The deformation of chains in shear mode is the focus of this study, so the hydraulic interaction is neglected. A schematic of the deformation of a single chain is presented in **Figure 5**. With the magnetic field, the identical spherical particles dispersed in the carrier oil align themselves in the direction of the magnetic field. According to the minimum energy principle, the field energy would be minimized when d = 2R, where d is the vertical distance between the centers of the adjacent particles and R is the radius of the particle. We assume that there is no relative motion between the particles and the carrier oil, and then the chain would be stretched and deviates an angle θ from the direction of the magnetic field. Meanwhile, the minimum energy principle would allow a uniform distance between the two adjacent particles. Under magnetic field, only the interaction between the two adjacent particles would be considered, and then the restoring force F H induced by the deformation of a chain can be calculated by taking the derivative of the energy with respect to the displacement. It can be expressed as

$$F^{H} = \frac{A}{2d} \frac{2\chi\left(\wp^2 + 1\right) - 5\wp\left(\wp^2 - 2\right)}{\left(\wp^2 + 1\right)^{3.5}} \tag{2a}$$

$$A = \frac{m^2}{4\pi\mu\_0\mu\_0 d^3} \tag{2b}$$

$$\nu = \tan \theta \tag{2c}$$

$$
\hat{F}^H = \frac{2dF^H}{A} \tag{2d}
$$

where m= |**m**| and **m** (= 3µfµ0βV**H**0) is the dipole moment when a particle is placed in the magnetic field **H**0. β = (µp−µf) (µp+2µf) , µp and µf are the relative permeabilities of the particles and medium, respectively, µ0 is the vacuum permeability, V (= 4 3 πR 3 ) is the volume of a particle and γ is the shear strain. Fˆ H is defined as the normalized restoring force to study the relationship between the chain restoring force and shear strain under different magnetic fields.

**Figure 6** shows the relationship between the normalized restoring force Fˆ H and shear strain of a single chain of MR fluids. As seen from the figure, in the initial deformation stage, as the strain increases, Fˆ H quickly reaches the peak. The corresponding strain is defined as the yield strain. Fˆ H gradually decreases to zero after the yield strain. It should be noted that the yield strain is a constant value independent of the magnetic field.

In addition, **Figure 6** presents the schematic of the test results of the restoring force vs. strain of a single chain (Furst and Gast,

2000). It is seen from **Figure 6**, the yield strain based on the magnetic dipole model is in good agreement with the test results, but after the yield strain, the chain of the MR fluids ruptures and the corresponding restoring force drops to zero sharply. Therefore, it is unreasonable to derive the yield stress of MR fluids based on the assumption of consistent deformation of the chain clusters (i.e., the deformation of all chains of MR fluids is consistent). The yield strain in the dipole model is derived from the derivation of the yield stress. The relationship between the restoring force and strain before the yield strain provides clues for the deformation of the chain clusters.

An assumption is made here during the expansion of a single chain to the entire chain clusters: under magnetic fields, the structural evolution of the chain clusters of MR fluids in the shearing motion is in dynamic equilibrium state from the micro deformation of chain to rupture and reconstruction. Specifically, as seen from the structural evolution of the chain clusters in **Figure 7**, the ferromagnetic particles are polarized into chains in a static state, and the chains of MR fluids are not in an absolute parallel with the magnetic field direction. There are slight differences between the chains. As seen from **Figure 7**, under the shearing motion, the inclination angle of the chains gradually increases, and due to the difference of the initial inclination angle, part of the chains reach the yield strain and then rupture occurs. As the shearing motion advances, more chains rupture to yield stress and the previously ruptured chains reconstruct and form new chains with the adjacent broken chains. The rupture and reconstruction of the chains reach a dynamic equilibrium under the steady-state conditions. In other words, the number of chains ruptured at a certain instant is equal to the amount of chains reconstructed. Thus, it exhibits a stable mechanical property. The non-absolute parallel hypothesis in the static state is verified with the results of MR fluids under electron microscope (De Vicente et al., 2011). Also, the shear tests of a single chain of MR fluids show that the restoring force of the MR fluids abruptly decreases to zero (Furst and Gast, 2000), which

indicates that the structural evolution of the chain clusters of MR fluids is not consistent. Therefore, the assumption of a dynamic equilibrium of the chain clusters of MR fluids is reasonable. Based on such assumption and the dipole model of the single chain of MR fluids [i.e., equation (2)], **Figure 8** shows the stress-strain relationship of MR fluids under shearing motion. As seen from **Figure 8**, before the yield strain, the stress increases rapidly to the peak with the increase of the overall strain of the chain clusters. When reaches the dynamic equilibrium of the rupture and reconstruction, MR fluids exhibit stable stress characteristics. Consistent with the normalized restoring force-strain plot of a single chain of MR fluids, the yield stress under the evolution of the chain clusters structure is also a magnetic field-independent constant. It should be noted that the yield stress and also the corresponding yield strain of MR fluids and the stable stress are not consistent in numerical values.

# Hysteresis Mechanism of MR Fluids Under Reciprocating Displacement Excitation

Based on the stress-strain plot of the chain clusters of MR fluids obtained in **Figure 8**, under the reciprocating displacement excitations, the MR fluids stress increases rapidly and gradually

FIGURE 7 | Structural evolution of the multi-chain of MR fluids under magnetic field.

reaches the stable. When the displacement excitation direction changes, the transient shear rate of the MR fluids can be seen as zero. Then the chain ruptured at the previous moment maintains the trend to the parallel direction of the magnetic field, while the unruptured chains maintain the previous shear strain. Therefore, when a new shearing motion starts (i.e., the shear direction changes), the restoring force of part of the chains is opposite to the shear rate, and part of the chains begin to undergo new deformation. Thus, the overall stress direction is opposite to the shear rate. As the shearing motion progresses, the stress of MR fluids gradually approaches a new stability until the new shear strain direction-change point.

**Figures 9A,B** provide the dipole model-based hysteresis characteristics of MR fluids under reciprocating displacement excitations with large and small amplitudes, respectively. As shown in **Figure 9A**, the simulation results with coupled viscous properties of MR fluids are also provided for comparison. Consistent with **Figures 6**, **8**, the distance from the strain direction-change point to the stress stable point is a magnetic field-independent quantification. It is numerically twice of the yield strain. This agrees with the test results of the hysteresis of MR fluids. However, in the hysteresis characteristics tests of MR fluids, the macroscopic mechanical performance is affected by the friction and compressibility of MR fluids. The yield strain converted from yield displacement is not identical with the theoretical value.

As seen from **Figure 9B**, when the excitation amplitude is small, the excitation strain is insufficient to reach the yield strain, and majority of the chains of MR fluids are not ruptured. The stress generated by the MR effect maintains good coincidence during the reciprocating processes, and its energy consuming characteristics are mainly reflected by the viscosity characteristics of MR fluids. This phenomenon is in good agreement with the results of MR elastomers tests. Under low shear strain amplitudes, the influence of MR effect on the macroscopic properties of MR elastomers is mainly manifested in the stiffness characteristics (Li et al., 2013). The energy consumption characteristics is influence by the MR effect (Lopez-Lopez et al., 2016), so the damping characteristics of MR elastomers is also affected by the excitation amplitudes.

# FURTHER EXTENSIONS

# Hysteresis in MR Elastomers

The experimental tests and macroscopic modeling analysis indicate that the hysteresis also happened in MR elastomers where the corresponding strain is very small (Tian et al., 2011; Li et al., 2013) and it can be effectively modeled by Bouc-Wen model (Yang et al., 2013; Behrooz et al., 2014). Fortunately, the particles in MR elastomers are fixed in the rubber matrix, and especially for the anisotropic one, the deformation of the chains can be reasonably predicted. Then two properties of the proposed theoretical model can be experimentally verified: (i) the similarity in **Figure 9B** would be checked under quasi-static tests, and (ii) as shown in **Figure 10**, the yield strain can be directly measured in MR elastomers (Tian et al., 2011). Then the comparison of the yield strain would be done between experiment and theory. In MR fluids, it is not easy to measure the yield strain. The yield displacement is a vague value in the force-displacement plot, and the mixed air or the machining error would be amplified on the value of the yield strain.

# Response Time of MR Fluids

Researchers believe that the response time of MR actuators has three main sources: response time of MR fluids, inductance of coil, and eddy current in the coil bobbin (Bai et al., 2018b). Under a fixed applied current, the response time from inductance of MR damper coil and eddy current in the coil bobbin would be a constant value regardless of the excitation velocity. The measured results of response time vs. excitation velocity (Koo et al., 2006) shown in **Figure 11** indicate that with increasing velocity, the response time sharply decreases before the convergence. If we take the stable value as the constant value from inductance of MR actuator coil and eddy current in the coil bobbin, the response time from MR fluids seems to be inverse proportion to the excitation velocity. Hence, we can make a conjecture that instead of the response time, the response displacement is more suitable to interpret the zero-stare response of MR actuators and

it would be a constant value. This conjecture is consistent with the constant yield displacement or strain in the hysteresis, which also provides another way to the measurement of the yield strain.

# Yield Strain in Theory of Dipole Model

The yield strain in shear mode is derived with the simple dipole model, and it should be noted that the yield strain would be different if another dipole model is used. **Figure 12** presents the comparison of the normalized restoring force response between simple dipole model and local field dipole model (Zhang et al., 2004). Ignoring the difference of the maximum restoring force, the corresponding yield strain is different. In addition, the yield strain is also different related with the working mode (Chen et al., 2017b). The comparison/difference between shear mode and valve mode is presented in **Figure 13**.

FIGURE 10 | Measured stress-strain curve of MR elastomers (Tian et al., 2011).

# Discussion

The comparison between the experimental tests (refer to **Figures 2–4** and Figures A1,A2 in **Appendix A**) and the theoretical results (**Figure 9A**) indicates that the hysteresis in force-displacement plot is consistent with each other and satisfies the requirement of rate-independence of hysteresis and the invariance of the experimental yield displacements under different currents and theoretical yield strain under different fields. It is also noted that (i) in the case of the double-rod MR damper, the yield displacement is almost current-dependent, and (ii) in theory, the distance between the direction-change point and yield point is approximately twice of yield strain. Hence, the tested yield displacement can be easily converted to a sort of strain, and the direct comparison of its value with the yield strain from theory would strongly prove the proposed theory. In addition, the tested stable damping force would be

FIGURE 12 | Comparison of normalized restoring force response between simple dipole model and local field dipole model.

converted to a kind of stress, and the comparison with stable stress would provide a clue to the dynamic equilibrium of multichain structural evolution. We can realize the precise prediction of the hysteresis of MR fluids and MR fluid-based actuators before experimental tests, as long as we figure out the above.

# CONCLUSIONS

Aiming at understanding the hysteresis mechanism of MR fluids, a self-developed double-rod MR damper was tested and the hysteresis mechanism of MR fluids using a dipole model was theoretically analyzed and explained. The doublerod MR damper under triangle displacement excitations were tested and a normalization concept was applied, to eliminate the compressibility of the accumulator and the influence of the viscous damping on macroscopic hysteresis characteristics. Test results, especially the uniformity of yield displacements under different excitation conditions, indicate that the hysteresis characteristics of MR fluids are mainly reflected in the forcedisplacement plot. Based on the theory of the dipole model and the dynamic equilibrium hypothesis of chain clusters rupture and reconstruction, the hysteresis mechanism of MR fluids under different excitation amplitudes was derived. Consistent with the experimental results, the theoretically derived yield strain is also independent of the excitation conditions. The theoretically derived yield strain shows difference in the magnitude of the strain corresponding to the yield displacement, due to the influence of other factors in the tests of the hysteresis characteristics of MR fluids. But the consistent rate-independence characteristics provide fundamentals for the further work on the MR effect mechanism. The reasonable deductions on the response time of MR fluids as well as the stressstrain properties of MR elastomers are helpful for the related research or applications.

From the view of future research on the MR effect mechanism, three significant issues are worthy of in-depth study. (i) Detailed physical process for portraying and explaining the MR effect mechanism should be mathematically formulated to in fullscale verify the deduction of this work, which was using only a preliminary analytical model. (ii) Tests of the yield displacements of MR fluids when filled in gaps with different widths but an identical cross-sectional area can be conducted to verify the deduction of this work: smaller gap width, smaller yield displacement. (iii) Tests of the yield strain of MR elastomers, especially the anisotropic ones, can be done to verify the deduction on the MR elastomers in this work.

# DATA AVAILABILITY

The datasets generated for this study are available on request to the corresponding author.

# AUTHOR CONTRIBUTIONS

X-XB conceived the conception, investigated the technical background, and coordinated the study, and revised the manuscript. PC carried out the modeling and computation work, and drafted the manuscript.

# ACKNOWLEDGMENTS

The authors wish to acknowledge the Key Research and Development Projects of Anhui Province (Grant No. 1704E1002211) for its support of this research.

# REFERENCES

# SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmats. 2019.00036/full#supplementary-material

**Conflict of Interest Statement:** PC is employed by the company Guangzhou Automobile Group, China.

The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Bai and Chen. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Performance Evaluation of a Magnetorheological Fluid Damper Using Numerical and Theoretical Methods With Experimental Validation

### Ali K. El Wahed\* and Hao Chen Wang

*Mechanical Engineering, University of Dundee, Dundee, United Kingdom*

Magnetorheological (MR) fluids which can exhibit substantial reversible rheological changes under the excitation of external magnetic fields, have enabled the construction of many novel and robust electromechanical devices in recent years. Generally, Bingham plastic model is utilized for the estimation of the characteristics of MR fluids. However, when the geometry and design of the MR device as well as the rheological conditions of the fluid itself become complicated due to the engineering application requirements, the accuracy of Bingham plastic model, which simplifies the relation between the fluid shear stress, and shear rate into a linear function, is degraded. In this paper, a multi-degree-of-freedom (MDOF) magnetorheological fluid damper with a novel ball-and-socket structure was developed, which was aimed to enhance the human shoulder rehabilitation treatment. The performance of the proposed smart device with its complex design was estimated numerically using a finite element method (FEM) with a Herschel-Bulkley model and theoretically with a model that is based on a Bingham plastic fluid characteristics. The performance of the developed damper was validated experimentally using a dedicated testing facility for various input conditions. It was found that the FEM simulations with the Herschel-Bulkley model showed a better agreement with the experimental results in comparison with the theoretical predictions which were somewhat degraded with the employed Bingham plastic model.

