination 92.88% 91.98%
R-Sq (adj) Adjusted Coeff. of Determination 96.33% 94.66%
The small difference between R-Sq and R-Sq (adj) indicates no insignificant terms and that no excess blocking parameters are present in the models. The small values of PRESS of 0.715 for RC and 3.42035 for RH and the R-Sq (pred) value of 91.98% and 92.88% for RC and RH respectively shows the predictability of the model. Model adequacy checking can also be performed easily by graphical analysis of residual plots for RC and RH as shown in Figure 4 and Figure 5 respectively.
Figure 4 & Figure 5 shows that in this model, the Normal probability plot is a straight line with no grouping of data and no outliers, hence shows the normal distribution of residuals over the range which proves the normal distribution of errors. The Residual Vs Fitted plot indicates the homoscedasticity, i.e. residuals must be randomly scattered above and below the mean residual zero line with constant variance [11]. In both plots here, there is no systematic curvature; no major outliers and points are equally distributed with same variance. In the residual vs. order plot, order has no strong trend which indicates the random variation in experimental data.
Fig. 4. Residual Plots for RC
Fig. 5. Residual Plots for RH
3.3. Analysis of variance (ANOVA)
Table 5. Analysis of Variance for RC (m/s2) (coded units)
Source DF Seq SS Adj SS Adj MS F P
Blocks 1 1.15520 1.15520 1.15520 133.09 0.000
Main Effects 6 2.84555 2.84555 0.47426 54.64 0.000
typ(psi) 1 0.00405 0.00405 0.00405 0.47 0.502
cma(deg) 1 0.36980 0.36980 0.36980 42.61 0.000
ks(N/m) 1 0.12500 0.12500 0.12500 14.40 0.001
cs (N-s/m) 1 1.02245 1.02245 1.02245 117.80 0.000
toe (mm) 1 0.53045 0.53045 0.53045 61.11 0.000
m 1 0.79380 0.79380 0.79380 91.46 0.000
2-Way Interactions 0.84725 0.84725 0.42363 48.81 0.000
typ(psi)*cma(deg) 1 0.61605 0.61605 0.61605 70.98 0.000
typ(psi)*m 1 0.23120 0.23120 0.23120 26.64 0.000
Residual Error 22 0.19095 0.19095 0.00868
Lack of Fit 6 0.07515 0.07515 0.01253 1.73 0.178
Pure Error 16 0.11580 0.11580 0.00724
Total 31 5.03895
Table 6. Analysis of Variance for RH (m/s2) (coded units)
Source DF Seq SS Adj SS Adj MS F P
Blocks 1 0.3828 0.3828 0.38281 6.74 0.019
Main Effects 6 15.4594 15.4594 2.57656 45.38 0.000
typ(psi) 1 4.7278 4.7278 4.72781 83.26 0.000
cma(deg) 1 0.4753 0.4753 0.47531 8.37 0.010
ks(N/m) 1 0.0078 0.0078 0.00781 0.14 0.715
cs (N-s/m) 1 7.5078 7.5078 7.50781 132.22 0.000
toe (mm) 1 0.6903 0.6903 0.69031 12.16 0.003
m 1 2.0503 2.0503 2.05031 36.11 0.000
2-Way Interactions 31.1997 31.1997 4.45710 78.49 0.000
typ(ps i)*cm a(deg) 1 1.4028 1.4028 1.40281 24.70 0.000
typ(psi)*ks(N/m) 1 2.1528 2.1528 2.15281 37.91 0.000
typ(psi)*cs (N-s/m) 1 3.1878 3.1878 3.18781 56.14 0.000
typ(psi)*toe (mm) 1 7.7028 7.7028 7.70281 135.65 0.000
typ(psi)*m 1 6.9378 6.9378 6.93781 122.18 0.000
ks(N/m)*cs (N-s/m) 1 3.0628 3.0628 3.06281 53.94 0.000
ks(N/m)*m 1 6.7528 6.7528 6.75281 118.92 0.000
Residual Error 17 0.9653 0.9653 0.05678
Lacks of Fit 1 0.0703 0.0703 0.07031 1.26 0.279
Pure Error 16 0.8950 0.8950 0.05594
Total 31 48.0072
The appropriate procedure for testing the equality of several means is the ANOVA [11] and is depicted in Table 5 and Table 6 for RC and RH respectively. As suggested by the F-value and P-value, rotational speed, which was considered within blocks, is significantly influential. The P-values of lack of fit, 0.178 for RC and 0.279 for RH, shows its insignificance and depicts the fitment and credibility of the models generated. Also the negligible pure error values of 0.00724 and 0.05594 for the RC and RH model respectively indicates that the experimentation is having good reproducibility.
