Geometric parameter optimization of magneto-rheological damper using design of experiment technique
- S K Mangal^{1}Email author and
- Ashwani Kumar^{1}
https://doi.org/10.1186/s40712-015-0031-1
© Mangal and Kumar; licensee Springer. 2015
Received: 24 August 2014
Accepted: 26 January 2015
Published: 31 March 2015
Abstract
Background
Magneto-rheological (MR) damper is one of the most promising semi-active devices. The MR dampers offer a reliability of a passive system yet maintain the versatility and adaptability of the fully active control devices.
Methods
In this paper, an optimization process is developed to optimize the geometrical parameters of an MR damper using finite element method (FEM) coupled with Taguchi approach which is rarely available in the literature. The damping force of the MR damper is selected as an objective function. To achieve this objective, 18 FEM models, based on Taguchi orthogonal array, are developed on ANSYS platform.
Results
These results have been analyzed by using the design of experiment (DoE) methodology and an optimized solution is then arrived. The optimal solution is validated experimentally as well as through FEM for 95% confidence level. These results are found to be in good agreement with each other.
Conclusions
This paper establishes that numerical technique results, e.g., FEM, can be used over the real experimental results for the geometric parameter optimization of an MR damper. The proposed methodology will save time and resources for designing an optimized MR damper for automotive and other applications.
Keywords
Optimization Magneto-rheological damper Finite element method Taguchi technique Design of experiment Geometric parametersBackground
Smart materials are the materials having multiple tunable properties. These material properties are significantly altered in a controlled and reversible manner by some external stimuli, e.g., current, electric, or magnetic fields, etc (Ashwani and Mangal 2012). Magneto rheological fluid (MRF) is one of such smart materials. The discovery of the MR fluids is credited to Jacob Rabinow in 1948 at the US National Bureau of Standard (Rabinow 1948). Excellent features of the MRF technology, e.g., fast response, simple interface between electrical power input and mechanical power output, and precise controllability, make it most attractive for many industrial applications. These features have triggered considerable research activities on the modeling and design of MR devices, e.g., dampers, valves, clutches, and brakes, etc. When this technology is employed for an automotive damper, it gives a variable damping coefficient which mainly depends on the intensity of the magnetic field induced. This makes vibration control/isolation effective over a wide frequency spectrum and is more useful in a real practical sense. A typical magneto-rheological damper consists of cylinder, piston, excitation coil, and the MR fluid which is enveloped in a cylinder. The MR valves and dampers are designed analytically (Zhu et al. 2012; Wei et al. 2003) as well as using finite element method (Li and Guo 2003; Parlak et al. 2012). An analytical optimization design method is also proposed (Rosenfield and Werely 2004) for the MR valves and dampers which are based on the assumption of constant magnetic flux density throughout the magnetic circuit. In the analysis (Rosenfield and Werely 2004), it has been assumed that one region of the magnetic circuit does not saturate prematurely. As the valve performance not only depends on the magnetic circuit but also on the geometry of the ducts through which the MR fluid passes, the above assumption has led to a sub-optimal solution. One, thus, can say that the research on optimal design of an MR damper is still in its nascent age.
The objective of this paper is to optimize geometric parameters of an MR damper to have its optimized damping performance. The optimization of the MR damper is based on the design of experiment (using Taguchi methodology) and finite element method which is rarely available in the literature. Based on the critical literature survey, four geometric parameters of the MR damper, which influences the damping force the most are selected. Based on Taguchi methodology, L_{18} orthogonal array (OA) is selected. As the authors have found that the FEM results were in good agreement with the experimental results (Ashwani Kumar et al. 2014; Ashwani and Mangal 2014), the response parameter, i.e., damping force of the MR damper as obtainable by the FEM, is employed in the Taguchi technique in place of the real experimental results. Further, the use of the FEM-based modeling saves the cost of optimization process. The response parameter of these models is analyzed in the ANOVA to get an optimized solution. The confirmation experiment of the optimized MR damper is performed by fabricating the MR damper with optimized geometric parameters as obtained by design of experiment (DoE) analysis. The field-dependent damping force for the optimized damper is determined by the FEM (on ANSYS platform) as well as experimentally. The confirmation experiment on the optimized MR damper is found to have good conformity with the optimal design results for 95% confidence level. The main contribution of this paper is to establish the approach of optimization of the MR damper geometry with the sole objective of maximizing the damping force using DoE technique and finite element analysis. The optimization process proposed here has used the numerical technique results, e.g., FEM over the real experimental results in the optimization process and saved time and resources for designing of an optimized MR damper.