Keywords: MDOF smart damper, magnetorheological fluids, Herschel-Bulkley model, Bingham plastic model, finite element modeling

# INTRODUCTION

Magnetorheological (MR) fluids belong to the general area of smart materials, which consists of micron-size magnetisable particles suspended in non-magnetic oil based liquid carrier. When the magnetic field is applied, the suspended particles become magnetically polarized, and align themselves into chains, which increases the apparent viscosity and yields stress of the MR fluid. This fast and reversable MR fluid rheological changes can be controlled by the applied magnetic field intensity and therefore, a continuously variable fluid characteristics could be realized. As a result, these smart properties have enabled MR fluids to be utilized in the construction of various novel electromechanical devices (El Wahed and McEwan, 2011).

MR fluids have been utilized into different modes of operation, which are shear (Wereley et al., 2007), flow (Wang and Gordaninejad, 2000), or squeeze (El Wahed and Balkhoyor, 2015) modes.

Edited by:

*Seung-Bok Choi, Inha University, South Korea*

#### Reviewed by:

*Tianhong Yan, China Jiliang University, China Jianbo Yin, Northwestern Polytechnical University, China*

> \*Correspondence: *Ali K. El Wahed<EMAIL_ADDRESS>
#### Specialty section:

*This article was submitted to Smart Materials, a section of the journal Frontiers in Materials*

Received: *05 December 2018* Accepted: *08 February 2019* Published: *28 February 2019*

#### Citation:

*El Wahed AK and Wang HC (2019) Performance Evaluation of a Magnetorheological Fluid Damper Using Numerical and Theoretical Methods With Experimental Validation. Front. Mater. 6:27. doi: 10.3389/fmats.2019.00027*

More recently, two new modes have been reported which are the pinch (Goncalves and Carlson, 2009) and mixed (El Wahed and Balkhoyor, 2016) modes of operation. The most successful exploitation of the MR fluids has been realized in the area of vibration control (Chrzan and Carlson, 2001) with a specific successful commercialization in the automotive and structural industries when some passenger cars and buildings are now equipped with smart shock absorbing systems (Nguyen and Choi, 2009) and large seismic dampers (Dyke et al., 1998), respectively. In addition, rotary smart fluid devices, such as clutches or brakes, have been developed (Olabi and Grunwald, 2007). Currently, rotary MR fluid devices exist primarily in two different configurations, namely, disc type and cylindrical type, which permit one degree-of-freedom (DOF) movements. As a result, these devices are not useful if they are proposed to control the joints of an upper limb rehabilitation training machines, since the human arm is capable of handling multi degrees-of freedom (MDOF) motions along a multiple-axis system as it benefits from a flexibility offered by the natural arm joints with a ball-andsocket structure. For example, the arm could be raised above the head, lowered beside the body, extended from the body or moved forward across the body. In addition, the arm rotates in a 360 degree circle when held to the side. Consequently, any developed orthotic device aimed for the rehabilitation of human upper limbs should have similar flexibility at its joints. Accordingly, a ball-and-socket configuration was chosen by the authors to design a novel type of a smart MR damper (El Wahed and Balkhoyor, 2018), **Figure 1A**, which should allow movements that are similar to those offered by the human shoulder joint, **Figure 1B**. Accordingly, the controllable rheological properties of the MR fluid that fills the gap between the ball and socket components should enable the smart damper to offer the predefined kinematics and force constraints required at the joints of the upper-limb rehabilitation orthosis. Therefore, this novel damper design, which is proposed to be incorporated at the joints of the rehabilitation device, should maximize the working function and reduce the overall size of current rehabilitation training systems.

The comparative performance of the ball-and-socket damper using numerical, theoretical, and experimental procedures is reported in this article. In order to estimate the characteristics of the MR fluid in the developed device, a proper relation between the shear stress and shear rate of the MR fluid should be addressed. This relation is assumed to be linear by the Bingham plastic model which has widely been used in recent years by numerous research teams for the theoretical modeling of magnetorheological fluids (Ghaffari et al., 2014). However, the shear thinning or shear thickening characteristics of MR fluids are poorly modeled by the Bingham plastic model (Wang and Liao, 2011). One major reason for this modeling shortage is that the Bingham plastic model only includes two parameters which assumes a linear fluid shear stress/shear rate relation, while the experimental results indicate that the slope of the fluid characteristics curve changes with the variation of the shear rate (Zubieta et al., 2009). Consequently, when the MR device design and the rheological conditions of the MR fluid become complicated due to the requirements of the engineering application, the Bingham plastic model was deemed to be insufficient to accurately predict the performance of the MR fluid (Zhu et al., 2012). As a result, other fluid models, such as the biviscous model (El Wahed, 2011), were utilized for the efficient modeling of smart fluids characteristics.

In this study, the resistive torque of the ball-and-socket damper was first estimated using a theoretical model based on the assumption of a Bingham plastic fluid characteristics for different input velocity inputs. Subsequently the device torque performance was numerically investigated using finite element analyses, which were performed using Ansys Fluent computer code with a Herschel-Bulkley fluid model. Furthermore, a dedicated experimental facility was then utilized to validate the device performance under the same sets of input conditions.

# BALL-AND-SOCKET DAMPER PERFORMANCE EVALUATION PROCEDURES

The new smart ball-and-socket damper was designed with an opening angle (from one socket edge to another) of 126◦ . The MR fluid is proposed to fill the gap between the ball and socket components to control the impedance of the damper, which is proportional to the electromagnetic field intensity generated by the electromagnetic coil element that is imbedded inside the socket component, as shown in **Figure 2**. The overall size of the device was designed to be ∼150 mm in diameter. Due to the compact size of the electromagnetic circuit of the smart damper, which was designed and optimized using electromagnetic finite element methods, the electromagnetic coil element only requires few volts to generate the magnetic field required for the excitation of the MR fluid and therefore, the smart device is considered to be electrically safe in the normal rehabilitation training environment.

In the authors' previous study (Wang and El Wahed, 2018), it was found that the early design of the ball-and-socket damper was capable to deliver a maximum torque output of about 26 Nm using Lord Corporation commercial MR fluid, type MRF122- 2ED under a magnetic flux density excitation of about 1.1 Tesla and an input angular velocity of about 1 rad/s. Accordingly, this fluid was employed in the current investigation.

In the present theoretical model, the total damping torque Tt delivered by the smart ball-and-socket damper was assumed to consist of three components, which are the controllable fielddependent torque, the viscous friction torque and the mechanical friction torque (El Wahed and Balkhoyor, 2018). The shear stress, τ of the MR fluid in the present model was accounted for using the Bingham plastic fluid model which is given by:

$$
\pi = \mathfrak{r}\_{\mathcal{Y}}(H) + \eta \mathcal{Y} \tag{1}
$$

where η and γ are the fluid dynamic viscosity and shear rate, respectively whilst τy (H) is the fluid yield stress which depends on the magnetic field intensity H. Accordingly, the total damping

torque of the device was derived into the following equation:

$$T\_t = \pi \, r^3 \, \mathfrak{r}\_\circ(H) \, (\varphi \, - \, \sin \varphi \, \cos \varphi)$$

$$+ \frac{8 \, \eta \, \pi \, r^4 \, \omega}{3 \, h} \sin^4 \left(\frac{\varphi}{2}\right) \, (\cos \varphi \, + \, 2) \, + \, T\_f \tag{2}$$

where r, ω, and h are the ball radius, input angular velocity and MR fluid gap size, respectively whilst ϕ is the socket angle which is measured from the lower end (6 o'clock) to one of the socket ends. Tf is the mechanical frictional torque, which was measured experimentally in this study and will be detailed at the end of this section. The fluid temperature was assumed to be maintained at 40◦C whilst the density and viscosity of the employed fluid, which are required to complete the theoretical modeling as well as the FEM simulations of the new damper, were provided as 2,380 kg/m3 and 70 mPa.s, respectively (Adhesives Coatings Vibration Motion Control Sensing Magnetically Responsive Technologies, 2018). The yield stress of the adopted MR fluid as a function of the magnetic flux density is presented in **Figure 3** (Adhesives Coatings Vibration Motion Control Sensing Magnetically Responsive Technologies, 2018). Using the estimated yield stress values (**Figure 3**) and Equation (2) together with the measured mechanical frictional torque, Tf , the total damping torque of the damper was then estimated theoretically for a range of magnetic flux densities of up to 0.7 Tesla and for a ball angular speed of 10 RPM.

A numerical technique was then developed to estimate the performance of the developed ball-and-socket damper, which was based on finite element methods (FEM) that were performed using Ansys Fluent computer code. A model representing the fluid volume filling the gap between the ball and socket components of the damper was first created using SolidWorks CAD software, and was then exported into the Ansys Fluent environment. The magnetic flux density is assumed to be uniformly distributed along the fluid gap whilst the yield stress of the MR fluid required for the FEM simulations was again derived from the results presented in **Figure 3**. The fluid volume was meshed with a minimum element size of 3.5 × 10−4 m. As part of the boundary conditions set up for these simulations, the fluid

volume that is adjacent to the ball component was assumed to move at the ball angular speed (sliding motion), while the surface which is in contact with the socket is assumed to be stationary (no-slip condition). The top horizontal surface of the fluid at the socket opening was also considered as a stationary wall since it is in contact with a large lip-seal that is designed to seal the fluid gap between the ball and socket. In the current FEM settings, the stationary wall boundary condition was realized when its velocity is set to zero along the three coordinates, while the moving wall condition was achieved when the applied angular speed was set in the direction along which the torque is estimated. Since the applied angular speed is low, the MR fluid flow inside the gap initiated by the ball motion was assumed to be steady, laminar, and incompressible. In addition, thermal interaction inside the MR fluid was ignored and therefore, the flow was assumed to be under adiabatic condition. The minimum pressure magnitude was also assumed to be above the fluid vapor pressure so that any cavitation was excluded from the analysis.

The MR fluid behavior was characterized using the Ansys built-in Herschel-Bulkley model which is represented by the following shear stress equation (Zubieta et al., 2009):

$$
\pi = \mathfrak{r}\_{\mathcal{V}}(H) + k\mathcal{Y}^{\mathfrak{n}} \tag{3}
$$

where k is referred to as the consistency index and n is the pseudoplastic index. The relationship between the shear stress and shear rate estimated by the Bingham plastic model is shown in **Figure 4** for a magnetic flux density of 0.5 Tesla. It can be seen that the changes in the shear stress values over the shear rate range were small. This is ascribed to the fact that the fluid viscosity of 70 mPa.s, which was assumed in this model, was small and therefore, the resulting shear stress does not see dramatic changes when the shear rate changes. The lack of response in the fluid shear stress to variations in the shear rate usually affect the accuracy of the simulated performance of the MR fluid device and hence, degrade its agreement with the experimental results. However, unlike the Bingham plastic model, the shear stress-shear rate dependency is represented more accurately by the Herschel-Bulkley model through the added pseudoplastic and consistency indexes which are used to describe the shear thinning/shear thickening effects of the MR fluid. In this study, the well-recognized analysis (Zubieta et al., 2009), which was done on the same MR fluid employed in the current investigation (MRF122-2ED), was utilized for the quotation of the n and k indexes under different operation conditions. This enabled the estimation of the shear stress-shear rate characteristics of the employed MR fluid using the Herschel-Bulkley model, which are also presented in **Figure 4** and compared with those estimated using the Bingham plastic model for an applied magnetic flux density of 0.5 Tesla.

In order to experimentally verify the performance of the smart damper, a dedicated testing facility was designed and built, which comprises an AC motor with its associated speed controller type IMO Jaguar, model CUB8A-1 to supply the input rotational motion to the damper, TorqueSense Technology, model RWT320 speed and torque transducers and a magnetic particle brake type Warner Electric, model MPB240M-24-24 to apply and simulate resistive torques at the output of the smart damper, as shown in **Figure 5**.

In addition, a National Instruments analog-to-digital converter, model NI9205 in conjunction with a cDAQ-9172 CompactDAQ USB chassis capable of simultaneous sampling, which was controlled by a National Instruments data acquisition software, type LabVIEW running on an IBM compatible personal computer, was used to collect and record the data from the sensors and power supplies used to energize the smart damper and the magnetic particle brake. In order to allow a continuous supply of power to the electromagnetic coil of the smart damper while it is under a rotational input operation, a special arrangement was designed which consists of a plastic disc to which two copper rings were attached. The two copper rings were electrically insulated from each other and the electrical resistance between them was measured using a digital multimeter, which was found to be in access of 5 kOhm. This resistance was deemed to be high enough to prevent any charge leakage between the two copper electrodes across the plastic shank of the disc. The plastic disc was fixed on the rotating shaft just upstream the smart damper, **Figure 5**, and the damper's coil wires were soldered to the two copper rings. The connection of the power supply to the copper rings was achieved using two carbon brush mechanisms which were equipped with tensioning springs to ensure a continues contact with the copper rings.

