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Optimal hydraulic engine mount parameters using design of experiment (DoE) and response surface methodology

  • Dr. Zeliha Kamış Kocabıçak received her PhD degree in Mechanical Engineering from Bursa Uludağ University. She is now an associate professor at the Department of Automotive Engineering at Bursa Uludağ University. Her research interests are vehicle dynamics, mechatronic systems, electromechanical systems, automatic control, and system dynamics.

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    Zafer Açar received his Master degree in Automotive Engineering from Bursa Uludağ University, Turkey. His research interests include hydraulic engine mounts.
Published/Copyright: March 6, 2025
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Materials Testing
From the journal Materials Testing Volume 67 Issue 4

Abstract

This study experimentally investigated the parameters such as dynamic hardening, inertia track cross-sectional area, decoupler hardness, and fluid volume affecting the damping properties of passive hydraulic engine mounts. Two levels were determined for these parameters, and the full factorial design of experiment (DoE) was created. According to the DoE, hydraulic engine mounts with various design configurations were assembled and tested. Based on the test results, a response surface was created in the Hyperstudy software, and the optimal parameters were obtained via the surface for the desired hydraulic mount performance. Another mount close to the optimum design configuration was then analyzed by the Hyperstudy, and the analysis results were confirmed with the test results. It was observed that the experimental and analysis results were consistent. As a result, it has been demonstrated that the mount parameters can be decided with the response surface generated with the DoE. So, both time and cost advantages can be achieved by eliminating trial and error in production.

Keywords: damping properties; design of experiment; design parameters; dynamic stiffness; phase angle; response surface

1 Introduction

The vehicle engine-chassis-body system is subjected to unwanted vibrations from the engine, the road, and the wheels. Engine mounts play an essential role in dampening vibrations while supporting the engine weight, and thus, they increase ride comfort. Small amplitude vibrations occur at high frequencies due to engine oscillation, while higher amplitude vibrations occur at low frequencies due to idling of the engine, rough road conditions, and sudden acceleration. The engine mount should be stiff and have high damping properties to control higher amplitude vibrations. However, a low-damping mount is required for small amplitude vibration isolation and acoustic comfort. The engine mount must satisfy these two conflicting criteria [1], [2].

Engine mounts typically consist of rubber–metal combinations and have various structural designs for engine types and applications. They are classified into four categories: conventional rubber mounts, hydraulic mounts, semi-active mounts, and active mounts [3]. The most commonly used are hydraulic engine mounts, as conventional mounts are insufficient for damping, and semi-active and active mounts have complex structures and high-cost design processes. Hydraulic engine mounts have variable damping properties in different frequencies, thus ensuring driving comfort. In these mounts, high damping is provided by the inertia track for low-frequency and large-amplitude vibrations, while low damping is provided by the decoupler for high-frequency and small-amplitude vibrations [1], [2].

Many studies have been done in the literature on modeling, designing, and optimizing hydraulic engine mounts for years. In modeling studies, linear and nonlinear model approaches were generally used to obtain the dynamic behavior of hydraulic engine mounts. Design studies were often carried out together with modeling and optimization [1], [4], [5], [6], [7]. As the decoupler is an essential part of the hydraulic engine mounts, there are also studies on it [8], [9]. Optimization studies aimed to improve vehicle driving comfort [10], [11], [12] and damping properties of the mount at specific frequencies [4], [13], [14], [15]. Various methods were utilized, including artificial life algorithms (EALA) [13], sequential quadratic programming (SQP) [15], root mean square (RMS) [14], and random vibration methods [11] in optimization. The DoE applications of hydraulic engine mounts and their assembly are available in the literature [16], [17]. Kocabicak and Acar [17] applied Taguchi-based grey relational analysis to determine the design parameters of a hydraulic engine mount for the low-frequency region. However, no study has been reported yet to optimize mount parameters with response surface using DoE considering both low and high-frequency regions.