3.4. Regression model
Once, all the assumptions were verified and consolidated, an experimental model explaining the behavioural relationship between all the selected suspension and steering geometry variables are shown in Eq. (1) and (2).
RC = -0.2102(typ)-2.18875(cma) + 1.56250E - 05(ks)-0.00140196(cs)-0.02575(toe)
- 0.055875(m) + 0.05550(typ x cma)+ 0.00170(typ x m)-0.190(n) + 8.61814 (1)
RH = 1.44759(typ) + 3.01875(cma)-0.00165775(ks) + 0.0275858(cs) + 1.50125(toe) + 0.210234(m)-0.08375(typ x cma) + 2.59375E - 05(typ x ks)-9.90196E - 04(typ x cs)
- 0.039250(typ x toe) + 0.00170(typ x m) + 6.06618E - 07(ks x cs) + 5.74219 - 06(ks x m) (2)
- 0.109375(N)- 41.3005
4. Response optimization
To determine the set of optimal variables, a response optimization plot was generated as shown in Figure 6. The objective of this research is to maximize Ride Comfort and Road holding. RC is inversely related to the R.M.S. acceleration of the sprung mass and RH is inversely related to the relative displacement between the wheel center and the main frame. Hence the optimization goals were to minimize R.M.S. acceleration and the displacement, representing the responses.
The individual desirability is calculated for each response on the basis of the weights assigned to each of the responses. These values are combined to determine the composite desirability of the multi response suspension system.
Opbmdl iri 1JDD № [35,0 35,0- inrdi'tt: 1 3,0 3,0 "l.or MN/m) 26000,0 [13000,01 18000,3 csfN-i'm 673.0 673.0 "418.0" toe [mm] 20.0 ID.O "1D.0" ms MJ0 ¿1.0] "41.0
Composite DtairaMy l.OOOO v \
RC_ms (m Minimum 1 = 0,2663 d = 1,0000 _______
RiH(an)
Minimum f — -0.5125 d = 1,0000 ----
Fig. 6. Response optimizer plot
5. Verification of regression model
The Verification test of Regression Model is performed in the Quarter Car Test-Rig for response parameters RC and RH with factors setting as Damping coefficient 673 N-s/m and Spring stiffness 18000 N/m at a Tire pressure of 35 psi with 3 degree positive Camber and a Toe-in of 10 mm supports a Mass of 41 kg. The verification test result is tabulated in Table 7.
Table 7. Verification Test Result of RC and RH
RC from Regression Model RC from Experimentation Accuracy RH from Regression Model RH from Experimentation Accuracy
0.266 m/s2 0.302 m/s2 86.5% -0.513 cm -0.675 cm 70.6%
6. Conclusion
A quarter car test rig was developed to practically evaluate and analyze the influence of the various parameters individually as well as of their interactions, on ride comfort and road holding. Experimental models have been developed for RC &RH which mathematically define the relationship between ride comfort, road holding and a variety of steering geometry and suspension parameters. The model exhibits an R-sq value of 96.21% for RC and 97.99% for RH along with a R-sq (pred) value of 91.98% and 92.88% for RC and RH respectively, which denotes the credibility and predictability of the model over the sample range. Apart from obtaining an optimum set of all the parameters for the respective responses, the flexibility of the response optimizer enables the suspension design engineer to pinpoint upon the near optimal combination for a pre-specified set of variables. This work also helps to demarcate those input variables which have to be granted more attention while designing a suspension system as per their sensitivity.
Acknowledgements
The authors are thankful to the MESCOE-NI LabVIEW Academy Lab, Department of Mechanical Engineering, Modern Education Society's College of Engineering, Pune, INDIA for providing the necessary testing facilities.
References
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