The output speed and torque of the smart damper are expected to change in response to both the level of the electrical current supplied to the electromagnetic coil element of the damper and the magnitude of the resistance applied by the magnetic particle brake. In order to allow a direct comparison between the braking torque results measured experimentally and those estimated theoretically and numerically using Equation (2) and the FEM procedure, respectively the relationship between the magnetic field density generated by the damper's magnetic circuit and its coil energizing current was first established using a 3-D finite element electromagnetic approach that was executed using Ansys Workbench software. In these simulations, coil energizing currents similar to those used in the experimental assessments of the smart damper were assumed and the corresponding average magnetic field

FIGURE 4 | Shear stress vs. shear rate of MR fluid type MRF122-2ED based on Bingham Plastic and Herschel-Bulkley models for a magnetic flux density of 0.5 Tesla.

density values along an imaginary path spanning the MR fluid gap from one socket end to the other were estimated. **Figure 6** shows the magnetic field density distribution along this imaginary median path inside the MR fluid gap of the ball-and-socket damper for a coil energizing current value of 1.0 A.

**Figure 7** shows the variation of the average magnetic field density simulated inside the MR fluid gap of the smart damper as a function of the damper's coil energizing current in the range between 0.25 and 2.1 A. It can be seen that a maximum energizing current of 2.1 A supplied to the electromagnetic coil of the smart damper produced an average magnetic field density in the MR fluid gap of about 1 Tesla, which is the magnetic excitation level under which the employed MR fluid becomes saturated (Adhesives Coatings Vibration Motion Control Sensing Magnetically Responsive Technologies, 2018).

The simulated data presented in **Figure 7** enabled the application of coil energizing currents at the required magnetic field densities and the corresponding braking torque values of the smart ball-and-socket damper were measured for an input speed of 10 RPM. The measured torque was limited to a maximum of 20 Nm which is the maximum range of the employed torque

transducers. This equipment limitation made it difficult to extend the tests beyond magnetic flux densities of about 0.6 Tesla otherwise the measured torques become higher than the maximum capability of the employed torque transducers. In addition, it is worth mentioning that velocities around 10 RPM did not produce any real difference in the measured torque values, which is expected under such low velocity range that is typical of the aimed rehabilitation application of the developed smart device. However, it was thought that despite the above hardware limitation, the reported results would still provide a useful insight into the performance of the developed device and its aimed rehabilitation application.

Finally, the mechanical friction torque, Tf , which is mainly caused by the friction between the ball and the lip-seal components of the smart damper, was measured experimentally. In this test, the socket component was fixed to a sturdy bench while a metallic shaft was attached to the center of the ball component and set at a horizontal position using a spirit level tool. Whilst the smart damper is not energized, the ball shaft was gradually loaded with static weights, **Figure 8**, until the ball

rotates, indicating that the damper's mechanical resistance is breached. This test was repeated several times and the weight that caused the ball rotation was used to estimate the damper's mechanical torque which was found to be about 1.16 Nm. This mechanical torque value was added to the total damping torques estimated theoretically (Equation 2) and also to those simulated numerically (FEM model).

# RESULTS AND DISCUSSION

The theoretical, numerical, and experimental procedures were then executed for the intended yield stresses which are related

to the magnetic field density levels through their relationship presented in **Figure 3**. **Figure 9** shows an isometric view of the velocity contour simulated in the fluid gap under a magnetic excitation of 0.3 Tesla when the ball was allowed to rotate with an angular speed of 10 RPM about its z axis. It can be seen that the fluid velocity varies from zero on the socket side to its maximum value on the ball side. In addition, the velocity appears to increase from the center of the socket where the fluid appears to be stationary to its maximum nearby the socket opening.

For the same magnetic field excitation and input velocity conditions, the shear stress distribution was simulated along the

fluid volume, which is shown in **Figure 10**. The wall shear stress appears to increase from its minimum magnitude, which occurs at the bottom end of the socket, to a maximum magnitude that occurs in areas close to the socket opening. This shear stress pattern is attributed to the fact that the fluid shearing force becomes larger with increasing angle of the socket opening, which changes from zero at the bottom of the socket to 90 degrees nearby the socket opening.

The damping torque of the smart damper as a function of the magnetic flux density was estimated using the three employed techniques for a rotational speed of 10 RPM and the results are shown in **Figure 11**.

It can be seen that higher magnetic flux densities and hence larger fluid yield strengths caused the smart damper to produce higher damping torques. The damping torques appeared to increase almost linearly with the magnetic flux density particularly the current range of the fluid magnetic excitation is far from those magnetic field levels that cause fluid saturation. However, the simulated damping torque results seem to be closer to those obtained experimentally in comparison with the theoretical results. This is ascribed to the fact that the numerical approach with its employed Herschel-Bulkley model contributed to a more accurate estimation of the fluid shear stress in comparison with those produced theoretically in association with the Bingham plastic model (**Figure 4**). It could also be seen in this figure that when the magnetic field density is <0.4 Tesla, the theoretical results with their assumed Bingham plastic fluid characteristics seem to depart further from the experimental results. This might be caused by the fact that the shear thinning effect of the MR fluid is more obvious when the applied magnetic field is weak, which is not accounted for by the utilized Bingham plastic model unlike the Herschel-Bulkley model which takes care of this effect.

Furthermore, a deviation of 5–7% was observed between the experimental and numerical results which could be ascribed to the fact that although the electromagnetic circuit of the smart damper was designed through the electromagnetic FEM to generate a uniform magnetic field along the fluid gap, the prototype smart damper, due to various experimental deviations, may not exactly maintain this field uniformity. Overall, and according to the three assessment approaches, the smart damper appears to deliver a damping torque of about 22 Nm under a magnetic excitation of about 0.6 Tesla.

# CONCLUSION

In this study, theoretical, numerical, and experimental approaches were developed to assess the performance of a novel smart MR fluid damper which was designed with a ball and socket structure to enable a multi-degrees-offreedom device output. The theoretical model assumed a Bingham plastic fluid characteristics whilst the numerical technique employed the Herschel-Bulkley model which resulted in a more accurate fluid shear stress estimation. The mechanical torque of the device, which was caused by the friction between the ball and lip-seal components, was also measured experimentally, and was added to the theoretical and numerical torque results. A dedicated testing facility was utilized to verify the performance of the smart damper, which was found to be in a good agreement with the simulated device performance in comparison with that estimated theoretically.

# AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

# REFERENCES

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 El Wahed and Wang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Rheological Properties of Polyurethane-Based Magnetorheological Gels

Guang Zhang1 , Yancheng Li 2,3 \*, Huixing Wang1 and Jiong Wang1 \*

*1 School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China, 2 College of Civil Engineering, Nanjing Tech University, Nanjing, China, 3 School of Civil and Environmental Engineering, University of Technology Sydney, Ultimo, NSW, Australia*

The paper tests the influence of mass fractions of carbonyl iron particles (CIPs) on the rheological properties of magnetorheological (MR) gels. Polyurethane-based MR gels with different weight fraction of CIPs, i.e., 40, 60, and 80%, were firstly prepared by mechanical mixing, respectively. The changes of shear stress and viscosity with shear rate under different magnetic flux density were tested and analyzed. It was found that the shear stress increases with mass fraction under magnetic flux density. The viscoelastic properties of MRGs were achieved by oscillatory shear measure. The effects of strain amplitude and frequency on viscoelastic of MRGs under different magnetic flux density were measured and analyzed. The study results shown that the elastic characteristics become more obvious with the increase of CIPs mass fraction. However, it has opposite effect on the viscous properties of materials.

### Edited by:

*Miao Yu, Chongqing University, China*

### Reviewed by:

*Luwei Zhou, Fudan University, China Xianzhou Zhang, Independent Researcher, Tomago, NSW, Australia*

### \*Correspondence:

*Yancheng Li<EMAIL_ADDRESS><EMAIL_ADDRESS>Jiong Wang<EMAIL_ADDRESS>
#### Specialty section:

*This article was submitted to Smart Materials, a section of the journal Frontiers in Materials*

Received: *26 November 2018* Accepted: *20 March 2019* Published: *10 April 2019*

### Citation:

*Zhang G, Li Y, Wang H and Wang J (2019) Rheological Properties of Polyurethane-Based Magnetorheological Gels. Front. Mater. 6:56. doi: 10.3389/fmats.2019.00056*

Keywords: magnetorheological gel, rotation shear, oscillatory shear, Payne effect, loss factor, linear viscoelasticity

# INTRODUCTION

MRG is a new generation of MR smart materials with soft magnetic particles uniformly suspending in non-magnetic carriers. Fast and reversible magnetorheological effect will occur under the applied of magnetic field (Gan et al., 2017). It was more than two decades when Shiga et al. first reported silicone-based MR gel for solving the problem of particle settling in 1995 by dispersing the CIPs into silicone polymer colloid uniformly and since then MR gel has been considered as a momentous member of MR intelligent materials (Shiga et al., 1995).  MR gel is normally composed of micron or submicron soft magnetic particles (such as CIPs and pure iron powders), crosslink polymer liquid (such silicone resin and polyurethane), and additives (Ju et al., 2013). Notably, the MR gel shows a colloidal with a certain shear yield stress without magnetic field due to its matrix. Once the magnetic field is applied, the MR gel will transform into a solid state in a very short time (within milliseconds) and will exhibit a higher degree of shear yield stress. This process has a continuous and reversible characteristic (Hu et al., 2010; An et al., 2012). The above characteristics indicate that MR gel carries the basic rheological properties of the MR material and has larger magnetorheological effect and better settlement resistance, which offers a reliable and simple solution to design brakes (Wilson et al., 2002), dampers (Yang et al., 2015), and isolators

(Xu et al., 2013). However, the research on MR gel-like material is still in its early stage and much work are to be conducted. The researchers in the field were initially from chemistry with focus on heat flow and conversion of the polymeric matrix, and it is now gradually shifting to the stage with more engineers involved. From an application point of view, the mechanical properties of the material under influence of magnetic field, such as shear yield stress, viscosity, storage modulus, loss factor and MR effect, are of great interest and hence should be carefully investigated.

Owing to its great potentials, understanding its rheological properties holds the key to unlock reliable and efficient usage in engineering applications. Among the main composition, the soft magnetic particles play the key role to activate the MR effect and hence their impact should be carefully investigated. The influences of CIP contents on magneto-mechanical performances of MR materials have been tested by different researchers. Fuchs et al. prepared two silicone-based MR gel samples with different CIP contents. Variable magneto-induced features were examined by rheometer sweeping of shear rate from 20 to 6,000 s−1 . It was found that the silicone-based MR gel with 84.5 wt% CIPs has a stable shear yield stress over a wide range of shear rate (Fuchs et al., 2004). Xu et al. prepared several MR gels consisting plastic polyurethane matrix swollen by non-volatile solvent in different weight fractions of CIPs and their MR properties (both shear yield stress and modulus) were tested and analyzed. It was shown that the carrier has little effect on the linear viscoelastic (LVE) region of MRGs, though the magnitude the storage modulus G' can be greatly changed by the solvent content (Xu et al., 2013). The dynamic magneto-induced properties of the shear-stiffening gel under compression was measured by Wang et al. It was found that CIP contents have great influences on dynamic properties (Wang et al., 2016). Xu et al. developed MR gels with different weight fractions and the stress evolution characteristics of MRGs under stepwise shear loading are tested. It was found that the mass fraction of CIPs has a significant effect on the rheological properties of prepared materials. The dynamic modulus and the plain modulus increase along with CIPs weight fraction (Xu et al., 2017). These results indicate that the CIP weight fraction has a significant impact on the magneto-mechanical features of MR materials.

In addition, the basic carrier has a great impact on the rheological properties of MR materials (Xu et al., 2011). Mitsumata et al. firstly prepared carrageenan/iron oxide MR gels and the reversible rheological properties were tested. It was found that great variety of the storage modulus was almost not exhibited when the carrageenan concentration was 2 wt%; however, the MR effect appeared on reduced concentration. The limit variation in the relative storage modulus was 24 when the carrageenan concentration was 0.6 wt% (Mitsumata and Abe, 2011). Zhang et al. developed silicone-based MR gels by with 30, 50, and 70 wt% CIPs and the rheological properties were systematically tested, respectively. It was found that the content of silicone has a great influence on the zero-field viscosity, shear stress and response rate, and MR gel with 30 wt% silicone has the best MR effect (Zhang et al., 2018). Wilson et al. self-developed series of PUs and silicones matrix by controlling the weight of reactants and the content of modifier (reacting or non-reacting) and then developed PU-based and silicone-based MR gels, respectively. It was found that rheological property can be qualitatively controlled of as-developed MR products by adjusting the ratio of reactants and diluents. The PU and silicone polymers have three existing states, that is solid, gel, and liquid forms, according to the crosslinking and dilution (Wilson et al., 2002). Xu et al. developed a novel high-performance PU-based MR material. The dynamic properties of the MR material were systematically measured and the influences of the PU contents were analyzed. It was found that the material with 20% PU matrix weight fraction shows a high dynamic property (Xu et al., 2011). Fuchs et al. developed polyurethane (PU)-based and silicone-based MR gels, respectively. In this work, tunable rheological properties and settling rate were investigated. The results show that PU-based has the better particle settling resistance and has a high shear yield stress (23 kPa at 350 mT). Both dynamic and static shear stress values of the samples were found to be similar in magnitude: the dynamic and static shear stress of both PU and siliconebased produces with 84.5% weight mass CIPs under 120 mT range from 5 to 8 kPa (Fuchs et al., 2004). PU have attracted the attention of researchers among the various polymer matrixes due to better degradation stability than natural rubber and superior mechanical properties compared with silicone rubber. Interestingly, it is found that PU can be tuned from flow-able liquid to semi solid (gel like) depending upon the degree of crosslinking (Mordina et al., 2016). Accordingly, an appropriate carrier should be selected to prepare stable MR gels for obtaining a suitable modulus and wider magnetorheological effect. In addition, MRG based on PU has better sedimentation resistance and particle aggregation resistance (Wilson et al., 2002; Yang et al., 2015). The above characteristics can greatly simplify the sealing structure in the device structure design with MRG as the medium, thus reducing the cost, and is of certain significance to improve the stability of the device.