In this paper, four parameters affecting the damping properties of hydraulic engine mounts were investigated. These parameters are the inertia track cross-sectional area, the fluid volume, the decoupler hardness, and the dynamic hardening of the rubber. The full factorial design of experiment (DoE) method was applied for these parameters, considering two levels. As a result of four parameters and two levels, 16 different mounts were assembled, and these mounts were tested by applying high and low amplitude vibrations. The peak dynamic stiffness Kd1 and phase angle φ and their frequencies in the frequency range of 0–30 Hz for a vibration amplitude of ±1.5 mm, and the dynamic stiffness Kd2 at 50 Hz frequency for a vibration amplitude of ±0.1 mm were determined in these tests. Another mount with a larger cross-sectional area and a larger fluid volume was tested to expand the response surface, and the results were added to the DoE. Response surface-based design optimization was performed in the Hyperstudy using data for 17 mounts, and the optimum design configuration was derived. After that, a hydraulic engine mount close to the optimal parameters was experimentally tested and analyzed in Hyperstudy. The analysis results were confirmed by the test results. This study offers innovation in including the DoE application and the response surface methodology to determine optimal design parameters for hydraulic engine mounts.

2 Hydraulic engine mount

Hydraulic engine mounts are widely used in engine suspension systems. Although they have different structural designs, their functions are similar. Unlike traditional rubber–metal combination mounts, hydraulic engine mounts use hydraulic fluid, generally a mixture of ethylene glycol and antifreeze, in two chambers at the bottom and top. A decoupler acts as a floating element between the chambers. An upper rubber, which carries the static load of the engine and acts as a piston, pumps the fluid from the upper chamber to the lower chamber (see Figure 1) [1], [17].

Figure 1: Hydraulic engine mount.
Figure 1:

Hydraulic engine mount.

The stiffness and damping characteristics of hydraulic engine mounts can vary with excitation frequencies and amplitudes. In low-amplitude impulses from the engine, the free decoupler only travels within the travel gap, so most of the fluid passes through the lower resistance decoupler. In high-amplitude impulses from the road or the engine at idle, the traveling distance of the free decoupler may exceed its travel gap, so the fluid follows the inertia track with higher resistance. In summary, the decoupler provides low damping, while the inertia track provides high damping. Therefore, the decoupler and the inertia track for the hydraulic engine mount are quite effective [1], [14].

3 Experimental tests and design of experiment (DoE)

In this study, hydraulic engine mounts were tested by MTS 831.50 servohydraulic elastomer testing device with 1,000 Hz frequency capacity (see Figure 2). In this study, static and dynamic characteristics were experimentally determined by the device for the DoE.

Figure 2: MTS 831.50 servohydraulic elastomer testing device [17], [18].
Figure 2:

MTS 831.50 servohydraulic elastomer testing device [17], [18].

3.1 Dynamic hardening

Two various rubbers were used in the design configurations of hydraulic engine mounts, and the dynamic hardenings of these rubbers were determined for the DoE. So, two disc-shaped rubber samples with a diameter of 29 mm and a thickness of 12.5 mm were produced, and the static and dynamic stiffnesses of the samples were experimentally obtained to determine dynamic hardenings.

Static stiffness is the resistance ability of rubbers under static or constant loads and expresses the relationship between the applied force and the resulting displacement. In this study, static tests were carried out at a constant speed of 10 mm/min, and force–displacement curves were obtained by compressing the samples in the range of 0–3 mm (see Figure 3). The slope of these curves was determined as the static stiffness [18].

Figure 3: Static characteristics for rubber discs.
Figure 3:

Static characteristics for rubber discs.

Dynamic stiffness is the ability of the mount to resist a dynamic load, and phase angle expresses the inelastic behavior of a material, measuring the energy loss. In rubbers, the dynamic stiffness and phase angle varies with the frequency. The phase angle is an important parameter to determine the amount of energy absorption during a vibration or oscillation. As the phase angle increases, the damping ratio of the mount also increases [17], [19]. In this study, dynamic stiffness was obtained by the MTS 831.50 servohydraulic elastomer testing device to determine the dynamic hardening. The disc samples were compressed 2 mm and subjected to ±0.2 mm vibration in the 1–30 Hz frequency range. The dynamic stiffness corresponding to the 30 Hz frequency was accepted as the reference value (see Figure 4).

Figure 4: Dynamic characteristics for rubber discs.
Figure 4:

Dynamic characteristics for rubber discs.