Methods
Modeling and experimental studies of an MR damper
Dimensions of a prototype MR damper
Serial number | Parameter | Dimensions (mm) |
---|---|---|
1 | Pole length (L) | 23 |
2 | Distance between the poles (ℓ) | 22 |
3 | Radius of the piston (R) | 23 |
4 | Piston rod radius (r) | 06 |
5 | Radial distance from piston rod to coil width (H) | 07 |
6 | Clearance between piston and cylinder (h) | 01 |
7 | Thickness of the cylinder (t) | 08 |
Thereafter, using the magnetic flux density as determined in the above modeling, the corresponding values of the yield shear stress is thus determined.
FEM and experimental damping force of an MR damper prototype
Current (A) | Total damping force - FEM model (N) | Total damping force - experimental (N) |
---|---|---|
0.10 | 206.38 | 224.40 |
0.20 | 303.20 | 327.66 |
0.30 | 371.95 | 394.36 |
0.40 | 418.33 | 436.77 |
0.50 | 448.02 | 463.14 |
0.60 | 466.67 | 481.73 |
0.70 | 480.06 | 504.65 |
Based on the above modeling (Ashwani Kumar et al. 2014; Ashwani and Mangal 2014), an MR damper is fabricated of the dimensions as listed in Table 1. The LORD MRF-122EG (www.lord.com) MR fluid is used in the fabricated damper for evaluating its performance (Ashwani Kumar et al. 2014). The input current supplied to the MR damper is varied using Wonder Box kit provided by LORD® Corp. Inc., Cary, USA (www.lord.com). The experimental damping force for different input currents as experienced by the damper is tabulated in the third column of Table 2. These results are found to be matching well with the FEM results.
Results and discussion
Scheme of experiments and optimization
A design based on Taguchi methodology is developed with the objective of maximizing the damping force of the damper. During this optimization process, the values of geometric parameters of the damper that yields the maximum damping force are determined. The geometric parameters are searched between lower and upper bounds.
Selection of orthogonal array and parameter assignment
As listed in Table 1, there are seven basic geometric parameters of an MR damper which affect the magnetic flux density and subsequently the damping force. Based on the exhaustive literature survey, four parameters, which affect the damping force the most, are selected. These four critical geometrical parameters came out as pole length (L), radial distance from piston rod to coil width (H), clearance between piston and cylinder (h), and thickness of the cylinder (t).
Input parameters and their range
Serial number | Parameter | Parameter name | Lower range | Mid range | Upper range |
---|---|---|---|---|---|
Dimensions (mm) | |||||
1 | Pole length (L) | A | 18 | 23 | 28 |
2 | Radial distance from piston rod to coil width (H) | B | 05 | 07 | 09 |
3 | Clearance between piston and cylinder (h) | C | 0.8 | 1.0 | 1.2 |
4 | Thickness of the cylinder (t) | D | 06 | -- | 08 |
The damping force is ideally be determined by conducting real experimental studies for the L_{18} OA. The fabrication and experimental testing of the 18 MR dampers as suggested by L_{18} OA is neither economical (as it increases the cost of experimentation) nor feasible (as it is time consuming). This in turn would have defeated the very basic purpose of obtaining an optimized solution economically. FEM is usually carried out worldwide to reduce the actual experimentation cost. Moreover, the authors have found that the FEM results are in good agreement with the experimental results. Because of the above facts, the FEM result of the MR dampers is used to get the response parameters for the L_{18} OA.
The L _{ 18 } (2 ^{ 1 } * 3 ^{ 7 } ) OA (parameters assigned) with a response parameter
Run | Factors | ||||
---|---|---|---|---|---|
Thickness of cylinder (mm) | Pole length (mm) | Radial distance from piston rod to coil width (mm) | Clearance between piston and cylinder (mm) | Damping force calculated using ANSYS (N) | |
(A) | (B) | (C) | (D) | (Y1) | |
1 | 6 | 18 | 5 | 0.8 | 216.81 |
2 | 6 | 18 | 7 | 1 | 164.11 |
3 | 6 | 18 | 9 | 1.2 | 127.73 |
4 | 6 | 23 | 5 | 0.8 | 262.26 |
5 | 6 | 23 | 7 | 1 | 195.52 |
6 | 6 | 23 | 9 | 1.2 | 150.01 |
7 | 6 | 28 | 5 | 1 | 232.26 |
8 | 6 | 28 | 7 | 1.2 | 183.49 |
9 | 6 | 28 | 9 | 0.8 | 318.92 |
10 | 8 | 18 | 5 | 1.2 | 138.38 |
11 | 8 | 18 | 7 | 0.8 | 213.13 |
12 | 8 | 18 | 9 | 1 | 199.35 |
13 | 8 | 23 | 5 | 1 | 204.34 |
14 | 8 | 23 | 7 | 1.2 | 161.97 |