To this point, this research is to investigate the influence of the CIP fractions on their rheological properties with commercially available PU matrix. PU-based MR gels with CIP mass fractions of 40, 60, and 80% are freshly developed and the magnetic properties and microstructure were tested and analyzed accordingly. Then the magneto-mechanical features of MR gel under continuous shear with different CIP weight fractions are measured and discussed. Finally, the viscoelastic properties of MRGs were achieved by oscillatory shear measure. The effects of magnetic flux density, shear rate, strain amplitude and driving frequency on the dynamic properties of MR gel with different CIP weight fractions were discussed comprehensively.

# MR GELS PREPARATION

In this study, the synthesis of the MR gels was carried out by mixing CIPs (type: JCF2-2, JiLin Jien Nickel Industry Co., Ltd, China, with an average particle size of about 5 µm) into a commercial PU (Shanghai mile Chemical Technology Co., Ltd, China). The several important physical properties of PU employed in the study are exhibited in **Table 1**. The CIPs mass fraction of MR gels are selected as 40, 60, and 80%, respectively.

There are three-prongs in the development of MR gels. Firstly, weighing the exact quantity of the PU and CIPs. Placing PU matrix into three 250 ml beakers. Secondly, the carrier (PU) was mechanically stirred at 400 rpm for 30 min in the environment of a constant temperature (65◦C) in order to make the CIPs dispersed more uniformly. Finally, the CIPs with 40, 60, and 80% weight fractions were added into the accommodating matrix and were stirred at 750 rmp until the PU matrix and CIPs were fully and evenly mixed. In this paper, the three MRG samples were named as MRG-40, MRG-60, and MRG-80, respectively.

# PROPERTIES CHARACTERIZATION

The magnetic hysteresis characteristic of CIP and MR gels with CIPs weight fraction of 40, 60, and 80 % were measured by using the vibrating sample magnetometer (VSM, Lake Shore 7407, USA) at the temperature of 25◦C. A commercial rheometer (Physica MCR 302, Anton Paar Co., Austria) with plate (the diameter is 20 mm) was employed to measure the magnetic-induced mechanical properties of MR gels by continuous shear and oscillatory shear tests. The magnetic field generated by the coil can be controlled by regulating the current through the coil. The gap between the plate and the base was maintained at 1 mm so as to emerge symmetrical magnetic flux density range from 0 to 1,200 mT through the samples by adjusting the current in the coil from 0 to 5 A.

Rotational and oscillatory shear test are the most frequently used testing methods to investigate the rheological properties of materials. Scanning test of magnetic flux density (changing from 0 to 1,200 mT) was carried out under a constant shear rate of 50 s −1 during shear rotation test. The shear stress and viscosity of the products were tested under different magnetic flux densities (0, 240, 480, 720, and 960 mT), with shear rate from 1 to 100 s−1 . The dynamic properties of samples were captured by mean of oscillation shear. The amplitude changes from 0.01 to 10% under the strain amplitude sweeping at a constant frequency of 5 Hz. The oscillation frequency changes from 5 to 100 Hz for scanning of frequency measurements at a constant strain amplitude of 0.01%. Both the scanning measurements of strain amplitude and frequency were carried out under the four magnetic flux densities, which are 240, 480, 720, and 960 mT. In order to ensure the comparability of the test data, the pre-shearing process with a shear rate of 50 s−1 for 3 min was carried out before each step was measured.

# RESULTS AND DISCUSSION

# Magnetic Properties

The magnetic hysteresis properties of pure CIP and MR gels with different CIP content, i.e., 40, 60, and 80 wt%, were investigated by VSM. **Figure 1** display the magnetic properties of as-developed MR gels with various weight fraction of CIPs, which indicated that the samples exhibits obvious soft magnetic property. The moment increases linearly with the increase of magnetic field and then goes to saturation value. For CIP, the yielding starts around 5,000 Oe and when the external magnetic field strength increases to 8,000 Oe, CIP reaches a magnetic saturation state with a saturation moment of 206 emu/g. For MR gels, the CIPs weight fraction has great influence on saturation moment. MR gel with higher CIP weight fraction have higher saturated moment, i.e., about 54 emu/g for MRG-40, 91 emu/g for MRG-60, and 107 emu/g for MRG-80.

# Magnetic Field Sweep

The magnetic flux density dependence of shear stress for different samples in small strain (linear viscoelastic range) was shown in **Figure 2**. The magnetic flux density has a significant influence on the mechanical properties of samples. Shear stress increases with the enhancement of the magnetic flux density under the constant shear rate. When the magnetic flux density is very small, i.e., B < 100 mT, the shear stress of the samples changes slightly. With the increase of the magnetic flux density, the shear stress of the materials changes approximately linear at moderate magnetic field. When the magnetic flux densities are 700 and 900 mT, the shear stresses of MRG-40 and MRG-60 reach saturation value, 8 and 20 kPa, respectively; however, when the magnetic flux density increases to 1,200 mT, the shear stress of MRG-80 does not reach the saturation value, but its growth rate decreases obviously.

FIGURE 2 | (A) Shear stress as a function of magnetic flux density at · γ = 50 *s* −1 for samples; (B) microscopic chain structure (red solid line represents polyurethane polymer, and solid small circle represents CIPs).

Therefore, the change is roughly divided into three kinds of growth: the initial growth (from **Figures 3A,B**), the linear growth (from **Figures 3B,C**), and the saturate tendency (from **Figures 3C,D**). The change of magnetic-induced micro-structure of samples can be interpolated as the process that the CIPs inside material attempt to overcome the internal friction resistance (mainly the resistance of the polymer matrix). At the initial stage, the intertwined polymer chains are flexible along the moving direction under the drive of particles, and the damping force to restrict particles motion weakens slightly. Therefore, the chain forming process is also slow, and the change of microstructure is as shown from **Figures 3A,B**. With the increase of magnetic flux density, the particle chain presents a linear growth process in the flexible polymer chain environment as shown from **Figures 3B,C**. Further enhancing the magnetic field, the free particles combine into chains and become scarce as shown from **Figures 3C,D**, which leads to the saturated shear stress with the increasing of magnetic flux density. This phenomenon coincide with the hysteresis curve of samples in **Figure 1**.

# Rheology Properties in Rotational Shear

The shear stress and viscosity curves along shear rate of MR gels with various CIP weight fractions under different magnetic flux densities are exhibited in **Figures 4**, **5**, respectively. As shown in **Figure 4A**, in the absence of an external magnetic field, the shear stress increases linearly along with shear rate, which shows Newtonian fluid characteristics. With the influence of the magnetic flux density, the MR gel behaves as non-Newtonian fluid which needs to overcome a certain amount of the stress (named as yield stress) to become fluidic state, i.e., Bingham plastic behavior. It is shown that the yield stress increases with weight fraction at a given magnetic flux density. The magnetic flux density has a great impact on the yield stress of prepared MR materials, which changes from 2 to 10 kPa for 40 wt% MR gel and from 5.6 to 45 kPa for 80 wt% MR gel sample. This is due to the stronger interaction in chain-like structure at higher magnetic flux density level. After the yield stress, the shear stress has a slight increase along shear rate for the magnetic flux density below saturated magnetic flux density, which should be below 960 mT as under such conditions the MR gel has distinct saturation

yield stress. It implies that the better damping property at lower magnetic flux density levels. Under the magnetic flux density of 960 mT, the MR gel presents a slight shear thinning behavior, especially for 80 wt% sample, which has slight decreasing shear stress against shear rate.

The viscosity of the MR gel decreases along shear rate at low shear rate level, i.e., below 20 s−1 , shown in **Figure 5**. Such behavior is more distinct under the influence of the magnetic flux density. The CIP content has considerable impact on the viscosity of the MR gel with and without magnetic flux density. For example, at the magnetic flux density of 960 mT, the MRG-80 has a viscosity of 503 Pa.s at the shear rate of 100 s−1 ; with lower fraction of CIPs as 40 wt% the viscosity of the sample has significant reduction to 139 Pa.s.

# Rheological Properties Under Oscillatory Shear

Storage modulus and loss modulus are the key mechanical parameters used to reveal the dynamic properties of materials (Xu et al., 2013). Among them, the storage modulus is an important parameter to characterize the elastic properties of

materials, which can show the ability of materials to store energy (have the feature that all the energy completely available after the external load is removed) after shear deformation (Zhang et al., 2011). The storage modulus of the samples was studied by scanning shear strain amplitude change from 0.01 to 10% under the condition of constant strain frequency of 5 Hz at different constant magnetic flux density of 0, 240, 480, 720, and 960 mT, respectively. The results are shown in **Figure 6**.

As shown in **Figure 6A**, in the absence of an external magnetic flux density, storage modulus decreases rapidly along shear strain amplitude and then tends to stabilize beyond certain strain. It can be concluded that the ability of energy storage for PU matrix decreases with the increase of shear strain amplitude. With the influence of the magnetic flux density, as can be seen in **Figures 6B–E**, MR gels exhibit obvious linear viscoelastic region at the small strain range, which was the same as the dynamic properties of MR grease (Wang et al., 2019). It should be noted that the data is plotted with logarithmic horizontal axis to clear present the linear region. The shear strain amplitude has great impact on the storage modulus of samples. Firstly, the storage modulus of the material does not change with the increase of strain amplitude at small shear strain, indicating the linear viscoelasticity (LVE). Further increasing with the strain amplitude, the storage modulus decreases with the strain amplitude, which is called Payne effect (Arief and Mukhopadhyay, 2015), i.e., the impact of the applied strain amplitude on the storage modulus. Above an approximately 0.1% strain, the storage modulus decrease rapidly along with applied

strain amplitude. This threshold strain is called the critical strain amplitude of the material and is dependent on the fillers of the content in the matrix. The critical strain increases along with magnetic flux density and mass fraction of the CIP content for MRG and the critical strain values of samples under different magnetic flux density is shown in **Table 2**.

The linear viscoelastic properties of the MR gels have special physical meaning: in the linear viscoelastic region, the internal structure of the material is elastic deformation under shear strain. Once withdrawn, the structure is restored to its original shape, and the change has a continuous and reversible property.

Another important measure of the MR material is the MR effect. The MR effect is related to the zero field storage modulus and magneto-induced storage modulus at the same time. It increases with the increase of magneto-induced storage modulus and decreases with the increase of zero-field modulus. The specific expressions are as follows (Xu et al. 2011):

$$MR\,\widetilde{g\,\text{left(\(\%\)}} = \frac{G\_B^{\prime} - G\_{B=0}^{\prime}}{G\_{B=0}^{\prime}} \times 100\,,$$

where G ′ B is storage modulus under magnetic field, G ′ B=0x is the storage modulus without applied magnetic field, G ′ B − G ′ B=0 is magneto-induced storage modulus.

The magnetic flux density dependence of storage modulus for the materials is shown in **Figure 7**. It is found that the storage

B = 960mT).

TABLE 2 | The critical strain amplitude of samples under different field.

moduli of materials increase with the increase of CIP content under the same magnetic flux density. Interestingly, the MR effect of the 60 wt% MR gel is higher than that of 80 wt% MR gel (as shown in **Figure 8**). The MR effect of the samples with different mass concentrations of CIPs under different magnetic flux densities are shown in **Figure 8**. It should be noted that the MR effect was calculated based on the storage moduli measured at maximum strain value of linear viscoelastic range at saturated magnetic field flux density 960 mT and zero magnetic field. As indicated in **Figure 6** and **Table 2**, the strain value used for MR effect calculation is 0.02% below which is the strain to define linear viscoelastic range of the MR gel for all magnetic field levels. Each measurement was repeated five times to ensure accuracy of data and then the average values and standard error were taken. Among three samples, the 60 wt% MR gel has demonstrated the highest MR effect. In addition, it was shown that the MR effect does not increase along with the CIPs content. For instance, for MRG-60 and MRG-80, the MR effect at the magnetic flux density of 240, 480, 720, and 960 mT decreases as shown in **Figure 8**. Such behavior attributes to the off-state modulus of the samples, with MRG-80 has highest off-state modulus (Xu et al., 2011). The MR effect is determined by two factors in the LVE region, which are (i) the induced storage modulus of MR samples under magnetic field due to inter-action between the CIP particles, and (ii) the offstate storage modulus of the samples. Higher CIP content may increase the formation of the chain structure in the sample and lead to higher storage modulus. However, the high off-state shear modulus due to the high particle concentration compromises the relative increase of the modulus.

The storage properties and loss behavior of the samples were studied by scanning strain frequency from 5 to 100 Hz under different magnetic field at shear strain amplitude of 0.01%, which is within the linear viscoelastic range for all samples. The results are shown in **Figures 9**, **10**, respectively.

**Figure 9** shows the characteristic curves of storage modulusfrequency of the samples under different magnetic flux densities. At low frequency (<10 Hz), the shear frequency has a great influence on the storage modulus and increases with the increase of the storage modulus. However, the frequency dependence of storage modulus disappears when the frequency is beyond 10 Hz. This interesting phenomenon may be caused by changes in the internal microstructures of PU-based MR gels: PU-based matrix polymers in MR gels intertwined with each other initially. The orientation of these polymer chains distributes along the shear direction under the action of shear oscillation (Zhang et al., 2018). Therefore, the resistance of particles moving in the matrix decreases under the application of magnetic flux density, which makes the storage modulus of MR gels increase

FIGURE 7 | The magnetic flux density dependence of storage modulus for the samples with different mass concentration of CIPs.

firstly. This phenomenon is more obvious at the higher magnetic flux density. However, further increasing the shear frequency, the storage modulus no long changes, which indicates that the weakening of the storage modulus caused by molecular chain winding is compensated under low shear frequency. From **Figure 9**, in addition, it was shown that elastic performance (storage modulus) is also strongly dependent on CIPs mass fraction, which increases along CIPs mass fraction under the magnetic field.