There is a relationship between static stiffness and dynamic stiffness, referred to as dynamic hardening. The dynamic hardening is always greater than 1. Static and dynamic stiffnesses and dynamic hardening can be respectively expressed as follows:

(1) K s = Δ F s Δ x s

(2) K d = Δ F d Δ x d

(3) η = K d K s

with: Ks, Kd: static and dynamic stiffness (N mm−1), η: dynamic hardening, Δxs, Δxd: displacement under static and dynamic force (mm), ΔFs, ΔFd: static and dynamic force (N).

The static stiffness, dynamic stiffness, and dynamic hardening values were obtained from Figures 3 and 4 using Equations (1)–(3) for two different rubbers using disc-shaped samples, as given in Table 1.

Table 1:

Rubber parameters.

Parameters Defining parameters Rubber 1 Rubber 2
Ks (N mm−1) Static stiffness 314 302
Kd (N mm−1) Dynamic stiffness 525 663
η Dynamic hardening 1.7 2.2

3.2 Design of experiment (DoE)

Design of experiment (DoE) is a systematic method to determine the relationship between factors and the output of a system. It provides an advantage as a method that reduces experimental costs in a shorter time [20], [21]. In this study, DoE was used to obtain the optimal hydraulic engine mount parameters. So, the dynamic hardening, the inertia track cross-sectional area, the decoupler hardness, and the fluid volume were considered as the design parameters. For each parameter, two levels were determined considering the manufacturability of the mount components (see Table 2).

Table 2:

DoE parameters and levels.

Parameters Defining parameters Level 1 Level 2
η Dynamic hardening 1.7 2.2
A (mm2) Inertia track cross-sectional area 37.5 66.5
HSd (shA) Decoupler hardness 50 58
V (mm³) Fluid volume 22,256 44,512

This research aims to find the optimum design parameters of a hydraulic engine mount, considering all possible combinations for four factors and two levels (2ˆ4) using a full factorial DoE method. The first 16 rows of Table 3 were created according to the full factorial DoE method. Additionally, the parameters of another existing hydraulic engine mount with a larger inertia track cross-sectional area and fluid volume were also added to Table 3 as the 17th row for a larger response surface. All mounts in Table 3 were tested on the test device, and test results were used to optimize the design parameters of hydraulic engine mounts.

Table 3:

Full factorial DoE table for hydraulic engine mount parameters.

Experiment no η (−) A (mm2) HSd (shA) V (mm³)
1 2.2 37.5 58 22,256
2 1.7 66.5 58 22,256
3 2.2 37.5 58 44,512
4 2.2 37.5 50 44,512
5 2.2 66.5 50 44,512
6 2.2 37.5 50 22,256
7 2.2 66.5 58 44,512
8 1.7 66.5 50 44,512
9 1.7 66.5 50 22,256
10 2.2 66.5 50 22,256
11 1.7 37.5 50 44,512
12 1.7 37.5 50 22,256
13 1.7 37.5 58 22,256
14 2.2 66.5 58 22,256
15 1.7 37.5 58 44,512
16 1.7 66.5 58 44,512
17 1.8 79.5 50 51,223

4 Results and discussion

4.1 Test results

Hydraulic engine mounts in Table 3 were tested on the MTS 831.50 servohydraulic elastomer testing device under the test conditions given in Table 4. Dynamic stiffness (Kd) and phase angle (φ) values were obtained based on frequency, and frequency-dependent Kd and φ graphs were created. These results for Experiment No: 1 are given in Figure 5 for the Test 1 condition and Figure 6 for the Test 2 condition. The results obtained in other experiments also have similar characteristics [17], [18].

Table 4:

Test conditions.

Test 1 Test 2
Amplitude (mm) ±1.5 ±0.1
Preload (N) 750 750
Frequency (Hz) 1–30 1–50
Figure 5: Dynamic stiffness and phase angle in Test 1 (Experiment no: 1).
Figure 5:

Dynamic stiffness and phase angle in Test 1 (Experiment no: 1).

Figure 6: Dynamic stiffness in Test 2 (Experiment no: 1).
Figure 6:

Dynamic stiffness in Test 2 (Experiment no: 1).