15 | 8 | 23 | 9 | 0.8 | 298.53 |
16 | 8 | 28 | 5 | 1.2 | 191.52 |
17 | 8 | 28 | 7 | 0.8 | 295.99 |
18 | 8 | 28 | 9 | 1 | 253.58 |
Selection of optimal levels for parameters
ANOVA summary of percentage contribution
Parameter | Term | DOF | Sum of squares | Mean square | Percentage contribution |
---|---|---|---|---|---|
Model | A | 1 | 620.54 | 620.54 | 1.16 |
Model | B | 2 | 14,441.85 | 7,220.92 | 26.97 |
Model | C | 2 | 1,634.83 | 817.41 | 3.05 |
Model | D | 2 | 35,586.23 | 17,793.11 | 66.46 |
Error | E | 2 | 459.28 | 229.64 | 0.86 |
Error | F | 2 | 230.15 | 115.08 | 0.43 |
Error | G | 2 | 155.48 | 77.74 | 0.29 |
Error | H | 2 | 189.71 | 94.85 | 0.35 |
Error | AB | 2 | 225.72 | 112.86 | 0.42 |
Complete ANOVA summary and vital data
Source | Sum of squares | DF | Mean square | F value | Prob > F | |
---|---|---|---|---|---|---|
Model | 52,283.45 | 7 | 7,469.06 | 59.26 | <0.0001 | Significant |
A | 620.54 | 1 | 620.54 | 4.92 | 0.0508 | |
B | 14,441.85 | 2 | 7,220.92 | 57.29 | <0.0001 | |
C | 1,634.83 | 2 | 817.41 | 6.49 | 0.0156 | |
D | 35,586.23 | 2 | 17,793.11 | 141.18 | <0.0001 | |
Residual | 1,260.35 | 10 | 126.03 | |||
Cor total | 53,543.79 | 17 |
Optimized geometric parameters and solution for the MR damper
Serial number | Factor | Dimensions |
---|---|---|
1 | Factor A: thickness of cylinder (t) | 8 mm |
2 | Factor B: pole length (L) | 28 mm |
3 | Factor C: radial distance from piston rod to coil width (H) | 9 mm |
4 | Factor D: clearance between piston and cylinder (h) | 0.8 mm |
5 | Damping force | 321.03 N |
6 | Desirability | 1.00 |
Estimation of optimum performance characteristics
where α is the risk, F _{α} (1, f _{ e }) is the F ratio at the confidence level of (1-α) against DOF, i.e., 17 and error DOF (f _{ e }) 10, N is the total number of results, i.e., 18 (treatment = 18 and repetition = 1), R is the sample size for confirmation experiments, and V _{ e } is the error variance, i.e., 126.03.
Modeling of optimized MR damper
After optimizing the significant MR damper parameters, the FEM modeling and the experimental study are performed and are illustrated in this section.
FEM modeling
Total damping force comparison for the optimized MR damper
Current (A) | Total damping force - FEM model (N) | Total damping force - experimental (N) | Percentage error of experimental results with relation to FEM one |
---|---|---|---|
0.10 | 314.18 | 331.20 | 5.42 |
0.20 | 476.26 | 501.81 | 5.37 |
0.30 | 583.67 | 609.79 | 4.48 |
0.40 | 649.10 | 668.99 | 3.06 |
0.50 | 688.12 | 707.99 | 2.89 |
0.60 | 712.92 | 731.40 | 2.59 |
Experimental testing
Confirmation experiment
Conclusions
In this paper, the optimization of geometric and response parameters of an MR damper using statistical tools coupled with FEM is presented. The geometric parameters are searched between lower and upper bounds having two/three levels for each of these parameters. The FEM models in accordance with Taguchi’s methodology based on orthogonal array (L_{18} OA) are developed on ANSYS platform for the MR damper at 0.1 A. The results are statistically analyzed using ANOVA to determine the optimal geometric parameters. From the ANOVA analysis, it is concluded that the working clearance between piston and cylinder (h) parameter showed the maximum contribution for the damping force while pole length (L) and radial distance from piston rod to coil width (H) parameters are found to have intermediate contribution and the cylinder thickness (t) parameter had the least contribution for the optimization process. The optimized solution of the damper given by the optimization process is tested experimentally as well as through FEM for 95% confidence level at 0.1 A. The results on the optimized damper conformed well to the optimal design results (as given by the DoE). It, thus, validated the proposed model of optimization of damping force for an MR damper.
This paper demonstrates and establishes an optimization of geometric parameters of MR damper using statistical tools, i.e., DoE and FEM results. The proposed method not only saves the time but also the resources for the designing of an optimized MR damper. The process illustrated in this paper will be useful for future automotive design engineers for predicting an optimized damping force of an MR damper.
Declarations
Authors’ Affiliations
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