The loss factor is an important parameter that was determined by both the storage and loss modulus of materials. The specific influence mechanism is explained by the following definition: the loss factor can be defined as the ratio of loss modulus to storage modulus. Therefore, the loss factor characterizes the damping performance of materials (Chandra et al., 1999).

When the frequency is <20 Hz, loss factor of samples shows a downward trend along with strain frequency. However, when the frequency is higher than 20 Hz, the frequency dependence of loss factor nearly disappears for both samples under the magnetic flux density. As we all know, the loss factor has something to do with the ability of energy dissipation for the material. This is mainly due to the interaction of different structures within the materials. That is to say the energy dissipation of as-prepared MR gels primarily determined by the interaction between CIPs and PU-based matrix. The position of CIPs changes under low frequency shear. During this process, the movement of CIPs are hindered by PU-based polymer chains and energy dissipation occurs. However, when the frequency increases to the threshold, the segment with strong partial bound has not yet been cut off, so the loss factor decreases along with applied shear frequency and finally tends to a stable state.

# CONCLUSIONS

Three PU-based MRGs with a CIPs mass fraction of 40, 60, and 80% were prepared and named MRG-40, MRG-60, and MRG-80, respectively. The static and dynamic tests of the materials were carried out. The conclusions are as follows: the influence of magnetic flux density on the mechanical properties of samples is remarkable, and its tendency with magnetic flux density can be divided into the initial growth, the linear

# REFERENCES

growth and the saturate tendency. In the absence of an external magnetic flux density, the shear stress increases linearly with the increase of the shear rate, which showing Newtonian fluid characteristics. The shear stress of the samples increases with the increment of the CIPs percentage. The shear strain amplitude has different influence on the storage modulus of the materials under different magnetic flux density, and the amplitude of LVE critical strain increases with the increase of magnetic flux density and CIPs mass fraction. It was found that the relative MR effect does not increase with the increasing of CIPs content. Storage modulus is also strongly dependent on CIPs mass fraction, which increases along CIPs mass fraction under the magnetic flux density while loss factor has the opposite trend.

# AUTHOR CONTRIBUTIONS

GZ conducted the research and wrote the paper. HW assisted the research. YL and JW supervised the research. YL edited the paper.

# FUNDING

This work is supported by the National Natural Science Foundation of China (No.51675280, No.51805209, and No.51705467) and the Postgraduate Scientific Innovation Research Foundation of Jiangsu Province (NO. KYCX18\_0457).

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Zhang, Li, Wang and Wang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Ride Quality Control of a Full Vehicle Suspension System Featuring Magnetorheological Dampers With Multiple Orifice Holes

Jong-Seok Oh1 \* and Seung-Bok Choi 2 \*

*1 Division of Mechanical & Automotive Engineering, Kongju National University, Cheonan-Si, South Korea, 2 Smart Structures and Systems Laboratory, Department of Mechanical Engineering, Inha University, Incheon, South Korea*

This study proposes a relationship between the ride comfort of passenger vehicles and two different types of magnetorheological (MR) dampers, with and without orifice holes in the piston. To achieve superior ride comfort, two cylindrical-type MR dampers with identical dimensions (piston radius, pole lengths, and the distance between two poles) are proposed. One of the MR dampers adds the orifice holes in the piston bobbin to obtain a relatively low damping force slope in the low piston velocity region. To enhance the ride quality of a passenger vehicle, the damping force slope of the rear damper should be more gradual than that of the front damper. Thus, it can be inferred that identical semi-active vehicle systems require normal MR dampers in the front and MR dampers with orifice holes in the rear, with proper control strategies. To evaluate ride performance, a robust sliding mode controller was designed. It is demonstrated through simulation that the proposed vehicle system produces better ride comfort than vehicle systems equipped with only one type of MR damper.

Keywords: magnetorheological fluid, MR damper with orifice hole (OMRD), ride quality, damping force, sliding mode controller, passenger vehicle

# INTRODUCTION

Magnetorheological (MR) fluid is considered a smart material because its rheological properties can be controlled by the application of magnetic fields. Specifically, the yield shear stress of MR fluid is easily controlled by the intensity of the magnetic field. Owing to this salient feature, numerous studies have been conducted on the development of new application devices and systems using this material, and continuous advancements are being made. Among its numerous applications, MR dampers for vehicle suspension systems have been commercialized and installed in numerous vehicles of different types, such as passenger vehicles and sport utility vehicles, for the improvement of the ride quality by controlling unwanted vibrations. Conventionally, the primary design parameters of MR dampers for vehicle suspension applications are: the magnetic gap in which MR fluids flow between the upper and lower chambers, the radius of the piston, and the bobbin structures with coil turns. By appropriately selecting these primary design parameters, successful vibration control performance can be obtained. Furthermore, when a control device malfunctions during the operation of an MR suspension system, it can still provide vibration control because of the viscosity of the MR fluid serving as its carrier liquid. Active suspension systems of vehicles also provide excellent vibration control capability during normal operation.

### Edited by:

*Ilkwon Oh, Korea Advanced Institute of Science & Technology (KAIST), South Korea*

#### Reviewed by:

*Hargsoon Yoon, Norfolk State University, United States Youngjae Chun, University of Pittsburgh, United States Taihong Cheng, Wenzhou University, China*

#### \*Correspondence:

*Jong-Seok Oh<EMAIL_ADDRESS>Seung-Bok Choi<EMAIL_ADDRESS>
#### Specialty section:

*This article was submitted to Smart Materials, a section of the journal Frontiers in Materials*

Received: *30 November 2018* Accepted: *15 January 2019* Published: *04 February 2019*

#### Citation:

*Oh J-S and Choi S-B (2019) Ride Quality Control of a Full Vehicle Suspension System Featuring Magnetorheological Dampers With Multiple Orifice Holes. Front. Mater. 6:8. doi: 10.3389/fmats.2019.00008*

**538**

However, vibration control stability of an active suspension system could be lost because of a malfunction of the numerous sensors and actuators that require a sophisticated control logic and are significantly costly (Sunwoo et al., 1991).

The benefits of a semi-active MR damper are fast response time, easy controllability, and a simple structure. Dyke et al. researched an MR damper for absorbing seismic vibrations and verified the validity of a proposed analytical model of the MR damper (Dyke et al., 1996). Carson et al. researched an MR damper for vehicle suspension systems and applied a sky-hook controller to evaluate vibration control performance (Carlson et al., 1996). Choi et al. proposed a novel controller to improve the ride quality of a vehicle using the MR damper (Choi et al., 2009; Sung and Choi, 2012). In addition to the above studies, a number of studies have been conducted on the vibration control performance of passenger vehicles using electrorheological (ER) or MR dampers (Ahmadian and Pare, 2000; Choi et al., 2001; Yao et al., 2002; Poussot-Vassal et al., 2006; Brigley et al., 2008; Choi and Sung, 2008; Sung et al., 2013). All MR dampers used in these previous studies were cylindrical types in which MR fluid flows only through the magnetic gap (or orifice). This type of MR damper exhibits a steep slope of the field-dependent damping force in the low range of piston velocities, which could degrade the smooth motion of the vehicle body at low speeds. Therefore, a number of researches have proposed an MR damper which has orifice holes to allow increased MR fluid flow without any magnetic effect like in the passive viscose-resistance holes (Hong et al., 2007; Bai et al., 2013; Sohn et al., 2015; Park et al., 2016). Hong et al. researched a hydro-mechanical model to analyze the field-dependent damping force of an MR damper with orifice holes (Hong et al., 2007). Bai et al. researched an MR damper featuring inner orifice holes for increased MR fluid flow and applied it to land-vehicle suspensions for vibration control (Bai et al., 2013). Sohn et al. researched an MR damper with orifice holes in the piston and investigated its field-dependent damping force characteristics (Sohn et al., 2015). Recently, Park et al. reported that an MR damper with orifice holes exhibited a relatively lower damping force slope than an MR damper without orifice holes (Park et al., 2016).

Different ride frequencies and damping ratios are experienced by a vehicle as the front and rear wheels experience different static loads because of the weight distribution. Therefore, a difference in optimum values between the front and rear damping should be anticipated (Georgiou and Natsiavas, 2009; Albinsson and Routledge, 2019). Typically, the slope of the damping force of the front damper is high because of the mass of the engine, as shown in **Figure 1**. Therefore, in this study, MR dampers with (or without) orifice holes were used as rear or front dampers. The ride quality of the total vehicle system is then evaluated. Despite the number of studies on MR dampers with orifice holes, the relationship between the ride comfort of a vehicle and the effect of using different types of front/rear MR dampers has not yet been reported on.

The originality of this study lies in demonstrating the superior ride quality achieved by using two different types of MR dampers as opposed to one. To achieve this aim, two MR dampers, applicable to middle-sized passenger cars, are considered based

on a mathematical model. Prior to investigating the ride comfort, the field-dependent damping force characteristics of two MR dampers were evaluated via simulation, and a full car mathematical model was derived. A sliding mode controller was then designed. Vibration control performance and ride quality were then investigated and evaluated under two different road profiles: bumps, and random road excitations. The reductions in both body displacements and body accelerations in the ride comfort of a vehicle equipped with two different types of MR dampers is significantly improved compared to with one using the same type of MR dampers.

 The MR damper can be divided into upper and lower chambers, and it is filled with MR fluid. The MR fluid flows from one chamber to the other through the orifice. The gas chamber acts as an accumulator for absorbing sudden pressure variations in the lower chamber of the MR damper induced by the fast motion of the piston. By neglecting frictional forces, the damping force of the MR damper can be written as follows:

$$F\_{d\\_MRD} = k\_e x\_p + F\_\nu + F\_{MR} \text{ sgn} \left( \dot{x}\_p \right) \tag{1}$$

where xp and x˙p are the piston displacement and velocity, respectively.

The first term in Equation (1) represents the spring force from the gas compliance, and the spring constant of the air chamber can be expressed as follows (Choi and Han, 2012):

$$k\_{\text{e}} = \frac{A\_r r^2}{C\_\text{g}} = \frac{P\_0 \kappa}{V\_0} A\_r r^2 \tag{2}$$

where Ar is the piston-rod area; P0 and V0 are the initial volume and pressure of the gas chamber, respectively; Cg is the gas compliance in the gas chamber;κ is the specific heat ratio.

The second term in Equation (1) represents the damping force due to the viscosity of the MR fluid. The viscous damping force of the damper is as follows:

$$F\_V = \Delta P \left( A\_p - A\_r \right)$$

$$\Delta P = \rho g h\_f \tag{3}$$

where Ap and Ar are the cross-sectional areas of the piston and piston head, respectively; 1P is the pressure difference between the upper and lower chambers; hf is the head loss induced by the viscous friction force. As mentioned earlier, the MR fluid flows through the gap and the orifice holes. Therefore, the head loss for the annular duct and orifice holes should be derived. Initially, the annular duct flow is assumed as the flow of a duct between two parallel plates (Choi and Han, 2012). This assumption is valid because the radius of the duct is greater than the radius of the gap. From this assumption, the head loss for the annular duct is as follows:

$$h\_{\rm duct} = f\_{\rm duct} \frac{L\_{\rm duct}}{D\_{\rm duct}} \frac{V\_{\rm duct}}{2g} = \frac{96 \eta V\_{\rm duct} L\_{\rm duct}}{2g \rho D\_{\rm duct}^2}$$

$$D\_{\rm duct} = \frac{4 \,\text{Wd}}{2d + 2 \,\text{W}} = \lim\_{W \to \infty} \frac{4 \,\text{Wd}}{2d + 2 \,\text{W}} \cong 2d\tag{4}$$

where fduct, Dduct , and Lduct are the friction coefficient, the diameter, and the length of the duct, respectively; Vduct is the flow velocity through the duct; η is the viscosity constant of the MR fluid. As the total flow rate is identical to the flow rate at the orifice, the velocity of the duct and the viscous damping force can be obtained as follows:

$$\begin{aligned} \dot{\varkappa}\_{\mathcal{P}} \left( A\_{\mathcal{P}} - A\_{r} \right) &= V\_{\text{dact}} A\_{\text{dact}} \\ F\_{\text{v\\_MRD}} &= \rho g h\_{\mathcal{f}} \left( A\_{\mathcal{P}} - A\_{r} \right) = \frac{12 \eta L\_{\text{dact}}}{d^{2}} \frac{\left( A\_{\mathcal{P}} - A\_{r} \right)^{2}}{A\_{\text{dact}}} \dot{\varkappa} \end{aligned} \tag{5}$$

The third term in Equation (1) is deduced from the yield stress of the MR fluid, which can be controlled by the magnitude of the magnetic field. This phenomenon is due to the polarization induced in the particles by applying a magnetic field. The induced dipoles cause the particles to form columnar structures parallel to the applied magnetic field. This phenomenon increases the restriction in the flow direction. To describe the rheological behaviors of MR fluids, the Bingham model is adopted as follows:

$$\pi\_{\mathcal{Y}}(B) = A\_0 + A\_1B + A\_2B^2 + A\_3B^3 + A\_4B^4 + A\_5B^5 + A\_6B^6$$

$$B = a\_0 + a\_1H + a\_2H^2 + a\_3H^3 + a\_4H^4 + a\_5H^5 + a\_6H^6 \quad \text{(6)}$$

where τy (B) is the yield shear stress and is a function of the magnetic flux density, B. This function can be expressed by the polynomial function of magnetic intensity, H. It is known that [a0 , a1, a2, a3, a4, a5, a6] = [−155.548 328630593 − 277283388 119373779 − 27459273 3198253 − 146313.95]. In this study, the commercial MR fluid (RMS Corp., MRF 500CP) was used. Based on the Bingham model, the controllable damping force induced from the yield stress of the MR fluid can be represented as follows:

$$F\_{MR} = \left(A\_{\mathcal{P}} - A\_r\right) \frac{cL\_m}{h\_m} \mathbf{r}\_{\mathcal{V}}(B) \tag{7}$$

where Lm is the length of the magnetic pole; hm is the gap between the magnetic poles; c is the coefficient dependent on the flow velocity profile and has a value of 2.0–3.0.