In the low frequency-high amplitude Test 1 conditions, the displacement of the mount and the fluid flow in the inertia track are in the same phase up to a specific frequency value (f0) when the decoupler is closed, as shown in Figure 5. Therefore, the fluid passes through the inertia track from the upper chamber to the lower chamber. However, as the frequency increases, the fluid moving through the inertia track creates extra damping, and thus, the dynamic stiffness rises until it reaches the maximum point, the resonance frequency (f2). In the frequency range f0 and f2, the fluid in the inertia track moves in the opposite phase with the displacement of the mount. The phase angle characteristics show that the highest damping occurs at the f1 frequency, between the f0 and f2 frequencies. After the maximum point, the damping decreases until the damping ratio of the rubber (see Figure 5) [3], [17], [18]. In the high frequency-low amplitude Test 2 conditions, the free decoupler only travels within the travel gap, so most fluid transport between the chambers is via the decoupler. So, the dynamic characteristics of the hydraulic engine mount are also primarily determined by the rubber [3].

The test results for all the mounts given in Table 3 are provided in Table 5. In the low frequency-high amplitude Test 1 conditions, the peak phase angle and its frequency were obtained from the phase angle curve (see Figure 5, φ, f1), and the peak dynamic stiffness and its frequency (see Figure 5, Kd1, f2) were determined from the dynamic stiffness curve. In the high frequency-low amplitude Test 2 conditions, dynamic stiffness at 50 Hz frequency was derived (see Figure 6, Kd2). The optimization method was performed according to these numerical values.

Table 5:

Test results.

Experiment no Test 1 Test 2
φ (°) f1 (Hz) Kd1 (N mm−1) f2 (Hz) Kd2 (N mm−1)
1 25 10 590 15 906
2 23 12 463 16 489
3 27 9 511 15 723
4 27 9 480 15 640
5 36 12 505 17 631
6 24 9 567 15 857
7 38 12 520 17 661
8 33 11 447 16 388
9 26 12 486 16 471
10 31 13 604 17 873
11 22 8 410 13 398
12 19 9 463 14 479
13 20 9 463 14 484
14 32 13 600 18 888
15 26 8 420 14 393
16 33 12 453 17 410
17 30 12 383 16 351

4.2 Optimal hydraulic mount parameters

HyperStudy is a multidisciplinary design and parameter optimization software used to analyze, optimize, and improve complex and multivariate engineering problems. HyperStudy analyzes and optimizes design variables and constraints according to nonlinear relationships and multiple objective functions. It uses genetic algorithms and optimization techniques to understand the impact of parameters in a design space, identify the best design points, and optimize product performance, efficiency, or other objectives [22].

In this study, the DoE matrix (see Table 3) and the test results (see Table 5) were transferred to the HyperStudy, and a response surface was created in the program. The response surface is a model that characterizes the relationship between inputs and outputs [23], [24]. It utilizes the cross-validation R-Square (R-Sq) coefficient for comparison purposes. The R-Sq coefficients for the created response surface are shown in Figure 7. According to these results, the success of the obtained response surface in predicting the outputs is reliable, and the model fits the data well. The response surface is also considered suitable for practical use and accurate predictions.

Figure 7: R-Sq coefficients of the design parameters.
Figure 7:

R-Sq coefficients of the design parameters.

The hydraulic engine mount requirements based on the demands of an automobile manufacturer have been determined in Table 6. According to Table 6, the optimization step for the hydraulic engine mount was started by using the response surface. In this stage, parameter ranges and the mount targets were defined, considering the data in Tables 2 and 6. HyperStudy’s global response search method (GRSM) was employed as the optimization method. This method uses the response surface model to find the best solution for multivariate and complex design problems by applying a search strategy to optimize the design parameters [22]. The flowchart of the method is given in Figure 8.

Table 6:

Hydraulic engine mount requirements.

φ (°) f1 (Hz) Kd1 (N mm−1) f2 (Hz) Kd2 (N mm−1)
≥ 32 12 ± 1 460 ± 15 % 17 ± 1 372 ± 15 %
Figure 8: Global response surface method (GRSM) flowchart [22].
Figure 8:

Global response surface method (GRSM) flowchart [22].

In this study, the optimization was carried out for scenarios with and without constraints based on the response surface. All constraints listed in Table 2 were considered in the constrained optimization. In the unconstrained optimization, the objective was to maximize the phase angle by eliminating all constraints. The results from both optimization runs are presented in Table 7. As observed in Table 7, the parameters obtained in Test 1 show consistency in both optimization results, while in Test 2, the dynamic stiffnesses at 50 Hz frequency exceed the target value. However, both analysis results essentially meet the mount targets.