# MR Damper With Orifice Holes

The schematic configuration of the proposed MR damper utilizing an orifice hole is shown in **Figure 3**. The piston head comprises a bobbin, orifice holes, and a coil. The MR fluid flows through the orifice hole and the gap between the bobbin and the outer housing of the piston head. As the orifice hole is closer to the center of the non-magnetic hollow cylinder than the coil, the magnetic flux induced from the coil is mainly applied to gap. Since the magnetic field has little effect on orifice hole, the viscous damping force model of OMRD is different with that of MRD. More information related to magnetic analysis can be found in our previous study (Sohn et al., 2015; Park et al., 2016). Since the MR fluid of the OMRD flows through the annular duct and orifice holes, the head loss for the orifice hole is represented as follows:

$$h\_{b\gamma} = f\_{b\gamma} \frac{L\_{b\gamma}}{D\_{by}} \frac{V\_{by}^2}{2g} = \frac{64\eta V\_{by} L\_{by}}{2g\rho D\_{by}^2} \tag{8}$$

where fby, Dby, and Lby are the friction coefficient, the diameter, and the length of the orifice hole, respectively. Particularly, the other components of damping force model are identical to Equation (1). As the inlet and outlet for the annular duct and orifice hole are identical, the velocities of the annular duct (Vduct) and the orifice hole (Vby) are obtained as follows:

$$V\_{b\text{\textquotedblleft}} = \dot{\mathbf{x}}\_{\text{\textquotedblleft}} \frac{\left(A\_{\text{\textquotedblleft}} - A\_{r}\right)}{\left(A\_{b\text{\textquotedblleft}} + \frac{2L\_{\text{dry}}}{3D\_{\text{by}}^{2}} \frac{D\_{\text{duct}}}{L\_{\text{duct}}} A\_{\text{duct}}\right)},$$

$$V\_{\text{duct}} = \dot{\mathbf{x}}\_{\text{\textquotedblleft}} \frac{\left(A\_{\text{\textquotedblleft}} - A\_{r}\right)}{\left(A\_{\text{duct}} + \frac{3L\_{\text{duct}}}{2D\_{\text{duct}}} \frac{D\_{\text{by}}}{L\_{\text{dy}}} A\_{\text{by}}\right)}\tag{9}$$

By substituting Equations (8, 9) into Equation (3), the damping force induced by the viscous friction force is represented as follows:

$$F\_{\rm V\\_OMRD} = \rho g h\_f \left( A\_{\rm P} - A\_r \right) = \frac{32 \eta L\_{\rm by}}{D\_{\rm by}^{\prime 2}} \frac{\left( A\_{\rm P} - A\_r \right)^2}{\left( A\_{\rm by} + \frac{2L\_{\rm by}}{3D\_{\rm by}} \frac{D\_{\rm davt}}{L\_{\rm davt}} A\_{\rm duct} \right)} \dot{\mathbf{x}}\_{\rm P}$$

$$= \frac{12 \eta L\_{\rm davt}}{d^2} \frac{\left( A\_{\rm p} - A\_r \right)^2}{\left( A\_{\rm duct} + \frac{3L\_{\rm davt}}{2D\_{\rm davt}} \frac{D\_{\rm bv}}{L\_{\rm bv}} A\_{\rm bv} \right)} \dot{\mathbf{x}}\_{\rm P} \tag{10}$$

From the obtained viscous damping force model in Equations (5, 10), it is observed that the obtained viscous damping force of the OMRD is smaller than that of the MRD. In addition, when magnetic input is applied to the coil, and the damper is moved at a low piston velocity, it is difficult for the MR fluid to flow in the annular duct. The viscous damping force in the orifice hole is expressed as follows:

$$F\_{\nu\_{\text{\tiny or}}\text{or}\text{\tiny cfee}} = \rho g h\_{\text{\tiny f}} \left( A\_{\text{\tiny p}} - A\_{\text{\tiny r}} \right) = \frac{32 \eta L\_{\text{by}}}{D\_{\text{by}}^{\text{-}2}} \frac{\left( A\_{\text{\tiny p}} - A\_{\text{\tiny r}} \right)^{2}}{A\_{\text{by}}} \dot{\mathbf{x}}\_{\text{\tiny p}} \tag{11}$$

The orifice holes are located close to the center of the bobbin to avoid the MR fluid effect on the flow motion through the orifice hole. When magnetic input is applied to the MR damper, fluid friction induced from yield stress makes the MR fluid flow via only the orifice hole. However, at high piston velocity, the viscous damping force in the orifice hole is larger than the viscous and the controllable damping force in the orifice, as shown in **Figure 4**.

Therefore, the total damping force of the (OMRD) is expressed as follows:

$$F\_{d\_{\text{-}OMRD}} = \min\left(F\_{\nu\_{\text{-}O}\text{fict}}, F\_{\nu\_{\text{-}OMRD}} + F\_{\text{MR}}\text{sgn}\left(\dot{\mathbf{x}}\_{\text{P}}\right)\right) + k\_{\text{\textdegree}}\tag{12}$$

where min () means the minimum value between two damping forces.

## Characteristics of Damping Force

From the damping force models in Equations (1, 12), analytical calculations were implemented on a personal computer for MRD and OMRD. Appropriate design parameters were obtained to generate a maximum damping force of 4,000 N, which is the required damping force for a middle-sized passenger car. Design parameters were selected based on an input current of 3 A. The properties of the MR fluid and the design specifications of MR dampers are presented in **Table 1**. To reasonably compare the ride comfort of the vehicle under the different conditions, all design parameters of the two dampers were identical, except for the orifice holes. The number of orifice hole is 4, and the diameter of the orifice hole is 2.5 mm.

**Figures 5A–C** shows the calculated damping force curves. Firstly, under the same input current, the maximum damping force of the OMRD is lower than that of the MRD. The maximum damping forces of each damper are 4,238 N, 3,890 N, and 3,657 N, respectively. Additionally, the damping force gradients at 0 A are 1,534 N · s/m, 1,303.5 N · s/m, and 1,148 N · s/m, respectively. This is the result of the additional flow rate via the orifice holes, which are not affected by the input current, reducing the damping force. It can be inferred from these results that the orifice hole limits the maximum damping force. However, this does not imply that the damping force can be controlled by orifice holes. Secondly, parameter study of MR damper with orifice hole had been conducted and the results can be found in our previous study (Sohn et al., 2015). From previous study results, the number of orifice holes is considered as dominant factor among many design parameters. From **Figure 5**, it is known that the damping force of OMRD is smaller than that of MRD. Also, the low damping characteristic is generally known as essential for superior ride quality (Els et al., 2007). So, it can be expected that MR damper with many orifice hole ensure

good ride quality. Although the main objective of this work is to evaluate the ride quality of MRD and OMRD, optimal design of MR damper related to damping capability also very important for commercialization so it will be conducted as a future study. Thirdly, **Figures 5B,C** show that the orifice holes reduce the occurrence of sudden increases in the field-dependent damping force at low piston velocities. In other words, the damping force with 4 orifice holes is smaller than that with 2 orifice holes. The maximum difference in damping force is 1831.5 N at low velocity (approximately 0.05 m/sec) at 3 A. This difference in the trend of damping force controllability by the magnitude of the current will result in different ride qualities for the vehicles. Accordingly, in order to compare the performance in ride quality, MRD and OMRD with 4 orifice holes will be considered at next chapter.

# Performance Evaluation of Ride Comfort

As discussed earlier, as the front and rear wheels experience different static loads because of weight distribution, different values are applied. Therefore, it is anticipated that the required damping force characteristics of the front or rear suspension are in agreement with those of the MRD or OMRD. To investigate this, different vehicle case studies were conducted:

**Vehicle I**: Four identical MRDs are installed for the front and rear suspension.

**Vehicle II**: Two MRDs (or two OMRDs) are installed for the front (or rear) suspension.

In addition, a robust sliding mode controller was designed and applied identically to all vehicles. By comparing the control performance, we aim to demonstrate the effectiveness of the proposed method.

# Vehicle Suspension System

The mathematical model of the full car system with four MR shock absorbers is constructed as shown in **Figure 6**. The vehicle body (sprung mass) is assumed to be rigid and has three degrees of freedom (vertical, pitch, and roll directions). The sprung mass is connected to four unsprung masses that have

a vertical degree of freedom. The full car model includes body bounce (zg ), body roll (ϕ ), body pitch (θ ), wheel hop (z1, z2, z3, and z4), and independent road excitations (r1, r2, r3, and r4). The ride comfort of a passenger could be significantly affected because of the vibrations in the bounce, pitch, and roll directions. Therefore, in this study, the design configuration of the proposed MR damper and controllers was simulated to consider these multiple vibration modes. From **Figure 6**, the governing equations of motion are derived as follows (Jazar, 2017):

Mx¨ = −cf x˙ − ˙x1 + b1φ˙ − a1θ˙ − cf x˙ − ˙x2 − b2φ˙ − a1θ˙ − cr x˙ − ˙x3 − b2φ˙ + a2θ˙ − cr x˙ − ˙x4 + b1φ˙ + a2θ˙ − kf (x − x1 + b1φ − a1θ) − kf (x − x2 − b2φ − a1θ) − kr(x − x3 − b2φ + a2θ) − kr(x − x4 + b1φ + a2θ) + FMR1 + FMR2 + FMR3 + FMR4 Ixφ¨ = −b1cf (x˙ − ˙x1 + b1φ˙ − a1θ˙) + b2cf (x˙ − ˙x2 − b2φ˙ − a1θ˙) + b2cr(x˙ − ˙x3 − b2φ˙ + a2θ˙) − b1cr(x˙ − ˙x4 + b1φ˙ + a2θ˙) − b1kf (x − x1 + b1φ − a1θ) + b2kf (x − x2 − b2φ − a1θ) + b2kr(x − x3 − b2φ + a2θ) − b1kr(x − x4 + b1φ + a2θ) + b1FMR1 − b2FMR2 − b2FMR3 + b1FMR4 Iyθ¨ = a1cf (x˙ − ˙x1 + b1φ˙ − a1θ˙) + a1cf (x˙ − ˙x2 − b2φ˙ − a1θ˙) − a2cr(x˙ − ˙x3 − b2φ˙ + a2θ˙) − a2cr(x˙ − ˙x4 + b1φ˙ + a2θ˙) + a1kf (x − x1 + b1φ − a1θ) + a1kf (x − x2 − b2φ − a1θ) − a2kr(x − x3 − b2φ + a2θ) − a2kr(x − x4 + b1φ + a2θ) − a1FMR1 − a1FMR2 + a2FMR3 + a2FMR4 mf x¨1 = cf (x˙ − ˙x1 + b1φ˙ − a1θ˙) + kf (x − x1 + b1φ − a1θ) − ktf (x1 − y1) − FMR1 mf x¨2 = cf (x˙ − ˙x2 − b2φ˙ − a1θ˙) + kf (x − x2 − b2φ − a1θ) − ktf (x2 − y2) − FMR2 mrx¨3 = cr(x˙ − ˙x3 − b2φ˙ + a2θ˙) + kr(x − x3 − b2φ + a2θ)

### TABLE 2 | Parameters of passenger vehicle system.

$$-\left.k\_{\rm tr}(\mathbf{x}\_3 - \mathbf{y}\_3) - F\_{\rm MR3}\right|$$

$$m\_r \ddot{\mathbf{x}}\_4 = c\_r(\dot{\mathbf{x}} - \dot{\mathbf{x}}\_4 + b\_1 \dot{\boldsymbol{\phi}} + a\_2 \dot{\boldsymbol{\theta}}) + k\_r(\mathbf{x} - \mathbf{x}\_4 + b\_1 \boldsymbol{\phi} + a\_2 \boldsymbol{\theta})$$

$$-\left.k\_{\rm tr}(\mathbf{x}\_4 - \mathbf{y}\_4) - F\_{\rm MR4}\right|\tag{13}$$

where M is the sprung mass; mf and mr are the front and rear unsprung masses, respectively; Ix and Iy are the longitudinal and lateral mass moments of inertia, respectively; kf and kr are the front and rear suspension stiffness constant, respectively; kt is the tire stiffness; cf and cr are the front and rear suspension damping coefficients, respectively; and a1, a2, b1, and b2 are the distances from the center of gravity to each sprung mass and shock absorber.

By defining the state vector of the vehicle dynamic system as **X** = - x x˙ φ φ θ ˙ θ˙ x1 x˙1 x2 x˙2 x3 x˙3 x4 x˙4 T , the state space model for the vehicle dynamic system can be rewritten as follows:

$$\begin{aligned} \dot{\mathbf{X}} &= \mathbf{A}\mathbf{X} + \mathbf{B}\mathbf{U} + \Gamma \mathbf{D} \\ \mathbf{Y} &= \mathbf{C}\mathbf{X} \end{aligned} \tag{14}$$

Where **A**, **B**, Ŵ, **C**, **U**, and **D**are defined in **Appendix 1**. **Y**is the piston velocity matrix of each damper. **Table 2** presents the mechanical properties of the vehicle system, and in it the spring and damping properties of the front and rear suspensions are different.

## Controller Design

To evaluate the control performance, a sliding mode controller (SMC), which has an inherent robustness against system uncertainties and disturbances (Edwards and Spurgeon, 1998; Utkin et al., 1999), was designed. Before designing the SMC, multiple inputs of the vehicle system in Equation (13) are transformed as follows:

$$
\begin{bmatrix} u\_1 \\ u\_2 \\ u\_3 \\ u\_4 \end{bmatrix} = T \begin{bmatrix} F\_{MR1} \\ F\_{MR2} \\ F\_{MR3} \\ F\_{MR4} \end{bmatrix} = \begin{bmatrix} 1 & 1 & 1 & 1 \\ b\_1 & -b\_2 & -b\_2 & b\_1 \\ -a\_1 & -a\_1 & a\_2 & a\_2 \\ -1 & 0 & 0 & 0 \end{bmatrix} \begin{bmatrix} F\_{MR1} \\ F\_{MR2} \\ F\_{MR3} \\ F\_{MR4} \end{bmatrix} \tag{15}
$$

To regulate the generalized inputs, the sliding surfaces are designed as follows:

$$\begin{aligned} s\_1 &= \mathbf{G}\_1 \mathbf{X} = c\_1 \mathbf{x} + \dot{\mathbf{x}} \\ s\_2 &= \mathbf{G}\_2 \mathbf{X} = c\_2 \boldsymbol{\phi} + \dot{\boldsymbol{\phi}} \\ s\_3 &= \mathbf{G}\_3 \mathbf{X} = c\_3 \boldsymbol{\theta} + \dot{\boldsymbol{\theta}} \\ s\_4 &= \mathbf{G}\_4 \mathbf{X} = c\_4 \boldsymbol{\omega}\_1 + \dot{\boldsymbol{\omega}}\_1 \end{aligned} \tag{16}$$

A control law must be selected to drive the system state to the sliding surface s = 0, in which the following reachability condition is satisfied:

$$\left|s\_{i}\dot{s}\_{i}\right| \leq -\eta \left|s\_{i}\left(t\right)\right|, \ i = 1,2,3,4\tag{17}$$

where η is a strictly positive constant. To satisfy the reachability condition in Equation (17), the control input is determined as follows:

$$u\_i = -(\mathbf{G}\_i \mathbf{B}\_i)^{-1} \left[ \mathbf{G}\_i \mathbf{A} \mathbf{X} \begin{pmatrix} t \end{pmatrix} + k\_i \cdot \text{sgn} \left( s\_i \begin{pmatrix} t \end{pmatrix} \right) \right] \tag{18}$$

where sgn (·) is a signum function andki is the discontinuous gain which is designed to overcome the uncertainty of the passenger vehicle system. The left side of Equation (16) is expressed as follows:

$$\begin{aligned} s\dot{s} &= s\_l \mathbf{G}\_l \dot{\mathbf{x}} \\ &= s\_l \left[ \mathbf{G}\_l \mathbf{A} \mathbf{X} + \mathbf{G}\_l \mathbf{B}\_l \mathbf{U} + \mathbf{G}\_l \Gamma \mathbf{D} \right] \\ &= s\_l \left[ \mathbf{G}\_l \mathbf{A} \mathbf{X} - \left[ \mathbf{G}\_l \mathbf{A} \mathbf{X} + k\_l \cdot \text{sgn}\left(s\left(t\right)\right) \right] + \mathbf{G}\_l \Gamma \mathbf{D} \right] \\ &= s\_l \left[ -k\_l \cdot \text{sgn}\left(s\left(t\right)\right) + \mathbf{G}\_l \Gamma \mathbf{D} \right] \\ &\leq \left| s\_l \right| \left( -k\_l \right) \end{aligned} \tag{19}$$

Therefore, to ensure that the condition (17) holds, the discontinuous control gain in Equation (18) is chosen as follows:

$$k\_i \succ |\mathbf{G}\_i \Gamma \mathbf{D}| \tag{20}$$

Moreover, the signum function is switched with a saturation function to avoid the problem of chattering:

$$\text{sat}\left(s\_i\left(t\right)\right) = \begin{cases} \frac{s\_i(t)}{\varepsilon}, & |s\left(t\right)| \le \varepsilon\\ \text{sgn}\left(s\_i\left(t\right)\right), & |s\left(t\right)| > \varepsilon \end{cases} \tag{21}$$

where ε is the boundary layer width of the saturation function. Finally, the control input voltage is determined as follows:

$$u\_i = - (\mathbf{G}\_i \mathbf{B}\_i)^{-1} \left[ \mathbf{G}\_i \mathbf{A} \mathbf{X} + k\_i \cdot \text{sat} \left( \mathbf{s}\_i \left( t \right) \right) \right] \tag{22}$$

Then the generalized inputs are transformed to original inputs of the vehicle system via the inverse matrix of T.

The block diagram of the control strategy is shown in **Figure 7**, from which the minimum and maximum damping forces are calculated based on the damping force model and piston velocity. When the desired damping force is obtained from the sliding mode controller in Equation (22), the final damping force is determined by comparing the minimum and maximum values.

# RESULTS AND DISCUSSIONS

The MR suspension system should be installed on an actual vehicle and its effectiveness for ride comfort should be evaluated under various road conditions. However, it is expensive to manufacture a full vehicle system from scratch with hardware. Therefore, the ride quality performance and MR dampers are evaluated by computer simulation. A number of previous studies have reported that simulation results are in relatively good agreement with field test results (Seong et al., 2011, 2012; Park et al., 2016).

In this study, suspension control performance was evaluated under two types of road conditions. The first excitation, which is typically used to reveal the transient response characteristics, is a bump described by:

$$y\_i = z\_b \left(1 - \cos\left(\frac{2\pi V}{D}t\right)\right), \quad i = 1, 2, 3, 4\tag{23}$$

where zb is half of the bump height (0.035 m), and D is the width of the bump (0.8 m). In the bump excitation, the vehicle crosses the bump at a constant vehicle velocity of 40 km/h (11.12 m/s). The second type of road excitation is a stationary random process with zero mean, described by White (1994):

$$
\dot{\nu}\_i + \rho\_r V \dot{\nu}\_i = W\_n, \quad i = 1, 2, 3, 4 \tag{24}
$$

where Wn is the white noise with intensity 2σ 2ρrV; ρr is the road roughness parameter, 0.45 m−1 ; σ 2 is the covariance of white noise, 300 mm2 . For random excitations, the road irregularity values were chosen by supposing that the vehicle drives on a paved road at a constant velocity of 72 km/h (20 m/s).

**Figures 8**, **9** show road bump responses under road bump excitation. It is typically accepted that the acceleration of the sprung mass is used to evaluate ride comfort. As seen in **Figure 8**, unwanted vibrations induced from the bump excitations have been significantly reduced by adopting the different damper combinations. It was also observed from the vertical displacement of the sprung mass, vertical acceleration of the sprung mass, pitch angle, and roll angle that the ride comfort of **Vehicle II** is superior to that of **Vehicle I**.

**Figure 10** shows random road responses at a constant vehicle velocity of 72 km/h (20 m/s). The power spectral density (PSD) of the vertical acceleration is plotted against frequency. As anticipated, the PSDs for the vertical acceleration of **Vehicle II** are significantly decreased compared to those of **Vehicle I,** from 2.62 to 0.1364 (m/s2 ) 2 /Hz at 3.1 Hz. The suspension control performances shown in **Figures 8**–**10** indicates that the ride comfort of the vehicle can be simultaneously improved by employing two front MRDs and two rear OMRDs.

# CONCLUSION

In this study, the ride comfort of passenger vehicles equipped with different combinations of front/rear suspension systems featuring two different types of MR dampers, with and without orifice holes, were compared. To achieve this aim, the damping force model of the two different MR dampers were analyzed. It was observed that the OMRD exhibited a smaller damping force than the MRD. To evaluate the ride quality, a robust sliding mode controller was designed. It was demonstrated that displacement, acceleration of the vehicle body, and pitch angle could be significantly reduced by activating the MR dampers under two road conditions: bumps, and random roads. In particular, it was shown that the ride quality performance of the vehicle with different damper combinations was superior to that of a vehicle with the same type of MR dampers. This was because of the small damping force in the low piston velocity range. In other words,

# REFERENCES

Edwards, C., and Spurgeon, S. (1998). Sliding Mode Control. London: CRC Press.

by eliminating sudden increases in the field-dependent damping force, smooth and comfortable vehicle motions are obtained. In the second phase of this study, two semi-active MR dampers will be manufactured, and the ride comfort of both will be tested under various road conditions.

# AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

# ACKNOWLEDGMENTS

This work was supported by the Technology Innovation Program (Intelligent landing gear with variable damping force for 1500lb class) (10073291) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea).

and Magnetorheological Suspensions. (Singapore, World Scientific Publishing Company). 438–444.

Jazar, R. N. (2017). Vehicle Dynamics: Theory and Application. Berlin: Springer

Utkin, V., Guldner, J., and Shi, J. (1999). Sliding Mode Control in Electromechanical Systems. London; Boca Raton, FL: CRC Press.

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Oh and Choi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# APPENDIX I

# Swelling, Thermal, and Shear Properties of a Waste Tire Rubber Based Magnetorheological Elastomer

Ubaidillah1 \*, Endra Dwi Purnomo1 , Hanafi Ismail 2 , Seung-Bok Choi 3 \*, Aishah Abdul Aziz 4 and Saiful Amri Mazlan4 \*

*1 Fungsional Materials and Actuators Laboratory, Mechanical Engineering Department, Universitas Sebelas Maret, Surakarta, Indonesia, 2 School of Materials and Mineral Resources Engineering, USM Engineering, Nibong Tebal, Malaysia, 3 Department of Mechanical Engineering, Inha University, Incheon, South Korea, 4 Engineering Materials and Structures (eMast) iKohza, Malaysia Japan International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, Kuala Lumpur, Malaysia*

Edited by: *Miao Yu, Chongqing University, China*

### Reviewed by:

*Rongjia Tao, Temple University, United States Jie Zhang, Chongqing University, China*

#### \*Correspondence:

*Ubaidillah<EMAIL_ADDRESS>Seung-Bok Choi<EMAIL_ADDRESS>Saiful Amri Mazlan<EMAIL_ADDRESS>
#### Specialty section:

*This article was submitted to Smart Materials, a section of the journal Frontiers in Materials*

Received: *27 November 2018* Accepted: *27 February 2019* Published: *26 March 2019*

#### Citation:

*Ubaidillah, Purnomo ED, Ismail H, Choi S-B, Aziz AA and Mazlan SA (2019) Swelling, Thermal, and Shear Properties of a Waste Tire Rubber Based Magnetorheological Elastomer. Front. Mater. 6:47. doi: 10.3389/fmats.2019.00047* In this study, the achievement of revulcanization, thermal stability, and rheological behaviors of waste tire rubber (WTR), based magnetorheological elastomers (MREs), were evaluated to convince their applicability as one of smart material possessing the field-dependent tuning capability of material characteristics such as complex modulus. The cross-linking density of the MREs was assessed through the swelling test to ratify the degree of reclaiming. The behavior of MREs to the temperature enhancement was evaluated via thermogravimetric analysis and thermomechanical analysis. Meanwhile, the alteration of shear stress depending on the magnetic fields was investigated at both steady and oscillatory states, measured using a rheometer. It has been shown that the increment of shear stress is proportional to the increment of the magnetic field. More specifically, it has been found that the WTR based MRE can achieve the maximum static stress ranging from 9 to 13 kPa (at 656 mT) with a linear viscoelastic (LVE) region above 3% strain amplitude. In addition, from the oscillatory test it has been determined that the highest MR effect of 24.71% can be achieved, which directly indicates the augmentation of both storage and loss moduli under ramped frequency and strain. Finally, it has been shown that the highest degree of reclamation based on swelling test can be achieved up to 54%, confirming the occurrence of the crosslinking during the reclamation process.

#### Keywords: waste tire rubber, magnetorheological elastomer, thermal analysis, swelling test, MR effect

# INTRODUCTION

Reclaiming waste tire is usually performed by blending waste tire rubber (WTR) to the virgin rubber or revulcanization the inert rubber by treating them in physical and chemical ways. Reclamation of rubber is mainly scission or cleavage of sulfur-sulfur, carbon-sulfur, or carbon-carbon to break down three-dimensional network structures from the vulcanization process. At the same time, the division bonds are reformed through a revulcanization mechanism obtaining new rubber products.

So far, recycled rubber-based products exhibit non-tunable mechanical properties. The WTR reclamation would draw attentions when the reclaimed articles have smart material characteristics. Here, smart features refers to the capability of goods reacting to the external condition in which smart materials only own the behavior. Such capability could enhance the economic value of the recycled product. According to the advancement of rubber reclaiming technologies, waste tire rubber has the potential to be reclaimed as smart materials, namely, magnetorheological elastomers (MREs). MREs have taken a prominent position in actively tunable vibration devices such as automotive bushing, rotating machine mounting and a seismic damper, due to their tunable properties by the intensity of the magnetic fields (Li et al., 2014; Ubaidillah et al., 2015). MREs are also compatible with the sensory application and morphing structure devices (Ottaviani et al., 2005; Li et al., 2009; Ghafoorianfar et al., 2013; Ausanio et al., 2014; Bica et al., 2014).