Table 7:

Optimization results.

Constrained optimization Unconstrained optimization
η 1.8 2.1
A (mm2) 80 80
HSd (shA) 56 56
V (mm³) 52,264 45,435
φ (°) 38 41
f1 (Hz) 13 13
Kd1 (N mm−1) 459 543
f2 (Hz) 18 18
Kd2 (N mm−1) 430 596

4.3 Verification of analysis results

In the final part of the study, to validate the optimization results, a mount with dimensions close to the optimal parameters was analyzed using the created response surface in the HyperStudy software and experimentally tested under Test 1 and Test 2 conditions. The mount parameters and the analysis and test results are presented in Tables 8 and 9, respectively. As observed in Table 9, the analysis results are quite consistent with the test results. Therefore, it has been demonstrated that automotive manufacturer requirements can be met if the hydraulic engine mount is manufactured according to the parameters determined by the DoE and response surface. This approach offers advantages in terms of both time and production costs.

Table 8:

Hydraulic engine mount parameters for verification.

η A (mm2) HSd (shA) V (mm³)
2.2 79.5 58 44,512
Table 9:

Comparison of analysis and test results.

φ (°) f1 (Hz) Kd1 (N mm−1) f2 (Hz) Kd2 (N mm−1)
Analysis results 40 14 544 18 663
Tets results 39 14 547 19 653
Deviation 2.5 % 0 % 0.6 % 5.6 % 1.5 %

5 Conclusions

In this study, a full factorial design of experiment (DoE) was created by determining two levels for the parameters affecting the damping performance of hydraulic engine mounts, including dynamic hardening, inertia track cross-sectional area, decoupler hardness, and fluid volume. Hydraulic engine mounts were assembled for all possible combinations of these parameters and tested at high and low amplitude vibrations. Another mount with a larger inertia track cross-sectional area and fluid volume was also tested under the same conditions, and these results expanded the DoE. A response surface was generated in the Hyperstudy software using all the test results, and an optimization study was performed based on this response surface to achieve the desired damping characteristics for the mounts. The optimization study was carried out in two ways, with and without constraints. The constrained optimization included parameter levels, while the unconstrained optimization aimed to maximize the phase angle without parameter levels. Since the same response surface was used in both optimization processes, the calculated parameters were very close to each other, confirming that the results met the expected damping properties of the mount. A hydraulic engine mount with dimensions close to the optimum parameters was analyzed using the response surface and tested to validate the analysis results. When the analysis and experimental results are compared, it is observed that the phase angle, which is the most critical parameter for damping, was verified with a deviation of 2.5 %. The most significant deviation was found in the frequency of peak dynamic stiffness, which is 5.6 %.

In conclusion, this study has demonstrated that the analysis results with the response surface are realistic for hydraulic engine mounts. When response surfaces are correctly created for different sizes and levels, it will also be possible to determine various design parameters corresponding to other mount requirements. This approach can significantly decrease the number of trials in the automotive industry, leading to time and cost savings.

Corresponding author: Zeliha Kamış Kocabıçak, Bursa Uludag University, Bursa, Türkiye, E-mail:

About the authors

Zeliha Kamış Kocabıçak

Dr. Zeliha Kamış Kocabıçak received her PhD degree in Mechanical Engineering from Bursa Uludağ University. She is now an associate professor at the Department of Automotive Engineering at Bursa Uludağ University. Her research interests are vehicle dynamics, mechatronic systems, electromechanical systems, automatic control, and system dynamics.

Zafer Açar

Zafer Açar received his Master degree in Automotive Engineering from Bursa Uludağ University, Turkey. His research interests include hydraulic engine mounts.

Acknowledgments

The authors would like to thank Bayrak Lastik Corp. for its support in the tests.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: None declared.

  7. Data availability: The raw data can be obtained on request from the corresponding author.

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Published Online: 2025-03-06
Published in Print: 2025-04-28

© 2025 the author(s), published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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Keywords for this article
damping properties; design of experiment; design parameters; dynamic stiffness; phase angle; response surface
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Articles in the same Issue

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  2. Bending of wavy spider web honeycomb sandwich structures using PLA
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  4. Impact breaking energies and transition temperatures of construction steels produced from scrap
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