Based on the survey provided by Ubaidillah et al. (2015), all scientific reports published since the 1990s proposed MREs using virgin elastomers in which the vulcanization mechanism did not become the main issue. And so far, most of the research interests have been addressed on the enhancing rheological properties such as MR effect, storing, and dissipating energy performances. Some efforts were carried out for enhancing MREs properties such as; (a) manipulating the matrix, either by using single type matrix or mixed matrix, (b) controlling the particle types, size, morphology, and composition, and (c) manipulating cross-link density through operating additives and processing condition. The latest research relating to the vulcanizing issue was undertaken by considering self-crosslinking between two different compounds. Wang et al. (2015) fabricated new class MREs by blending polychloroprene rubber with epoxidized natural rubber, without curing agents that the so-called self-cross-linking MREs. This work indeed provided a breakthrough for the MREs preparation since there was no additive involvement in the vulcanization process. Again, the self-cross-linked MREs preparation incorporated virgin rubber. Therefore, the MREs fabrication based on waste tire rubber would be a fascinating exploration of some aspects in terms of manufacturing and performance.

Regarding to the challenges, Ubaidillah et al. (2016a,b,c) have successfully reclaimed WTR as the primary matrix of MREs. First, Ubaidillah et al. (2016c) fabricated MREs utilizing WTR as the matrix as well as Fe3O4 (magnetite) powders obtained from electronic wastes. In this work, the specimen's physicochemical properties and stress-strain behaviors were evaluated through the static compression test. Pursuing the complete investigation on dynamic compression properties, the magneto-induced rheological properties of the samples were determined as can be found in Ubaidillah et al. (2016b). It became evident that the MR effect of WTR based MREs featuring magnetite achieved about 15% MR effect under dynamic compression loadings. To enhance the magnetic properties, the magnetite powders were then replaced with carbonyl iron (CI) particles. As reported by Ubaidillah et al. (2016a), WTR based MREs were examined for their physicochemical and rheological properties under dynamic shear loadings. The MREs achieved a higher MR effect that was about 24.71%. As surveyed from the literatures Ubaidillah et al. (2016a,b,c), both swelling problem and thermal analysis have not yet been treated, even though these are important issues to be addressed in order to ensure high stability and reliability of the field-dependent rheological properties of the WTR based MREs.

Consequently, the technical originality of this work was to investigate the swelling, thermal, steady state, and dynamic properties of the WTR based MREs. This study is important as

it is necessary to determine why the hesitation on the reliability issue, since it is known that the waste rubber is hard to be reclaimed without incorporating virgin rubber. Swelling tests are first conducted to ensure the revulcanization process within MREs based on the obtained swelling parameters. Thermal analyzes are provided to study the stability of the synthesized samples. The properties, such as the dependence magnetic fields, are explored through the rheological test in both absence and presence of magnetic fields in the shear direction. The steady state loading reveals the stress-strain properties of waste tire based MREs including understanding in the linear viscoelastic region. Authors believe that the utilization of the WTR for raw materials of the MREs is a useful idea for waste tire management and a clean environment.

# MATERIALS AND RECLAMATION PROCESS

The company of PT Bengawan Sumber Baru, Indonesia, provided the WTR with the average size of ≈2.8 mm. It was obtained from discarded tires (passenger and commercial vehicles) which were ground mechanically and free from metals and textiles. Screening was then carried out to get the uniform size of WTR (about mesh 60). The additives employed were chosen based on the typical rubber reclamation process such as stearic acid (98%, Justus Kimia Raya, Indonesia), zinc oxide (99%, <1µm, Bratachem, Indonesia), sulfur (Bratachem, Indonesia). The magnetizable particles were carbonyl iron (CI) particles, having an average size of 6µm, type CN supplied by BASF, Germany. The additional latex solution was used as first raw material bonding between CI particles and WTR.

The HPHT sintering method implements the same principle concepts with the mechanical approach in that they both apply high temperature and high pressure. **Figure 1** depicts the schematic mechanism of the HPHT sintering process. The HPHT is conducted using simultaneous high temperature (between 200 and 240◦C) and high-pressure compaction (above 20 MPa) on the ground tire rubber in a mold for a specified duration. Therefore, the process does not involve the twin screw extruder or roll mill that operates through shearing the waste rubber at a temperature of ±180◦C. In this process, the cleavage and reforming of the rubber vulcanizates happen in a single step process. According to the working principle of the HPHT sintering process, the recycling procedure is simpler than that of the common mechanical approach.

The MRE samples were prepared through two major steps: mixing and reclamation. First, the WTR (100 phr) and additives (1.5 phr stearic acid, 5 phr ZnO, and 2 phr sulfur) were mixed in a laboratory mechanical stirrer at 250 rpm until the mixture was visually homogenous. Unlike the virgin rubber-based MREs that require a roll mill for compounding, homogenous mixtures were easily achieved since all raw materials were in powdered form except the latex solutions. The CI particles in contents of 10, 20, 30, and 40 wt% were then mixed homogeneously with the WTR mixtures using a mechanical stirrer. Hereafter, the 10 phr latex solution was added to the mixed raw materials and then further assorted until well blended. The formulation of WTR based MRE was detailed in **Table 1**.

Second, the reclamation process was conducted using the laboratory HPHT sintering device which could exert 20 tons of hydraulic pressure (Krisbow, Indonesia) and was equipped with a heat controller. The molding kit was fabricated using the conventional machine and was made of mild steels. The thickness could be adjusted based on the amount of molded mixtures. Two heater cartridges were equipped with the mold having heat power of 150 W each. Heater controller was constructed of current driver, display monitor, K-type thermocouple, and circuit breaker. The samples were fabricated in a mold with a bore diameter of 30 mm. The final mixtures were placed in the cavity, and the hydraulic pressure of 25 MPa was applied at a temperature of 200◦C for 1 h to accomplish revulcanization. This procedure adopted the reclamation technique by Morin et al. (2002) and Tripathy et al. (2002). The heating rate from ambient to a steady temperature was 10◦C/min. Following the revulcanization process, the heater controller was turned off, and the mold was then allowed to cool until reaching ambient temperature.

# CHARACTERIZATION

# Morphological Examination

Field emission scanning electron microscopy (FESEM), SUPRATM 35SV, ZEISS, USA, was utilized for capturing the morphology of CI particles and their distribution within the MRE matrix. The device was operated at an accelerating voltage of 10 kV. During observation, the MRE samples were

TABLE 2 | Apparent flux densities corresponding to the applied current.

crushed using a hammer after immersion in liquid nitrogen. The observed surfaces were coated with a thin layer of gold.

# Swelling Test

The swelling test was conducted to examine the degree of revulcanization process of the MREs. The synthesized sample was subjected to an equilibrium swelling in toluene at ambient temperature. Small sliced MREs were initially weighed (m1) and then immersed in 100 ml toluene and allowed to swell for 72 h. The sample was then wiped to remove the toluene on its surfaces and quickly weighed to measure the swollen weight (m2 ). The step was followed by drying in an oven at 80◦C to remove small molecular weight substance until reaching same dried weight (m3).

The swelling parameters such as soluble fraction, swelling degree, cross-link density, and the degree of reclaiming were determined based on the recorded weight. The following relation (Equation 1) is useful for determining soluble fraction (SF),

$$SF = \frac{m\_1 - m\_3}{m\_1} \text{x100\%} \tag{1}$$

The swelling degree (Q) was calculated in accordance with Equation (2) as follows,

$$Q = \frac{m\_2 - m\_1}{m\_1} x 100\% \tag{2}$$

Meanwhile, the cross-link density of the MREs was determined based on ASTM D 6,814 that according to the Flory-Rehner formula (Flory and Rehner, 1943) without Kraus correction (Equation 3),

$$\nu = \frac{-\left[\ln\left(1 - V\_r\right) + V\_r + \chi \left|V\_r\right|^2\right]}{\left[\frac{V\_1\left(V\_r^{\frac{1}{3}} - V\_r\right)}{2}\right]} \tag{3}$$

where: v -cross-link density, mol/cm3 ; Vr-represents volume fraction in the swollen sample; V1-molar volume of toluene (106.2 cm3 /mol) (Yazdani et al., 2011); χ-parameter of rubbersolvent interaction (in calculation, it was assumed to be 0.391; Formela et al., 2014).

The volume fraction of rubber was calculated according to Equation (4),

$$V\_r = \frac{\frac{m\_\ell}{\rho\_\ell}}{\frac{m\_\ell}{\rho\_\ell} + \frac{m\_\ell}{\rho\_t}}\tag{4}$$

where: me-mass of dry MREs in gram (g); ρe-density of dry MREs in g cm3 ; mt-mass of absorbed toluene by MREs in gram (g); ρt-density of toluene in g cm3 .

The achievement of revulcanization process through HPHT sintering was determined on the basis of alteration in the crosslinking density of the reclaimed MREs (v1) relative to the ground tire rubber without reclamation (v0), regarding Equation 5 as follows,

$$\text{Degree of relaining} = \frac{\nu\_0 - \nu\_1}{\nu\_0} \text{x100\%} \tag{5}$$

# Thermal Test

The thermogravimetric tests were undertaken using TGA Q50, TA Instruments (US). The test samples had masses of 5–10 mg, and the temperature was varied from 30 to 600◦C. The heating rate was 20◦C/min under a nitrogen gas environment (100 ml/min flow rate). The thermal expansion of MREs was evaluated using TMA Q400 TA Instruments (US). An expansion probe was equipped to measure the dimension change of an MRE sample that measured 5 × 5 × 10 mm. Data were collected at a heating rate of 10◦C/min from an ambient temperature of 150◦C while the initial load was set to 0.05 N.

# Rheological Test

Viscoelastic properties of the WTR based MREs were witnessed in a rotational shear mode using the parallel-plate rheometer (model Physica MCR 302, Anton Paar, Austria) equipped with a magnetorheological device MRD 70/1T. The diameter of parallel plate disk was 20 mm (PP20/MRD/T1/P2). A temperature control Viscotherm VT2, Anton Paar was also utilized for maintaining the desired testing temperature of 25◦C. The rheological measurement system with parallel-plate is described in standards ISO 6721-10 and DIN 53019-1 (Sorokin et al., 2015). An electromagnet unit in MRD 70/1T can generate a homogeneous magnetic field perpendicular to the sample and non-magnetic measurement plate. The variation of magnetic flux could be from 0 until 690 mT by applying current from 0 to 4 A. **Table 2** exhibits how the flux density alters with the current which means the flux density across the MREs samples would be different as the consequences of CI particles fraction.

Under steady condition test, the MREs sample was sheared at a constant shear rate of 100 s−1 at a zero magnetic field for 30 s. The pre-conditioning was objected to making a uniform distribution of particle within the sample. The step was also

aimed at releasing the possible stored residual stress. Then, it was followed by preliminary magnetic energizing for 30 s to make a homogeneous static attraction between iron particles within the sample. After running the preconditioning step, the sequence of steady testing was allowed to proceed. The steadystate measurement was then applied by twisting the sample in a constant strain swept with a very low strain rate. The treatment was nearly similar to a static shear test.

The magneto-induced dynamic properties of the samples were evaluated through the oscillatory test. The storage modulus changes which can be represented by the effect of ramped magnetic flux was assessed under strain amplitude of 1%, and excitation frequency of 1 Hz. The ramp magnetic flux was realized by driving an electric current from 0 to 5 A in a linear fashion. Moreover, the frequency swept tests from 0.1 to 100 Hz were carried out under a constant strain amplitude of 1%. Meanwhile, the strain amplitude was set from 0.01 to 10% ramped logarithmically and the excitation frequency was fixed at 1 Hz. During both frequency and strain swept tests, the samples were energized by different magnetic fields of 0, 1A, 2A, 3A, and 4 A, respectively.

# RESULTS AND DISCUSSION

# Morphological Appearances

The morphologies of the cross-sectional MREs with a different weight fraction of CI particles are depicted in **Figure 2**. A random dispersion of CI particles within the MREs matrix is the primary requirement of the consistent performance in their functional

FIGURE 3 | Thermogravimetric curves of WTR based MREs.

TABLE 4 | Residual mass of decomposed WTR based MREs.

behavior. A random distribution will ensure the magnetic flux to flow uniformly through the MREs. The dispersion of particles can be clearly observed in the SEM micrograph shown in **Figure 2**. The random distribution type of the MREs is confirmed by nonaligned dispersion of particles in the observed area. It can be seen that the CI particles adhere completely in the matrix. The weight percentage of each sample can be visually differentiated from the micrographs. The MREs with higher weight fraction of CI particles seem to be a closer distance and tend to agglomerate.

According to **Figure 2**, the micrograph of WTR based MRE confirmed that the fractured samples show well-blended rubber matrix. This fact indicates that the WTR has mixed thoroughly with each other as the results of high-pressure and hightemperature treatment. The blending of WTR can be considered as the occurrence of the revulcanization process. If the WTR only adhered to each other without curing, the matrix appearance of the fractured sample would exhibit different patterns. It would definitely show the WTR borders as the effect of non-blended WTR. Besides, the cryogenic effect during sample preparation would easily break the WTR interfaces when the rubber was not cured. The curing reaction during the reclamation process does not leave any particle boundaries among WTR.

# Swelling Properties

A common issue that occurs in WTR reclamation is a revulcanization (crosslinking) achievement because the WTR belongs to inert materials. Therefore, the swelling test is often used to facilitate the evaluation of crosslinking of waste rubber reclamation. In this study, the degree of vulcanization of the MRE samples was also assessed by a swelling test to confirm the success of the revulcanization. The swelling properties including the soluble fraction, the swelling degree, the crosslinking density, and the degree of reclamation are listed in **Table 3**. Based on the calculation, the values are comparable to that of waste rubber reclamation through either a twin extruder or roll mills (Yazdani et al., 2011; Formela et al., 2014). For comparison purposes, **Table 3** also provides the summary data of swelling properties obtained from the previous work. The values of the soluble